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This paper presents modified relations for worst-case and root-sum-square (RSS) tolerance accumulation models for tolerance analysis of mechanical assemblies with asymmetric tolerances. The common models do not consider the sign of the sensitivity factors and thus are applicable to symmetric tolerances only. Using the new models, the accumulation of asymmetric tolerances results in asymmetric assembly tolerances. New relationships for estimation of percent contributions of individual tolerances are also introduced which yield percent contributions of upper and lower bounds of independent variables (manufacturing dimensions) on the upper and lower bounds of dependent variables (assembly dimensions). The modified methods and new relations are applied to linear and nonlinear examples and their results are discussed.

Tolerance analysis is essential for estimation of final error of key product characteristic (KPC) in a mechanical assembly caused by errors in production and assembly of individual parts. Many mechanical assemblies, especially in automotive and aerospace industries, include sheet metal parts with a small ratio of thickness to width or length. Such parts are substantially flexible and thus, are prone to large errors due to elastic deformations during assembly production. Phenomena such as deformation due to fixture force, spring back, welding distortion and so on are common to such parts. Unlike tolerance analysis of rigid parts, here, the elastic deformation of the parts plays a significant role in the error, and thus stress analysis of the parts, e.g. using finite element method, is necessary. In this article, the influence of tolerance between locator and pin hole in the assembly fixture on the KPC error is studied using a probabilistic design approach.

The process capability indices are widely used to measure the capability of the process to manufacture objects within the required tolerance. Fit quality is mainly dominated by the distribution of fit dimensions, i.e., a gap dimension. As the fit dimensions are very difficult to be measured in mass production, they are not to be considered as a direct inspection objective. The quality inspection and evaluation relative to fit quality are focused on whether the processes of assembly requirements are conformed with their specification limits respectively. Fit quality specification can be indicated by the process capability indices of mating parts. In this paper, the statistical-based process capability analysis method is presented to estimate ability of manufacturing process for considering of assembly requirements and fit quality in a mechanical assembly with asymmetric tolerances.

In this paper, a tolerance allocation approach is proposed which attempts to select tolerances for individual dimensional variables of a product in a way that minimizes the cost while maintaining critical design requirements. The algorithm uses a reciprocal power cost-tolerance function which incorporates variable sensitivities computed in a DLM-based tolerance analysis technique. The process capabilities are applied as constraints and the genetic algorithm is used to find the optimum solution. The method is applied to a heavy duty brake problem and its results are presented.

Radial forging and indentation forging processes are two processes used for sizing and/or internal profiling of tubes. In this paper, the two processes are simulated using finite element method and their results are compared with Experimental results. The purpose of this paper is to compare the pattern of residual stresses in both processes.

The design process always has some known or unknown uncertainties in the design variables and parameters. The aim of robust design is minimization of performance sensitivity to uncertainties. Tolerance allocation process can significantly affect quality and robustness of the product. In this paper, a methodology to minimize a product's sensitivity to uncertainties by allocating manufacturing tolerances is presented. The robust tolerance design problem is formulated as a multi-objective optimization based on the combined function-uncertainty-cost model. Genetic algorithm is utilized to solve the multi-objective optimization and a case study is presented to illustrate the methodology.

Angular contact ball bearings are the most commonly used types of bearings. Although simple in appearance, these bearings have a complicated and nonlinear behavior, and have significant effect on the dynamics of a rotating system. Accounting for high speed effects adds to the complexity of their behavior. The governing equations of the bearing amount to the solution of a set of nonlinear equations for each rolling element at each iteration, which represents a tedious and expensive solution. In this work, a simplified model for angular contact ball bearings under the action of arbitrary loading including high speed effects and preload is presented. The model considers five degrees of freedom for relative displacement of rings and a mean contact angle for inner and outer raceway contacts are introduced which renders the solution for all rolling elements to that for a single one.