非圆齿轮传动误差及齿侧间隙的数值模拟与试验

doi:10.13229/j.cnki.jdxbgxb.20221060

Abstract

Abstract:

The difficulty in establishing the transmission error model of non-circular gears and obtaining the backlash limit its application in precision occasions. In order to improve the transmission accuracy of non-circular gears， the non-circular gear transmission error model and backlash model under bidirectional transmission are established based on the meshing line incremental method considering the eccentricity error. The influence of eccentricity and eccentricity error on bidirectional transmission error and backlash are analyzed， and the correctness of theoretical analysis is verified by transmission test. The analysis shows that the backlash of the non-circular gear can be obtained by the bidirectional transmission error. With the increase of eccentricity and eccentricity error， the two-way transmission error shows an increasing trend. Optimizing the initial phase can reduce the transmission error and backlash to a certain extent. As the load increases， the transmission error and backlash also show an increasing trend. And due to the existence of gear tooth deformation， there is a certain cumulative value of the backlash.

Key words: mechanical manufacturing and automation, non-circular gear, meshing line increment, transmission error, gear backlash, transmission experiment

CLC Number:

TH132.4

Chang-bin DONG,Long-kun LI,Yong-ping LIU,Wang-peng PEI. Numerical simulation and experiment of non-circular gear transmission error and backlash[J].Journal of Jilin University(Engineering and Technology Edition), 2024, 54(4): 865-873.

Figures/Tables 15

Fig.1

Fig.2

Fig.3

Table 1

Non-circular gear pair parameters"

名称	数值
模数m/mm	3
中心距a/mm	150
顶隙系数C^*	0.25
偏心率k	0.2
齿数Z	47
齿顶高系数 $h a *$	1
齿宽B/mm	30
节曲线方程r	$64.667 1 ± 0.3287 c o s ? θ$

Table 1

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Table 2

Detailed configuration information of non-circular gear transmission test rig"

部件名称	型号	规格
转矩传感器	YH-502	测量量程：20 N·m和2000 N·m；测量精度：±0.1%；电源电压：24 V DC；输出信号：10±5 kHz；扭矩精度： $< ± 0.1 % F ? S$ ；频率响应： $100 ? μ s$
噪声传感器	RS-ZS-V05-2	量程：30~120 dB；频率范围：0.02~12.5 kHz；测量误差：±1.5 dB
红外温度传感器	CK-01A	温度范围：-20~300 ℃；光谱范围： $8$ ~ $14 ? μ m$ ；测量精度：±1%；响应时间：50~300 ms可选；
振动传感器	CA-YD-107	频率响应：0.5~6000 Hz；最大横向灵敏度：≤5%；轴向灵敏度： $50 ? P C / g$ ；磁灵敏度：2 g/T；基座应变： $0.2 ? m g / μ g$
圆光栅	K-100	电源电压：24 V DC；分辨率：48 000 P/R；防护等级：IP50
交流伺服电动机	MSME504G	额定转速：3000 r/min；额定电压：400 V AC（三相）；转矩：15.9 N·m；防护等级：IP67
伺服电动机驱动器	MFDTA464	额定电压：400 V AC（三相）
PLC	S7-200SMART	电源电压：220 V AC；I/O点：30；AO通道：4
数据采集卡	NI-6351	采样率：1.25 MS/s；AI通道：16；A/D精度：16位；AO通道：2；DIO通道：24；计数通道：4

Table 2

Fig.11

Fig.12

Fig.13

References 16

1	董长斌, 刘永平, 魏永峭. 不同载荷条件下椭圆柱齿轮动态接触特性分析[J]. 华中科技大学学报: 自然科学版, 2019, 47(8): 103-107.
	Dong Chang-bin, Liu Yong-ping, Wei Yong-qiao. Dynamic contact characteristics analysis of elliptic cylinder gear under different load conditions[J]. J Huazhong Univ of Sci & Tech(Natural Science Edition) 2019, 47(8): 103-107.
2	董长斌. 椭圆齿轮传动系统的啮合特性研究[D]. 兰州: 兰州理工大学机电工程学院, 2021.
	Dong Chang-bin. Study on meshing characteristics of elliptic gear transmission system[D]. Lanzhou: School of Mechanical & Electronical Engineering,Lanzhou University of Technology, 2021.
3	Kim S C, Moon S G. Macro geometry optimization of a helical gear pair for mass, efficiency, and transmission error[J]. Mechanism and Machine Theory, 2020, 144: No. 103634.
4	刘国政, 史文库, 陈志勇. 考虑安装误差的准双曲面齿轮传动误差有限元分析[J]. 吉林大学学报: 工学版, 2018, 48(4): 984-989.
	Liu Guo-zheng, Shi Wen-ku, Chen Zhi-yong. Finite element analysis of transmission error for hypoid gears considering installation error[J]. Journal of Jilin Univeraity (Engineering and Technology Edition), 2018, 48(4): 984-989.
5	Rezaei M, Poursina M, Jazi S H. Multi crack detection in helical gear teeth using transmission error ratio[J]. Journal of Mechanical Science and Technology, 2019, 33(3): 1115-1121.
6	Hotait M A, Kahraman A. Experiments on the relationship between the dynamic transmission error and the dynamic stress factor of spur gear pairs[J]. Mechanism and Machine Theory, 2013, 70: 116-128.
7	Liu D W, Ba Y B, Ren T Z. Flow fluctuation abatement of high-order elliptic gear pump by external noncircular gear drive[J]. Mechanism and Machine Theory, 2019, 134: 338-348.
8	刘大伟, 任廷志, 巴延博, 等. 基于弹性转角分离的非圆齿轮扭振模型及其动态特性[J]. 振动与冲击, 2016, 35(23): 228-233.
	Liu Da-wei, Ren Ting-zhi, Ba Yan-bo, et al. Torsional vibration model and its dynamic characteristics for a noncircular gear based on separation of elastic rotating angle[J]. Journal of Vibration and Shock, 2016, 35(23): 228-233.
9	Liu D W, Wang G H, Ren T Z. Transmission principle and geometrical model of eccentric face gear[J]. Mechanism and Machine Theory, 2017, 109: 51-64.
10	David B D, Domenico M. Unloaded transmission error and instantaneous gear ratio for non-circular gears with misalignments[J]. Mechanism and Machine Theory, 2022, 170: No.104728.
11	Dong C, Liu Y, Wei Y, et al. Analysis on meshing characteristics and transmission error of elliptic gears[J]. Mathematical Problems in Engineering, 2020(1): 1-10.
12	Margielewicz J, Gąska D, Litak G. Modelling of the gear backlash[J]. Nonlinear Dynamics, 2019, 97(1):355-368.
13	Wang G, Chen L, Li Y. Research on the dynamic transmission error of a spur gear pair with eccentricities by finite element method[J]. Mechanism and Machine Theory, 2017, 109:1-13.
14	邹帅东, 王光建. 双齿轮偏心的传动误差计算与研究[J]. 电子科技大学学报, 2017, 46(6): 955-960.
	Zou Shuai-dong, Wang Guang-jian. Research on transmission error of dual-eccentric gears[J]. Journal of University of Electronic Science and Technology of China, 2017, 46(6): 955-960.
15	邹帅东, 王光建, 蒋宇将, 等. 交变负载下变齿厚齿轮副侧隙控制试验研究[J]. 机械工程学报, 2020, 56(15): 152-160.
	Zou Shuai-dong, Wang Guang-jian, Jiang Yu-jiang, et al. Experimental investigation on backlash control of variable tooth thickness gear pair under varying load excitation[J]. Journal of Mechanical Engineering, 2020, 56(15): 152-160.
16	Han J, Li D, Tian X, et al. Meshing principle and transmission analysis of a beveloid non-circular gear[J]. Advances in Mechanical Engineering, 2020, 12(11):1-11.

Related Articles 11

[1]	Fei WU,Hao-ye NONG,Chen-hao MA. Tool wear prediction method based on particle swarm optimizationlong and short time memory model [J]. Journal of Jilin University(Engineering and Technology Edition), 2023, 53(4): 989-997.
[2]	Lin SONG,Li-ping WANG,Jun WU,Li-wen GUAN,Zhi-gui LIU. Reliability analysis based on cyber⁃physical system and digital twin [J]. Journal of Jilin University(Engineering and Technology Edition), 2022, 52(2): 439-449.
[3]	Guo-long LI,Xiao-hui TAO,Kai XU,Zhe-yu LI. Rapid measurement and identification of position dependent geometric errors of CNC machine tool turntable [J]. Journal of Jilin University(Engineering and Technology Edition), 2021, 51(2): 458-467.
[4]	Yun-wei ZHAO,De-xu GENG,Xiao-min LIU,Qi LIU. Implementation and stability on turning with constant radius of pneumatic flexible hexapod robot [J]. Journal of Jilin University(Engineering and Technology Edition), 2020, 50(2): 472-482.
[5]	Chun-zheng DUAN,Fang-yuan ZHANG,Wen-neng KOU,Bin WEI. Martensitic transformation of surface white layer in high speed hard cutting [J]. Journal of Jilin University(Engineering and Technology Edition), 2019, 49(5): 1575-1583.
[6]	LIU Guo-zheng, SHI Wen-ku, Chen Zhi-yong. Finite element analysis of transmission error for hypoid gears considering installation error [J]. 吉林大学学报(工学版), 2018, 48(4): 984-989.
[7]	ZONG Chang-fu, REN Ming-hui, WAN Ying, CHEN Tao, BAI Ying-bo. Optimization of macro-geometric parameters of helical gears of transmissions to reduce vibration [J]. 吉林大学学报(工学版), 2016, 46(6): 1772-1779.
[8]	REN Shu-nan, YANG Xiang-dong, WANG Guo-lei, LIU Zhi, CHEN Ken. Base position planning of mobile manipulator for large parts painting [J]. 吉林大学学报(工学版), 2016, 46(6): 1995-2002.
[9]	GUO Li-bin, ZHANG Bin, CUI Hai, ZHANG Zhi-hang. Structural parameters of 3D roughness for micro wire electrical discharge machining surface [J]. 吉林大学学报(工学版), 2015, 45(3): 851-856.
[10]	ZHANG Lei, ZHAO Yun-wei, YANG Zhuo, ZHAO Ji. Shear yield property of electrorheological polishing fluid [J]. , 2012, 42(05): 1145-1150.
[11]	ZHANG Lei,HE Xin-sheng,ZHANG Ying,YANG He-ran. Development of new type ER fluid-assisted polishing tool and its polishing experiment [J]. 吉林大学学报(工学版), 2010, 40(04): 1009-1014.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed

Comments

Recommended 0

No Suggested Reading articles found!

Numerical simulation and experiment of non-circular gear transmission error and backlash

RICH HTML

PDF (PC)