Surface stresses around an asperity that passes an elastohydrodynamic contact
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Surface stresses around an asperity that passes an elastohydrodynamic contact Carl-Magnus Everitt cmev@kth.se 7/10-2015 Tribodays Nynäshamn Aim – To determine the surface stresses around an asperity in the surface of a spur gear teeth Rolling direction Local point load (3D) Global line load (2D) Positive surface stresses Source: http://www.hercus.com.au/spur-gears/ Asperity RCF crack Source: D. Hannes 2014 .On fatigue crack growth modelling of surface initiated rolling contact fatigue using the asperity point load mechanism Assumptions • A long cylinder with an asperity against a flat surface • Full film lubrication • The asperity is modeled as one cosine cycle • The viscosity lubricant is pressure dependent but temperature independent • The density of the lubricant is Pressure dependent • Elastic material Rolling cylinder Rotational symmetric asperity (note different scales) Numerical model – the equations Name Equation Elastic deformation π€ π₯, π¦ = Reynolds time dependent equation π π ,π‘ 3 π₯−π 2 + π¦−π‘ 2 ππ ππ‘ π πβ3 ππ π πβ ππ π’1 + π’2 π πβ π πβ + − − =0 ππ₯ 12π ππ₯ ππ¦ 12π ππ¦ 2 ππ₯ ππ‘ π 5.9 β 108 + 1.34π = π0 5.9 β 108 + π Dawson and Higginson's PressureDensity relation Roeland’s PressureViscosity equation 2 ππΈ′ π πΌπ0 π = exp −1 + 1 + π0 π π0 Load balance π π π π₯, π¦ π ππ₯ππ¦ = π¦πππ − π¦0 π ππ»πππ‘π§ 2 Used parameters Parameter Value Speed of top surface π’1 = 20 ±3 [π/π ] Speed of bottom surface π’2 = 20 ±3 [π/π ] Slide to roll ratio ππ π = 0 ±0.3 [−] Maximum Hertzian pressure ππ»πππ‘π§ = 2.3 [πΊππ] Equivalent elastic modulus Equivalent radius Viscosity-pressure coefficient Referents pressure Viscosity-pressure exponent πΈ′ = 226 [πΊππ] π = 6.8 [ππ] πΌ = 2.17 β 10−8 ππ π0 = 198 [πππ] π = 0.68 [−] Asperity height ππ πβ = 1.5 [ππ] Asperity width ππ ππ€ = 100 [ππ] −1 π [MPa] Used Model Single grid model • 150x60 nodes • 150 time steps • Isometric grid, DX=DY Multigrid model • Planed for the future π¦ π - π₯ π Simulation Simulation – Centerline Asymmetric pressure for different SRR Surface stresses – 1st principal [MPa] π¦ π - π₯ π Surface stresses – Only positive values of 1st principal [MPa] [MPa] π¦ π₯ π π Conclusion • The pressure on the asperity is asymmetric • The stresses around the asperity are asymmetric • Tensile in-surface stresses outside the asperity (for EHD) Thank you Max 1st principal stress as function of asp position Max 1st principal stress as function of asp position Simulation Used Scales Parameter Horizontal dimension Vertical scale Pressure Time Value π₯ π π¦ π= π βπ π»= 2 π π π= ππ»πππ‘π§ ππ π= π‘ π π= Results – in real numbers Parameter Value H_min H_center P_max without asperity 2.3 [GPa P_max with asperity 6.9 [GPa]
