Optimized configuration of the joint stiffness for a dual differential feed system

To avoid the crawling zone of the motor at low speed, the dual differential feed system is designed based on the nut-driven ball screw and the hollow servo motor. Joint stiffness has an important influence on the dynamic characteristics of the dual differential feed system. To improve the vibration resistance together with the stability of the table for the dual differential feed system, a method to determine the optimized configuration of the joint stiffness is proposed. The detailed finite element model of the dual differential feed system considering the joints is established, whose validity is confirmed by experimental measurements. To avoid blindly discussing the stiffness of all joints and modes of the dual differential feed system, the weak modes and the weak joints of the dual differential feed system are found via the computations of modal flexibility and energy distribution, respectively. The aim is to gain the optimized configuration of the joints stiffness, a multi-objective optimization model with the stiffness values of all the weak joints as the design variables and the minimum weak modal flexibility of each weak modal as the objectives is established. To solve the multi-objective optimization problem, the orthogonal experiment method and the gray relational analysis are introduced. The obtained optimized configuration of the stiffness of joints is reapplied to the finite element model. The optimization shows that the modal flexibility of the first mode in the X direction, the second mode in the Y direction, and the sixth mode in the Z direction is reduced by 20.60%, 5.26%, and 17.04%, respectively, compared with those before optimization. The optimization results indicate that the dynamic characteristics of the table in three directions of X, Y and Z have been improved.