Position: Home > Articles > Three-dimensional resonant characteristic analysis of horn-gear system based on ritz method
Journal of Chinese Agricultural Mechanization
2015,36
(4)
52-55+64
基于里兹法的变幅杆—齿轮系统三维谐振特性分析
作 者：
李一;吕明;王时英
单 位：
太原理工大学机械工程学院
关键词：
里兹法;特征值;谐振特性;三维弹性振动
摘 要：
在超声齿轮加工振动系统设计时,需要将齿轮和变幅杆作为整体建模,由于现有求解方法对变幅杆采用一维振动理论、对齿轮采用二维振动理论,使二者的耦合边界条件难以匹配,同时两个理论对振动方式的描述也不完善,求解精度差。针对这些不足,提出基于里兹法,应用三维弹性动力学方程与能量变分原理建立数学模型,通过将变幅杆―齿轮系统划分为三个积分区域,求得关于系统谐振特性的特征值方程,避免了对变幅杆―齿轮接触处边界条件的耦合设置,并全面反映了系统的振动特性。求解结果表明:使用该方法求得的数值解与ANSYS分析结果接近,且模型避免了ANSYS分析不同对象模型时所需的复杂前处理过程。该方法具有较好的收敛特性,利于计算机编程求解,易于实现参数化设计。
译 名：
Three-dimensional resonant characteristic analysis of horn-gear system based on ritz method
作 者：
Li Yi;Lu Ming;Wang Shiying;College of Mechanical Engineering,Taiyuan University of Technology;
关键词：
Ritz method;;eigenvalue;;resonant characteristic;;three-dimensional elastic vibration
摘 要：
In the design of ultrasonic vibration machining system,the horn and gear should be regarded as one unit to modeling.But the horn is analyzed by one-dimensional vibration theory and the gear is analyzed by two-dimensional theory,making the two coupling boundary conditions very difficult to match,and these two methods can not comprehensively reflect the vibration characteristic and the precision of results are imperfect.To solve these problems,the three-dimensional elastic dynamic equation and energy variational principle based on Ritz method was used to establish the mathematic model and the horn-gear system model was divided into three integral domains to achieve the eigenvalue of the system resonant characteristic,so that it can avoid setting the boundary conditions and reflect the system's vibration characteristic comprehensively.The values worked by the Ritz method are close to them worked by ANSYS and have acceptable convergence properties.Also it is convenient to achieve the goal of programming and realize the parametric design.
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