The precision and stiffness of the ball screw feed drive system (BFDS) in machine tools will be reduced after a long working life, which affects the production process and the quality of the products. Accordingly, monitoring and evaluating the health condition of the ball screw is crucial. It is possible to determine and predict a machine's operating condition based on its mechanical characteristics, such as vibrations, temperature, sound signals, etc., with vibration frequency being the most used. In fact, the stiffness of the rolling joints including bearings and ball nuts (of the ball screw) is considered to have an influence on the overall stiffness of the BFDS and is reflected by vibration. This paper presents an investigation method based on the vibration frequency by approaching the 4-DOF dynamic model of the BFDS. In addition, a new approach to validate the BFDS's dynamic model using the Runge–Kutta four-order (RK4th) numerical simulation method, in order to predict the vibration responses from axial vibrations merely is presented. The results obtained from the theoretical simulation are compared with the results of experimental measurements. From there, the achievement of this study will be the foundation for extending and approaching machine condition monitoring methods.