Measurement and prediction of backlash based on two-sided transmission error

WANG Guang-jian; ZHOU Lei; ZOU Shuai-dong

doi:10.13374/j.issn2095-9389.2019.10.18.004

Volume 42 Issue 8

Aug. 2020

Turn off MathJax

Article Contents

Article Navigation > Chinese Journal of Engineering > 2020 > 42(8): 1055-1064

WANG Guang-jian, ZHOU Lei, ZOU Shuai-dong. Measurement and prediction of backlash based on two-sided transmission error[J]. Chinese Journal of Engineering, 2020, 42(8): 1055-1064. doi: 10.13374/j.issn2095-9389.2019.10.18.004

Citation:

WANG Guang-jian, ZHOU Lei, ZOU Shuai-dong. Measurement and prediction of backlash based on two-sided transmission error[J]. Chinese Journal of Engineering, 2020, 42(8): 1055-1064. doi: 10.13374/j.issn2095-9389.2019.10.18.004

Citation:

PDF( 1808 KB)

Measurement and prediction of backlash based on two-sided transmission error

doi: 10.13374/j.issn2095-9389.2019.10.18.004

WANG Guang-jian^{1, 2
,
,},
ZHOU Lei^{1, 3},
ZOU Shuai-dong^{1, 3}

1.
State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing 400044, China
2.
School of Automotive Engineering, Chongqing University, Chongqing 400044, China
3.
College of Mechanical Engineering, Chongqing University, Chongqing 400044, China

More Information

Corresponding author: E-mail: gjwang@cqu.edu.cn
Received Date: 2019-10-18
Publish Date: 2020-09-11

Abstract

Abstract

Transmission error in gear system and backlash are important factors that affect the accuracy of precision transmission systems. The main sources of the complete cycle transmission errors and periodic backlash are eccentric errors due to imperfections in machining and assembling. Therefore, analyzing the transmission error in gear system and backlash under the effect of eccentricity error is necessary. Scholars from around the world have conducted extensive research on the transmission error of the gear system. They observed that the back-side contact of the gear tooth generally happens in high-speed light-load conditions, or when alternate load torque occurs or anti-backlash gear has been used. However, the existing literature does not evidently show the calculation method of the transmission error of the back-side tooth mesh. Therefore, analyzing the transmission error of the back-side tooth mesh is of great significance. The present work develops a calculation model of drive- and back-side (two-sided) transmission error of an involute gear pair with eccentricities to construct the equivalence of time-varying backlash calculation formula to demonstrate the continuous measurement of gear backlash based on two-sided transmission error that can also be realized in theory. The experimental transmission error and the corresponding hysteresis were acquired under various load torques and different initial conditions, such as initial position of the gear unit. The continuous backlash curve of the gear pair was obtained from the two-sided transmission curves, and the backlash of the whole cycle could be predicted. The result of the experiment shows that the continuous measurement curve agrees with the mechanical hysteresis method, and the prediction of backlash perfectly reflects the variation range and trend of backlash. Moreover, both the continuous measurement method of backlash and prediction of backlash demonstrate that the model is practicable and have higher efficiency, and the overall data retain instructional significance, reference value for nonlinear research, anti-backlash control, and gear accuracy of gear transmission.
- time-varying backlash,
- two-sided transmission error,
- continuous measurement,
- backlash prediction,
- eccentric error

FullText(HTML)

References(26)

References

[1]	Wang G J, Chen L, Yu L, et al. Research on the dynamic transmission error of a spur gear pair with eccentricities by finite element method. <italic>Mech Mach Theory</italic>, 2017, 109: 1 doi: 10.1016/j.mechmachtheory.2016.11.006
[2]	Yu L, Wang G J, Zou S D. The calculation of meshing efficiency of a new type of conical involute gear. <italic>Strojni?ki vestnik-J Mech Eng</italic>, 2017, 63(5): 320 doi: 10.5545/sv-jme.2016.3843
[3]	Zou S D, Wang G J, Yu L. Research on calculation of unloaded transmission error of planetary gear train caused by eccentricity // ASME 2017International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Cleveland, 2017: 1
[4]	Michalec G W. Precision Gearing: Theory and Practice. New York: Wiley, 1966
[5]	吳慈生. 齒輪偏心誤差所引起的傳動誤差. 南京工學院學報, 1982(4):133 Wu C S. The turning angle error from gears eccentric error. <italic>J Nanjing Inst Technol</italic>, 1982(4): 133
[6]	鄒帥東, 王光建. 雙齒輪偏心的傳動誤差計算與研究. 電子科技大學學報, 2017, 46(6):955 doi: 10.3969/j.issn.1001-0548.2017.06.027 Zou S D, Wang G J. Research on transmission error of dual-eccentric gears. <italic>J Univ Electron Sci Technol China</italic>, 2017, 46(6): 955 doi: 10.3969/j.issn.1001-0548.2017.06.027
[7]	Yu L, Wang G J, Zou S D. The experimental research on gear eccentricity error of backlash-compensation gear device based on transmission error. <italic>Int J Precis Eng Manuf</italic>, 2018, 19(1): 5 doi: 10.1007/s12541-018-0001-7
[8]	王朝兵, 陳小安, 陳宏, 等. 誤差隨機性對行星齒輪系傳動精度的影響特性. 重慶大學學報, 2012, 35(9):41 Wang C B, Chen X A, Chen H, et al. Influence of error's randomness on transmission accuracy of planetary gear. <italic>J Chongqing Univ</italic>, 2012, 35(9): 41
[9]	Guo Y, Parker R G. Dynamic modeling and analysis of a spur planetary gear involving tooth wedging and bearing clearance nonlinearity. <italic>Eur J Mech-A/Solids</italic>, 2010, 29(6): 1022 doi: 10.1016/j.euromechsol.2010.05.001
[10]	Guo Y C, Parker R G. Analytical determination of back-side contact gear mesh stiffness. <italic>Mech Mach Theory</italic>, 2014, 78: 263 doi: 10.1016/j.mechmachtheory.2014.03.011
[11]	Yu W N, Mechefske C K, Timusk M. Influence of the addendum modification on spur gear back-side mesh stiffness and dynamics. <italic>J Sound Vib</italic>, 2017, 389: 183 doi: 10.1016/j.jsv.2016.11.030
[12]	Shi J F, Gou X F, Zhu L Y. Modeling and analysis of a spur gear pair considering multi-state mesh with time-varying parameters and backlash. <italic>Mech Mach Theory</italic>, 2019, 134: 582 doi: 10.1016/j.mechmachtheory.2019.01.018
[13]	Raghuwanshi N K, Parey A. Effect of back-side contact on mesh stiffness of spur gear pair by finite element method. <italic>Procedia Eng</italic>, 2017, 173: 1538 doi: 10.1016/j.proeng.2016.12.239
[14]	Shi Z G, Zuo Z Y. Backstepping control for gear transmission servo systems with backlash nonlinearity. <italic>IEEE Trans Autom Sci Eng</italic>, 2015, 12(2): 752 doi: 10.1109/TASE.2014.2369430
[15]	李小彭, 牟佳信, 潘五九, 等. 具有分形特性的齒側間隙對齒輪-軸承系統動態特性的影響. 機械工程學報, 2018, 54(9):153 Li X P, Mu J X, Pan W J, et al. Influence of fractal backlash on dynamic behavior of gear-bearing system. <italic>J Mech Eng</italic>, 2018, 54(9): 153
[16]	Chen Q, Ma Y B, Huang S W, et al. Research on gears’ dynamic performance influenced by gear backlash based on fractal theory. <italic>Appl Surf Sci</italic>, 2014, 313: 325 doi: 10.1016/j.apsusc.2014.05.210
[17]	Yi Y, Huang K, Xiong Y S, et al. Nonlinear dynamic modelling and analysis for a spur gear system with time-varying pressure angle and gear backlash. <italic>Mech Syst Signal Process</italic>, 2019, 132: 18 doi: 10.1016/j.ymssp.2019.06.013
[18]	靳廣虎, 龍珊珊, 高鵬, 等. 圓柱齒輪分扭傳動系統的均載特性及試驗研究. 中南大學學報: 自然科學版, 2019, 50(7):1592 Jin G H, Long S S, Gao P, et al. Load sharing characteristics and experimental research of cylindrical gear split-torque transmission system. <italic>J Central S Univ Sci Technol</italic>, 2019, 50(7): 1592
[19]	桂永方, 朱如鵬, 靳廣虎, 等. 間隙非線性圓柱齒輪分流傳動系統動力學與均載特性分析. 振動與沖擊, 2014, 33(18):177 Gui Y F, Zhu R P, Jin G H, et al. Dynamic and load sharing characteristic analysis of a nonlinear cylindrical gear split-torque transmission system with backlash. <italic>J Vib Shock</italic>, 2014, 33(18): 177
[20]	齒輪手冊編委會. 齒輪手冊. 2版. 北京: 機械工業出版社, 2006 Gear manual editorial board. Gear Manual. 2nd Ed. Beijing: China Machine Press, 2006
[21]	陳林. 偏心激勵下新型變齒厚齒輪系統動態傳動誤差仿真研究[學位論文]. 重慶: 重慶大學, 2015 Chen L. Simulation on the Dynamic Transmission Error of a New Type of Variable Tooth Thickness Gear System with Eccentric Gears[Dissertation]. Chongqing: Chongqing University, 2015
[22]	Yu L, Wang G J, He L L. The electrically controlling anti-backlash based on variable tooth thickness gear // <italic>The International Conference on Gears</italic>. <italic>Munich</italic>, 2015: 591
[23]	楊政. 消隙齒輪系統精密裝配關鍵參數及其動力學性能影響研究[學位論文]. 長沙: 國防科學技術大學, 2014 Yang Z. Study on Precision Assembly Key Parameters and Its Effects on Dynamics Performance of Anti-Backlash Gear System[Dissertation]. Changsha: National University of Defense Technology, 2014
[24]	喻立. 新型變齒厚齒輪側隙控制方法研究[學位論文]. 重慶: 重慶大學, 2017 Yu L. The Research on Backlash Control Based on New Type of Conical Involute Gear [Dissertation]. Chongqing: Chongqing University, 2017
[25]	成大先. 機械設計手冊. 6版. 北京: 化學工業出版社, 2016 Cheng D X. Handbook of Mechanical Design. 6th Ed. Beijing: Chemical Industry Press, 2016
[26]	顧伯忠, 周于鳴, 楊德華. 滾珠花鍵副的剛度的計算及應用. 天文研究與技術, 2006, 3(4):365 Gu B Z, Zhou Y M, Yang D H. Stiffness calculation and application of spline-ball bearing. <italic>Astron Res Technol</italic>, 2006, 3(4): 365