Axial stiffness identification of a ball screw feed system using generalized frequency response functions

Contact of balls in screw nuts and bearings causes the nonlinearity of a ball screw feed system. The identification of nonlinear stiffness helps to understand and control the feed system. The axial vibration of the ball screw feed system can be descripted by a single-degree-of-freedom (SDOF) system with polynomial nonlinear terms. Since generalized frequency response functions (GFRFs) can be expressed in terms of linear and nonlinear system parameters, one can estimate these parameters based on the measured GFRFs. In this effort, both single-tone and multitone harmonic inputs are employed to measure GFRFs, and a simple search algorithm is proposed to find the suitable frequency set of the multitone input. Parameter identification based on these two methods has been compared by numerical simulation and experiment. Since the response spectrum measured from vibration experiment of a ball screw system has even and odd harmonics, it is suitable to simplify the restoring force with square and cubic nonlinearity form. Static experiment is also conducted to verify the identified parameters, and the results show that the method based on single-tone inputs performs effectively in identifying axial stiffness of a ball screw feed system, but the method based on multitone inputs gets the incorrect results in practical application