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． According to Timoshenko’s theory, the amplitude distribution and resonance frequency equations of the symmetric three-step ultrasonic bending bending vibration arbor are deduced. The three-dimensional curved surface representing the influence of the step arbor size on the resonance frequency and node pitch is drawn through the computer program. From the contour maps of these three-dimensional surface, it can be seen that the influence of the length of the beam on the resonance frequency and the pitch of the nodes is greater than the length of the middle beam, so a new method is proposed to reduce the length of the middle beam A new method of keeping the spacing of the rear arbor nodes constant. Experiments show that the theoretical calculation and the actual difference is small, and the calculation errors of resonance frequency and node pitch are 3% and 5% respectively. This provides a convenient and accurate tool for the design of vibrating turning shank.