( 1. School of Mechanical and Electrical Engineering, Xuzhou Normal University, Xuzhou 221116, Jiangsu China;2. School of Physics and Electronics, Xuzhou Normal University, Xuzhou 221116, Jiangsu China )
The mechanical model and the time-varying differential equation of bending vibration was established. It was pointed out that the natural frequency and vibration modes have a time-dependent feature. Using the ABAQUS software the pre-stress effect modal analysis of the turning work-piece on the lathe was analyzed and the natural frequencies and vibration modes at different turning length were obtained. The calculation indicates that with the increase in turning length, the first-order natural frequency increased, then it decreased and curve of the natural frequency-turning length displayed as a parabolic distribution.