From the Rolls-Royce experimental archive: a quarter of a million communications from Rolls-Royce, 1906 to 1960's. Documents from the Sir Henry Royce Memorial Foundation (SHRMF).
Analysis of tooth action, sliding, and pressures in spiral bevel and hypoid gears.
| Identifier | ExFiles\Box 114\1\ scan0079 | |
| Date | 11th January 1937 guessed | |
| be expected since the sliding is zero at that point. These diagrams show how it is possible to control the extremes of slide-roll ratio by varying the properties of the tooth length above and below the pitch line. You observe that the ratio becomes infinity for the old Brown and Sharp proportions and is quite moderate in the Maag proportions. The involute tooth action of spiral bevel gears is only slightly different from that in spur gear (cylindrical gears). A common approximation is to consider the tooth action to be that of equivalent spur gears the diameters of which are equal to twice the length of the normals from the pitch cone element to the gear axis. Actually, however, the tooth action at points of contact other than at the pitch line involves a slight longitudinal sliding action along the tooth. This ordinarily is so small as to be regarded as of negligible importance; and the spiral shape or curvature of the tooth has little influence. The tooth action in hypoid gears involves, in addition to the involute sliding action, a relative sliding motion longitudinally along the teeth as indicated in Figure 8. Here the slide due to involute action is represented by the vector (a) and the longitudinal slide due to the hypoid offset is represented by (b), the resultant sliding being shown by (c). The angle changes throughout the meshing cycle and varies in magnitude, being minimum at the pitch line and maximum at the root and addendum of the tooth. A comparison of relative absolute sliding values for spiral bevel and for hypoid tooth action is shown in Figure 9 and reveals two essential facts; (1) that the absolute value of the maximums for the hypoid is not much greater than for the spiral bevel; and, (2) that the minimum values occur at the pitch line. The theoretical value being zero for the spiral bevel. The tooth action, that is, as to sliding, can be varied to some extent by the choice of pitch, tooth heights, pressure angles, long and short addendum proportions for both types of gearing: but for the hypoid the pinion offset is a most important factor in affecting slide. TOOTH PRESSURES The instantaneous surface pressures occurring in the contact zones of a pair of meshing teeth is high and is affected by many variables. Gear men, of course, understand that the no load contacts are lines of infinitesimal width and occur simultaneously on several teeth assuming, of course, perfect tooth spacing. Under load, mutual compression takes place at the contacts and the lines become areas of finite width, of a dimension that is very narrow as compares to the working surface of the teeth. The distribution of load between all the pairs of teeth in contact is quite indeterminate and depends upon the elastic deformation, both general and local of the gear teeth, the relative curvature of the tooth surfaces in contact, the thickness of the tooth, the number of pairs of tooth in contact, the deformation of the gear mountings permitting relative displacement of the gear and pinion, the pressure, and spiral angles and, of course, the load. Even if we could assume that the mountings be perfectly rigid, the load distribution between the teeth will not be anywhere near equal, but the pair which are in mesh nearest the pitch line will be the most heavily loaded. The maximum tooth loading of the hypoid gear set will be less than the tooth loading in a spiral bevel gear set of the same ring gear diameter and with the same number of teeth in gears and pinion in contact. The tooth loading, however, is not reduced in direct proportion to the increase in number of pairs of teeth in contact, because the contacts vary in position along the tooth and as to location above and below pitch line. However, the gear designer has some latitude in choosing the proportions of the gear teeth - 4 - | ||