Proceedings of IMECE 2004 2004 ASME International Mechanical Engineering Congress and Exposition Anaheim, California, USA, November 13-19, 2004 IMECE2004-60521 PRODUCT TOLERANCE ALLOCATION IN COMPLIANT MULTISTATION ASSEMBLY THROUGH VARIATION PROPAGATION AND ANALYTICAL TARGET CASCADING Zhijun Li, Jianpeng Yue, Michael Kokkolaras ∗ , Jaime Camelio, Panos Y. Papalambros, and S. Jack Hu {zhijunl,yuej,mk,jcamelio,pyp,jackhu}@umich.edu Department of Mechanical Engineering University of Michigan Ann Arbor, Michigan ABSTRACT Compliant sheet metal assembly is a hierarchical manufac- turing process that plays a significant role in automotive product development. Parts are joined in different stations to form the fi- nal product (e.g., the vehicle body structure). Dimensional varia- tion is a product attribute of major importance that characterizes quality, and is mainly affected by the variability of parts, fix- tures, and joining methods at each of the multiple stations. The propagation of dimensional variation through the multistation as- sembly system is modeled as a linear process, where all three aforementioned sources of variability are taken into account at each station using finite element models. In this article we ap- ply the analytical target cascading process to the tolerance allo- cation problem in multistation assembly systems. Specifically, we translate final product variation targets to tolerance specifica- tions for subassemblies and incoming parts. We demonstrate the methodology by means of a vehicle side frame assembly exam- ple. INTRODUCTION Product tolerance allocation is the process of determining component tolerances using appropriate rules to satisfy final as- sembly tolerance targets that are known from design require- ments [1]. It is performed early in the product development cycle, before any parts have been produced or tooling ordered. ∗ Corresponding author, Phone/Fax: (734) 615-8991/647-8403 In order to optimally allocate tolerances in a multistation as- sembly process, the interrelations between tolerance, quality and cost need to be understood and demonstrated. Overall, there are three key elements to realize the optimization process: a varia- tion propagation model, a tolerance-variation relation, and a cost function. Station-to-station variation propagation in multistation man- ufacturing processes is described using a state space represen- tation. Some multistation variation propagation models have been developed for different processes, such as rigid-part assem- bly [2, 3, 4], compliant-part assembly [5], machining [6, 7], and stretch forming [8], where the multistation process is treated as a sequential dynamic system but the time index in the traditional state space model is replaced with a station index. With these de- velopments it is possible to conduct tolerance allocation in mul- tistation manufacturing processes. Design evaluation of multistation manufacturing processes depends on a group of critical features that are important to sat- isfy performance requirements. In the automotive industry, this group of critical features are known as KPCs (Key Product Char- acteristics). The key parameters for processes, known as KCCs (Key Control Characteristics) have an impact on KPCs’ dimen- sional accuracy and in turn affect the final product quality. There- fore, tolerance-variation relation for KPCs, KCCs, and their in- terrelation need to be addressed. Under the assumption that di- mensional variations occur randomly, the production process is said to be in statistical control [9]. Thus, tolerance is always related to parameters of probabilistic distributions, such as vari- 1 Copyright c  2004 by ASME