Three Dimensional Manufacturing Tolerance Design Using Convex Sets

High demand of wide use of three-dimensional operation models in process planning has resulted in an urgent exploration of new approaches to 3D manufacturing process design. In this paper, 3D process dimension and manufacturing tolerance design issue is studied. A 3D tolerance zone calculation method is developed. The method consists of two procedures including 3D tolerance zone modeling and its calculation. Small displacement torsors (SDT), in conjunction with the robotics kinematics, are utilized to establish the algebra model of the 3D tolerance zone and the tolerance propagation model. Convex sets theory is applied in the calculation and optimization of the size of the zone. The proposed method facilitates the design of the tolerance of the zone by using the variation ranges of uncertain parameters instead of the tolerance distribution. An example of 3D manufacturing tolerance design for a prismatic part is provided with Monte Carlo simulation results to illustrate the effectiveness of the proposed approach.