Most of today’s automotive electronic systems are composed of two major mechanical elements: an equipment chassis or enclosure, and a printed circuit board (PCB) assembly. The PCB is composed of laminated copper and FR-4 glass epoxy. These systems often operate in severe vibration environments for extended periods without failing. The vibrations transmitted throughout the PCB induce strains in the connectors, components, and most importantly, the solder joints attaching the components to it.
Damping plays a key role in dynamic response prediction. It is of great importance in dynamic design of electronic control units (ECUs), especially for response prediction and vibration control. Dynamic response of a structure is determined by dynamics characteristics of the structure and external loads. Resonance plays a key role in the dynamic response of a structural system. Two critical parameters of resonance are resonance frequency and damping ratio, which are determined by mass, stiffness, and damping characteristics of the system.
The objective of this work is to understand and predict the dynamic behavior of the system using various mechanical tests and simulations. The material properties of the PCB are obtained from standard tensile testing based on ASTM D638. The modal response of the model, including modal frequencies and mode shapes, is acquired through testing. Next, the same model is also analyzed by finite element simulations to determine the same dynamic properties. Thus, the results obtained through both approaches are compared.
With an effort to understand the force response behavior of the system, a swept sine vibration test is carried out on the same model using specified vibration level as an input excitation, and results in response amplitude curves at specified locations. This same scenario is simulated with finite element analysis (FEA) using commercial software assuming different damping ratios. These simulation results are compared with the testing results for deducing the appropriate damping ratio. As different kinds of electronic components (like transformers, capacitors, or chips) are mounted on both sides of the PCB using solder joints, adhesive, etc., various complexities are encountered while modeling them for analysis. For this reason, simple PCBs without any components are used in this work.
Finite element analysis is the most frequently used, effective, and versatile computational tool for analysis. In this study, commercially available software is used for modeling and analysis of the bare PCBs. The common analysis procedure includes geometry modeling, discretization or mesh generation using suitable elements, defining materials to different parts, applying loads, obtaining a solution, and reviewing results. The board is modeled as isotropic material, and is fixed at four corner locations. The model is composed of higher-order quadratic elements; about 8,000 elements are used. The Lanczos mode extraction method is used in this study because it is the recommended method for medium to large models.
One of the common reasons for the experimental modal analysis is to acquire the modal parameters by testing directly on the physical system, and to correlate/verify with those from FEA and validate the FE model. These modal parameters are determined via data curve-fitting algorithms from a set of frequency response functions (FRFs) obtained from measurements taken at various points throughout the structure. The FRFs are acquired by exciting the PCBs, usually by a random motion shaker or an instrumented impact hammer, and measuring the response by means of an accelerometer. Sufficient numbers of points are considered all over the structure for the efficient frequency response measurements.
The FRFs measured are analyzed to obtain the modal parameters. Operating vibrations can be divided into three main classes: swept sine vibrations, random vibrations, and mechanical shocks. Applying a sine vibration to a product can assist in finding out the potential weaknesses in its design. This is done by exposing the product to a desired range of frequencies, one frequency at a time. This frequency range is generally selected to cover the entire operating range that the product might see in actual use, but the intensity of the vibration may be increased over real-world expectations. In swept sine vibration analysis, all loads, as well as the structure's response, vary sinusoidally at the specific frequency. A typical harmonic analysis results in the response (usually displacements or accelerations) of the structure to cyclic loads over a frequency range. “Peaks” are identified from response graphs and then reviewed at those peak frequencies.
The modal parameters of the PCBs obtained through the FEA software and experimental methods show good correlation. Further, swept sine vibration analysis is carried out using finite element software on the same model using specified vibration level as an input excitation. The same scenario is replicated in vibration testing, and the results are compared for deducing the damping ratio, which is found to be 9%.
This work was done by Rahul Jagdale and Prashant Bardia of John Deere India Pvt Ltd., and Mark Schmaltz of John Deere Electronic Solutions. The full technical paper on this technology is available for purchase through SAE International at https://papers.sae.org/2013-01-2799.