Mechanical Engineering

Design and Analysis for Actively Modified Gear with Zero Amplitude of Loaded Transmission Error

Expand
  • 1.School of Automotive/Key Laboratory of Automotive Transportation Safety Techniques of Ministry of Transport,Chang’an University,Xi’an 710064,Shaanxi,China
    2.College of Mechanical Engineering,Northwestern Polytechnical University,Xi’an 710072,Shaanxi,China
蒋进科(1981-),男,博士生,工程师,主要从事齿轮传动等研究。

Received date: 2021-12-01

  Online published: 2022-04-23

Supported by

the Fundamental Research Funds for the Central Universities(300102221105);the Natural Science Basic Research Plan in Shaanxi Province of China(2021JM-175)

Abstract

To eliminate stiffness excitation, this paper proposed an approach of design and analysis for actively modified gears with zero amplitude of loaded transmission error (ALTE). Firstly, the maximum bearing deformation of mesh cycle was obtained based on tooth contact analysis and loaded tooth contact analysis (LTCA) for predesign modified gears. Secondly, taking bearing deformations of meshing period being equal to the maximum value as the known condition, a novel equation for LTCA was developed, then compensating tooth gaps from pitch error (additional modifications) were determined by solving the equation in reverse. Thirdly, the compensating gaps characterized by equal values along instantaneous contact line of tooth were constrained according to the meshing positions, and was added to the predesigned modified pinion to produce novel modified gears with zero ALTE. The method integrated geometric analysis and mechanical analysis of tooth, and it can accurately and quickly obtain any modified gears with zero ALTE. The results show that shape and size determined by the compensating gaps surface are related to the locations of tooth, the predesign modification and load. On the one hand, when the differences of predesigned modification is small, the rule of compensation modification curve is basically opposite to the ALTE of predesigned tooth modification, that is, the larger the bearing deformation is, the smaller the compensation gaps is.Then the overall compensation modification is also small due to only compensating the bearing deformation differences actually. On the other hand, when the differences of the predesigned modification is large, the overall compensation modification is also large due to compensating the differences of both bearing deformation and predesigned modification at the meshing position. Besides, the tooth contact pattern is not changed with the compensation modification and ALTE are reduced on wider loads for gears with zero ALTE based on preset topology modification. Appropriate locations and predesign modifications make the additional modification well integrate into the predesigned and modified surface, so as to obtain the machinable modified pinion with zeros ALTE. It provides a theoretical reference for design and analysis of tooth with vibration reduction and high performances.

Cite this article

JIANG Jinke FANG Zongde . Design and Analysis for Actively Modified Gear with Zero Amplitude of Loaded Transmission Error[J]. Journal of South China University of Technology(Natural Science), 2022 , 50(9) : 99 -108 . DOI: 10.12141/j.issn.1000-565X.210751

References

1 MUNRO R G, MORRISH L, PALMER D. Gear transmission error outside the normal path of contact due to corner and top contact[J].Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,1999,213(4):389-400.
2 PODZHAROV E, SYROMYATNIKOV V, NAVARRO J P P,et al .Static and dynamic transmisson error in spur gears[J].Open Industrial & Manufacturing Engineering Journal,2008,1:37-41.
3 STADTFELD H J, GAISER U .The ultimate motion graph[J].Journal of Mechanical Design,2000,122:317-322.
4 LITVIN F L, VECCHIATO D, YUKISHIMA K,et al .Reduction of noise of loaded and unloaded misaligned gear drives[J].Computer Methods in Applied Mechanics and Engineering,2006,195(41):5523-5536.
5 LI S .Finite element analyses for contact strength and bending strength of a pair of spur gears with machining errors,assembly errors and tooth modifications[J].Mechanism and Machine Theory,2007,42(1):88-114.
6 SIMON V V .Loaded tooth contact analysis and stresses in spiral bevel gears[C]∥ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference.USA:American Society of Mechanical Engineers,2009:271-279.
7 唐进元,刘艳平 .直齿面齿轮加载啮合有限元仿真分析[J].机械工程学报,2012,48(5):124-131.
7 TANG Jinyuan, LIU Yanping .Loaded meshing simulation of face-gear drive with spur involute pinion based on finite element analysis[J].Journal of Mechanical Engineering,2012,48(5):124-131.
8 刘国政,史文库,陈志勇,等 .驱动桥准双曲面齿轮传动误差有限元分析与试验[J].汽车工程,2018,40(7):820-825.
8 LIU Guozheng, SHI Wenku, CHEN Zhiyong,et al .Finite element analysis and test of the transmission error of hypoid gear in drive axle[J].Automotive Engineering,2018,40(7):820-825.
9 郑昌启,黄昌华,吕传贵 .螺旋锥齿轮加载接触分析计算原理[J].机械工程学报,1993,29(4):50-54.
9 ZHENG Changqi, HUANG Changhua, Chuangu Lü .Computational principle of loaded tooth contact analysis of spiroid gears[J].Journal of Mechanical Engineering,1993,29(4):50-54.
10 黄昌华,温诗铸,李润方,等 .弧齿锥齿轮和准双曲面齿轮润滑加载接触分析[J].清华大学学报(自然科学版),1996(4):48-53.
10 HUANG Changhua, WEN Shizhu, LI Renfang,et al .Preliminary design tool-LLTCA for spiral bevel and hypoid gear[J].Journal of Tsinghua University(Science and Technology),1996(4):48-53.
11 王延忠,周云飞,周济,等 .考虑轮齿制造误差的螺旋锥齿轮加载接触分析[J].机械科学与技术,2002,21(2):224-227.
11 WANG Yanzhong, ZHOU Yunfei, ZHOU Ji,et al .Load tooth contact analysis of bevel gear based on manufacture error[J].Mechanical Science and Technology.2002,21(2):224-227.
12 方宗德.修形斜齿轮的轮齿接触分析[J].航空动力学报,1997,12(3):247-250.
12 FANG Z D .Loaded tooth contact analysis of modification of helical gears[J].Journal of Aerospace Power,1997,12(3):247-254.
13 曹雪梅,张华,方宗德 .航空弧齿锥齿轮承载传动误差的分析与设计[J].航空动力学报,2009,24(11):2618-2624.
13 CAO Xuemei, ZHANG Hua, FANG Zongde .Design and analysis of loaded transmission errors for aviation spiral bevel gears[J].Journal of Aerospace Power,2009,24(11):2618-2624.
14 魏静,王刚强,秦大同,等 .考虑修形的斜齿轮系统非线性激励与动力学特性研究[J].振动工程学报,2018,31(4):561-572.
14 WEI Jing, WANG Gangqiang, QIN Datong,et al .Nonlinear excitation and dynamic characteristics of helical gear system[J].Journal of Vibration Engineering,2018,31(4):561-572.
15 魏冰阳,杨建军,聂少武 .差曲面拓扑的齿轮啮合刚度计算与承载接触分析[J].航空动力学报,2019,34(12):222-229.
15 WEI Bingyang, YANG Jianjun, NIE Shaowu .Calculation of gear meshing stiffness and loaded tooth contact analysis based on ease-off surface topolgy[J].Journal of Aerospace Power,2019,34(12):222-229.
16 UMEYAMA M, KATO M, INOUE K .Effects of gear dimensions and tooth surface modifications on the loaded transmission error of a helical gear pair[J].Journal of Mechanical Design,1998,120(1):119-125.
17 蒋进科,方宗德,苏进展 .基于承载传动误差幅值最小的斜齿轮齿面修形优化设计[J].航空动力学报,2013,28(7):1637-1643.
17 JIANG Jinke, FANG Zongde, SU Jinzhan .Optimal design of modified helical gear tooth surfaces based on minimum amplitude of loaded transmission error[J].Journal of Aerospace Power,2013,28(7):1637-1643.
18 JIANG Jinke, FANG Zongde .Design and analysis of modified cylindrical gears with a higher-order transmission error[J].Mechanism and Machine Theory,2015,88:141-152.
19 LEE C K .Manufacturing process for a cylindrical crown gear drive with a controllable fourth order polynomial function of transmission errors[J].Journal of Materials Processing Technology,2009;209(1):3-13.
20 KOLIVAND M, KAHRAMAN A .An ease-off based method for loaded tooth contact analysis of hypoid gears having local and global surface deviations[J].Journal of Mechanical Design,2010,132(7):071004.
21 刘玄,方宗德,赵宁,等.高重合度斜齿轮多齿对啮合的补偿修形设计与分析[J].西安交通大学学报,2020,54(11):56-64.
21 LIU Xuan, FANF Zongde, ZHAO Ning,et al.Design and analysis of compensation modification for multi-pair contact of high contact ratio helical gears[J].Journal of Xi’an Jiaotong University,2020,54(11):56-64.
22 FAGGIONI M, SAMANI F S, BERTACCHI G,et al .Dynamic optimization of spur gears[J].Mechanism & Machine Theory,2011,46(4):544-557.
23 蒋进科,刘钊,彭先龙 .Ease-Off 修形准双曲面齿轮减振优化设计[J].华南理工大学学报(自然科学版),2020,48(5):138-145.
23 JIANG Jinke, LIU Zhao, PENG Xianlong .Optimization design of Vibration reduction for hypoid gears with ease-off flank modification[J].Journal of South China University of Technology(Natural Science Edition),2020,48(5):138-145.
24 蒋进科,方宗德,刘钊 .Ease-off拓扑修形准双曲面齿轮齿面多目标优化设计方法[J].西安交通大学学报,2019,53(6):44-53.
24 JIANG Jinke, FANG Zongde, LIU Zhao .Design of multi-objective tooth optimization for hypoid gear with ease-off topological modification[J].Journal of Xi’an Jiaotong University,2019,53(6):44-53.
25 蒋进科 .高速渐开线圆柱齿轮齿面设计及数控加工技术研究[D].西安:西北工业大学,2015
Outlines

/