东北大学学报（自然科学版）

东北大学学报(自然科学版) ›› 2008, Vol. 29 ›› Issue (6): 877-880.DOI: -

• 论著 • 上一篇    下一篇

超声加工振动系统波动方程的定解分析

张楠;侯晓林;闻邦椿;   

  1. 东北大学机械工程与自动化学院;中冶京诚工程技术有限公司;东北大学机械工程与自动化学院 辽宁沈阳110004;北京100176;辽宁沈阳110004
  • 收稿日期:2013-06-22 修回日期:2013-06-22 出版日期:2008-06-15 发布日期:2013-06-22
  • 通讯作者: Zhang, N.
  • 作者简介:-
  • 基金资助:
    国家自然科学基金资助项目(50535010)

Analysis of definite solution to wave equation of ultrasonic machining vibration system

Zhang, Nan (1); Hou, Xiao-Lin (2); Wen, Bang-Chun (1)   

  1. (1) School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110004, China; (2) Capital Engineering and Research Incorporation Ltd., Beijing 100176, China
  • Received:2013-06-22 Revised:2013-06-22 Online:2008-06-15 Published:2013-06-22
  • Contact: Zhang, N.
  • About author:-
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摘要： 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.

关键词: 波动系统, 超声波振动, 分段线性的非线性方程, 复合变幅杆, 非线性系统

Abstract: 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.

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