Contact Response Analysis of Vertical Impact between Elastic Sphere and Elastic Half Space

Abstract

At present, the contact problem between the particle and the plane plate is generally equivalent to the rigid sphere impacting the elastic half space or the elastic sphere impacting the rigid surface. However, in the actual contact process, there will be no rigid body, and both contact and contacted object will deform and absorb energy. The research results obtained from the equivalent of the contact material to the rigid body are less accurate. In order to obtain the accurate mechanical relation and contact response, we took the research of impact between particles and the metal plate as a breakthrough in which the particle is equivalent to an elastic sphere and the metal plate is equivalent to an elastic half space and established the theory of vertical impact contact between elastic sphere and elastic half space by the Hertz contact theory. Through the dynamic simulation of an elastic sphere which has similar properties with rock impacting target in elastic half space in LS-DYNA, the correctness of the established theory and the feasibility of the contact process simulated by LS-DYNA are verified. Based on the established theory and 3D simulation, we studied the influence law of material parameters on the contact response and analyzed the differences of the collision vibration signals caused by the different contact objects. From the above research results, we obtain that the theoretical model is more accurate to predict the maximum contact force and contact displacement in this paper than traditional Hertz theory. And the sphere radius and both contact objects’ elastic modulus have larger influence on the contact response than sphere density, while the Poisson’s ratio has the smallest influence on the contact response results. Different material properties will cause the different contact response. The conclusions of this paper provide a theoretical calculation method for contact and a 3D simulation method for elastic half space and provide theoretical guidance for the differences analysis of the vibration signal.

An Analytical Solution for Non-Linear Viscoelastic Impact

“…The most recent research studies concerning the viscoelastic impact phenomenon employ recent results from the theory of differential equations [52,53] validated by experimental results. There are also new theoretical models that simulate the behavior of materials via numerical methods [54], or, some that use for validation experimental data from the classical literature [42,43].…”

Influence of Coal Gangue Volume Mixing Ratio on the System Contact Response When Multiple Coal Gangue Particles Impacting the Metal Plate and the Study of Coal Gangue Mixing Ratio Recognition Based on the Metal Plate Contact Response and the Multi-Information Fusion

“…In this process, there are collisions between coal and gangue, single particle of coal gangue and the metal plate of the hydraulic support, multiple particles of coal gangue and the metal plate of the hydraulic support, coal gangue particles group and the metal plate of the hydraulic support, as shown in Figure 2. Yang et al [6], [7] studied the system contact dynamic response when a single particle elastic impacting the metal plate or elastic half-space by theoretical and simulation methods, and used the research idea of breaking up the whole into parts and the point-tosurface research thinking [8] to disassemble the complex top coal gangue identification problem and completed the coal gangue identification when the single coal gangue impacts the center position of the metal plate. Zeng et al [9] analyzed the dynamic process and impact response of the metal plate after the impact of the single particle coal gangue.…”

Vibration Test of Single Coal Gangue Particle Directly Impacting the Metal Plate and the Study of Coal Gangue Recognition Based on Vibration Signal and Stacking Integration

“…According to the previous research achievements on the spherical contact and the spherical plate contact [45]- [60], and after the collision and slippage behavior analyze between the coal gangue and the metal plate of the hydraulic support in the process of top coal caving, we have studied the systematic dynamic and contact response for the rock sphere elastic impact on the metal plate and for the coal ganguelike elastic spherical particle impact on the elastic half-space [61], [62], and preliminarily proved the exist of the difference between the contact responses and the vibration signals when coal gangue impact on the metal plate respectively, which explains the identifiability of coal and gangue. Based on the above research, and in order to finally break through the problem of the coal gangue surface identification in the top coal mining, we innovatively put forward to disassemble the complex coal gangue recognition problem in top-coal caving, adopt the approach of breaking up the whole into parts and research from point to face, and took the single particle coal gangue recognition as a breakthrough point, through constructing the vibration testbed of single particle impacting metal plate and conducting large sample single particle coal gangue impact test, combined with signal acquisition, signal interception, Hilbert-Huang transform and other processing methods, as well as machine learning and deep learning and other classification methods, the identification of the single particle coal gangue based on the impact vibration signal of metal plate is completed finally, and the recognition scheme is discussed considering the different recognition sample data and the specific application requirements.…”