Theoretical Modelling Of Thermal-Hoop Stress Around The Tooth Of A Spur Gear In A Filler Machine

The study employed the finite element method to develop a validated theoretical model to investigate the distribution of thermal hoop stress around the teeth of a spur gear operating in a filler machine. Three cases of temperature distribution along the radius of a gear tooth were assumed and investigated. The outcome showed that the maximum effective stress occurs at the tip of the gear tooth and decreased circumferentially deep into the gear material. The results also demonstrated that a nonlinear distribution of the temperature around the gear teeth makes the gear material susceptible to penetrating stress and therefore increase the tendency of fatigue failure. Keywords—Filler machine, stress analysis, temperature variation, rotating spur gear, mechanics. Nomenclature 1. σθθ = hoop stress i.e. stress in the circumferential direction 2. r2 = radius of the gear 3. σrθ = shear stress in θ direction 4. σrz = stress in the Z – direction 5. Fθ = local body force for unit volume 6. θ = angular coordinate 7. ρ = density of the material 8. ω = angular velocity 9. μ = Poisson ratio 0.303 ≃ 10. E = Modulus of elasticly 11. T = Temperature (normal in O C) 12. ri = internal radius at the root 13. r0 = outer radius 14. σcg = stress at the tip of the tooth 15. σcs = stress at the bottom of the tooth 16. α = constant = linear expansively = 12.6 x 10 -6 / o C 17. β = constant 18. δ = constant 19. To = constant temp (minimum temperature in o C)