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Models of the mine shaft hoist installation for the analysis of the conveyance emergency overwinding |
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Models of the mine shaft hoist installation for the analysis of the conveyance emergency overwinding the boundary positions Author: M. Wójcik
The problem of modeling the mechanical system of the mine shaft hoist installation for simulation one of the most dangerous emergency states which is the conveyance overwinding the boundary positions has been discussed in the paper. Presented review of the mechanical models of the hoist installation allows to choose one of them for the analysis of the conveyance emergency braking process. On the scheme of the mine hoist installation with the tower mounted machine its main elements and kinetics were characterized. Forces and torques acting on the model simulating the state of conveyance emergency braking were then discussed. Assumptions and simplifications assumed in modeling ropes, conveyances and the hoist installation were given. The basic model of the hoist installation with parameters distributed with conveyances in boundary positions, in which physical quantities are expressed by continuous variable functions were presented. Partial differential equations determine dependencies between these quantities. The equation of motion for the elementary rope segments with boundary and initial conditions for such model was given. The next model is a result of splitting the hoist mechanical system into two independent systems. Such a model with the assigned fundion of velocity of the upper rope end in the case of braking the descending cage was presented in figure 4. Equation of motion and boundary conditions for this model were given. From the group of models with concentrated parameters the mode, in which hoist and balance rope masses were digitized by Lagrange's method, was presented. The model described by the system of nordinary differential equations was obtained. System of equations for this model with conveyance braking forces was given as well. The last presented hoist installation model takes into account rope longitudinal oscillations, transverse oscillations of the deformable conveyance and reciprocal coupling of these oscillations. For this model the equation of dynamic equilibrium of the elementary rope segment and the expression for dynamic force acting in a rope were given. In the last chapter the problem of determining the actual values of parameters which are indispensable to claborate the mathematical model of the hoist installation was discussed. Attention was paid to the record of the braking force functions and the problem of taking into account the force from the emergency brake of the hoist machine and driving torque from the motor of the machine in the analysis of emergency braking process. Theoretical runs of drive torque in function of braking time for hoist installation motors operating in two different electrical systems were presented as well.
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2011