Engineering Innovations Volume 11

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Volume 11 of
Engineering Innovations
ISSN print 2813-0995
ISSN web 2813-1002

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Table of Contents

Simulation of Stress Intensity Factor and J-Integral on UIC 54 Railway Failure Using A Fracture Mechanics Approach

Pradhana Kurniawan, Darto Darto, Agus Iswantoko, Feliks Sutrisno

The Behavior of Thin-Walled Cylinders with Ribs Regarding the Energy Absorption Capability on High-Velocity Impact

Witono Hardi, Mohammad Shalahuddin Abdul Aziz, Amat Umron

Topology Optimization of Motorbike Footsteps Using Finite Element Method

I Made Gatot Karohika, Januar Teguh Prasetyo, I Made Parwata, I Nyoman Gde Antara, I Nyoman Budiarsa

Analytical Prediction of Crushing Thin-Walled Square Tube with Static Axial Loads Using Elliptical Holes as Crush Initiators

Endarto Tri Wibowo, Jos Istiyanto, Danardono Agus Sumarsono, Dony Hidayat

A Bibliometric Analysis of Suspension System Development for Enhancing Comfort in Family Passenger Vehicles

Fattah Maulana, Dicky Permana Adji Santosa, Cahyo Hadi Wibowo, Yudha Priatama, Sariwulan Nurcholis, Adhe Lingga Dwi

Muffler Design for Noise Reduction and Pressure Loss Optimization Using Multiobjective Genetic Algorithm

Muhammad Yandi Pratama, Prihanto Trihutomo, Suprayitno Suprayitno

Development of Savonius Rotor Based on Bezier Curve for Vertical Axis Marine Current Turbine at Sunda Strait, Hindia Ocean

Dedy Triawan Suprayogi, Hadi Setiawan, Alwan Habibie, Muhammad Adjie, Faqih Atard Rahman

The Effect of Deflector Angle on the Performance of Turbine Combination Darrieus-Savonius

Rizki Irfin, Satworo Adiwidodo, Eko Yudiyanto, Bagus Wahyudi, Fauzan Baananto

Minimizing Conditional Mean Tardiness and Mean Earliness on a Single Machine with the Due Windows Approach

Saheed Akande, Ganiyu O. Ajisegiri, Temitayo Mufutau Azeez

Keywords Index

Authors Index

The original version of this eBook is available on https://www.scientific.net/book/engineering-innovations-vol-11/978-3-0364-1606-9

Engineering Innovations, ISSN: 2813-1002, Vol. 11, pp 1-8

doi: 10.4028/p-qvAF50

© 2024 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2023-12-10

Revised:
2024-01-02

Accepted:
2024-01-03

Online:
2024-06-26

Simulation of Stress Intensity Factor and J-Integral on UIC 54 Railway Failure Using A Fracture Mechanics Approach

The original version of this paper is available on https://www.scientific.net/EI.11.1.pdf

Pradhana Kurniawan , Darto Darto , Agus Iswantoko , Feliks Sutrisno

¹Mechanical Engineering Department, Faculty of Engineering, University of Merdeka Malang, Terusan Dieng Street No. 62-64 Klojen, Pisang Candi, Malang, East Java 65146, Indonesia

Department of Mechanical and Industrial Engineering, Faculty of Engineering, State Universty of Malang, Semarang Street 5, Lowokwaru, Malang, Eas Java, Indonesia

pradhana.kurniawan@unmer.ac.id, darto@unmer.ac.id, agus.iswantoko@unmer.ac.id, dmazmur118@gmail.com

Keywords: Stress Intensity Factor, J-Integral, Crack Defects, Railroads, Fracture Mechanics.

Abstract

Repeated loading on the railroad tracks will result in fatigue failure. Fatigue failure combined with a defect in the form of a crack in the railroad track will result in a decrease in strength. Defects in the form of cracks are formed due to improper manufacturing and treatment processes. One treatment that can cause the formation of defects in the form of cracks is thermite welding. Improper and non-standard thermite welding techniques can trigger the formation of defects in the form of cracks in the railroad joints. Based on these problems, this simulation aims to obtain information about the value of maximum stress, SIF, J-Intergal, number of cycles, and crack extension from variations in crack size to repeated loading. The method consists of preprocessing, processing and postprocessing. Preprocessing begins with the design of the UIC 54 railroad crack which consists of 3 variations of crack length, namely , and 20 mm . The design was tested through static structural simulation using the ANSYS 2021 R2 application. Meshing is configured using an element size of 5 mm and uses curvature capture. The results of the simulation obtained maximum stress values, SIF, J-Integral, number of cycles, and crack extension. Based on the simulation of SIF 1 and J-Integral values on the specimen design with a crack length of 10 mm it shows 362.03 Mpa. of , for an initial crack length of 15 mm that is equal to 482.81 Mpa. and , and for an initial crack length of 20 mm , it is and . The results show that the increase in SIF 1 and J-Integral will be proportional to the increase in the initial crack length value.

Introduction

The original version of this paper is available on https://www.scientific.net/EI.11.1.pdf

Rails serve as a path of rail transportation. Railroad rails have various types that are adjusted based on the type of train [1]. Coal transport type trains pass through the UIC 54 type railroad [2]. UIC 54 rail is the type of rail used for coal transport trains in the South Sumatra area of Indonesia.

Repetitive loading of the rail combined with the presence of defects will result in fatigue failure. Based on the classification, the railway (UIC 54) is included in class I where the rail transport capacity is tons/year. Each train car carries coal with a coal load capacity of around 50 tons and the carriages have a separate load of 22 tons. The transport train passes through a railroad connection, where the technique used to connect the railroad tracks is using thermite welding. Thermite welding has a weakness that can be a factor in the occurrence of railroad faults [3], [4]. These weaknesses include low ductility and toughness, rough surface grains, dendritic structure, inclusions, and the formation of porosity. Porosity or the presence of holes in the connecting parts between the rails is the cause of cracks and fractures on railway tracks [2]. Thermite welding, which is a heat treatment technique, can cause changes in mechanical properties including strength, hardness, ductility and toughness [5]-[7].

Research on failure due to fatigue where the high speed of the train affects the condition of the railway track UIC 54. The high speed of the train moving over the track can trigger unsafe conditions for the railroad track. Failure due to fatigue can occur without a sign so that cracks that eventually
result in fractures can occur. The loading occurs in the direction perpendicular to the crack surface, where the stages begin with initiation, propagation and finally cracking [8], [9]. A similar study is concerned with the fracture toughness of high-speed rail in Malaysia. The Tanah Melayu Berhad (KTMB) train runs on UIC 54 railroad tracks with 900A class steel used on Electrical System Train (ETS) train tracks. Loading on train tracks will produce bending stress, axial stress, and Hertzian pressure during contact with the train track. These stresses can trigger failure when there are defects in the railroad tracks [10].

Based on several previous studies which discussed the toughness of railway tracks against repeated loading which produces fatigue. This research aims to simulate variations in crack length with respect to SIF 1 and J-Integral values due to loading from coal trains. The simulation was carried out using ANSYS 2021 R1 software with the fatigue method to obtain information regarding the maximum stress, SIF, J-Integral, number of cycles, and crack extension that occurred on the UIC 54 railway track. The simulation was carried out on the design of the UIC 54 railway track. with a length of 100 mm . Variations in crack length are given in the design, namely , and 20 mm , with the same crack height, namely 1 mm .

Methods

The original version of this paper is available on https://www.scientific.net/EI.11.1.pdf

Pre-processing. The research began with design modeling in the form of the UIC 54 railroad track. The design modeling of the UIC 54 railroad track was carried out using the Inventor application. There are 3 types of designs that will be used in testing through simulation. Information regarding the design used in the simulation based on the size of the crack is shown in Table 1 and Figure 1.

Table 1. Specimen Crack Design and Size

Specimen | Crack Type | Crack Length (mm) | Crack Height (mm)
1 | Single edge crack | 10 | 1
2 | Single edge crack | 15 | 1
3 | Single edge crack | 20 | 1

Fig. 1. Geometry of the UIC 54 Railway Tracks with Crack Lengths (a) 10 mm (b) 15 mm and (c) 20 mm

After the UIC 54 railroad track design process is determining the properties of the materials used by the UIC 54 railroad track. Configuration of the properties of the UIC 54 railroad track is done via ANSYS 2021 R2 software. The mechanical properties of the UIC 54 railroad are shown in Table 2.

Table 2. UIC 54 Railway Specifications [2], [8], [10]

Characteristics | Value
Young Modulus | 210 GPa
Poisson's Ratio | 0,29
Bulk Modulus | 166,67 GPa
Shear Modulus | 81,395GPa
Tensile Yield Strength | 879 Mpa
Tensile Ultimate Strength | 948 MPa
Coefficient of Thermal Expansion | 2,3 × 10⁻⁵ C⁻¹
Material Constant C (Paris Law) | 1,31935 × 10⁻¹² (mm, tonne mm s⁻²)
Material Constant m (Paris Law) | 3,2825 (mm, tonne mm s⁻²)

After inputting the UIC 54 rail material into the engineering data, the next process is meshing. Crack coordinate configuration needs to be done to set the direction in which the crack occurs. The Y -axis configuration has a direction perpendicular to the surface of the UIC 54 train track that will contact the train wheels. The X axis has a direction parallel to the movement of the train wheels. The crack coordinate configuration is shown in Figure 2. The meshing stages were carried out with the configuration shown in Table 3 and the results are in Figure 3.

Table 3. Meshing Configuration

Parameter | Configuration
Element size | 5 mm
Capture Curvature | Yes
Method | Tetrahedrons
Edge Sizing | Sphere radius 9 mm, Element size 1 mm, Sphere Center (crack coordinate system)

Fig. 2. (a) Coordinate System Configuration for Crack Propagation and Crack Direction Configuration

Fig. 2. (a) Coordinate System Configuration for Crack Propagation and Crack Direction Configuration

Fig. 3. (a) Meshing configuration and (b) Meshing configuration on the crack section

Fig. 3. (a) Meshing configuration and (b) Meshing configuration on the crack section

After meshing, the next process is adding fracture features and configuring cracks using premeshed cracks accompanied by smart crack growth. Previously, named selection was performed to create a nodal named selection, which is required as one of the parameters in the pre-meshed crack configuration. There are 3 named selections, namely at the ends of the 2 cracked surfaces, the upper cracked surface area, and the lower cracked surface area. The next step is to select a nodal named selection at the ends of the 2 cracked surfaces as crack fronts. Activate the crack faces nodes and select the top face nodes and bottom face nodes as the top face nodes and bottom face nodes. The coordinate system is set based on the configuration that has been previously set from Figure 3. Next, do the configuration for smart crack growth where the configuration uses fatigue settings. Crack initiation is selected based on the previous configuration of the pre-meshed crack. The material used is a material whose properties have been configured as shown in Table 2.

The analysis configuration stage begins by determining the number of steps that are configured in 1 stage with a time of 1 second. The crack control configuration is set alternately, you can do an analysis based on SIF first then J-Integral or vice versa. Next, set the part that becomes the fixed support and the location where the contact occurs for the force from the railroad wheels to the UIC 54 railroad as shown in Figure 5. The loading on the UIC 54 railroad 100 mm long is regulated by a train that has a load consisting of a body trains, boogies, and transported products. Based on research regarding failure in the form of fractures on the UIC 54 train tracks due to loading from coal trains [1]. The largest load is on the part of the carriage that transports coal products, namely 77 tons. The load is the load from one coal train car carrying coal. The direction of the load is perpendicular to the surface of the UIC 54 railway track which is the route of the coal carrying train. There are 2 UIC 54 railroad tracks that support the load of one coal carriage and there are 2 boogies in one carriage. Each boogie consists of 4 train wheels, so that each side of the train track has 4 train wheels. The loading of the train is explicitly explained in Table 4 and Figure 5. Based on Table 4, the load of one wheel on one side of the rail is 94421.25 N .

Table 4. Distribution of the Train Load on the UIC 54 Railroad

Railway Section | Value | Load
Coal wagons and their transport | 1 | 77000 kg (77 ton)
Boogie | 2 | 38500 kg by one boogie
Wheels on Every Boogie | 4 | 9625 by one wheel

Fig. 4. Boundary Conditions

Fig. 4. Boundary Conditions

Processing. Processing is a computational process that works to solve predetermined and configured problems. The computing system will solve problems based on the problems and the required results.

Post-processing. Post-processing is the result of a simulation in solving predetermined and configured problems. Simulation results include equivalent von misses, Stress Intensity Factor, JIntegral, number of cycles and crack extension.

Results and Discussion

The original version of this paper is available on https://www.scientific.net/EI.11.1.pdf

Based on the SIF and J-Integral simulation results for cracks of length , and 20 can be seen in Figure 5-7.

Fig. 5. (a) SIF Mode 1 and (b) J-Integral for Crack Length 10 mm

Fig. 5. (a) SIF Mode 1 and (b) J-Integral for Crack Length 10 mm

Fig. 6. (a) SIF Mode 1 and (b) J-Integral for Crack Length 15 mm

Fig. 6. (a) SIF Mode 1 and (b) J-Integral for Crack Length 15 mm

Fig. 7. (a) SIF Mode 1 and (b) J-Integral for Crack Length 20 mm

Fig. 7. (a) SIF Mode 1 and (b) J-Integral for Crack Length 20 mm

Table 5. Simulation Data Results

Crack Length | Equivalent Von Misses (MPa) | Mode I of Stress Intensity Factor (Mpa.mm1/2) | J-Integral (mJ/mm²) | Number of Cycles | Crack Extension (mm)
10 mm | 239,81 | 362,03 | 0,5708 | 3109 | 0,98492
15 mm | 297,96 | 482,81 | 0,91738 | 1431 | 1,1405
20 mm | 382,39 | 600,54 | 1,4465 | 691 | 1,1568

Based on the results of the simulation in Table 5 and the graphical comparison of crack lengths of and 20 mm , namely for maximum stress, SIF mode 1, J-Integral, crack extension, and number cycles. Information can be obtained regarding the effect of crack length on UIC 54 railroad specimens. Figure 8 shows a comparison of the maximum stress values for 3 different specimens. The highest maximum stress is found in a crack with a length of 20 mm which is 382.39 Mpa, followed by a crack with a length of 15 mm and finally a crack with a length of 10 mm which is respectively 297.96 Mpa and 239.81 Mpa . The stress value increases with the increase in the initial value of the crack is directly proportional to the value [11]. As the SIF value increases as the initial length of the crack increases, the stress value will also increase. This is in accordance with the equation for determining the SIF value [12].

Fig. 8. Equivalent Von Misses Comparison of Crack Lengths , and 20 mm

Fig. 8. Equivalent Von Misses Comparison of Crack Lengths , and 20 mm

Figure 9 shows a comparison of SIF mode 1 and J-Integral values on 3 different specimens. Specimens with a crack length of 20 mm had the highest SIF 1 and J-Integral values, namely and respectively. SIF 1 and J-Integral values were followed by specimens with a crack length of 15 mm and the lowest was for specimens with a crack length of 10 mm . SIF 1 and J-Integral values for 15 mm crack length respectively are 482.81 Mpa.mm and . The SIF 1 and J-Integral values for a crack length of 10 mm respectively are and . The value of the specimen with a crack length of 20 mm is the highest compared to the specimen with a crack length lower than 20 mm indicating that the greater the crack length with the same crack height, the value of SIF mode 1 and J-Integral will increase [11]. The value of SIF mode 1 and J-Integral which increases with the value of the length of the crack with the same height is also related to the maximum stress value, where the equation for determining the value of SIF 1 and J-Integral is directly proportional to the stress [13]. Increased SIF 1 and J-Integral values also affect the condition of the number of cycles [14].

Fig. 9. Comparison of Crack Lengths , and 20 mm for Values of (a) SIF Mode I and (b) JIntegral

Fig. 9. Comparison of Crack Lengths , and 20 mm for Values of (a) SIF Mode I and (b) JIntegral

Figure 10 is a comparison of the number of cycles of 3 different specimens. Specimens with a crack length of 10 mm have a higher number of cycles than specimens with a crack length of 15 mm and 20 mm . Specimens with a crack length of 10 mm have a number of cycles value of 3109, followed by specimens with a crack length of 15 mm and 20 mm respectively, namely 1431 and 691 . Based on the value of the number of cycles at the same time it shows that the longer the cracks on the specimen the UIC 54 railroad, the age of the railroad will decrease [14]. The decreasing number of cycles value indicates that the size of the defect in the specimen has a greater length and/or width, thus affecting the age of the specimen. The decreased number of cycles value indicates that the voltage value increases [11].

Fig. 10. Comparison of Number of Cycles for Crack Lengths of , and 20 mm

Fig. 10. Comparison of Number of Cycles for Crack Lengths of , and 20 mm

Figure 11 is a comparison of the crack ekstension from 3 different specimens. Based on Table 5 , the value of the increase in crack length in the specimen with a crack length of 20 mm experienced an increase in crack length of 1.1568 mm . Specimens with a crack length of 15 mm experienced an increase in crack length of 1.1405 mm , and for specimens with a crack length of 20 mm experienced an increase in crack length of 0.98492 mm . The increase in crack length is influenced by the value of the initial crack length and SIF [15]. The greater the value of the initial length of the crack, the more the SIF value increases, the value of the increase in crack length will increase. Based on Figure 9, the value of the increase in crack length increases when the initial length of the crack is 10 mm to 15 mm , and begins to decrease when the initial length of the crack is more than 15 mm . This shows that the speed of crack propagation has a maximum speed when the initial length of the crack is more than 15 mm to 20 mm .

Fig. 11. Comparison of Crack Ekstension for Crack Lengths of , and 20 mm

Fig. 11. Comparison of Crack Ekstension for Crack Lengths of , and 20 mm

Summary

The original version of this paper is available on https://www.scientific.net/EI.11.1.pdf

The aim of this simulation is to analyze the SIF, J-integral, equivalent von misses, number of cycles and crack extension in the failure of the UIC 54 railway track. The highest stress result is 382.39 MPa at a crack length of 20 mm . The increase in stress value is directly proportional to SIF ( ), J-Integral ( ), Number of Cycles ( 691 cycles) and Crack Extensions ( 1.1568 mm ). This condition can be concluded that the greater the value of the initial crack length with the same crack height, the greater the value of SIF mode 1 and J-Integral. A large
initial crack length value will also have a lower lifespan compared to specimens that have a shorter crack length. The increase in crack length will increase along with the increase in the initial length of the crack until at a certain size it will reach the condition of maximum propagation speed.

References

The original version of this paper is available on https://www.scientific.net/EI.11.1.pdf

T. A. Zucarelli, M. A. Vieira, L. A. Moreira Filho, D. A. P. Reis, and L. Reis, "Failure analysis in railway wheels," Procedia Structural Integrity, vol. 1, pp. 212-217, 2016, doi: 10.1016/j.prostr.2016.02.029.

A. Ihlas, "Analysis of Damage to Coal Transport Rail Rails," Journal of Materials and Engineering Goods Technology, vol. 7, p. 7, Jun. 2017, doi: 10.37209/jtbbt.v7i1.89.

S. Kwon, D.-H. Lee, S. Kwon, and B. Goo, "Failure Analysis of Railway Wheel Tread," Key Engineering Materials - KEY ENG MAT, vol. 321-323, pp. 649-653, Oct. 2006, doi: 10.4028/www.scientific.net/KEM.321-323.649.

G. Fedorko, V. Molnár, P. Blaho, J. Gašparík, and V. Zitrický, "Failure analysis of cyclic damage to a railway rail - A case study," Engineering Failure Analysis, vol. 116, p. 104732, Oct. 2020, doi: 10.1016/j.engfailanal.2020.104732.

A. Andoko and P. Puspitasari, "The Fatigue Crack Growth Rate Due to Single-Step Austempered Heat Treatment in Nodular Cast Iron," MATEC Web Conf., vol. 97, p. 01028, 2017, doi: 10.1051/matecconf/20179701028.

Pradhana, A. Andoko, and P. W. Sunu, "Leaf spring type simulation with finite element method approach," IOP Conf. Ser.: Mater. Sci. Eng., vol. 1034, no. 1, p. 012015, Feb. 2021, doi: 10.1088/1757-899X/1034/1/012015.

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M. A. Rojan, M. S. M. Azmi, M. S. A. Majid, R. Daud, and K. S. Basaruddin, "Fracture toughness of railway for higher speed rail corridors in Malaysia," IOP Conf. Ser.: Mater. Sci. Eng., vol. 670, no. 1, p. 012065, Nov. 2019, doi: 10.1088/1757-899X/670/1/012065.

A. Lal, B. M. Sutaria, and K. Mishra, "Fracture analysis of single edge cracked functionally graded material plate under various loading conditions by extended finite element method," IOP Conf. Ser.: Mater. Sci. Eng., vol. 814, no. 1, p. 012014, Mar. 2020, doi: 10.1088/1757899X/814/1/012014.

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This ePub file was created using machine-generated methods and automated software to convert the source text into an ePub format and may contain formatting inconsistencies from the original version. Formatting may vary depending on the device used.

The original version of this eBook is available on https://www.scientific.net/book/engineering-innovations-vol-11/978-3-0364-1606-9

Engineering Innovations, ISSN: 2813-1002, Vol. 11, pp 9-18

doi: 10.4028/p-2nQNMA

© 2024 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2023-12-01

Revised:
2023-12-30

Accepted:
2024-01-02

Online:
2024-06-26

The Behavior of Thin-Walled Cylinders with Ribs Regarding the Energy Absorption Capability on High-Velocity Impact

The original version of this paper is available on https://www.scientific.net/EI.11.9.pdf

Witono Hardi , Mohammad Shalahuddin Abdul Aziz and Amat Umron

Mechanical Engineering, Universitas Khairun, Jl. Jusuf Abdul Rahman, Kampus 2 Unkhair, Gambesi, Ternate Selatan, Kota Ternate, Indonesia

Mechatronic, Electronic Engineering Polytechnic Institute of Surabaya (EEPIS), JI. Raya ITS Kampus ITS Sukolilo, Surabaya, Indonesia

witono@unkhair.ac.id, shalahuddinabdulaziz@gmail.com, amatumron@unkhair.ac.id

Keywords: rib, deformation mode, wall thickness, energy absorption, reaction force.

Abstract

Many industries and automotive companies use thin-walled cylinders as energy-absorbing devices. Researchers have previously investigated various parameters related to thin-walled cylinders and their behavior under impact loads. When the impactor hits the thin-walled cylinder from the axial direction, it causes the bending of the cylinder wall on an axisymmetric or non-axisymmetric pattern, depending on the ratio of diameter divided by wall thickness. In addition, the length of the specimen influences the deformation mode that occurs. This study discusses how installing ribs on the cylinder walls affects energy absorption capabilities. We conducted the research by making modeling based on the finite element method by making various specimens according to the experimental scenarios. We experimented with an aluminum alloy cylinder with a diameter of 50 cm , a thickness of 1.5 mm , and a length of 200 mm . Then, successively, we installed ribs with a length of 2 mm and a thickness of 3.5 mm , one rib, two ribs, three ribs, four ribs, and five ribs. The impactor hits the specimen from the axial direction to one end at high speed while the other is given fixed support. The results obtained from the experiment are total deformation, reaction force, absorbed energy, and deformation pattern. The experimental results show that adding ribs changes the deformation pattern from previously non-axis-symmetric to axis-symmetric. The total deformation decreases, the reaction force becomes smaller, and the ability to absorb energy equals the total kinetic energy. This result is a recommendation for manufacturing in an energy absorption structural system.

Introduction

The original version of this paper is available on https://www.scientific.net/EI.11.9.pdf

Thin-walled structures have been widely used in impact energy absorption. This occurs because thin-walled structures have a unique behavior concerning energy absorption. Automotive technology has long used thin-walled structures as frames that not only make the structure lighter but also improve its ability to absorb energy.

Research related to railway vehicles by adding a crash box to the Indonesian high-speed train and testing using FEM on the 2019 SNI 8826 standard. The simulation results show that installing a crash box can reduce the damage due to impact and improve passenger safety [1]. Computer modeling is used to analyze impacts on city cars with ANSYS LS DYNA, obtaining a safe chassis structure from the side of max deformation according to MFSS (Motor Vehicle Safety Standard) [2]. In addition, various methods of energy absorption in automotive systems have also been studied. [3]. In automotive, some parts are deliberately sacrificed during a collision. It must absorb as much energy as possible while protecting passengers. Research on improving design crashworthiness by controlling energy absorption in different collision situations obtained an optimal design. [4]. In addition, aluminum composites are also used to enhance crashworthiness performance in analyzing aluminum tube composites in automotive use [5], including filling the tube with rubber and leaving it empty [6].

In an impact structure, energy results from force multiplication and deformation. A good system has a low and uniform reaction force throughout the collision. In addition, deformation is also attempted long enough so that the energy absorbed is considerable. [7] When a thin tube gets an
axially impeping force, there will be a bend in the wall. This wrinkle is axisymmetric or nonaxisymmetric depending on the ratio of diameter and wall thickness [8]

Experimental and numerical studies related to thin aluminum tubes were also carried out and obtained compatibility between simulation and testing [8]. The shape of the cross-section dramatically affects the energy absorption ability of thin-walled prisms. The circle has the best power of the various cross-section shapes 9]. Some of the research on the response of thin-walled tubes to impact includes behavior under different dimensional and loading conditions [11], buckling dynamics on shell cylinders when exposed to impact loads [11], And analysis of aluminum tubes with and without caps [13]. Energy absorption on thin walls occurs by the method of folding walls in various types of equipment [14]

The effect of impact speed on reaction force, deformation mode, and deformation length on thin aluminum tubes has been studied. In general, high rates cause less deformation than low speeds [15] Selain itu higher initial impact velocity could enlarge the absorbed energy because of compressive deformation just after impact, as indicated by the FEA [16]

Applying multiple segments in the cylinder has improved the energy absorption ability[17]. Multicell hexagonal crash box using the Taguchi method with the quality characteristics of the ability to absorb impact energy significantly better, namely the position of the hole ( P ), inner wall, hole position distance, crash box thickness, and hole diameter. The thickness of the crash box ( t ) has the highest contribution of in increasing the impact energy absorption value [18]. Research on Two Segment Crash Box Optimization using rubber joints with the Response Surface Methodology method to get optimal deals compared to only one segment [19]. In addition, rubber variations are also carried out to determine their effect on maximum energy absorption [20].

The use of lattice structures also increases energy absorption, as in the Experimental and numerical crushing performance of crash boxes filled with re-entrant and anti-tetrarchical auxetic designs [21] and multi-cell tubes [22]

In several studies, stiffeners were used to improve energy absorption performance and obtain the effect of stiffeners on thin-walled tubes made of composites on lateral loading [23]

Research on the effect of ribs on aluminum tubes was carried out experimentally, and simulations found that the presence of ribs could control the behavior of the tubes when getting impact loading [24]. This study discusses The Behavior of Thin-Walled Cylinders with Ribs Regarding the Energy Absorption Capability on High-Velocity Impact. By adding ribs, we expect a change in deformation mode to control the specimen's behavior to get the best performance.

Methodology

The original version of this paper is available on https://www.scientific.net/EI.11.9.pdf

The research was carried out by the following method. We are modeling aluminum cylinders with a length of 200 mm , diameter of 50 mm , and thickness of 1.5 mm . The impactor is steel measuring 75 , as shown below.

Fig. 1 Specimen and Impactor

Fig. 1. Specimen and Impactor

Ribs having a thickness of 3.5 mm are installed around the walls of the tube. We make eight specimens consisting of no ribs, one rib, two ribs, three ribs, four ribs, five ribs, six ribs, and seven ribs mounted at equal distances along the specimen.

Fig. 2 Rib

Fig. 2. Rib

Discretization or meshing divides the structure into small elements with a finite number.

Fig. 3 Meshing

Fig. 3. Meshing

One end of the specimen is fastened with a fixed pedestal, and a steel impactor impacts the other. A steel collider weighing 2.2078 kg hit the model from the axial direction at . The final result of the experiment is as follows.

Fig. 4 Result

Fig. 4. Result

This analysis obtains each specimen's maximum deformation value, maximum reaction force, absorbed energy, and deformation mode.

Table 1 Material Properties

Properties | Specimen | Impactor
Material | Al 6063 | Structural Steel
Young's modulus (GPa) | 68.3 | 211
Yield stress (MPa) | 245 |
Poisson Ratio | 0.3 | 0.3
Tensile strength (MPa) | 295 |
Density (kg/m3) | 2710 | 7850

Result and Discussion

The original version of this paper is available on https://www.scientific.net/EI.11.9.pdf

The impactor hits the specimen in the axial direction at a speed of . The reaction force response as a function of time is shown in the following Fig..

Fig. 5 Reaction Force History

Fig. 5. Reaction Force History

Fig. 5 represents reaction force history. During the energy absorption process, the reaction force must be constant and not too fluctuating. This study measured the reaction force at 0.005 seconds until the entire energy absorption process was completed. The maximum reaction force is kept low and maintained constant during the energy absorption process [7]

Fig. 6 Maximum Reaction Force

Fig. 6. Maximum Reaction Force

Maximum Reaction Force, or Initial Peak Force (Pmax), is the ultimate force on the specimen during loading. An energy-absorbing structure must have a relatively small . In Fig. 6, it can be seen that the greater the number of ribs, the smaller the maximum force that occurs.

Fig. 7 Deformation History

Fig. 7. Deformation History

After the collision is complete, the specimen undergoes permanent plastic deformation. Fig. 7 shows the deformation history of all models with a time of 0.005 seconds.
Fig. 8 shows the maximum deformation on all specimens. The greater the number of ribs that occur, the ultimate tendency to deformation decreases.

Fig. 8 Maximum Deformation

Fig. 8. Maximum Deformation

The absorbed energy is the area under the force curve as a deformation function occurs during specimen deformation, both elastic and plastic deformation. Plastic deformation predominates at the time of energy absorption. Absorbed energy (EA) is formulated as follows:

Where P is the force and is the deformation that occurs during the crushing process.

Fig. 9 Energy Absorption History

Fig. 9. Energy Absorption History

Maximum energy is defined as the energy absorbed until the crushing process ends. The following Fig. is the ultimate energy in each specimen.

Fig. 10 Maximum Energy

Fig. 10. Maximum Energy

The Mean Crushing Force or MCF parameter is defined as EA divided by the maximum deformation of the specimen . It is formulated as follows.

Fig. 11 represents the MCF on all specimens. MCF is the average force required during the energy absorption process. When a thin-walled cylinder is exposed to an impact force, it usually fluctuates due to bending on the thin wall. A large MCF indicates the average force required in an energy absorption process.

Fig. 11 MCF as Energy/ Deformation

Fig. 11. MCF as Energy/ Deformation

The following parameter is Crush Force Efficiency (CFE), which compares MCF with . It is defined as follows.

Fig. and MCF

Figure 12. Fig. and MCF

The following is a graph of CFE on all specimens that have been examined in this study.

Fig. 13 Crush Force Efficiency (CFE)

Fig. 13. Crush Force Efficiency (CFE)

Specimen 8 ( 7 ribs) has the most considerable CFE value, indicating this specimen can absorb energy optimally and uniformly during crashworthy structures [25]
SEA (Specific Energy Absorption) is defined as the absorbed energy divided by the mass of the specimen. Formulated as:

Fig. 14 SEA (Specific Energy Absorption)

Fig. 14. SEA (Specific Energy Absorption)

As the number of ribs increases, the specific energy absorption decreases. This is because the installation of ribs also increases the mass amount of the specimen.

Fig. 15 Deformation Mode

Fig. 15. Deformation Mode

Fig. 15 shows the deformation mode on all specimens after undergoing plastic deformation. More ribs tend to deform modes of axisymmetry than others. This is because ribs block the occurrence of non-axis-symmetry deformations. The presence of ribs makes the tube wall bend by axisymmetry [24]

Conclusion

The original version of this paper is available on https://www.scientific.net/EI.11.9.pdf

Our research by placing stiff ribs on thin-walled cylinders has been shown to affect the ability to absorb energy. Stiff ribs can change the deformation mode from non-axisymmetric to axisymmetric. The placement of ribs can regulate the characteristic ability of energy absorption.

The maximum reaction force decreases with increasing number of ribs, as does the total deformation. The mean crushing force experienced a significant increase in ribs equal to seven. Crush force efficiency has increased, and specific energy absorption has decreased. This result is a recommendation for manufacturing crash boxes as impact energy-absorbing structures.

References

The original version of this paper is available on https://www.scientific.net/EI.11.9.pdf

D. A. Musyaffa, Moch. A. Choiron, Y. S. Irawan, N. A. Hidayati, T. Taryono, and S. Gorbatyuk, "COMPUTER SIMULATION INVESTIGATION OF CRASH BOX DESIGN AS SAFETY-PROTECTION TECHNOLOGY FOR INDONESIA HIGH SPEED TRAIN," International Journal of Mechanical Engineering Technologies and Applications, vol. 4, no. 1, pp. 97-103, Jan. 2023, doi: 10.21776/MECHTA.2023.004.01.11.

W. Hardi, Analisis elemen hingga untuk uji tabrakan mobil dengan ansys ls dyna. Bandung: Media Sains Indonesia, 2022.

R. B. Shinde and K. D. Mali, "An Overview on Impact Behaviour and Energy Absorption of Collapsible Metallic and Non-Metallic Energy Absorbers used in Automotive Applications," IOP Conf Ser Mater Sci Eng, vol. 346, no. 1, 2018, doi: 10.1088/1757-899X/346/1/012054.

W. J. Witteman, Improved Vehicle Crashworthiness Design by Control of the Energy Absorption for Different Collision Situations. 1999. doi: 10.6100/IR518429.

J. Bouchet, E. Jacquelin, and P. Hamelin, "Static and dynamic behavior of combined composite aluminum tube for automotive applications," Compos Sci Technol, vol. 60, no. 10, pp. 18911900, 2000, doi: 10.1016/S0266-3538(00)00058-0.

H. R. Zarei and M. Kröger, "Crashworthiness optimization of empty and filled aluminum crash boxes," International Journal of Crashworthiness, vol. 12, no. 3, pp. 255-264, 2007, doi: 10.1080/13588260701441159.

Guoxing Lu and Tongxi Yu, Energy absorption of structures and materials. Cambridge: CRC Press LLC, 2003.

N. Jones, Structural Impact. Cambridge, 1989.

D. Al Galib and A. Limam, "Experimental and numerical investigation of static and dynamic axial crushing of circular aluminum tubes," Thin-Walled Structures, vol. 42, no. 8, pp. 11031137, 2004, doi: 10.1016/j.tws.2004.03.001.

W. Hardi, "IOP Conference Series : Materials Science and Engineering The behavior of various thin-walled aluminum prisms subjected by axial impact loading in relation to the energy absorption abilities," in Tarumanagara International Conference on Appalications of Technology and Engineering, Jakarta: IOP Publishing, 2018, p. 11.

F. Mat, K. A. Ismail, S. Yaacob, and O. Inayatullah, "Impact response of thin-walled tubes: A prospective review," Applied Mechanics and Materials, vol. 165, no. March 2014, pp. 130134, 2012, doi: 10.4028/www.scientific.net/AMM.165.130.

Z. G. Wei, J. L. Yu, and R. C. Batra, "Dynamic buckling of thin cylindrical shells under axial impact," Int Impact Eng, vol. 32, no. 1-4, pp. 575-592, 2006, doi: 10.1016/j.ijimpeng.2005.07.008.

A. Ghamarian and M. Tahaye Abadi, "Axial crushing analysis of end-capped circular tubes," Thin-Walled Structures, vol. 49, no. 6, pp. 743-752, 2011, doi: 10.1016/j.tws.2011.01.006.

A. A. A. Alghamdi, "Collapsible impact energy absorbers: An overview," Thin-Walled Structures, vol. 39, no. 2, pp. 189-213, 2001, doi: 10.1016/S0263-8231(00)00048-3.

W. Hardi, "The effect of impact velocity to the reaction force, the deformation length and the deformation mode on a thin aluminum tube," J Phys Conf Ser, vol. 1569, no. 4, 2020, doi: 10.1088/1742-6596/1569/4/042088.

M. Higuchi, Y. Hamaguchi, S. Suzuki, and T. Adachi, "Dynamic Behavior of a Circular Tube Subjected to High Impact Loading," 6th International Symposium on Advanced Science and Technology in Experimental Mechanics, pp. 3-5, 2011.

M. A. Choiron, A. Purnowidodo, E. Siswanto, and N. A. Hidayati, "Crash energy absorption of multi-segments crash box under frontal load," 2016, doi: 10.11113/jt.v78.8334.

M. Rismanto, Moch. A. Choiron, and S. Sugiono, "Optimasi Parameter Desain Multi-Cell Hexagonal Crash Box terhadap Absorbsi Energy Impact dengan Metode Taguchi," Jurnal Rekayasa Mesin, vol. 11, no. 3, pp. 427-440, Dec. 2020, doi: 10.21776/UB.JRM. 2020.011.03.15.

M. A. Choiron, M. A. Yaqin, and A. Yaqin, "Optimization of two segments crash box with rubber joint using response surface methodology ARTICLES YOU MAY BE INTERESTED IN Optimization of Two Segments Crash Box with Rubber Joint Using Response Surface Methodology," vol. 2278, p. 20012, 2020, doi: 10.1063/5.0014583.

"View of Energy Absorption and Deformation Pattern on Two Segment Crash Box with Rubber Connection Variation." Accessed: Mar. 06, 2023. [Online]. Available:

K. Günaydın, O. Gülcan, and H. S. Türkmen, "Experimental and numerical crushing performance of crash boxes filled with re-entrant and anti-tetrachiral auxetic structures," International Journal of Crashworthiness, vol. 28, no. 5, pp. 649-663, 2023, doi: 10.1080/13588265.2022.2115962.

Q. Gao, G. Yin, C. C. L. Wang, and W. H. Liao, "Crushing and theoretical analysis of multicell tube filled with auxetic structure under axial impact loading," Mechanics of Advanced Materials and Structures, vol. 30, no. 24, pp. 5034-5046, 2023, doi:10.1080/15376494. 2022.2111730.

P. K. A and A. K. G, "Effect of the number of stiffeners on the lateral deformation behavior of additively manufactured thin-walled cylindrical tubes," Mechanics of Advanced Materials and Structures, 2023, doi: 10.1080/15376494.2023.2172235.

T. Adachi, A. Tomiyama, W. Araki, and A. Yamaji, "Energy absorption of a thin-walled cylinder with ribs subjected to axial impact," Int J Impact Eng, vol. 35, no. 2, pp. 65-79, 2008, doi: 10.1016/j.ijimpeng.2006.11.005.

Z. Ahmad, "Impact and Energy Absorption of Empty and Foam-filled Conical Tubes," Proceedings of COBEM, no. December, 2009.

This ePub file was created using machine-generated methods and automated software to convert the source text into an ePub format and may contain formatting inconsistencies from the original version. Formatting may vary depending on the device used.

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Engineering Innovations, ISSN: 2813-1002, Vol. 11, pp 19-27

doi: 10.4028/p-8EHMyY

© 2024 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2023-12-02

Revised:
2023-12-29

Accepted:
2024-01-02

Online:
2024-06-26

Topology Optimization of Motorbike Footsteps Using Finite Element Method

The original version of this paper is available on https://www.scientific.net/EI.11.19.pdf

I Made Gatot Karohika , Januar Teguh Prasetyo , I Made Parwata , I Nyoman Gde Antara , I Nyoman Budiarsa

¹Mechanical Engineering Department Udayana University, Indonesia

gatot.karohika@unud.ac.id, teguh.januar123@gmail.com, md_parwata@unud.ac.id, dantara@unud.ac.id, nyoman.budiarsa@unud.ac.id

Keywords: Optimization, Topology, finite element, waste, footstep.

Abstract

Footsteps are a foothold for motorbike riders and passengers; they also play a role in maintaining stability when driving. Footsteps must have a solid and lightweight material to support the load from the feet and body of the rider and passengers. In this study, the footstep with the material made from the waste drum brake shoe varied by reducing mass through the static structural simulation process and topology optimization process using Ansys Workbench to get optimal mass, total deformation, equivalent stress, maximum principal stress, and safety factor from each variation. The footstep geometry will be subjected to a load of 1000 N and provided with the necessary support. Based on the data obtained during this study, the initial footstep geometry produces data in the form of total deformation ( 1.383 mm ), equivalent stress ( 21.013 MPa ), and safety factor ( 1.227 ). The variation produces data in the form of total deformation , equivalent stress , and safety factor ( 1.2538). The variation yields data in the form of total deformation ( 0.98037 mm ), equivalent stress ( 18.111 MPa ), maximum principal stress ( 18.41 MPa ), and safety factor (yield strength: 1.4236. At the same time, the 25% variation produces data in the form of total deformation , equivalent stress ( 22.27 MPa ), and safety factor (1.1577).

Introduction

The original version of this paper is available on https://www.scientific.net/EI.11.19.pdf

Motorbikes are a vehicle that many Indonesian people choose as a mode of transportation because of their affordable price, as well as because public transportation in Indonesia does not provide good service. Based on data from the Association of Indonesia Motorcycle Industry, there will be an increase in the distribution of motorbikes, dominated by scooters, in 2023 as shown in Fig. 1 [1].

Fig. 1. Distribution domestic of motorbikes [1]

Fig. 1. Distribution domestic of motorbikes [1]

Footsteps are a motorbike component that uses aluminum as the main material. Footsteps play a role as a foothold for motorbike riders and passengers, apart from that, footsteps also play a role in maintaining stability when driving. For this reason, this component is one of the components that is always present on motorbikes. Footsteps are required to have strong and light material so that they can support the weight of the feet and body of the rider and passenger. However, OEM footsteps on the market tend to have quite high prices.

Alternative materials need to be developed to reduce footfall prices, one way is by recycling metal waste. In Indonesia, metal waste accounts for of various types of waste [2]. The use of metal waste to be recycled back into new products has been carried out by several researchers, such as the use of waste motorbike brake shoes which are cast into brake handles [3], and as a footrest holder [4].

The simulation process using engineering software has been widely carried out by researchers and manufacturers to analyze the quality of a product or component [5]-[17]. Analysis using engineering software has advantages in terms of cost, time, and resources because there is no need to create a product to carry out the necessary analysis. Likewise with the optimization process [18], [19].

Based on the problems above, this research will analyze the strength of aluminum-based footsteps from brake shoe waste using the finite element method using the ANSYS Workbench R2 2021 application. This research aims to determine the strength of the product, in this case, the stress, strain, and safety factors. Furthermore, based on the simulation results of the product, topology optimization will be carried out to get a product that is lighter but does not reduce the strength of the product.

Material and Method

The original version of this paper is available on https://www.scientific.net/EI.11.19.pdf

The material used in this research is waste motorbike brake shoes which are cast using the sand casting method to obtain their mechanical characteristics. Based on the tensile test results, Young's modulus value was 1.4 GPa , the yield stress was 25.78 MPa , and the ultimate stress value was 101.94 MPa. This data is entered into the ANSYS Workbench software's Engineering Data section's table. Fig. 2 shows the waste brake shoe used.

Fig. 2. Waste brake shoes on the motorcycle

Fig. 2. Waste brake shoes on the motorcycle

The next stage is to model the footstep with geometry and size as shown in Fig. 3 and Ansys Space Claim Geometry in Fig. 4.

Fig. 3. Footstep drawing

Fig. 3. Footstep drawing

Fig. 4. Footstep model

Fig. 4. Footstep model

The load given to the footstep section is the full load of the weight of one passenger with a mass of 100 kg . Assuming the acceleration due to gravity is , the passenger load will be 1000 N .

The element used is Tet10 with a mesh size that will be used initially of 1 mm which is then smoothed to a fine resolution at level 7. The mesh shape and mesh settings can be seen in Fig. 5 and Fig. 6. This mesh size was chosen because it produces very good skewness values, the skewness of the mesh matrix spectrum can be seen in Figure 7.

Fig. 5 Mesh on footstep

Fig. 5. Mesh on footstep

Fig. 6 Mesh setting

Fig. 6. Mesh setting

Fig. 7 Skewness mesh metric spectrum

Fig. 7. Skewness mesh metric spectrum

After the meshing process continues with the setup process where the load and support points are placed on the geometry which can be seen in the Fig. 8.

Fig. 8 Footstep setup

Fig. 8. Footstep setup

The process continues by entering the solution settings, this process inputs the desired final result. Where the desired final results are von Mises stress, deformation, and safety factor.
After getting the desired results, continue with topology optimization by setting up the optimization region and response constraints according to the variations made.

Result

The original version of this paper is available on https://www.scientific.net/EI.11.19.pdf

Table 1 shows the initial design and design after the topology optimization process at a mass reduction of , and .

Table 1 Initial design and after mass reduction

Condition | Shape
Initial | Initial shape - elongated rectangular component with rounded left end
10% mass reduction | Shape after 10% mass reduction - similar to initial but slightly modified
20% mass reduction | Shape after 20% mass reduction - more curved and organic shape
25% mass reduction | Shape after 25% mass reduction - significantly modified angular shape

Table 2 shows the simulation results in the form of total deformation and von Mises stress for initial conditions and after undergoing topology optimization

Table 2 The stress and total deformation for each model.

Mass
Von Mises Stress
Total Deformation

Initial
21.013 Max
4.003e-6 Min
1.383 Max
0 Min

10%
mass
reduction
20.564 Max
3.796e-5 Min
1.4369 Max
0 Min

20%
mass
reduction
18.111 Max
3.0742e-5 Min
0.98037 Max
0 Min

25%
mass
reduction
22.27 Max
3.249e-5 Min
1.3058 Max
0 Min

Table 3 The result of topology optimization of the footstep

Mass Reduction | Mass (kg) | Von Mises Stress (MPa) | Total Deformation (mm) | Safety Factor
Initial | 2.048 | 21.013 | 1.383 | 1.227
10% | 1.903 | 20.564 | 1.4369 | 1.2538
20% | 1.783 | 18.111 | 0.98037 | 1.4236
25% | 1.553 | 22.27 | 1.3058 | 1.1577

Table 3 shows details of the initial conditions and after the topology optimization process. Based on these data, the best footstep design is a design with a mass reduction of because when compared with other conditions it produces von Mises stress results, the smallest total deformation, while the safety factor is the largest. Even though a mass reduction provides the smallest mass reduction, there is an increase in total deformation and von Mises stress, resulting in the safety factor decreasing again.

Conclusion

The original version of this paper is available on https://www.scientific.net/EI.11.19.pdf

From the results of topology optimization, there was a reduction in mass from the initial 2.048 kg to . The results show the best design is footstep with a mass reduction of from the initial shape.

References

The original version of this paper is available on https://www.scientific.net/EI.11.19.pdf

Association Of Indonesia Motorcycle Industry, "Association Of Indonesia Motorcycle Industry," Association Of Indonesia Motorcycle Industry. Accessed: Sep. 25, 2023. [Online]. Available: Https://Www.Aisi.Or.Id/Statistic/

"SIPSN - Sistem Informasi Pengelolaan Sampah Nasional", Accessed: Sep. 23, 2023. [Online]. Available:

I. N. G. Antara, K. G. Made, and G. Ketut, "Application of sand casting to recycle aluminum alloy for motorcycle brake handle," in Key Engineering Materials, 2016. doi: 10.4028/www.scientific.net/KEM.705.357.

I. M. G. Karohika and I. N. G. Antara, "The utilization of aluminum alloy waste as a footrests support for motorcycle," 2023, p. 040017. doi: 10.1063/5.0115571.

D. Nurhadiyanto, S. Haruyama, K. Kaminishi, I. M. Gatot Karohika, and D. Mujiyono, "Contact Stress and Contact Width Analysis of Corrugated Metal Gasket," Applied Mechanics and Materials, vol. 799-800, pp. 765-769, 2015, doi: 10.4028/www.scientific.net/amm.799800.765.

I. M. G. Karohika and S. Haruyama, "Analysis of three-layer gasket performance affected by flange surface," EUREKA: Physics and Engineering, no. 4, pp. 57-66, Jul. 2022, doi: 10.21303/2461-4262.2022.002290.

I. N. Budiarsa, I. N. G. Antara, I. M. G. Karohika, I. W. Widhiada, and N. L. Watiniasih, "Identification Plastic Properties of Spot Welded Joints Using the Instrumented Indentation Technique," IOP Conf Ser Mater Sci Eng, vol. 811, no. 1, 2020, doi: 10.1088/1757899X/811/1/012020.

W. Widhiada, I. M. Widiyarta, I. N. G. Antara, I. N. Budiarsa, and I. M. G. Karohika, "Remote Pressure Water Valve Control System Based on PLC," Int J Adv Sci Eng Inf Technol, vol. 11, no. 3, pp. 981-986, 2021, doi: 10.18517/ijaseit.11.3.14486.

I. M. G. Karohika, S. Haruyama, I. N. G. Antara, I. N. Budiarsa, and I. M. D. B. Penindra, "Sealing Performance Layered Metal Gasket Based on the Simulation Method," Teknik, vol. 41, no. 1, pp. 14-19, 2020, doi: 10.14710/teknik.v41i1.26125.

I. M. G. Karohika and I. N. G. Antara, "The metal gasket sealing performance of bolted flanged with fem analysis," in IOP Conference Series: Materials Science and Engineering, 2019. doi: 10.1088/1757-899X/539/1/012018.

W. Widhiada, I. N. G. Antara, I. N. Budiarsa, and I. M. G. Karohika, "The Robust PID Control System of Temperature Stability and Humidity on Infant Incubator Based on Arduino at Mega 2560," in IOP Conference Series: Earth and Environmental Science, 2019. doi: 10.1088/17551315/248/1/012046.

I. M. G. Karohika and I. N. G. Antara, "Gasket Process Parameter in Metal Forming," in IOP Conference Series: Earth and Environmental Science, 2019. doi: 10.1088/17551315/248/1/012044.

I. N. Budiarsa, I. N. G. Antara, and I. M. G. Karohika, "Indentation Size Effect of the Vickers Indentation to Improve the Accuracy of Inverse Materials Properties Modelling Based on Hardness Value," in IOP Conference Series: Earth and Environmental Science, 2019. doi: 10.1088/1755-1315/248/1/012009.

I. M. G. Karohika, I. N. G. Antara, and I. M. D. Budiana, "Influence of dies type for gasket forming shape," in IOP Conference Series: Materials Science and Engineering, 2019. doi: 10.1088/1757-899X/539/1/012019.

I. M. G. Karohika and I. N. G. Antara, "Proses Pembentukan Gasket berlapis dengan Metode Elemen Hingga," Jurnal Energi Dan Manufaktur, 2018, doi: 10.24843/jem.2018.v11.i02.p06.

Dzikri Amali Musyaffa, Moch. Agus Choiron, Yudy Surya Irawan, Nafisah Arina Hidayati, Taryono Taryono, "Computer Simulation Investigation Of Crash Box Design As SafetyProtection Technology For Indonesia High-Speed Train", International Journal of Mechanical Engineering Technologies and Application, vol. 4, No. 1, pp. 97-103, 2023. DOI: .

Fauzan Aulia, Achmad As'ad Sonief, Nafisah Arina Hidayati, Sanjay M R," Stress Distribution Analysis On Ligament Augmentation And Reconstruction System (Lars) Using Finite Element Method (FEM)", International Journal of Mechanical Engineering Technologies and Application, vol. 4, No. 1, pp. 61-68, 2023. DOI: .

I. M. G. Karohika et al., "An Approach to Optimize the Corrugated Metal Gasket Design Using Taguchi Method," Int J Adv Sci Eng Inf Technol, vol. 10, no. 6, pp. 2435-2440, 2020, doi: 10.18517/ijaseit.10.6.12992.

I. N. Budiarsa, I. M. Astika, I. N. G. Antara, and I. M. G. Karohika, "Optimization on strength spot welding joint trough finite element modeling indentation approach," IOP Conf Ser Mater Sci Eng, vol. 539, no. 1, 2019, doi: 10.1088/1757-899X/539/1/012042.

This ePub file was created using machine-generated methods and automated software to convert the source text into an ePub format and may contain formatting inconsistencies from the original version. Formatting may vary depending on the device used.

The original version of this eBook is available on https://www.scientific.net/book/engineering-innovations-vol-11/978-3-0364-1606-9

Engineering Innovations, ISSN: 2813-1002, Vol. 11, pp 29-41

doi: 10.4028/p-fRQ6q8

© 2024 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2023-12-01

Revised:
2024-01-03

Accepted:
2024-01-07

Online:
2024-06-26

Analytical Prediction of Crushing Thin-Walled Square Tube with Static Axial Loads Using Elliptical Holes as Crush Initiators

The original version of this paper is available on https://www.scientific.net/EI.11.29.pdf

Endarto Tri Wibowo , Jos Istiyanto , Danardono Agus Sumarsono , Dony Hidayat

Department of Mechanical Engineering, Faculty of Engineering, Universitas Indonesia, Kampus UI Depok, Depok 16424, Indonesia

*Email: enda043@brin.go.id, josist@eng.ui.ac.id, dasumarsono@gmail.com, dony.hidayat@brin.go.id

Keywords: Impact energy absorber, analytical, square tube, elliptical hole.

Abstract

In the structure of passenger vehicles there are components that absorb the impact load, which components are commonly thin-walled square tube. The design of the impact energy absorber model can be carry-out by experiment, simulation, and analysis. In the design of this impact energy absorbing component, an elliptical hole was used as a crush initiator to reduce peak loads and set the start of the bending pattern. Analytical predictions were made to reduce costs and speed up time to obtain mean load and peak loads values from the same shape model. In this study, a thin-walled square tubes model is used with an elliptical hole that have ratio of horizontal axis and vertical axis is from 3:7 until 7:3. The result of this study showed that the prediction of the peak load and average load by analytical means has a good conformity with the simulation.

1. Introduction

The original version of this paper is available on https://www.scientific.net/EI.11.29.pdf

According to data from the Indonesian Central Statistics Agency (BPS), it was known that there is an increase in the number of vehicles by around every year [1]. So, it is very important to have criteria from vehicle design to ensure the safety and security of passengers in the event of an accident / crushes (crashworthiness). Criteria in crashworthiness are important for application in the design of motorized vehicles, cars, buses, trains and ships. Where in the design of the vehicle structure there is a collision energy absorption zone (crumple zone) which functions to protect passengers so that they remain safe in the passenger compartment when a crushing occurs.

Several factors that affect crashworthiness are the absorptive energy value of a structure including the load from the impact force, the crash initiator (trigger from the folding direction), the geometry of the shape of the object, the type of material and the mass of the specimen . The criteria for the impact energy absorption model include energy absorption (EA), specific energy absorption (SEA), mean crushing force (MCF), peak crushing force (PCF), and crushing force efficiency (CFE). The CFE is obtained from a comparison between the MCF and PCF values. The PCF value is expected not too high, this is to avoid serious injury or death of passengers due to the influence of high decelerations toward the limits of the abilities human body if the collision was happened. While SEA is obtained from the comparison between the EA value and the mass of the material [7].

Fig. 1. Location of the component structure for energy absorption / crashworthiness of the vehicle [8].

Fig. 1. Location of the component structure for energy absorption / crashworthiness of the vehicle [8].

In the process of analysing energy absorption in structures, which can commonly be carried out analytically, numerical simulations, and validation processes with experiments. Where on the experiment need specimen or test objects, sensors, and equipment that do not slightly, while in the simulation possible more a little equipment, however still need a computer with specification high specific and also analysis software collisions (ANSYS LS-DYNA, ABAQUS, and Pam Crash), where both of methods require significant costs. So that analytical calculations were developed to make it easier in calculating the predictions on the estimated value of the mean load and peak load when the crushing occurs. This will be faster because the calculation time is relatively fast with the equations that have been made and it is easier with less resource requirements.

In this paper, analytical prediction was developed on the mean load and peak load calculation when the static axial impact loads occur in a thin-walled square tube with an elliptical hole. Where is the elliptical hole as the crush initiator and controls when the first bending occurs. The elliptical hole consists of a major axis in horizontal position (a) and a minor axis in vertical position (b), with variations in the size ratio (a/b) that influencing the load impact values. After the results of the analytical calculations are obtained, then comparing with the simulation to show trend of result.

2. Materials and Methods

The original version of this paper is available on https://www.scientific.net/EI.11.29.pdf

In predicting the energy absorption value of static axial load on thin-walled square tube by analytical calculations, it has started from the basic folding mechanism method presented by Abramowicz and Wierbicki [10]. Where in modeling the buckling deformation in general there are 2 types of buckling models, namely inextensional collapse modes (mode I) and extensional collapse mode (II) [11].

In the deformation of modes I for simplifying the calculation amount of energy absorption rate in terms of the basic folding mechanism in movement of the bent deformation on the square tube there are 3 different mechanism parts, namely the energy rate on the surface part of the toroidal ( ), the energy rate in the horizontal bending line ( ), and energy rate in the inclination bending line ( ) [9, 10]. As for the extensional deformation (mode II) in calculating values of the energy absorption rate from the bending deformation motion, there are also 3 different mechanisms, namely the energy rate on the trapezoidal surface ( ), the energy rate on the horizontal bending line ( ), and energy rate at the inclination bending line .

Fig. 2. Basic folding mechanism, (a). inextensional collapse modes (Mode I) [10,19] (b). extensional collapse mode (Mode II) [13].

Fig. 2. Basic folding mechanism, (a). inextensional collapse modes (Mode I) [10,19] (b). extensional collapse mode (Mode II) [13].

When the collision occurs, there will be deformation in the form of bending on the surface of the energy absorbing structure. This bending causes a change in length before and after the collision, as well as a change in angle ( ). Referring to Fig. 2.a and 2.b, the relationship between the distance of the change in length ( ) and the change in angle ( ) is as follows:

Where, H is a half wavelength of the bending, from Eq. 1 it can be seen that when then ( ); which means (no folds yet), while at ( ); means (maximum fold). Meanwhile, the value of the horizontal displacement distance ( s ) at point C (Fig. 2), is:

Then from Eq. 1 it can be derived to be the axial motion velocity , with the following Eq.:

Meanwhile, from Eq. 2 it is derived to be the horizontal velocity ( ), with the following Eq.:

For the relationship between corner , referring to the type of mode I in Fig. 2.a, are as following [9][19].

Where
In the inextensional deformation type (mode I) for the equation of the energy absorption rate consist of 3 constituent parts [9,10,12], that is,
a. The energy dissipation rate on the toroidal surface ( ), with the following Eq.:

With Eq. I is,

Where, is integral value on the toroidal section; is fully plastic membrane force; is fully plastic bending moment; is the small radius from toroidal surface.
b. The energy dissipation rate on the horizontal bending line ( ), with the following Eq.:

Where, C is length of the horizontal bending line.
c. The energy dissipation rate at the inclination bending line ( ), the Equation is.

Where is,

2.1 Equation for calculating the internal energy absorption of a basic folding element in a square tube without holes.

According from reference [11], the absorption energies consist of type I and type II on the square tube, respectively,

While from reference [10,18] for the average load ( ) and peak load ( ) of the square tube without holes, respectively, are

Where is geometry coefficient, for square tube without hole is 16,41 .

2.2 Energy calculation of the horizontal hinge line on a square tube with 2 elliptical holes on opposite sides.

The existence of a hole will influence the amount of absorption energy in mode I, where the effect of a round hole on a square tube has been calculated [18, 19]. While here it is studied for the influence of elliptical holes on 2 opposite sides which affect the horizontal hinge line, with the following calculations:

Fig. 3. Geometry model with elliptical holes on square tube.

Fig. 3. Geometry model with elliptical holes on square tube.

From Fig. 3 it can be seen that the length of the horizontal line is C, while the horizontal line with the elliptical hole is , for A is the area of the field without the elliptical hole, is the area of the field with the elliptical hole, and is the distance of the horizontal axis on the ellipse, and is distance of the vertical axis on the ellipse, so the equation is obtained,

There is an influence of the elliptical shape factor on the ratio of the length between the vertical axis and the horizontal axis when the collision occurs, which influence the magnitude of the peak load value as stated in reference [21]. So that the ratio of the length of the vertical axis to the horizontal becomes a coefficient.
In this study to determine the coefficient of an elliptical shape similar with a circle, where the calculation of area of the circle is influenced by the dimension (radius) while for the ellipse it is influenced by the dimensions a (major axis) and (minor axis). So that square is equivalent to times b . When viewed from the calculation of the circumference, the circle is influenced by the diameter (2r) while for the ellipse the size of the circumference is influenced by the summission of a and . The equation is as follows,

Area Area

can written too
Circumference Circumference

If, so,

The quantity Area Area when is given constanta multiplier, is obtained

Where according on reference data [21] it is known that the influence of dimensions of the horizontal axis (a) is about 10 times greater than the vertical axis (b) for the result of peak loads. By using the weighting coefficient on the values of a and b , where and . So, the coefficient a is different with b . Another effect for the elliptical hole on 1 side is related to the energy dissipation with the horizontal hinge line effect is or . To estimate the elliptical shape coefficient is as follows:

Then, the effect of for the energy rate dissipation ( ) on the horizontal hinge line with the condition of 2 elliptical holes on the opposite sides, so that the value of on the square tube is composed of 12 horizontal hinge lines C and 4 horizontal hinge lines . So, the following equation is obtained:

Simplified to be,

By substituting Eq. 14 into Eq.16.b, we get,

Where the value of is from 0 to , so when integrated, the energy dissipation value obtained is,

2.3 Symmetric collapse mode with 2 elliptical holes on opposite sides.

For calculation of the mean load from the absorption energy in symmetric collapse mode where the external energy balance is equal to the internal energy, so the external energy value is 4 times energy of type I [10, 11]. So, the absorption energy equation for symmetric collapse on a square tube with 2 elliptical holes is obtained, by the following equation is,

By substitution Eq.6, 18.c, and 8 into Eq.19.c, hence the result,

If,.
The Eq.20.b can be simplified with these coefficients. So, the following form of the equation is obtained, namely,

Where according to reference [10] for a square tube ( ), the value of , and are obtained. Whereas for,

By substituting the values , and with Eq.22a, 22b, and 22c into Eq.21, so the following equation is obtained,

It's known that , then the value of the mean force is

Based on reference [11] for the effective crushing distance ( ) in symmetric collapse mode, is

By dividing Eq. 24 by Eq. 25 and inserting the effect of the ellipse shape coefficient (k) from Eq.15a, so the value of mean static force ( ) is,

The peak crushing force is the instantaneous peak value at the collision, with a value above of the mean static force so it is necessary to have a peak collision force coefficient , and geometry coefficient where from reference [18] the value of . So that is obtained,

Based on reference [18] for the calculation of is

For the values and related to the value of the angle when peak crushing was occur. So, the equation is

Whereas for it is influenced by the value of on the horizontal hinge line and also the influence of elliptical shape was affecting the weight values on a and b . so we get the equation,

2.4 Size and dimensions of models

As for size of the model specimen was based on reference [20]. With a square tube cross section size is ; Side width (C) is 36.55 mm ; square tube wall thickness (h) is 0.85 mm ; the total length of the specimen model (L) is 200 mm . Then in this study using 2 ellipse holes which are located on 2 opposite sides with the distance between the center point of the ellipse and the tip (H) is 20 mm , for illustration can be seen in Fig.4. While shape of the elliptical hole is made with varying sizes on the horizontal axis (a) and the vertical axis (b) with sizes shown in Table 1.

Fig.4. Size of square tube with crush initiator.

Fig.4. Size of square tube with crush initiator.

Table 1. Size variation of the horizontal and vertical axis on the elliptical holes.

No
Specimen models
Size of axis
Ratio
Size of
area
[mm²]

Horizontal
axis (a)
[mm]
Vertical
axis (b)
[mm]
a/b

1
Square tube without holes

0
0

2
With elliptical
holes a<b
3:7
3
7
0.43
65.94

3
4:6
4
6
0.67
75.36

4
5:7.5
5
7.5
0.67
117.75

5
5:6
5
6
0.83
94.2

7
With elliptical
holes a>b
6:5
6
5
1.20
94.2

8
6:4
6
4
1.50
75.36

9
7.5:5
7.5
5
1.50
117.75

10
7:3
7
3
2.33
65.94

2.5 Simulation with the Finite Element method

In this study the analytical results were compared with the simulation results obtained from the LS-Dyna software. A thin-walled square tube model was created in the LS-Dyna software with the size and dimensions as previously described (section 2.4). The crushing simulation model consists of

2 components, namely a thin-walled square tube as a specimen model and the beam model as an impactor.

Setting of a thin-walled square tube model for mesh of the wall column using Belytschko-Lin-Tsay-4-nodes with a mesh size of , it gives optimal and convergence results, so the phenomenon of plastic deformation in the form of indentation in the square tube wall during crash can be properly simulated. In material behaviour a piecewise linear plasticity model is used. As for its material properties are Young's modulus (E) is 195 GPa , density is , and the value of yield stress ( ) is 265 Mpa [20].

Boundary condition at the bottom end of the square tube is set in fix, there is no displacement , , and ). While the direction of impactor movement is only in the downward Z direction ( , , and ). Loading is given by the impactor with a constant speed of in line with the axis of the square tube. This condition in static axial loading simulation. For illustration can be seen in Fig.5.

As for the impactor beam model, it is made more rigid than square tube, for material type using rigid bodies models. The relation between the surface of square tube and the impactor uses an automatic node to surface contact, where this type of contact prevents penetration and sliding between the impactor wall and the square tube when loading contact occurs. The internal surface relations on the square tube uses automatic-single-surface-contact where this type of contact prevents penetration from between the indentation of square tubes wall when progressive buckling occurs [21].

Fig. 5. Loading model with an impactor on a square tube.

Fig. 5. Loading model with an impactor on a square tube.

3. Results and Discussion

The original version of this paper is available on https://www.scientific.net/EI.11.29.pdf

3.1 The comparing results between simulation and analytical calculations of square tube without hole.

In the first row of Table 2 and Table 3 is a comparison between analytical and simulation results of a square tube without hole. For the average force ( ) of analytical calculation is obtained 7944.07 N , while at the peak load is 29863.29 N , where for and when compared to the simulation there have deviation and respectively. While the peak load of simulation is 29942 N , when compared to the experimental results on reference [20] there is a difference of 2.7%.

3.2 The comparing results between simulation and analytical calculations of square tube with eliptical holes.

For analytical calculations of the peak load ( ) on square tube with elliptical holes, the angle value of is according to reference [18], the calculation results are obtained as follows in Table 2 and Table 3. Analytical calculations have been carried out on several elliptical size variations
of the ratio . The results of the comparison between the simulation and analytical values for the average load ( ) of several elliptical hole size models obtained an average difference of about with a range between to . The result as in the Table 2. While the comparing results for the peak load ( ) between the simulation and analytical calculation of several elliptical hole size models obtained an average difference of about with a range between to . The result as in the Table 3.

The graph of Fig. 6 shows the influence the ratio of elliptical holes size on the peak load value. The highest value is on a square tube without holes or the ratio is zero, both by simulation and analytical calculations, namely 29942 N and 29863.3 N respectively, (for detailed numbers in Table 3). The lowest value is in an elliptical shape with a ratio of 1.5 with a size of with simulated and analytical values is 24303 N and 26592.93 N respectively. So that from graph of Fig. 6 showed that the greater ratio of the elliptical holes, the trend of peak load value will be decrease. The square tube with elliptical holes size or the ratio less than 1 , the values is higher than with elliptical holes size .

Table 2. The comparing results between simulation and analytical calculations on the values.

No
Specimen models
a:b
Size of axis
Ratio
a/b
Size of area
Ellips
[mm²]
Pmean Values
deviation
[N]
%
deviation

Dimension of
Horizontal axis
(a)
[mm]
Dimension of
Vertical axis
(b)
[mm]

Simulation
[N]
Analytics
[N]

1
Square Tube
without holes
0
0
7871
7944.07
73.07
0.9%

2
With elliptical holes
a<b
3:7
3
7
0.43
65.94
7744
7473.88
270.12
3.5%

3
4:6
4
6
0.67
75.36
7849
7459.93
389.07
5.0%

4
5:7,5
5
7.5
0.67
117.75
7608
7485.29
122.71
1.6%

5
5:6
5
6
0.83
94.2
7805
7461.23
343.77
4.4%

6
With elliptical holes
a>b
6:5
6
5
1.20
94.2
7585
7449.03
135.97
1.8%

7
6:4
6
4
1.50
75.36
7631
7437.68
193.32
2.5%

8
7.5:5
7.5
5
1.50
117.75
7814
7450.78
363.22
4.6%

9
7:3
7
3
2.33
65.94
7646
7429.32
216.68
2.8%

Average
3.02%

Table 3. The comparing results between simulation and analytical calculations on the values.

No
Specimen models
a:b
Size of axis
Ratio
a/b
Size of area
Ellips
[mm²]
Ppeak Values
deviation
[N]
%
deviation

Dimension of
Horizontal axis
(a)
[mm]
Dimension of
Vertical axis
(b)
[mm]

Simulation
[N]
Analytics
[N]

1
Square Tube
without holes
0
0
29942
29863.3
78.71
0.3%

2
With elliptical holes
a<b
3:7
3
7
0.43
65.94
27878
26755.52
1122.48
4.0%

3
4:6
4
6
0.67
75.36
27223
26691.07
531.93
2.0%

4
5:7.5
5
7.5
0.67
117.75
26329
26716.09
387.09
1.5%

5
5:6
5
6
0.83
94.2
26435
26666.62
231.62
0.9%

6
With elliptical holes
a>b
6:5
6
5
1.20
94.2
25698
26623.03
925.03
3.6%

7
6:4
6
4
1.50
75.36
25841
26611.47
770.47
3.0%

8
7.5:5
7.5
5
1.50
117.75
24303
26592.93
2289.93
9.4%

9
7:3
7
3
2.33
65.94
25093
26595.98
1502.98
6.0%

Average
3.40%

COMPARISONON PRESULTS BETWEEN SIMULATION AND ANALYTIC TOWARD THE RATIO OF ELLIPSE SIZE (A/B)

The original version of this paper is available on https://www.scientific.net/EI.11.29.pdf

Fig. 6. Graph of comparison on results between simulation and analytic toward the ratio of ellipse size (a/b).

Fig. 6. Graph of comparison on results between simulation and analytic toward the ratio of ellipse size (a/b).

COMPARISON ON PRESULTS BETWEEN SIMULATION AND ANALYTIC TOWARD THE RATIO OF ELLIPSE SIZE (A/B)

The original version of this paper is available on https://www.scientific.net/EI.11.29.pdf

Fig. 7. Graph of comparison on results between simulation and analytic toward the ratio of ellipse size (a/b).

Fig. 7. Graph of comparison on results between simulation and analytic toward the ratio of ellipse size (a/b).

Fig. 8. Graph of comparison on results between simulation and analytic toward the area of the ellipse.

Fig. 8. Graph of comparison on results between simulation and analytic toward the area of the ellipse.

COMPARISON ON P RESULTS BETWEEN SIMULATION AND
ANALYTIC TOWARD THE AREA OF THE ELLIPSE

Fig. 9. Graph of comparison on results between simulation and analytic toward the area of the ellipse.

Fig. 9. Graph of comparison on results between simulation and analytic toward the area of the ellipse.

The graph of Fig. 7 shows the effect of the ratio at elliptical hole toward the average load. For the highest value in the square tube without holes both in simulation and analytical calculations, namely 7871 N and 7944.07 N , respectively (for detailed numbers in Table 2). The lowest value for a square tube with elliptical holes at the ratio where in the simulation at a ratio of is 7585 N , while in the analytic calculation at a ratio of is 7429.32 N . On the simulation graph the difference between the highest and lowest values is 286 N or , while on the analytical chart the difference between the highest and lowest values is or . So that the presence of holes can reduce the value. Meanwhile, the ratio have relatively small effect on the average load value.

The graph from Fig. 8 and 9 showed the and the value, respectively consists of 4 types of graphs that shows the comparing of the results by simulation and analytic, each consisting of elliptical ratio and . The graph of Fig. 8 showed the effect of the elliptical area size on the peak load. The highest value is in an elliptical shape with a size ratio with an area of , namely the simulation results are 27878 N , while the analytical results are 26755.52 N (for detailed number in Table 3). The lowest value for on an ellipse with a size ratio with an area of , namely the simulation results are 24303 N , while the analytical results are 26592.93 N . On the simulation graph the difference between the highest and lowest values is 3575 N , from this value there is a significant difference, while on the analytical chart the difference between the highest and lowest values is 162.59 N . So that from graph of Fig. 8 showed that the influence of the area in elliptical hole with the size orientation toward the values, where the wider of the elliptical area, so the value to be lower.

The graph of Fig. 9 shows the effect of the size of the elliptical area on the average load. For the highest value from the simulation results is on elliptical shape with a size ratio with an area of the value is 7849 N , while the lowest value is in elliptical size ratio with an area of the value is 7585 N , for the difference between the highest and lowest values is 264 N or , (for detailed numbers in Table 2). For analytical calculations the highest results are in elliptical shapes with a size ratio with an area of the value is 7485.29 N , while the lowest is in elliptical size ratio with an area of the value is 7429.32 N , for the difference between the highest and lowest value is 55.97 N or . The difference in the size of elliptical area with a range from until has no significant effect on the average load.

4. Conclusion

The original version of this paper is available on https://www.scientific.net/EI.11.29.pdf

Analytical calculations have been carried out on a square tube with 2 elliptical holes on opposite sides with variations in the size of the elliptical ratio of with static axial impact loads, then compared with the simulation results it shows that the difference
between the analytical calculations and the simulation for and is and respectively.

The formula for predicting the load from a thin-walled square tube with a static axial impact loads for the prediction of the average load is in equation 26, while the prediction formula is in equation 27. From the comparison of the analytical calculations and simulations results showed a good conformity.

The influence of the orientation of the ratio and the size of the area on the elliptical hole has a significant effect on the value. Where the greater of ratio and the wider of area, so the value to be lower.

Acknowledgments

The original version of this paper is available on https://www.scientific.net/EI.11.29.pdf

The author would like to thank the Universitas Indonesia for financial support through the-Hibah PUTI 2022 (Grant No. NKB-335/UN2.RST/HKP.05.00/2022).

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The original version of this paper is available on https://www.scientific.net/EI.11.29.pdf

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Engineering Innovations, ISSN: 2813-1002, Vol. 11, pp 43-62

doi: 10.4028/p-um3VJO

© 2024 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2023-12-01

Revised:
2023-12-24

Accepted:
2023-12-29

Online:
2024-06-26

A Bibliometric Analysis of Suspension System Development for Enhancing Comfort in Family Passenger Vehicles

The original version of this paper is available on https://www.scientific.net/EI.11.43.pdf

Fattah Maulana , Dicky Permana Adji Santosa , Cahyo Hadi Wibowo , Yudha Priatama , Sariwulan Nurcholis , Adhe Lingga Dwi

¹Department of Mechanical Engineering, Faculty of Engineering, Sebelas Maret University, Surakarta, Central Java, Indonesia.

Department of Mechanical Engineering, Faculty of Engineering, Institut Teknologi Sumatera, South Lampung, Lampung, Indonesia.

Division of Manpower and Transmigration, Government Central Java Province, Semarang, Central Java, Indonesia.

Department of Computer Science, School of Computer Science, Bina Nusantara University, Semarang, Central Java, Indonesia.

a,*fattah0303@student.uns.ac.id, ajidicky89@gmail.com, cahyohaw@student.uns.ac.id, yudha.118170021@student.itera.ac.id, swnurcholis@student.uns.ac.id, adhe.dewi@binus.ac.id

Keywords: Passenger comfort, suspension system, bibliometric analysis, suspension technology, development suspension

Abstract

In daily-used family passenger cars, passenger comfort is crucial. Vehicle suspension is a major factor in passenger comfort. A detailed suspension domain knowledge evaluation is necessary. Despite continual comfort technology advances, studies have yet to use bibliometric analysis to track suspension system history and expansion. This study analyzes keywords, citations, h-index, publishing years, journals, affiliations, nations, authors, and review articles in a novel way. Based on Scopus, the analysis is performed in CSV format and incorporated into bibliometric.org's Biblioshiny, VOSviewer, and R-studio apps. The US leads this study, followed by India and Canada. Indian publications are the most prolific. For suspension technology makers, this research may help them discover rivals and predict future trends. This study promotes suspending technology development through educated decision-making, strategic planning, and innovation.

Introduction

The original version of this paper is available on https://www.scientific.net/EI.11.43.pdf

When crossing road surfaces, vehicles are familiar with roll movements when turning corners, pitch when braking or accelerating, and bounce when vibrating vertically due to following a bumpy road surface [1]. This phenomenon causes discomfort and can affect the safety of passengers. The car's active suspension system ensures adequate stability, maintains continuous road wheel contact, and improves suspension performance [2], [3]. The main function of the suspension system is to support the car body and then isolate the body from irregular road surface disturbances [4], [5]. In the active suspension system, the implementation of the control system plays a very important role in balancing the trade between driving comfort and handling [6]. Suspension systems in cars are classified into various types. In general, you will learn three types of suspensions, namely independent, dependent, and semi-independent. Independent suspension is a system where the left and right wheels are not in a rigid line. Independent suspension (rigid) occurs because the right and left wheels are in a rigid line. At the same time, the semi-independent suspension is a combination of rigid and independent suspension. More specifically, the automotive world recognizes the following types of car suspensions.

Macpherson suspension: This type is most widely used in light vehicles such as Sedans, MPVs, Hatchbacks, etc [7]. This type of front suspension is classified as an independent suspension type where the right and left wheels of the car are not adrift. Macpherson suspension is very good because it can dampen vibrations quite well. This type of suspension design is quite simple and does not take up space, so it is suitable for use on small cars. Macpherson has several components. Among these
components, a coil spring or coiled spring is used because it is minimalist in shape, and the elastic is quite flexible. Furthermore, a shock absorber is located inside the coil spring, so these two things are one component unit [8]. There is also a lower arm, which is a suspension arm that links the wheels and the car body. In addition, a ball joint or 360-degree hinge is located at the end of the lower arm, allowing the wheel to move in any direction as desired. Lastly, there is the knuckle arm and stabilizer. The knuckle arm is a place to put suspension components, such as lower arms, shock breakers, tie rods, and wheels. At the same time, the stabilizer is located in the shock absorber tube, which is connected to the knuckle arm.

Double Wishbone Suspension This type of suspension is widely used by crossover vehicles such as the Double Cabin and Big SUV [9]. This type of suspension is classified as independent of the type of front suspension. At first glance, the double wishbone suspension looks similar to the Macpherson. However, the double wishbone suspension design is more robust and complicated [10]. This suspension has two arms: the lower arm at the bottom and the upper arm at the top. These two suspension arms make the vertical movement of the wheels more balanced. Rigid suspension: This type can only be found on buses and trucks. This suspension includes a dependent suspension with the right and left wheels on a rigid block. This type of suspension can be located on the front or rear suspension. Rigid suspension has advantages in the level of durability. This type is the most powerful suspension capable of receiving large loads. This is because the rigid block where the right and left wheels are attached also supports the vehicle body. The rigid suspension also has several components, such as leaf springs, shock absorbers, rigid blocks, and stabilizer bars. For the first component, this spring is elongated and arranged in stages to increase spring strength.

Furthermore, a shock absorber is located between the rigid block and the car body. The rigid block or axle is a cross-shaped beam from the left to the right wheel, or it can also be called an ice block, and on the front wheel, this section uses a rigid axle. Multi-Link Suspension This type of suspension has several links. These links or links work like suspension arms but are three or more in number. The existing links are designed in such a way that they can support the movement of the wheels while dampening vibrations. Torsion Beam Suspension Torsion beam suspension is also known as semiindependent suspension [11]. This suspension has a basic design, such as a rigid suspension, which is innovated in such a way as to produce a better suspension effect. The basic form of an elongated rigid suspension is innovated to resemble the letter H. This shape makes the left and right wheel swings somewhat free. This will make the car more comfortable to drive. The elasticity possessed by the spring is used to dampen all the vibrations generated by the wheels due to the road surface. The suspension works as a barrier to the collision of the wheels with the car body.

Suspension Components The suspension system's main component is a steel spring, which is elastic and strong. This spring is later used to absorb vibrations on the road surface. However, the suspension components are not only springs. Several other components support it. Here are some of them. The suspension arm is a liaison between the wheels and the car chassis. This component is made of hinges, which can later be moved vertically. This vertical movement will help the wheel to move up or down, depending on the load received by the wheel. Shock Absorber's main function is to dampen the shock of the car's suspension, as the name implies. The suspension uses springs as its main component, but this spring has the disadvantage of having a return power when pressed. This will cause the car body to sway or oscillate despite no vibration. This component will prevent this from happening and can be used to prevent sudden spring movement. Shock absorbers can make the suspension effect harder and keep it stable because they can absorb shock effects well. This also causes no shock to the car-car-stabilizer, whose function is to balance the car body when the suspension works. Simply put, the car will lean outward when turning due to centrifugal force. This force can cause the car to roll over. Stabilizer serves to prevent and overcome this. This component also keeps the car in a safe and controlled condition.

Currently, many researchers are researching to improve the suspension system's performance. Using a quarter-car model, present an analysis of the ride comfort and road holding of passive and semi-active suspension systems [12]. The semi-active suspension system with magnetorheological (MR) damper is modeled as a non-parametric model-based magnetic flux density in the fluid flow gap [13]. Nagarkar et al. [14] presented the modeling, control, and optimization of a nonlinear quarter
car suspension system. A nonlinear quarter car mathematical model and seat and driver were developed and simulated in the Matlab/Simulink environment [14]. Ebrahimi et al. [15] compared the effects of various damping coefficients and spring stiffness values to identify which combination led to better suspension system performance. They developed a versatile semi-active suspension system with variable stiffness magnetorheological elastomer (MRE) isolator (VS) and variable damping magnetorheological (MR) damping (VD) for high-speed trains, aiming to improve ride comfort by avoiding body resonance car and eliminate vibration energy [16]. The quality of the set of vehicle suspension springs is relatively small, the displacement in the vertical direction is relatively small, and the turnaround time is relatively short. So, if you want to achieve the same vehicle suspension effect as the offering vehicle, we need to optimize the suspension parameters. The approach in this paper can also be used to make dynamic analysis for suspension and whole suspension. Optimization of system characteristics is the right step to overcome excessive control force. Therefore, this paper is expected to provide information regarding the bibliography of the system on the car suspension that has been developed so far.

Methodology and Data Sources

The original version of this paper is available on https://www.scientific.net/EI.11.43.pdf

The analysis is based on publications related to "suspension" published from 2000 to 2022. Literature was obtained through Scopus.com, with the search formulas for "suspension", "car", and "calculation" displaying document types from the related field. The results were from 2000 to 9 August 2022, with 1003 documents from the Scopus.com dataset using Vosviewer and R-studio Biblioshany from bibliometric.org [17].

Result

The original version of this paper is available on https://www.scientific.net/EI.11.43.pdf

The data shown in Table 1 were obtained from an overview using R-studio Biblioshiny from bibliometric.org. From the main information menu, you can also see the development of productivity, making a journal about this suspension as the growth speed of the suspension can be seen in the annual scientific production year graph (Fig. 1) [18].

Table 1 Main Information Overview

Description | Results
2 | 2000:2022
Sources (Journals, Books, etc) | 472
Documents | 1003
Annual Growth Rate % | 11.69
Document Average Age | 7.58
Average citations per doc | 21.5
References | 37201
Keywords Plus (ID) | 6764
Author's Keywords (DE) | 2726
Authors | 2708
Authors of single-authored docs | 68
Single-authored docs | 84
Co-Authors per Doc | 3.66
International co-authorships % | 13.86
Article | 616
Book | 8
Book chapter | 20
Conference paper | 312
Conference review | 13
Retracted | 1
Review | 32
Short survey | 1

Fig. 1 Graph of Annual Scientific Production

Fig. 1. Graph of Annual Scientific Production

Using the overview menu on this three-field plot unit, we can reference data based on the inputs in this case so that later, the data displayed is the most 20 or the best of the resulting plots (Fig. 2). In this case, the author will try to compile how an author in the middle refers to previous journal authors for digitizing in the left column and then using keywords on the right [19].

Fig. 2 Three Field Plot Reference-author-keywords

Fig. 2. Three Field Plot Reference-author-keywords

With the source menu in the most relevant source unit, we can see that the SAE technical paper is the one that appears the most, 56 times, followed by IOP conference series materials science and engineering in second place with 29 and vehicle system dynamics as many as 25 (Fig. 3). The connection between the selection of these sources is due to the habit of writing or the availability of
journal writing regarding suspension, bed linen; as we know, journal writing is also the result of the collaboration of the author and their writing habits, so that the selection of appropriate sources and the terms and conditions of publication are carried out by sources providing scientific journal publications.

Fig. 3 Most Relevant Source

Fig. 3. Most Relevant Source

With the source menu in the most locally cited source unit, we can see that Computer Simulation Of Liquids: Second Edition are the most common with 6044 citations, followed by Biomacromolecules in second place with 2082 times and Vehicle System Dynamics with 864 times (Fig. 4). In the source menu, we can also see source impact in Fig. 5, and get the h-index, g-index, and m-index tables as well as the number of citations which will be shown in Table 2 and source dynamics in Fig. 6.

Fig. 4 Most Locally Cited

Fig. 4. Most Locally Cited

Table 2 H-index, g-index and m-index Tables

Element | h_index | g_index | m_index | TC | NP | PY_start
VEHICLE SYSTEM DYNAMICS | 16 | 25 | 0.696 | 864 | 25 | 2001
JIXIE GONGCHENG XUEBAO/JOURNAL OF MECHANICAL ENGINEERING | 9 | 11 | 0.600 | 161 | 20 | 2009
JOURNAL OF SOUND AND VIBRATION | 8 | 9 | 0.364 | 505 | 9 | 2002
PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS, PART F: JOURNAL OF RAIL AND RAPID TRANSIT | 8 | 12 | 0.615 | 181 | 12 | 2011
INTERNATIONAL JOURNAL OF AUTOMOTIVE TECHNOLOGY | 7 | 7 | 0.500 | 121 | 7 | 2010
MECHANICAL SYSTEMS AND SIGNAL PROCESSING | 7 | 7 | 0.875 | 280 | 7 | 2016
PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS, PART D: JOURNAL OF AUTOMOBILE ENGINEERING | 7 | 13 | 0.318 | 181 | 20 | 2002
SAE TECHNICAL PAPERS | 7 | 9 | 0.292 | 154 | 56 | 2000
TIEDAO XUEBAO/JOURNAL OF THE CHINA RAILWAY SOCIETY | 6 | 11 | 0.353 | 136 | 16 | 2007
ZHONGGUO TIEDAO KEXUE/CHINA RAILWAY SCIENCE | 6 | 10 | 0.300 | 133 | 19 | 2004

Fig. 5 Most Local Impact

Fig. 5. Most Local Impact

Fig. 6 Source Dynamics

Fig. 6. Source Dynamics

In this author menu, select the most local and relevant citations, author production over time, author influence, related author affiliations, country scientific production, and most cited countries. This menu will discuss which countries have published the most scientific papers regarding the keyword suspense. The countries that published the most scientific journals about this suspension were China 1,557 times, the United States 224 times, and India 171 times. Here, we present the countries that will publish their journal production in Table 3. The author's menu yields the most relevant author units and the most locally cited author units, as shown in Fig. 7 and 8.

Fig. 7 Most Relevant Author

Fig. 7. Most Relevant Author

Fig. 8 Most Locally Cited Author

Fig. 8. Most Locally Cited Author

This discussion is an interesting topic where the document menu will display several sections that can be explained in the bibliography so that the journal's quality will appear based on citations carried out by the next author. This number of citations impacts the author so that the value of the h-index, m-index, and g-index will increase as the citations obtained by the author increase from the citations obtained [20]. The following are the top 10 Most Global Cited Documents with the top 10 best rankings where Allen MP was ranked first for 6044 citations, followed by Azizi Samir Mas, in second place with 2082 times and Yang Z, 677 times (Fig. 9).

Fig. 9 Most Global Cited Document

Fig. 9. Most Global Cited Document

Fig. 9 shows keywords that the writer uses in determining keywords, making it easier for future writers to write every future article. For keywords that the author often uses, suspension ranks first, which was made 32 times, then ride comfort 26 times, then vehicle dynamics 26 . In the data displayed, the suspension (components) will come first on the subtopic discussion of self-suspension. Here, we show the most relevant word in Fig.10, word cloud in Fig. 11, and the tree map in Fig. 12.

Fig. 10 Most Relevant Words

Fig. 10. Most Relevant Words

Fig. 11 Word Cloud

Fig. 11. Word Cloud

Fig. 12 Tree-map

Fig. 12. Tree-map

In the conceptual structure menu, we can see the co-authors' role through the development of scientific journal writing, where not all co-authors focus on writing suspension journals. These coauthors act as people who provide suggestions and ideas to the author in writing scientific journal publications. Different backgrounds will further add to and open up new gaps in writing pending scientific journal publications.

Next, to see the development of journal writing based on keywords, we can see the development of journal writing by looking at its conceptual structure, where in the picture, the conceptual data on the development of journal writing based on existing keywords will be displayed. Fig. 13 will be displayed in the conceptual structure map. The term factorial map is in Fig. 14, the most contributed map is in Fig. 15, and the most cited map is in Fig. 16.

Fig. 13 Conceptual Structure Map

Fig. 13. Conceptual Structure Map

Fig. 14 Term Factorial Map

Fig. 14. Term Factorial Map

Fig. 15 Factorial Map of the Documents with the Highest Contribution

Fig. 15. Factorial Map of the Documents with the Highest Contribution

Fig. 16 Most Cited Map

Fig. 16. Most Cited Map

In the conceptual structure, we can see how it develops based on keywords so that new keywords are linked to keywords or journals cited to illustrate the development of scientific writing journals published as a thematic evolution. In this thematic evolution, we can see the timeline mapping of journal development by looking at the timeline, the thematic evolution network, and evolution data and keyword clusters in the development of journal writing.

In the conceptual structure of the co-occurrence structure unit, we can see the relationship between the use of existing keywords (Fig. 17); this will continue to increase the number of existing keywords and give rise to new keywords to fill existing gaps seen in the network (Fig.18).

Fig. 17 Co-occurrence Network

Fig. 17. Co-occurrence Network

Fig. 18 Word Dynamic

Fig. 18. Word Dynamic

It will be very interesting to look at the bibliography of journal writing about suspension from using these keywords; later, we will find out how the word coupling is used. We will be able to find developments about writing suspension journals and how the technology develops by looking at word coupling to see and determine existing and new gaps, or we will add gaps to gaps that have been created (Fig. 19).

Fig. 19 Thematic Evolution

Fig. 19. Thematic Evolution

In the intellectual structure menu of the co-citation network unit, we can see the relationship between citation collaborations based on existing authors (Fig. 20), including papers (Fig. 21) and sources (Fig. 22).

Fig. 20 Co-conceptual Structure - Author

Fig. 20. Co-conceptual Structure - Author

abdullah s .

Fig. 21 Co-conceptual Structure - Paper

Fig. 21. Co-conceptual Structure - Paper

Fig. 21 Co-conceptual Structure - Paper

Fig. 22 Co-conceptual Structure - Sources

In the collaboration network menu, we can see the network formed from collaboration in writing scientific journals. As we know, most scientific journal authors are academics or professionals. Therefore, this collaboration is a place for authors to conduct studies or work for agencies or companies to establish good collaborative relationships. Promote the development of scientific journal writing by the author's interest in scientific interests. This development occurs when there is a relationship between the author and other authors so that they become co-authors (Fig. 23), the author exchanges studies at other institutions (Fig. 24), or the writer is developing in another country so that a network can be formed that can be presented (Fig. 25). So that from the social structure, the exchange of ideas and knowledge can be obtained in the development of journal publication writing which is depicted by the world collaboration map (Fig. 26).

Fig. 23 Collaboration Network Author

Fig. 23. Collaboration Network Author

Fig. 24 Collaboration Network Institution

Fig. 24. Collaboration Network Institution

Fig. 25 Collaboration Network Country

Fig. 25. Collaboration Network Country

Fig. 26 Image of Country Collaboration Map

Fig. 26. Image of Country Collaboration Map

Discussion

The original version of this paper is available on https://www.scientific.net/EI.11.43.pdf

The critical importance of passenger comfort, particularly in family vehicles subjected to daily use, underscores the need for comprehensive examination. The suspension system is very important among the many factors that influence comfort. Therefore, this paper emphasizes the need for a comprehensive review of the existing knowledge base in the suspension domain. Despite the progress in suspension technology, a notable void persists due to the absence of prior research incorporating historical evolution and growth analysis using bibliometric techniques.

The paper introduces an innovative method, showcasing an intricate analysis encompassing keywords, citations, h-index, publication years, affiliations, and more. This analysis is based on the esteemed scopus.com database, processed and integrated into applications offered by bibliometric.org. The outcomes reveal the United States as a dominant force in suspension research,
closely trailed by India and Canada. The implications of this study extend to suspension technology developers, offering insight into competitors and emerging trends. As a result, this research enables decision-making, strategic planning, and innovation in suspension technology development.

Additionally, this research provides a global overview of contributions to anti-ballistic technology. Notably, China emerged as a significant contributor, surpassing the United States in several publications, raising questions about potential technological shifts. However, it will raise questions about China's rising prominence and potential future technological leadership. In conclusion, the paper underscores passenger comfort's relevance in vehicular travel, especially for family vehicles. The paper's bibliometric approach fills knowledge gaps, offering valuable insights to practitioners and researchers and facilitating strategic decisions and innovation. Additionally, the study's focus on anti-ballistics technology highlights China's presence, prompting considerations about future technological trajectories and shifts in global leadership.

Future Implications and Prospects

The original version of this paper is available on https://www.scientific.net/EI.11.43.pdf

Future developments in automotive technology are expected to be driven by efforts to achieve better passenger comfort in family passenger vehicles. In a contemporary period characterized by an increasing desire for an uninterrupted travel experience, the importance of suspension systems in facilitating such comfort has become increasingly clear. So, a thorough assessment of the current knowledge is required.

Nevertheless, despite the continuous advancements in suspension comfort technology, a notable study deficiency is attributed to the absence of historical perspectives offered by bibliometric analysis. Addressing this void can enhance our comprehension of the progression of suspension systems and stimulate novel perspectives and advancements. By utilizing novel approaches and bibliometric tools, forthcoming scholars can delve further into the historical progression of suspension systems, thereby uncovering intrinsic trends and patterns that influence their evolution.

The results of this analysis, which emphasize the prominent positions of the United States, India, and Canada, provide a basis for possible collaborations and the sharing of information across borders. The discovery above, in conjunction with China's involvement in anti-ballistics technology, raises thought-provoking questions on the dynamics of global technical supremacy. Subsequent investigations may explore the ramifications of these patterns on global alliances, the dissemination of technology, and cooperative enterprises.

This study establishes a foundation for a promising trajectory in vehicle technology research. The text urges researchers, industry executives, and legislators to actively involve themselves with historical viewpoints and utilize data-driven insights to design a transportation future that is both technologically sophisticated and provides enhanced comfort. This study reiterates the significance of passenger comfort and suspension systems while promoting a proactive mindset that embraces innovation, collaboration, and prospective changes in global technology environments.

Conclusion

The original version of this paper is available on https://www.scientific.net/EI.11.43.pdf

This study highlights the importance of prioritizing passenger comfort, particularly in family vehicles regularly subjected to extensive daily usage. The importance of the suspension system in ensuring passenger comfort underscores the need for a thorough examination of suspension-related information. Despite the significant progress made in suspension technology, a notable void exists in the literature pertaining to the historical examination of this field utilizing bibliometric methodologies. This research presents a novel methodology that utilizes the scopus.com database to analyze essential dimensions, which are afterward integrated into bibliometric.org tools.

The study's findings demonstrate the United States' prominent position in suspension research, with India and Canada following suit. India has emerged as a noteworthy participant in suspension technology development, providing valuable insights for developers by recognizing competitors and discerning emerging trends. This study provides valuable insights for decision-making, strategic planning, and fostering creativity. Furthermore, this research delves into the realm of anti-ballistics
technology, particularly emphasizing China's prominent position in this field. This investigation prompts inquiries regarding potential forthcoming technological transformations.

This study emphasizes the significance of suspension, explains the utilization of bibliometric analysis, and offers valuable insights for developers. It facilitates the cultivation of well-informed decision-making, strategic planning, and innovative thinking while concurrently prompting thoughtful reflection on technological trends and changes in global leadership. Using bibliometric analysis is a valuable instrument for prospective researchers to forecast trends and enhance suspension technology.

Funding Information: The authors state no funding involved.

Author Contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

Conflict of Interest: The authors state no conflict of interest.

Data Availability Statement: All data generated or analyzed during this study are included in this published article.

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The original version of this paper is available on https://www.scientific.net/EI.11.43.pdf

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G. Z. Yao, F. F. Yap, G. Chen, W. H. Li, and S. H. Yeo, "MR damper and its application for semi-active control of vehicle suspension system," Mechatronics, vol. 12, no. 7, pp. 963-973, Sep. 2002, doi: 10.1016/S0957-4158(01)00032-0.

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The original version of this eBook is available on https://www.scientific.net/book/engineering-innovations-vol-11/978-3-0364-1606-9

Engineering Innovations, ISSN: 2813-1002, Vol. 11, pp 63-68

doi: 10.4028/p-y9u7Me

© 2024 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2023-12-06

Revised:
2024-01-02

Accepted:
2024-01-03

Online:
2024-06-26

Muffler Design for Noise Reduction and Pressure Loss Optimization Using Multiobjective Genetic Algorithm

The original version of this paper is available on https://www.scientific.net/EI.11.63.pdf

Muhammad Yandi Pratama , Prihanto Trihutomo , and Suprayitno

Department of Mechanical and Industrial Engineering, Faculty of Engineering, Universitas Negeri Malang, Malang, Indonesia

muhammad.yandi.2205168@students.um.ac.id, prihanto.trihutomo.ft@um.ac.id, suprayitno@um.ac.id

Keywords: muffler design, optimization, noise reduction, pressure loss, multiobejctive genetic algorithm.

Abstract

The muffler plays a crucial role in reducing the noise generated by the internal combustion engine exhaust gases. Therefore, an effective muffler design should be capable of significantly reducing noise levels. However, we must also consider backpressure, which can negatively impact engine performance. Backpressure is the additional pressure exerted by the muffler towards the engine, and it can have adverse effects on engine performance, thus requiring minimization. These two objectives often conflict with each other. Hence, in this research, we utilize multiobjective genetic algorithms as a tool to optimize muffler design. Inspired by the natural selection process, genetic algorithms aim to find a muffler design that is not only effective in reducing noise but also produces minimal backpressure. Thus, this study aims to achieve a balance between noise reduction and backpressure minimization in muffler design. The multiobjective genetic algorithm proposes 105 muffler design solutions. These solutions are not dominated by each other against both TL and PL objectives. The design that has the best value in the TL objective is solution 1 with TL and PL values of 26.06 dBA and 2.27 kPa . The design that has the best value in the PL objective is solution 3 with TL and PL values of 8.36 dBA and 1.87 kPa . The muffler compromise design chosen was a solution 41 with TL and PL values of 17.78 dBA and 2.07 kPa .

Introduction

The original version of this paper is available on https://www.scientific.net/EI.11.63.pdf

Vehicle mufflers have a major role in dampening the noise generated by internal combustion engines[1]-[3]. Excessive noise can be annoying and needs to be reduced, because the adverse effects can be felt by the surrounding environment and human health, as well as cause discomfort[4], [5]. Therefore, an effective muffler design is one that is able to significantly reduce noise levels. However, in the muffler design process, we must also consider the back pressure. Back pressure is the additional pressure generated by the muffler that can negatively impact engine performance[6], [7]. This back pressure can reduce engine power and increase specific fuel consumption[8]. The challenge is that these two parameters, i.e. noise dampening and minimizing back pressure, often contradict each other. When muffler designs are optimized to suppress noise, the resulting backpressure tends to increase, and vice versa. In situations like this, where a good muffler design is needed for both aspects, namely reducing noise and minimizing back pressure, a multi-objective optimization approach is the right choice.

Until now, there have been many multi-objective optimization studies that use evolutionary algorithms, such as multiobjective genetic algorithm (MOGA), to obtain optimal muffler designs[8][14]. They used this method on different types of mufflers in various studies. The achievements of the study show that computational intelligence such as genetic algorithms are superior in terms of finding optimal designs. So that in this research researchers will also carry out the same goal where optimizing the design of a muffler by considering both objectives using the help of MOGA to achieve an optimal design both in reducing noise and minimizing back pressure. The result of this study is an optimal muffler design that excels at dampening noise and minimizing back pressure. By obtaining an optimal design for a muffler, it can help reduce noise pollution and produce a low reverse pressure muffler design, which in turn will improve engine performance and reduce specific fuel consumption.

Research Method

The original version of this paper is available on https://www.scientific.net/EI.11.63.pdf

The parameters of the noise reduction ability of a muffler consist of 3 indicators, namely transmission loss (TL), insertion loss (IL), and level difference (LD)[3]. Generally, TL and IL are often used in many studies. TL is the difference in sound power inside the inlet and the transmitted sound wave. IL is the difference in sound power at the same point by using and not using a muffler. For back pressure, the parameter used is pressure loss (PL). PL is the pressure difference at the muffler inlet and outlet. PL represents the backpressure produced due to an increase or decrease in PL in line with the backpressure[1], [10], [15].

In this study noise reduction parameters use TL and minimizing backpressure use PL. The TL value can be approximated using the following equation, refer Eq. 1 Sduct is the area of the inlet/outlet , is the area of the expansion space , is the length of the expansion space area is the number of waves, which can be calculated using Eq. 2, visual analyser software is used to measure the frequency of the muffler sound at idle engine speed [16].

Where,
TL = Transmission loss (dBA)
Sduct = Cross-sectional area of duct (m2)
Sexp = Cross-sectional expansion chamber (m2)
k = Number of waves in a distance
L = Expansion chamber length (m)
\lambda = Wavelength (m)
f = frequency (Hz)

Then, for PL it can be approached using the following equation, refer Eq. 4 and 5. Where, is PL (Pa), is exhaust gas density is the flow velocity is the inlet/outlet diameter (m), is the muffler diameter, and is the length of the muffler expansion section (m) [16].

The TL and PL equations above are used as an approach to evaluate the performance of the selected parameters, and are used as fit functions in the optimization process using a multiobjective genetic algorithm.

Optimization Formulation. In this study, the design objective is to maximize TL and minimize PL. The objective functions of TL and PL have been shown in Eq. 1 and 4. Then for design space consists of three design variable, namely inlet / outlet diameter ( ), muffler diameter ( ), muffler expansion section length . Description of design variables and their space are presented in Fig. 1 and Table 1.

Fig. 1 Design Variable

Fig. 1. Design Variable

Table 1 Desription of Design Variables & Spaces

Description | Code | Design Space
Diameter of inlet/outlet | x₁ | 30 mm ≤ x₁ ≤ 50 mm
Diameter of muffler | x₂ | 110 mm ≤ x₂ ≤ 190 mm
Length of expansion section | x₃ | 300 mm ≤ x₃ ≤ 420 mm

Result and Discussion

The original version of this paper is available on https://www.scientific.net/EI.11.63.pdf

Optimization Procedure. The optimization process uses widely used optimization market software. The first step is to create an objective function which is then stored as a fitness function to be called upon in the optimization process, objective function using Eq. 1 and 4. The second stage is to determine the population size of 300 and the initial population number of 150 , the number of generation 100, choose the mutation function adaptive feasible,choose the intermediate crossover function and choose plot functions pareto front, refer Fig. 2. After the optimization stage is set correctly, then finallys, the process runs.

Fig. 2 Optimization Procedure.

Fig. 2. Optimization Procedure.

Fig. 3 Pareto Front Solutions

Fig. 3. Pareto Front Solutions

Figure 3 above is a pareto front solutions chart. The result of optimization using a multiobjective approach is the production of optimal design solutions that are not dominated by each other on both objectives called non-dominated solutions. These solutions, if graphed against two objectives, will form a graph of pareto solutions. Green dots are optimal muffler design solutions totaling 105 design solutions, where the design solutions are not dominated by each other on TL and PL performance. While the red dot, the initial design of the muffler, is not included in the row of pareto front solutions, meaning that the initial design of the muffler is not an optimal design. After getting pareto front solutions that contain optimal muffler designs, the second stage in optimization is to choose one of the design solutions according to user references. The options according to user reference are presented in Table 2.

Table 2 Description of Geometrical Data and Performances

Configuration | x1 (mm) | x2 (mm) | x3 (mm) | TL (dBA) | PL (kPa)
Best TL pareto front (solution 1) | 30.00 | 190.00 | 345.34 | 26.06 | 2.27
Best PL pareto front (solution 3) | 48.85 | 110.52 | 418.89 | 8.36 | 1.87
Initial design | 40 | 140 | 390 | 15.63 | 2.12
Best TL (sol. 90) | 30.58 | 134.01 | 416.67 | 19.24 | 2.11
Best PL (sol. 99) | 30.92 | 110.21 | 418.51 | 15.70 | 2.00
Compromise (sol. 41) | 30.26 | 121.84 | 418.25 | 17.78 | 2.07

From Table 2, it can be seen carefully that the TL and PL values of the initial design are surpassed by other designs. Solution 1 is a muffler design solution when referring to user references who have the highest TL muffler desire which means the best in noise reduction. While solution 3 is a muffler design solution when referring to user referrals who have the desire for a muffler with the lowest PL which means the best in minimizing back pressure. Solution 90 is the best muffler design solution in TL and slightly better in PL when compared to the initial design. Solution 99 is the best muffler design solution in PL and slightly better in TL than the initial design. The last is solution 41 as a compromise solution, where this solution is a muffler design solution that has a position in the middle if we look at the graph of pareto solutions, refer Fig. 3, the value of TL and PL in the compromise solution still has a better value than the initial design, so users can also choose this design as a muffler design solution that is good in TL and PL parameters.

Conclusions

The original version of this paper is available on https://www.scientific.net/EI.11.63.pdf

Multiobjective genetic algorithms produce a set of solutions. The best muffler design solutions in terms of TL and PL that are not dominated by each other. Users can correctly select each muffler design solution at pareto solutions, and will not find the design is not optimal. MOGA can help in solving optimization cases where the desired performance parameters are found to conflict with each other like this simple muffler case. The multiobjective genetic algorithm proposes 105 muffler design solutions. These solutions are not dominated by each other against both TL and PL objectives. The design that has the best value in the TL objective is solution 1 with TL and PL values of 26.06 dBA and 2.27 kPa . The design that has the best value in the PL objective is solution 3 with TL and PL values of 8.36 dBA and 1.87 kPa . The muffler compromise design chosen was a solution 41 with TL and PL values of 17.78 dBA and 2.07 kPa .

Acknowledgment

The original version of this paper is available on https://www.scientific.net/EI.11.63.pdf

This work was supported by the PNBP UM 2023 under Grant No. 5.4.878/UN32.20.1/LT/2023

References

The original version of this paper is available on https://www.scientific.net/EI.11.63.pdf

M. A. Habib, A. U. Patwari, A. S. Anwar, S. Shadman, and O. H. Abir, "3D CFD Based Optimization Technique for Muffler Design of a Motorcycle," Appl. Mech. Mater., vol. 860, pp. 52-57, 2017, doi: 10.4028/www.scientific.net/AMM.860.52.

R. Li, Y. Zhou, Y. Xue, and S. Han, "Local Structural Optimization Method Based on Orthogonal Analysis for a Resistant Muffler," IEEE Access, vol. 9, pp. 40560-40569, 2021, doi: 10.1109/ACCESS.2021.3063768.

J. K. Lee, K. S. Oh, and J. W. Lee, "Methods for evaluating in-duct noise attenuation performance in a muffler design problem," J. Sound Vib., vol. 464, p. 114982, 2020, doi: 10.1016/j.jsv.2019.114982.

A. Jahanbakhshi, M. Yousefi, S. Karami-Boozhani, K. Heidarbeigi, and Y. AbbaspourGilandeh, "The effect of combined resistance muffler on noise pollution and the allowable driver exposure in Massey-Ferguson tractors (MF 285 and MF 299)," J. Saudi Soc. Agric. Sci., vol. 19, no. 6, pp. 409-414, 2020, doi: 10.1016/j.jssas.2020.06.002.

M. Mohammadi and S. E. Razavi, "Investigation of the Efficiency of Various Reactive Mufflers by Noise Reduction and Transmission Loss Analyses," J. Theor. Appl. Vib. Acoust., vol. 4, no. 2, pp. 1-8, 2018.

A. Kashikar, R. Suryawanshi, N. Sonone, R. Thorat, and S. Savant, "Development of muffler design and its validation," Appl. Acoust., vol. 180, p. 108132, 2021, doi: 10.1016/j.apacoust.2021.108132.

S. Thirumurugaveerakumar, "Design and optimization of muffler back pressure," AIP Conf. Proc., vol. 2270, no. November, 2020, doi: 10.1063/5.0019700.

D. Siano, F. Bozza, and F. Auriemma, "Acoustic and fluid-dynamic optimization of an automotive muffler," Proc. Inst. Mech. Eng. Part D J. Automob. Eng., vol. 227, no. 5, pp. 735747, 2013, doi: 10.1177/0954407012465689.

Y. C. Chang, M. C. Chiu, and M. R. Wu, "Acoustical assessment of automotive mufflers using FEM, neural networks, and a genetic algorithm," Arch. Acoust., vol. 43, no. 3, pp. 517-529, 2018, doi: 10.24425/123923.

S. Chao and H. Liang, "Comparison of various algorithms for improving acoustic attenuation performance and flow characteristic of reactive mufflers," Appl. Acoust., vol. 116, pp. 291296, 2017, doi: 10.1016/j.apacoust.2016.09.034.

M. C. Chiu, "Genetic algorithm optimization on a venting system with three-chamber hybrid mufflers within a constrained back pressure and space," J. Vib. Acoust. Trans. ASME, vol. 134, no. 2, pp. 1-11, 2012, doi: 10.1115/1.4005220.

S. Zuo, K. Wei, and X. Wu, "Multi-objective optimization of a multi-chamber perforated muffler using an approximate model and genetic algorithm," Int. J. Acoust. Vib., vol. 21, no. 2, pp. 152-163, 2016, doi: 10.20855/ijav.2016.21.2405.

C. Lu, W. Chen, Z. Liu, S. Du, and Y. Zhu, "Pilot study on compact wideband micro-perforated muffler with a serial-parallel coupling mode," Appl. Acoust., vol. 148, pp. 141-150, 2019, doi: 10.1016/j.apacoust.2018.12.001.

Y. C. Chang, M. C. Chiu, and S. E. Huang, "Numerical analysis of circular straight mufflers equipped with three chambers at high-order-modes," Appl. Acoust., vol. 155, pp. 167-179, 2019, doi: 10.1016/j.apacoust.2019.05.021.

A. Elsayed, C. Bastien, S. Jones, J. Christensen, H. Medina, and H. Kassem, "Investigation of baffle configuration effect on the performance of exhaust mufflers," Case Stud. Therm. Eng., vol. 10, pp. 86-94, 2017, doi: 10.1016/j.csite.2017.03.006.

D. A. Bies, C. H. Hansen, and C. Q. Howard, Engineering Noise Control, Fifth edit. CRC Press Taylor & Francis Group, 2018. [Online]. Available: AfS6MTgAQ&redir_esc onepage& loss factor for materials table&f=false%5Cnhttp://books.google.com.sg/books?id=LU8U3mka-DUC&pg=PA665&

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Engineering Innovations, ISSN: 2813-1002, Vol. 11, pp 69-74

doi: 10.4028/p-tVV8PQ

© 2024 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2023-12-05

Revised:
2024-01-04

Accepted:
2024-01-07

Online:
2024-06-26

Development of Savonius Rotor Based on Bezier Curve for Vertical Axis Marine Current Turbine at Sunda Strait, Hindia Ocean

The original version of this paper is available on https://www.scientific.net/EI.11.69.pdf

Dedy Triawan Suprayogi , Hadi Wahyudi , Alwan Habibie , Muhammad Adjie , Faqih Atard Rahman

Departement of Mechanical Engineering, Faculty of Engineering, Universitas Sultan Ageng Tirtayasa, Indonesia

dedy.ts@untirta.ac.id, hadi@untirta.ac.id, habibiealwann@gmail.com, m.adjie.barakaat@gmail.com, faqihatard@gmail.com

Keywords: Savonius rotor, bezier curve, double stacking.

Abstract

Due to its strategic location and ocean currents, the Sunda Strait has the potential to produce energy that might be used as a source of electricity. As a result, this strait area urgently needs a suitable turbine design. This strait's most significant sea current speed is 1 (one) . The Savonius rotor is one of the rotor kinds of turbines that can operate in the slow sea current-modifying the rotor from semi-circular to use the Bezier curve for the shape to optimize the performance. This paper will discuss the design of the Savonius rotor using the Bezier curve, that have improved performance. The rotor with double stacking will also enhance the performance of the rotor. This design is a novelty for vertical marine current turbine applications in ocean renewable energy.

Introduction

The original version of this paper is available on https://www.scientific.net/EI.11.69.pdf

With 17,805 islands and an estimated size of more than 5.4 million km 2 , Indonesia is an archipelagic nation with the second-longest coastline in the world, behind Canada, with a total length of . Naturally, given these circumstances, Indonesia is the nation with the largest potential for marine energy in the entire world.

Ocean energy is a source of power that is created using a variety of oceanic natural processes and methods and technologies that are constantly evolving. Because there are no CO 2 emissions produced during the process of producing marine energy, it is a particularly eco-friendly and green energy source. Theoretically, the ocean has about 1.8 TW of energy, so given that the oceans cover of the earth's surface, it becomes a significant enough source of energy. As a result, Indonesia has the biggest area of ocean, making it a country with a lot of marine energy.

Ocean currents known as tidal currents develop from tide movements brought on by the sun's and moon's gravitational pull. Ocean currents created by this movement have kinetic energy that can be utilised to turn the turbine's rotor. The generator is then linked to the turbine to allow it to produce power. This turbine can be built in a variety of locations and will be in the ocean.

Indonesia has a total potential of 61 GW , which includes tidal currents of 18 GW , sea waves of 2 GW , and OTEC of 41 GW , according to research findings from the Marine Geology Research and Development Center - Pusat Penelitian dan Pengembangan Geologi Kelautan (P3GL). The best opportunity to use these three energy sources is through ocean currents. This results from its predictable behavior, straightforward mechanical design, and offshore location, which insulates it from societal or population-related issues.

The energy of these tidal currents has been the subject of numerous studies on tides that have been carried out by various researchers. According to Orhan et al. (2016), the energy potential of the system at a present speed of is illustrated in Table 1 below. According to this table, the Alas Strait has 2.258 GW of electricity, whereas the Sunda Strait has 335 MW [1].

Introducing turbines in the Sunda Strait region will undoubtedly serve as a model for their use in other Indonesian straits. The Sunda Strait has the potential to concentrate on becoming a Vertical Axis Marine Current Turbine research pilot project because it is close to research facilities from the National Research and Innovation Agency - Badan Riset dan Inovasi Nasional (BRIN) or universities
in Indonesia, as well as, of course, close to the center of government. The tide simulation for the Sunda Strait is depicted in Figure 1. According to this number, the marine currents' speed ranged from 0.4 to , indicating a low marine current situation [2].

Table 1. Tidal current energy map in the waters surrounding Indonesian territory [1]

Strait | Density Energy | Power Plant Energy | Total Energy
Bali | 14.75 | 1,459 | 1,045
Larantuka | 10.20 | 1,25 | 299
Boling | 3.49 | 430 | 736
Alas | 3.07 | 396 | 2,258
Lombok | 2.36 | 236 | 865
Sunda | 1.56 | 165 | 335
Badung | 1.52 | 161 | 551

Fig. 1. Simulation Tidal current speed at Sunda Strait

Fig. 1. Simulation Tidal current speed at Sunda Strait

Currently, the high potentioal to develope is Vertical Axis Marine Current Turbine (VAMCT). Suprayogi et al (2023) also briefly describes and classifies some of the most common VAMCTs being currently developed [3]. The type of VAMCT can run in low marine current is Savonius Turbine. This turbine have the rotor with Savonius type as wind energy power.

Savonius Turbine. The rotor of a Savonius turbine is rotated using the drag force principle. This particular model of wind turbine is quite well-known. This turbine was created in 1929 by S.J. Savonius, a Finnish engineer. It is a wind turbine powered by drag forces, and its two paddles are fixed in opposition to one another to its central shaft. By catching the wind and turning the shaft, each paddle propels the opposite paddle into the current. The shaft continues to rotate and completes a full rotation as this paddle then repeats the operation. The spinning shaft is used to drive a pump or a small generator throughout this operation, which continues as the wind blows. Despite the fact that typical maximum power coefficient values for other types of wind turbines range between and . The majority of researchers assert that the Savonius turbines are normally no greater than 25% [4].

Several types of Savonius rotors in the turbine have also been developed. First, the rotor used in the Pelton turbine or impulse turbine (not considering overlap ratio) and second, the type of Savonius with considering overlap ratio. The impulse turbine with Savonius rotor is quite interesting to develop; this rotor needs the inlet casing to increase the flow to be increased. Figure 2 shows the impulse turbine with the Savonius rotor. This type of turbine needs a casing to be suitable for the rivers (one direction) but is not appropriate for sea applications with many flow directions.

Fig. 2. The geometry of (a) turbine, (b) Savonius rotor, (c) casing [5]

Fig. 2. The geometry of (a) turbine, (b) Savonius rotor, (c) casing [5]

Other type of the rotor, the Savonius with considering the overlap ratio, aspect ratio and also no need the casing. The ratio aspect of the rotor's height (H) to diameter (D) is a crucial factor in determining a Savonius rotor's aerodynamic performance. A high aspect ratio ( ) number should significantly increase this effectiveness. For a typical Savonius rotor, coefficients of power about 4 tend to produce the greatest results [6]. Savonius rotor with single stacking is shown in Figure 3.

where:
Aspect ratio
= Height of rotor
D = Diameter of rotor

Fig. 3. Scheme of a single stacking Savonius rotor. (a) Front view; (b) Top view (conventional Savonius rotor : ) [6]

Fig. 3. Scheme of a single stacking Savonius rotor. (a) Front view; (b) Top view (conventional Savonius rotor : ) [6]

Another parameter is overlap ratio , which affects the overlap (e) and diameter of the paddle (d). Overlap ratio ( ) is given by the following equation:

Where:
= Overlap ratio
= Overlap between the paddle
Diameter of paddle
The best efficiencies were obtained for values of overlap ratio between 0.20 and 0.30 [6]. Gupta [7] reported the maximum power coefficient in the overlap ratio of . In the previous design, the Savonius rotor use semi-circular that show in Figure 4.

Fig. 4. Savonius rotor previous design

Fig. 4. Savonius rotor previous design

Discussion

The original version of this paper is available on https://www.scientific.net/EI.11.69.pdf

The discussion will describe about the Bezier curve and also stacking rotor for Savonius turbine. Bezier curve is new trens shape of Savonius rotor that previously is used for wind energy application. This is will a novelty if use for Savonius rotor of marine current application (water) that have different with wind energy (air). The stacking of rotor also will be discussed to get improvement performance.

Bezier Curve. Future work could include developing a 3D Discrete Vortex Method solver, modeling airfoils using different curve methods like splines or Bezier curves, defining a boundary for airfoil coordinates optimization, using CFD as a solver to determine the power coefficient of a new wind turbine, and conducting experimental research on the ideal Savonius airfoil, among other things [8]. The blades are separated into two halves, and a novel technique for creating blade shapes is suggested in this paper [9]. Each blade is optimized independently using the six-control point method and a Bezier curve.

Savonius rotors are a type of vertical axis wind turbine that utilize drag forces to generate torque. Many studies have explored ways to improve the performance of these rotors. Putranto et al found that modifying the Savonius rotor to have an elliptic shape increased its static torque coefficient at low wind speeds [10]. Yoshida et al also found that modifying the Savonius rotor's blade shape, specifically giving it an elliptical curvature, improved its power coefficient [11].

Díaz et al computationally analyzed five different Savonius rotor designs and found the helical rotor to have the best power and torque coefficients, outperforming the traditional rotor by [12]. Alit et al studied a multi-level Savonius rotor and found that its performance decreased as the angle between rotor levels increased. At an angle of , the rotor reached a maximum rotation speed of 150.6 rpm at a wind speed of [13].

The modification of savonius rotor to improve the performance by use the Bezier curve. This application of this design for marine current vertical axis marine current turbine is a novelty that marine current is a regular phenomena of the sea. As well known that sea water have higher density compare with fresh water and air (wind turbine application).

Stacking of Savonius Rotor. Comparison between stacking of Savonius rotor also done by Suprayogi 2010 [14]. The reseach showed that the double stacking can generate higher average torque than single stacking. Beside that Nakajima (2008) showed that a "double-step" Savonius rotor with a more complex blade shape produced higher power coefficient than a standard rotor [15]. Saha (2008) found that two- and three-stage rotors produced higher power output than single-stage rotors [16].

As above discussion, Bezier Curve is the method to make curve tahat can apply for Savonius rotor. The previous rotor of Savonius is semicircular that change using Bezier Curve. This curve can improve the performace of the Savonius rotor due to considering airfoil shape and also torque value
higher that semi circular shape. The Bezier curve will have longer distance between the center of rotor and highest point of shape compare with semicircular shape. Thus, the torque will higher compare with semicircular shape.

Based on above discussion the Savonius rotor with two stacking will have higher performance that singgle stacking. With use the the Bezier curve on the paddle this will make improvement of the performance. Figure 5 show the Savonius rotor use Bezier curve on the paddle and two stacking to get improvement of the rotor for vertical marine current turbine.

Fig. 5. Savonius rotor using Bezier curve with double stacking

Fig. 5. Savonius rotor using Bezier curve with double stacking

Summary

The original version of this paper is available on https://www.scientific.net/EI.11.69.pdf

As discussion above the Savonius rotor using Bezier curve and have double stacking have improvement performance compare with semi circular and single stacking. This rotor also can be used for marine current application that this is a new development for ocean renewable energy. In summary, optimizing the Savonius rotor through experimentation and computation has led to major performance improvements.

Acknowledgement

The original version of this paper is available on https://www.scientific.net/EI.11.69.pdf

We would like to express our gratitude to the Engineering Faculty of Universitas Sultan Ageng Tirtayasa, Indonesia that supported this study by Institutional Grant - Research of Senior Lecturer Grant 2024

References

The original version of this paper is available on https://www.scientific.net/EI.11.69.pdf

Orhan, K., Mayerle, R., Narayanan, R., & Pandoe, W., Investigation of the energy potential from tidal stream currents in Indonesia, 2016.

Orhan, K., Mayerle, R., Mayer, B. About the Influence of Density-Induced Flow on Tidal Stream Power Generation in the Sunda Strait, Indonesia. 2019.

DT Suprayogi, A Sudrajad, MP Pinem, Y Yusuf, Development of Vertical Axis Marine Current Turbine for Sunda Strait Application, Trends in Mechanical Engineering Research (TiMER), 2023.

Islam, M, et al. Aerodynamic models for Darrieus-type straight-bladed vertical axis wind turbines. Renewable and Sustainable Energy Reviews. 2008. Vol (12): pp 1087-1109.

Sasongko, Herman, et al. "Numerical Approach of The Blade Shape and Number on The Performance of Multiple Blade Closed Type Impulse Wind Turbine." International Journal of Mechanical Engineering Technologies and Applications, 2023, 4.2: 220-235.

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The original version of this eBook is available on https://www.scientific.net/book/engineering-innovations-vol-11/978-3-0364-1606-9

Engineering Innovations, ISSN: 2813-1002, Vol. 11, pp 75-82

doi: 10.4028/p-SfjZn0

© 2024 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2024-01-04

Revised:
2024-01-07

Accepted:
2024-01-08

Online:
2024-06-26

The Effect of Deflector Angle on the Performance of Turbine Combination Darrieus-Savonius

The original version of this paper is available on https://www.scientific.net/EI.11.75.pdf

Irfin Rizki , Satworo Adiwidodo , Eko Yudiyanto , Bagus Wahyudi , Fauzan Baananto

State Polytechnic of Malang, Indonesia

irfinrizki9@gmail.com, satworo.adiwidodo@polinema.ac.id, eko.yudiyanto@polinema.ac.id,

Keywords: vertical axis turbine, Darrieus-Savonius combination, deflector, pitch angle, CFD simulation.

Abstract

The Savonius and Darrieus are vertical-axis wind turbines. This turbine has resistance on one side of the blade that makes it difficult for the shaft to rotate resulting in reduced efficiency. However, the vertical shaft turbine type provides the advantage of being able to accept wind speeds from any direction without an additional tail. Savonius and Darrieus turbines show different characteristics in terms of their performances. Savonius turbine has a high power coefficient (CP) in the range of low tip speed ratio (TSR), when its TSR increases the CP will fall. In contrast to Darrieus, high CP is achieved if the TSR is also high but the CP achievement will fall at a low TSR. If it is compared to Savonius, Darrieus has higher power efficiency although it is difficult to self-start. In contrast to Savonius, Darrieus has a better self-starting ability but a lower efficiency. This study aims to improve the performance of vertical shaft wind turbines by creating a new design combination of Darrieus and Savonius turbines with deflectors to produce CP achievement on a wide TSR. The combination of the Darrieus-Savonius turbine is to improve efficiency to make self-start easier. The research method uses numerical simulation by employing CFD Ansys software. On the airfoil with a deflector angle of 70 deg, it shows that there is an increase in speed in several parts of the Darrieus blade airfoil. The increase in speed causes the decrease of static pressure in the area. The pressure difference between the sides of the airfoil surface causes a force. The direction of the force causes the turbine shaft to rotate. The deflector acts as a directional headwind, increasing the local flow velocity to counter the resistance on one side of the rotor blades The average torque produced at an angle of 70 deg is 0.5 Nm . Whereas, at an angle of 90 deg , the average torque generated is lower by around 0.15 Nm .

Introduction

The original version of this paper is available on https://www.scientific.net/EI.11.75.pdf

In a country's economic development, electricity plays a critical function as an energy system. Particularly at this time, new issues and dimensions that mankind is confronting due to population increase and aspects of daily life that must be addressed through an ever-increasing supply of power are arising. As the welfare of the population increases, various attempts are being made to provide electricity in isolated villages because there is a great need for it in both urban and rural areas [1,2,3]. One of the VAWTs that is most frequently employed in rural regions is the Savonius turbine. The Savonius turbine's simplicity of construction is a benefit, but it has low efficiency because of poor aerodynamics [4,5].
The problems that occur in the vertical axis wind turbine (VAWT) performance are less efficient than the horizontal axis wind turbine, even though this type of turbine has the advantage of being able to receive fluid flow from all directions. The wind received by the vertical axis turbine (VAWT) is divided into two parts, namely on the left and right sides of the axis (shaft), so that the flow leading to the left side will rotate the rotor to drive the blade, while the flow leading to the right side will be opposite to the blade movement and become an obstacle to the turbine rotation movement. As a result, the researchers previously pioneered ways to counteract negative torque, such as by inserting deflector plates on the vertical shafts of turbines [6,7,8]. Compare the startup torque values of

Savonius rotors in the center with traditional H-Darrieus rotors on either side of the hybrid VAWTS. The findings demonstrate that hybrid turbines may start up at any azimuth angle and that the Reynolds number exceeds that of H-Darrieus. Several simulation studies to obtain results close to experiments have been carried out . The simulation demonstrates that the deflector can modify the direction of flow towards the concave side of Savonius and impede the flow towards the opposite side . The deflector can generate a region of low pressure on the upstream (convex) surface of the blade, resulting in a decrease in blade resistance. The dual action mechanism demonstrates exceptional performance in generating maximum torque [15]. Throughout its development, the Vertical Axis Wind Turbine (VAWT) has undergone modifications aimed at enhancing its power efficiency. One of them is the Savonius turbine, the many modifications made to connect the two ends of the cylindrical blades in reverse pairs to resemble the letter s perfectly [16,17]. In Savonious turbines without overlap or gap, this does not produce optimal coupling force pairs and can even cause a wider Vortex field in the concave part of the thrust Blade. The incorporation of tandem blades results in the creation of a constricted compartment that resembles a nozzle. This compartment facilitates the reversal of fluid flow direction and enhances the pressure differential required for blade propulsion [18]. The principle of cross-flow in the Savonius turbine can be developed by adding its corners to be double layered or called tandem blades. The incorporation of tandem blades results in the creation of a constricted compartment that resembles a nozzle. This compartment facilitates the reversal of fluid flow direction and enhances the pressure differential required for blade propulsion [18]. Sasongko [19] conducted research on impulse turbine blades by comparing blades with entry and exit angles of 90 degrees and 180 degrees, where it was found that the 180 angle produced a greater moment. Another type of vertical axis turbine that is often used is the Darrieus turbine. Compared to Savonius, Darrieus has higher power efficiency, but it is difficult to self-start, in contrast to Savonius, which has better self-starting ability but lower efficiency. The number of turbine blades has a significant impact on the self-starting wind speed. The impact of the pitch angle on the selfstarting speed of wind is contingent upon the number of blades [20]. The enhancement in Savonius rotor performance is attributed to the presence of a passive deflector. The passive deflector exhibits a consequential impact on enhancing the performance of the Savonius rotor. The implementation of passive deflectors resulted in a enhancement in rotor performance. Stable alignment can be adaptively achieved using passive deflectors in response to the wind direction. The enhancement of Savonius rotor performance can be achieved through the utilization of passive deflectors, which serve to mitigate the adverse torque exerted on the blades during their return phase. The presence of unstable aerodynamic forces results in a minor deviation in pitch angle between the stable position and the initial position of the passive deflector [21].

Material and Method

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A 2D simulation of a Savonius-Darrieus combination turbine with a deflector was conducted using Ansys CFD. The selection of the computational domain size was made to ensure that it did not exert any influence on the final results. The computational domain for the simulation test of the SavoniusDarrieus combination turbine rotor with a deflector consists of two distinct regions: the stationary zone, characterized by a rectangular shape, and the rotary region, which is determined by the wind turbine and spans multiple diameters of the turbine.
The inclusion of a well-organized grid is a crucial aspect in the evaluation of models, as it serves to prevent issues such as non-convergence or instability, ultimately leading to the attainment of more precise simulation outcomes. The present portion commences by constructing a simulated environment in the shape of a mesh. In the process of wind turbine design, it is necessary to ensure that the arithmetic field is sufficiently large to prevent any interference from the field wall with the flow region, as depicted in Figure 3. Additionally, the size of the system should be such that computational resources are utilized optimally. The fundamental objective of ANSYS meshing technology simulation is to generate a mesh that is well-suited for comprehending the solution employed in the project, as it adheres to the requisite criteria. To construct an optimal network, the
attainment of precise flow modeling necessitates the utilization of a mesh that exhibits superior quality in terms of boundary layers and vortices.
Development and design of the Savonius-Darrieus turbine rotor with deflector is done using CAD Inventor software. Rotor Diameter rotor Diameter D=300 mm and blade height H=500 mm. The thickness of the Savonius turbine blades is , and the deflector plates are modeled as winddirection reversing plates with a thickness of 0.5 mm each. Fig. 1 and Fig. 2 apply the wind speed is for each case, while the pressure at the outlet of the domain is equivalent to atmospheric pressure.

Fig. 1 Savonius-Darrieus combinatorial turbine computing domain with deflector angle

Fig. 1. Savonius-Darrieus combinatorial turbine computing domain with deflector angle

Fig. 2 Savonius-Darrieus combinatorial turbine computing domain with deflector angle

Fig. 2. Savonius-Darrieus combinatorial turbine computing domain with deflector angle

Fig. 3 Meshing of modeling

Fig. 3. Meshing of modeling

The following boundary conditions have been used by the simulation program ANSYS. The stationary domain is moving freely. As beginning circumstances, hydrodynamic pressure conditions are used. The default boundary conditions in simulation software are Inlet and Outlet. Initial conditions call for a relative pressure on an outlet of with an inlet velocity of . The turbine blade surface is regarded as a wall condition. Calculations of characteristics like surface force are possible under this circumstance.
The mesh report provides information on element 320666. The solver used in this study is pressurebased, transient, and two-dimensional. The viscous model employed in this study is the standard kepsilon model. The material under consideration is air. Boundary conditions refer to the set of conditions that are imposed on a system or problem at its boundaries. The velocity magnitude at the inlet is , whereas the gauge pressure at the outlet is 0 Pascal. The wall remains stationary wall. The absence of slip characterizes the shear condition. The operating conditions are set at atmospheric pressure, specifically 1.0132 bar. The solution controls for pressure-velocity coupling set coupled with spatial discretization of fluids.

Result and Discussion

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The pressure contour produced by the Savonius-Darrieus combination turbine with a deflector is depicted in Fig. 4. The flow velocity was , and the deflector angle was 70 degrees. As a result, the airfoil responsible for capturing flow energy experiences an increase in pressure, and it seems that the deflector can change the flow direction to the side of the Savonius turbine to increase local velocity and decrease negative torque. Outstanding double effect for maximum torque.

Fig. 4 Pressure contour of the savonius-darrieus combination turbine with deflector, , .

Fig. 4. Pressure contour of the savonius-darrieus combination turbine with deflector, , .

The pressure contour at the flow speed is , and the deflector angle is 90 degrees produced by the Savonius-Darrieus combination turbine with deflector as shown in Fig. 5. The Savonius turbine can't rotate as efficiently as it should since the airfoil responsible for absorbing the flow energy looks to receive additional pressure, and it appears that the deflector can change the flow's direction so that it doesn't directly hit the turbine's side.

Fig. 5 Pressure contour of the Savonius-Darrieus combination turbine with deflector, ,

Fig. 5. Pressure contour of the Savonius-Darrieus combination turbine with deflector, ,

The simulation results are displayed as contour velocity in Fig. 6. The Darrieus airfoil has several areas on the blade where the speed increases. Simulation of Savonius-Darrieus combination turbine with deflector simulation shows that deflector can change the direction of flow towards the concave side of Savonius and block the flow to the other side. The static pressure in the area decreases as speed increases. The airfoil surface pressure differential generates a force (F), the direction of which drives the spinning of the turbine shaft. To overcome the resistance of one side of the blade, the deflector changes the wind's direction and raises the local flow velocity. A decrease in static pressure results from an increase in the local flow velocity as shown on the Blade Darrius's back. The Darrieus turbine blades experience a suction effect as a result of the pressure drop, which aids in the blades' rotation and continues to the turbine shaft.

Fig. 6 Velocity contour of the savonius-darrieus combination turbine with deflector, .

Fig. 6. Velocity contour of the savonius-darrieus combination turbine with deflector, .

Fig. 7 shows the simulation results in the form of the contour velocity of the Savonius-Darrieus combination turbine with a deflector at the flow speed is , and a deflector angle is 90 degrees. The Savonius turbine cannot rotate as efficiently as a 70 degree deflector because the airfoil which is responsible for absorbing the flow energy appears to be under additional pressure. To prevent the flow from immediately striking the side of the turbine, the deflector alters the flow directionless.

Fig. 7 Velocity contour of the Savonius-Darrieus combination turbine with deflector, ,

Fig. 7. Velocity contour of the Savonius-Darrieus combination turbine with deflector, ,

The correlation between flow time and torque is depicted in Fig. 8 and Fig. 9. The angle in the image is 70 degrees, and the max torque is almost 0.5 Nm . When the object is positioned at a 90 -degree angle, the generated torque falls by a max of 0.15 Nm .

Fig. 8 Torque with deflector

Fig. 8. Torque with deflector

The decrease in torque observed in a combined turbine with a deflector angle of 90 degrees, as opposed to a deflector angle of 70 degrees, can be attributed to the higher pressure difference between the bottom and upper surfaces of the Darrius blade in the 70 -degree deflector configuration. The pressure gradient generates a substantial change in force, resulting in a higher torque.

Fig. 9 Torque with deflector

Fig. 9. Torque with deflector

The reduction in torque at a 90 -degree angle is also attributed to the ineffective positioning of the deflector plate, which fails to properly guide the wind flow to strike the Savonius blade at the desired angle. The Savonius turbine's contribution of torque is minimal and may even decrease due to the drag it generates. In general, this leads to impaired rotation of the tube shaft and a reduction in torque.

Conclusion

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It may be inferred that an angle of 70 degrees has the potential to induce a wind direction reversal and enhance the local flow velocity to counteract resistance on one side of the blade thus producing high torque. At a bigger deflector angle in this case 90 degrees, the flow on the deflector is not aligned directly behind the Savonius turbine which can reduce torque.

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The original version of this paper is available on https://www.scientific.net/EI.11.75.pdf

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S. Adiwidodo, B. Wahyudi, E. Yudiyanto, Subagiyo, M. Hartono, and F. Baananto, Simulation study of Savonius tandem blade wind turbine using an adjustable deflector, In IOP Conference Series: Materials Science and Engineering, IOP Publishing Vol. 732 (2020), No. 1, 8(2) p. 012093.

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The original version of this eBook is available on https://www.scientific.net/book/engineering-innovations-vol-11/978-3-0364-1606-9

Engineering Innovations, ISSN: 2813-1002, Vol. 11, pp 83-98

doi: 10.4028/p-i6uNLi

© 2024 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2024-01-14

Revised:
2024-03-24

Accepted:
2024-03-25

Online:
2024-06-26

Minimizing Conditional Mean Tardiness and Mean Earliness on a Single Machine with the Due Windows Approach

The original version of this paper is available on https://www.scientific.net/EI.11.83.pdf

Saheed Akande , Ganiyu, O Ajisegiri , Temitayo, M. Azeez ,

Department of Mechanical and Mechatronics Engineering, Afe Babalola University, Ado-Ekiti, Nigeria

Department of Industrial and Production Engineering, University of Ibadan, Nigeria

sakande1@abuad.edu.ng, ajisegiriganiyu@gmail.com, Azeeztemitayo221@abuad.edu.ng

Keywords: Conditional Mean Tardiness, Conditional Mean Earliness, Ideal Just-In-Time, Schedule, Due Window, Benchmarking

Abstract

A Multicriteria scheduling problem that involves four due date-based performance measures; the total tardiness, proportion of tardy jobs, total earliness as well as the proportion of early jobs was reduced to an equivalent bicriteria problem of minimizing conditional mean Tardiness and conditional mean earliness. A schedule that optimizes these measures tend towards an ideal Just-InTime (JIT) schedule. Two solution methods named GOA 1 and GOA 2 were proposed to solve the equivalent reduced problem. A single machine and due window approach was explored. The ideal JIT schedule with zero tardiness and zero earliness was set as the optimal and used for benchmarking the proposed solution as well as other methods found in the literature. The results show that the proposed heuristics yielded results that are not significantly different from the optimal in some instances.

Introduction

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The Just-In-Time (JIT) scheduling problems have two major application areas: Production and computer science. The production system is considered in this work. The problem application is related to the due date-based types of scheduling problems [1]. Just-in-time is a Production Planning and Control (PPC) philosophy that seeks zero waste and zero inventories [2]. Completing a task before or after the due date incurs additional cost, which is a waste of resources in JIT philosophy. Therefore, in JIT system, it is desirable to complete a task within its due date windows. The advantages of achieving JIT schedule include minimization of complexity associated with detailed material planning, ease of control of shop-floor activities, and minimization of inventory cost among others [3]. However, JIT schedule is an ideal schedule [4], and involves a balance between two opposing due date performance measures; tardiness and the earliness based. To achieve JIT, both the earliness and the tardiness parameters must be zero. This is almost impossible or requires a prohibitive computation time and there is always an associated deviation. To minimize this deviation, total tardiness, the proportion of tardy jobs, total earliness as well as the proportion of early jobs must be minimized simultaneously. However, aggregation of these four performance measures will yield a multicriteria scheduling problem which mostly is NP-hard [5]. However, Akande et al., [6] stated that the complexity of scheduling problems grows as the number of objectives increases. Thus, to minimize the complexity associated with solving the four performance measures of interest, the problem is reduced to a Bicriteria scheduling problem using methodology of (Akande et al., [7]) .

Notation Used

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Table 1 is the list of notations used in this work

Reducibility of the Multicriteria Problem to Bicriteria Problem

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The scheduling problem of interest involves multiple criteria in which the objective function is the minimization of the total tardiness, the proportion of tardy jobs, total earliness as well as the proportion of early jobs.
This problem can be expressed mathematically as Eq. 1

Subject to Where:
is the set of feasible solutions, is the decision vector,
Where:
and are the are relative weights of tardiness ( ), earliness ( ), number of tardy jobs, ( ) and proportion of early jobs ( ) to be optimized respectively

These criteria tardiness ( ), earliness ( ), number of tardy jobs, ( ) and proportion of early jobs ( ) are all defined as follows in Eq. 2 - Eq. 6.

The total tardiness is defined

for
The total number of tardy jobs is given by

Where

The Conditional Mean Tardiness (CMT) is defined as a measure of the average amount of tardiness for the completed jobs which are found to be tardy. Mathematically, CMT is defined by Eq. 7

The definition of earliness that applies to JIT problem according to Akande et al, [8] is given as:

for
The total earliness is given as

for
The Proportion of early jobs ( ) is given as

Where

The Conditional Mean Earliness (CME) is a measure of the average amount of earliness for the completed jobs which are found to be early. CME is defined mathematically by Eq. 12

Substitute Eqn (7) and Eqn (12) into Eqn (1) using the Akande et al., [7] reducibility of multicriteria to bicriteria problem procedure. The multicriteria scheduling problem can then be reduced to Eq. 13

Where and are constant and measure the priority or importance attached to conditional mean tardiness and conditional mean earliness respectively.

Assuming equal importance to the two performance measures. Then

Therefore, the problem is reduced to a bicriteria scheduling problem. [7] stated that multicriteria scheduling problems can be solved effectively using a polynomial-time algorithm that solves bicriteria or single criteria equivalent problems. In this regard, two non-regular performance measures; Conditional mean tardiness (CMT) and conditional mean earliness (CME) are minimized with a due window subject to static constraint. Minimizing these performance measures will ensure that the inevitable deviation from the perfect JIT schedule is minimized. Thus, the cost of inventory, wastage as well as other penalty costs associated with early and tardy jobs can be minimized.

Literature Review

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Job tardiness is an important scheduling objective and can be measured through several performance measures like total tardiness, maximum tardiness, and Conditional Mean Tardiness (CMT) among others. While other measures have been exhausted by different researchers, the use of CMT is sparse in the literature. The conditional mean tardiness measures the average amount of tardiness for the
completed jobs which are found to be tardy [9]. For instance, consider two scheduling solution methods that yield the same value of the total tardiness, the solution method that has a greater number of tardy jobs will exhibit less conditional mean tardiness than the other. CMT is not a regular performance measure, It means that it can decrease while the completion times are not decreasing [10]. [11] explored modified operation due date (MOD) rule for mean job tardiness and the proportion of tardy jobs, and the two measures together imply the conditional mean tardiness. The MOD rule was compared to several well-known tardiness-oriented priority rules, such as minimum slack-peroperation (S/OPN), smallest critical ratio (SCR), and COVERT. The MOD rule tends to achieve lower levels of mean tardiness than the other rules and lower CMT for a given proportion of the number of tardy jobs, except under conditions of high differences in due dates. [9] proposed an effective procedure to estimate the first two central moments (i.e., the mean and the variance) of the conditional mean tardiness and from this to compute a probabilistic bound for the maximum tardiness. These estimates are computed from the evaluation of the total tardiness, the number of tardy jobs, and the root mean square tardiness obtained through a stochastic simulation. Different evaluations done by simulation show the effectiveness of the bound obtained. It was concluded the bound is effective from the results obtained. [12] reported that that the use of critical ratio priorities is effective for minimizing the conditional mean tardiness (CMT).
Different criteria which are derivatives of job earliness have also been considered by different researchers. However, most researchers have considered earliness as a bicriteria performance measure by optimizing hierarchically, simultaneously or in Pareto form with tardiness, number of tardy jobs, or some measures as criteria. For instance, Rosa et al., [13] solved the single machine scheduling problem with distinct time windows and sequence-dependent setup times. The objective was to minimize the total weighted earliness and tardiness. The problem involves determining the job execution sequence and the starting time for each job in the sequence. An implicit Enumeration algorithm (an exact algorithm), and a general variable neighborhood search algorithm (a heuristic algorithm) were proposed to determine the job scheduling. The Enumeration algorithm yielded optimal solutions of all instances up to 15 jobs within a feasible computational time while the proposed general variable neighborhood search algorithm produces better-quality solutions for larger problem instances with less computational time compared with the other algorithm from the literature. [14] proposed a Pareto-optimal solution algorithm that efficiently generated Pareto-optimal solutions for any possible number of tardy jobs for a single-machine scheduling problem to minimize the summation of the weighted earliness and tardiness, subject to the number of tardy jobs. The work was benchmarked against scheduling on a single machine against restrictive and unrestrictive common due dates( see [15]) to show the superior accuracy and run time of the proposed Pareto solution. The computational analysis also shows that approximately of the nodes in the branching tree can be eliminated. [16] developed an approximation optimization approach, which is based on the imperialist competitive algorithm hybridized with an efficient neighborhood search for solving a job shop problem for minimizing the sum of the maximum earliness and tardiness criteria. A mixed integer linear programming (MIP) formulation of the job shop scheduling problem with the objective function was developed. The MIP model was validated on different problem sizes through a set of experiments and the effectiveness of the proposed approach was demonstrated through an experimental evaluation.
However, while different researchers have considered different variants of earliness and tardinessbased scheduling problems, literature is sparse where a multicriteria scheduling problem with four due date-based performance measures was reduced to two non-regular bicriteria problems. In this work, two non-regular performance measures; Conditional Mean Tardiness (CMT) and Conditional Mean Earliness (CME) are minimized with a due window subject to a static constraint. The problem is assumed to be deterministic, and the machine is assumed to be available continually and can only process one job at a time.

Problem Definition

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Using the Garaham notation [17], the problem of interest can be represented as

Subject to
Where:
is the set of feasible solutions, is the decision vector,
Where:
and are the are relative weights of tardiness ( ), earliness ( ), number of tardy jobs, ( ) and proportion of early jobs ( ) to be optimized respectively

This problem has been reduced to

Subject to
Where:
is the set of feasible solutions, is the decision vector,
Where
are the are relative weights of and respectively
is defined as the conditional mean tardiness and,
is called the conditional mean earliness
Therefore, the problem consists of scheduling n jobs in the set on a single machine with the due window and zero release dates. The target is to minimize the conditional mean tardiness and conditional mean earliness simultaneously to achieve an approximate JIT schedule. Fig. 1 illustrate that the two performance measures (the conditional mean tardiness and conditional mean earliness) is an indication of deviation of Just In -Time (JIT) schedule. The parameters involved in the problem are completion time, due date, number of tardy jobs and number of early jobs

Fig. 1. Variation of JIT Schedule with problem parameters

Fig. 1. Variation of JIT Schedule with problem parameters

JIT schedule is an ideal schedule where the due date is equal to the completion time. It is impossible to always achieve JIT, thus, the following conditions denoted by Eq. 19 - Eq. 22 is inevitable

The upper deviation (jobs completed after the due dates) from the equilibrium JIT is measured by total tardiness and the number of tardy jobs. The conditional mean tardiness measures the average amount of tardiness for the completed jobs which are found to be tardy. The lower deviation (jobs completed before the due date) is measured by total earliness and the number of early jobs. The conditional mean earliness is defined as the mean earliness for a set of early jobs.

The Proposed Solution Method

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Two solution methods named, GOA 1 and GOA 2 are proposed for solving the problem. The algorithms for the solution methods are outlined as follows.

GOA 1

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This algorithm modified the critical ratio rule to solve the problem.
Initialization
JobSet set of given jobs. JobSet , set of scheduled job
STEP I: Compute the due date allowance ( ) associated with the due window for all the jobs in the JobSet A
STEP 2: Compute the modified critical ratio (MCR) defined as associated with all the JobSet A in JobSet A
STEP 3: Arrange the JobSet A in increasing order of and put the same in JobSet B
STEP 4: Compute the Linear Composite Objective Function (LCOF) of the JobSet B
STEP 7: Stop .

GOA 2

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This algorithm uses the same priority index as the Modified Due Date (MDD) rule, but with a different concept for job selection for processing. Interested readers can contact [12] for further reading on MDD Rule
Just like the MDD rule, this algorithm at any time computes the priority index, which is given by:

Where t is the starting time of the next unscheduled job which can either be the completion time of the job in position i-1 or the release date of job i, is the processing time, and is the due date.
The step of the algorithm is outlined as follows :
Initialization
JobSet set of given jobs. JobSet , set of scheduled job
Initialization
JobSet set of given jobs. JobSet , set of scheduled job

STEP I: Compute priority index, for all the jobs in the jobSetA set
STEP 2: For , schedule job I if if there is a tie break the tie using the EDD, if the tie still uses SPT, if a tie still exists break arbitrarily. If JobSeT B is null (Empty) Go to STEP 3, else Go To STEP 7.

STEP 3: then, For , schedule job i if , if there is a tie break the tie using the EDD, if a tie still exists use SPT, if a tie still exist break arbitrarily. If JobSeT B is null (Empty) Go to STEP 4, else Go to STEP 7,

STEP 4: For , schedule job i if , if there is a tie break the tie using the EDD, if a tie still exists use SPT, if the tie exists again break arbitrarily. If JobSeT B is null (Empty) Go to STEP 5, Else Go To STEP 7

STEP 5: For , schedule job i if , if there is a tie, break the tie using the EDD, if a tie still exists use SPT, if the tie exists again break arbitrarily. If JobSeTB is null (Empty) Go to STEP 6, Else Go To STEP 7

STEP 6: For , schedule job i if i has the lowest there is a tie use EDD, if tie exist again break arbitrarily, Else Go To STEP 7

STEP 7: For , set where is the completion time of the last scheduled job in Job set B .

STEP 8: Repeat Steps 1 to 7 until all the jobs have been scheduled
STEP 9: Compute LCOF for the schedule obtained in the JobSetB

Experimentation

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Single processor scheduling problems with due window were simulated using the desktop tool module (editor) on MATLAB R2010 programming language. The number of jobs ( ), the processing times (pi), and the due windows (di) time interval were generated using the Süer et al., [18] and [19]. The processing time follows the uniform distribution . For the due window, each job entering the system is allocated to ascertain the due date using Total Work Content (TWK) method as explored by Süer et al [18].

The earliest due date ( ), and the latest due dates ( ) computed from the original due date ( Dj ). The due window is denoted by Eq. 25 - Eq. 27.

Where
is the flow allowance assigned to job j at time zero ( .). It is set at ( of )

In this work, the three due windows were explored

Results and Discussion

The original version of this paper is available on https://www.scientific.net/EI.11.83.pdf

The two proposed heuristics named GOA 1 and GOA 2 and some existing solution methods; the Smallest Critical Ratio (SCR), Modified Due Date (MDD), and Earliest Due Date (EDD) from the literature were implemented to obtain the values of Condition Mean Earliness (CME), Condition

Mean Tardiness (CMT) as well as the unnormalized Linear Composite Objective Function (LCOF). Table 2 to 11 shows the results obtained. The CME and the CMT results were explored to analyze the performance of all the solution methods concerning the ideal JIT schedule. The ideal JIT schedule is assumed the zero values of CME and CMT. The LCOF values were not used for results analysis because it is not normalized (See Akande et al., [20] ) on Normalization of Composite Objective Function for Multicriteria Scheduling Problems with Zero Release Dates).

Table 2. Results of the performance measures for the solution methods for problem size

Earliest Due Date
Original Due Date
Latest Due Date

Solution
Method
∑ni=1 CMTi
∑ni=1 CMEi
LCOF
∑ni=1 CMTi
∑nCMi=1 Ei
LCOF
∑ni=1 CMTi
∑ni=1 CMEi
LCOF

SCR
6.95
12.00
7.02
0.00
15.40
10.49
10.90
34.81
14.56

MDD
6.26
1.10
4.57
5.00
4.33
3.46
0.00
9.27
6.99

GOA 1
6.95
12.00
7.01
0.00
15.40
10.49
7.65
10.32
6.73

GOA 2
0.00
12.00
8.44
0.00
22.60
12.27
0.00
35.07
15.85

EDD
0.00
11.41
4.25
0.00
19.20
9.19
0.00
34.87
14.65

Table 3. Results of the performance measures for the solution methodsfor problem size

Earliest Due Date
Original Due Date
Latest Due Date

Solution
Method
∑CMTi
i=1
∑CMEi
i=1
LCOF
∑CMTi
i=1
∑CMEi
i=1
LCOF
∑CMTi
i=1
∑CMEi
i=1
LCOF

SCR
19.67
2.48
10.75
7.83
5.50
12.53
14.12
24.31
14.72

MDD
18.30
2.00
7.37
7.86
3.00
4.68
0.00
9.89
5.19

GOA 1
19.67
2.48
10.76
8.00
5.50
12.52
15.41
7.65
10.29

GOA 2
17.69
8.03
13.36
8.00
18.00
13.77
0.00
23.69
16.10

EDD
14.75
4.35
6.41
5.00
6.00
5.60
0.00
22.59
9.14

Table 4. Results of the performance measures for the solution methodsfor problem size

Solution
Method
Earliest Due Date
Original Due Date
Latest Due Date

∑CMTi
i=1 to n
∑CMEi
i=1 to n
LCOF
∑CMTi
i=1 to n
∑CMEi
i=1 to n
LCOF
∑CMTi
i=1 to n
∑CMEi
i=1 to n
LCOF

SCR
29.12
1.53
16.70
33.10
3.80
16.23
18.64
15.78
18.91

MDD
20.90
0.00
11.89
17.80
3.80
8.19
2.25
8.61
5.68

GOA 1
29.12
1.53
16.72
33.10
3.80
16.25
27.78
2.76
16.26

GOA 2
25.74
9.62
17.25
21.25
21.71
17.94
12.15
26.76
17.51

EDD
15.64
3.93
11.40
17.00
4.00
8.39
0.00
14.84
6.82

Table 5. Results of the performance measures for the solution methods for problem size

Earliest Due Date
Original Due Date
Latest Due Date

Solution
Methods
n
∑ CMTi
i=1
n
∑ CMEi
i=1
LCOF
n
∑ CMTi
i=1
n
∑ CMEi
i=1
LCOF
n
∑ CMTi
i=1
n
∑ CMEi
i=1
LCOF

SCR
43.20
4.65
23.00
29.37
5.00
22.34
37.20
6.16
22.33

MDD
30.46
0.55
16.23
15.33
0.00
13.89
20.39
4.67
11.04

GOA 1
45.19
1.60
23.00
29.37
5.00
22.43
45.27
0.65
23.22

GOA 2
32.70
7.64
21.44
20.80
23.44
22.87
26.67
16.60
22.74

EDD
31.03
0.81
15.69
14.35
1.67
14.36
19.17
6.10
11.24

Table 6. Results of the performance measures for the solution methodsfor problem size

Solution
Methods
Earliest Due Date
Original Due Date
Latest Due Date

∑CMTi
i=1
n
∑CMEi
i=1
n
LCOF
∑CMTi
i=1
n
∑CMEi
i=1
n
LCOF
∑CMTi
i=1
n
∑CMEi
i=1
n
LCOF

SCR
44.86
0.00
22.73
104.89
7.33
49.43
87.90
4.53
47.19

MDD
33.86
0.00
16.28
75.10
1.00
33.06
64.92
3.90
30.47

GOA 1
44.86
0.00
22.72
104.89
7.33
49.43
104.15
0.00
51.46

GOA 2
33.07
9.22
21.72
70.03
23.55
40.84
67.37
22.98
40.51

EDD
31.02
1.25
15.67
77.47
3.33
34.28
61.72
6.89
31.19

Table 7. Results of the performance measures for the solution methods for problem size

Solution
Methods
Earliest Due Date
Original Due Date
Latest Due Date

∑ni=1 CMTi
∑ni=1 CMEi
LCOF
∑ni=1 CMTi
∑ni=1 CMEi
LCOF
∑ni=1 CMTi
∑ni=1 CMEi
LCOF

SCR
123.09
0.00
64.54
101.27
0.00
62.95
106.13
5.60
59.11

MDD
94.69
0.00
49.53
65.78
1.00
44.26
61.96
3.47
39.63

GOA 1
123.09
0.00
64.53
101.33
0.00
62.97
121.57
1.50
63.91

GOA 2
86.01
9.86
49.51
63.58
18.14
50.29
67.76
19.19
49.03

EDD
88.43
0.50
47.19
65.92
1.00
45.35
65.27
3.25
40.47

Table 8. Results of the performance measures for the solution methods for problem size

Earliest Due Date
Original Due Date
Latest Due Date

Solution
Method
n
∑ CMTi
i=1
n
∑ CMEi
i=1
LCOF
n
∑ CMTi
i=1
nCM
∑ Ei
i=1
LCOF
n
∑ CMTi
i=1
n
∑ CMEi
i=1
LCOF

SCR
230.64
0.00
137.33
275.61
3.00
136.54
264.88
3.30
133.18

MDD
171.76
0.55
107.07
195.53
0.00
98.23
192.10
0.93
94.46

GOA 1
230.61
0.00
137.34
275.44
3.00
136.52
276.27
0.00
139.22

GOA 2
141.79
8.53
95.51
183.35
17.86
98.13
181.28
11.89
98.62

EDD
156.19
0.00
101.37
198.00
1.67
99.87
193.53
0.93
95.92

Table 9. Results of the performance measures for the solution methods for problem size

Solution
Method
Earliest Due Date
Original Due Date
Latest Due Date

∑i=1n CMTi
∑i=1n CMEi
LCOF
∑i=1n CMTi
∑i=1n CMEi
LCOF
∑i=1n CMTi
∑i=1n CMEi
LCOF

SCR
423.49
0.00
211.22
423.52
0.00
208.17
403.03
2.85
205.39

MDD
321.43
0.00
166.28
314.95
1.00
151.87
282.49
0.38
148.79

GOA 1
423.52
0.00
211.22
423.52
0.00
208.18
417.88
0.00
212.10

GOA 2
267.10
9.30
142.49
208.44
17.21
144.48
250.19
30.46
144.32

EDD
305.44
0.00
157.46
318.69
1.00
153.78
286.76
1.15
150.94

Table 9. Results of the performance measures for the solution methods for problem size

Solution
Method
Earliest Due Date
Original Due Date
Latest Due Date

n
∑ CMTi
i=1
n
∑ CMEi
i=1
LCOF
n
∑ CMTi
i=1
n
∑ CMEi
i=1
LCOF
n
∑ CMTi
i=1
n
∑ CMEi
i=1
LCOF

SCR
560.26
0.00
283.52
560.75
3.00
280.72
558.31
3.62
277.60

MDD
436.19
0.60
220.62
418.84
1.00
203.91
388.64
2.62
200.85

GOA 1
559.90
0.00
283.49
560.78
3.00
280.72
575.58
0.25
284.49

GOA 2
359.65
9.76
185.71
363.22
15.80
188.47
358.15
20.40
189.80

EDD
411.63
0.95
208.76
426.03
1.50
206.80
394.50
2.31
203.49

Table 10. Results of the performance measures for the solution methods for problem size

Earliest Due Date
Original Due Date
Latest Due Date

Solution
Method
n
∑ CMTi
i=1
n
∑ CMEi
i=1
LCOF
n
∑ CMTi
i=1
n
∑ CmEi
i=1
LCOF
n
∑ CMTi
i=1
n
∑ CMEi
i=1
LCOF

SCR
876.98
0.00
430.80
862.09
0.00
422.96
837.49
2.60
422.15

MDD
675.85
0.43
338.29
624.50
0.00
307.09
603.58
2.05
307.93

GOA 1
876.86
0.00
430.77
861.91
0.00
422.95
853.73
0.00
429.32

GOA 2
546.81
6.30
277.64
549.45
14.31
275.03
534.83
22.08
280.37

EDD
637.01
1.43
320.35
633.69
1.33
311.32
613.81
1.83
311.77

Table 11. Results of the performance measures for the solution methods for 400 x 1 problem size

Solution Methods | Earliest Due Date | Original Due Date | Latest Due Date
∑i=1n CMTi | ∑i=1n CMEi | LCOF | ∑i=1n CMTi | ∑i=1n CMEi | LCOF | ∑i=1n CMTi | ∑i=1n CMEi | LCOF
SCR | 1176.10 | 0.00 | 577.53 | 1161.00 | 6.00 | 573.87 | 1123.00 | 0.700 | 570.49
MDD | 915.23 | 0.43 | 450.57 | 847.45 | 2.00 | 418.63 | 808.06 | 0.35 | 413.90
GOA 1 | 1176.30 | 0.00 | 577.40 | 1161.00 | 6.00 | 573.83 | 1143.00 | 0.00 | 578.18
GOA 2 | 735.70 | 4.94 | 367.08 | 727.28 | 15.35 | 369.70 | 708.97 | 21.77 | 370.60
EDD | 864.28 | 1.60 | 426.76 | 860.51 | 2.75 | 424.33 | 820.42 | 0.35 | 419.39

Performance Evaluation

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The results obtained (as depicted in Table 2 to 11) were analyzed for the three windows. The values of the CMT and CME were plotted against the problem sizes. The t -test using Paired Two Sample for Means at was also used to quantify the significance of the differences between the solution methods and the ideal JIT schedule for different problem sizes.

Analysis of the Results Based on the Earliest Due Window

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Figure 2 illustrates the plot of CMT against the problem sizes. The plot shows the GOA2 heuristic exhibits the minimum conditional tardiness deviation from the JIT schedule. GOA 1 and SCR plots align.

Fig. 2. The plot of Conditional Tardiness values against the problem sizes for the earliest Due window

Fig. 2. The plot of Conditional Tardiness values against the problem sizes for the earliest Due window

NOTE In Fig. 2 . SCR completely align with GOA 1, thus the SCR plot seems invisible
The t-test also shows that the GOA 2 heuristics is not significantly different from the imaginary JIT schedule for problem sizes: . Table shows the results of the t-test.

Table 12. t-test results for the JIT schedule against GOA 2 for problem sizes;

JIT Schedule | GOA 2
Mean | 0 | 14.47666667
Variance | 0 | 173.3810333
Observations | 3 | 3
Pearson Correlation | #DIV/0! |
Hypothesized Mean Difference | 0 |
Df | 2 |
t Stat | -1.90427 |
P(T<=t) one-tail | 0.098589 |
t Critical one-tail | 2.919986 |
P(T<=t) two-tail | 0.197178 |
t Critical two-tail | 4.302653 |

Fig. 3. The plot of Conditional Earliness against the problem sizes for the earliest Due window

Figure 3 illustrates the plot of conditional earliness against the problem sizes. The plot shows that for problem sizes , all the solution methods have a higher deviation from the optimal with the GOA 2, the highest, and MDD exhibits the lowest deviation. The t-test shows that EDD, SCR, and GOA 1 solution methods are not significantly different from the imaginary JIT schedule for problem sizes; . The approximate P-value (one-tail) for both the SCR and GOA 1 is .

Analysis of the results based on the original due window

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The plot of conditional tardiness against the problem sizes(Figure 4) for the original due window shows little deviation among all the heuristics as well as the optimal JIT schedule for problem sizes . As problem sizes, n increases, a higher deviation is noticed between the JIT schedule and other solution methods. At higher problem sizes , GOA 2 has the lowest deviation from the JIT. However, at , the EDD shows a positive deviation in performance.

Fig 4. The plot of Conditional Tardiness values against the problem sizes for the original Due window

Fig 4. The plot of Conditional Tardiness values against the problem sizes for the original Due window

Furthermore, for problem sizes , the t-test shows that all the solution methods are not significantly different from the JIT schedule. The P values of the solution methods are shown in Table 13

Table 13. The P values for solution methods for problem sizes

Solution method | P values (One Tail) | Inference
GOA 2 | 0.1281 | Not Significantly difference
EDD | 0.1416 | Not Significantly difference
MDD | 0.0595 | Not Significantly difference
SCR | 0.1526 | Not Significantly difference
GOA 1 | 0.1516 | Not Significantly difference

Fig. 5. The plot of Conditional Earliness against the problem sizes for the Original Due window

Fig. 5. The plot of Conditional Earliness against the problem sizes for the Original Due window

The plot of conditional earliness against the problem sizes for the original due window (Figure 5) shows an alternating in the performance of all the heuristics. GOA 2 shows the highest deviation for all the problem sizes. The t -test(using Paired Two Sample for Means) at also reveals that all the solution methods are significantly different from the t -test with their respective P - values less than 0.05 .

Analysis of the results based on the latest due window

The original version of this paper is available on https://www.scientific.net/EI.11.83.pdf

The plot of conditional tardiness against the problem sizes reveals a small deviation for problem sizes among all the solution methods including the imaginary JIT schedule. As , a more feasible deviation is observed between the JIT plot and other solution methods. However, GOA 2 heuristics shows the lowest deviation from the JIT schedule while the SCR, MDD, and GOA 1 solution methods align. Table 14 shows the P -values for all the solution methods against the imaginary JIT schedule when subjected to a t-test at a significant difference for problem sizes .

Table 14. P-values for all the solution methods against the imaginary JIT schedulefor .

Solution Methods | P values | Inference
GOA 2 | 0.1116 | Not Significantly difference
EDD | 0.1955 | Not Significantly difference
MDD | 0.1674 | Not Significantly difference
SCR | 0.02 | Significantly difference
GOA 1 | 0.0308 | Significantly difference

Fig. 6. The plot of Conditional Tardiness against the problem sizes for the latest Due window

Fig. 6. The plot of Conditional Tardiness against the problem sizes for the latest Due window

Fig. 7. The plot of Conditional Earliness against the problem sizes for the latest Due window

Fig. 7. The plot of Conditional Earliness against the problem sizes for the latest Due window

The plot of the conditional Earliness against the problem sizes shows that for the problem sizes; 20, there is a very high deviation between the imaginary JIT schedule and all other solution methods. However, when , the GOA 1 performance improves and almost aligns with the JIT schedule. The t-test also reveals that for problem sizes , only the GOA 1 heuristic yields a result that is not significantly different from the JIT schedule. Table 15 shows the result of the t -test of GOA 1 against the JIT schedule.

Table 15. The result of the t -test of GOA 1 against the JIT schedule.

| JIT | GOA 1
Mean | 0 | 0.3
Variance | 0 | 0.287857
Observations | 8 | 8
Pearson Correlation | #DIV/0! |
Hypothesized Mean Difference | 0 |
Df | 7 |
t Stat | -1.58153 |
P(T<=t) one-tail | 0.078885 |
t Critical one-tail | 1.894579 |
P(T<=t) two-tail | 0.15777 |
t Critical two-tail | 2.364624 |

Conclusion and Recommendation

The original version of this paper is available on https://www.scientific.net/EI.11.83.pdf

In this paper, we reduced a multicriteria scheduling problem that involves four due date-based performance measures to an equivalent bicriteria problem of minimizing conditional mean Tardiness and conditional mean earliness. Two proposed solution methods named GOA 1 and GOA 2 as well as some other dispatching heuristics were benchmarked against the ideal JIT schedule ( a schedule with zero tardiness and zero earliness). The results show that the proposed heuristics yielded results that are not significantly different from the optimal in some instances. Further research can focus on implementing the results in terms of the Linear composite objective function after carrying out the normalization procedure for the two performance measures involved in the reduced bicriteria problem.

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The original version of this paper is available on https://www.scientific.net/EI.11.83.pdf

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Keywords Index

A

Analytical Analytical Prediction of Crushing Thin-Walled Square Tube with Static Axial Loads Using Elliptical Holes as Crush Initiators

B

Benchmarking Minimizing Conditional Mean Tardiness and Mean Earliness on a Single Machine with the Due Windows Approach

Bezier Curve Development of Savonius Rotor Based on Bezier Curve for Vertical Axis Marine Current Turbine at Sunda Strait, Hindia Ocean

Bibliometric Analysis A Bibliometric Analysis of Suspension System Development for Enhancing Comfort in Family Passenger Vehicles

C

CFD Simulation The Effect of Deflector Angle on the Performance of Turbine Combination Darrieus-Savonius

Conditional Mean Earliness Minimizing Conditional Mean Tardiness and Mean Earliness on a Single Machine with the Due Windows Approach

Conditional Mean Tardiness Minimizing Conditional Mean Tardiness and Mean Earliness on a Single Machine with the Due Windows Approach

Crack Defects Simulation of Stress Intensity Factor and J-Integral on UIC 54 Railway Failure Using A Fracture Mechanics Approach

D

Darrieus-savonius Combination The Effect of Deflector Angle on the Performance of Turbine Combination Darrieus-Savonius

Deflector The Effect of Deflector Angle on the Performance of Turbine Combination Darrieus-Savonius

Deformation Mode The Behavior of Thin-Walled Cylinders with Ribs Regarding the Energy Absorption Capability on High-Velocity Impact

Development Suspension A Bibliometric Analysis of Suspension System Development for Enhancing Comfort in Family Passenger Vehicles

Double Stacking Development of Savonius Rotor Based on Bezier Curve for Vertical Axis Marine Current Turbine at Sunda Strait, Hindia Ocean

Due Window Minimizing Conditional Mean Tardiness and Mean Earliness on a Single Machine with the Due Windows Approach

E

Elliptical Hole Analytical Prediction of Crushing Thin-Walled Square Tube with Static Axial Loads Using Elliptical Holes as Crush Initiators

Energy Absorption The Behavior of Thin-Walled Cylinders with Ribs Regarding the Energy Absorption Capability on High-Velocity Impact

F

Finite Element Topology Optimization of Motorbike Footsteps Using Finite Element Method

Footstep Topology Optimization of Motorbike Footsteps Using Finite Element Method

Fracture Mechanics Simulation of Stress Intensity Factor and J-Integral on UIC 54 Railway Failure Using A Fracture Mechanics Approach

I

Ideal Just-in-time Minimizing Conditional Mean Tardiness and Mean Earliness on a Single Machine with the Due Windows Approach

Impact Energy Absorber Analytical Prediction of Crushing Thin-Walled Square Tube with Static Axial Loads Using Elliptical Holes as Crush Initiators

J

J-integral Simulation of Stress Intensity Factor and J-Integral on UIC 54 Railway Failure Using A Fracture Mechanics Approach

M

Muffler Design Muffler Design for Noise Reduction and Pressure Loss Optimization Using Multiobjective Genetic Algorithm

Multiobejctive Genetic Algorithm Muffler Design for Noise Reduction and Pressure Loss Optimization Using Multiobjective Genetic Algorithm

N

Noise Reduction Muffler Design for Noise Reduction and Pressure Loss Optimization Using Multiobjective Genetic Algorithm

O

Optimization Topology Optimization of Motorbike Footsteps Using Finite Element Method; Muffler Design for Noise Reduction and Pressure Loss Optimization Using Multiobjective Genetic Algorithm

P

Passenger Comfort A Bibliometric Analysis of Suspension System Development for Enhancing Comfort in Family Passenger Vehicles

Pitch Angle The Effect of Deflector Angle on the Performance of Turbine Combination Darrieus-Savonius

Pressure Loss Muffler Design for Noise Reduction and Pressure Loss Optimization Using Multiobjective Genetic Algorithm

R

Railroads Simulation of Stress Intensity Factor and J-Integral on UIC 54 Railway Failure Using A Fracture Mechanics Approach

Reaction Force The Behavior of Thin-Walled Cylinders with Ribs Regarding the Energy Absorption Capability on High-Velocity Impact

Rib The Behavior of Thin-Walled Cylinders with Ribs Regarding the Energy Absorption Capability on High-Velocity Impact

S

Savonius Rotor Development of Savonius Rotor Based on Bezier Curve for Vertical Axis Marine Current Turbine at Sunda Strait, Hindia Ocean

Schedule Minimizing Conditional Mean Tardiness and Mean Earliness on a Single Machine with the Due Windows Approach

Square Tube Analytical Prediction of Crushing Thin-Walled Square Tube with Static Axial Loads Using Elliptical Holes as Crush Initiators

Stress Intensity Factor Simulation of Stress Intensity Factor and J-Integral on UIC 54 Railway Failure Using A Fracture Mechanics Approach

Suspension System A Bibliometric Analysis of Suspension System Development for Enhancing Comfort in Family Passenger Vehicles

Suspension Technology A Bibliometric Analysis of Suspension System Development for Enhancing Comfort in Family Passenger Vehicles

T

Topology Topology Optimization of Motorbike Footsteps Using Finite Element Method

V

Vertical Axis Turbine The Effect of Deflector Angle on the Performance of Turbine Combination Darrieus-Savonius

W

Wall Thickness The Behavior of Thin-Walled Cylinders with Ribs Regarding the Energy Absorption Capability on High-Velocity Impact

Waste Topology Optimization of Motorbike Footsteps Using Finite Element Method

Authors Index

A

Adiwidodo, S. The Effect of Deflector Angle on the Performance of Turbine Combination Darrieus-Savonius

Adjie, M. Development of Savonius Rotor Based on Bezier Curve for Vertical Axis Marine Current Turbine at Sunda Strait, Hindia Ocean

Ajisegiri, G. Minimizing Conditional Mean Tardiness and Mean Earliness on a Single Machine with the Due Windows Approach

Akande, S. Minimizing Conditional Mean Tardiness and Mean Earliness on a Single Machine with the Due Windows Approach

Antara, I. Topology Optimization of Motorbike Footsteps Using Finite Element Method

Azeez, T. Minimizing Conditional Mean Tardiness and Mean Earliness on a Single Machine with the Due Windows Approach

Aziz, M. The Behavior of Thin-Walled Cylinders with Ribs Regarding the Energy Absorption Capability on High-Velocity Impact

B

Baananto, F. The Effect of Deflector Angle on the Performance of Turbine Combination Darrieus-Savonius

Budiarsa, I. Topology Optimization of Motorbike Footsteps Using Finite Element Method

D

Darto, D. Simulation of Stress Intensity Factor and J-Integral on UIC 54 Railway Failure Using A Fracture Mechanics Approach

Dwi, A. A Bibliometric Analysis of Suspension System Development for Enhancing Comfort in Family Passenger Vehicles

H

Habibie, A. Development of Savonius Rotor Based on Bezier Curve for Vertical Axis Marine Current Turbine at Sunda Strait, Hindia Ocean

Hardi, W. The Behavior of Thin-Walled Cylinders with Ribs Regarding the Energy Absorption Capability on High-Velocity Impact

Hidayat, D. Analytical Prediction of Crushing Thin-Walled Square Tube with Static Axial Loads Using Elliptical Holes as Crush Initiators

I

Irfin, R. The Effect of Deflector Angle on the Performance of Turbine Combination Darrieus-Savonius

Istiyanto, J. Analytical Prediction of Crushing Thin-Walled Square Tube with Static Axial Loads Using Elliptical Holes as Crush Initiators

Iswantoko, A. Simulation of Stress Intensity Factor and J-Integral on UIC 54 Railway Failure Using A Fracture Mechanics Approach

K

Karohika, I. Topology Optimization of Motorbike Footsteps Using Finite Element Method

Kurniawan, P. Simulation of Stress Intensity Factor and J-Integral on UIC 54 Railway Failure Using A Fracture Mechanics Approach

M

Maulana, F. A Bibliometric Analysis of Suspension System Development for Enhancing Comfort in Family Passenger Vehicles

N

Nurcholis, S. A Bibliometric Analysis of Suspension System Development for Enhancing Comfort in Family Passenger Vehicles

P

Parwata, I. Topology Optimization of Motorbike Footsteps Using Finite Element Method

Prasetyo, J. Topology Optimization of Motorbike Footsteps Using Finite Element Method

Pratama, M. Muffler Design for Noise Reduction and Pressure Loss Optimization Using Multiobjective Genetic Algorithm

Priatama, Y. A Bibliometric Analysis of Suspension System Development for Enhancing Comfort in Family Passenger Vehicles

R

Rahman, F. Development of Savonius Rotor Based on Bezier Curve for Vertical Axis Marine Current Turbine at Sunda Strait, Hindia Ocean

S

Santosa, D. A Bibliometric Analysis of Suspension System Development for Enhancing Comfort in Family Passenger Vehicles

Setiawan, H. Development of Savonius Rotor Based on Bezier Curve for Vertical Axis Marine Current Turbine at Sunda Strait, Hindia Ocean

Sumarsono, D. Analytical Prediction of Crushing Thin-Walled Square Tube with Static Axial Loads Using Elliptical Holes as Crush Initiators

Suprayitno, S. Muffler Design for Noise Reduction and Pressure Loss Optimization Using Multiobjective Genetic Algorithm

Suprayogi, D. Development of Savonius Rotor Based on Bezier Curve for Vertical Axis Marine Current Turbine at Sunda Strait, Hindia Ocean

Sutrisno, F. Simulation of Stress Intensity Factor and J-Integral on UIC 54 Railway Failure Using A Fracture Mechanics Approach

T

Trihutomo, P. Muffler Design for Noise Reduction and Pressure Loss Optimization Using Multiobjective Genetic Algorithm

U

Umron, A. The Behavior of Thin-Walled Cylinders with Ribs Regarding the Energy Absorption Capability on High-Velocity Impact

W

Wahyudi, B. The Effect of Deflector Angle on the Performance of Turbine Combination Darrieus-Savonius

Wibowo, C. A Bibliometric Analysis of Suspension System Development for Enhancing Comfort in Family Passenger Vehicles

Wibowo, E. Analytical Prediction of Crushing Thin-Walled Square Tube with Static Axial Loads Using Elliptical Holes as Crush Initiators

Y

Yudiyanto, E. The Effect of Deflector Angle on the Performance of Turbine Combination Darrieus-Savonius