On The Tribological Behavior Of Modified Cylindrical Helical Gears Under Elastohydrodynamic Lubrication Condition

Gears have been widely applied in modern transmission systems due to their features regarding excellent meshing performance,high load capacity and compact structure.Gear transmissions suffer from more and more high-speed and heavy-load working conditions,resulting in higher performance requirements.Gears transfer motion and torque through the frictional contact between the conjugate tooth surfaces.Therefore,tribological behaviors are crucial to transmission performance.Gear tribology is significant for the design and optimization of high performance gear transmission.Involute cylindrical gears are usually applied in high-speed and heavy-load transmissions.In this paper,the tooth contact characteristics,load distribution,lubrication behaviors and friction loss of cylindrical helical gears with modifications and misalignments are investigated,forming tribology design method.Gear meshing theory,elastic mechanics,elastohydrodynamic lubrication(EHL)and numerical methods are used for modeling and solution.The tooth surface equation of double-crowned cylindrical helical gear is derived.The tooth surface contact model of helical gears with modifications and misalignments is proposed.The effects of modifications and misalignments on meshing characteristics of helical gears are studied.Results indicate that edge contact occurs at the beginning and the end of mesh because of misalignments.When profile modification is applied,the middle of contact path is oriented longitudinally.While lead modification inclines contact pattern to longitudinal direction.Misalignment deviates contact pattern towards the ends of tooth profile.An efficient model of load distribution for helical gears with modifications and misalignments is proposed.Instant contact points are obtained by unloaded meshing simulation.The instantaneous contact line under load is determined based on the tooth surface gap model and the full numerical method for elliptical Hertzian contact.Then the load distribution is derived from the minimization of potential energy.The proposed model is numerically implemented by a fixed-point iteration method based computational scheme.In the absence of the complex calculation of the three-dimensional elastic deformation of tooth surface,the model is characterized by simple calculations and high efficiency.Then it is verified by finite element analysis.The effects of profile crowning,lead modification,misalignment and input torque on load distribution are investigated.Results indicate that contact pattern shrinks with increasing magnitude of profile crowning and decreasing input torque,resulting in abrupt load transitions between two and three meshing tooth pairs.While lead modification can transfer load from the edge of tooth surface to the center by inclining contact pattern to longitudinal direction,providing desirable load distribution.In addition,misalignment deviates contact pattern and sharing load respectively towards the ends of tooth profile and meshing cycle.A Newtonian isothermal EHL model for helical gears with modifications and misalignments is introduced.An asymmetric spherical roller contact model is proposed for the contact between the modified tooth surfaces incorporating misalignments,considering side leakage.The geometric parameters of EHL model are determined.The multilevel method and the multilevel multi-integration method are applied to solve the EHL model.Several specific numerical techniques are applied for the severe convergence due to edge contact.Eventually,pressure distribution and film thickness are obtained.The effects of modifications and misalignments on lubrication behaviors are investigated.Results indicate that the edge contact at both ends of mesh leads to high pressure and thin film thickness.The double-crowning improves lubrication performance and provides a superior tolerance for misalignments.Considering thermal effect and non-Newtonian property of fluid,a novel EHL model for helical gears with modifications and misalignments is proposed.On the basis of the iterative calculation of equivalent viscosity,the energy equation is solved by the marching method.Then a pressure-temperature iteration based computational scheme is applied for solving the EHL model.The effects of modifications and misalignments on temperature rise are investigated.And the influences of non-Newtonian property and thermal effect on the lubrication behaviors of helical gears are studied.Results indicate that the edge contact at both ends of mesh leads to high temperature rise.The effects of misalignments on temperature rise are alleviated by the double-crowning.In the absence of edge contact,pressure distribution is almost immune to temperature rise,while film thickness reduces with temperature rise.However,temperature rise has a significant effect on pressure distribution in the presence of edge contact.The effect of temperature rise on film thickness in edge area is related to edge effect.The non-Newtonian property has a significant influence on oil film shear stress.A model of friction loss for helical gears is proposed,considering lubrication,modifications,misalignments and edge effect.The film shear stresses on tooth surfaces are obtained by solving the non-Newtonian thermal EHL model of helical gears.Based on the analysis of film slideroll effect,the rolling and sliding friction forces are derived by integrating shear stresses.Then the method for friction force is verified by experiments with a ball-on-disk type arrangement.The rolling and sliding friction losses and average friction loss are determined from friction forces and velocities.The effects of modifications and misalignments on friction loss are investigated.Results indicate that the friction loss of double-crowning is higher than that of profile-crowning without misalignment.Whereas the double-crowning makes friction loss almost immune to misalignment,providing a superior tolerance for assembly errors.