并联测量机柔性动力学建模与误差耦合

为解决目前高速机构存在的高速与高精度之间的矛盾,研究了高速并联测量机的柔性问题。应用弹性梁运动学理论和Galerkin模态截断法推导了一维弹性梁运动学变形位移模型;以欧拉-贝努利梁为假设,应用Hamilton原理建立了考虑中线变形的柔性结构耦合动力学模型。最后,基于中线耦合动力学模型,测试了不同速度下弹性振动产生的误差,提出了通过调节黏滞摩擦系数来降低振动耦合误差,进而提高测量精度的方法。基于仿真实验验证了提出方法的有效性和可行性。结果表明:在忽略结构误差前提下,角速度为300rad/s时产生的横向一阶振动耦合误差最大值为28.6μm;合理调整黏滞摩擦在0.4~0.5时,振动耦合误差降低至15μm以内,相比调整前误差降低了13.6μm。提出的方法为进一步解决高速与高精度之间的矛盾和研究高阶弹性振动与精度的耦合机理提供了理论基础。

Flexible dynamic modeling and error coupling of parallel measuring machine

To solve the contradiction between speed and precision for a high speed mechanism, the flexible problem of a 3-RR-P parallel measuring machine was researched. On the basis of the elastic beam kinematics theory and Galerkin modal truncation method, a kinematics deformation model of one-dimensional elastic beam was established. Then, a flexible rod was assumed to be Euler-Bernoulli beam, the flexible structure coupling dynamics model considering the deformation of midline was built based on Hamilton principle. Finally, the measuring error generated by vibration of elastic beam was tested at different speeds based on midline coupling dynamics model. A method to reduce vibration coupling error by adjusting reasonably the viscous friction coefficient was proposed to improve the test accuracy. Experiment results show that the max lateral one-order coupling error is 28.6 μm when angular velocity comes to 300 rad/s in ignoring structure errors. Moreover, when viscous friction coefficient is adjusted to be 0.4-0.5, the vibration coupling error is reduced to less than 15 μm, reducing by 13.6 μm as compared to that of the previous adjustment. These data have been verified to be effective and feasible for solving the contradiction between high speed and high precision. It offers a foundation for research on the coupling principle between high order elastic vibration and accuracy.