| As an important part of high precision machines such as CNC machine tools,ball screw feed systems are often used in manufacturing areas such as aerospace,automotive and marine.With the continuous progress of modern science and technology,these manufacturing industries require higher and higher levels of processing accuracy for their products,which requires ball screw feed systems with good positioning accuracy and tracking accuracy.From the point of view of the whole ball screw feeding system,the components are closely coordinated and interdependent,so how to carry out a more complete theoretical modelling and vibration characteristics study of the whole system has been a popular research area at home and abroad.In this paper,we adopt the research idea of "model building-theoretical derivation-experimental verification-numerical simulation and analysis" to study a certain type of ball screw feeding system,and carry out research and analysis in the following aspects:(1)Based on the Timoshenko beam theory,the ball screw in the ball screw feed system is firstly simplified to a flexible beam,while the rest of the constituent parts are regarded as concentrated masses,and then the physical model,rigid-flexible coupling dynamics model and mathematical model of the system are established using the hybrid method.(2)Based on the established dynamics model,the Galerkin equation and modal analysis theory were used to predict and identify the five modal parameters(modal stiffness,modal mass,modal damping,modal inherent frequency and modal damping ratio)of the system.The accuracy of the identification of the modal parameters is then determined by comparing the results of the identification of the first four modal parameters(modal inherent frequency and modal damping ratio)with the experimental results of the force hammer excitation experiments,which also show that the rigid-flexible coupled dynamics model established in this paper meets the requirements of engineering practice and simulation analysis.Finally,by analysing the influence of structural parameters on the first four modal frequencies and damping ratios of the system,the first four modal vibrations of the system are initially judged to be coupled and timevarying.(3)In order to confirm the coupling and time-varying nature of the first four modes of the system,a systematic study of the vibration characteristics of the ball screw feeding system was carried out.The majority of the coupled vibrations are in the axial direction of the spindle and the lateral direction of the table and the rotation of the spindle around its transverse axis.Then,the effect of the screw support method on the modal frequencies and modal shapes of the system is investigated.Finally,the time-varying parameters of table mass and table position were considered separately,and the time-varying mode shapes of the system in each direction were analysed using different time-varying parameters.(4)Analysis of the experimental results of force hammer excitation shows that there must be nonlinear factors in the vibration of the ball screw feed system.In this paper,firstly,among all the factors that may produce nonlinear vibration,based on Hertz contact theory,the nonlinear factor of the system axial vibration is the nonlinear segmental recovery force generated by the single-nut ball screw pair in the preload condition,and the nonlinear coupling of the system axial vibration is established.The kinetic model is developed.Then,the response characteristics of the axial non-linear vibration of the system are investigated by considering the damping constant,the initial contact angle between the ball and the raceway and the number of balls respectively,and it is found that a larger damping constant,a larger number of balls and a design initial contact angle of 45° are all beneficial for the vibration state of the system to become more stable.Finally,considering the bifurcation parameter as the mass of the table,the stability of the system axial non-linear vibration under the action of different external excitation amplitude and frequency is analysed.The results show that the reduction of the external excitation amplitude or the increase of the frequency will help the system vibration state become more stable. |
