超声加工振动系统波动方程的定解分析

建立超声振动系统的泛定方程,结合线性和非线性边界条件,确定系统的定解.基于波动原理,确定指数型过渡复合变幅杆的泛定方程,设定线性边界条件求解分段线性的非线性方程,推导出指数型过渡复合变幅杆波节点位置和放大系数的一般公式;通过设定非线性边界条件确定系统的非线性动力学模型的定解.并用数据表明,该系统定解正确地表示了超声振动系统的动力学特性和复合变幅杆的波动性质,并为其他超声振动系统提供了理论依据和参考.

Analysis of Definite Solution to Wave Equation of Ultrasonic Machining Vibration System

A universal defining equation of ultrasonic vibration system is derived,with its definite solution ascertained involving both linear and nonlinear boundary conditions.Then,based on the wave theory,universal defining equation of composite radius-changing horn is given in exponential form,and the linear boundary condition is set to solve the sectionalized nonlinear equation to derive the general expressions of wave node position and amplification coefficient relevant to the horn.Furthermore,the nonlinear boundary condition is set to provide the definite solution to the nonlinear dynamic model of the system.The numerical results reveal that the definite solution gives a correct expression to the dynamic characteristic of ultrasonic vibration system and wave motion of the horn,thus providing theoretically a reference for other ultrasonic vibration system.