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).
The differences between cone and hypoid gear surfaces and a comparison of gear tooth action.
| Identifier | ExFiles\Box 114\1\ scan0078 | |
| Date | 11th January 1937 guessed | |
| For toothed gears an obvious requirement is that the pitch spacing of the teeth must be constant in order that the teeth register properly with its mating tooth at each revolution. This requirement is met in bevel gears with straight line cone elements along which the cones are tangent. The hypoid elements are also straight and the hypoid pitch surfaces are tangent along one rectilinear element. The essential difference between the cone surfaces and the hypoid surfaces is that in the former the action between the two cones is pure rolling with tangency along a rectilinear conical element while in the latter the pitch surfaces roll and slide on one another as they rotate with a constant velocity ratio. The tangency is along a rectilinear element and the motion between the two is composed of pure rolling, perpendicular to the element, and pure sliding, longitudinally along the element. It is also evident that as (A), the pinion offset, is diminished the pitch surfaces approach nearer and nearer to conical surfaces. If now we put teeth on these two types of pitch surfaces providing for the proper tooth to tooth spacing and tooth profiles of such shape as to meet the conditions of constant velocity ratio we get respectively bevel gears or skew bevel gears. If we make the teeth straight, following the pitch element of the surfaces, we will have respectively straight tooth bevel gears or skew bevel gears. If we make the tooth elements curved, such as circular arcs, and displace them so that tangents to their mid points make an angle to the pitch surface elements we get what we familiarly know as spiral bevel gears or hypoid gears respectively. COMPARISON OF TOOTH ACTION A large part of the fundamental knowledge of the gear engineer is the kinematics of tooth action during the meshing cycle. The most elemental action between two meshing teeth occurs in ordinary spur gears the pitch surfaces of which are cylinders with parallel axes, and the velocity ratio of which is equal to the ratio of their diameters. The action between two meshing involute* teeth is not pure rolling but a mixture of rolling and sliding the ratio of slide to roll changing throughout the meshing interval. This is demonstrated in Figure 6 and 7. In Figure 6 the right half shows two contacting tooth profiles with portions shaded to show the relation of sliding action to rolling action. For instance, the portion (7) of the right hand gear contacts with the relatively narrow portion (1) of the left hand gear. Since these two portions go through contact in simultaneously equal time periods, it is evident that they must slide on one another, and the amount of sliding is a function of the difference in the profile lengths. For this portion of contact the sliding is high as compared with the portions (4-4) which are of equal length and consequently indicates pure rolling action in the neighborhood of the pitch line. The left hand portion of Figure 6 shows the relative profile engagements laid out on a flat plane, the contacts of the portions being as follows: (7) with (1), (6) with (2), (5) with (3), (4) with (4), (3) with (5), (2) with (6), and (1) with (7). It is easily seen that the sliding is greatest at the root of the tooth, becomes zero at the pitch line, and high again at the end of the tooth. The relative sliding at different points on the profile is better shown by the sliding diagrams in Figure 7, the factor expressing the ratio of the slide to roll. All the diagrams pass through zero at the pitch line which, of course, is to * two types of tooth profiles provided for constant velocity ratio, the cycloidal and the involute. The cycloidal type has become obsolete. - 3 - | ||