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260 W. HOTINE [J. S. M. P. E.
latter is equal to the force pressing the plates together multiplied by the coefficient of friction. Hence we may write
T = R\f (6)
If we eliminate/ from equations 5 and 6 there results
T - (7)
Equation 7 gives the torque delivered to the take-up spindle in terms of the various mechanical constants of the mechanism.
The torque delivered by the clutch will be a constant for a given adjustment of the spring pressure, as shown by the above derivation. The torque can never exceed this constant value, as an additional load will automatically lessen the torque transmitted to the driven clutch-disk as the spring is compressed by the climbing motion of the driving-pin up the cam surface, increasing the axial force on the driving-pin. The film is thus protected at all times from a damaging tension. A constant torque at the take-up spindle means that the film tension will be inversely proportional to the radius of the film pile on the reel. If this radius increases from two to seven inches during the take-up operation, it follows that the film tension at the end will be only 30 per cent of that at the start. The ordinary clutch does not deliver a constant torque at a variable speed because the coefficient of friction decreases with increased slip-speed of the clutch faces. In winding film, when the film pile increases in diameter, thus slowing down the take-up reel and increasing the slip-speed of the clutch faces, the torque of the ordinary clutch decreases, resulting in a loosely wound film pile at the larger diameter. This condition is aggravated by the increased film weight at large diameters. If the spring pressure is adjusted for sufficient torque to overcome this condition, the film tension at the start of the winding is generally excessive, and is conducive to film damage. The improved clutch delivers a constant torque at variable speeds, because any change in the coefficient of friction substantially cancels itself out, and has little effect on the torque, as can be seen by inspection of equation 7. This constant torque can not be exceeded, thus affording definite protection from excessive film tension under ah1 conditions, and as the torque is maintained regardless of the film pile diameter, a tightly wound reel always results, even with film