A cusp catastrophe model for the friction catastrophe of mine brake material in continuous repeated brakings

The frictional performance of the brake material used in mine hoisters varies abnormally under some extreme braking conditions. Its friction coefficient runs the danger of falling suddenly in such a braking. Based on the catastrophe theories and the energy transforming ideas, this article established a cusp catastrophe model to describe and predict the friction catastrophe behaviors of the brake material in some continuous repeated brakings of mine hoisters. The predictive capability of the model was verified by some braking experiments. It is shown that the catastrophe phenomena of the friction catastrophe in braking can be described by the catastrophe theories as a cusp catastrophe. The friction coefficient can be taken as its state variable. The initial braking velocity and braking frequency can be taken into account for one control variable while another control variable may contain the braking pressure and braking time. Moreover, the friction catastrophe of the brake material has a critical braking state. The cusp model built in this article can properly predict its critical braking frequency. However, in the present state, the exact time that the friction catastrophe occurs in a critical braking cannot be accurately located.