Fig. 2082.
If it is desired to produce a wheel with angle teeth it is necessary, after having arranged the cutter as shown in [Fig. 2076], and while the forward motion of the carriage takes place, that the wheel r shall turn with a slow, regular movement until the tooth operated upon is finished. After this the tool retraces its path at a somewhat higher speed. This automatic motion is obtained from a shaft ([Fig. 2076]), on which are placed the pinions e2 e3. This shaft carries a third pinion p2, which, by means of one or more pairs of wheels mounted two by two on a swinging frame p, as shown by p3 p4 p5, turns the shaft p′ ([Fig. 2080]), which carries at one of its extremities the wheel p5 and at the other the screw h3. This screw, by proper intermediates, operates the toothed wheel g, [Fig. 2080], which in its rotation carries along the piece f, with all the parts supported by it. In this movement the pinion h3 does not turn, nor does the second pinion h4, which slides on the former. The screw h′ slightly turns the large wheel h, which, as previously mentioned, is mounted on the shaft d, [Fig. 2078]. When the special tooth operated upon is finished the movement is reversed by operating the lever l. The table and the wheel r, [Fig. 2077], then move in the opposite direction. When the original position is reached by the cutter, the reversing lever is thrown out of gear; the handle e′ is then used so as to effect the proper division, and the machine is again started.
As has been shown, only a small portion of the circumference of the wheel g is subjected to wear. In this way it would be possible to limit the operation of cutting the teeth to a certain length of arc only. In that case, however, considerable wear would be produced; for this reason the constructor has preferred to provide the whole circumference with teeth, in order to change the working point from time to time, so as to distribute the wear. In order to permit this displacement it is necessary to disengage the worm k ([Fig. 2076]), which is accomplished by turning the hand wheel v, mounted on the shaft v′, [Fig. 2078]. This shaft carries at each extremity small pinions, v2, v3, gearing with other pinions fixed at the extremity of each of the supports of the shaft p′.
In order to make the operation of this machine better understood, we will conclude our description by some practical examples of the calculations required in making helical teeth. It will be observed that the two small movements necessary in cutting an angle tooth in a given inclination are obtained first by the screw e, [Fig. 2077], feeding the cutter head, and second by the tangent screw k, [Fig. 2076], that governs the rotary motion of the wheel g, and consequently of the shaft d, carrying the face plate and the blank to be cut. The second wheel h, mounted on this shaft, is driven by the endless screw h′, [Fig. 2080], the supports of which are fixed on the wheel g. It will be observed at the same time that the speed of the screw e acting upon the tool holder is the same as that of the shaft carrying the wheels e2 e3 and p2, since the wheels e4 e5 e6 e7 have the same number of teeth. It is obvious, therefore, that that ratio of speed which will exist between the tangent screw k and the shaft of wheels e2 e3 and p2 will have to be the same as that between the driving screw e of the cutter head and the tangent screw k. Consequently, the combinations of wheels that connect this tangent screw k to the shaft e2 e3 and p2 will produce the same effect as if they were connected directly with the feed screw e. This being established, the general formulæ determining the gearing to be employed in order to produce helical teeth inclined at a certain angle are obtained in the following manner: It should here be observed that the teeth produced will be what in the United States are called angle teeth, corresponding, however, so nearly to the helix as to be considered helical. Suppose that the number of teeth in the wheel g is 300, and that the pitch of the driving screw of the cutter head is 5 mm., using for convenience the French system of measurements. Let x/y be the ratio of the four wheels that it is necessary to mount. Let m designate the degrees of inclination of the teeth. Let p equal the pitch of the desired helix, and d the diameter of the wheel to be operated upon. We then have cotan. m = p/(d × 3.14), from which we find p = cotan. m × d × 3.14, and in order to make the cutter head run over a distance corresponding to this pitch, the driving screw e must make a number of turns equal to
| cotan. m × d × 3.141 |
| 5 |
But while the cutter head passes over a distance equal to the pitch, the wheel g makes one turn and the tangent screw 300 turns; consequently, the ratio to be established between the speed of the tangent screw and between that of the screw driving the carriage will be represented by
| x | = | 1500 |
| y | cotan. m × d × 3.141 |
Thus, for a wheel with a diameter of 1.75 inches, the machine ought to have an inclination of 15° to the primitive circumference, and we would have, for the ratio to be established between the tangent screw and the driving screw,
| x | = | 1500 | = | 1500 |
| y | cotan. 15° × 1.75 × 3.141 | 20.51778 |