Approximate method of determining the highest tension of the mine hoisting rope for the entire lifting period
Abstract
Approximate determination of the tension of hoisting mine ropes is used in order to overcome the two main difficulties arising in justifying the calculation of ropes for strength. If with a known approximation can justify the application of Hooke's law for the tension of the rope, taken in theory as a perfectly elastic thread of constant cross-section, then to account for internal resistance in the rope, as well as in a rectilinear homogeneous rod, quite reasonable formula is not available. The source of the second difficulty lies in the complex form of one of the boundary conditions of the problem of mathematical physics about the longitudinal vibrations of an elastic thread of variable length with a load at the lower end, to which the determination of the tension of hoisting mine ropes is given. It is about the upper end of the rope, which due to the coiling on the drum and the assumed absence of sliding on the drum should have a given speed, coinciding with the speed of the points of the outer surface of the rotating drum.
References
- Dinnik A. N. On the work on the theory of elasticity. Applied Mathematics and Mechanics, Vol. I, No. 2, 1933, pp. 335.
- Lyav A. Mathematical Theory of Elasticity. ONTI NKTG1, 1935, pp. 128-129.
- Neronov N. P. About elastic deformations in a hoisting rope. Applied Mathematics and Mechanics. New Series, vol. I, No. 1, pp. 91 -116, 1937.
- Savin G. N. Dynamic forces in a hoisting rope during the removal of a load from a fixed base. RAS USSR, 1954, No. 2.
- Neronov N. P. Determination of stresses in hoisting ropes for large heights of ascent and descent. Journal of Mining Institute, vol. XX, pp. 88, 94-97, 1948.