采用NURBS曲线的钢球减速器的型线设计研究

王娟娟; 平雪良; 周忠良; 蒋路明

doi:10.13433/j.cnki.1003-8728.20200258

采用NURBS曲线的钢球减速器的型线设计研究

doi: 10.13433/j.cnki.1003-8728.20200258

1.
江南大学机械工程学院江苏省食品先进制造装备技术重点实验室, 江苏无锡 214122
2.
森力茂(无锡)智能科技有限公司, 江苏无锡 214176

基金项目:

江苏省研究生科研与实践创新计划项目 KYCX191879

详细信息

作者简介:
王娟娟(1996-), 硕士研究生, 研究方向为机电一体化, 1251991560@qq.com

通讯作者:
平雪良, 教授, 博士, ping@jiangnan.edu.cn

中图分类号: TH132
计量
- 文章访问数: 118
- HTML全文浏览量: 38
- PDF下载量: 22
- 被引次数: 0
出版历程
- 收稿日期: 2020-01-04
- 刊出日期: 2021-12-05

Research on Profile Design of Cycloid Steel Ball Reducer using NURBS Curve

1.
Jiangsu Province Key Laboratory of Advanced Food Manufacturing Equipment and Technology, School of Mechanical Engineering, Jiangnan University, Wuxi 214122, Jiangsu, China
2.
Senlimao (Wuxi) Intelligent Technology Co., Ltd., Jiangsu Wuxi 214176, Jiangsu, China

摘要

摘要: 摆线钢球减速器在摆线盘型线设计与优化过程中对型线的自由度与可控性要求越来越高，由此本文提出了将NURBS曲线应用到减速器摆线盘的型线设计过程中，深入研究基于NURBS的摆线型线，通过对已知摆线型线进行采样，获取样本点，反求控制点、权因子、节点矢量，得到符合精度要求的拟合型线，并以此型线完成虚拟样机与试验样机的设计，仿真与实验结果显示NURBS曲线表示方法可以保证摆线钢球减速器的传动精度，为进一步提高摆线盘型线设计的灵活性与局部可调整性奠定了基础，并验证了减速器样机的传动误差和噪音等性能明显优于传统的行星减速器。
- 摆线钢球减速器 /
- 型线设计 /
- NURBS曲线 /
- 性能
Abstract: Higher requirements for the degree of freedom and controllability of the profile in the process of designing and optimizing the profile of the cycloidal disc have been proposed. Therefore, the NURBS curve is proposed to be applied in the profile design process of the reducer cycloid disc in this study. After in-depth study of the cycloid profile using NURBS, by sampling the known cycloid profile, obtaining sample points, inversely finding the control points, weight factors and node vectors to obtain a fitted profile that meets the accuracy requirements, the design of virtual prototype and test prototype are completed with this profile. Simulation and experimental results show that the NURBS curve representation method can ensure the transmission accuracy of the cycloid steel ball reducer, which has laid a foundation for further improving the flexibility and local adjustability of the cycloid plate design. It is verified that the transmission error and noise performance of the reducer prototype is obviously superior to the traditional planetary reducers.
- cycloid steel ball reducer /
- profile design /
- NURBS curve /
- performance

HTML全文

图 1 摆线钢球减速器结构图

下载: 全尺寸图片幻灯片

图 2 摆线形成原理图

下载: 全尺寸图片幻灯片

图 3 NURBS曲线设计流程

下载: 全尺寸图片幻灯片

图 4 NURBS曲线拟合型线的误差图

下载: 全尺寸图片幻灯片

图 5 NURBS型线法摆线盘模型

下载: 全尺寸图片幻灯片

图 6 虚拟样机角速度仿真结果

下载: 全尺寸图片幻灯片

图 7 传动误差

下载: 全尺寸图片幻灯片

图 8 传动误差测试平台

下载: 全尺寸图片幻灯片

图 9 实验测试结果

下载: 全尺寸图片幻灯片

图 10 噪音检测试验

下载: 全尺寸图片幻灯片

表 1 摆线设计计算公式

参数	计算公式
钢球数n_b	传动比确定
偏心距A	传递功率和机型
钢球直径d_b	传递功率和机型
外摆基圆半径r_e	r_e=R_bn_e/n_b
内摆基圆半径r_h	r_h=R_bn_h/n_b
滚圆半径r₀	r₀=R_b/n_b
钢球分布圆半径r_s	r_s=n_br₀
外摆线波数n_e	n_e=n_b+1
内摆线波数n_h	n_h=n_b+1
短幅系数K	k=An_b/(2R_b)
球径系数K₂	K₂=[d_zsin(π/n_b)]/d_b

下载: 导出CSV

表 2 摆线盘型线设计参数

钢球数	偏心距	钢球半径	短幅系数	滚圆半径
21	1.4	3.5	0.894 25	1.118 25

下载: 导出CSV

表 3 摆线方程法传动误差分析

速度	最小值/arc min	最大值/arc min	平均值/arc min
1 000 d	0.796	1.125	1.024 5
500 d	0.875	1.115	1.035 7
100 d	0.915	1.070	1.022 9

下载: 导出CSV

表 4 NURBS型线法传动误差分析

速度	最小值/arc min	最大值/arc min	平均值/arc min
1 000 d	0.875	1.085	1.021 6
500 d	0.955	1.124	1.036 5
100 d	0.942	1.069	1.026 8

下载: 导出CSV

表 5 不同品牌行星减速器性能对比

品牌	减速比	误差/arc min	噪音值/dB
台湾精工	1∶10	精密≤3 标准≤8	≤65
纽格特	1∶10	7~10	≤60
样机	1∶10	1.049	47.6

下载: 导出CSV

参考文献(16)

[1]	王猛. 基于概率的摆线钢球传动回差的研究[D]. 马鞍山: 安徽工业大学, 2018 WANG M. Research on the return difference of cycloid steel ball transmission based on probability[D]. Maanshan: Anhui University of Technology, 2018 (in Chinese)
[2]	杨荣刚, 安子军, 段利英. 摆线钢球行星传动自由振动分析[J]. 中国机械工程, 2016, 27(14): 1883-1891 doi: 10.3969/j.issn.1004-132X.2016.14.008 YANG R G, AN Z J, DUAN L Y. Analysis of free vibration of cycloid ball planetary transmission[J]. China Mechanical Engineering, 2016, 27(14): 1883-1891 (in Chinese) doi: 10.3969/j.issn.1004-132X.2016.14.008
[3]	TERADA H. The development of gearless reducers with rolling balls[J]. Journal of Mechanical Science and Technology, 2010, 24(1): 189-195 doi: 10.1007/s12206-009-1155-0
[4]	TERADA H, SUEKI R, MAKINO K, et al. Development of an outer groove rotor type precession motion ball reducer[C]//Nephron Clinical Practice. The 14th IFToMM World congress. Taipei, China: IFToMM, 2015: 499-504
[5]	洪诚, 安子军, 夏婧琪, 等. 实时无隙钢球精密传动啮合副本体温度场分析[J]. 机械强度, 2017, 39(6): 1391-1397 https://www.cnki.com.cn/Article/CJFDTOTAL-JXQD201706024.htm HONG C, AN Z J, XIA J Q, et al. Analysis of bulk temperature field of constantly no clearance precision steel ball transmission[J]. Journal of Mechanical Strength, 2017, 39(6): 1391-1397 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JXQD201706024.htm
[6]	张晓美, 安子军, 薛进. 双级摆线钢球行星传动应力和强度的研究[J]. 机械强度, 2016, 38(5): 1041-1045 https://www.cnki.com.cn/Article/CJFDTOTAL-JXQD201605024.htm ZHANG X M, AN Z J, XUE J. Research on stress and strength of wo-stage cycloid ball planetary transmission[J]. Journal of Mechanical Strength, 2016, 38(5): 1041-1045 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JXQD201605024.htm
[7]	安子军, 杨荣刚, 宜亚丽. 精密钢球传动啮合法向力与弹性回差[J]. 机械工程学报, 2016, 52(9): 42-48 https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201609006.htm AN Z J, YANG R G, YI Y L. Engagement normal force and elastic backlash of precision ball transmission[J]. Journal of Mechanical Engineering, 2016, 52(9): 42-48 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201609006.htm
[8]	杨荣刚, 安子军. 基于谐波平衡法的摆线钢球行星传动等速输出机构非线性动态特性研究[J]. 振动与冲击, 2017, 36(2): 153-158 https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201702025.htm YANG R G, AN Z J. Nonlinear dynamic characteristics of the equal speed output mechanism of cycloid ball planetary transmission based on harmonic balance method[J]. Journal of Vibration and Shock, 2017, 36(2): 153-158 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201702025.htm
[9]	段利英, 安子军, 付志强. 实时无隙钢球精密传动空间速度矢模型[J]. 中国机械工程, 2018, 29(9): ; 069-1075 doi: 10.3969/j.issn.1004-132X.2018.09.010 DUAN L Y, AN Z J, FU Z Q. Space velocity vector model of real-time non-clearance ball precise transmissions[J]. China Mechanical Engineering, 2018, 29(9): 1069-1075;in Chinese doi: 10.3969/j.issn.1004-132X.2018.09.010
[10]	DUAN L Y, AN Z J, YANG R G, et al. Mechanical model of coupling rolling and sliding friction in real-time non-clearance precision ball transmission[J]. Tribology International, 2016, 103: 218-227 doi: 10.1016/j.triboint.2016.06.032
[11]	张鹏, 安子军. 摆线钢球行星传动动力学建模与固有特性分析[J]. 中国机械工程, 2014, 25(2): 157-162 doi: 10.3969/j.issn.1004-132X.2014.02.004 ZHANG P, AN Z J. Dynamics model and natural characteristics of cycloid ball planetary transmission[J]. China Mechanical Engineering, 2014, 25(2): 157-162 (in Chinese) doi: 10.3969/j.issn.1004-132X.2014.02.004
[12]	张悦, 安子军, 杨荣刚, 等. 摆线钢球行星传动十字槽等速输出机构的力学性能[J]. 中国机械工程, 2019, 30(14): 1665-1672 doi: 10.3969/j.issn.1004-132X.2019.14.005 ZHANG Y, AN Z J, YANG R G, et al. Mechanics properties of cross-groove equi-speed output mechanisms for cycloid ball planetary transmissions[J]. China Mechanical Engineering, 2019, 30(14): 1665-1672 (in Chinese) doi: 10.3969/j.issn.1004-132X.2019.14.005
[13]	SU S H, TSENG C H. Generating conjugate shapes using piecewise cubic spline functions[J]. Computer Methods in Applied Mechanics and Engineering, 2000, 187(1-2): 245-260 doi: 10.1016/S0045-7825(99)00133-4
[14]	黄海楠, 何雪明, 张荣, 等. 基于NURBS曲线的螺杆转子型线反向设计研究[J]. 食品与机械, 2018, 34(3): 93-97, 145 https://www.cnki.com.cn/Article/CJFDTOTAL-SPJX201803024.htm HUANG H N, HE X M, ZHANG R, et al. Study on inverse design of screw rotor profile based on NURBS curve[J]. Food & Machinery, 2018, 34(3): 93-97, 145;in Chinese https://www.cnki.com.cn/Article/CJFDTOTAL-SPJX201803024.htm
[15]	龙骥, 何雪明, 吴佳, 等. 螺杆转子型线正向设计中的曲线连续性研究[J]. 机械科学与技术, 2019, 38(2): 190-197 doi: 10.13433/j.cnki.1003-8728.20180151 LONG J, HE X M, WU J, et al. Exploring curve continuity in forward design of screw rotor profile[J]. Mechanical Science and Technology for Aerospace Engineering, 2019, 38(2): 190-197 (in Chinese) doi: 10.13433/j.cnki.1003-8728.20180151
[16]	PIEGL L, TILLER W. 非均匀有理B样条[M]. 2版. 赵罡, 穆国旺, 王拉柱, 译. 北京: 清华大学出版社, 2010: 34-59, 86-93, 209-210 PIEGL L, TILLER W. The NURBS book[M]. 2nd ed. ZHAO G, MU G W, WANG L Z, trans. Beijing: Tsinghua University Press, 2010: 34-59, 86-93, 209-210 (in Chinese)