# Modeling and Simulation of Mild Wear of Spur Gear Considering Radial Misalignment

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## Abstract

An appropriate clearance is required between mating gears for effective power transmission. In the present work, the effect of radial misalignment on mild wear of spur gear is modeled and simulated. The changes in the gear tooth contact geometry due to progressive wear have also been accounted in the model. The simulation results show that in the pinion dedendum region, pressure angle increases, while the contact pressure and wear depth decrease with increase in number of wear cycles. As far as the effect of radial misalignment is concerned, contact pressure decreases and wear depth increases with the increase in misalignment. In the pinion addendum region, pressure angle and wear depth increase with the increase in wear cycles, while the contact pressure and wear depth decrease with the increase in misalignment. The pressure angle and pitch point change from initial 20° (23rd pitch point) to 20.95° (26th pitch point) and 21.86° (28th pitch point) due to 0.5- and 1-mm radial misalignment, respectively. The wear depths after 50,000 wear cycles are − 1.32 × 10^{−2} μm, − 3.33 × 10^{−3} μm and − 4.39 × 10^{−4} μm at 23rd, 26th and 28th pitch points, respectively. The effect of radial misalignment on backlash, pressure angle, pitch point, contact ratio, double tooth contact region and speed ratio is also discussed.

## Keywords

Spur gear Wear simulation and modeling Progressive wear Radial misalignment Backlash## List of symbols

*a*_{H}Semi-Hertzian contact width

*E*Equivalent young’s modulus

*E*_{p}Young’s modulus of pinion material

*E*_{g}Young’s modulus of gear material

*F*_{t}Transmitted load

*H*Hardness

*K*Dimensionless wear coefficient

*k*Specific wear coefficient \(\left( { = \frac{K}{H}} \right)\)

*P*Contact pressure

*r*_{A}Radius at point ‘A’ on involute profile

*r*_{B}Radius at point ‘B’ on involute profile

*S*_{A}Tooth thickness at point ‘A’ on involute profile

*S*_{B}Tooth thickness at point ‘B’ on involute profile

*t*Sliding duration

*v*Sliding velocity

*y*Distance between pitch point and the instantaneous point of contact

*ω*_{p}Angular speed of pinion

*ω*_{g}Angular speed of gear

*φ*Pressure angle at pitch point ‘P’

*φ*_{A}Pressure angle at point ‘A’

*φ*_{B}Pressure angle at point ‘B’

## Subscript

*p*Pinion

*g*Gear

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