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Influence of tooth profile and surface roughness on wear of spur gears considering temperature

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Abstract

Gear wear is an important failure mode in gear systems that changes the tooth profile. Gear wear is closely related to the sliding friction force, and the temperature rise due to friction may change the lubricant regime. Therefore, this study analyzed the wear characteristics of spur gears considering the temperature for tooth profile and surface roughness. To this end, the spur gear load with friction was obtained by solving simultaneous equations comprising load-deformation equations and a moment balance equation. Subsequently, the contact pressure and the heat flux at the meshing position were calculated. The bulk temperature due to the heat flux was obtained by performing finite element analysis. Further, the flash temperature was calculated. The wear analysis included the parameters accounting for the effects of the temperature rise on the lubricant film properties. The wear depth of spur gears was calculated using the modified Archard wear formula with the parameters. The results indicate that the surface roughness slightly increases the wear depth whereas the temperature effects reduce the wear depth. Wear is altered by the tooth profile and increases transmission error.

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Abbreviations

a H :

Hertz contact half-width (m)

b :

Face width (m)

c p :

Specific heat capacity (J/(kg·K))

e :

Tooth error, modification (m)

E :

Young’s modulus (Pa)

E e :

Heat adsorption of oil molecules on surfaces

E e :

Equivalent elastic constant (Pa)

G :

Dimensionless material number

h :

Convective heat transfer coefficient

h w :

Wear depth (m)

H :

Hardness of the contact surface (Pa)

H v :

Vickers hardness (Pa)

h m :

Minimum film thickness (m)

H m :

Dimensionless minimum film thickness

k :

Thermal conductivity (W/(m·K))

k w :

Dimensional wear coefficient (m2/N)

K w :

Dimensionless wear coefficient

L a :

Asperity load ratio of two contact surfaces (percentage)

m t :

Index constant

n :

Revolutions per minute

p :

Hertz maximum contact pressure (Pa)

q :

Heat flux (W/m2)

Q :

Compliance (m/N)

r :

Radius of curvature (m)

Y e :

Equivalent radius of curvature (m)

R :

Arbitrary radius of the gear surface (m)

R b :

Base circle radius of gears (m)

R g :

Gas constant (J/mol K)

s :

Sliding distance (m)

t 0 :

Fundamental time of the vibration of a molecule in adsorbed state (s)

T :

Temperature (K)

T 0 :

Environment temperature (K)

T b :

Bulk temperature (K)

T f :

Flash temperature (K)

T s :

Surface temperature (K)

T 1 :

Input torque of gears (N·m)

u r :

Rolling speed (m/s)

U :

Dimensionless speed number

V :

Dimensionless hardness number

v :

Velocity perpendicular to the line of action (m/s)

v s :

Relative sliding velocity (m/s)

V w :

Volume of the worn-out material (m3)

W n :

Normal load (N)

W :

Dimensionless load number

X :

Diameter of area associated with an adsorbed lubricant molecule

Z :

Pressure viscosity index

α :

Pressure viscosity coefficient (m2/N)

β :

Heat flux density distribution coefficient between the driving and driven gears

γ :

Amount of heat friction transferred for solids (0.9–0.95)

μ :

Friction coefficient of gear

μ 0 :

Inlet viscosity (Pa·s)

v :

Kinematic viscosity

ρ :

Density (kg/m3)

σ :

Surface roughness

\(\bar \sigma \) :

Dimensionless surface roughness number

ψ :

Fractional film defect

ω :

Rotational speed of the gear (rad/s)

Δ :

Transmission error

1 :

Driving gear

2 :

Driven gear

f :

Fluid

i :

Contact point

-:

Mean

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Acknowledgments

This research was supported by a Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education (NRF-2020R1I1A3A04036891).

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Authors and Affiliations

  1. Dept. of Mechanical Engineering, Gangneung-Wonju National University, Wonju, Gangwon-do, Korea

    Chan Il Park

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  1. Chan Il Park
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Correspondence to Chan Il Park.

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Chan IL Park received B.S., M.S., and Ph.D. in mechanical engineering at the Seoul National University. He worked at Hyundai Motor Company for eight years. He has served as a Dean of the College of Engineering at Kangnung National University and as the President of KSME. He is a Professor of mechanical engineering at the Gangneung-Wonju National University, and his research interests are gears, plates, shells, optimal design, thermal analysis, wear, noise, and vibrations.

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Park, C.I. Influence of tooth profile and surface roughness on wear of spur gears considering temperature. J Mech Sci Technol 37, 5297–5306 (2023). https://doi.org/10.1007/s12206-023-0931-6

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