Tolerance allocation for compliant beam structure assemblies

This paper presents a tolerance allocation methodology for compliant beam structures in automotive and aerospace assembly processes. The compliant beam structure model of the product does not require detailed knowledge of product geometry and thus can be applied during the early design phase to develop cost-effective product specifications. The proposed method minimizes manufacturing costs associated with tolerances of product functional requirements (key product characteristics, KPCs) under the constraint(s) of satisfying process requirements (key control characteristics, KCCs). Misalignment and fabrication error of compliant parts, two critical causes of product dimensional variation, are discussed and considered in the model. The proposed methodology is developed for stochastic and deterministic interpretations of optimally allocated manufacturing tolerances. An optimization procedure for the proposed tolerance allocation method is developed using projection theory to considerably simplify the solution. The non-linear constraints, the ellipsoid defined by τ (stochastic case) or rectangle defined by T_x (deterministic case) lie within the KCC region, are transformed into a set of constraints that are linear in σ (or T_x)-coordinates. Experimental results verify the proposed tolerance allocation method.