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
The paper presents the results of modelling the contact and elastohydrodynamic lubrication (EHL) eVects between the teeth of worm gears. A number of diVerent practical worm gear designs have been studied covering a wide range of sizes and potential applications, from small instrument drives to high power units. All the designs are of the popular ZI type, in which the worm is an involute helicoid, with deliberate mismatch of tooth conformity in order to avoid damaging edge contact. The results cover loaded tooth contact analysis (`loaded TCA') under dry conditions, predicted ®lm-generating behaviour with lubrication, surface and oil ®lm temperatures, and calculated values of friction and transmission eYciency. It is demonstrated that regions of poor ®lm formation may be predicted in a qualitative way on the basis of loaded TCA together with consideration of the kinematics of entrainment at the contacts. NOTATION a; b Hertzian contact major and minor semidimensions (m) c 0 speci®c heat (J/kg K) k 0 thermal conductivity (W/m K) S 0 lubricant parameter x Cartesian coordinate in the contact plane (m) y Cartesian coordinate in the contact plane (m) Z lubricant parameter " 0 oil thermal expansivity …K ¡1 † ² 0 absolute viscosity at zero pressure (Pa s) 0 reference (bulk, or inlet) temperature (K) » 0 density at zero pressure (kg/m 3 ) ½ L limiting shear stress (Pa) ½ 0 Eyring shear stress (Pa)
No abstract
The work principle of flat-plate structure under shearing mode is expounded based on a vertical type rheometer for MRF which combined data acquisition with treatment and result display. The formula to calculate shearing stress is deduced. Based on different recipe for MRF, experiments under different working gap length were done by altering the intensity of magnetic field. The rheological model for MRF was established and the relationships between shearing stress, viscosity and magnetic field intensity were deduced. Experiments indicate that MRF has the flowing characters: with an increase of the magnetic induction and the nominal shear rate, the shear stress of MRF increases. However, as the working gap decreases, the shear stress increases. MRF has shear thinning property under magnetic field.
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