Stochastic mathematical model for rock cutting force generation

A mathematical model describing the formation of dynamic load components acting on the working units of mining machines during rock cutting is an essential component of the digital twin of a mining shearer and is used for engineering analysis, design calculations, process simulation, and machine-parameter optimization. The application of various numerical methods to cutting-force modeling, including FEM and DEM, is constrained by the need to identify a large number of parameters, typically 10 to 20, many of which are difficult to determine either analytically or experimentally. A stochastic mathematical model of the rock cutting process has been developed by representing the process as a flow of random events, namely elementary loading events and fracture events associated with the failure of a certain volume of rock mass, that is, chip formation events. The interval between elementary loading events in time or space is treated as a random variable. The closest agreement with experimental data obtained from tests of a shearer cutting a full-scale coal-cement block was achieved with a model based on a truncated exponential distribution of the interval between successive fracture events. For each elementary loading event, the maximum cutting force at which chip formation occurs is determined analytically from the known expected value of the cutting force. For the cutting force acting on an individual pick, the modeling error does not exceed 7% for the expected value and standard deviation and 15% for the maximum value. Good agreement was also confirmed between the histograms of the force distribution and the spectral density plots obtained from full-scale and computational experimental data. The proposed model contains no more than three parameters requiring identification and can be used as a component of the digital twin of a mining shearer. The same approach is also applicable to mathematical modeling of the cutting of hard soils using the working tools of earthmoving machines and to modeling the operating processes of crushing machines.