Prediction method of cutting stability of roadheader based on the Newton–Lagrange mixed discrete method

In order to study the influence of the multiple interaction of coal and rock and the velocity effect of the cutting head on the flutter stability of the cantilever roadheader, considering the physical characteristics of coal and rock, the structural parameters of the cutting head and the motion parameters of the cutting head, the functional expression of the cutting depth of the cutting head and the participating cutting teeth is fitted, the cutting state mechanical characteristic equation of the dynamic cutting of the cutting teeth is established, and based on the mapping relationship between the cutting teeth and the cutting head, a cutting dynamic model including multiple interactions between cutting head and coal and rock and the speed effect is constructed. An improved discrete method based on Newton–Lagrange mixed interpolation is proposed, and the influence law of the coupling effect of regeneration effect and velocity effect on the stability of cutting flutter under cutting state is clarified. The improved full discrete method is compared with the full discrete method and the semi-discrete method, and the superiority of the improved full discrete method based on the mixed interpolation method is proved. Based on the improved total discrete method, the influence of different cutting system dynamic parameters on the stability is studied. A cutting head coal rock system is built to simulate the flutter of the cutting system. The results show that the improved fully discrete method can reasonably predict the actual cutting state.