Simulation of Mating Between Non-Analytic Surfaces Using a Mathematical Programming Formulation

2005 ◽  
Author(s):  
Robert Scott Pierce ◽  
David Rosen
Keyword(s):  
Constrained Optimization ◽  
End Milling ◽  
Tolerance Analysis ◽  
Mechanical Assembly ◽  
Solution Algorithms ◽  
Solution Methods ◽  
Gradient Based ◽  
Unconstrained Problem ◽  
Typical Component ◽  
Randomized Search

In this paper we describe a new method for simulating mechanical assembly between components that are composed of surfaces that do not have perfect geometric form. Mating between these imperfect form surfaces is formulated as a constrained optimization problem of the form “minimize the distance from perfect fit, subject to non-interference between components.” We explore the characteristics of this mating problem and investigate the applicability of several potential solution algorithms. The problem can be solved by converting the constrained optimization formulation into an unconstrained problem using a penalty-function approach. We describe the characteristics of this unconstrained formulation and test the use of two different solution methods: a randomized search technique and a gradient-based method. We test the algorithm by simulating mating between component models that exhibit form errors typically generated in end-milling processes. These typical component variants are used as validation problems throughout our work. Results of two different validation problems are presented. Using these results, we evaluate the applicability of the mating algorithm to the problem of mechanical tolerance analysis for assemblies and mechanisms.

Assembleability Analysis Using GapSpace Model for 2D Mechanical Assembly

2002 ◽  
Author(s):  
Zhihua Zou ◽  
Edward P. Morse
Keyword(s):  
Sufficient Conditions ◽  
Tolerance Analysis ◽  
Necessary And Sufficient Conditions ◽  
Statistical Analyses ◽  
Important Task ◽  
Assembly Model ◽  
Mechanical Assembly ◽  
Worst Case ◽  
Solution Methods ◽  
Necessary And Sufficient

The most fundamental, and perhaps most important, task in tolerance analysis is to test whether or not the components with tolerances are actually able to fit together. This problem doesn’t get much explicit attention because it is implicitly included in current tolerance analysis methods. However, for complex assemblies, especially for over-constrained assemblies, the implicit assumptions of assembly may not be valid. This paper proposes an assembly model, called GapSpace, which can capture the necessary and sufficient conditions needed to execute assembleability analysis. Assembleability analyses for both nominal components and those with tolerances are presented using the GapSpace model. Both worst case and statistical analyses are performed. The model and its attendant solution methods are more suitable to GD&T tolerancing than traditional plus/minus tolerancing.

Statistical Tolerance Analysis of Over-Constrained Mechanical Assemblies With Form Defects Considering Contact Types

2019 ◽  
Vol 19 (2) ◽  
Author(s):  
Edoh Goka ◽  
Lazhar Homri ◽  
Pierre Beaurepaire ◽  
Jean-Yves Dantan
Keyword(s):  
Tolerance Analysis ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
Behavior Modeling ◽  
Functional Requirements ◽  
Mechanical Assembly ◽  
Mechanical Assemblies ◽  
Statistical Tolerance ◽  
The Individual ◽  
Statistical Tolerance Analysis

Tolerance analysis aims toward the verification impact of the individual tolerances on the assembly and functional requirements of a mechanism. The manufactured products have several types of contact and are inherent in imperfections, which often causes the failure of the assembly and its functioning. Tolerances are, therefore, allocated to each part of the mechanism in purpose to obtain an optimal quality of the final product. Three main issues are generally defined to realize the tolerance analysis of a mechanical assembly: the geometrical deviations modeling, the geometrical behavior modeling, and the tolerance analysis techniques. In this paper, a method is proposed to realize the tolerance analysis of an over-constrained mechanical assembly with form defects by considering the contacts nature (fixed, sliding, and floating contacts) in its geometrical behavior modeling. Different optimization methods are used to study the different contact types. The overall statistical tolerance analysis of the over-constrained mechanical assembly is carried out by determining the assembly and the functionality probabilities based on optimization techniques combined with a Monte Carlo simulation (MCS). An application to an over-constrained mechanical assembly is given at the end.

Lateral Dynamics Optimization of a Conventional Railcar

1975 ◽  
Vol 97 (3) ◽  
pp. 293-299 ◽  
Author(s):  
N. K. Cooperrider ◽  
J. J. Cox ◽  
J. K. Hedrick
Keyword(s):  
Constrained Optimization ◽  
High Speed ◽  
Optimization Problem ◽  
Ride Comfort ◽  
Stability Margin ◽  
Railway Vehicle ◽  
Constrained Optimization Problem ◽  
Stroke Length ◽  
Car Body ◽  
Unconstrained Problem

The attempt to develop a railway vehicle that can operate in the 150 to 300-mph(240 to 480-km/h) speed regime is seriously hampered by the problems of ride comfort, curve negotiation, and “hunting.” This latter phenomena involves sustained lateral oscillations that occur above certain critical forward velocities and cause large dynamic loads between the wheels and track as well as contributing to passenger discomfort. This paper presents results of an initial effort to solve these problems by utilizing optimization procedures to design a high speed railway vehicle. This study indicates that the problem is more easily treated as a constrained optimization problem than as an unconstrained problem with several terms in the objective function. In the constrained optimization problem, the critical “hunting” speed was maximized subject to constraints on 1) the acceleration of the car body, 2) the suspension stroke length, and 3) the maximum suspension stroke while negotiating a curve. A simple, three degree-of-freedom model of the rail vehicle was used for this study. Solutions of this constrained problem show that beyond a minimum yaw stiffness between truck and car body the operating speed remains nearly constant. Thus, above this value, the designer may trade off yaw stiffness, wheel tread conicity and stability margin.

A Variational Framework for Solution Method Developments in Structural Mechanics

1998 ◽  
Vol 65 (1) ◽  
pp. 242-249 ◽  
Author(s):  
K. C. Park ◽  
C. A. Felippa
Keyword(s):  
Rigid Body ◽  
Virtual Work ◽  
Full Rank ◽  
Structural Mechanics ◽  
Direct Construction ◽  
Parallel Solution ◽  
Variational Functional ◽  
Solution Algorithms ◽  
Variational Framework ◽  
Solution Methods

We present a variational framework for the development of partitioned solution algorithms in structural mechanics. This framework is obtained by decomposing the discrete virtual work of an assembled structure into that of partitioned substructures in terms of partitioned substructural deformations, substructural rigid-body displacements and interface forces on substructural partition boundaries. New aspects of the formulation are: the explicit use of substructural rigid-body mode amplitudes as independent variables and direct construction of rank-sufficient interface compatibility conditions. The resulting discrete variational functional is shown to be variation-ally complete, thus yielding a full-rank solution matrix. Four specializations of the present framework are discussed. Two of them have been successfully applied to parallel solution methods and to system identification. The potential of the two untested specializations is briefly discussed.

scholarly journals On a New Optimization Method With Constraints

2020 ◽  
Vol 12 (5) ◽  
pp. 27
Author(s):  
Bouchta x RHANIZAR
Keyword(s):  
Constrained Optimization ◽  
Optimization Problem ◽  
Convex Set ◽  
Optimization Method ◽  
New Method ◽  
Constrained Optimization Problem ◽  
Numerical Examples ◽  
Unconstrained Problem ◽  
Closed Convex Set

We consider the constrained optimization problem  defined by: $$f(x^*) = \min_{x \in  X} f(x) \eqno (1)$$ where the function  $f$ : $ \pmb{\mathbb{R}}^{n} \longrightarrow \pmb{\mathbb{R}}$ is convex  on a closed convex set X. In this work, we will give a new method to solve problem (1) without bringing it back to an unconstrained problem. We study the convergence of this new method and give numerical examples.

On Solution Algorithms for Large Sparse Systems of Normal Equations in Photogrammetry

1981 ◽  
Vol 35 (1) ◽  
pp. 37-51
Author(s):  
Franz Steidler
Keyword(s):  
Bundle Adjustment ◽  
Solution Technique ◽  
Systems Of Equations ◽  
Direct Solution ◽  
Band Matrices ◽  
Normal Equations ◽  
Simple Version ◽  
Solution Algorithms ◽  
Solution Methods ◽  
Sparse Systems

The question of which algorithm is most appropriate for the solution of normal equations with different structures has been investigated. The solution methods are a direct solution for banded and banded-bordered matrices, a special direct solution technique for arbitrary sparse systems of equations and the method of conjugate gradients. The algorithms have first been applied to photogrammetric bundle adjustment with self-calibration, which leads to a banded-bordered matrix of the normal equations, and secondly to calculations of digital height models that are generated by a simple version of the method of finite elements and which lead to band matrices.

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