In accordance with the vibration characteristics of ball screw feed systems, a hybrid modeling method is proposed to study its dynamic behavior. Partially, the ball screw is modeled as a continuous body, and the remaining components are considered lumped masses, allowing for a realistic description of the dynamics of the feed system. The axial, torsional, transverse, and bending vibration models of a ball screw carriage system are established via the Rayleigh-Ritz series method based on the Timoshenko beam assumption. The established model that added the Timoshenko beam assumption obtains the coupling vibration displacement between the transverse and bending vibrations of the lead screw, which is close to real situations. Numerical simulations are conducted to investigate the changes of the natural frequency and modal shapes of ball screw systems with carriage positions. Results show that the carriage position has significant influence on the amplitude and direction of axial and transverse vibrations, substantial influence on the direction of the bending vibration, and minimal influence on the amplitude and direction of torsional vibration. These results indicate that the proposed hybrid model performs well to predict the vibration characteristics of the feed system. Moreover, the carriage position and carriage load also have a remarkable effect on the frequency response of the feed system. These results, along with the modeling approach, provide an important basis for the further study of in-machining monitoring and vibration controller design.

根据滚珠丝杠进给系统的振动特性，提出了一种混合建模方法来研究其动态行为。滚珠丝杠部分地被建模为一个连续的主体，其余组件被视为集总质量，从而可以对进给系统的动力学进行实际描述。滚珠丝杠支架系统的轴向，扭转，横向和弯曲振动模型是基于Timoshenko梁假设通过Rayleigh-Ritz级数方法建立的。建立的模型加上Timoshenko梁假设，可以得到丝杠的横向振动和弯曲振动之间的耦合振动位移，这与实际情况非常接近。进行了数值模拟，以研究带有托架位置的滚珠丝杠系统的固有频率和模态形状的变化。结果表明，滑架位置对轴向和横向振动的幅度和方向有很大的影响，对弯曲振动的方向有很大的影响，而对扭转振动的幅度和方向的影响很小。这些结果表明，提出的混合模型可以很好地预测进料系统的振动特性。此外，滑架的位置和滑架负载对进料系统的频率响应也有显着影响。这些结果以及建模方法，为进一步研究机械加工中的监控和振动控制器设计提供了重要的基础。