# Simulation of tooth surface model of spur gear

According to the parameters of spur gear, the indexing circle radius R2 of spur gear is:

Where:

M2 — modulus of spur gear (mm);

Z2 — number of teeth of spur gear

The root circle radius RF2 of the gear is:

Tip pressure angle of gear end face α t α 2 is:

According to the formula, the tooth surface equation of spur gear. Because the research of spur gear hobbing only focuses on the involute profile of spur gear tooth surface, the drawn tooth surface starts from the base cylinder (pressure angle is zero) to the pressure angle of end face tooth top αtα2。

The parametric equation of the base cylinder is as follows:

In the gear coordinate system: SG, (OG: XG, YG, ZG), the included angle between any point Q, ogq on the base circle and the positive direction of XG axis is recorded as θ b 。 The parametric equation of the base cylinder is as follows:

The simulated base cylinder and the right tooth surface model of the gear in Figure 1 are shown in Figure 2.

To draw the left tooth surface model of spur gear, just change the symbol of XF on the right tooth surface to obtain the left tooth surface equation of spur gear:

Fig. 1 left tooth surface of spur gear tooth and angle of gear φ G take:

The left and right tooth surface models of one tooth of spur gear obtained by simulation are shown in Figure 3.

The gear tooth surface in the above spur gear coordinate system SG is taken as the first tooth and the right tooth surface of the first tooth φ G = 0, draw the right tooth surface of all teeth of spur gear and the rotation angle of gear φ G take:

Where: n — the nth tooth of spur gear, taking a positive integer

The left tooth surface of all teeth of spur gear and the angle of gear φ G take:

The left and right tooth surfaces of the whole gear are simulated from the left and right tooth surface equations of the spur gear, as shown in Figure 4.

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