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Dynamic Analysis for Healthy and Defective Gears: A Review

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Recent Developments in Acoustics

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

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Abstract

There are ample literature addressing the dynamic analysis for gears. In this paper, some important literature on dynamics of both healthy gears and gears with defects have been reviewed. Dynamic analysis of gears is significant from the condition monitoring point of view. Single degree of freedom dynamic model for spur gears has been detailed first. Dynamic study for worm gear with force analysis has been reported. Also, the effect of defects like crack and spall on dynamic behavior of gears studied by researchers has been included in this review. The study of defect model can be utilized in improving the efficiency of the system and preventing the failures in industries as well.

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Abbreviations

c1, c2:

Damping coefficients of first and second tooth pair in mesh, respectively

c m :

Mesh damping coefficient

D(t):

Instantaneous defect width along the contact line

e(t):

Static transmission error

e 1, e 2 :

Displacement excitations due to gear error

F 0 :

External torque load

Fx, Fy, Fz:

Three orthogonal force components

F(t):

Defect morphology

G(t):

Time-periodic defect excitation generated by tooth shape deviations and errors

I1, I2:

Mass moments of inertia of gear no. 1 and 2, respectively

Jw, Jg, J4:

Moment of inertias of the worm, worm gear, and the flywheel, respectively

Kw, Kg:

Elastic constants of the worm shaft and the worm gear shaft, respectively

k :

Total mesh stiffness of the gear pair

k 0 :

The mesh stiffness per unit contact length

k1, k2:

Stiffness of first and second tooth pair in mesh, respectively

k a :

Axial compressive stiffness

k m :

Mean mesh stiffness of one pair contacted with healthy teeth

k t :

Stiffness of a single tooth

\( k_{f} \), \( k_{b} \), \( k_{s} \):

Fillet-foundation, bending, shear stiffness, respectively

k i :

Mesh stiffness of the ith tooth pair

k tooth :

Total mesh stiffness due to teeth deformation of N tooth pairs

\( k_{{s\_{\text{crack}}}} \), \( k_{{b\_{\text{crack}}}} \):

Shear and bending stiffness of cracked tooth, respectively

m e :

Equivalent mass

T1, T2:

Input and output torques, respectively

P(η):

Defect depth along the contact line

R1, R2:

Base radii of gear

rw, rg:

Pitch radii of the worm’s helical tooth and the worm gear, respectively

W0:

Static load

Wf, Wn:

Friction force, normal force

ɸ1, ɸ2:

Angular displacements of gear number 1 and 2, respectively

ɸ’, ɸ”:

First- and second-order derivatives of ɸ, respectively

θ1, θ2, θ3, θ4:

The rotation angles of worm shaft, worm’s body, worm- gear body, and flywheel, respectively

\( \phi_{n} \) :

The pressure angle

λ :

The worm’s lead angle

λ1, λ2:

Correction coefficients of the fillet-foundation stiffness for driving and driven gears, respectively

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Authors and Affiliations

  1. ITMMEC, IIT Delhi, New Delhi, 110016, India

    Swati Gautam & N. Tandon

  2. ZHCET, Aligarh Muslim University, Aligarh, 202002, Uttar Pradesh, India

    Sidra Khanam

Authors
  1. Swati Gautam
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  2. Sidra Khanam
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  3. N. Tandon
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Corresponding author

Correspondence to Swati Gautam .

Editor information

Editors and Affiliations

  1. Department of Physico-Mechanical Metrology, CSIR-National Physical Laboratory, New Delhi, Delhi, India

    Mahavir Singh

  2. Mechanical Engineering Department, Aligarh Muslim University, Aligarh, Uttar Pradesh, India

    Yasser Rafat

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Gautam, S., Khanam, S., Tandon, N. (2021). Dynamic Analysis for Healthy and Defective Gears: A Review. In: Singh, M., Rafat, Y. (eds) Recent Developments in Acoustics. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-5776-7_18

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  • DOI: https://doi.org/10.1007/978-981-15-5776-7_18

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-5775-0

  • Online ISBN: 978-981-15-5776-7

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