Analysis Of Magnetic Pulse Pressure And Numerical Simulation Of Dynamic Forming During Electromagnetic Bulging Of Cylindrical Shell

The relationship between the discharge parameters and deformation is hard to figure with simple mathematical formulation for the real-time coupling of the electrical and geometrical parameters during the magnetic pulse forming of cylindrical shell. Whilst, the magnetic pulse force, which is attenuating instantaneously and non-uniform along the axial direction of shell, is body force that contributes to the obstacle to the researches on the laws of dynamic bulging of cylindrical shell. For the simple analysis and calculation, the pulsed magnetic force was transformed into the magnetic pressure acting on the surface of the workpiece, such as the cylindrical shell. Up to now, the effects of axial coordinate on the distribution and those of radial deformation on the magnitude of the magnetic pressure were neglected in the old model of equivalent magnetic pressure. So there are prominent differences between the real deformation and the results based on the old model of magnetic pressure. And the coupling effects of electromagnetic field and deformation are ignored in the numerical simulation of single-separate modeling of magnetic pulse forming process that can not be used to simulate the dynamic forming. Therefore, in this thesis, the equivalent magnetic pressure, which presents the time-space characteristics more accurately, was established by theoretical analysis. The law of dynamic deformation of aluminum cylindrical shell and the effects of main parameters on the deformation were systematically studied by numerical simulation. The main results obtained show as follows:(1) The formulation of the new equivalent magnetic pressure has been established based on the old magnetic pressure model and the electromagnetic analysis of magnetic pulse bulging of cylindrical shell. It includes the influences of longitudinal coordinate and radial displacement and presents the time-space characteristics of magnetic pressure more accurately.(2) The nominal peak value of the magnetic pressure is proportional to the capacitance and the square of discharge voltage, is inversely proportional to the coil length and the gap area between shell and coil, and decreases with the increasing radial displacement. The magnetic pressure distributes nonuniformly along the axial direction and its magnitude at shell ends is less than that in the middle.(3) Based on the theory of finite element analysis of electromagnetic- deformation coupled field, the mathematic model for the electromagnetic analysis during magnetic pulse bulging is established; the boundary conditions and axial symmetry of the electromagnetic field model are investigated and presented; and the elastic-plastic FE theory of deformation is introduced, including yielding criterion, hardening conditions and the constitutive equations.(4) The deformation process of cylindrical shell bulging was investigated by the numerical simulation. The results show that the radial displacement of shell bulging is non-uniform along the axial direction and increases with the discharge voltage. With the discharge energy held constant, there is an optimum discharge frequency and the special frequency range for the radial deformation, which is about 4.0 kHz and 3.76-4.36 kHz in this thesis, respectively. Under the same discharge voltage, the radial displacement of the bulged shell increases with the decreases of the yield stress of the material of tube.(5) The numerical simulation of cylindrical shell bulging under the new magnetic pressure model formulated in this thesis was investigated. The effects of longitudinal coordinate and radial displacement considered in the equivalent magnetic pressure or not play a key role in the deformation analysis. The deformation in the middle of shell is larger than that at shell end that is close to the simulation results from the coupling field modeling. However, the deformation result mentioned above is reverse to that from the old model of magnetic pressure, which is different from the real deformation in practice.The studying results indicate that the new model of magnetic pressure can reflect the space-time characteristics of magnetic pressure acting on the cylindrical shell more accurate that form the old model. And the simulation results based on the sequential coupling simulation of the magnetic pulse bulging of cylindrical shell can present the dynamic forming more precisely.