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

Presents algorithms to propagate and control variation in mechanical assemblies using the state transition model approach. It exploits the modeling environment and uses concepts from control theory to model variation propagation and control during assembly. The assembly process is modeled as a multistage linear dynamic system. Two types of assemblies are addressed: Type-1 where the assembly process puts together parts at their pre-fabricated mating features and Type-2 where the process can incorporate in-process adjustments to redistribute variation. Algorithms are developed to determine and control variation in final assembly propagated through the combined effect of individual part variations and choice of assembly methods. Algorithms to propagate variation in the presence of adjustments are also presented. In-process adjustments in Type-2 assemblies are determined by the type of interface features between parts being assembled which are modeled as control inputs to the dynamic system. An optimal control problem is formulated to design these interfaces. Variation associated with final assembly dimensions, cost of making adjustments, and assembly sequence effects are included in the optimization procedure.