Optimal tolerance design of mechanical assemblies for economical manufacturing in the presence of alternative machines – a genetic algorithm-based hybrid methodology P K Singh 1 *, P K Jain 2 , and S C Jain 2 1 Department of Mechanical Engineering, Sant Longowal Institute of Engineering and Technology, Longowal, India 2 Department of Mechanical and Industrial Engineering, Indian Institute of Technology, Roorkee, India The manuscript was received on 30 July 2007 and was accepted after revision for publication on 22 January 2008. DOI: 10.1243/09544054JEM967 Abstract: Traditional practice to tolerance design has been based on a sequential approach to design and manufacturing considerations. Integrated tolerance design involving simultaneous selection of design and manufacturing tolerances was introduced in the last decade. Choice of manufacturing processes (or machines) from among the alternatives, frequently encoun- tered in different stages of realization of individual dimensions, is an important issue in product development. The problem becomes more complicated if the available alternative manufactur- ing processes (or machines) have a non-overlapping precision range. The optimal tolerance design problem formulated with these issues considering both the cases of overlapping and non-overlapping precision range, based on different stack-up conditions, such as the worst case, root sum square, and Spotts’ modified criteria is the focus of this study. The resulting opti- mization problem involving a combinatorial, non-linear, non-convex search space cannot be effectively solved for a global solution using conventional optimization techniques. Genetic algorithm, a non-traditional optimization technique, is useful to solve such a complex problem to obtain a near-global solution. This solution may further be improved by making subsequent use of conventional techniques appropriately. In this research a hybrid approach has been pro- posed based on this philosophy. In the first step, a near-global solution is obtained using the genetic algorithm; in the second step the optimal solution obtained in the first step is refined using the MATLAB-optimization-toolbox. The study has been planned to obtain a better insight into solution of the tolerance design problem, and has been demonstrated with the help of a numerical example. Keywords: tolerance design, design tolerances, manufacturing tolerances, machine selection, overlapping and non-overlapping precision ranges, genetic algorithms, MATLAB-optimization- toolbox 1 INTRODUCTION Tolerance design plays an important role in product design and development process. It is an important link between the product-functional-requirements and the manufacturing cost. Unnecessarily tight tolerances lead to higher manufacturing cost, while the loose ones may result in malfunctioning of the assembly. The topic has been the focus of attention of a large number of researchers for decades. A review of research on the topic has been presented by several authors [1–5]. Traditionally, the tolerance design is carried out sequentially in steps: (a) toler- ance design in computer-aided design (CAD), to obtain an appropriate set of design tolerances for individual dimensions considering functionality of the product; and (b) tolerance design in computer- aided process planning (CAPP), to obtain an appro- priate set of manufacturing tolerances for various *Corresponding author: Department of Mechanical Engineering, Sant Longowal Institute of Engineering and Technology, Longowal, Sangrur, Punjab 148106, India. email: pkschauhan@ yahoo.com 591 JEM967 Ó IMechE 2008 Proc. IMechE Vol. 222 Part B: J. Engineering Manufacture