Elastic–plastic Contact Analysis And Adhesive Wear Method Of Rough Gear Surface

The gear develops towards the direction of high precision,long service life and lightweight.The precision and service life of a gear pair is affected by wear.In detail,the microscopic morphology of tooth surface is a key factor of gear adhesive wear.However,it’s rarely investigated by researchers.In this work,the wear of a cylinder gear pair is simulated.A semi–analytical geometric asperities model is proposed based on the valley–peak ratio of highest peak.On the basis of measured surfaces,the asperities are reconstructed using proposed model.Then,the real contact pressure and area between two rough surfaces and the contact character istics of rough of adhesively–bonded interface are briefly analyzed.Furthermore,an adhesive wear model of rough gear surface considering the time–varying mesh stiffness is established based on the geometric position of two tooth pairs contact.The mutual influences of rough tooth surface morphology,time–varying mesh stiffness and wear depth of gear pair are investigated.The main content and concl usion are as below:（1）A novel three–dimensional paraboloid asperities model of rough surface is proposed based on valley–peak ratio of highest peak.The single paraboloid asperity shape function is derived based on the least square method.According to c onnected domain theory,the rough surface is divided into many connected domains.In single connected domain,the center and projection region of the asperity is obtained by the valley–peak ratio of highest peak.Combined with the region and the shape function of asperity,the asperities are reconstructed using measured surfaces.The smallest profile error between rough surface and asperities is calculated to obtain the best valley–peak ratio value.The results indicate that the best valley–peak ratio interval is[0.01,0.1].Effects of measured surfaces,simulated surfaces and different sampling intervals on profile fitting error are investigated.Compared with traditional nine–point method,the proposed model demonstrates a smaller profile fitting error of mutational rough surface,the absence of interference among asperities,and more stable surface parameters under different sampling intervals.The proposed model is verified by comparing with nine–point method.（2）On the basis of measured surfaces,the e lastic–plastic contact（i.e.real contact area and load）between two rough surface under different sampling intervals is calculated by ZMC model.The contact condition that the real contact area is 30%of the nominal contact area is analyzed.The adhesivel y-bonded interface application between two rough surfaces is discussed briefly.Results show that the real contact area and load under different sampling intervals calculated by proposed model are more than that obtained by nine–point method.When the real contact area is 30%of the nominal contact area,as the sampling interval increases,the proportion of asperity in elastic stage increases,while that in plastic stage decreases;the real contact area of strong anaerobic adhesive is much smaller than that of weak anaerobic adhesive to obtain the same shear strength.（3）A novel adhesive wear model of rough gear surface considering modified time–varying mesh stiffness is proposed based on the geometric position of double tooth pair contact.The initial mesh stiffness is calculated by potential energy method.On the basis of the geometric position of double tooth pair contact,the time–varying mesh stiffness is modified by considering the rough tooth surface morphology and cumulative wear depths.According to modified time–varying mesh stiffness,the load distribution factor is calculated.Since a spur gear pair contact can be equivalent to the contact of two cylinders with variable curvature radius,the pressure of mesh point of line of action is obtained by Hertz theory.Combined with contact pressure and sliding distance,the wear depth of line of action is calculated using Archard model.（4）The adhesive wear model of rough gear surface considering modified load distribution factor is compared with Flodin model to verify the validity of the proposed model.On the basis of the simulated rough surfaces by Fast Fourier Transform,the effects of roughness on wear depth and tooth surface mesh stiffness are investigated by proposed model.Taking two meshing po ints in the double tooth pairs contact stage as an example,the mutual influences among rough surface morphology,mesh stiffness and wear depth are discussed detailly and the variation of roughness with the increment of mesh cycles is analyzed.Finally,the effects of different modules,tooth widths,input toques and mesh cycles on mesh stiffness,load distribution factor and wear depths are investigated.Results indicate that I)the mesh stiffness,load distribution factor and wear depth of the rough tooth surface oscillate back and forth around that of smooth tooth surface.As the roughness（Ra）of tooth surface increases,the oscillation becomes large.II)the value of wear depth is determined by profile error E₁₂ rather than roughness（Ra）.III)The roughness of tooth surface decreases and then increases with the increment of mesh cycle.IV)As the module and the tooth width decrease or the input torque and mesh cycle increase,the wear depth and the roughness of the surface morphology increase.