State space modeling of dimensional variation propagation in multistage machining process using differential motion vectors

In this paper, a state space model is developed to describe the dimensional variation propagation of multistage machining processes. A complicated machining system usually contains multiple stages. When the workpiece passes through multiple stages, machining errors at each stage will be accumulated and transformed onto the workpiece. Differential motion vector, a concept from the robotics field, is used in this model as the state vector to represent the geometric deviation of the workpiece. The deviation accumulation and transformation are quantitatively described by the state transition in the state space model. A systematic procedure that builds the model is presented and an experimental validation is also conducted. The validation result is satisfactory. This model has great potential to be applied to fault diagnosis and process design evaluation for complicated machining processes.