An Elastodynamic Modeling Method for a 3-RPS Parallel Kinematic Machine
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摘要: 运用子结构综合和模态缩聚技术，提出了一种全柔性3自由度并联动力头（3-RPS）的弹性动力学建模方法．在建模过程中，将机构划分为动平台子结构和3条RPS伸缩支链子结构．模型中考虑了所有铰链和支链柔度对整机动态特性的影响．将球铰和转动副处理为具有等效刚度的虚拟弹簧；通过有限元软件和模态缩聚技术对伸缩支链进行处理，进而建立支链的弹性动力学方程；通过引入变形协调条件，对系统整体刚度矩阵进行组装， 建立了3-RPS并联动力头的整体动力学方程．研究结果表明，整机的各阶固有频率随着机构位姿的变化而变化，并且呈三对称形式分布．通过模态实验验证了该方法所得的固有频率和振型．Abstract: An elastodynamic model for a fully flexible 3-RPS parallel kinematic machine (PKM) is proposed based on the component mode synthesis (CMS) and modal reduction technology. In the modeling process, the whole system is divided into moving platform subsystem and three retractable RPS limb subsystems, in which all joint and limb compliances are included. In the elastodynamic model, the sphere joint and the revolute joint are treated as lumped virtual springs with equal stiffness, and the elastodynamic equations of RPS limbs are developed by the modal reduction techniques with the aid of the finite element software. By introducing the compatibility conditions, a global dynamic equation of the system is then proposed. The conclusion reveals that the natural frequencies of different orders vary with the changes of the configuration, and are three-symmetrically distributed. The natural frequencies and vibration modes obtained by the proposed method are further validated by the modal experimental results.
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