Research Papers

A New Technique of Gear Mesh Stiffness Measurement Using Experimental Modal Analysis

[+] Author and Article Information
Naresh K. Raghuwanshi

Department of Mechanical Engineering,
Madhav Institute of Technology and
Science Gwalior,
Gola ka Mandir, Gwalior 474005, India
e-mail: raghuwanshink@gmail.com

Anand Parey

Discipline of Mechanical Engineering,
Indian Institute of Technology Indore,
Khandwa Road,
Simrol 453552, Madhya Pradesh, India
e-mail: anandp@iiti.ac.in

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 14, 2018; final manuscript received November 20, 2018; published online January 16, 2019. Assoc. Editor: Karsten Stahl.

J. Vib. Acoust 141(2), 021018 (Jan 16, 2019) (13 pages) Paper No: VIB-18-1200; doi: 10.1115/1.4042100 History: Received May 14, 2018; Revised November 20, 2018

Accurately measured mesh stiffness (MS) of gear pair is used in the mathematical model of the gearbox for doing the vibration analysis. Mesh stiffness measurement by experimental techniques is an import aspect for measuring the MS accurately of the physical structure of gear pair. Analytical methods (AMs) of MS require large mathematical equations and modifications in these equations for different gear geometries and cracks. Finite element method (FEM) requires huge computational time. In this paper, a new experimental technique based on the experimental modal analysis (EMA) is proposed to measure the MS of spur gear pairs. EMA technique is also used in the paper for measuring the MS of cracked gear tooth pairs and found a significant difference in the MS of healthy and cracked tooth pair. In the last, the experimental MS results are compared with the MS results obtained by the AM and digital image correlation (DIC) experimental technique and found a good agreement. This shows the usefulness of the EMA for measuring the MS. So, it can be used as an alternative method of MS measurement or to validate the analytical and FEM MS results.

Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.


Yang, D. C. H. , and Lin, J. Y. , 1987, “ Hertzian Damping, Tooth Friction and Bending Elasticity in Gear Impact Dynamics,” ASME J. Mech., Trans., Autom. Des., 109(2), pp. 189–196. [CrossRef]
Tian, X. H. , 2004, “ Dynamic Simulation for System Response of Gearbox Including Localized Gear Faults,” Master's thesis, University of Alberta, Edmonton, AB, Canada.
Wu, S. , Zuo, M. J. , and Parey, A. , 2008, “ Simulation of Spur Gear Dynamics and Estimation of Fault Growth,” J. Sound Vib., 317(3–5), pp. 608–624. [CrossRef]
Pandya, Y. , and Parey, A. , 2013, “ Simulation of Spur Gear Tooth for Different Gear Parameters and Its Influence on Mesh Stiffness,” Eng. Failure Anal., 30, pp. 124–37. [CrossRef]
Pandya, Y. , and Parey, A. , 2013, “ Failure Path Based Modified Gear Mesh Stiffness for Spur Gear Pair With Tooth Root Crack,” Eng. Failure Anal., 27, pp. 286–296. [CrossRef]
Liang, X. , Zuo, M. J. , and Pandey, M. , 2014, “ Analytically Evaluating the Influence of Crack on the Mesh Stiffness of a Planetary Gear Set,” Mech. Mach. Theory, 76, pp. 20–38. [CrossRef]
Ma, H. , Pang, X. , Feng, R. , Zeng, J. , and Wen, B. , 2015, “ Improved Time-Varying Mesh Stiffness Model of Cracked Spur Gears,” Eng. Failure Anal., 55, pp. 271–287. [CrossRef]
Wan, Z. , Cao, H. , Zi, Y. , He, W. , and Chen, Y. , 2015, “ Mesh Stiffness Calculation Using an Accumulated Integral Potential Energy Method and Dynamic Analysis of Helical Gears,” Mech. Mach. Theory, 92, pp. 447–463. [CrossRef]
Pandya, Y., and Parey, A., 2013, “Crack Behavior in a High Contact Ratio Spur Gear Tooth and its Effect on Mesh Stiffness,” Eng. Failure Anal., 34, pp. 69–78.
Zhou, X. , Shao, Y. , Lei, Y. , and Zuo, M. , 2012, “ Time-Varying Meshing Stiffness Calculation and Vibration Analysis for a 16 Degree of Freedom Dynamic Model With Linear Crack Growth in a Pinion,” ASME J. Vib. Acoust., 134(1), p. 011011. [CrossRef]
Chaari, F. , Baccar, W. , Abbes, M. S. , and Haddar, M. , 2008, “ Effect of Spalling or Tooth Breakage on Gearmesh Stiffness and Dynamic Response of a One-Stage Spur Gear Transmission,” Eur. J. Mech.-A/Solids, 27(4), pp. 691–705. [CrossRef]
Chen, Z. , and Shao, Y. , 2013, “ Mesh Stiffness Calculation of a Spur Gear Pair With Tooth Profile Modification and Tooth Root Crack,” Mech. Mach. Theory, 62, pp. 63–74. [CrossRef]
Chen, Z. , and Shao, Y. , 2011, “ Dynamic Simulation of Spur Gear With Tooth Root Crack Propagating Along Tooth Width and Crack Depth,” Eng. Failure Anal., 18(8), pp. 2149–64. [CrossRef]
Fernandez, A. , Viadero, F. , Iglesias, M. , Garcia, P. , De-Juan, A. , and Sancibrian, R. , 2013, “ A Model for the Study of Meshing Stiffness in Spur Gear Transmissions,” Mech. Mach. Theory, 61, pp. 30–58. [CrossRef]
Sanchez, M. B. , Pleguezuelos, M. , and Pedrero, J. I. , 2017, “ Approximate Equations for the Meshing Stiffness and the Load Sharing Ratio of Spur Gears Including Hertzian Effects,” Mech. Mach. Theory, 109, pp. 231–249. [CrossRef]
Parey, A. , Badaoui, M. E. , Guillet, F. , and Tandon, N. , 2006, “ Dynamic Modelling of Spur Gear Pair and Application of Empirical Mode Decomposition-Based Statistical Analysis for Early Detection of Localized Tooth Defect,” J. Sound Vib., 294(3), pp. 547–561. [CrossRef]
Fernandez, A. , Viadero, F. , Iglesias, M. , De-Juan, A. , Garcia, P. , and Sancibrian, R. , 2012, “ Effect of Cracks and Pitting Defects on Gear Meshing,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 226(11), pp. 2805–2815. [CrossRef]
Zouari, S. , Maatar, M. , Fakhfakh, T. , and Haddar, M. , 2007, “ Three-Dimensional Analyses by Finite Element Method of a Spur Gear: Effect of Cracks in the Teeth Foot on the Mesh Stiffness,” J. Fail. Anal. Preven., 7(6), pp. 475–481. [CrossRef]
Raghuwanshi, N. K. , and Parey, A. , 2017, “ Effect of Back-Side Contact on Mesh Stiffness of Spur Gear Pair by Finite Element Method,” Procedia Eng., 173, pp. 1538–1543. [CrossRef]
Chaari, F. , Fakhfakh, T. , and Haddar, M. , 2009, “ Analytical Modelling of Spur Gear Tooth Crack and Influence on Gear Mesh Stiffness,” Eur. J. Mech.- A/Solids, 28(3), pp. 461–468. [CrossRef]
Ma, H. , Zeng, J. , Feng, R. , Pang, X. , and Wen, B. , 2016, “ An Improved Analytical Method for Mesh Stiffness Calculation of Spur Gears With Tip Relief,” Mech. Mach. Theory, 98, pp. 64–80. [CrossRef]
Zhan, J. , Fard, M. , and Jazar, R. , 2017, “ A CAD-FEM-QSA Integration Technique for Determining the Time-Varying Meshing Stiffness of Gear Pairs,” Measurement, 100, pp. 139–149. [CrossRef]
Pandya, Y. , and Parey, A. , 2013, “ Experimental Investigation of Spur Gear Tooth Mesh Stiffness in the Presence of Crack Using Photoelasticity Technique,” Eng. Failure Anal., 34, pp. 488–500. [CrossRef]
Raghuwanshi, N. K. , and Parey, A. , 2015, “ Mesh Stiffness Measurement of Cracked Spur Gear by Photoelasticity Technique,” Measurement, 73, pp. 439–452. [CrossRef]
Raghuwanshi, N. K. , and Parey, A. , 2016, “ Experimental Measurement of Gear Mesh Stiffness of Cracked Spur Gear by Strain Gauge Technique,” Measurement, 86, pp. 266–275. [CrossRef]
Raghuwanshi, N. K. , and Parey, A. , 2017, “ Experimental Measurement of Spur Gear Mesh Stiffness Using Digital Image Correlation Technique,” Measurement, 111, pp. 93–104. [CrossRef]
Salawu, O. S. , and Williams, C. , 1995, “ Review of Full-Scale Dynamic Testing of Bridge Structures,” Eng. Struct., 17(2), pp. 113–121. [CrossRef]
Schmitz, T. L. , and Smith, K. S. , 2012, Mechanical Vibrations, Modeling and Measurement, Springer, New York.
Ewins, D. J. , 2000, Modal Testing: Theory, Practice, and Application, 2nd ed., Research Studies Press, Baldock, UK.
Yesilyurta, I. , Gub, F. , and Ball, A. D. , 2003, “ Gear Tooth Stiffness Reduction Measurement Using Modal Analysis and Its Use in Wear Fault Severity Assessment of Spur Gears,” NDTE Int., 36, pp. 357–372. [CrossRef]
Amarnath, M. , Sujatha, C. , and Swarnamani, S. , 2009, “ Experimental Studies on the Effects of Reduction in Gear Tooth Stiffness and Lubricant Film Thickness in a Spur Geared System,” Tribol. Int., 42(2), pp. 340–352. [CrossRef]
Sainsot, P. , Velex, P. , and Duverger, O. , 2004, “ Contribution of Gear Body to Tooth Deflections-A New Bi-Dimensional Analytical Formula,” ASME J. Mech. Des., 126(4), pp. 748–752. [CrossRef]


Grahic Jump Location
Fig. 1

Equivalent spring-mass-damper model with two degrees-of-freedom (2DOFs)

Grahic Jump Location
Fig. 2

Flowchart of MS measurement using EMA

Grahic Jump Location
Fig. 3

Individual spring-mass-damper system in modal coordinates

Grahic Jump Location
Fig. 4

Experimental setup

Grahic Jump Location
Fig. 6

Crack lengths and crack direction on gear tooth root

Grahic Jump Location
Fig. 7

Imaginary part of the FRF for the healthy gear pair at 0 deg

Grahic Jump Location
Fig. 8

Imaginary part of the FRF for the healthy gear pair at 0 deg (zoomed view)

Grahic Jump Location
Fig. 9

Imaginary part of the FRF for the healthy gear pair at 0 deg (zoomed view) with additional mass

Grahic Jump Location
Fig. 10

Modal fit to the healthy gear pair direct FRF at 0 deg angular rotation

Grahic Jump Location
Fig. 11

Directions of impact force on gears

Grahic Jump Location
Fig. 12

Forces on the gear tooth [2]

Grahic Jump Location
Fig. 13

Geometrical parameters of the gear for the filet-foundation deflection [13,32]

Grahic Jump Location
Fig. 14

Real and Imaginary parts of the direct and cross FRFs for healthy pairs (a)–(c); β = 0 deg and (d)–(f); β = 12 deg)

Grahic Jump Location
Fig. 15

Real and imaginary parts of the direct and cross FRFs for 1 mm crack pairs

Grahic Jump Location
Fig. 16

Real and imaginary parts of the direct and cross FRFs for 2 mm crack pair

Grahic Jump Location
Fig. 17

Real and imaginary parts of the direct and cross FRFs for 3 mm crack pair

Grahic Jump Location
Fig. 18

Real and imaginary parts of the direct and cross FRFs for 4 mm crack pairs

Grahic Jump Location
Fig. 19

Real and imaginary parts of the direct and cross FRFs for 5 mm crack pairs

Grahic Jump Location
Fig. 20

Mesh stiffness by EMA

Grahic Jump Location
Fig. 21

Mesh stiffness comparison between EMA and AM for different crack lengths



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In