Suppression of the time-varying vibration of ball screws induced from the continuous movement of the nut using multiple tuned mass dampers

• Optimization of MTMD to reduce time-varying and multi-mode vibration of ball screws.
• Tenfold improvement in the lateral dynamic stiffness of the screw shaft is obtained.
• Robust design strategy of MTMD to ensure the practicability and feasibility.

Considering the time-varying vibration characteristics of the ball screw caused by the continuous movement of the nut, this paper takes the form of a hollow screw shaft structure containing multiple tuned mass dampers (MTMD) to achieve the lateral multi-mode vibration control of the screw shaft. The screw shaft is modeled as an Euler–Bernoulli beam with elastic supports at both ends and the position of the nut. Each tuned mass damper (TMD) is connected to the screw shaft via an elastic spring and a viscous damping element. After establishment of the lateral dynamic model of the screw shaft which taking into account the changing positon of the nut and the multiple resonant responses of the shaft, the optimum design parameters of each TMD can be determined using a numerical optimization algorithm based on the mode summation method. The multiple resonant responses of the screw shaft installed with the optimally designed MTMD are analyzed to demonstrate the robust design of the MTMD for the lateral time-varying vibration control of the screw shaft. Theoretical studies and experimental results show that the proposed design method of the MTMD can remarkably improve the lateral dynamic stiffness of the screw shaft.