考虑负载影响的阶梯形超声变幅杆动力特性

考虑与加工工件表面高频重复撞击对结构动力特性的影响，基于瞬态波传播理论，研究周期激励下阶梯形超声变幅杆重复撞击加工工件的瞬态动力响应，及负载对变幅杆放大特性的影响。首先，建立阶梯形变幅杆力学模型，采用瞬态波响应法分别对接触过程和分离过程动力控制方程进行求解，得到适用于任意级数的阶梯形变幅杆的特征项传递函数，和重复撞击系统的瞬态响应理论解。以工程中常用的三级阶梯形变幅杆为算例，分析了不同外载频率下变幅杆重复撞击动力特性和负载工件对变幅杆聚能效果的影响，得出考虑加工件撞击产生的瞬态响应下的变幅杆放大系数，小于自由振动空载的设计值。可为精细超声加工变幅杆的设计提供更为精确的理论依据

Dynamical performance of ultrasonic stepped horn with consideration of loading effect

The influence of high frequency repeated impacts upon the dynamic performance of ultrasonic horn was investigated based on the theory of propagation of longitudinal wave,and the effect caused by the load of workpiece on the amplifying rate of horn was analyzed.The governing equations and initial-boundary conditions of a stepped horn were established,and the transient dynamical response solutions in contact phase and separation phase were solved theoretically by using the method of transient wave expansion of eigenfunctions.In addition,the transfer function of eigenfunction for stepped horn with arbitrary number of different sections was obtained.The numerical results of a 3-section stepped horn,widely used in practical engineering,indicate that the transient response under multi-impact is simulated successfully,and the features of transient wave propagating in the stepped horn are revealed properly.The influences of the frequency of impulses and the load of work piece on dynamical performance of ultrasonic machining system were analyzed.The amplifying rate considering the impact-induced transient wave effects is less than the one considering only the free vibration in no load state.The present analysis provides reference to more accurate design of ultrasonic machining system.