Metal Mining - Acceleration Stresses in Wire Hoisting-ropes (with Discussion)

In previous discussions on stresses in hoisting ropes, little has been said concerning the effect of the elasticity of the rope itself on the stresses due to acceleration. Laschinger1 has calculated acceleration stresses for several cases but he has ignored the elasticity of the rope as a factor, except as it compresses the drum and stretches itself as it winds thereon. He also deals with steam plants and he shows the effect of the "jerky" start of the engine. This effect would actually be reduced by the elasticity of the cable. With the advent of the motor-driven hoist, new conditions have arisen. The jerk mentioned by Laschinger has been eliminated and smoother starting made possible. But the elastic properties of the rope seem to introduce considerable periodic acceleration stresses in the rope. The following discussion of acceleration stresses is based on the assumption of a constant acceleration at the drum. To be exact, the mathematical work is based upon the assumption that the top is moving upward with a constant acceleration, and ignores the fact that the cable is shortening as it winds. However, the effect of the shortening would be inconsiderable during the first part of the acceleration period. Most hoisting engineers make the assumption of constant acceleration at the drum. Under the older method of calculating acceleration stresses, this would be true with a constant torque motor. But if stresses vary, as this paper attempts to show that they do, constant torque would not give constant acceleration, although the velocity-time curves obtained in the full size test herein described showed that they approach rather closely to this condition, at least as nearly as could be measured. Theoretical Discussion According to elementary physics, the force required to accelerate a Wf body of weight W at the rate of f ft. per sec.2 is wf . To raise the body Wf with acceleration of f ft. per see.2 the total force required is I + Wf, in if