تجزیه و تحلیل حساسیت از مدل های المان محدود صفحه مدار چاپی ساده

Many items of electronic equipment are subjected to harsh vibrations during their lifetime, these vibrations can damage electronic components and potentially risk total device failure. One approach to assess this risk is to compare the predicted vibration response of the Printed Circuit Board against a vibration level that is experimentally determined to produce component failure. Theoretically the vibration response can be determined using a simplified model of the PCB, where the components are modelled using a “smeared” approach; however, the error due to using such a simplified approach has not yet been defined. This paper shows a process to calculate the errors produced by such simplification techniques and derives factors of safety that can be used for all future vibration response models, using these factors ensures that future predictions do not underestimate the real response. Additionally, the errors depends on several other values besides the simplification technique, namely the Printed Circuit Board properties and the component: type, location and density. To account for these factors the process will use a sensitivity analysis approach to consider many possible design cases, this approach involves the creation of a large number of randomly created cases, all with different input values and giving different factors of safety. In this way the statistics of the factor of safety can be built up, giving much greater confidence in the results and insight into the drivers of the modelling error.

Shock and vibration loads imposed on a Printed Circuit Board (PCB) cause stresses on the PCB substrate, component packages, component leads and solder joints. These stresses are due to a combination of the bending moments in the PCB and the inertia forces due to component mass and acceleration [1]. In a worst case scenario these stresses may cause one of the following failure modes: PCB delamination, solder joint fracture, lead fracture or component package fracture, if any single one of these modes occurred total failure would very likely ensue. The probability that one of these failures occurs within a given time depends on the package type, PCB properties, and frequency and amplitude of both bending moments and inertial forces. It is possible to predict the probability of mechanical failure by a two-stage Physics of Failure (PoF) approach [2], [3] and [4]. The first stage of this process, defined here as the response prediction stage, calculates the vibration response of the board through a finite element (FE) model of the PCB/component system, incorporating various assumptions to simplify the modelling process. The second stage relates this calculated response to some pre-determined component failure criteria, to show whether the attached components 1 can withstand this curvature or acceleration. The work presented here is a contribution to the initial response prediction stage of the PoF process and does not consider in detail the failure criteria stage. A major difficulty with response prediction is that the PCB’s vibration response is altered when a component is attached to it, as the components effectively increase the mass and stiffness of the PCB, this is particularly true when heavy or large components are present as these increase the effective mass and stiffness of the PCB the most. The problem can be solved, in theory at least, by building a detailed finite element model of the PCB and components (where each component is modelled in detail as in Fig. 1); however, this approach is rarely used as it requires a long time to build and solve the model. Instead, the standard practice is to create simplified models where the components geometry is not modelled at all. Instead of detailed component models, the component effects are included by increasing the Young’s modulus and density of the PCB FE model so it effectively behaves as if components were present. The relative simplicity and speed of these simplified methods has led them to be more favourable than detailed methods. Full-size image (19 K) Fig. 1. Example of a detailed FE model of an individual component, a detailed model of a PCB would incorporate several of these and other components over its surface. Figure options This work will build on previous work [5] and [6] by showing a process to calculate the additional error that is realised when using any one of the several possible simplification techniques. Using a Monte Carlo style sensitivity analysis approach, the calculation will be performed for a variety of different hypothetical configurations to ensure that the results are valid over a greater range of cases than previously possible. This method has already been presented in a previous paper [7], except that the previous work focuses upon the preliminary exploratory stages of choosing the input variables, whilst the current work focuses more upon the creation of safety factors; additionally, the current paper is based upon a more relevant set of input variables than the original, is more practical in nature, and better describes the process used to create the variables. The results of the analysis will be used to create factors of safety; these factors can then be used on subsequent simplified models of any equipment, as long as the equipment falls within the bounds of the different hypothetical configurations that were tested.

A process has been illustrated that calculates factors of safety for FE models of electronic equipment, these factors of safety are useful when local properties smearing is not possible. The factors of safety are calculated using a Monte Carlo style sensitivity analysis approach to ensure that many possible configurations are considered. The resulting factors of safety can be used on a wide range of equipment (as defined in the limits of applicability) and can be decomposed into different variables (in this case thickness, simplification type and equipment type) to increase relevancy. The factors of safety can be used to ensure that any response calculated using a simplified PCB FE model is conservative. The process that is described here is an improvement on the current state of the art for the following reasons. Firstly, the very large number of configurations that can be tested ensure that the results are accurate in many different cases. Secondarily, as the error is calculated for the variable that is directly linked to component failure (curvature), the factors of safety that are calculated can be applied directly to the results of subsequent real-life analyses. Furthermore, the error in the curvature variable is measured for a very large number of nodes, further increasing the confidence in the results. In addition to the process described here some additional observations have been made during the analysis, notably the importance of accurately modelling the mass and boundary conditions if accurate results are required.