Complete stiffness model and stiffness performance of 5-U P S/ P RPU redundantly actuated parallel machine tool

ZHOU Xin; XU Yun-dou; YAO Jian-tao; ZHENG Kui-jing; Zhao Yong-sheng

doi:10.3788/OPE.20152304.1070

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Complete stiffness model and stiffness performance of 5-U P S/ P RPU redundantly actuated parallel machine tool

更新时间：2020-08-13

- Complete stiffness model and stiffness performance of 5-U P S/ P RPU redundantly actuated parallel machine tool
- Optics and Precision Engineering Vol. 23, Issue 4, Pages: 1070-1080(2015)
- 作者机构：
  
  1. 燕山大学河北省并联机器人与机电系统实验室,河北秦皇岛,066004
  2. 燕山大学先进锻压成型技术与科学教育部重点实验室,河北秦皇岛,066004
- 作者简介：
- 基金信息：
- DOI：10.3788/OPE.20152304.1070
  CLC： TG659
- Received：09 August 2014，
  
  Revised：20 September 2014，
  
  Published：25 April 2015
- 稿件说明：
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周鑫, 许允斗, 姚建涛等. 5-UPS/PRPU冗余驱动并联机床完整刚度模型及其刚度特性[J]. 光学精密工程, 2015,23(4): 1070-1080

ZHOU Xin, XU Yun-dou, YAO Jian-tao etc. Complete stiffness model and stiffness performance of 5-U P S/ P RPU redundantly actuated parallel machine tool[J]. Editorial Office of Optics and Precision Engineering, 2015,23(4): 1070-1080
周鑫, 许允斗, 姚建涛等. 5-UPS/PRPU冗余驱动并联机床完整刚度模型及其刚度特性[J]. 光学精密工程, 2015,23(4): 1070-1080 DOI： 10.3788/OPE.20152304.1070.

ZHOU Xin, XU Yun-dou, YAO Jian-tao etc. Complete stiffness model and stiffness performance of 5-U P S/ P RPU redundantly actuated parallel machine tool[J]. Editorial Office of Optics and Precision Engineering, 2015,23(4): 1070-1080 DOI： 10.3788/OPE.20152304.1070.

摘要

基于全雅可比矩阵和虚功原理建立了5-UPS/PRPU冗余驱动并联机床的完整刚度模型。首先基于螺旋理论推导出约束分支中的约束雅可比矩阵;然后锁定分支中的主动副并利用互易积原理求得驱动雅可比矩阵

最后提出了冗余驱动雅可比矩阵。利用约束力、驱动力和冗余驱动力与外力的映射关系

结合虚功原理

得到系统整体刚度矩阵。考虑虎克铰、轴承等传动部件的轴向变形对分支轴向刚度的影响

构造了各个分支的轴向刚度模型。借助激光跟踪仪对所建立的刚度模型进行了实验测试。结果表明:该刚度模型的误差为2%~5%

验证了理论分析的可靠性。在此基础上

以机床的线刚度和角刚度的最小值为刚度性能指标

分析了其在工作空间内的分布情况。分析显示:机床线刚度的最小值主要分布在

轴两侧

角刚度的最小值则主要分布在-0.05≤

≤0.05 m和-0.11≤

≤-0.05 m

因此

在进行并联机床工具规划时应该尽量避免该区域。文中内容可为并联机床刀具运动轨迹的优化提供参考依据。

Abstract

A complete stiffness model of the 5-UPS/PRPU redundantly actuated parallel machine tool was constructed based on the overall Jacobian matrix and the principle of virtual working. Firstly

the Jacobian matrix of a constraint limb was derived by using screw theory; then

the Jacobian matrix of actuations was derived by using the theory of reciprocal screw and by locking actuated joint in each limb; finally

a redundant Jacobian matrix was designed. By using the mapping relationship between constraint forces

actuated forces

redundantly actuated forces and external forces

the complete stiffness model of the overall system was obtained combining with the principle of virtual work. Furthermore

by taking the effect of the axial deformation of a universal joint

a spherical joint and some other transmission parts on the linear stiffness of each limb into consideration

the axial line stiffness model of each single limb was constructed. The stiffness model was further validated by a laser tracker. The experiment results show that the error of stiffness model is 2%-5%

which means that the theoretical analysis is acceptable. On this basis

the stiffness performance of the machine tool was evaluated by utilizing the minimum linear/angle stiffness values

the minimum stiffness distribution in the workspace was investigated

and the minimum stiffness area was generalized. It shows that the minimum linear stiffness distributes on both sides of

-axis

the minimum angle stiffness distributes on the -0.05≤

≤0.05 m and -0.11≤

≤-0.05 m

which suggests that the programmer should avoid this area when the trajectory of the Parallel Machine Tool(PMT) is planned. The research provides a theoretical reference for the track programming of the 5-UPS/PRPU redundantly actuated PMT.

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references

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