An analytical and experimental study is performed to investigate the behavior of a compliant split press-fit pin and a plated through hole (PTH) in printed circuit board. Two models for numerical analysis are considered. To utilize the energy method efficiently, a beam type structure model called semi-analytic model is suggested. For the finite element analysis, two-dimensional models were used as an approximation to the original 3 dimensional problem with a plane of symmetry. Both plane stress and plane strain analyses were made. Although experiences from practical applications of the system in electronics and communications area have been accumulated, detailed simulations of the complex phenomena with friction and plasticity have not been available in the literature. Most studies have been concentrated on the reaction between pin and PTH on the radial plane perpendicular to the axis of the PTH. The main feature of the present study is the inclusion of frictional forces and an incremental analysis with displacement input for the insertion and extraction process. The effect of plasticity is also included in the finite element analysis.
A simulation study and then parametric studies are performed and the results compared with experiments. Geometric factors such as lengths and angles of corners were taken for design study. Since friction coefficient is an important input but rarely measurable, a few friction coefficients were studied and the best matching with the experiments is taken as the coefficient for design study.
The histories of insertion and extraction forces are obtained from experimental measurements. A typical curve is monotonically increasing until the first peak appears. The first peak force of insertion is shown when the inclined part of the pin is moved into PTH completely. After that point, the force reduces for a while and increases again gradually to the second peak, which is the maximum insertion force.
At the beginning of extraction, the direction of the force applied at the left end of the pin is reversed. The amount of force decreases rapidly to the peak force of extraction caused by the mode change of the pin from compression to tension. The peak of extraction force is observed when the right end of compliant part of pin starts to slip along the wall of PTH. Then the extraction force decreases to zero gradually as the pin is separated from the PTH.
The numerical results from the models obtained follow the history of insertion and extraction forces relatively well. A friction coefficient of 0.3 matches the semi-analytic solutions well with the experiments. For the finite element analysis, a coefficient of 0.37 is obtained. The maximum insertion forces obtained are 4.61, 4.5, and 5.08 from measurement, semi-analytic approach and finite element analysis, respectively. The maximum extraction forces are about 91% of the maximum insertion forces in the experiments. From the insertion and extraction forces, the total contact pressure forces against the PTH wall can be estimated based on the friction coefficient obtained from semi-analytic approach and/or finite element analysis. In the case of the semi-analytic approach, they are 15.4 kgf and 14.0 kgf for insertion and extraction, respectively.
Although the detailed phenomena of friction and plastic deformation in the pin and the PTH can be obtained by the finite element numerical analysis and more suitable for design study, the simpler semi-analytic approach has shown its applicability for simulation and design study. It has predicted the general trend of the behavior relatively well without too much computation effort and hence can be used for initial design purpose.
