Optimal tolerance allocation for precision machine tools in consideration of measurement and adjustment processes in assembly

The high geometric accuracy requirement of precision machine tools represents a challenge for tolerance design and assembly process planning that guarantee the final assembly accuracy. Component tolerances should be allocated in association with assembly processes. However, tolerance design and assembly process planning are usually considered separately and lack quantitative analysis. In this paper, to integrate the geometric tolerance of components and variation propagation in assembly process, a state space model is developed. The measurement and adjustment process are expressed as observation matrix and control inputs. An optimal control problem is formulated to determine the adjustment process in consideration of the loss of final assembly accuracy and costs of remachining adjustment process. Tolerances of components can be optimally allocated based on the variation propagation in this deterministic assembly process. The generality and effectiveness of this approach are validated by applying the model on a four-axis horizontal machining center.