Dynamic Response Analysis of the Coal Gangue-like Elastic Rock Sphere Impact on the Massless Tail Beam Based on Contact-Structure Theory and FEM

The impact and collision behavior between the coal gangue and the hydraulic support widely exists in the top coal caving. However, due to the complex interactions between the large number of coal gangue particles in the mining surface and the limitations of the coal mining technology and other factors, it becomes a difficult problem to study the collision behavior and the contact response between the coal gangue and the hydraulic support or its main components under the actual caving conditions. In order to accurately grasp the contact response law when the coal gangue impacts the tail beam of the hydraulic support, in combination with the equivalent stiffness of the tail beam jack, the Lankarani–Nikravesh (L-N) nonlinear spring-damping contact model, the structural mechanics model of the tail beam, and the energy conservation law, this paper firstly establishes the system contact-structure dynamic model when the particles impact on the tail beam based on the tail beam equivalent kinematics model. Then, to further study the system contact response, the spring damper module is used in the finite element software for the first time to replace the hydraulic cylinder, and four different types of the rigid-flexible coupling simulations when the impact heights, the impact positions, the rock radii, and the rock materials change are conducted, respectively. Through the combination of the theory and the simulation, the contact response law when the particles impacting the massless tail beam under different working conditions is obtained, and the system contact response differences as well as the coal gangue identifying feasibility on the basis of the response differences after the coal gangue impact are analyzed. The conclusions will provide theoretical reference and simulation method for the study of the impact-contact behavior between the coal gangue and the hydraulic support.