Product and process tolerance allocation in multistation compliant assembly using analytical target cascading

Tolerance allocation is the process of determining allowable dimensional variations in products ( parts and subassemblies) and processes ( fixtures and tools) in order to meet final assembly quality and cost targets. Traditionally, tolerance allocation is conducted by solving a single optimization problem. This "all-in-one" (AIO) approach may not be desirable or applicable for various reasons: the assembler of the final product may not have access to models and/or data to compute appropriate tolerance values for all subassemblies and parts in the case of outsourcing; optimization algorithms may face numerical difficulties when solving very large-scale, simulation-based nonlinear problems; interactions are often obscured in AIO models and trade-offs may not be quantifiable readily. This paper models multistation compliant assembly as a hierarchical multilevel process and proposes the application of analytical target cascading for formulating and solving the tolerance allocation problem. Final product quality and cost targets are translated into tolerance specifications for incoming parts, subassemblies, and station fixtures. The proposed methodology is demonstrated using a vehicle side frame assembly example. Both quality- and cost-driven tolerance allocation problems are formulated. A parametric study with respect to budget is conducted to quantify the cost-quality trade-off. We believe that the proposed multilevel optimization methodology constitutes a valuable new paradigm for tolerance design in multistation assembly involving a large number of parts and stations, and creates research opportunities in this area.