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浙江大学学报(工学版)
浙江大学学报(工学版)  2024, Vol. 58 Issue (8): 1533-1542    DOI: 10.3785/j.issn.1008-973X.2024.08.001
机械工程、能源工程     
全齿轮耦合机器人齿侧间隙建模与公差仿真
蒋君侠1(),仲笑欧1,吕林灿1,来建良2,金丁灿2
1. 浙江大学 机械工程学院，浙江 杭州 310058
2. 杭州景业智能科技股份有限公司，浙江 杭州 310051
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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摘要：

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    
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 words: fully gear-coupled robot    gear backlash    cylinder gear mechanism    bevel gear mechanism    tolerance simulation
收稿日期: 2023-08-12 出版日期: 2024-07-23
CLC:  TH 132  
基金资助: 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.
作者简介: 蒋君侠（1968—），男，研究员，博导，从事智能装备结构创新设计与开发的研究. orcid.org/0000-0001-7920-8282. E-mail：jiangjx@zju.edu.cn
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蒋君侠
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引用本文:

蒋君侠,仲笑欧,吕林灿,来建良,金丁灿. 全齿轮耦合机器人齿侧间隙建模与公差仿真[J]. 浙江大学学报(工学版), 2024, 58(8): 1533-1542.

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.

链接本文:

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

图 1  全齿轮机器人的结构与传动原理
图 2  肩关节传动链的原理
图 3  肩关节摆动传动链的结构
图 4  齿轮副齿侧间隙
图 5  圆锥齿轮副与假想圆柱齿轮副的示意图
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—
${b_{\min }}$/μm—2
${b_{\max }}$/μm—30
表 1  圆柱齿轮机构的参数与公差
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
表 2  圆柱齿轮传动参数
图 6  圆柱法向侧隙的仿真结果
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
表 3  圆柱齿轮公差的贡献度
项目jnmin/μm$\mu_{j_{\mathrm{n}}} $/μmjnmax/μm
理论建模325374
三维仿真345475
表 4  圆柱齿轮机构法向侧隙的对比
图 7  圆锥齿轮副与假想圆柱齿轮副的侧隙关系图
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
表 5  圆锥齿轮机构的参数与公差
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}}'' $/μm19
P/μm12
表 6  圆锥齿轮传动参数
图 8  圆锥法向侧隙的仿真结果
序号尺寸名称公差/mm贡献度/%
1主动轮齿厚偏差0.01130.0
2从动轮齿厚偏差0.01130.0
3主动轮几何偏心0.02815.1
4从动轮几何偏心0.02810.2
5面轮廓度误差0.0129.1
6轴交角偏差0.0203.6
7轴承径向游隙0.0102.0
表 7  圆锥齿轮的公差贡献度
项目jnmin/μm$\mu_{j_{\mathrm{n}}} $/μmjnmax/μm
理论建模7090110
三维仿真7290108
表 8  圆锥齿轮机构法向侧隙的对比
图 9  机器人肩关节的L型姿态
图 10  末端位置测量实验
图 11  手持式探针三坐标仪
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