Papers by Keyword: Mathematical Models

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Authors: Chuan Sheng Wang, Shan Hu Li, Ping Fu, Chun Lei Lü
Abstract: The physical, mathematical and finite element model of the extruding part of mixing-extruding machine was established to carry on the finite element simulation of the extrusion part flow field. Results showed that the double cone screw have better mixing and feeding properties than single screw.
Authors: Bo Sun, Long Chen
Abstract: The unfolding is the first step for the manufacturing of the sheet-metal part, which plays a major role for the accuracy and quality of the final product. Unfortunately, the inefficiency of the traditional drawing-based method made the process boring and sometime confusing. The CAD method made benefit for the designer. By means of the 3D modeling kernel and the mathematic model of unfolding process, the automatic design system of sheet-metal part was developed, in which the models are parametric and in 3D environment.
Authors: Zhi Qiang Liang, Hong Chao Jian, Xi Bin Wang, Wen Xiang Zhao, Su Yan Zhang, Yusuke Otani, Si Yi Xue
Abstract: Micro-drilling become more widely used from precision mechanics to electronics. Nowadays, the main commercial tools are planar point micro-drills. However, that geometry often causes a high thrust force, high temperature, and rapid wear during micro-drilling. Furthermore, it is difficult to adjust the four flank surfaces to accurately intersect at one point, particularly when the drill diameter becomes smaller. To solve this problem, non-coaxial helical drills points have been proposed by some researchers, and is characterized by a continuous helical flank instead of the piecewise planar flank. Its drilling performance is improved compared with planar drill point. This study presents a 5-axis coordinated CNC grinding method of the non-coaxial helical drill flank. Mathematical models of the drill flank and its engagement line between cylinder grinding wheel and drill tool are established, and then the path of the grinding wheel with respect to the drill tool is obtained. In order to verify the availability of the proposed methods, three dimension (3D) grinding simulation of non-coaxial helical drills with diameter 0.5mm was carried out using the CAD software, and then were fabricated on a 6-axis Makino CNC tool grinder. The ground micro-drills examined by 3D laser scanning microscope show good identity with the simulated result. These indicate that the manufacturing model presented in this paper provides a practical and efficient method to grind the flank of a non-coaxial helical micro-drill.
Authors: Wei Gong, Zhou Hua Jiang, Dong Ping Zhan
Abstract: In the paper, the superiority-inferiority in various calculations of hardenability has been compared, and the method of nonlinear regression equation was chosen to establish a mathematical model. The model was modified through the actual production of the gear steel hardenability data. Based on the model, a prediction platform was developed with computer tools to calculate the hardenability of gear steel. The hardenability prediction software can calculate random Jominy distance hardness according to chemical composition and grain size. The forecast accuracy is better than that of unmodified nonlinear regression equation and multiple linear regression equation, but equal to that of artificial neural network.
Authors: Shao Gui Wu, Jia Yang Wang
Abstract: This paper investigates a bus waiting problem quantitatively by building a mathematical model. The problem is when a passenger is between two stations, which station to choose is favorable for him to catch a bus? Here, several related factors are discussed to explore their influences on the bus-waiting problem, including the original bus position, the average velocity of bus, the length between two bus stations, passenger’s position and his velocity. Finally, some important conclusions are drawn.
Authors: Sam Yang, Scott Furman, Andrew Tulloh
Abstract: A mathematical model has been developed for predicting material compositional microstructures using measured data as constraints. Examples of measured data include 3-D sets of tomography data, 2-D sets of compositional data on surfaces and sections, and material absorption and interaction properties. The model has been partially implemented as a MS-Windows application. Reasonable agreement has been obtained between the numerical predictions from the software and the simulated data. The predicted microstructures could be used to study various material properties such as porosity distribution, diffusion and corrosion.
Authors: Mao Fu Liu, Xiong Hua Guo, Hui Xian Han
Abstract: A design-analysis and simulation approach of complex ball-end cutter was proposed by using computer graphics and OpenGL control in this paper. The mathematical models of rake face and flank face of a complex ball-end cutter were built as the simulation condition. A computer-aided design and simulation processing system of complex tool was presented through pre-modeling OpenGL control. Some 3D simulation models of complex ball-end cutter including spiral cylinder, ball-head (including rake face, chip groove, first flank face and second flank face) and grinding wheel were created respectively. According to mathematical models and VC++ software platform, transformation and machining animation simulations of ball-end cutter were designed and realized visually using OpenGL control interface technique. The results of Three-dimensional design and simulation will offer sufficient theory foundation for virtually manufacturing ball-end cutter.
Authors: Wen Lin Wang, Xiao Feng Xia, Gao Xin Xu
Abstract: To improve accuracy in the engineering design of hydraulic dampers, a dynamic mathematic model for its working fluid density, viscosity, modulus and stiffness is established. The dynamic flow loss due to volumetric change and pressure leakage is also formulated, wherein the dynamic back pressure in the air chamber is coupled. Simulation results show that most of the fluid properties change obviously when the damper is subjected to external excitations, they are not constant values. The viscosity would drop 74.68% and the flow loss would soar 298.68% with the increase of fluid temperature; the modulus and the stiffness would also drop over 20% when the entrapped air ratio increases, but the density is relatively robust to both variations. The established mathematic model gives a dynamic representation of the fluid property under real service conditions, it has already been applied to the engineering design of several hydraulic damper products in industry, and the effectiveness is validated by pertinent product experiments.
Authors: Qian Wang, Wei Huang
Abstract: In the distribution network fault location, the impact of information distortion needs to be to focus on, especially when the short-circuit current is used as the fault information. Considering the distortion or failure of real-time information and other issues, the quick location method of the failure point in distribution network is analyzed. Based on the mathematical model of distribution network fault location, firefly algorithm is applied. According to the characteristics of fault location objective function in distribution network, convergence criterion is proposed, which is suitable for fault location mathematical model.
Authors: Tie Neng Guo, Ya Hui Cui, Li Gang Cai
Abstract: Based on force analysis of angular contact ball bearings, this paper proposes a generic mathematical modeling method. This paper conducts in-depth research for these aspects: all directions of the stiffness characteristics under different load conditions of angular contact ball bearings, internal contact deformation and the change of bearing parameters. This article eventually gets the variation of the bearing characteristics under different load conditions.
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