Determination of equivalent elastic properties of printed circuit boards

Abstract

Printed Circuit Boards (PCBs) are indispensable components in modern electronic equipment. They are widely used in various fields such as aerospace, military and defense products, industrial, medical, automotive, telecommunications, maritime, and consumer electronics. Some of these products, the PCBs have a higher volume than other parts of the products. PCBs have significantly effects on these products design and mechanical durability. PCBs are crucial components in the CubeSats and PocketQubes satellites. CubeSats have main six subsystems and these subsystem except one (that is structure) made from PCB or it is controlled from PCB. PocketQubes are made from PCB also structural system. In this application PCBs can affect other systems and be affected by the environment. PCB contains various layers, which are substrate, conductive, solder mask, and silkscreen layers. Each layer has a specific duty. Substrate ensures mechanical and thermal durability, insulation between conductive layers. Solder mask, silkscreen layers are used to help for integrating PCB assemblies. The conductive layers are the main layers of the PCBs, and their number is named PCB. The main duty is conducting electronic parts with electronic ways or surfaces. PCBs are made up of layers that are stacked with epoxy. Due to the variability in design and materials, the mechanical properties of PCBs must be thoroughly tested. However, considering budget and time constraints, this is not always feasible in engineering practice. This study proposes an equivalent model to efficiently and accurately model the mechanical properties of PCBs used in CubeSats and PocketQubes. The study is divided into two main parts: creating a data pool for elastically equivalent model values and solving an optimization problem to assign coefficients to the equivalent model. Commercial software and software developed for other projects were used. Modal frequency analyses were performed for the equivalent models and detailed natural frequency analyzes were performed using package software. For the optimization problem, the natural frequencies of geometries simulating the primary structure were determined using the differential quadrature method. The database was created with 2-layer, 4-layer, 6-layer, and 8-layer PCBs with two samples of each. Solid models of each conductive layer were extracted from Altium Designer and modeled in CATIA based on the stack-up design. Layer fill ratios were calculated based on maximum dimensions. Due to the small thickness of some conductive (starting at 0.0175 mm) and insulating layers (starting at 0.26 mm), layers were modeled as shells for finite element analysis. Detailed surface models were prepared in Ansys SpaceClaim and transferred to PATRAN for finite element analysis. Results were obtained from NASTRAN and added to the data pool for optimization and validation. To run the optimization code, the natural frequencies were calculated using the differential quadrature method. The material model was based on the Halpin-Tsai model, the normalized root mean square error between the database results and those calculated with quadrature method is minimized for optimization. A brute force approach was used to obtain the material parameters that minimize the selected objective function. The final comparison showed an average difference of around 3.47 % between the equivalent model results obtained with the differential quadrature method and detailed finite element analysis results. One PCB, with a non-rectangular geometry, was solved using finite element analysis due to the inability to use the differential quadrature method. The detailed analysis of the model, solved using a finite element analysis program, took 28,695.00 seconds on a computer with 24 cores and 64 GB of memory, while the analysis modeled with elastic equivalent material model took 1,583.00 seconds on a computer with 12 cores and 32 GB of memory. The solution time was reduced by 94.48 % compared to the detailed finite element analysis with average 2.54 % difference in results. Further validation involved comparing the results with the Voigt model, the Halpin-Tsai model is more accurate than the Voigt model, with their differences being around 3 % compared to detailed model. The primary goal of reducing analysis time was achieved with a 2.54 % mode similarity. Future work could expand creating the database through material property tests and optimizing the equivalent model with more data from more analysis and resonance survey of PCBs with varying fill volumes.