The second component in that face contact ratio equation is the face width. There are almost as many “rules of thumb” for determining the “proper” face width as there are fallacies about helix angle. One of the benefits of being in the gearbox repair business was the opportunity to see the long-term effects of those design decisions. The widespread adoption of crowning and, more recently, highly modified leads has mitigated some of the more serious problems but I caution against using micro-geometry to resolve macro-geometry issues.
One popular rule of thumb was making the face width half the center distance. This worked reasonably well if the gear ratio was not too high. As the ratio went higher the face width to pinion pitch diameter quickly got into the “danger zone.” Years ago that red line was set at 2.00. Modern design practice has scaled that back to 1.25 to 1.50 depending upon the application.
Why this retrenchment? Torsional deflection of the pinion; yes, you can account for this with modifications but there is a dark side to modifications few people talk about. For any “optimizing” change in micro-geometry you must select a specific load point. If your load varies, and most do, you are sub-optimized for all other points in the duty cycle. In some cases, the optimizing load occurs for only a small portion of the cycles and the rest of the time contact area is actually diminished and problems result. The most stunning example of this was recounted in a technical paper some years ago; a Royal Navy ship damaged its main propulsion gear set by only running one gas turbine. The change in loading was counter to the optimized design point. We’ll revisit this issue in a future posting.
A gearbox we had to repair frequently had two 7:1 reduction stages in a concentric arrangement, both of which had face widths that were half the center distance. The pinion twist could be calculated, of course, but the load varied so much that no optimization was possible. We tried a variety of modifications and the teeth still failed like clockwork every three to six months. Unfortunately, the machine it powered had no room for a bigger gearbox and the customer had to budget for those repairs until the machine itself could be replaced.