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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.

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Figures

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Fig. 1

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

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Fig. 2

Flowchart of MS measurement using EMA

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Fig. 3

Individual spring-mass-damper system in modal coordinates

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Fig. 4

Experimental setup

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Fig. 6

Crack lengths and crack direction on gear tooth root

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Fig. 7

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

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Fig. 8

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

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Fig. 9

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

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Fig. 10

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

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Fig. 11

Directions of impact force on gears

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Fig. 12

Forces on the gear tooth [2]

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Fig. 13

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

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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)

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Fig. 15

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

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Fig. 16

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

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Fig. 17

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

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Fig. 18

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

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Fig. 19

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

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Fig. 20

Mesh stiffness by EMA

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Fig. 21

Mesh stiffness comparison between EMA and AM for different crack lengths

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