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Journal of ZheJiang University (Engineering Science)  2024, Vol. 58 Issue (8): 1533-1542    DOI: 10.3785/j.issn.1008-973X.2024.08.001
    
Gear backlash modeling and tolerance simulation of fully gear-coupled robot
Junxia JIANG1(),Xiaoou ZHONG1,Lincan LV1,Jianliang LAI2,Dingcan JIN2
1. School of Mechanical Engineering, Zhejiang University, Hangzhou 310058, China
2. Hangzhou Jingye Intelligent Technology Limited Company, Hangzhou 310051, China
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Abstract  

The robot’s structure and transmission principles were analyzed given the characteristics of long gear transmission chains and high reverse frequency in fully gear-coupled robots. Theoretical modeling of gear backlash and a three-dimensional tolerance simulation analysis method were proposed to reduce the impact of backlash on the transmission accuracy of robots. The theoretical modeling and the tolerance simulation analysis of gear backlash were conducted for the cylindrical gear mechanism at the drive end. The two results were consistent. An equivalent backlash modeling method that equivalents the bevel gear pair as a hypothetical cylindrical gear pair was proposed for the bevel gear mechanism in joints, and the theoretical modeling analysis result accorded with the tolerance simulation analysis results. The end error of the robot was calculated by taking the robot shoulder joint swing transmission chain as the analysis object. The calculation method of bevel gear backlash and the motor angle compensation method were proposed to reduce gear backlash and the return error of the transmission chain caused by the gear backlash. The effectiveness of this compensation method was validated through experiment.



Key wordsfully gear-coupled robot      gear backlash      cylinder gear mechanism      bevel gear mechanism      tolerance simulation     
Received: 12 August 2023      Published: 23 July 2024
CLC:  TH 132  
Fund:  2022年度浙江省科技计划资助项目(2022C01054);浙江大学机器人研究院自主科研项目资金资助项目.
Cite this article:

Junxia JIANG,Xiaoou ZHONG,Lincan LV,Jianliang LAI,Dingcan JIN. Gear backlash modeling and tolerance simulation of fully gear-coupled robot. Journal of ZheJiang University (Engineering Science), 2024, 58(8): 1533-1542.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2024.08.001     OR     https://www.zjujournals.com/eng/Y2024/V58/I8/1533


全齿轮耦合机器人齿侧间隙建模与公差仿真

鉴于全齿轮耦合机器人齿轮传动链长、反转频率高的特点,分析机器人的结构和传动原理. 为了减小侧隙对机器人传动精度的影响,提出齿侧间隙理论建模及三维公差仿真分析方法. 针对驱动端的圆柱齿轮机构,对齿侧间隙进行理论建模和公差仿真分析,两者相吻合. 针对关节处的圆锥齿轮机构,提出将圆锥齿轮副等效为假想圆柱齿轮副的侧隙建模方法,与公差仿真分析结果吻合. 以机器人肩关节偏摆传动链为分析对象计算机器人末端误差,为了降低齿侧间隙及其导致的传动链回程误差,提出圆锥齿轮加垫的计算方法和电机转角补偿方法,通过实验验证该补偿方法的有效性.


关键词: 全齿轮耦合机器人,  齿侧间隙,  圆柱齿轮机构,  圆锥齿轮机构,  公差仿真 
Fig.1 Structure and transmission principle of fully gear-coupled robot
Fig.2 Principle of shoulder joint transmission chain
Fig.3 Structure of shoulder joint swing transmission chain
Fig.4 Backlash of gear pair
Fig.5 Schematic diagram of bevel gear pairs and imaginary cylindrical gear pairs
项目主动轮从齿轮
$z$28110
m/mm2.52.5
$\alpha $/(°)2020
d/mm70275
$ {E_{{\text{ss}}}} $/μm?19?21
$ {E_{{\text{si}}}} $/μm?30?32
${F''_{\text{i}}}$/μm2731
S/μm8
${b_{\min }}$/μm2
${b_{\max }}$/μm30
Tab.1 Parameter and tolerance of cylindrical gear mechanism
参数数值
减速比3.929
中心距$a$/mm172.5
齿轮精度等级5-f
中心距极限偏差/μm±20
最小极限法向侧隙/μm15
Tab.2 Cylindrical gear transmission parameter
Fig.6 Simulation result of cylindrical normal backlash
序号尺寸名称公差/mm贡献度/%
1主动轮齿厚偏差0.00522.0
2从动轮齿厚偏差0.00522.0
3齿轮副中心距偏差0.04021.7
4从动轮几何偏心0.01613.0
5轴承径向游隙0.01410.6
6主动轮几何偏心0.0149.9
7减速器输出轴圆跳动0.0080.8
Tab.3 Contribution of cylindrical gear tolerance
项目jnmin/μm$\mu_{j_{\mathrm{n}}} $/μmjnmax/μm
理论建模325374
三维仿真345475
Tab.4 Comparison of normal backlash of cylindrical gear mechanism
Fig.7 Side backlash relationship between bevel gear pairs and imaginary cylindrical gear pairs
参数数值
z31
m/mm3.5
$\alpha $/(°)20
d/mm108.5
B/mm9
${d_{\text{m}}}$/mm102.1
$ {E_{{\text{ss}}}} $/μm?32
$ {E_{{\text{si}}}} $/μm?53
${b_{\min }}$/μm10
${b_{\max }}$/μm30
Tab.5 Parameter and tolerance of bevel gear mechanism
参数数值
减速比1
$ {f_{\text{a}}} $/μm9
$ {E_\Sigma } $/μm10
$ F_{{{{\mathrm{i}}\Sigma }}}{{{''}}} $/μm20
齿轮精度等级5-f
$j_{\mathrm{nmin}}'' $/μm19
P/μm12
Tab.6 Bevel gear transmission parameter
Fig.8 Simulation result of bevel normal backlash
序号尺寸名称公差/mm贡献度/%
1主动轮齿厚偏差0.01130.0
2从动轮齿厚偏差0.01130.0
3主动轮几何偏心0.02815.1
4从动轮几何偏心0.02810.2
5面轮廓度误差0.0129.1
6轴交角偏差0.0203.6
7轴承径向游隙0.0102.0
Tab.7 Tolerance contribution of bevel gear
项目jnmin/μm$\mu_{j_{\mathrm{n}}} $/μmjnmax/μm
理论建模7090110
三维仿真7290108
Tab.8 Comparison of normal backlash of bevel gear mechanism
Fig.9 L-shaped posture of robot shoulder joint
Fig.10 End position measurement experiment
Fig.11 Handheld probe coordinate measuring machine
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