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Journal of Mechanical Science and Technology

, Volume 33, Issue 11, pp 5117–5127 | Cite as

Dynamics responses analysis in frequency domain of helical gear pair under multi-fault conditions

  • Lin HanEmail author
  • Houjun Qi
Article

Abstract

This work aims to investigate dynamic characteristics of a helical gear pair under multiple faults condition, through model-based dynamic analysis. Two kinds of faults, tooth spalling and local breakages are considered. Firstly, influences of each kind of fault on meshing stiffness of gear pair with one or more faulted teeth were revealed. Then an 8 degree of freedom lumped-parameter model was developed to obtain dynamic responses. Furthermore, frequency spectrum analysis of the responses was conducted and compared with those under healthy condition. Results indicate that spalling or local breakage introduce different affects into mesh stiffness, and consequently displacement & velocity amplitudes of pinion appear with different waveforms, especially for the case only tooth breakages happen. This work could provide useful instructions for fault detection diagnosis of geared transmissions under multiple fault conditions.

Keywords

Helical gear Multi-fault Dynamics Frequency analysis 

Nomenclature

b

Tooth width

bi

Constant coefficients used for calculating coefficient of friction (i = 1,2,...,9)

cm

Meshing damping

cij

Supporting damping of pinion and gear respectively(i = x, y, z, and j = 1,2)

dov, doh

Variables describing center’s locations of spalling defect

E

Elastic modulus

F

Normal force between meshing teeth

Ff1, Ff2

Friction forces acting on pinion and gear

Fm

Meshing force between pinion and gear

Fij

i = x,y,z, force acting on gears along i-direction, j = 1,2 representing pinion and gear

Fk(ik, j)

Friction force of ith segment of kth tooth of pinion at jth meshing instant

fk(ik, j)

Load per unit of length of contact line at ith segment of kth tooth of pinion at jth meshing instant

f

Auxiliary variable for calculating coefficient of friction

fm, fn

Meshing and rotating frequency

hs

Height of spalling defect

hb

Height of local tooth breakage defect

I1, I2

Moment of inertia of pinion and gear

Ie

Equivalent moment of inertia of gear pair

Iv

Auxiliary variable for calculating fk(ik,j)

ka, kb, kh, kf, ks

Stiffness components for healthy tooth

ksa, ksb, kss

Stiffness components for defected tooth

km

Meshing stiffness of gear pair

kij

i = x, y, z, supporting stiffness along i-direction, j = 1, 2 representing pinion and gear

ksingle

Meshing stiffness of single tooth-pair

ktotal

Meshing stiffness of gear pair, = km

ls

Length of spalling defect

lAP

Distance between points A and P in plane of action

m1,2

Mass of pinion and gear, respectively

n

Auxiliary variable for calculating km

n1

Rotating speed of pinion

Ph

Hertzian contact pressure

R

Effective radius of curvature at contact point

rb1,2

Radii of base circles of pinion and gear

S

Surface roughness parameter

T1,2

Driving and loading torque

Tf1, Tf2

Friction torque action on pinion and gear

Ve

Entraining velocity

wb, ws

Width of local breakage, spalling

xi,i,i

Vibration displacement,velocity and acceleration of pinion (i = 1 or p) and gear (i = 2)

yi, , ÿ

Vibration displacement,velocity and acceleration of pinion (i = 1 or p) and gear (i = 2)

zi,żi,i

Vibration displacement,velocity and acceleration of pinion (i = 1 or p) and gear (i = 2)

α

Variable used in integration operation

α′1, α2, αs1, αs2

Auxiliary variables for calculating stiffness terms

βb

Helix angle at basis circle

ε

Total contact ratio of helical gear pair

μ

Coefficient of friction

ν0

Viscosity of lubricant

θi, θ̇i, θ̈i

Angular dispacement, velocity and acceleration of pinion for i = 1 and gear for i = 2

ζ

Damping ratio

\(\overline G \)

Auxiliary variables for calculating fk(ik, j)

Δl

Width of each sliced segment of tooth

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Notes

Acknowledgments

This work was supported by the project funded by Tianjin Municipal Education Commission (Grant No. JWK1601), Natural Science Foundation of Tianjin (Grant No. 18JCQNJC75200) and Innovation Team Training Plan of Tianjin Universities and colleges (Grant No. TD13-5096), China.

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Copyright information

© KSME & Springer 2019

Authors and Affiliations

  1. 1.Tianjin Key Laboratory of High-speeding Cutting and Precision MachiningTianjin University of Technology and EducationTianjinChina

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