A new tolerance modeling and analysis methodology through a two-step linearization with applications in automotive body assembly

This paper presents a new tolerance modeling and analysis methodology through a two-step linearization with applications in automotive body assembly. The first step is to establish, for every single component in the assembly, a linear relationship between the deviation input at locating sources, and the deviation output at any user-defined key product/process characteristic (KPC) points on the component. The second step is to linearize the relationship between the first step output (at component level) and the final assembly deviation output (such as gaps and flushness). The novelty of the two-step linearization method is in its ability to separately linearize the geometric relationship at component and assembly levels, eliminating the need to linearize the nonlinear, multicomponent assembly relationships analytically or numerically. The statistical models for position tolerances are studied, as frequently occur in automotive body assembly (that is, pin + hole locating). A case study is presented to demonstrate the new method. The limitation of the new method is discussed along with examples of nonlinearizable assemblies. The linearized tolerancing method presented is advantageous to the traditional Monte Carlo simulation in its computational efficiency, thus enabling advanced manufacturing process syntheses such as tolerance allocation and optimization, and assembly sequence optimization.