振动车削刀杆的计算机辅助设计与实验研究

由Timoshenko理论推导出对称三阶梯超声频弯曲振动刀杆的振幅分布解和谐振频率方程,并通过编制的计算机程序绘制了表示阶梯刀杆尺寸对谐振频率和节点间距影响的三维曲面.从这些三维曲面的等高线图可以看出,两端梁的长度对谐振频率和节点间距的影响比中间梁长度对两者的影响大,所以提出一种通过缩短中间梁长度来保持重磨后刀杆节点间距不变的新方法.实验表明,理论计算与实际差距很小,谐振频率和节点间距的计算误差分别为3％和5％.从而为振动车削刀杆设计提供了方便、准确的手段. 

Design of Flexural Vibration Holder for Vibration Cutting

The resonance frequency and nodal pitch of symmetrical three step flexural vibration holder have been calculated precisely based on Timoshenko beams theory, and the 3D curved surfaces displaying the variations of the resonance frequency and nodal pitch with the tool holder sizes have been drawn by a computer. It can be from the contour line diagram of these relational surfaces seen that the influence of the length of side beam on the resonance frequency and nodal pitch is larger than the influence of the length of middle beam on that, so a new method to make the nodal pitch of reground tool unchanged by shorting the middle beam has been proposed. The theoretical calculation results show good agreement with the experimental results, the calculating error of resonance frequency and nodal pitch are 3% and 5% , respectively, so that the present method for designing flexural vibration holder is a convenient and accurate method.