Rational Design of Hoisting Drums

Abstract

Abstract The main problem of hoisting-drum design resolves itself into two parts: determination of flange shape and thickness, and determination of the thickness of the drum body. Other factors, such as brake, clutch, and bearings, have already been investigated and are therefore not considered in this paper. The correct proportioning of drum flanges is obviously dependent upon the side pressure brought to bear against them, by the coils of rope wound about the drum. In other words, flange thickness is a function of (a) rope tension and (b) depth of winding. Previous theoretical investigations have recognized these factors, but have failed to take account of the friction between adjacent coils of rope, and between rope and drum, which tends to hold the coils in position without the aid of the flanges, and have also disregarded the flattening of the inside coils under pressure from the outer layers. This flattening, which is quite appreciable on account of the soft core of hoisting rope, results in a shortening of the inner coils, thereby relieving them of a part of their tension, and reducing the pressure against the flanges. A theoretical formula is deduced for the total pressure against a drum flange caused by the winding-on of rope to a given depth and under a given initial tension. Two other formulœ are then deduced, which relate this total pressure to the flange thickness and the maximum allowable tensile and shearing stresses in the material. By means of these formulæ a flange of the usual straight-sided or the mushroom type may be designed to withstand safely the pressure of the rope wound upon the drum. The drum body is subjected to combined stresses, since it is under compression from the coils wound upon it, under tension due to the lateral pressure against the flanges, and under combined torsion and bending caused by the load which is to be hoisted. Formulæ are derived which may be used to obtain the correct thickness both at the center of the drum, where the normal stresses are greatest, and at the ends of the drum, where the shearing stresses are most prominent. In order to check the theoretical formula for flange pressure, tests were made with small-size rope wound upon a special drum, which was so arranged that the side thrust against one flange could be directly measured while the rope was being wound on or unwound. These tests show conclusively that formulæ for flange pressure which do not take account of rope friction and flattening give excessively large results.