组合阶梯梁振动特性计算方法及应用

    Solution and Application for Vibration Characteristics of Combined Stepped Beam

    • 摘要: 在机械加工过程中,对机床主轴进行结构优化或者合理选择刀柄刀具可以改善机床主轴刀柄刀具系统的振动特性,从而提高加工质量和效率.针对机床主轴刀柄刀具系统的振动特性问题,提出了一种基于组合阶梯梁模型的计算方法.基于伯努利-欧拉梁模型,提出了悬臂梁状态下的变截面阶梯梁的固有频率和振型的计算方法;基于实际应用中的刀柄铣刀配合系统,将阶梯梁模型进一步改进为组合阶梯梁模型,提出了梁组合部分的等效弯曲刚度和密度的计算方法,并将该方法应用于刀柄装夹铣刀系统的振动特性分析中,通过有限元法和实验结果验证了该方法的有效性.结果表明:与铁木辛柯梁理论相比,本文算法在计算机床刀柄刀具系统等具有大长径比并且考虑模态阶次较低的情况下,计算误差小,计算效率提高1倍.

       

      Abstract: In the process of machining, vibration characteristics of the machine tool spindle tool system can be improved by structure optimization of machine tool spindle and appropriate selection of tool and toolholder, reaching a higher machining quality and efficiency with good vibration characteristics. To study the vibration characteristics of the machine tool spindle, this paper proposed a method based on combined stepped beam model. The method for solving bending vibration natural frequency and mode of stepped cantilever beam was developed with the use of Euler-Bernoulli beam theory. Based on the tool-toolholder coupled system from the practical condition, this paper refined the stepped beam model to the combined stepped beam and gave the equivalent bending rigidity and density of the combined part. This method was applied to calculate the vibration characteristics of the tool-toolholder coupled system and it was verified though the finite element method (FEM) and experiment. Results show that compared with the Timoshenko beam theory, this method doubles the computational efficiency whereas calculation error keeps small in condition of large ratio of length to diameter and low order of modal is considered like the machine tool spindle tool system.

       

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