Numerical Simulation and Parameter Analysis of Electromagnetic Riveting Process for Ti-6Al-4V Titanium Rivet

Electromagnetic riveting process (EMR) is a high-speed impact connection technology with the advantages of fast loading speed, large impact force and stable rivet deformation. In this work, the axisymmetric sequential and loose electromagnetic-structural coupling simulation models were conducted to perform the electromagnetic riveting process of a Ti-6Al-4V titanium rivet, and the parameter analysis of the riveting setup was performed based on the sequential coupled simulation results. In addition, the single-objective optimization problem of punch displacement was conducted using the Hooke–Jeeves algorithm. Based on the adaptive remeshing technology adopted in air meshes, the deformation calculated in the structural field was well transferred to the electromagnetic field in the sequential coupled model. Thus, the sequential coupling simulation results presented higher accuracy on the punch speed and rivet deformation than the loose coupling numerical model. The maximum relative difference of electromagnetic force (EMF) on driver plate and radial displacement in the rivet shaft was 34.86% and 13.43%, respectively. The parameter analysis results showed that the outer diameter and the height of the driver plate had a significant first-order effect on the response of displacement, while the platform height, transition zone height, angle, and transition zone width of the amplifier presented a strong interaction effect. Using the obtained results on the optimal structural parameters, the punch speed was effectively improved from 6.13 to 8.12 m/s with a 32.46% increase. Furthermore, the displacement of the punch increasing from 3.38 to 3.81 mm would lead to an 80.55% increase in the maximum radial displacement of the rivet shaft. This indicated that the deformation of the rivet was efficiently improved by using the optimal rivet model.

Comparative Research on the Rebound Effect in Direct Electromagnetic Forming and Indirect Electromagnetic Forming with an Elastic Medium

In the process of electromagnetic forming (EMF), the rebound effect caused by high speed collision between sheet and die will affect the fittability, which results in a bad forming quality of workpiece. In this paper, finite element models of direct EMF and indirect EMF with an elastic medium are established, the influence factors of fittability in indirect EMF are studied, the two forming processes are compared, and the mechanisms of reduced rebound effect in indirect EMF are revealed. The results show that: in indirect EMF, with the increase of the discharging voltage or thickness of rubber, the fittability increases and then decreases; when the thickness of driver plate is equal to the skin depth of the driver plate, the fittability is the best. The optimal process parameters of indirect EMF are as follows: the discharging voltage is 10 kV, the thickness of the rubber is 20 mm and the thickness of driver plate is 2 mm. The rebound effect in indirect EMF is reduced compared with direct EMF for the following reasons: the impact force caused by the collision between the sheet and die is balanced by the pressure provided by the rubber; the sheet is always under tensile stress state due to the friction force provided by rubber; the remaining kinetic energy of sheet after collision with the die is absorbed by rubber. Therefore, the rebound effect in indirect EMF is suppressed compared with direct EMF. So, the fittability of the workpiece is improved, which results in a better forming quality.

Distribution of Magnetic Flux Density and Magnetic Force in EMR

Distribution of magnetic flux density and magnetic force in electromagnetic riveting was investigated with the electromagnetic field coupling model established by the finite element method. The results show the radial magnetic flux density presents a sinusoidal exponential decaying form at a point and the maximum value of radial magnetic flux density lies in about half of the driver plate radius along the driver plate radius direction. The distribution of magnetic force is determined by that of magnetic flux density and the magnetic force is a body force, which weakens very quickly from the inside to the outside of the driver plate. In order to prevent penetration of magnetic field, the thickness of driver plate is an important parameter to increase the energy utilization ratio.

ANALYTICAL MODEL OF TEMPERATURE DISTRIBUTION OVER AN ELECTRONIC CIRCUIT BOARD

The thermal model of an electronic circuit board with installed heat dissipating components is presented as a two-dimension steady-state heat conduction problem with multiple sources distributed over a rectangular region. The corresponding energy equation includes a source term and a temperature-dependent term to account for linear heat transfer in z-direction. Boundary conditions are of first type with unique temperature along the perimeter. The integral-transform technique is applied to obtain closed-form integral solution. Assuming that all dissipated components have a rectangular contact area with the plate, multiple integrals for each dissipated sub-region are easily found. A temperature map over the board is calculated from the closed expression with a triple sum of series with respect to each coordinate and source. The error is evaluated by the estimation of the truncated terms. The solution was applied to obtain the temperature distribution over the electronic Driver Plate of the CEP block of the CIMEX Brazilian experiment for flight qualifying of the Optical Block Detector Assembling.

ANALYTICAL MODEL OF TEMPERATURE DISTRIBUTION OVER AN ELECTRONIC CIRCUIT BOARD

The thermal model of an electronic circuit board with installed heat dissipating components is presented as a two-dimension steady-state heat conduction problem with multiple sources distributed over a rectangular region. The corresponding energy equation includes a source term and a temperature-dependent term to account for linear heat transfer in z-direction. Boundary conditions are of first type with unique temperature along the perimeter. The integral-transform technique is applied to obtain closed-form integral solution. Assuming that all dissipated components have a rectangular contact area with the plate, multiple integrals for each dissipated sub-region are easily found. A temperature map over the board is calculated from the closed expression with a triple sum of series with respect to each coordinate and source. The error is evaluated by the estimation of the truncated terms. The solution was applied to obtain the temperature distribution over the electronic Driver Plate of the CEP block of the CIMEX Brazilian experiment for flight qualifying of the Optical Block Detector Assembling.