円筒巻きロープのクロスオーバの変分解析

概要

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The crossover of ropes in many layers around a drum is analyzed on differential geometry and calculus of variation with movable boundaries. As a geometrically nonlinear problem for linearly elastic ropes, the center line of ropes is modeled as a space curve which is restricted by the surface of the first-layer rope. The bending stiffness, tensile force and friction force acting on the rope and geometrical parameters of the hoisting drum are taken into account. The virtual work of the non-conservative tensile force and the bending energy of the cross-over are expressed by the first and second fundamental forms of the restrictive surface. Thereby the variational equation and boundary conditions are obtained. By the transformation of variables, the Euler equation is changed into an implicit form of the variable, and the expression of crossover is obtained. An experiment measuring the central angle of the cross-over is made to examine the result of theoretical analysis.
一般社団法人日本機械学会の論文
1998-11-25