Reliability analysis of regenerative chatter stability in turning tool systems by modified control variate method

Turning is one of the most common cutting methods in metal machining. During turning, relative movement occurs between the lathe, the tool, and the workpiece, causing self-excited vibration, i.e., chatter. Moreover, the structural and dynamic parameters of the turning system are uncertain due to the inevitable effect of the processing environment, assembly errors, and other factors. To better predict and prevent turning chatter, it is necessary to analyze the chatter stability and reliability of the turning tool system with its dynamic characteristics to better predict and avoid turning chatter. Despite the importance of chatter prediction in turning, there is a lack of research on the reliability of chatter stability for the turning tool system. In this paper, the dynamic model and the chatter stability model of a turning tool system are established, and the measured parameters are used to analyze the chatter stability of the system. Modal test, static stiffness test, and cutting force tests of the turning system are conducted on a CNC lathe test platform to determine the dynamic parameters of the turning chatter stability analysis. Parameter randomness is considered, and the distribution and characteristic numbers of the parameters are analyzed. The results are consistent with the turning test results, verifying the accuracy of the chatter stability model of the turning tool and machining systems. Furthermore, the chatter reliability model of a turning tool system is established. Since the turning chatter reliability model is more complex and nonlinear, this paper proposes an efficient method for solving the high nonlinear reliability problem is proposed in this paper. The control variable (CV) method is used, and the second-order reliability method is introduced. In addition, a small number of samples generated by Latin hypercube sampling are used to estimate the failure probability by the saddle point approximation method. The applicability of this method is verified by comparison with a variety of methods. The results show that the proposed improved CV method can efficiently analyze the chatter reliability of the turning tool system.