复频超声加工中的非线性特征研究

Nonlinear characteristics of multi-frequency ultrasonic machining

在复频超声加工过程中,自由质量块由于多次随机碰撞会产生复杂的非线性运动,针对这一问题,在分析了自由质量块运动特性的前提下,建立了其振动系统的时域离散动态映射状态矩阵,求得了振动过程的吸引子或吸引盆。根据初始状态参数和动力学参数,采用面向集合的数值计算方法(GAIO),求出了自由质量块的位移函数曲线和速度函数曲线;分别取不同的细分次数n=8,16,24,对自由质量块的位移函数曲线进行了对比分析,将通过高速摄像机拍摄的自由质量块的非线性运动结果和GAIO计算的非线性运动结果进行了对比分析。研究结果表明:在不同细分次数的比较过程中,在准确性上,细分次数n=16时绘制的位移函数曲线优于n=8时绘制的曲线,在计算时间上要少于n=24;高速摄像机拍到的实验结果与GAIO算法下的计算结果的相对误差均在5%以内,证明了GAIO算法的优越性。

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.