Abstract: A single degree of freedom dynamic model in z direction for turning machine system was established. The frequency response function of the tool holder of CJ0625 turning machine was obtained through the hammer test， with the dynamic parameters identified. The timedomain simulation was conducted using a variable stepsize method that can dynamically adjust the stepsize according to the spindle speed and thus ensure the algorithm convergence and required accuracy. The software for the timedomain simulation of the turning process was designed and written based on the Matlab platform. The timedomain solution method was compared with the frequency domain flutter prediction method (stability lobe diagram)， and the displacement vs time history curves of vibration were given under the conditions of stable cutting， critical stable cutting and unstable cutting. The results show that the errors of absolute stable cutting widths determined using these two methods are both below 607%.

Key words: numerical integration, turning process, timedomain simulation, frequency domain prediction, GUI software