# Calculation of instantaneous temperature on tooth surface of spur gear

Tooth surface instantaneous temperature is the instantaneous high temperature generated by contact points during gear meshing, which is mainly distributed on the surface of the teeth and is very easy to cause damage to the surface of the teeth instantaneously.According to Blok flash temperature theory, the instantaneous temperature Tf of tooth surface is calculated as

In this equation, the temperature rise factor is read as zeta, for spur gear, zeta=0.83_ is the friction coefficient of the tooth surface; PE is the normal load of the tooth surface on the unit tooth width; G1 and G2 are the thermal conductivity coefficients of the main and driven wheels respectively; Rh1 and Rh2 are the density of the main and driven wheels respectively; C1 and C2 are the specific heat capacity of the main and driven wheels respectively; B is the half width of the contact belt; V1 and V2 are the tangential direction of the main and driven wheels at the engagement point respectively.Speed is a function of time t.

In this paper, if not specified, the subscriptions i=1 and 2, where 1 represents the driving wheel and 2 represents the driven wheel.

The tangential velocity at the engagement point is calculated by

In the formula, the radius of the base circle of the driven and rbi-dominated wheels, the distance from the engagement point to the center of the driven and main wheels, and the angular speed of the driven and i-dominated wheels are calculated as follows:

In the formula, the speed of ni-dominated and driven wheels.

The distance RCI (t) from the engagement point to the center of the master and driven wheels can be obtained from equation (5), i.e.

In the formula, ra2 is the radius of the top circle of the driven gear teeth.

According to Hertzian contact theory, the half-width Bi(t) expression of the contact belt of the master and driven wheels is

In this equation, is the calculation coefficient, =1.128Poisson’s ratio of main and driven wheels with mu; elastic modulus of main and driven wheels with Ei; radius of curvature of tooth profile of main and driven wheels at meshing point with R1 and R2 respectively; the calculation formula is

In the equation, the pressure angle at the meshing point on the driven wheel with alpha i(t) as the main component is expressed as follows:

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