contact stress analysis in gear ( spur gear )

contact stress

1. Introduction Gear are toothed wheels which can transmit power and motion from one shaft to another by successive engagement of teeth. In helical gear teeth are inclined to the axis of parallel shaft, provide quite operation due to gradual engagement of teeth compare to spur gear . 12 August 2024 1 Fig. Nomenclature of Helical Gear

2. Introduction - contd., Gearbox has many advantages, including compact structures, stable transmission capability, and low noise. Used of gear in renewable energy, advanced manufacturing, vehicle, mining, aerospace, material handling, oil & gas and power industry as shown in Fig. 12 August 2024 2 Fig. Applications of the gearbox transmission: some examples

3. Importance of Helical Gears Helical Gears are important because they provide smooth, quiet and efficient transmission of motion and power. Helical gears are widely used in many applications, including automotive transmissions, industrial machinery, aerospace and robotics. 12 August 2024 3 Fig. Helical Gear pair

4. Literature Review 12 August 2024 4 Author Details of article Proposed Methodology Key Findings Patil et al. 2014 Contact stress analysis of helical gear pairs, including frictional coefficients Finite Element Method applied to 0°, 5°, 15°, 25° helical gear sets. Lagrange multiplier algorithm used to determine stresses. Varying friction at contact for nonlinearity. Range of static coefficients of friction from 0 to 0.3 considered. Examined variation of contact stresses with helix angle and friction coefficients. Utilized ANSYS software and compared results with analytical calculations. Patil et al. 2015 Contact Stress Evaluation of Involute Gear Pairs, Including the Effects of Friction and Helix Angle Friction factors developed by comparing contact stresses with and without friction using FEM and Lagrange multiplier algorithm. Validation of models for various helical gear pairs. Friction factors developed based on contact stresses with different coefficients of friction.

5. Literature Review – contd., 12 August 2024 5 Author Details of article Proposed Methodology Key Findings Nestorovski et al. 2016 Analytical and Numerical Contact Stress Analysis of Spur Gears The effect of pressure angle on contact pressure in involute spur gears is studied, with 3D representations (17.5° to 25°) created using SolidWorks and Finite Element Analysis (FEM) conducted by ANSYS. Examining the effect of an increase in the pressure angle reveals a decrease in the maximum contact pressure. The observation validates that the difference between the results becomes more pronounced at higher pressure angles. Jyothirmai et al. 2014 A Finite Element Approach to Bending, Contact and Fatigue Stress Distribution in Helical Gear Systems Comparative finite element analysis assesses single, herringbone, and crossed helical gear systems. Matlab examines the AGMA-standard theory for single helical gears, while ANSYS covers structural, contact, and fatigue assessments. Examining the results, it is observed that the predicted values from FEA closely align with those obtained through analytical analysis for a single helical gear system. In terms of tooth bending stress, the FEA values are reasonably close to the values derived from analytical analysis, validating their proximity.

6. Problem Formulation Main aim of this study to find the contact stress which will leads to gear failures like surface wear, scuffing and pitting. The research focuses on contact stress and coefficient of friction related to helix angle in helical gear pairs under static conditions. The examination includes helical gear sets with helix angles of 0° (spur), 5°, 15°, and 25°. The main goal is to investigate how the helix angle affects contact stress and friction in helical gear pairs . 12 August 2024 6

7. Finite Element Method Analysis This work focuses on studying the contact stresses among helical gear pairs under static conditions using the 3D finite element method. Contact stress for various pairs of mating gears has been determined through finite element analysis (FEA) to investigate the effects of the coefficient of friction on gears. Additionally, stress variations were analyzed for gears with different helix angles. The (3D) finite element method (FEM) and the Lagrange multiplier algorithm have been employed to assess contact stresses. The results were validated for their initial values using Hertz and AGMA equations. 12 August 2024 7

8. Contact Stress Contact stress is distribution of force or pressure at contact interface between two meshing gears. It is a critical consideration in gear design to ensure that gears can transmit power efficiently without failure. Contact stress is influenced by factors such as gear geometry, material properties and operating conditions. AGMA contact stress equation: where C p is the elastic coefficient in terms of , F t is the Transmitted tangential force in Newton, b is the face width in mm, d is the pitch circle diameter in mm, I is the geometry factor, K o is the overload factor, K v is the dynamic factor, K m is the load distribution factor, Ks is the size factor and Z R is the surface condition factor.   12 August 2024 8

9. Contact Stress – Contd., Elastic coefficient factor ( C p ) where E and υ are Young's modulus and Poisson's ratio, respectively . Geometry Factor (I) where speed ratio i =n 1 /n 2 =d 2 /d 1 and α is transverse pressure angle. Contact Ratio (CR) where r is pitch circle radius, r b is base circle radius, suffix 1 is for pinion and 2 is for gear and a is addendum. Contact Ratio is crucial in gear design for efficient and failure-free power transmission. 12 August 2024 9

10. Contact Stress - Contd., Hertz contact stress equation : where C p is the elastic coefficient, d p is the pitch diameter of pinion, L is the length of contact. C p can be represented by equation 12 August 2024 10

11. Methodology 12 August 2024 11 Fig. steps of proposed methodology

12. 12 August 2024 12 Technical Details Table: Technical specification of gear pair (a) Specifications of gear sets. ( b) Material properties

13. FEM Analysis and Simulation 12 August 2024 13 Gear Characteristics: Four set of gear pair was prepared for analysis i.e. spur gear, 5°, 15° and 25° helical gear pairs. Material: All gear sets are constructed using structural steel. Model Generation: The involute of standard gear profile was created using a macro that was generated in ANSYS APDL. The involute standard gear profile was copied three times to create a three-tooth segment of pinion and similarly that of gear. Meshing Configurations: Gear pair volumes were discretized (meshed) using linear finite element SOLID185. The mapped mesh (Hex-Sweep) option was used to complete the mesh of the 3-tooth segments of pinion and gear. Additional Insight: It showcases impact of contact stress on helical gears, considering variations in coefficient of friction.

14. Results and Discussion 12 August 2024 14 Conducted numerical analysis to study helical gear behavior under operational conditions. Focus on the helix angle and coefficient of friction's impact on contact stress, a critical factor in potential gear failure. Graph illustrates the combined influence of helix angle and static coefficient of friction on maximum contact stress along contact elements. Graph depicts an upward trend, indicating that maximum contact stress values increase with a rise in the coefficient of friction.

15. Results and Discussion – contd., 12 August 2024 15 Fig. contact stress distribution for a spur gear pair:(a) μ = 0.0 and(b) μ = 0.15 Fig. contact stress distribution for 5° helical gear pair:(a) μ=0.0 and(b) μ=0.15.

16. Results and Discussion – Contd., 12 August 2024 16 Fig. contact stress distribution for 15° helical gear pair:(a) μ = 0.0 and(b) μ = 0.15 Fig. contact stress distribution for 25° helical gear pair:(a) μ=0.0 and(b) μ=0.15.

17. Results and Discussion – Contd., 12 August 2024 17 Table : Maximum contact stress with respect to friction coefficient by increasing helix angle .

18. Contact Stress Vs Helix Angle 12 August 2024 18 Fig. Maximum contact stress for different helix angular gear sets.

19. Contact Stress Vs Coefficient of Friction 12 August 2024 19 Fig. Maximum contact stress for varying coefficient of friction.

20. Conclusion 12 August 2024 20 FE gear model was verified with Hertz/AGMA equations for zero coefficient of friction. Helix angles ranging from 0° to 25°, revealing a discernible trend: contact stresses increased proportionally with the rise in coefficient of friction (0.05 to 0.3). Noted variations in the relationship between contact stress and coefficient of friction based on helical angle. Smaller helical gears exhibited a less pronounced increase in contact stress with rising coefficient of friction compared to gears with higher helical angles. The validated FE model and observed trends significantly contribute to a deeper understanding of critical factors in gear design and performance.

21. S. S. Patil, S. Karuppanan , I. Atanasovska , and A. A. Wahab, “Contact stress analysis of helical gear pairs, including frictional coefficients,” Int J Mech Sci, vol. 85, pp. 205–211, 2014, doi : 10.1016/j.ijmecsci.2014.05.013. S. S. Patil, S. Karuppanan , and I. Atanasovska , “Contact stress evaluation of involute gear pairs, including the effects of friction and helix angle,” J Tribol , vol. 137, no. 4, Oct. 2015, doi : 10.1115/1.4030242. Omran Abdallah and Sadok Sassi b, “Contribution of friction-induced vibration to the realistic failure analysis of spur gear cracked teeth, Engineering Failure Analysis 158 (2024) 107956. Blagoja Nestorovski and Petar Simonovski , “Analytical and Numerical Contact Stress Analysis of Spur Gears” Science, Engineering and Technology, Vol. 3, No. 1, pp. 44-49, April 2023, doi : 10.54327/set2023/v3.i1.79. K. Feng, J. C. Ji, Q. Ni, and M. Beer, “A review of vibration-based gear wear monitoring and prediction techniques,” Mechanical Systems and Signal Processing, vol. 182. Academic Press, Jan. 01, 2023. doi : 10.1016/j.ymssp.2022.109605. 12 August 2024 21 References

22. 12 August 2024 22 Thank you