Efficient modeling of printed circuit boards structures for ... - IEEE Xplore

Efficient modeling of printed circuit boards structures for dynamic simulations

Elena Zukowski,Thomas Kimpel,Daniel Kraetschmer,Andreas Roessle Engineering Design ECUs for Transmission,Sensors and Battery,Product Optimization (AEIEDT) 72703 Reutlingen,Germany [email protected]

Abstract

Printed circuit boards (PCB) are complex geometrical and functional systems that may be exposed to a combination of external and internal loads. In order to evaluate the dynamic behaviour of PCBs in early stages of the development process, modal finite element (FE) simulations are used. Realistic results for a wide frequency range can only be achieved if all the geometrical features, such as PCB assembly, copper layer thicknesses, prepreg structures, etc. with the appropriate material properties are taken into account. To model a printed circuit board including all details such as glass fiber-epoxy compounds and copper traces is possible, but is found to be very time-consuming. A method to model PCBs was developed taking into account the corresponding functional board layout and assembly. In order to ensure an appropriate representation of the layout-dependent local material properties for FE applications without considering the geometry in full detail, a simplified approach based on general composite theory, domain-specific mixture rules and generalized laminate theory was developed. The analytically calculated material property distributions of the PCB such as local stiffness values and densities can be transferred to the meshed geometry. To verify the developed method by comparison with experimentally achieved results, operational modal analysis (OMA) for a frequency up to 25 kHz was carried out by piezo patch transducer. It can be shown that both simulated mode shapes and natural frequencies of the non-assembled board show a very good agreement with the experimental results. 1.

circuit board. Vibration loads imposed on a printed circuit board may interfere with the function of the sensor. A transfer function is influenced by the local PCB vibration response. In order to provide an optimal sensor position on PCB, an understanding of the impact of individual components and their interactions in the control unit are needed. Then, the PCB's local vibration response is to be predicted. The aim of this investigation was to describe the dynamic behaviour of unpopulated printed circuit boards in wide frequency region (up to 25 kHz). To provide more detailed information of the dynamic structural behaviour of PCB structures the most convenient and commonly used method of predicting the local vibration response is the finite element modal analysis. Using an experimental approach it will be verified how accurately FE models can predict a given PCB's response. 2.

Experiment

PCB natural modes and frequencies in a free vibration can be determined through both experimental and numerical modal analysis. The first one is represented by an experimental test carried out by using the OMA. The second one consists in a numerical modelling involving the use of Finite Element Method (FEM). The main aim is to verify the numerical model to the real sample, thus checking the dynamic behaviour of FE-model. To verify the simulation results an operational modal analysis (OMA) to 25 kHz were carried out at the Fraunhofer LBF in Darmstadt. Modal analysis was used to identify the natural frequencies and mode shapes.

Introduction

Every year are registered thousands accidents caused by vehicles around the world. The objective of the UN Decade of Action for Road Safety 20 I 1-2020 is to reduce the projected number of road fatalities worldwide (1.9 million in 2020 on past trends) by 50%. [1]. Advances in passive (airbag) and active safety systems (ABS I ESP) have made passengers safer by assisting the driver. In order to identify the dynamic critical situations of vehicle, inertial sensors are installed in airbag and ABS/ESP vehicle control units. Since electronic control units (ECU) are often exposed to various conditions and stress factors (loads) - depending on their location in the car - reliability of their sensors can also be influenced by those functional loads during the life cycle of the ECU. Therefore,in order to achieve a robust ECU design, the sensors functionality at different loads must be estimated. The mechanics of the ECU transfers a vibration from its installation place to a local sensor position on the printed-

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Figure I: 3D-scanning vibrometer setup

Figure shows the experimental setup for the measurement of the mode shapes using 3D scanning

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2015 16th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems

vibrometer. This test's setup provides the determination at higher number of measuring points for both in-plane and out-of-plane mode shapes of the circuit board. After the test runs, the piezoelectric patch transducer was selected for further studies as the most appropriate method for structural excitation to 25 kHz. For the operational modal analysis by piezo-transducer the inverse piezoelectric effect was used: patch transducer transferred voltage electrical energy into mechanical energy. The electric field strength determines the contraction of the ceramic (Figure 2). This deformation is transmitted to the circuit board through the glue. Since the reaction to a change of the electric field is extremely fast, vibrations can be generated up to the kilohertz range.

the springs used in the experiment, eight spring elements COMBIN14 with appropriate spring strength k = 0.004 were used for a model construction. The mass of the piezo patch transducer with 0.04g was modelled by mass element MASS21 (Figure 3). COMBIN 14 Spring stiffness k=O. 004

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Figure 2: Functional principle of piezoelectric patch transducer 3.

FE-model

3.1 Current practice

The FE-model must provide equivalent structural dynamic behavior. The quality of the numerical calculation depends on the geometry, material properties, and boundary conditions. These parameters should be adjusted to reality, to make an equivalent loading in simulation. The main difficulty in creating a model of a PCB is not in creating the geometrical model but in specifying the properties: stiffness moduli, poisson ratio and density. These properties not should be easy measured. In the current practice of FE simulation a PCBs is usual modeled as a homogeneous continuum according to corresponding outer LP geometry. Therefore only the outer LP contours at FE-model preparation were taken into account, the internal structure of the LP was not modeled. The material properties that are required for the modal analysis are: the E-modulus, the Poisson's ratio and the density. These data were taken from the literature for FR4 [2-4]:

In the modal analysis, the structure is dynamic excited and the modal structure behavior is calculated. As a result, the modal natural frequencies and the mode shapes can be mathematically calculated. The agreement of experimental and numerical modes was controlled by Modal Assurance Criterion (MAC). The aim is to identify geometrically unambiguously the particular mode shape. In the frequency range from 0 Hz to 25 KHz the mode pairs and their frequency deviations are determined by using the MAC values. The calculated and the measured mode shapes are combined according to the degree of agreement. Figure 4 shows the corresponding measured and calculated modal shapes.

Table 1: PCB material properties

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Poisson ratio

Ex,y = 23000 MPa

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Density P = 1963 kg 1m3

The next step after creating the PCB model was to apply the boundary conditions. For a simulation,the mechanical boundary conditions were considered realistic. To model

Figure 4: Measured and calculated modal shapes.

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The comparison between calculated and measured frequency responses is used to verify the modeling. While the experimental and the calculated mode shapes show a good agreement, some differences were detected between the calculated and the experimentally measured natural frequencies (Figure 5). This indicates inaccuracies in the FE model.

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This is caused by details of the circuit board, which were not considered in the simulation. The contradiction between the reality and the assumption about the material model leads to an uncertainty in the approach of the material properties. As a result the dynamic behavior of the circuit board is described not correctly. In fact, the circuit boards are complex geometrical and functional systems that may be exposed to a combination of external and internal loads. The board consists of conductive copper layers and insulating prepreg layers (Figure 6). anisotropic and non-uniformly distributed properties that are not sufficiently involved in modeling.

The correct numerical description of inhomogeneous materials and material systems is a challenge in the FE simulation due to their direction-dependent material behavior. The numerical description of complex geometry circuit boards for the mechanical design is complicated due to specific interconnect structures, design elements and insulating prepreg. To overcome this problem techniques have been developed, which allows a simplistic description of the micro structure (homogenization algorithms). The material values required for structural-mechanical description, which are often difficult to determine experimentally, can be layout specifically determined taking into account the circuit board assembly by means of such approach. The technical literature describes various analytical methods using which the elastic behavior of a composite material such as printed circuit boards can be calculated [5-13]. In such approaches a structure of the composite block can be described by effective material properties, based on detailed geometry of the individual phases or structures. In this paper a method of PCB modeling has been developed, which takes into account the corresponding functional circuit board layout and PCB design simplified (Figure 7). The effective material model for printed circuit boards has been developed on the basis of homogenization,involving two stages. The printed-circuit board notionally breaks into elementary cells. In the first stage,the properties of the resin-fiber composite (prepreg) and the structured copper layer (resin-copper composite) are being calculated,locally for each cell.

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The effective material model for printed circuit boards has been developed on the basis of homogenization,involving two stages. The printed-circuit board notionally breaks into elementary cells. In the first stage, the properties of the resin-fiber composite (prepreg) and the structured copper layer (resin-copper composite) are being calculated, locally for each cell. The method for the determination of effective material properties of prepreg and resin-copper composite is based on linear mixing rules. Effective properties are calculated as an average from the respective properties of the individual phases according to their volume fractions. In the second stage, the layer-specific formulation of the printed circuit board, consisting of insulating and layout-specific copper layers, is converted in a homogeneous block in the thickness direction.

distribution over the LP could be found by the homogenization approach. It enables to reproduce all experiment frequency responses by the simulation in good agreement. Figure 9 shows examples of the distribution of the modulus in the X direction (in-plane) for investigated board. From these images, it can be seen that the material's properties vary not only over the LP surface depending on the Cu content according to the layout, but also each board their individual material map and as a result has its own effective material parameters. It is noteworthy that PCBs have still different effective material's properties with the same number of layers and Cu thickness. This study confirmed the applicability of this approach for quite mechanically-dynamic problems. PCB#3 (6-layer) PCB#5 (4-layer)

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The proposed method provides a substantial improvement in the agreement between experimental and calculated data (Figure 8). A correct stiffness and density

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4.

Conclusions

The simulated mode shapes and natural frequencies for the unpopulated board show that the calculated natural frequencies and mode shapes have a very good agreement with experimental results and confirmed the applicability of the PCB material's properties determination method for dynamical FE models. The accuracy of the FE model with a respectively calculated PCB layout material property allows to implement a further numerical analysis without experimental validation. An extension of the procedure on populated PCBs allows developers to predict early stages of development in addition to functional and mechanical requirements for printed circuit board assemblies. The use of the homogenization method is always useful when a more accurate forecast continuum mechanics is needed by considering details of a composite material, such as for PCB structures at dynamic analysis Acknowledgments

The authors gratefully acknowledge the valuable assistance of Fraunhofer LBF, Darmstadt. In particular, we thank Mr. O. Heuss for his co-operation and experimental contributions.

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Road SafetyAnnual Report 2014

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