Modeling and controlling variation in mechanical assemblies using state transition models

This paper presents a State Transition Model model of assembly and concepts from control theory to model variation propagation and control during assembly. The assembly process is modeled as a multi-stage linear dynamic system. Two types of assemblies are addressed: Type-1 where the assembly puts together parts at their pre-fabricated mating features, and Type-2 where the assembly process can incorporate in-process adjustments to redistribute variation. The model builds on the concept of the Datum Flow Chain. 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. An optimal control problem is formulated to develop a scientific approach to designing assembly features.