Modeling and controlling variation propagation in mechanical assemblies using state transition models

This paper presents algorithms to propagate and control variation in mechan ical assemblies using the State Transition Model approach, It exploits the modeling environment and uses concepts from control theory to model variati on propagation and control during assembly, The assembly process is modeled as a multistage linear dynamic system, Tyro types of assemblies are addres sed: Type-1 where the assembly process puts together parts at their pre-fab ricated mating features and Type-2 where the process can incorporate in-pro cess adjustments to redistribute variation. Algorithms are developed to det ermine and control variation in final assembly propagated through the combi ned effect of individual part variations and choice of assembly methods, Al gorithms to propagate variation in the presence of adjustments are also pre sented. In-process adjustments in Type-2 assemblies are determined by the t ype of interface features between parts being assembled which are modeled a s control inputs to the dynamic system. An optimal control problem is formu lated to design these interfaces, Variation associated with final assembly dimensions, cost of making adjustments, and assembly sequence effects are i ncluded in the optimization procedure.