Papers by Keyword: Dimensional Analysis

Abstract: In this investigation, the quantity of seepage through a homogeneous earth dam with a vertical drain on a permeable foundation was studied using the SEEP/W program. Moreover, the effects of the geometrical and geotechnical parameters (upstream slope, dam height, top width, free board, and permeability ratio) on leakage flow were analyzed with SPSS 20. To begin with, leakage flow values through an earth dam were estimated using SEEP/W by taking three values of each parameter, and then statistical analysis was performed with the help of dimensional analysis. In addition, an empirical equation and a neural network model dubbed q_ANN were developed to calculate leakage flow through an earth dam with a vertical drain. The validation of these models (empirical equation and q_ANN) is made by their applications to real case studies such as El-Haimeur and Boubrik dams located in Ghardaia City. In conclusion, the values of these models can prove that the performance of the models is high and accurate to predict leakage flow through a homogeneous earth dam with a vertical drain on a permeable base.

Abstract: Electro discharge machining (EDM) is a most commonly used machining process among all the non-conventional machining process which removes materials via electrical and thermal energy. The primary goal of EDM is to get more material removal rate (MRR) with lower radial overcut (ROC). Normally, the responses are predicted using empirical models which are limited to only machining parameters and they do not consider the effects of work material properties on the process performance. Therefore in this study, a model has been developed including machining parameter as well as thermo-physical property of work material. In this investigation, a semi-empirical model has been established for the material removal rate (MRR) and radial overcut (ROC) by adopting the dimensional analysis technique. Dimensional analysis is a technique of dimensions and a mathematical technique that deals with the physical quantities concerned with the experiments to formulate a model for the response in terms of response control parameters as well as some physical properties of the materials. Buckingham’s л theorem is a main theorem in dimensional analysis and it is a signification of Rayleigh’s method of dimensional analysis. The theory is applied to gather each and every variable presenting the problem in a number of the dimensionless products. For this study, the thermo-physical properties viz. density, thermal conductivity and coefficient of thermal expansion and machining parameters like peak current, pulse on time, gap voltage and duty cycle are considered as input factor. AISI 304 stainless steel used as work material and Tungsten carbide is used as tool material for this investigation.

Abstract: In our study we examined the behaviour of thin liquid layers at curved solid edges experimentally and numerically by coating investigations based on the laser-induced fluorescence technique (LIF) and by numerical film simulations based on the Volume-of-Fluid multiphase flow model (VOF), respectively. The main motivation was to find optimal combinations of influencing quantities to reduce the so-called Fat-Edge effect. Therefore, we performed a study of these influencing quantities, in which application parameters like edge curvature radii of the solid substrates and application layer thicknesses as well as determining liquid properties like viscosity and surface tension have been varied. Results are described qualitatively at corresponding Fat-Edge shapes and quantified by suitable Fat-Edge parameters, which had to be identified and selected.We can show that adverse and appropriate influencing parameter combinations exist, which generate conspicuous and less distinctive Fat-Edges, respectively. The experimental findings and proportionalities regarding Fat-Edge shapes and dimensions are found to be physically plausible. Furthermore, an order of significance of the influencing quantities has been established.Eventually, we could derive a dimensionless quantity by dimensional analysis, which describes the Fat-Edge effect. Thus, the Fat-Edge effect may also be described by the application of similarity theory and a corresponding dimensionless number.

Abstract: Scaling methods allow the estimation of the impact of changes in individual parameters on system performance. In the technical context, physical similarity is the focus. This paper demonstrates the extension of scaling methods to include uncertainty scaling. The advantages of using scaling uncertainty for the development of scaled products and the contribution of extended scaling methods to the analysis and assessment of uncertainty are illustrated. Uncertainty scaling based on dimensional analysis and complete similarity is derived. The potential of this method is demonstrated using a load carrying structure - a buckling beam.

Abstract: Penetration efficiency reflects high speed projectile penetration ability with the impact velocity (>800m/s) variation. To further study the penetration efficiency engineering model, the physical and mechanical parameters that affect the penetration efficiency of high-speed projectiles penetrating into concrete target are analyzed, penetration efficiency dimensionless quantities are determined, such as projectile’s length to diameter ratio, projectile and target strength ratio, etc. The dimensionless equation of penetration efficiency is got by using the homogeneous principles of the laws of physics dimensionless. According to experimental data, a function of dimensionless penetration efficiency and dimensionless projectile speed is fitted. Finally, the model is verified by test, and the model calculations and experiment results agree well. The model obtained in this paper can estimate the projectile’s impact velocity when the penetration efficiency reaches the maximum, it would be a theoretical guidance for high speed penetration effects experiments.

Abstract: The porous discharge flow tube has been widely used in agriculture, water supply and drainage, ventilation, chemical and other fields. Flow characteristics directly affect the flow uniformity of the porous tube, thereby affecting the efficient use of it. The theoretical analysis and experimental study on the capacity of the porous tube’s discharge (flux of water) have the important project value and theoretical significance. In this paper,the total flow calculation formula is derived by the knowledge of hydraulics, the relation of discharge discount rate is calculated through dimensional analysis and the average single hole discharge formula is established based on some experimental data. The results of the test data and engineering data showed that the formula results and the test results are quite identical.

Abstract: In the paper the analysis of the dimensional structure of different manufacturing process is made. There are shown that the different schemes of the designer sizes result in a different level of an optimality of a dimensional structure. At definition of number of the technological sizes as criterium of a optimality it is necessary to allow both formation of the intermediate sizes and the effect of errors compensation. The effect of errors compensation is the reason for the change of the sizes nominals and its limit deviations. The detail subjected to machining, is characterized by constructive dimensional links which reflect, eventually, its functionality. The character of the constructive dimensional links is defined by the designer who takes into account the technological features of machine tools, but not in detriment of functionality. Therefore, carrying out of the dimensional analysis on a joint of these two phases is very important with the purpose of improvement of dimensional adaptability to manufacture of made details. One of criterions of this optimality has the structural nature. The manufacturing process is considered optimum, if in the structure of all technological dimensional chaines number of the technological sizes is minimum. This condition executes if to each designer size there corresponds in a technological dimensional chain the unique technological size, and in dimensional circuits for machining allowances, each machining allowance is determined by two technological sizes or one technological size and one size on blank. For different variants of the linear dimensions are shown the way in which are changing the limit deviations of technological sizes and respectively of the constructive sizes of the equivalent details.

Abstract: In the given work it is shown, that at machining the technological dimensional structures are optimum if they are similar to the design dimensional structure of a detail. The conditions of the locating and fastening, and also some technical requirements interfere achievements of similarity. In these cases the directed change of the design dimensional structure of a detail is recommended due to recalculation of the sizes. From this point of view creation of technological process represents a compromise of mutual approche of the dimensional structures of a detail and of a technological system. Technological process may be built from operation elements, but they (the operation elements) do not have the necessary characteristics to create the dimensional structures. These characteristics are not formed during decomposition because the relevant details dimensional structure is not taken into account. The most appropriate entity as element of which may be built the technological process is a technological mounting. The mounting has a dimensional structure and includes the communication elements - the sizes up to locating surfaces Thus, the dimensional designing of technological processes results in optimality if it is possible to achieve the similarity of design and technological dimensional structures in the following order: creation of the blank's dimensional structure similar to the detail's dimensional structure; formation of optimum technological dimensional links of the first technological operations or mounting (roughing) by resizing if necessary of the blank and of the detail; formation of optimum technological dimensional links on the subsequent technological operations or mounting by resizing if necessary of the detail in progress; formation of optimum technological dimensional links on the final technological operations or mounting by resizing if necessary the detail; calculation of the minimal machining allowances; the dimensional analysis of technology with calculation of the operational sizes, their tolerances and limit deviations; formation of drawings of the blank.

Abstract: Marine oil spill often forms oil droplets in stormy conditions. Based on the dimensional analysis Rayleigh method, the relationship is established between entrainment rate of oil droplets and statistical physical quantities such as the energy dissipation rate, intrusion depth et al. An expression of size spectrum of oil droplets is derived based on theorem and relationship between the capillary number, the dimensionless intrusion time and viscosity ratio. Preliminary results show that the slope of the derived spectrum is-2.29, which agrees well with the measured slope-2.3 in laboratory. Shear rate, surface tension, droplet radius, oil and water viscosity is the main factors controlling the total number of the oil droplets.

Abstract: A 3-PUU parallel mechanism was studied, which can perform one-dimensional translation about z-axis and two-dimensional rotations about y-axis and x-axis. This paper shows the study about the precision analysis, the dimensional analysis and the synthesis problem of the parallel mechanism having less degree of freedom. First, the closed-loop vector model was built based on analyzing the branched-chains of 3-PUU, the pose error model was built through the differential geometry, and the error model of positive solutions was obtained which contains all the structural parameters errors. For the error of structural parameters given, the pose output error can be solved out by application of this model, the area of maximum error is found out. And the influence of pose output error was analyzed with postures changed. The dimensional analysis of 3-PUU was also done by this error model, and the reasonable selection of mechanism parameters was discussed. And then the rationality of structure dimensional design was discussed in this paper. Finally, this method also may be used in the dimensional analysis of other less freedom parallel mechanisms.