Contact and Bending Stress Analysis of Helical Gear Pair with Tip Relief

The importance of helical gear in power transmission system cannot be denied any further. Since its invention, it has been widely used in many areas. However, it is prone to failure due to the applied contact and bending stresses on the gear tooth. Hence, to reduce the risk of failure, the contact and bending stress distribution must be improved. Therefore, this study was conducted to discuss the effect of linear and parabolic tip relief modification on contact and bending stress in a helical gear pair, utilizing the 3D finite element analysis under static condition. An unmodified gear pair from previous literature which studied the effect of frictional coefficient on contact stress in helical gear [1] was chosen as a reference to compare the numerical analysis of the modified profile. The analysis was conducted by focusing on 5°, 15° and 25° helical gear. Finite Element Analysis (FEA) was performed on both unmodified and modified gears. The gear model was constructed in SolidWorks and imported into ANSYS to run the finite element analysis. The problem is approached by varying the length of modification, La while amount of modification, Ca is kept as constant. The range of normalized length of modification, ΔLn from 1/9 to 1 has been considered for this study. Next, Hertz contact stress theory and American Gear Manufacturers Association (AGMA) bending stress equation were utilized to validate the contact stress and bending stress of the unmodified gear model respectively, obtained from the simulation. FEA was in close agreement with analytical calculation with percentage difference of 5%. Stresses obtained from FEA of linear and parabolic tip relief modification are compared to determine which type of tip relief is more preferred. Parabolic tip relief reduced the contact stress up to 13.5% compared to linear tip relief which is 10%. In the case of bending stress, linear tip relief reduced up to 12% compared to parabolic which is 10.5%. Therefore, parabolic tip relief is preferred. Then, the mathematical equations to predict contact and bending stress were obtained from the trendlines of normalized stress, σ/σspur against normalized length of modification, ΔLn. The developed equations yield agreeable results with FEA with only 4% difference.