During the operation of CNC machine tools,the stiffness and inertia of the multi-axis ball screw feed system will change with the change of the poses of the feeding shafts,resulting in the time-varying characteristics of its dynamic characteristics.The high-fidelity modeling and analysis of the time-varying dynamic characteristics of the multi-axis ball screw feed system has become one of the bottlenecks in the accurate prediction of the contour error of CNC machine tools.Aiming at this problem,a rigid-flexible coupling dynamic modeling and analysis method of ball screw feed system based on Lagrange equation and Ritz series method was proposed.Taking the two-axis ball screw feed system of a five-axis machining center as the specific object,the rigid-flexible coupling dynamic model of the ball screw feed system was established by using the Lagrange equation,and the Ritz series method was used to solve the equation,and the numerical solution of the dynamic model was obtained.The influence of the poses of the feeding shaft on the natural frequency and modal shape of the two-axis feed system was analyzed by using the established dynamic model.It is found that the variation of the natural frequency and modal shape of each order with the poses of the feeding shaft is related to the dominant axis of the corresponding order.As the feed table of the main shaft moves from the fixed end to the support end,the natural frequency of the corresponding order gradually decreases,and the elastic vibration amplitude of the screw body in the corresponding modal mode gradually increases.In addition,the low-order modal shapes of the two-axis feed system are mainly dominated by the bearing shaft,and the high-order modal shapes are mainly dominated by the sub-shafts attached to the bearing shaft.Finally,the application of the proposed method is verified by modal experiments to prove the accuracy of the established dynamic model.The research results have important reference value for the accurate prediction of contour error of CNC machine tools.