Optimal tolerance allocation for five-axis machine tools in consideration of deformation caused by gravity

Due to the effect of gravity on machine tools, the small deformations inevitably exist. The existing tolerance allocation methods are based on the rigid body assumption, which ignore the small deformations. It will make optimization results inaccurate and increase manufacturing cost. Therefore, a new optimal tolerance allocation method, which integrates the small deformations, is presented in this paper. The establishment of a geometric error model based on tolerance is involved at first. Based on this model and multi-body system theory, the mapping relationship between tolerance and volumetric error of the five-axis machine tool (FAMT) is formulated. Secondly, the small deformations of the FAMT are obtained based on finite element analysis. Then, the optimal tolerance allocation model is established by integrating the small deformations into the constraint conditions. Thirdly, simulation analysis is carried out with this model by using a genetic algorithm. Then, the optimal tolerance allocation scheme is obtained, and the total manufacturing cost after optimization is reduced by approximately 11.5%. Finally, the volumetric errors of the FAMT are calculated based on the two tolerance allocation schemes. The results show that the volumetric errors are within the permitted ranges. Therefore, the proposed method in consideration of the small deformation is feasible and effective.