Product Tolerance Allocation in Compliant Multistation Assembly Through Variation Propagation and Analytical Target Cascading

Abstract

Compliant sheet metal assembly is a hierarchical manufacturing process that plays a significant role in automotive product development. Parts are joined in different stations to form the final product (e.g., the vehicle body structure). Dimensional variation is a product attribute of major importance that characterizes quality, and is mainly affected by the variability of parts, fixtures, and joining methods at each of the multiple stations. The propagation of dimensional variation through the multistation assembly 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 apply the analytical target cascading process to the tolerance allocation problem in multistation assembly systems. Specifically, we translate final product variation targets to tolerance specifications for subassemblies and incoming parts. We demonstrate the methodology by means of a vehicle side frame assembly example.

Compliant assembly tolerance analysis: guidelines to formalize the resistance spot welding plasticity effects

“…Manarvi et al [11] and Li et al [12] defined a framework for tolerance synthesis, which considered the assembly architecture, the manufacturing process and the part deformability by finite element analysis (FEA).…”

Sequential linearization in analytical target cascading for optimization of complex multilevel systems

“…Augmented Lagrangian uses an additional penalty in addition to the quadratic objective function as shown in equation (4). The λ are the Lagrange multipliers and their existence have shown to improve the efficiency of ATC for ill-conditioned cases.…”

“…4. The LATC top-down iteration 4 . Upon receiving the responses from the lower levels, equation (18) is re-run with the updated R 1,(k) 1 = R 1 * 1 The LATC for iteration k will converge at this point since all subsystems are linear and no further improvements can be made.…”

“…Originated from the automotive industries, the ATC has been demonstrated in many engineering applications such as tolerance allocation of multistation assembly line [4], vehicle suspensions [5], military vehicle design [6], and engine piston ring/cylinder liner design [7]. In addition to the engineering field, the ATC is also applied in multidisciplinary field such as architecture [8], enterprise decision making [9], and marketing [10].…”

Tolerance Analysis of a Deformable Component Using the Probabilistic Approach and Kriging-Based Surrogate Models

“…This strategy, known as the influence coefficients method, has been applied with success to multiple problems, see e.g. (Dahlström and Lindkvist 2006;Li et al 2004;Lindau et al 2015). The method is applicable only if (i) the coefficient of variation associated with the uncertain dimensions is sufficiently small (in order they have no effects on the stiffness matrix); (ii) the materials behavior is linear (or the strain is sufficiently small to have a linear material behavior).…”