Variation simulation for deformable sheet metal assembly.

Abstract

Currently, the most commonly used methods for dimensional variation simulation analysis are worst case analysis, root sum square method, and Monte Carlo simulation. In all these methods, individual parts are considered as rigid bodies, and aggregate behaviors are determined by geometric and/or kinematic relations between the parts. However, for assemblies that consist of deformable sheet metal parts, the variation of parts does not stack-up as these models predict because of possible part deformation. This dissertation presents a new approach--variation simulation using mechanistic models, or mechanistic variation simulation. Mechanistic variation simulation combines engineering structural models with statistical techniques for analyzing the variation stack-up of deformable sheet metal assemblies. Mechanistic variation simulation models can be obtained analytically or numerically. Analytical models and numerical models are developed based on the geometrical complexity of sheet metal parts. Analytical models are derived for assemblies with one-dimensional sheet metal parts using simple engineering structural models and fundamental statistics. An offset beam element is constructed to solve problems involving complex one-dimensional part assemblies. Numerical models are developed for predicting assembly variation with complex two or three-dimensional free-form surface parts using finite element methods. Experiments have been conducted to verify the mechanistic variation simulation models. A correlation coefficient of 0.92 is obtained between the experimental data and the results of simulation using mechanistic variation simulation. The mechanistic variation simulation models are applied to evaluating joint design and spot welding sequences for sheet metal assemblies. The variation characteristics of the three basic joints (lap joints, butt joints, and butt-lap joints) and the boxes made from them are evaluated. The mechanistic variation models are extended to investigate the impact of spot weld sequences on product dimensional variation. Based on the results of sequence evaluation, some guiding principles for the synthesis of spot weld sequences are proposed. The developed variation simulation models and analyses provide improved understandings of sheet metal product design and process design.