Hybrid modeling and analysis of structural dynamic of a ball screw feed drive system

Ball screw drives are widely used as the motion delivery mechanism due to their high stiffness and high accuracy. As the speed and precision requirements from machine tools increase, the effects of the structural flexibility of the drives on controller performance are becoming increasingly significant. The vibrations adversely affect the positioning accuracy and performance of the drive. The natural frequencies of a ball screw system vary as the nut moves along the screw. It is necessary to have an insight into the dynamic response of the rotating ball screw subjected to axially moving load during prototyping of the machine tool and controller [1]. Conventional dynamic modeling methods of the ball screw drives employ lumped parameter models [2-4], which cannot accurately characterize the high frequency mechanical resonance. More advanced models are obtained with the help of hybrid methods that consider torsional, axial, and possibly flexural vibrations. Varanasi et al. [5] and Whally et al. [6] captured the axial and torsional dynamics of a ball screw drive using beam formulations. In general, these models cannot accurately characterize the high frequency mechanical resonances. Frey et al. [7] proposed an approach aims at identifying the dominant effects of the ball screw and including them into a simple lumped mass model. Vicente et al. [8] studied the axial and torsional coupled vibration by Ritz serious method. Finite Element methods are often incorporated in modeling the drive systems. Zhou et al. [9] presented a model only considering the axial dynamics of the screw. However, neither model considers the flexural deformation. Okwudire et al. [10] proposed a model of ball screw using beam elements having axial, torsional, and lateral dynamics. This paper presents a hybrid model of a ball screw drive, in which the screw is considered as a Timoshenko’s beam having axial,torsional and flexural dynamics. The deformation of the screw is determined by assumed mode method. The method models the dynamic behavior of a ball screw considering the moving nut. The dynamic equations of a rotating screw subjected to the axially moving load with general boundary conditions are proposed.