Fig. 39.
Fig. 40.
In determining the diameter of a generating circle for a set or train of wheels, we have the consideration that the smaller the diameter of the generating circle in proportion to that of the pitch circle the more the teeth are spread at the roots, and this creates a pressure tending to thrust the wheels apart, thus causing the axle journals to wear. In [Fig. 39], for example, a a is the line of centres, and the contact of the curves at b c would cause a thrust in the direction of the arrows d, e. This thrust would exist throughout the whole path of contact save at the point f, on the line of centres. This thrust is reduced in proportion as the diameter of the generating circle is increased; thus in [Fig. 40], is represented a pair of pinions of 12 teeth and 3 inch pitch, and c being the driver, there is contact at e, and at g, and e being a radial line, there is obviously a minimum of thrust.
What is known as the Willis system for interchangeable gearing, consists of using for every pitch of the teeth a generating circle whose diameter is equal to the radius of a pinion having 12 teeth, hence the pinion will in each pitch have radial flanks, and the roots of the teeth will be more spread as the number of teeth in the wheel is increased. Twelve teeth is the least number that it is considered practicable to use; hence it is obvious that under this system all wheels of the same pitch will work correctly together.
Unless the faces of the teeth and the flanks with which they work are curves produced from the same size of generating circle, the velocity of the teeth will not be uniform. Obviously the revolutions of the wheels will be proportionate to their numbers of teeth; hence in a pair of wheels having an equal number of teeth, the revolutions will per force be equal, but the driver will not impart uniform motion to the driven wheel, but each tooth will during the path of contact move irregularly.
Fig. 41.