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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