The Dynamic Analysis Of The Machine Drive System

In manufacturing, the machine is main production equipment. With the development of the production and technology, the machine is develop for high-speed, high efficiency, precision and automation, and the need for its work performance is stricter which induce its structure becomes complex. With the processing efficiency it is urgent to improve the speed of machine spindle, so the vibration and dynamic response of the machine are get more and more attention. Very weak vibration is likely to impair the machine or its machining precision, so it is asked that the machine structure can reduce the vibration displacement. For many complex mechanical systems, a difficult task is to reduce or avoid the resonance frequency. Therefore, the research about the system's vibration frequency and dynamic response is important to reduce the structure's stress or its vibration diceplacement.The machine's processing accuracy and efficiency depend on the electric drive components and mechanical drive system. The drive system of the Machine transmits the movement and the power to the machine's performer, but also is needed to have good dynamic characteristic. The drive system of the machine is always subjected to exciting force or torque in the process of its working, so the shaft of the drive system is induced to axial or transverse or torsional vibration. The machine drive system is an important part, which affect the processing precision, vibration, resonance, as well as the performance of machine. So the machine drive system has been got more and more attention. In this paper, the machine drive system includes the servo motor, ball screw and the table which move along the screw with the nut. According to the characteristics of the ball screw drive system, the drive system can be simplified to rotating beam sysytem with a moving mass. Considering the contact elastic distortion of the system, the bearing, also the combination between the screw and the nut, is simplified as stiffness and damping in six directions. The combination between worktable and machine guide is plane, which can be equivalent to the stiffness and damping in corresponding normal direction. In order to comprehensive analysis the system characteristics, the longitudinal, torsional and transverse vibration of the screw, as well as the worktable's vibration in six degrees of the freedom are considered in setting up the system's kinematic equations which is deduced by Lagrange's equation.The primary problem of the dynamic analysis is to solve natural frequencies and mode of the vibration. The frequency equations of the screw's axial and torsional vibration are set up in elastic support condition to considering the bearings supporting rigidity. Its transverse vibration frequency equation is set up which is used the Timoshenko beam model and take into account the shear deformation and rotatory inertia, also the bearing stiffness, pre-tension axial force. The longitudinal vibration, torsional vibration and transverse vibration mode shape function are solved. System parameters affect the screw vibration frequency and its mode. For the longitudinal and torsional vibration of the screw, the vibration frequency is sharp when bearings stiffness is at a critical value. If the bearings supporting stiffness is simplified, when bearing stiffness is less than the critical stiffness, the bearings supporting can be seen as freedom; and when bearing stiffness is greater than the critical stiffness, it should be as a fixed support. The transverse vibration frequency of the screw increase when the bearing stiffness, the pretension axial force, or rotational speed increases. For a rotating system, resonance is a common concern. System parameters affect the screw's resonance, and its whirl speed is increasing with tension axial force and rotation speed increasing. If the screw rotational speed is constant, whether there is resonance or not in startup process depends on the diameter of screw. When the diameter is less than a critical value dc, the resonance does not happen, but the dc value is affect by pretension force, rotation speed and bearing stiffness. The resonance orders of the screw in its startup process relate to the screw diameter, and with the diameter of the screw increasing, the resonance orders are decreased. If the rotating speed increases sostenuto, the resonance orders are not unlimited. When the screw has experienced some orders of the resonance, even if the screw rotational speed continues to increase, the resonance would not happen. The orders of resonance are affected by the screw diameter.The dynamic response analysis of the system is another major problem. To the drive system of the machine, the vibration response maybe bring excessive dynamic displacement, which affect of machining quality and result in excessive noise.Through the analysis of affection of the system parameters on the vibration of the screw and the worktable, which include the bearing stiffness, contact stiffness between the screw and the nut, the contact stiffness between the worktable and the guide, pre-tension axial force, rotation speed, screw lead and worktable'mass. It can be found that it is screw lead (which is the speed of the worktable moving along the screw) and worktable'mass which affect the system's vibration universally.The position accuracy of the machine drive system depends on the axial fluctuations of the cutting point on the worktable table. The fluctuations of the cutting point is sourced in five aspects: displacement caused by screw axial vibration, displacement caused by screw torsional vibration, worktable's local vibration at contact point between screw and the nut, and axial displacement caused by the table's rotation in the y and z direction. In these five aspects, the displacement caused by worktable's local vibration is the most remarkable.In order to improve positioning accuracy, three system parameters should be priority to adjust in the design or assembly drive system of the machine, which are reduceing screw lead, reducing the mass of the worktable and increasing the contact stiffness between the screw and the nut. In engineering, double-nut is often used, which can effectively improve the positioning accuracy. When the screw is long or the temperature change is larger, the freedom supported at one end of the screw is often adopted in order to reduce the internal stress. This fixed-freedom supported of the screw will not affect positioning accuracy of the machine drive system comparing with fixed-fixed soported. The dynamic stability consists in all kinds systems. According to Liapunov stability theory, the dynamic stability focuses on the effect of disturbing factors on system's vibration. The effect of small disturbing factors on different system is different. In practice, the disturbing factors always exist inevitable, so the study about the system dynamic stability is important to both theory and practice.Because the mass of the worktable and the moving speed of the worktable along the screw affect the system vibration universal, the system stability boundary are plotted in tho non-dimensional plane which are the mass ratio of the worktable to the screw and the longth ratio of pitch to the longth of the screw. Through the numerical calculation, the effectt of the system parameters on the system stability is analyzed. It is screw diameter, rotational speed and the contact stiffness between the worktable and the bottom of the guide that affect on the system stability largely. In order to improve the system's dynamic, the small screw's diameter, small rotational speed and the lager contact stiffness between the worktable and the bottom of the guide can be chosed.