Catastrophe analysis on pillar instability considered mining effect
The instability of the pillar was discussed based on the potential energy principle and the cusp catastrophe theory, and a simplified mechanical model of the pillar was established considering the mining effect. The necessary-sufficient conditions, the jump value of displacement of pillar and the released energy expressions were deduced. The results show that the instability of the pillar is related to the properties of the rock, the external force and the relative stiffness of the elastic area to the plastic area. The instability of system is like to occur with the enlarging of the softening area or the decreasing of E/λ. The calculation done shows that the estimated results correspond to practical experience....
The analysis of the bending stiffness and intensity of cylindrical tubes
Based on the mechanics of material, the bending stiffness and intensity of cylindrical bar and tube are analyzed. By comparing the cylindrical tube whose ratio of outside diameter to internal diameter is 0.7 with the cylindrical bar, it is concluded that when both of them have the same mass, the section stiffness of the cylindrical tube is three times that of the cylindrical bar; when both of them have the same external diameter, the mass of the cylindrical tube is only 1/2 that of the cylindrical bar, but the section stiffness of the cylindrical tube is 3/4 that of the cylindrical bar.By virtue of the elemental elastic-plastic theory, the yield stress of the liquid-filled cylindrical tube is investigated. Due to the incompressibility of liquid and the strain hardening effect of material, the yield stress of the liquid-filled tube is enlarged compared with the hollow tube, thus raising its bending intensity. Under the dynamic load, compared with the hollow tube, the impact resistance of the liquid-filled tube is also raised due to elastic recovery. Because the hydraulic pressures perpendicular to the inner surface are identical everywhere, the local stress concentration resulting from the ovalisation of the tube would be decreased, and the resistance to buckling would be improved....
Impact of Modal Parameters on Milling Process Chatter Stability Lobes
Modals of the machine/tool and machine/part system are the principal factors affecting the stability of a milling process. Based on the modeling of chatter stability of milling process, the influence of modal parameters on chatter stability lobes independently or jointly has been analyzed by simulation. Peak-to-valley specific value, lobe coefficient and the corresponding calculation formula have been put forward. General laws and steps of modal simplification for multimodality system have been summarized....