12.2 ANALYSIS OF GEARS

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The involute profile of the gear means that the force applied at the gear teeth is not tangent to the pitch line, but actually tangent to the base circle. At the pitch point the force between the teeth acts at the pressure angle.

For spur gears the following values and equations can be used for the applied forces. Clearly there would be a reaction force that is not shown here. (Note: this applies even if multiple teeth are in contact).

If we are considering helical gears the helical spiral of the teeth adds a second angle to the contact force. This means that the contact force requires 3D analysis.

Straight bevel gears are not so easy to calculate because the force is applied at a variable distance from the center of the rotational axis.

In these gears we compromise by assuming the force is applied at the center of the tooth. In actuality this force will be further from the center of the gear.

We can calculate force components using the relationships below,

For all of these gears we need to use the calculated forces to design bearings and supports. Most notably the axial thrusts require thrust bearings be included in the design.