Three-dimensional tolerance analysis of discrete surface structures based on the torsor cluster model

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Chuanyuan Zhou ◽  
Zhenyu Liu ◽  
Chan Qiu ◽  
Jianrong Tan
Keyword(s):  
Mathematical Model ◽  
Cluster Model ◽  
Three Dimensional ◽  
Tolerance Analysis ◽  
Analysis Method ◽  
Discrete Elements ◽  
Content Type ◽  
Dimensional Tolerance ◽  
Discrete Surfaces ◽  
Discrete Surface

Purpose The purpose of this paper is to propose a novel mathematical model to present the three-dimensional tolerance of a discrete surface and to carry out an approach to analyze the tolerance of an assembly with a discrete surface structure. A discrete surface is a special structure of a large surface base with several discrete elements mounted on it, one, which is widely used in complex electromechanical products. Design/methodology/approach The geometric features of discrete surfaces are separated and characterized by small displacement torsors according to the spatial relationship of discrete elements. The torsor cluster model is established to characterize the integral feature variation of a discrete surface by integrating the torsor model. The influence and accumulation of the assembly tolerance of a discrete surface are determined by statistical tolerance analysis based on the unified Jacobian-Torsor method. Findings The effectiveness and superiority of the proposed model in comprehensive tolerance characterization of discrete surfaces are successfully demonstrated by a case study of a phased array antenna. The tolerance is evidently and intuitively computed and expressed based on the torsor cluster model. Research limitations/implications The tolerance analysis method proposed requires much time and high computing performance for the calculation of the statistical simulation. Practical implications The torsor cluster model achieves the three-dimensional tolerance representation of the discrete surface. The tolerance analysis method based on this model predicts the accumulation of the tolerance of components before their physical assembly. Originality/value This paper proposes the torsor cluster as a novel mathematical model to interpret the tolerance of a discrete surface.

A quasi-Monte Carlo statistical three-dimensional tolerance analysis method of products based on edge sampling

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Chuanyuan Zhou ◽  
Zhenyu Liu ◽  
Chan Qiu ◽  
Jianrong Tan
Keyword(s):  
Monte Carlo ◽  
Three Dimensional ◽  
Sampling Strategy ◽  
Tolerance Analysis ◽  
Analysis Method ◽  
Content Type ◽  
Dimensional Tolerance ◽  
Quasi Monte Carlo ◽  
Edge Sampling ◽  
The Impact

Purpose The conventional statistical method of three-dimensional tolerance analysis requires numerous pseudo-random numbers and consumes enormous computations to increase the calculation accuracy, such as the Monte Carlo simulation. The purpose of this paper is to propose a novel method to overcome the problems. Design/methodology/approach With the combination of the quasi-Monte Carlo method and the unified Jacobian-torsor model, this paper proposes a three-dimensional tolerance analysis method based on edge sampling. By setting reasonable evaluation criteria, the sequence numbers representing relatively smaller deviations are excluded and the remaining numbers are selected and kept which represent deviations approximate to and still comply with the tolerance requirements. Findings The case study illustrates the effectiveness and superiority of the proposed method in that it can reduce the sample size, diminish the computations, predict wider tolerance ranges and improve the accuracy of three-dimensional tolerance of precision assembly simultaneously. Research limitations/implications The proposed method may be applied only when the dimensional and geometric tolerances are interpreted in the three-dimensional tolerance representation model. Practical implications The proposed tolerance analysis method can evaluate the impact of manufacturing errors on the product structure quantitatively and provide a theoretical basis for structural design, process planning and manufacture inspection. Originality/value The paper is original in proposing edge sampling as a sampling strategy to generating deviation numbers in tolerance analysis.

Three-dimensional analysis of anchored wall with concrete bearing pads

2020 ◽  
Vol 18 (6) ◽  
pp. 1469-1486
Author(s):  
Hamed Arefizadeh ◽  
Hadi Shahir
Keyword(s):  
Design Methodology ◽  
Three Dimensional ◽  
Bending Moments ◽  
Dimensional Model ◽  
Discrete Elements ◽  
Three Dimensional Model ◽  
Content Type ◽  
Finite Element Software ◽  
Internal Forces ◽  
Soldier Pile

Purpose Anchorage with concrete bearing pad is commonly used in Iran for stabilization of excavations because of the ease of construction, less costs and less time consumption than the soldier pile method. In this method, a wall facing which includes the concrete bearing pads at the location of the anchors and a shotcrete layer between the bearing pads is constructed parallel to the excavation operation similar to the nailing method. Design/methodology/approach In this paper, using the finite element software Abaqus, a three-dimensional model of the above-mentioned type of wall is constructed, and the effect of spacing and size of bearing pads on the wall behavior is discussed. Findings According to the obtained results, the size of the concrete bearing pads has little effect on wall deformations, but the internal forces and bending moments developed in the shotcrete layer between the bearing pads are greatly influenced by the bearing pads dimensions and spacing. Originality/value Owing to the discrete elements of the wall facing, the behavior of this system is completely three-dimensional.

Three dimensional flow of an Oldroyd-B fluid with Newtonian heating

2015 ◽  
Vol 25 (1) ◽  
pp. 68-85 ◽  
Author(s):  
M. Ramzan ◽  
M. Farooq ◽  
M. S. Alhothuali ◽  
H. M. Malaikah ◽  
W. Cui ◽  
...  
Keyword(s):  
Temperature Profile ◽  
Design Methodology ◽  
Three Dimensional ◽  
Series Solutions ◽  
Analysis Method ◽  
Newtonian Heating ◽  
Three Dimensional Flow ◽  
Content Type ◽  
Homotopy Analysis ◽  
Layer Flow

Purpose – The purpose of this paper is to analyze the boundary layer flow of an Oldroyd-B fluid with Newtonian heating. Design/methodology/approach – Series solutions are found by homotopy analysis method. Findings – Temperature profile increases with an increase in conjugate parameter. Increase in parameter β and Prandtl number Pr decreases the temperature profile. Originality/value – This work does not currently exist in the literature.

A Comparative Study Of Tolerance Analysis Methods

2005 ◽  
Vol 5 (3) ◽  
pp. 247-256 ◽  
Author(s):  
Zhengshu Shen ◽  
Gaurav Ameta ◽  
Jami J. Shah ◽  
Joseph K. Davidson
Keyword(s):  
Patent Application ◽  
Three Dimensional ◽  
Tolerance Analysis ◽  
Analysis Method ◽  
Worst Case ◽  
Analysis Methods ◽  
Tolerance Charts ◽  
Parametric Constraint ◽  
Assembly Constraints ◽  
Tolerance Accumulation

This paper reviews four major methods for tolerance analysis and compares them. The methods discussed are: (1) one-dimensional tolerance charts; (2) parametric tolerance analysis, especially parametric analysis based on the Monte Carlo simulation; (3) vector loop (or kinematic) based tolerance analysis; and (4) ASU Tolerance-Map® (T-Map®) (Patent pending; nonprovisional patent application number: 09/507, 542 (2002)) based tolerance analysis. Tolerance charts deal with worst-case tolerance analysis in one direction at a time and ignore possible contributions from the other directions. Manual charting is tedious and error prone, hence, attempts have been made for automation. The parametric approach to tolerance analysis is based on parametric constraint solving; its inherent drawback is that the accuracy of the simulation results are dependent on the user-defined modeling scheme, and its inability to incorporate all Y14.5 rules. The vector loop method uses kinematic joints to model assembly constraints. It is also not fully consistent with Y14.5 standard. The ASU T-Map® based tolerance analysis method can model geometric tolerances and their interaction in truly three-dimensional context. It is completely consistent with Y14.5 standard but its use by designers may be quite challenging. The T-Map® based tolerance analysis method is still under development. Despite the shortcomings of each of these tolerance analysis methods, each may be used to provide reasonable results under certain circumstances. Through a comprehensive comparison of these methods, this paper will offer some recommendations for selecting the best method to use for a given tolerance accumulation problem.

A small displacement torsor model for 3D tolerance analysis of conical structures

2014 ◽  
Vol 229 (14) ◽  
pp. 2514-2523 ◽  
Author(s):  
Sun Jin ◽  
Hua Chen ◽  
Zhimin Li ◽  
Xinmin Lai
Keyword(s):  
Three Dimensional ◽  
Tolerance Analysis ◽  
Dimensional Euclidean Space ◽  
Small Displacement ◽  
Analysis Method ◽  
Tolerance Zone ◽  
Geometric Tolerances ◽  
Small Displacement Torsor ◽  
Conical Surfaces ◽  
Conical Structures

The small displacement torsor model is a classic three-dimensional tolerance analysis method. It uses three translational vectors and three rotational vectors to represent tolerance information in three-dimensional Euclidean space. However, the target features of this model mainly focused on planes and cylinders in previous studies. Little attention is invested to conical features and their joints which are used widely and more complex than the planar and cylindrical features. The objective of this article is to present a three-dimensional mathematical method of tolerance representation about conical surfaces and their joints based on the small displacement torsor model, and propose a mathematical model of variations and constraint relations of components of the small displacement torsor for conical surfaces caused by geometric tolerances limited by its tolerance zone. In addition, a simple example involving conical structures is used to demonstrate three-dimensional conical tolerance propagation. Both deterministic and statistical results are obtained by this model.

A variational model for 3D tolerance analysis with manufacturing signature and operating conditions

2018 ◽  
Vol 38 (1) ◽  
pp. 10-19 ◽  
Author(s):  
Andrea Corrado ◽  
Wilma Polini ◽  
Giovanni Moroni ◽  
Stefano Petrò
Keyword(s):  
Three Dimensional ◽  
Reference Value ◽  
Tolerance Analysis ◽  
Geometrical Model ◽  
Operating Conditions ◽  
Variational Model ◽  
Assembly Process ◽  
Functional Requirements ◽  
Content Type ◽  
Mechanical Assemblies

Purpose The purpose of this work is to present a variational model able to deal with form tolerances and assembly conditions. The variational model is one of the methods proposed in literature for tolerance analysis, but it cannot deal with form tolerances and assembly conditions that may influence the functional requirements of mechanical assemblies. Design/methodology/approach This work shows how to manage the actual surfaces generated by the manufacturing process and the operating conditions inside the variational model that has been modified to integrate the manufacturing signature left on the surfaces of the parts and the operating conditions that arise during an actual assembly, such as gravity and friction. Moreover, a geometrical model was developed to numerically simulate what happens in a real assembly process and to give a reference value. Findings The new variational model was applied to a three-dimensional case study. The obtained results were compared to those of the geometrical model and to those of the variational model to validate the new model and to show the improvements. Research limitations/implications The proposed approach may be extended to other models of literature. However, its limitation is that it is able to deal with a sphere–plane contact. Practical implications Tolerance analysis is a valid tool to foresee geometric interferences among the components of an assembly before getting the physical assembly. It involves a decrease in the manufacturing costs. Originality/value The main contributions of the study are the insertion of a systematic pattern characterizing the features manufactured by a process, assembly operating conditions and development of a geometrical model to reproduce what happens in a real assembly process.

Mathematical modeling of electron irradiation of oil

2018 ◽  
Vol 35 (5) ◽  
pp. 1998-2009
Author(s):  
Assylzhan Kizbayev ◽  
Dauren Zhakebayev ◽  
Ualikhan Abdibekov ◽  
Askar Khikmetov
Keyword(s):  
Mathematical Model ◽  
Electron Irradiation ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Hydrocarbon Mixture ◽  
Navier Stokes Equation ◽  
Content Type ◽  
The Matrix ◽  
Crank Nicolson

Purpose This paper aims to propose a mathematical model and numerical modeling to study the behavior of low conductive incompressible multicomponent hydrocarbon mixture in a channel under the influence of electron irradiation. In addition, it also aims to present additional mechanisms to study the radiation transfer and the separation of the mixture’s components. Design/methodology/approach The three-dimensional non-stationary Navier–Stokes equation is the basis for this model. The Adams–Bashforth scheme is used to solve the convective terms of the equation of motion using a fourth-order accuracy five-point elimination method, and the viscous terms are computed with the Crank–Nicolson method. The Poisson equation is solved with the matrix sweep method and the concentration and electron irradiation equations are solved with the Crank–Nicolson method too. Findings It shows high computational efficiency and good estimation quality. On the basis of numerical results of mathematical model, the effect of the separation of mixture to fractions with various physical characteristics was obtained. The obtained results contribute to the improvement of technologies for obtaining high-quality oil products through oil separation into light and heavy fractions. Mathematical model is approbated based on test problem, and has good agreement with the experimental data. Originality/value The constructed mathematical model makes developing a methodology for conducting experimental studies of this phenomenon possible.

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