In a serviceable clutch there are two general requirements which are applicable to all forms. These are gradual engagement and large contact surfaces, although the latter requirement may be made to lose much of its force by making the surfaces very efficient. In the cone clutch, gradual engaging qualities are secured by placing a series of flat springs under the leather or clutch lining. By means of these springs, acting against the main clutch spring, the clutch does not grab, since the large spring must have time in which to overcome the numerous small springs. In this way the engagement is gradual and the progress of the car is easy as well as continuous.
The specific necessity in a cone clutch, whether it be direct or inverted, is a two-fold one - sufficient friction surface, and proper angularity. As the latter, in a way, effects the former, as will be discussed more in detail later, this really reduces to one complex requirement.
The angularity varies in practice from 8 to 18 degrees. In arriving at these figures, a line of reasoning is followed somewhat like the following:
The force of the spring acts along one leg of a right triangle of which the resulting useful force is found to lie along the hypothenuse, the latter being perpendicular to the surface of the clutch. In this case, the ratio of the resulting useful force x to the original spring pressure A is the ratio of 1 to the sine of the angle of the clutch cone θ. Expressed in the form of proportion, it is x:A : : 1 : sin θ or as an equation x = 1
A sin θ
Since 1 is a constant, reducing sin increases the ratio. Reducing the sine, in turn, means reducing the angle itself, and this is the course usually pursued as a large ratio is desired. For this reason small clutch-cone angles are used. The actual angle is, however, partly determined from another basis.
Coefficient of friction is the name given to the adhesion of two materials one to the other, under just such conditions as are described above. Since it is impossible to have perfect adhesion, this coefficient is always less than unity. Now, the angle of the cone of a cone-type clutch is dependent solely upon the coefficient of friction of the materials selected and the condition of the friction surfaces. Quite frequently, in fact, usually, the materials of cone clutches are leather and cast iron; i.e., the female cone is either a part of a cast-iron flywheel or made of cast iron, while the male cone is usually some other material lined with leather. The ordinary male cone is of very light metal, so as to reduce the spinning action of this rapidly rotated mass. Of late years, aluminum has met with favor for this part.
The coefficient of friction for cast iron and leather has been determined as .30 dry, and .25 greased. Since the latter case is more usual this value will be used. Expressed mathematically, the coefficient of friction is the tangent of the angle of repose, so for this value it would be the angle of which .25 is the tangent. This is 14 degrees. A more conservative value of the coefficient is .20, for which the angle is but 11 degrees.
In the design of the clutch, however, a more accurate method than this is pursued. The twisting moment in foot-pounds M is equal to the horsepower P, reduced to foot-pounds, divided by the speed at which the power is to be transmitted. This gives the equation:
M= P33,000, or roughly, P5250.
2 πR R.
Let S represent the torsional resistance, to which the clutch must at least be equal, and F the mean or average radius of the male cone in inches:
P 63,000 then S= FR.
If, now, the resulting pressure from the clutch spring acting normal to the clutch surface is z, the axial pressure or total exerted by the spring is x, and the coefficient of friction is f, then x x f z = and S=zf= sin θ sin θ
Equating the two values for S, and solving for x:
P 63,000 sin θ x, spring pressure = FRf and solving for P xfFR.
63,000 sin θ P, powertransmitted =