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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2020, Vol. 54 Issue (2): 348-356    DOI: 10.3785/j.issn.1008-973X.2020.02.016
Mechanical and Energy Engineering     
Dynamic characteristics of spatial parallel mechanism with spherical joint clearance
Yan-biao LI(),Tao-tao XU,Hang ZHENG,Ze-sheng WANG
College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310032, China
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Abstract  

A rigid body dynamics model of a spatial parallel mechanism with multiple spherical joint clearances was established, in order to analyze the dynamic characteristics of the 5-PSS/UPU parallel mechanism with spherical joint clearances. A kinematic model of parallel mechanism with spherical joint clearances was established based on the 'contact-separation' two-state model. The normal and tangential contact force models between the kinematic joint elements were established based on an improved contact model and a modified Coulomb friction model, and the contact force was further transformed into the centroid of the component corresponding to the kinematic joint elements. The Newton-Eulerian method combined with the Lagrange multiplier was used to establish the dynamic model of the parallel mechanism with clearances and the dynamic characteristics were analyzed by numerical simulation.The root-mean-square error (RMSE) values of the angular acceleration of the moving platform with clearance of 0.05, 0.10, 0.20 and 0.40 mm were calculated, which were 40.046, 65.385, 98.489 and 145.715 rad/s2, respectively. Results show that in the case where there are multiple spherical joint clearances, when the clearance value increases, the dynamic performance of the spatial parallel mechanism visibly deteriorates.

Key words： parallel mechanism      spherical joint clearance      contact model      Newton-Eulerian method      dynamic characteristic     
Received: 29 April 2019      Published: 10 March 2020
CLC:  TH 113  
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Yan-biao LI
Tao-tao XU
Hang ZHENG
Ze-sheng WANG
Cite this article:

Yan-biao LI,Tao-tao XU,Hang ZHENG,Ze-sheng WANG. Dynamic characteristics of spatial parallel mechanism with spherical joint clearance. Journal of ZheJiang University (Engineering Science), 2020, 54(2): 348-356.

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http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2020.02.016     OR     http://www.zjujournals.com/eng/Y2020/V54/I2/348


含球面副间隙的空间并联机构动态特性

为了分析含球面副间隙的5-PSS/UPU并联机构的动态特性，建立含多个球面副间隙的空间并联机构的刚体动力学模型. 基于“接触-分离”二状态模型建立含球面副间隙的运动学模型；基于改进的接触模型和修正的Coulomb摩擦模型建立运动副元素之间的法向与切向接触力模型，进一步将接触力转化到运动副元素对应的部件质心；采用牛顿-欧拉法并结合拉格朗日乘子建立含间隙空间并联机构的动力学模型，利用数值仿真分析其动态特性，计算得到间隙分别为0.05、0.10、0.20、0.40 mm时的动平台角加速度均方根误差（RMSE）指标，分别为40.046、65.385、98.489、145.715 rad/s2. 结果表明，在存在多个球面副间隙的情况下，当间隙增加时，空间并联机构的动态性能严重退化.


关键词： 并联机构,  球面副间隙,  接触模型,  牛顿-欧拉法,  动态特性 
Fig.1 5-PSS/UPU parallel mechanism model
Fig.2 5-PSS/UPU parallel mechanism structure diagram
Fig.3 Kinematic model of spherical surface with clearance
Fig.4 Closed-loop vector diagram of parallel mechanism with clearance
Fig.5 local coordinate system of 5-PSS/UPU parallel mechanism component
参数 符号 数值
静平台外接圆半径 r2 0.633 m
动平台外接圆半径 r1 0.306 m
连杆长度 L 0.56 m
移动副与静平台夹角 θ π/6 rad
动平台质量 ${m_D}$ 8.2 kg
连杆质量 ${m_{\rm L}}$ 2.5 kg
滑块质量 ${m_{\rm S}}$ 0.84 kg
动平台转动惯量 ${I_{Dxx} }$ 0.237 251 kg·m2
动平台转动惯量 ${I_{Dyy} }$ 0.237 251kg·m2
动平台转动惯量 ${I_{Dzz} }$ 0.474 366 kg·m2
连杆转动惯量 ${I_{{\rm L}xx}}$ 0.057 488 kg·m2
连杆转动惯量 ${I_{{\rm L}yy}}$ 0.057 488 kg·m2
连杆转动惯量 ${I_{{\rm L}zz}}$ 0.000 775 kg·m2
球套半径 ${R_{\rm c}}$ 0.025 m
球头半径 ${R_{\rm b}}$ 0.024 95 m
球套弹性模量 ${E_{\rm c}}$ 206 GPa
球头弹性模量 ${E_{\rm b}}$ 206 GPa
球套泊松比 ${\mu _{\rm c}}$ 0.29
球头泊松比 ${\mu _{\rm b}}$ 0.29
Tab.1 5-PSS/UPU parallel mechanism structure parameters
Fig.6 Iterative calculation flow chart of 5-PSS/UPU parallel mechanism kinematic model with spherical clearance
Fig.7 Displacement curve of moving platform
Fig.8 Speed curve of moving platform
Fig.9 Acceleration curve of moving platform
Fig.10 Root-mean-square error of angular acceleration for different clearance sizes
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