Nonlinear characteristics of multi-frequency ultrasonic machining

LIU Zhi-yuan, WANG Shi-ying, LU Feng, LIU Bei-bei

(School of Mechanical and Transportation Engineering, Taiyuan University of Technology, Taiyuan 030000,China)

Abstract:  In the process of multi-frequency ultrasonic machining, complex nonlinear motion was generated by multiple random collisions of free masses. Aiming at this problem, the time-domain discrete dynamic mapping state matrix of the vibration system was established on the premise of fully understanding the motion characteristics of the free mass. The attractor or basin of attraction in the vibration process of the free mass was obtained. According to the initial state parameters and dynamic parameters, global analysis of invariant objects (GAIO) was used. The displacement function curve and velocity function curve of the free mass were obtained. Different subdivision times n=8, 16, 24 were taken to compare and analyze the displacement function curve of the free mass, and the nonlinear motion results of the free mass captured by the highspeed camera with the nonlinear motion results calculated by global analysis of invariant objects analyze were compared. The results show that in the comparison of different subdivision times, the displacement function curve drawn by the subdivision times n=16 is better than the displacement function curve drawn by the subdivision times n=8 in accuracy, and the calculation time is less than n=24; The relative errors between the results and the calculation results under the GAIO algorithm are both within 5%, which proves the superiority of the GAIO algorithm.