SpringerLink
Log in

Analytical Model of Spur Gear Tooth Crack for Evaluating the Effect of Crack Propagation Angle on Vibration Response

  • Conference paper
  • First Online:
Recent Advances in Aerospace Engineering (MRAE 2023)

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

Included in the following conference series:

  • 123 Accesses

Abstract

Vibration-based health monitoring is considered as an important tool since any anomaly present in the system is manifested through its own vibration signature. This vibration signature is unique in nature. This uniqueness is very well established and being utilized in industry effectively for obtaining vibration response of industrial gear boxes and this forms the basis of diagnosis of the extent to which the gears are working at the intended level of accuracy. In this study, the mathematical model is developed and based on eight degrees of freedom governing differential equations are formed consisting time varying meshing force. Further, this time varying mesh force is diffused in terms of time varying mesh stiffness. The eight degrees of freedom are four rotational and four translational. During mesh in spur gear pair, the load sharing is variable with respect to time along the line of contact and it also depends upon the number of teeth pair in contact. Different faults in gear can be enlisted as crack, spalling, pitting, etc., each contributing adversely on the system characteristics, mesh stiffness being one of those. A cracked gear tooth is attributed by many features such as crack depth, crack length, initiation zone of crack and crack propagation angle. Amidst these, the study associated with the influence of crack propagation angle on gear tooth vibrations has been undertaken and the results are presented in this paper. Time varying mesh stiffness equations are formulated based on potential energy theory and it is solved by using a MATLAB code. TVMS plot is generated to investigate the influence of propagation angle on TVMS.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Tandon N, Choudhury A (1999) A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings. Tribol Int 32:469–480

    Article  Google Scholar 

  2. Aherwar A (2012) An investigation on gearbox fault detection using vibration analysis techniques: a review. Aust J Mech Eng 10(2):169–184

    Article  Google Scholar 

  3. White MF (1984) Simulation and analysis of machinery fault signals. J Sound Vib 93(l):95–l16

    Google Scholar 

  4. Patel VN, Tandon N, Pandey RK (2010) A dynamic model for vibration studies of deep groove ball bearings considering single and multiple defects in races. J Tribol 132:1–10

    Article  Google Scholar 

  5. Randall RB (1982) A new method of modeling gear faults. J Mech Des 104:259–267

    Google Scholar 

  6. McFadden PD (1986) Detecting fatigue cracks in gears by amplitude and phase demodulation of the meshing vibration. ASME transactions. J Vib Acoustics Stress Reliab Des 108:165–170

    Article  Google Scholar 

  7. Weber C (1949) The deformation of loaded gears and the effect on their load-carrying capacity. Sponsored Research (Germany). Department of Scientific and Industrial Research. London. Report 3

    Google Scholar 

  8. Chakraborti J, Hunashikatti HG (1974) Determination of the combined mesh stiffness of a spur gear pair under load. ASME paper 74 -DET-39

    Google Scholar 

  9. Terauchi Y, Nagamura K (1981) On tooth deflection calculation and profile modification of spur gear teeth. In: Proceedings of international symposium on gearing and power transmission, Tokyo

    Google Scholar 

  10. Arafa MH, Megahed M (1999) Evaluation of spur gear mesh compliance using the finite element method. Article ARCHIVE Proc Instit Mech Eng Part C J Mech Eng Sci 1989–1996:203–210

    Google Scholar 

  11. Dogan O, Karpat F, Kopmaz O, Ekwaro-Osire S (2020) Influences of gear design parameters on dynamic tooth loads and time-varying mesh stiffness of involute spur gears. Sådhanå 45:258. 15 pages

    Google Scholar 

  12. Jia SX, Howard I, Wang J (2003) The dynamic modeling of multiple pairs of spur gears in mesh, including friction and geometrical errors, Taylor & Francis Inc. Int J Rotat Mach 9:437–442

    Google Scholar 

  13. Barot A, Kulkarni P (2023) Dynamic analysis of effect of progressive crack and variation in center distance on vibration of spur gears. Mater Today: Proc 77:603–613

    Google Scholar 

  14. Ozguven HN, Houser DR (1998) Dynamic analysis of high-speed gears by using loaded static transmission error. J Sound Vib 125(1):71–83

    Google Scholar 

  15. Zhang L, Chen C, Liu J, Zhao S (2018) Dynamic characteristic of spur gear with flexible support of gearbox. J Vibroeng 20(3):1530–1543

    Article  Google Scholar 

  16. Liu J, Wang C, Wu W (2020) Research on meshing stiffness and vibration response of pitting fault gears with different degrees. Hindawi. Int J Rotat Mach 2020, Article ID 4176430. 7 pages

    Google Scholar 

  17. Wu S, Zuo MJ, Parey A (2008) Simulation of spur gear dynamics and estimation of fault growth. J Sound Vib 317(3–5):608–624

    Google Scholar 

  18. Ma H, Zeng J, Feng R, Pang X, Wen B (2016) An improved analytical method for mesh stiffness calculation of spur gears with tip relief. Mech Mach Theo 98:64–80

    Google Scholar 

  19. Ma H, Zeng J, Feng R, Pang X, Wang Q, Wen B (2015) Review on dynamics of cracked gear systems. Eng Fail Anal 55:224–245

    Google Scholar 

  20. Tse DK, Lin HH (1992) Separation distance and static transmission error of involute spur gears. In: 28th joint propulsion conference and exhibit. Nashville. TN, U.S.A., 9 pages

    Google Scholar 

  21. Yang DCH, Lin JY (1987) Hertzian dam**, Tooth friction and bending elasticity in gear impact dynamics. J Mech, Trans Auto Des 109(2):189–196

    Google Scholar 

  22. Chen Z, Zhang J, Zhai W, Wang Y, Liu J (2017) Improved analytical methods for calculation of gear tooth fillet foundation stiffness with tooth root crack. Eng Fail Anal 82:72–81

    Google Scholar 

  23. Yang DCH, Sun ZS (1985) A rotary model for spur gear dynamics. ASME J Mech Trans Auto Des 107:529–535

    Google Scholar 

  24. Sainsot P, Valex P, Duverger O (2004) Contribution of gear body to tooth deflections—a new bidimensional analytical formula. J Mech Des 126:748–752

    Google Scholar 

  25. Ma H, Song R, Pang X, Wen B (2014) Time-varying mesh stiffness calculation of cracked spur gears. Eng Fail Anal 44:179–194

    Article  Google Scholar 

  26. Wu X, Luo Y, Li Q, Shi J (2022) A revised method to calculate time-varying mesh stiffness of the helical gear. MATEC Web Conf 355:01005

    Google Scholar 

  27. Kong Y, Jiang H, Dong N, Shang J, Yu P, Li J, Yu M, Chen L (2023) Analysis of time-varying mesh stiffness and dynamic response of gear transmission system with pitting and cracking coupling faults. MDPI, Mach 11(4)

    Google Scholar 

Download references

Funding

Not applicable.

Author information

Authors and Affiliations

  1. PVG’s COET & GKPWIOM, Pune, 411009, India

    Ami Barot & Pravin Kulkarni

Authors
  1. Ami Barot
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pravin Kulkarni
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ami Barot .

Editor information

Editors and Affiliations

  1. Amity Institute of Aerospace Engineering, Amity University, Noida, Uttar Pradesh, India

    Sanjay Singh

  2. Department of Mechanical Engineering, School of Mechanical, Materials and Chemical Engineering, Adama Science and Technology University, Adama, Ethiopia

    Perumalla Janaki Ramulu

  3. Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati, India

    Sachin Singh Gautam

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Barot, A., Kulkarni, P. (2024). Analytical Model of Spur Gear Tooth Crack for Evaluating the Effect of Crack Propagation Angle on Vibration Response. In: Singh, S., Ramulu, P.J., Gautam, S.S. (eds) Recent Advances in Aerospace Engineering. MRAE 2023. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-97-1306-6_1

Download citation

  • DOI: https://doi.org/10.1007/978-981-97-1306-6_1

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-97-1305-9

  • Online ISBN: 978-981-97-1306-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation