The Tolerance Optimization Problem Using a System of Experimental Design

1994 ◽  
Author(s):  
M. H. Gadallah ◽  
H. A. ElMaraghy
Keyword(s):  
Experimental Design ◽  
Optimization Problem ◽  
State Of The Art ◽  
Tolerance Analysis ◽  
Synthesis Methods ◽  
Manufacturing Cost ◽  
Mechanical Assembly ◽  
Manufacturing Tolerance ◽  
Mechanical Assemblies ◽  
Analysis And Synthesis

Abstract A new algorithm for manufacturing tolerance synthesis is proposed. In complex mechanical assemblies, most tolerance analysis and synthesis methods tend to be impractical. In this article, a methodology is proposed to minimize manufacturing cost by tightening important dimensional and/or geometrical tolerances. Analysis of variance and experimental design techniques are used to discriminate among various design dimensions to the overall functional requirement of the mechanical assembly. In this case, some, but not all, design dimensions will be controlled. This paper reviews the state-of-the art in the area of tolerance analysis and synthesis and highlights the contribution of this work.

Fuzzy Analysis of Geometric Tolerances Using Interval Method

2006 ◽  
Vol 220 (4) ◽  
pp. 489-497 ◽  
Author(s):  
W Wu ◽  
S S Rao
Keyword(s):  
Mechanical System ◽  
Current Approach ◽  
Distribution Functions ◽  
Manufacturing Cost ◽  
Mechanical Assembly ◽  
Geometric Dimensioning And Tolerancing ◽  
Analysis And Synthesis ◽  
Linear Interval ◽  
Linear Interval Equations ◽  
And Performance

The quality and performance of any mechanical system are greatly influenced by the GD&T (geometric dimensioning and tolerancing) used in its design. A proper consideration of the various types of tolerances associated with different components could not only satisfy the assembly requirements, but also minimize the manufacturing cost. To satisfy the design and functional specifications, one has to know how various tolerance patterns affect the manufacturability and assemblability of the designed parts. Therefore, a thorough understanding of how different forms of mechanical tolerances interact with each other becomes a must for designers and manufacturers. The effects of form, orientation, and position tolerances on the kinematic features and dimensions of mechanical systems are analysed using a new approach, based on fuzzy logic, in this article. In this approach, the α-cut method is used with the mechanical tolerances concerned as intervals. The proposed approach represents a more natural and realistic way of dealing with uncertain properties like geometric dimensions. A typical mechanical assembly system involving form, orientation, and position tolerances is used as an illustrative example. As the fuzzy approach leads to systems of non-linear interval equations, a modified Newton-Raphson method is developed for the solution of these equations. The current approach is found to be effective, simple, and accurate and can be extended to the analysis and synthesis of any uncertain mechanical system where the probability distribution functions of the uncertain parameters are unknown.

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.

Manufacturing Tolerance Analysis of a Robot Manipulator’s Joint Axis Orientation Employing Single Monte-Carlo Simulation

2006 ◽  
Author(s):  
Dong Hwan Choi ◽  
Hong Hee Yoo
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Robot Manipulator ◽  
Computing Time ◽  
Tolerance Analysis ◽  
Manufacturing Cost ◽  
Axis Orientation ◽  
Manufacturing Tolerance ◽  
Design Engineers ◽  
Joint Axis

The operation error of a robot manipulator that occurs inevitably due to the manufacturing tolerance needs to be controlled within a certain range to achieve proper performance. The reduction of manufacturing tolerance, however, increases the manufacturing cost in return. Therefore, system design engineers try to solve the problem of maximizing the tolerance to reduce the manufacturing cost while minimizing the operation error to satisfy the performance requirement. In the present study, a revolute joint model considering the variation of joint axis orientation due to joint clearance is employed to perform a tolerance analysis of the robot manipulator operation. This paper presents a hybrid method which employs the sensitivity-based analytic method and the single Monte-Carlo simulation. The proposed method provides rapid implementation and the accurate statistical properties using the only single integration or single iteration for one sample set, whereas the Monte-Carlo method necessitates integrations as the number of samples and cases. Significant reduction of computing time can be achieved with the proposed method. The present method is especially effective if sensitivity information is hard to be obtained for the analysis.

scholarly journals Reliability-based tolerance redesign of mechanical assemblies using Jacobian-Torsor model

2021 ◽  
Vol 104 (2) ◽  
pp. 003685042110132
Author(s):  
Bingxiang Wang ◽  
Xianzhen Huang ◽  
Miaoxin Chang
Keyword(s):  
Optimization Model ◽  
Economic Effect ◽  
Tolerance Analysis ◽  
Lambert W Function ◽  
Mechanical Assembly ◽  
Assembly Tolerance ◽  
Tolerance Optimization ◽  
Geometric Tolerances ◽  
Mechanical Assemblies ◽  
Proposed Model

The purpose of this paper is to present a new method to redesign dimensional and geometric tolerances of mechanical assemblies at a lower cost and with higher reliability. A parametric Jacobian-Torsor model is proposed to conduct tolerance analysis of mechanical assembly. A reliability-based tolerance optimization model is established. Differing from previous studies of fixed process parameters, this research determines the optimal process variances of tolerances, which provide basis for the subsequent assembly tolerance redesign. By using the Lambert W function and the Lagrange multiplier method, the analytical solution of the parametric tolerance optimization model is obtained. A numerical example is presented to demonstrate the effectiveness of the model, while the results indicate that the total cost is reduced by 10.93% and assembly reliability improves by 2.12%. This study presents an efficient reliability-based tolerance optimization model. The proposed model of tolerance redesign can be used for mechanical assembly with a better economic effect and higher reliability.

Application of Polynomial Chaos Expansion to Tolerance Analysis and Synthesis in Compliant Assemblies Subject to Loading

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Maciej Mazur ◽  
Martin Leary ◽  
Aleksandar Subic
Keyword(s):  
Polynomial Chaos ◽  
Process Integration ◽  
Computation Time ◽  
Tolerance Analysis ◽  
Polynomial Chaos Expansion ◽  
Practical Case ◽  
Chaos Expansion ◽  
Mechanical Assemblies ◽  
Analysis And Synthesis ◽  
Statistical Tolerance

Statistical tolerance analysis and synthesis in assemblies subject to loading are of significant importance to optimized manufacturing. Modeling the effects of loads on mechanical assemblies in tolerance analysis typically requires the use of numerical CAE simulations. The associated uncertainty quantification (UQ) methods used for estimating yield in tolerance analysis must subsequently accommodate implicit response functions, and techniques such as Monte Carlo (MC) sampling are typically applied due to their robustness; however, these methods are computationally expensive. A variety of UQ methods have been proposed with potentially higher efficiency than MC methods. These offer the potential to make tolerance analysis and synthesis of assemblies under loading practically feasible. This work reports on the practical application of polynomial chaos expansion (PCE) for UQ in tolerance analysis. A process integration and design optimization (PIDO) tool based, computer aided tolerancing (CAT) platform is developed for multi-objective, tolerance synthesis in assemblies subject to loading. The process integration, design of experiments (DOE), and statistical data analysis capabilities of PIDO tools are combined with highly efficient UQ methods for optimization of tolerances to maximize assembly yield while minimizing cost. A practical case study is presented which demonstrates that the application of PCE based UQ to tolerance analysis can significantly reduce computation time while accurately estimating yield of compliant assemblies subject to loading.

scholarly journals Concurrent optimization of dimensions and tolerances on structures and mechanisms

2020 ◽  
Vol 111 (11-12) ◽  
pp. 3141-3157
Author(s):  
Antonio Armillotta
Keyword(s):  
Tolerance Analysis ◽  
Functional Characteristic ◽  
Sequential Optimization ◽  
Manufacturing Cost ◽  
Power Cost ◽  
Concurrent Optimization ◽  
Mechanical Assemblies ◽  
Dimensional Parameters ◽  
Method Of Lagrange Multipliers ◽  
Planar Linkages

AbstractThe paper deals with a problem of robust optimization of mechanical assemblies, which combines the allocation of tolerances with the selection of dimensional parameters. The two tasks are carried out together with the aim of minimizing the manufacturing cost and the variation on an assembly-level functional characteristic. The problem is addressed in the specific context of planar linkages used in structures and mechanisms. The proposed solution is based on an optimality condition involving both tolerances and dimensions, which allows to define a joint optimization problem avoiding the need of two sequential optimization phases. The condition is developed with the method of Lagrange multipliers using an expanded formulation of the reciprocal power cost-tolerance function. The optimal tolerances depend on the stackup coefficients of the output characteristic, which are calculated with a tolerance analysis method based on a static analogy. The procedure is demonstrated on two examples to illustrate some application details and discuss potential advantages and limitations.

scholarly journals Robust CNN Compression Framework for Security-Sensitive Embedded Systems

2021 ◽  
Vol 11 (3) ◽  
pp. 1093
Author(s):  
Jeonghyun Lee ◽  
Sangkyun Lee
Keyword(s):  
Embedded Systems ◽  
Optimization Problem ◽  
State Of The Art ◽  
Classification Problems ◽  
Proximal Gradient Method ◽  
Knowledge Distillation ◽  
New Type ◽  
Adversarial Examples ◽  
Adversarial Training ◽  
Memory Efficient

Convolutional neural networks (CNNs) have achieved tremendous success in solving complex classification problems. Motivated by this success, there have been proposed various compression methods for downsizing the CNNs to deploy them on resource-constrained embedded systems. However, a new type of vulnerability of compressed CNNs known as the adversarial examples has been discovered recently, which is critical for security-sensitive systems because the adversarial examples can cause malfunction of CNNs and can be crafted easily in many cases. In this paper, we proposed a compression framework to produce compressed CNNs robust against such adversarial examples. To achieve the goal, our framework uses both pruning and knowledge distillation with adversarial training. We formulate our framework as an optimization problem and provide a solution algorithm based on the proximal gradient method, which is more memory-efficient than the popular ADMM-based compression approaches. In experiments, we show that our framework can improve the trade-off between adversarial robustness and compression rate compared to the existing state-of-the-art adversarial pruning approach.

The smallest extraction problem

2021 ◽  
Vol 14 (11) ◽  
pp. 2445-2458
Author(s):  
Valerio Cetorelli ◽  
Paolo Atzeni ◽  
Valter Crescenzi ◽  
Franco Milicchio
Keyword(s):  
Unsupervised Learning ◽  
Optimization Problem ◽  
Learning Algorithm ◽  
State Of The Art ◽  
Data Extraction ◽  
Source Code ◽  
Web Data ◽  
Web Data Extraction ◽  
New Family ◽  
Context Free

We introduce landmark grammars , a new family of context-free grammars aimed at describing the HTML source code of pages published by large and templated websites and therefore at effectively tackling Web data extraction problems. Indeed, they address the inherent ambiguity of HTML, one of the main challenges of Web data extraction, which, despite over twenty years of research, has been largely neglected by the approaches presented in literature. We then formalize the Smallest Extraction Problem (SEP), an optimization problem for finding the grammar of a family that best describes a set of pages and contextually extract their data. Finally, we present an unsupervised learning algorithm to induce a landmark grammar from a set of pages sharing a common HTML template, and we present an automatic Web data extraction system. The experiments on consolidated benchmarks show that the approach can substantially contribute to improve the state-of-the-art.

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