Contact stress analysis of a spur gear using Lewis and Hertz theory


  • Aisha Muhammad 2Faculty of Manufacturing and Mechatronic Engineering Technology, Universiti Malaysia Pahang, Malaysia
  • Ibrahim Haruna Shanono Department of Electrical Engineering, Bayero University, Kano, Nigeria.



Ansys, Finite Element Method, Safety factor, Contact stress, Finite element analysis


The rapid development of the automobile and aircraft industries has made applying gear technology necessary. Gears offer the benefits of efficiency, reliability, simplicity and a higher speed ratio with power transmission. However, they cannot transmit power over a long period, are more expensive when compared to belts and chain drives and requires continuous lubrication. They are used for transmitting high load in gear tools. The gear teeth fail when subjected to a high load beyond a certain limit. A deciding factor in gear design is the amount of stress developed on the contact surface of the mating gears. This paper deals with contact stress analysis of spur gear. The theoretical analysis presented in this paper aims to analyse rolling bearing contacts based on the principles of the Hertz and Lewis equations. A 3D domain-based finite element method was used to calculate the stresses between the contact surfaces of the structure. Contact analysis was performed using ANSYS Workbench software to figure out the deformation and optimum stress developed on the teeth of the gear. The simulation results indicated that the stress distribution on the gear contact surface has a maximum value of 144.82 MPa, while the deformation is at a maximum value of 0.01676 mm. The safety factor indicates the maximum level of 15, indicating the safety of the design.


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How to Cite

Muhammad, A., & Haruna Shanono, I. (2022). Contact stress analysis of a spur gear using Lewis and Hertz theory. Applied Research and Smart Technology (ARSTech), 2(2), 41–46.

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