Bevel gears are almost always produced from shaped blanks. Therefore, more care and attention has to be taken in the selection of the gear blank than with other gear forms. As with all gears, sufficient thickness of material is required under the gear tooth roots. The taper of the bevel gear has to be taken into consideration, and it is recommended that the minimum amount of material should be at least equal to the whole depth of the tooth. Gears that are going to be highly stressed need a thicker section.
The thickness must also be maintained under the small end of the teeth. The blank geometry is set together with the initial settings for the coordinated movement of the blank and cutter. Because of the complex nature of the bevel gear, the blank design is of major importance. It is also necessary to provide a flat clamping space, and the back of the gear should be machined square with the bore and parallel with the front clamping surface. The aerospace and helicopter industries have produced a large body of data on the application of bevel gearing. Of major significance have been the effects of rim thickness on gear tooth stresses. Some ring gears require a web-less type of blank. Then the thickness between the bottom of the tapped hole and the root line of the gear should be one-third the tooth depth. Figure 1
The blanks supplied for all bevel gears must be within acceptable limits. These tolerances are applied to the face and back angles, outside diameter, the crown to back, and bore. Proportions are also critical to gear performance; the bores, hubs, and locating surfaces must be in relative size to the gear diameter and pitch problems occur with small bores, thin sections, and any conditions that cause difficulties in holding the blank or provide excessive overhang.
Almost all bevel gears that have a center hole when being machined are held by a clamp plate on the front face. The blank must incorporate a suitable surface for this purpose. Any excessive local stresses and/or deflections will create a problem for the gear. The tooth thickness is especially critical to the control of the backlash. The functional thickness is observed by checking with the mating gear and measured by a vernier caliper. When meshed together at the proper mounting distance, the backlash can be checked. The tooth thickness is specified at the mean normal tooth section.
Basics of the Gear Design
A gear set design commences with the basics such as outside diameter, number of teeth, etc. The bevel gear design requires the ratio and the calculations for the size and capacity using the load carrying formulae from the recognized AGMA or ISO standards. The suggested factors are reliable, having been established with many test programs. An additional task is to design the Ease-Off. It is computed mathematically by determining the minimum meshing distance for a set number of teeth. This provides a graphical presentation of the pinion and ring gear crowning which affects the contact pattern and running condition. Straight bevel gears usually have a minimum of 12 teeth. The fewer number of teeth used by spiral and hypoid bevel gearing is possible through the additional overlap formed by the oblique teeth, permitting the teeth to be stubbed, which prevents undercutting and still provides an acceptable contact ratio. Straight bevels avoid stub teeth because of the reduction in contact ratio which would affect sound level and wear.
In theory, the tapered teeth become weaker as they are elongated, and full-length contact is unlikely as the teeth are lengthened. A general rule for the maximum face width is to divide the cone distance E by three. Figure 2
Teeth with either long or short addenda are used on gears other than miter gears to avoid undercutting, increase the tooth strength, and reduce the rate of wear. By adding the addendum angle to the pitch-cone angle, the face angle between the axis of the gear and tops of the teeth are obtained. The tangent of the addendum angle equals the dedendum divided by the cone distance E.