Skip to main content
SpringerLink
Log in

A novel method to predict static transmission error for spur gear pair based on accuracy grade

基于齿轮精度等级的直齿轮副静态传动误差预测方法

  • Published:
Journal of Central South University Aims and scope Submit manuscript

Abstract

This paper proposes a novel method to predict the spur gear pair’s static transmission error based on the accuracy grade, in which manufacturing errors (MEs), assembly errors (AEs), tooth deflections (TDs) and profile modifications (PMs) are considered. For the prediction, a discrete gear model for generating the error tooth profile based on the ISO accuracy grade is presented. Then, the gear model and a tooth deflection model for calculating the tooth compliance on gear meshing are coupled with the transmission error model to make the prediction by checking the interference status between gear and pinion. The prediction method is validated by comparison with the experimental results from the literature, and a set of cases are simulated to study the effects of MEs, AEs, TDs and PMs on the static transmission error. In addition, the time-varying backlash caused by both MEs and AEs, and the contact ratio under load conditions are also investigated. The results show that the novel method can effectively predict the range of the static transmission error under different accuracy grades. The prediction results can provide references for the selection of gear design parameters and the optimization of transmission performance in the design stage of gear systems.

摘要

: 本文提出一种基于齿轮精度等级的直齿轮副静态传动误差预测方法, 该方法综合考虑了加工误 差、安装误差、轮齿变形以及齿廓修形的影响。首先, 分别建立了根据ISO 齿轮精度等级生成误差齿 廓的离散齿轮模型, 轮齿变形模型, 以及传动误差模型; 随后, 将上述三个模型进行耦合, 从而实现 直齿轮副传动误差的预测。对比分析文献中实验结果与本文预测结果, 验证了该预测方法的正确性。 基于一系列仿真算例, 研究了加工误差、安装误差、轮齿变形以及齿廓修形对静态传动误差的影响规 律。此外, 还研究了加工误差和安装误差对时变啮合侧隙的影响规律, 以及受载条件下重合度的变化 规律。结果显示, 该方法可有效预测不同齿轮精度等级下直齿轮副静态传动误差范围。预测结果可为 齿轮设计参数的选择和齿轮系统设计阶段传动性能的优化提供参考。

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. VELEX P, MAATAR M. A mathematical model for analyzing the influence of shape deviations and mounting errors on gear dynamic behavior [J]. Journal of Sound and Vibration, 1996, 191(5): 629–660. DOI: https://doi.org/10.1006/jsvi.1996.0148.

    Article  Google Scholar 

  2. 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. DOI: https://doi.org/10.1243/0954406991522347.

    Google Scholar 

  3. MOHAMAD E N, KOMORI M, MURAKAMI H, KUBO A, FANG S. Analysis of general characteristics of transmission error of gears with convex modification of tooth flank form considering elastic deformation under load [J]. Journal of Mechanical Design, 2009, 131(6): 061015. DOI: https://doi.org/10.1115/1.3116261.

    Article  Google Scholar 

  4. MOHAMAD E N, KOMORI M, MURAKAMI H, KUBO A, FANG S. Effect of convex tooth flank form deviation on the characteristics of transmission error of gears considering elastic deformation [J]. Journal of Mechanical Design, 2010, 132(10): 101005. DOI: https://doi.org/10.1115/1.4002458.

    Article  Google Scholar 

  5. WANG Qi-bin, ZHANG Yi-min. A model for analyzing stiffness and stress in a helical gear pair with tooth profile errors [J]. Journal of Vibration and Control, 2015: 1077546315576828. DOI: https://doi.org/10.1177/1077546315576828.

  6. YUAN Bing, CHANG Shan, LIU Geng, CHANG Le-hao, LIU Lan. Quasi-static analysis based on generalized loaded static transmission error and dynamic investigation of wide-faced cylindrical geared rotor systems [J]. Mechanism and Machine Theory, 2019, 134: 74–94. DOI: https://doi.org/10.1016/j.mechmachtheory.2018.12.019.

    Article  Google Scholar 

  7. YUAN Bing, CHANG Shan, LIU Geng, WU Li-yan. Quasi-static and dynamic behaviors of helical gear system with manufacturing errors [J]. Chinese Journal of Mechanical Engineering, 2018, 31(1): 30. DOI: https://doi.org/10.1186/s10033-018-0238-1.

    Article  Google Scholar 

  8. PARK Chan IL. Tooth friction force and transmission error of spur gears due to sliding friction [J]. Journal of Mechanical Science and Technology, 2019, 33(2): 1311–1319. DOI: https://doi.org/10.1007/s12206-019-0232-2.

    Article  Google Scholar 

  9. LI Shu-ting. Effects of machining errors, assembly errors and tooth modifications on loading capacity, load-sharing ratio and transmission error of a pair of spur gears [J]. Mechanism and Machine Theory, 2007, 42(6): 698–726. DOI: https://doi.org/10.1016/j.mechmachtheory.2006.06.002.

    Article  MATH  Google Scholar 

  10. LIN Teng-jiao, HE Ze-yin. Analytical method for coupled transmission error of helical gear system with machining errors, assembly errors and tooth modifications [J]. Mechanical Systems and Signal Processing, 2017, 91: 167–182. DOI: https://doi.org/10.1016/j.ymssp.2017.01.005.

    Article  Google Scholar 

  11. SHWEIKI S, REZAYAT A, TAMAROZZI T, MUNDO D. Transmission Error and strain analysis of lightweight gears by using a hybrid FE-analytical gear contact model [J]. Mechanical Systems and Signal Processing, 2019, 123: 573–590. DOI: https://doi.org/10.1016/j.ymssp.2019.01.024.

    Article  Google Scholar 

  12. BAI Fan, CHEN Si-yu, TANG Jin-yuan. Comparisons of dynamic responses of a spur gear pair with two forms of profile deviation [J]. Australian Journal of Mechanical Engineering, 2018, 19: 1–9. DOI: https://doi.org/10.1080/14484846.2018.1465377.

    Google Scholar 

  13. LI Hao-nan, CHEN Si-yu, TANG Jin-yuan, CHEN Wei-tao, OUYANG Hong-wu. A novel approach for calculating no-load static transmission error based on measured discrete tooth surfaces [J]. Mechanism and Machine Theory, 2019, 138: 112–123. DOI: https://doi.org/10.1016/j.mechmachtheory.2019.03.044.

    Article  Google Scholar 

  14. TAMMINANA V K, KAHRAMAN A, VIJAYAKAR S. A study of the relationship between the dynamic factors and the dynamic transmission error of spur gear pairs [J]. Journal of Mechanical Design, 2007, 129(1): 75. DOI: https://doi.org/10.1115/1.2359470.

    Article  Google Scholar 

  15. XU Jin-li, ZENG Fan-cong, SU Xing-yi. Coupled bendingtorsional nonlinear vibration and bifurcation characteristics of spiral bevel gear system [J]. Shock and Vibration, 2017, 2017: Article ID 6835301. DOI: https://doi.org/10.1155/2017/6835301.

  16. KAHRAMAN A, BLANKENSHIP G W. Effect of involute tip relief on dynamic response of spur gear pairs [J]. Journal of Mechanical Design, 1999, 121(2): 313–315. DOI: https://doi.org/10.1115/1.2829460.

    Article  Google Scholar 

  17. HANDSCHUH M J, KAHRAMAN A, MILLIREN M R. Impact of tooth spacing errors on the root stresses of spur gear pairs [J]. Journal of Mechanical Design, 2014, 136(6): 061010. DOI: https://doi.org/10.1115/1.4027337.

    Article  Google Scholar 

  18. INALPOLAT M, HANDSCHUH M, KAHRAMAN A. Influence of indexing errors on dynamic response of spur gear pairs [J]. Mechanical Systems and Signal Processing, 2015, 60: 391–405. DOI: https://doi.org/10.1016/j.ymssp.2014.11.017.

    Article  Google Scholar 

  19. TALBOT D, SUN A, KAHRAMAN A. Impact of tooth indexing errors on dynamic factors of spur gears: experiments and model simulations [J]. Journal of Mechanical Design, 2016, 138(9): 093302. DOI: https://doi.org/10.1115/1.4034175.

    Article  Google Scholar 

  20. BENATAR M, HANDSCHUH M, KAHRAMAN A, TALBOT D. Static and dynamic transmission error measurements of helical gear pairs with various tooth modifications [J]. Journal of Mechanical Design, 2019, 141(10): 103301. DOI: https://doi.org/10.1115/1.4043586.

    Article  Google Scholar 

  21. AL-SHYYAB A, KAHRAMAN A. Non-linear dynamic analysis of a multi-mesh gear train using multi-term harmonic balance method: Period-one motions [J]. Journal of Sound and Vibration, 2005, 284(1, 2): 151–172. DOI: https://doi.org/10.1016/j.jsv.2004.06.010.

    Article  Google Scholar 

  22. SHEN Yong-jun, YANG Shao-pu, LIU Xian-dong. Nonlinear dynamics of a spur gear pair with time-varying stiffness and backlash based on incremental harmonic balance method [J]. International Journal of Mechanical Sciences, 2006, 48(11): 1256–1263. DOI: https://doi.org/10.1016/j.ijmecsci.2006.06.003.

    Article  MATH  Google Scholar 

  23. MORADI H, SALARIEH H. Analysis of nonlinear oscillations in spur gear pairs with approximated modelling of backlash nonlinearity [J]. Mechanism and Machine Theory, 2012, 51: 14–31. DOI: https://doi.org/10.1016/j.mechmachtheory.2011.12.005.

    Article  Google Scholar 

  24. SHANGGUAN Wen-bin, LIU Xue-lai, YIN Yu-ming, RAKHEJA S. Modeling of automotive drive line system for reducing gear [J]. Journal of Sound and Vibration, 2018, 416: 136–153. DOI: https://doi.org/10.1016/j.jsv.2017.07.052.

    Article  Google Scholar 

  25. CHEN Si-yu, TANG Jin-yuan, LUO Cai-wang, WANG Qi-bo. Nonlinear dynamic characteristics of geared rotor bearing systems with dynamic backlash and friction [J]. Mechanism and Machine Theory, 2011, 46(4): 466–478. DOI: https://doi.org/10.1016/j.mechmachtheory.2010.11.016.

    Article  MATH  Google Scholar 

  26. ROCCA E, RUSSO R. Theoretical and experimental investigation into the influence of the periodic backlash fluctuations on the gear rattle [J]. Journal of Sound and Vibration, 2011, 330(20): 4738–4752. DOI: https://doi.org/10.1016/j.jsv.2011.04.008.

    Article  Google Scholar 

  27. WANG Guang-jian, CHEN Lin, YU Li, ZOU Shuai-dong. 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. DOI: https://doi.org/10.1016/j.mechmachtheory.2016.11.006.

    Article  Google Scholar 

  28. MARGIELEWICZ J, GASKA D, LITAK G. Modelling of the gear backlash [J]. Nonlinear Dynamics, 2019, 97(1): 355–368. DOI: https://doi.org/10.1007/s11071-019-04973-z.

    Article  Google Scholar 

  29. KUROKAWA S, ARIURA Y, OHTAHARA M. Transmission errors of cylindrical gears under load-influence of tooth profile modification and tooth deflection [C]//Proceedings 7th ASME International Power Transmission and Gearing Conference. 1996, 88: 213–217.

    Google Scholar 

  30. ISO 1328/1. Cylindrical gears-ISO system of flank tolerance classification-part 1: Definitions and allowable values of deviations relevant to flanks of gear teeth [S]. 2013.

  31. OSWALD F, LIN H, LIOU C H, VALCO M. Dynamic analysis of spur gears using computer program DANST [C]//29th Joint Propulsion Conference and Exhibit. 1993: 2295. DOI: https://doi.org/10.2514/6.1993-2295.

  32. TAVAKOLI M S, HOUSER D R. Optimum profile modifications for the minimization of static transmission errors of spur gears [J]. Journal of Mechanisms, Transmissions, and Automation in Design, 1986, 108(1): 86–94. DOI: https://doi.org/10.1115/1.3260791.

    Article  Google Scholar 

  33. CORNELL R W. Compliance and stress sensitivity of spur gear teeth [J]. Journal of Mechanical Design, 1981, 103(2): 447–459. DOI: https://doi.org/10.1115/1.3254939.

    Article  Google Scholar 

  34. OTTEWILL J R, NEILD S A, WILSON R E. Intermittent gear rattle due to interactions between forcing and manufacturing errors [J]. Journal of Sound and Vibration, 2009, 321(3–5): 913–935. DOI: https://doi.org/10.1016/j.jsv.2008.09.050.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing, 400044, China

    Chang Liu  (刘昶) & Wan-kai Shi  (石万凯)

  2. Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Torino, 10129, Italy

    Francesca Maria Curá & Andrea Mura

Authors
  1. Chang Liu  (刘昶)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wan-kai Shi  (石万凯)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Francesca Maria Curá
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Andrea Mura
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

LIU Chang established the predicting model of static transmission error and drafted the manuscript. SHI Wan-kai obtained funding, proposed the concept of the predicting model, and contributed to the interpretation of the results. Francesca Maria CURÀ and Andrea MURA carried out data processing, performed data analysis, and contributed to the paper writing. All authors have read and approved the final manuscript.

Corresponding author

Correspondence to Wan-kai Shi  (石万凯).

Additional information

Conflict of interest

LIU Chang, SHI Wan-kai, Francesca Maria CURÀ and Andrea MURA declare that they have no conflict of interest.

Foundation item

Project(51675061) supported by the National Natural Science Foundation of China

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, C., Shi, Wk., Curá, F.M. et al. A novel method to predict static transmission error for spur gear pair based on accuracy grade. J. Cent. South Univ. 27, 3334–3349 (2020). https://doi.org/10.1007/s11771-020-4550-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11771-020-4550-4

Key words

关键词

Search

Navigation