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.

To deal with the problem that thermal flow density varies with time on absolutely sliding lining surface, this paper proposes on approximate method of calculating friction temperature in multi rope friction winder lining according to the integrate method of solution to thermal conduction problem.

Suggest that the safety improving anti-skidding assurance coefficient measure,to ensure that multi-rope friction hoist system works further.

In this paper,replacing options of inhaul cable of multi-rope friction hoist used for a tower medium deep shaft are discussed.

The research on the slide-proof way of wire ropes with multi-rope friction hoist has always been paid attention to by the mine users.