Dynamic analysis of the machine tools load-bearing system considering the ball arrangement and carriage flexibility

The balls in the machine tool load-bearing system inevitably alternate with the movement of the worktable, resulting in the worktable's posture to change periodically during the ball circulation process. In the past, the dynamic behaviors of the machine tool load-bearing system have been analyzed by assuming that the worktable is in a specific position, and few models consider the effects of the ball circulation motion. To address this problem, this paper presents a five degree-of-freedom (DOF) nonlinear dynamic model for the machine tool load- bearing system, taking into account the ball arrangement and carriage flexibility, which is used to predict the dynamic behaviors under both constant and excitation loads. Firstly, the relation between the contact load and the carriage flexibility is determined, and the contact load in the working phase is derived by homogeneous coordinate transformation. Secondly, the elastic release is discussed for different cases and the contact load in the transition phase is derived. Then, a nonlinear dynamic model for the machine tool load-bearing system is established by deriving the restoring loads and moments, and the validity of the proposed model is verified experimentally. Finally, the variation law of the nonlinear dynamic response for the machine tool load-bearing system is discussed.