# The Empirical Formula for the Stiffness of a Spur Gear Pair Based on Finite Element Solutions

## Authors

• Thiwa Nantapak Chulalongkorn University
• Kornsara Srisarakorn Chulalongkorn University
• Thanakorn Tantipiriyapongs Chulalongkorn University
• Nitchawat Deecharoen Chulalongkorn University
• Chanat Ratanasumawong Chulalongkorn University

## Keywords:

Tooth stiffness, Spur gear, Empirical formula, Finite Element Method

## Abstract

Gear meshing stiffness is commonly determined by the analytical method or the finite element method (FEM). Both methods can be used to determine the meshing stiffness but the calculation for the analytical method is more complicated, while the FEM is impacted by the tooth contact setting and large computation time. Thus, both methods have limitations for practical use. Here, an empirical formula was proposed to calculate meshing stiffness of a spur gear pair with gear ratio 1:1 in moderate to large load conditions. The formula was divided into two parts as 1) an equation used to calculate the stiffness of the gear cylinder derived from the elasticity equations, and 2) an empirical formula to determine the meshing stiffness of the tooth pair based on FEM solutions. The second part of the formula was constructed by selecting the related parameters, finding the appropriate formula pattern, and determining the relation between these parameters and tooth stiffness at any meshing position. Meshing stiffness of the gear pair was determined by combining the stiffness of two parts connected in series.  Accuracy of the empirical formula was verified by comparing the calculated meshing stiffness with previous research and indicated that the calculated meshing stiffness conformed well with other studies. Our proposed empirical formula can be applied to any spur gear pair with gear ratio 1:1 to accurately determine gear meshing stiffness.

## Author Biographies

Department of Mechanical Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok, Thailand

Department of Mechanical Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok, Thailand

Department of Mechanical Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok, Thailand

Department of Mechanical Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok, Thailand