Elastodynamic Model-Based Vibration Characteristics Prediction of a Three Prismatic-Revolute-Spherical Parallel Kinematic Machine

Parallel kinematic machines (PKMs) have been proposed as an alternative solution for high-speed machining (HSM) tool for several years. However, their dynamic characteristics are still considered an issue for practice application. Considering the three prismatic-revolute-spherical (3-PRS) PKM design as a typical compliant parallel device, this paper applies substructure synthesis strategy to establish an analytical elastodynamic model for the device. The proposed model considers the effects of component compliances and kinematic pair contraints so that it can predict the dynamic characteristics of the 3-PRS PKM. Based on eigenvalue decomposition of the characteristic equations, the natural frequencies and corresponding vibration modes at a typical configuration are analyzed and verified by numerical simulations. With an algorithm of workspace partitions combining with eigenvalue decompositions, the distributions of lower-order natural frequencies throughout the workspace are computed to reveal a strong dependency of dynamic characteristics on mechanism's configurations. In addition, the effects of the radii of the platform and the base along with the cross section of the limb on lower-order natural frequencies are analyzed to provide useful information during the early design stage. At last, frequency response analysis for the tool center point (TCP) is worked out based on the elastodynamic model to provide primary guideline for cutting chatter avoidance.