# Contact analysis of helical gear tooth elastic model

The elastic and elastoplastic models can be obtained by inputting two different strain curves. Among them, the elastic model only needs to add the linear elastic strain curve, while the elastic-plastic model only needs to add the yield strength (other parameters remain the same as the elastic model), and then input the curve ① in the figure.

If the material does not reach the yield strength, curve ② shows a linear elastic relationship, and the stress exceeds the yield strength（ σ S = 387mpa) is a linear strengthening relationship. When setting the material properties, add the curve ② in the figure:

The oblique line approximately simulates the stress-strain relationship of different strengthening degrees, so that the linear strengthening elastoplastic model can be obtained, namely:

When E1 = 0, it is an ideal elastic-plastic model.

(1) Convective heat transfer coefficient of helical gear end face.

In the formula: VF is the kinematic viscosity of lubricating oil; λ Is the thermal conductivity; RC is the radius of the contact point on the tooth surface; ω Is the helical gear angular speed; Ｎ μ Is Nusselt index; PR is the Prandtl index; J is the exponential constant; Take J = 2.

(2) Convective heat transfer coefficient of helical gear tooth meshing surface.

In the formula: HC is the height of helical gear teeth at any contact point; ρ ｆ、 υ F is the density and kinematic viscosity of lubricating oil respectively; ｃｆ、 λ Specific heat and thermal conductivity of lubricating oil; γ Is the thermal diffusion coefficient; Qtot is the standardized total cooling capacity; G is centrifugal acceleration; T is the total time of the ejection process.

(3) helical Gear friction heat flux.

The average heat flux density of the contact tooth surface of the driving and driven wheels is Q1 and Q2, expressed as:

In the formula: β S is the distribution factor of friction heat flux; η Is the coefficient of friction energy converted into heat energy; F is the friction coefficient; VGC is the relative sliding speed of the contact point of the meshing line of the driving wheel; PNC is the average contact pressure; T1h is the time when the friction heat flux in the contact area of the driving wheel passes through the contact width; T1 is the time for the driving wheel to engage for one week.

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