A Second-Order Method for Assembly Tolerance Analysis

Abstract

Abstract Linear analysis and Monte Carlo simulation are two well-established methods for statistical tolerance analysis of mechanical assemblies. Both methods have advantages and disadvantages. The Linearized Method, a form of linear analysis, provides fast analysis, tolerance allocation, and the capability to solve closed loop constraints. However, the Linearized Method does not accurately approximate nonlinear geometric effects or allow for non-normally distributed input or output distributions. Monte Carlo simulation, on the other hand, does accurately model nonlinear effects and allow for non-normally distributed input and output distributions. Of course, Monte Carlo simulation can be computationally expensive and must be re-run when any input variable is modified. The second-order tolerance analysis (SOTA) method attempts to combine the advantages of the Linearized Method with the advantages of Monte Carlo simulation. The SOTA method applies the Method of System Moments to implicit variables of a system of nonlinear equations. The SOTA method achieves the benefits of speed, tolerance allocation, closed-loop constraints, non-linear geometric effects and non-normal input and output distributions. The SOTA method offers significant benefits as a nonlinear analysis tool suitable for use in design iteration. A comparison was performed between the Linearized Method, Monte Carlo simulation, and the SOTA method. The SOTA method provided a comparable nonlinear analysis to Monte Carlo simulation with 106 samples. The analysis time of the SOTA method was comparable to the Linearized Method.