The analysis of the Timoshenko transverse vibrations of workpiece in the ultrasonic vibration-assisted turning process and investigation of the machining error caused by this vibration

Deformation of workpiece causes diametrical error in the turning process. In order to analyze the diametrical error, a model of elastic deformation of workpiece is required. In this article, an efficient elastic deformation model is developed by using of transverse vibration analysis of Timoshenko workpiece method. It is assumed that the workpiece is only held in one side with the chuck in lathe machine. The obtained results illustrated that in the ultrasonic vibration assisted turning process, diametrical error in workpiece after machining was about 35% less than the conventional machining method. Furthermore, by comparing different vibration analysis methods, it was observed that in the same experimental condition, there is a small difference in diametrical error between Euler-Bernoulli and Timoshenko methods and it is about 0.3 percent. The results of Timoshenko method are closer to experimental results compared with the Euler-Bernoulli method.