Journal of the Society of Motion Picture and Television Engineers (1950-1954)

1950 16-MM AND 8-MM SPROCKET DESIGN 227 Figure 3 shows two film positions, one in solid lines for a shrinkage of 1.5 per cent and one shown by broken lines for a shrinkage of 1 per cent. In each case the lower edge of the perforation is 0.026 in. above the root circle, and the film is just ready to leave the tooth. Specification of Shape of Tooth. So far, only two points on the profile of the tooth have been located, one at the maximum working height of 0.026 in. and the other at the intersection with the root circle. Obviously, the manner in which the film is allowed to slip to take care of the shrinkage differential is controlled by the shape of the tooth between these two points. However, the relationship between the way the film slips and the running life of the film is not directly evident. The ultimate solution lies in exhaustive wear tests, with due consideration to all the other factors involved. A convenient method of specifying the shape of the tooth is to state the radius A* of a circular arc and the distance B from the root circle to the center of the arc. (When B is positive, the center is inside the root circle.) This method is justified not only for its convenience but for practical considerations of manufacture. That the circular arc is adequate can be seen in Fig. 3 from the close agreement of the circular arc with the epicycloid. One logical procedure for defining the shape of the tooth has been completely worked out and is described here, followed by a brief discussion of an alternative procedure. The first method is based on the circular arc that best approximates the epicycloid. As the shrinkage differential increases, the radius K of the tooth (Fig. 1) remains constant, but B, the distance from the root circle to the center of the radius, is increased. This brings the upper end of the tooth to the proper terminal point and provides a uniform shrinkage adjustment as the film moves up the face of the tooth. It may be argued that the above procedure will result in a tooth that slants too much at its base for good driving action, particularly when the tension on the film is high. The alternative procedure for determining the shape of the tooth overcomes this objection. By this method, the value of B is made independent of the range of shrinkage and approximates the value given by the above equation for zero range of shrinkage. The value of K must then vary with the range of shrinkage, from about the value given above to lower values as more shrinkage is accommodated. The resulting tooth is very nearly tangent to the epicycloid at its base but never crosses to the left of the epicycloid. This gives the steepest permissible tooth at the base. Equations for this procedure have not been completely derived, but the shape for 1.5 per cent shrinkage on a 1 2-tooth, 1 6-mm sprocket is shown by a light line on Fig. 3. The running life of the film should be considered the most important criterion for the final choice. From the standpoint of flutter, there appears to be an advantage in the first procedure. It is also possible to specify an involute (with a given pressure angle) for the shape of the tooth. This is not recommended because it results in a tooth which is even more slanting at its base than the tooth obtained by the first procedure. Thickness of the Tooth at the Base. For the properly designed drive or holdback sprocket, the action of the tooth takes place at the end of the film path, where the tooth is leaving. For the cases of maximum differential between the pitch of the sprocket and that of the film, there may be interference at the entering tooth (at the outside face for drive sprockets and at the inside face for holdback sprockets) if proper attention is not given to the selection of the thickness of the tooth. As given in the recommendations, the equations apply to the first procedure for determining the shape. The formula for the thickness of the tooth includes the following reductions from the full longitudinal dimension of the perforation: one for the shrinkage of the film in the arc of contact; a second for the teeth in partial engagement; a third for the pitch tolerance allowed for the sprocket; and