Multi-asperity Elastic Plastic Contact Model For Rough Gear Surface And Its Prediction Method

Contacts usually occur between high asperities on contact surfaces due to the irregularity of rough surface caused by part manufacturing.Therefore,the real contact area is smaller than the nominal contact area of contact surfaces.On the contrary,the real contact stress is greater than the nominal contact stress,thereby affecting the friction and wear on contact surfaces and fatigue of sub-surface.Thus,to predict the actual contact area of the contact surface,a contact model is necessary to be established by the material properties,the topography characteristics,and the contact load,etc.In this paper,a geometric model for rough tooth surfaces is reconstructed based on the geometric parameters of the micro tooth surface obtained by an optical measurement.Then,an analytical model and a finite element model for the contacts of three-asperity and multi-asperity are established(The three-asperity is a cuboid with three rotated paraboloids in the same direction.The multi-asperity is a cuboid with more than three rotated paraboloids).The effects of geometric parameters and distribution parameters of the asperity on the contact properties of the rough surfaces are discussed.These works provide a theoretical reference for the precise design of tooth surface.The following contents are included.(1)An analytical model for the three-asperity contact on gear surfaces is established based on the measured micro-topography parameters.The Wyko NT9100 optical profiler is applied to measure the surface micro-topography of tooth surfaces,and the high-frequency filter is used to eliminate interference signals.The tooth surface topography is reconstructed and the topography parameters of the rough surface are obtained by the measured data.According to the micro-topography and the height distribution of the asperities,four elastic-plastic contact models for the three-asperity contact are deduced,namely LHH,HLH,LLH and LHL.(2)A finite element contact analysis for three-asperity including elasticity and plasticity is performed.These finite element contact models include two types: three-asperity with different heights and constant spacing,and the one with constant height and different spacing.The results show that the theoretical model is consistent with the finite element calculation results under a small displacement load.Parametric analysis shows that the distribution of asperities with constant spacing slightly affects the total contact load and contact area,but such distribution has significant effects on the local stress.In addition,the interaction between asperities gradually becomes small with an increase in the spacing.(3)An elastic-plastic analytical model for the multi-asperity contact is established.The elastic-plastic contact model for the multi-asperity,whose heights are in concordance with the Guassian distribution,on rough tooth surface is deduced.Based on the measured rough tooth surface parameters,two kind s of multi-asperity contact models are constructed.The first type is a 5×5 multi-asperity contact models with the same samples and different density,and the second type includes 5×5,6×6 and 7×7 multi-asperity contact models with the same density and different samples.(4)A finite element contact analysis of multi-asperity including elasticity and plasticity is carried out.Finite element analysis was performed on the two kinds of multi-asperity contact models.The effects of multi-asperity distribution on Von Mises stress,normal Von Mises stress,contact load and contact area are investigated.The analysis results of each model with different samples are in accord with analytical solution.The results are applicable in a small area of rough tooth surface.