The paper describes results obtained from the micro-elastohydrodynamic lubrication (micro-EHL) modeling of the gear tooth contacts used in micropitting tests together with a contact fatigue and damage accumulation analysis of the surfaces involved. Tooth surface profiles were acquired from pairs of helical test gears and micro-EHL simulations were performed corresponding to surfaces that actually came into contact during the meshing cycle. Plane strain fatigue and damage accumulation analysis shows that the predicted damage is concentrated close to the tooth surfaces and this supports the view that micropitting arises from fatigue at the asperity contact level. A comparison of the micropitting performance of gears finish-ground by two alternative processes (generation-grinding and form-grinding) suggests that 3D “waviness” may be an important factor in explaining their different micropitting behavior.
Worm gears used for power transmission commonly consist of a steel worm running against a bronze or phosphor bronze worm wheel. The wheel teeth are usually manufactured using an 'oversize' hob so that the initial elastic contact between the teeth is in the form of an ellipse with lubricant entrainment predominantly in the major axis direction. As a result of this unfavourable contact geometry, the lubricant film generated between the worm and wheel teeth is relatively thin. The kinematic configuration is close to that of simple sliding as the velocity of the wheel tooth surface relative to the nominal contact point is very low in comparison with that of the worm. The combination of poor film forming, high sliding and a soft gear material (to avoid scuffing) leads to the continuous wear seen in these gears. The article presents results obtained using a model for the prediction of wear for this configuration based on the well-known Archard wear law extended to take the variation of pressure and film thickness over the contact area into account in determining the wear rate. The pressure and film thickness distributions are obtained from elastohydrodynamic lubrication (EHL) modelling of the contact over the meshing cycle. Wear patterns are presented corresponding to different film thickness sensitivities in the wear formula, and these predictions, together with the calculated increase in backlash due to wear, give a basis for calibrating the model against experimental wear tests.
The paper presents the theoretical basis for modelling the contact conditions and elastohydrodynamic lubrication (EHL) of worm gears, the results of which are presented in Part 2. The asymmetric elongated contact that typi®es worm gears is non-Hertzian and is treated using a novel three-dimensional elastic contact simulation technique. The kinematic conditions at the EHL contact are such that the surfaces have a slide±roll ratio equal to almost 2, and the sliding direction varies over the contact area. These considerations require a non-Newtonian, thermal analysis, and the appropriate form of a novel Reynolds equation is developed that can incorporate any form of the nonNewtonian relationship between shear stress and strain rate. A form that incorporates both limiting shear stress and Eyring shear thinning is utilized in which the two eVects can be included both singly or together. NOTATION a contact semi-dimension (m) A area subject to lubricant pressure (m 2 ) c speci®c heat (J/kg K) C; D¯ow factors in the non-Newtonian Reynolds equation (ms) E 0 reduced elastic modulus (Pa) h ®lm thickness (m) h u undeformed ®lm shape (m) h 0 load-determining constant in the ®lm thickness equation(m) k thermal conductivity (W/m K) p pressure (Pa) p r @p=@r p s @p=@s q heat¯ux at the solid boundary (W/m 2 ) r coordinate in the local non-sliding direction (m) s coordinate in the local sliding direction (m) t time of heating (s) u¯uid velocity in the s direction (m/s) u mean surface velocity in the s direction (m/s) U¯uid velocity in the x direction (m/s) U mean surface velocity in the x direction (m/s) v¯uid velocity in the r direction (m/s) · v v mean surface velocity in the r direction (m/s) V¯uid velocity in the y direction (m/s) V mean surface velocity in the y direction (m/s) W load (N) x Cartesian coordinate in the contact plane (m) x 0 ; y 0 dummy variables in the de¯ection integral (m) y Cartesian coordinate in the contact plane (m)_ ® ® shear strain rate (s ¡1 ) " oil thermal expansivity (K ¡1 ) ² absolute viscosity (Pa s) temperature (K) ref bulk temperature of the component (K) 0 reference temperature for the viscosity relationship (K) l dummy variable in the surface temperature integral (s) » density (kg/m 3 ) ½ shear stress (Pa) ½ L limiting shear stress (Pa) ½ 0 Eyring shear stress (limit of Newtonian behaviour) (Pa) ¿ angle between the x and s directions The MS was
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