Theoretical Study On Roughness Factor Of Involute Spur Gear

The current design of gear contact fatigue strength is adapting the Hertztheory, which is only applicable to the contact of smooth tooth surface. Theload capacity calculation international standard (ISO/6336:1996) of involutecylindrical gears and it’s corresponding national standard (GB3840-1997) bothrecommended roughness coefficient, but the coefficient extrabold by a smallnumber of experiments have some limitations. With a large number ofmeasured roughness data, the aims of this study will propose theoreticalformulas of tooth surface roughness coefficient that adapts to several ofworking conditions.Based on the tooth surface rough outlines，the profile measurement oftooth surface with transverse stripes are measured. Then the function ofroughness is formed by Fourier nonlinear transformation, and superimposed onthe equation of film thickness to establish a numerical model of hybrid thermalEHL. Based on this model and keep with the fixed parameters of geartransmission and lubricant, calculate400groups numerical of the EHL with themulti-grid method by changing the tooth surface roughness values for the threeconditions are done: the light, the medium and the heavy-duty. In the end, the quantitative analysis on the effect of tooth surface roughness on the filmthickness and contact stress, and the corresponding formulas of different loadingconditions are established, which are used for calculating the roughnesscoefficients. The following conclusions can be obtained by analyzing andsummarizing the results of this study:(1) As the "pump effect" role of transverse rough stripes, the film thicknessof horizontal stripes rough tooth surface is greater than the smooth surface, andthe difference between the two is increasing with the growing of roughness andload.(2) Compared with the smooth tooth surface contact, the rough toothsurface pressure distribution and film thickness will be significant fluctuations;at the same time, the main shear stress distributions of sub-surface contact areaoccurs stress concentration, and with the load and the roughness increases, thisvolatility and stress concentration will become intense.(3) In heavy load conditions, with the increasing of the roughness and theload, the position of the main shear stress of sub-surface contact area isgradually moving in the direction of the tooth surface, which is more likely tofatigue failure of tooth surface.(4) For medium and heavy gear, with the increasing of roughness, themaximum main shear stress of sub-surface contact area is decreasing firstly andthen increasing.This doesn’t mean that less roughness, the lower contact stress.But the international standard (ISO/6336:1996) and the corresponding national standard (GB3840-1997) have recommended the roughness coefficient, whichchanges monotonically with roughness, means that the roughness is smaller,longer gear fatigue life. Thus, the scientific of coefficient is questionable.(5) Tooth surface roughness has a significant effect on the tooth contactstress. Commonly used in industrial enterprises, the heavy gear, when theroughness σ≤0.3(μm), the rough surface of the tooth contact stress is only aboutlarge5%than the smooth tooth surface. But when σ=0.515(μm), the former isabout15-20%large than the latter. This shows that the existing theory that Hertztheory as a basis for design of the gear contact strength beneath the science andsafety.(6) Tooth surface roughness coefficient formulas are established for threegears by using the multiple regression theory.The innovation of this paper is based on the measured roughness data,through a large number of numerical calculations, finally the theoreticalformulas of the tooth surface roughness coefficient are established underdifferent working conditions. The downside is that the numerical convergencedifficulties under the roughness is larger, which results that the present studyare subject to greater roughness in the range limitations.