The formula for the pres­sure angle

A crown gear­head like the EtaCrown impresses with its high level of effi­ciency. The key to this is the correct angle with which the gear tooth systems inter­lock.

Dr. Nikola Ell and Friedrich Ober­meyer – devel­op­ment of tech­nology and methods in indus­trial drive tech­nology (Photo | ebm-papst)

An impor­tant require­ment for a trans­mis­sion is its effi­ciency. The trans­mis­sion is supposed to pass on the energy that drives it — as far as possible without losses. After all, high losses mean that more energy is required for the same work.

Gear tooth systems work the most effi­ciently when the teeth roll against each other as much as possible and only slide slightly.

The key to this is the correct pres­sure angle of the pinion into the teeth of the crown gear. A crown gear­head consists of a normal spur gear, the pinion, whose teeth mesh in a disk-shaped crown gear. For normal spur gear trans­mis­sions, the pres­sure angle is usually 20 degrees. Here, you can achieve very good meshing and optimum effi­ciency.

We make use of this proven prin­ciple with our EtaCrown, as the pinion is designed with precisely this pres­sure angle. On the crown gear, on the other hand, the tooth pres­sure angle changes across the tooth width. Depending on the diam­eter (d) of the crown gear disk that you consider, there is a different pres­sure angle  — there is a more acute angle in the inner area of the teeth; towards the outside it becomes consid­er­ably larger than the ideal 20 degrees.

The point of contact between two tooth flanks moves throughout the entire meshing process on a straight line, the line of action. The angle by which the line of action is inclined is known as the pres­sure angle; it is usually 20 degrees. (Illus­tra­tion | ebm-papst)

However, the gear tooth systems still roll off each other to a large extent. After all, other geomet­rical vari­ables are also crucial for the optimum pres­sure angle. These include the number of teeth on the crown gear (z2) and the correct dimen­sion for the tooth size (m). These vari­ables are constant and perfectly matched for virtu­ally smooth rolling of the gear tooth systems.

This means the crown gear­head, such as the EtaCrown, has an advan­tage over other trans­mis­sions with sliding tooth contact, such as the worm gear: It has lower losses due to fric­tion and is there­fore more effi­cient.

In addi­tion, a crown gear­head is less sensi­tive and easier to handle than a bevel gear. The reason for this is that, during assembly, the crown gear and pinion only have to be set in two instead of three axial direc­tions for the perfect pres­sure angle. 

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