基于Gauss指数摩擦模型的3-RPS并联机构动力学建模

Dynamic Modeling of 3-RPS Parallel Mechanism Based on Gauss Exponent Friction Model

为定量分析关节摩擦对机构驱动力的影响,以一种新型3-RPS并联机构为研究对象,对其动力学模型进行了研究。首先,基于运动学分析得到机构的雅可比矩阵。其次,基于达朗贝尔原理对各运动副的关节约束力进行求解。最后,在忽略摩擦时,基于拉格朗日方程法建立机构的理想动力学模型。在考虑摩擦时,基于Gauss指数模型对摩擦所做负功进行定量描述,通过修正拉格朗日算子,建立含全部关节摩擦的动力学模型。结合数值算例,对忽略关节摩擦和考虑关节摩擦的动力学模型进行仿真对比。结果表明,模型误差均小于3. 5%,移动副1、2和3的驱动力相对误差分别为11. 7%、16. 3%和18. 5%,验证了模型的正确性和摩擦补偿的必要性。分析结果为基于摩擦模型的驱动力补偿提供了理论依据。

In order to analyze the influence of joint friction on mechanism driving force quantitatively, a novel 3-RPS parallel mechanism is taken as the research object, and the dynamic model of the mechanism is studied. Firstly, the Jacobi matrix is obtained based on the analysis of the kinematics. Secondly, based on the D＇ Alembert＇ s Principle, the joint constraints of each motion pair are solved. Finally, the ideal dynamic model of the mechanism is established based on Lagrange-equation method when the joint frictions axe ignored. Based on Gauss exponent model, the negative work done by frictions is described quantitative- ly when considering frictions, the dynamic model of including all joint friction is established by modifying Lagrange operators. Through numerical examples, the dynamic models of considering joint frictions and not are simulated and contrasted, the results show that the errors of both models are less than 3.5 %, the relative errors of the 1st, 2nd and 3rd driving forces are 11.7%, 16.3% and 18.5%, and the correctness of the model and the necessity of friction compensation are verified. The analysis results provide a theoretical basis for the driving force compensation based on the friction model.