23rd International Colloquium Tribology - January 2022 243 Wear analysis of spur gears in consideration of the temperature Chan IL Park Gangneung-Wonju National University/ Dept. of Mechanical Engineering, Gangwon-do/ Wonju, South Korea Corresponding author: pci@gwnu.ac.kr 1. Introduction The gear wear is one of the important failure modes in gear systems with the tooth bending fatigue, contact fatigue, and scoring. The gear wear can also cause the change of tooth profile from its designed tooth profile. It leads to the reduction of mesh stiffness and in turns, changes the noise and vibration characteristics of the gear system significantly. Gear teeth has the rolling and sliding motion except sole rolling at the pitch. Meshing teeth are separated by a lubricant film during the rolling and sliding motion. The lubricant film is not always enough to separate the meshing teeth when the temperature rise due to friction occurs. The temperature rise can cause to change the lubrication regime. Therefore, this study analysed the wear of spur gears in consideration of the temperature. To do so, the load of spur gears with friction is obtained by solving the simultaneous equations of load-deformation equations and moment balance equation. The sliding speed and the contact pressure at the meshing position are also calculated. Gear temperature is obtained by the commercial FE code and in-house program. Finally, the wear depth of spur gears under the mixed elastohydrodynamic lubrication is calculated in consideration of temperature. 2. Wear analysis Surface wear in the gear tooth contact with combined sliding and rolling motions is one of several failure modes. The most widely used wear model is the dry-contact Archard’s wear model as follows [1]; , (1) where V is the volume of the worn out material (m 3 ); K is the dimensionless wear coefficient; W is the applied normal load (N); s is the sliding distance (m); H is hardness of the contact surface (Pa). Under the assumption that the hardness of contacting surfaces is constant during the wear process, Archard’s wear equation can be reformulated as , (2) where h is the wear depth and k is a dimensional wear coefficient (k=K/ H). To consider the mixed elastohydrodynamic lubrication and the surface temperature, the modified equation with the asperity load ratio and the fractional film defect is given by [2-4] , (3) where L a is the asperity load ratio of the two contact surfaces (percentage) and the fractional film defect ѱ can be expressed as , (4) where X is the diameter of area associated with an adsorbed lubricant molecule (m); t 0 is the fundamental time of vibration of molecule in adsorbed state (s); E a is the heat of adsorption of oil molecules on surfaces. R g is the gas constant (J/ mol K); T s is the surface temperature (K). 3. Thermal analysis Contact surface temperature of gears consists of the bulk temperature T b and the flash temperature T f as follows; T s =T b + T f , (5) The bulk temperature is the average temperature while the flash temperature is the instantaneous temperature rise. The bulk temperature is calculated by FE thermal analysis. The heat flux due to the sliding friction of spur gears is expressed as , (6) where µ is friction coefficient of gear; v s is the relative sliding velocity; is the mean contact pressure. In FE modelling of a single tooth of gears, thermal boundary condition and heat flux on model faces are imposed [5,6]. Assuming that Hertz theory on the contacting surface is valid, the flash temperature predicts by Blok’s equation as follows; 244 23rd International Colloquium Tribology - January 2022 Wear analysis of spur gears in consideration of the temperature (7) Where W n is the normal load per the face width (N/ m); k t is thermal conductivity (W/ (m∙K)); ρ is density (kg/ m 3 ); c p is specific heat capacity (J/ (kg ºC)), v 1 ,v 2 are the perpendicular velocity to the line of action (m/ s); a H is Hertz contact half-width (m). 4. Results and discussion For the wear and thermal analysis, normal force and friction force of the spur gear with data of Table 1 and true involute profile are calculated in torque 20 N∙m, using the moment balance and force-deformation equations [7]. Gear material is SM45C and oil is SAE-80W-90. The heat flux at 3,000 rpm is calculated by in-house program. Bulk temperature is analyzed by MSC Nastran FE code as shown in Figure 1. Bulk temperature is higher at the approach than at the recess of driving gear, and average bulk temperature is 28.65 ºC. Flash temperature is calculated by Blok’s equation. Using the surface temperature, wear depth under the mixed elastohydrodynamic lubrication is calculated. Figure 2 shows wear depth at every 1000 cycle to 10,000 cycles. The gear approach suffers more wear than the gear recess and pitch point do not wear due to no sliding motion. Figure 1: Bulk temperature by FEA Table 1: Gear data Tabelle Driving Driven Normal module (mm) 2 Normal pressure angle 20° Center distance (mm) 58 Whole depth (mm) 4.26 Number of teeth 30 26 Face width (mm) 16 13 Outside radius (mm) 32.9 28.86 Pitch radius (mm) 30 26 Root radius (mm) 28.64 24.6 Addendum mo. co. 0.57 0.55 5. Conclusion This study analysed the wear of spur gears in consideration of the temperature. Bulk temperature and flash temperature for tooth surface temperature are calculated. Wear depth of spur gears under the mixed elastohydrodynamic lubrication is analysed. The gear approach suffers more wear than the gear recess and pitch point do not wear due to no sliding motion. Figure 2: Wear depth of driving gear Acknowledgement This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF- 2020R1I1A3A04036891). References [1] A. Flodin, S. 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