Nonlinear Elastodynamic Behaviour Analysis of High-Speed Spatial Parallel Coordinate Measuring Machines

Yu Deng,Deyong Wei,Xiulong Chen,Wenbin Li

doi:10.5772/52148

Abstract

In order to study the elastodynamic behaviour of 4- universal joints- prismatic pairs- spherical joints / universal joints- prismatic pairs- universal joints 4-UPS-UPU high-speed spatial PCMMs(parallel coordinate measuring machines), the nonlinear time-varying dynamics model, which comprehensively considers geometric nonlinearity and the rigid-flexible coupling effect, is derived by using Lagrange equations and finite element methods. Based on the Newmark method, the kinematics output response of 4-UPS-UPU PCMMs is illustrated through numerical simulation. The results of the simulation show that the flexibility of the links is demonstrated to have a significant impact on the system dynamics response. This research can provide the important theoretical base of the optimization design and vibration control for 4-UPS-UPU PCMMs.

Highlights

The PCMM, which has advantages of high stiffness, good dynamic performance, no accumulated precision errors, tight construction and strong modularization, has gained a lot of attention and developed rapidly[1,2]
There have been few efforts made oriented to spatial parallel machines and the links’ flexibility and the coupling effects of the flexible links’ elastic displacement have not been sufficiently considered
This paper takes the 4‐UPS‐UPU PCMM(see Figure 1), which consists of a stationary platform, a moving platform, four UPS(Universal joint‐Prismatic pair‐Spherical joint) actuating limbs, a UPU(Universal joint‐prismatic pair‐Universal joints) actuating limb and a working head, as an example

Summary

Introduction

The PCMM, which has advantages of high stiffness, good dynamic performance, no accumulated precision errors, tight construction and strong modularization, has gained a lot of attention and developed rapidly[1,2]. The dynamic behaviours of high‐speed PCMMs must be studied. There have been few efforts made oriented to spatial parallel machines and the links’ flexibility and the coupling effects of the flexible links’ elastic displacement have not been sufficiently considered. N9d, 1Y4u0D:2e0n1g2: 1 Nonlinear Elastodynamic Behaviour Analysis of High-Speed Spatial Parallel Coordinate Measuring Machines. The nonlinear elastodynamic model is established and the numerical simulation analysis of dynamic response for 4‐UPS‐UPU PCMM, including displacement error output response, velocity error output response, and acceleration error output response can be calculated

Model of the flexible beam element

Dynamic equations of the limbs

System dynamic equations

Numerical Simulation and Analysis

Conclusion