Applying the theory used to study function image in higher mathematics,the equiponderant tail rope system was analyzed,the heavy tail rope system and the light tail rope system in the friction hoist,the dynamic and static non-slip assurance coefficient change law in the normal hoist.

Based on the friction drive equation between the lining and wire rope,the characteristic of sliding process of friction hoist and the theory of heat conduction,a model of lining s transient temperature field was established and its analytic solution was obtained by an integral-transform method.

The results show that the high temperature friction coefficient of the steel/steel pairs appears the increasing trend with increasing test time,and the fast or slow of the increasing is a relation with the test parameters.

Based on Galerkin variation principle,an elastic finite element analysis model of coupling friction heat for wheel/rail was put forward,and the relations between wheel/rail friction heat and rail expanded displacement in touched area,wheel/rail frictional temperature,contact strain and stress.