Most gear types have efficiencies in a fairly tight range. On the other hand, worm gear efficiency can vary greatly. A large portion of losses in a worm gear set is due to the sliding friction between the worm and gear.
The sliding friction is dependent on the worm lead angle, λ and the coefficient of friction between the worm and gear, μ. In this article, we'll look at the relationship between worm lead angle, coefficient of friction and mesh efficiency.
For our purposes, we will assume that the worm is driving the gear. We'll also ignore other losses such as bearing and seal friction, oil drag, etc. The normal pressure angle is 20 degrees.
Worm Gear Efficiency Equation
The equation for worm gear efficiency is given by the following equation.
The coefficient of friction comes into play when calculating gear tangential force. Hence, efficiency is dependent upon lead angle and the coefficient of friction.
Efficiency Plots
To illustrate the relationship between lead angle and friction we can plot the variables a couple of different ways. In the plot below, the coefficient of friction is varied given a number of lead angles.
When lead angle is 1 degree, efficiency drops off much faster than larger lead angles as coefficient of friction increases.
Alternatively, we can plot worm gear efficiency vs. lead angle given a number of coefficients of friction. For the coefficients of friction shown on the plot, maximum efficiency is in the range of lead angles from ~40 to 45 degrees. As coefficient of friction increases, the lead angle where maximum efficiency occurs is lower.
In summary, the obvious conclusion is efficiency increases to 100% as the coefficient of friction goes to zero. For small lead angles, efficiency is low. When coefficient of friction is lower, there is a wider range of lead angles that are near the maximum.