A dynamic dimensional accumulation with propagations of part mating gaps for series-parallel assembly operations

Abstract

The changing spring-back effects of part mating gaps restrict the control of the overall dimensional error for the parts assembled by many sequential and parallel processes. So far, it has been merely adjusted by component positions or compensated by some joining processes, which is still limited and lack of a theory and tool for the general dynamic process. To obtain the dimensional response of current assembly when the part contacts with the other, this paper proposes algebraic modelling for dimensional error accumulations that organize the propagation through every part. A new contact graph firstly expresses the part liaisons. Then, a variable array encodes the displacements and the time when each contact finishes, which yields algebraic theorems for the conversion of contact graph to algebraic expression, and for estimating dimensional distortions. If propagations take finite element methods, the algebraic expression outputs the coupled spring-back effects for the current assembled parts that support both variation and tolerance analyses. The dynamic accumulation with propagations is validated by case studies, and the comparison indicates that the assembly with the largest number of parallel modes has the highest nonlinear variations caused by locating errors.