Free vibration analysis of printed circuit boards with different types of edge support
The high reliability and integrity of avionics required by the Avionics Integrity Program (AVIP), initiated by the Department of Defense, has led to intensive research on the design of electronic/avionic equipment. Vibration introduces excessive dynamic loading on printed circuit boards and their surface mounted components, thus, causing premature failure of the equipment. In order to develop highly reliable products, an accurate understanding of the response of a product subject to vibration is required. This study includes two parts. Part one utilizes the finite element method to determine the effect of such variables as the boundary conditions, component layout, stiffener location, point support, lead type, lead height and input force directions on the vibration-induced stresses in the printed circuit board. Part two investigates the effect of board geometry and different types of retainers used to support the printed circuit boards in avionics, on the resonant frequency and the damping of the board/retainer system.
For the first part, finite element models were generated using a software. Finite Element Analysis for Printed circuit boards (FEAP), developed by Engineering Mechanics Research Corporation. The finite element models included a plastic leaded chip carrier positioned at the geometric centers of the printed circuit boards which were supported by disparate boundary conditions. In some cases, a dual inline package and a stiffener or point support(s) were included in the finite element models. Forced random vibrations were then simulated using the finite element software. The maximum von Mises stresses within the critical leads of the chip carrier and the first three resonant frequencies of the board systems were computed. The orthogonal array L27 linear type-I relation of the robust design procedure was adopted for the experimental design.
The second part of the study was to determine the fundamental resonant frequency and damping of the printed circuit boards supported by different types of retainers. The printed circuit boards were clamped by various clamping devices on two opposite edges while the other two edges were left free of support. The main parameters of the study were the retainer type, length of clamped and free edges, and board thickness. Free vibration tests were conducted using a 3^f factorial experiment with two replications for each case. Computer simulations were also performed to compute the fundamental resonant frequencies of the corresponding cases. Displacements, measured at the geometric center of the boards, versus time were logged for the calculation of resonant frequency and damping value. The Logarithmic Decrement method was employed for the damping computation. Frictional damping at the supports of the board/retainer system was found to dominate the system damping. The measured resonant frequencies were lower than the finite element analysis results.
A statistical analysis software, SAS, was utilized to analyze both data sets of the computer simulations and the experiments. Three means, clamping board edges, positioning the stiffener close to and along the free edge or adding point support(s) at the free edge, were found to increase the resonant frequency. The maximum von Mises stresses were found at the interface between the leads and the solders. The experimental results showed that the retainers did not provide true clamped edge supports, which resulted in larger system damping and lower fundamental resonant frequency. The results are summarized in the form of general design guidelines and comparison is made among various strategies and tools available for PCB design. This study can be extended to find the effect of temperature, exciting frequency, dynamic loading and preloading of the board system on its damping and resonant frequency.