Rapid prediction and analysis of the static stiffness in the full working space of the CNC gear shaping machine

In order to solve the problem that it is difficult to achieve rapid prediction while ensuring the calculation accuracy in the analysis of the global static stiffness of the whole machine tool, a method for rapid prediction and analysis of the global static stiffness of the CNC gear shaping machine is proposed. Firstly, a static stiffness model of the substructure was established based on the static condensation and surrogate model, and a static stiffness model of the joint was established based on the static condensation and lumped parameter method. Secondly, the obtained substructure static stiffness matrix was combined with the joint static stiffness matrix to establish a semi-analytical static stiffness model of the entire machine tool that is position dependent. Thirdly, by comparing the computational efficiency and results of the finite element model with the proposed model, the correctness and effectiveness of the model were verified, and the distribution law of relative displacement at the end of the machine tool in the workspace under specific working conditions was analyzed. Finally, based on sensitivity analysis, the weak links in the static stiffness of the machine tool were identified. By improving the stiffness parameters of the corresponding links, the relative displacement at the end of the machine tool was effectively reduced.