An Analytical Approach to Ball Grid Array Components in Common
Aerospace Random Vibration Environments
by
Milan J Lucic
An Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING IN MECHANICAL ENGINEERING
Approved:
_________________________________________
Ernesto Guiterrez-Miravete, Project Adviser
Rensselaer Polytechnic Institute
Hartford, Connecticut
December 2010
(For Graduation August 2011)
i
© Copyright 2010
by
Milan J Lucic
All Rights Reserved
ii
CONTENTS
An Analytical Approach to Ball Grid Array Components in Common Aerospace
Random Vibration Environments ................................................................................. i
LIST OF TABLES ............................................................................................................. v
LIST OF FIGURES .......................................................................................................... vi
NOMENCLATURE ........................................................................................................ vii
ACKNOWLEDGMENT ................................................................................................ viii
ABSTRACT ..................................................................................................................... ix
1. INTRODUCTION ....................................................................................................... 1
1.1
Background Information ..................................................................................... 1
1.2
Lead vs. Lead Free Solder .................................................................................. 1
1.3
Random Vibration for Fixed Wing Aircraft ....................................................... 2
2. THEORY AND METHODOLOGY ........................................................................... 3
2.1
Analytical Model: PCB Normal Modes and Displacement ................................ 3
2.2
Finite Element Model: Random Vibration ......................................................... 5
2.3
FEA Model Optimization ................................................................................... 9
3. RESULTS AND DISCUSSION ................................................................................ 10
3.1
Analytical Results ............................................................................................. 10
3.2
FEA Model Optimization ................................................................................. 11
3.3
Finite Element Model ....................................................................................... 11
3.4
3.3.1
Finite Elements .................................................................................... 11
3.3.2
Material Properties ............................................................................... 11
3.3.3
Finite Element Model ........................................................................... 11
3.3.4
Natural Frequencies ............................................................................. 11
3.3.5
Random Analysis ................................................................................. 13
3.3.6
Inertial Analysis ................................................................................... 13
Miner's Damage Index Calculations ................................................................. 13
iii
3.5
Fatigue Life ....................................................................................................... 13
4. CONCLUSIONS ....................................................................................................... 14
4.1
Future Work and Model Improvement ............................................................. 14
Literature Cited ................................................................................................................ 15
iv
LIST OF TABLES
v
LIST OF FIGURES
Figure 2.1-1: PWB BGA Placement
Figure 2.1-2: PWB and Inteconnect Diagram
Figure 2-1-3: Gaussian Distribution for Stienberg 3 Band Method
Figure 2.2-1: RTCA DO-160 Vibration Levels for Fixed Wing Aircraft
Figure 2.2-2: Wedge Lock Card Guides
vi
NOMENCLATURE
vii
ACKNOWLEDGMENT
Type the text of your acknowledgment here.
viii
ABSTRACT
There are many analyses about electrical components concerning mechanical stresses in
electronics packaging for the aerospace industry. This approach is to investigate
common aerospace random vibration environments for Ball Grid Array (BGA)
components, specifically the 484-ball package. The Analysis includes looking at lead
vs. lead free solder packages, different vibration environments, and circuit card assembly
(CCA) placement. The result is not to find whether lead is better than lead free solder or
what placement is best for BGA components, but what combination of the two works
best in common vibration environments. The results will only take into account
mechanical stresses of each ball and the entire package to determine the optimized
placement
and
solder
ix
type.
1. INTRODUCTION
1.1 Background Information
The purpose of this project is to take a look at some of the major issues with electronics
packaging in the aerospace industry today. Namely, the application of Ball Grid Arrays
(BGAs) on rack style printed wiring boards (PWBs). There are many factors that affect
the BGA components on the circuit board: placement on the PWB, vibration level,
temperature levels, and solder type. In addition to all of these variables, every design is
slightly different with different resonances, and requirements. Rack card assemblies do
not have the ability to control the PWB resonances around the BGAs like other PWB
designs without significant design improvements; the goal is to keep the design simple.
The BGA that will be analyzed is the ACTEL 484 BGA. BGAs are used for
programmable logic devices as well as processors for high amounts of inputs and
outputs. These are essentially the brains of the electronics, and it is critical to make sure
they operate under all conditions. Lastly, BGA’s are unreliable in higher vibration
environments so proper understanding of how each of the above variables affects the
component is critical to having a good design the first time, and to not run development
testing under common environments that are shown in this paper.
1.2 Lead vs. Lead Free Solder
The main reason for looking at lead free solder is to transform the aerospace electronics
to green lead free solder. Each of the packages in the ACTEL 484 BGA are built as lead
free. This is because these components are not only for aerospace applications, but also
for cell phones or computers too. The aerospace field is looking to go to lead free
components for many reasons including green compliance, ROHS compliance, and to
avoid obsolescence of key parts, mostly due to the fact that aerospace products life is up
to 20 years of service. The difficulty is that high volume products whose life is around 12 years, which means high risk or a part obsolescence, drive the electronics industry. In
addition to different mechanical and thermal properties, lead free solder has concerns
with tin whisker growth, which will not be explained in this paper. The last reason that
aerospace is behind in making the change to lead free solder is due to the different
1
techniques and procedures to assemble these parts to the PWBs. Lead based solder will
not be around forever, hence the importance of studying the differences of lead vs. lead
free solders and their mechanical responses in BGAs.
1.3 Random Vibration for Fixed Wing Aircraft
Electronic controllers are not structural members of the aircraft and thus cannot be
analyzed by simple static analysis. The mechanical stress analysis is governed by the
requirements from RTCA-DO-160, which is an aerospace standard for environmental
tests. Obviously one cannot test the electronics under the actual loads of the aircraft
because it would take years to find out a result. RTCA DO-160 accelerates the vibration
environments to test each axis in 1-5 hours on average. The random analysis is used
primarily to solve frequency responses and find resonances/mode shapes of the PWBs.
Typically this analysis is matched with test data to calculate the number of cycles to
failure. The analysis is intended to be detailed and show a correlation of failure cycles to
vibration level, solder type and placement. More detail will be discussed in the theory
and methodology and chapter.
2
2. THEORY AND METHODOLOGY
2.1 Analytical Model: PCB Normal Modes and Displacement
The analysis will be done based on a 6”x9” Printed Circuit Board (PCB). Of course there
are many sizes and configurations that can be used to optimize the board design, but
boards of this size are common in the lower fuselage electronics bays of aircraft.
Placements will include the center of the board, upper right corner, lower left corner and
left center. This is shown by the figure below:
Figure 2.1-1: PWB BGA Placement
Each placement on the board will have different results based on the curvature of the
board and the board displacement at that point. This means that every single solder ball
will have a unique max stress based on the curvature and placement. This is one key
item to find in the analysis.
The first thing about doing a Finite Element Model, analytical calculations are
invaluable to determining if the solution is correct. There are some simple equations
from Steinberg’s Vibration Analysis for Electronic Equipment. The first equation is used
to solve for the first mode natural frequency of a PWB that is fixed on 3 edges and has 1
free edge (fixed means that the edge is controlled in all 6 degrees of freedom). The FEM
boundary conditions are modeled to be exactly like a circuit card in a chassis. The fixed
positions are from the connectors at one end of the PWB that connect to the
interconnect, and also the two card guides on the long edge of the PWB.
3
Interconnect
Fixed Edge (6DOF) (Card Guide)
b
Connectors
Fixed Edge (6DOF)
Free Edge
a
a
Fixed Edge (6DOF) (Card Guide)
Figure 2.1-2: PWB and Inteconnect Diagram
D
fn 

E * h3
[3]
12 * (1   2 )
 D .75
2
12 
   4  2 2  4  [3]
a
3 
a b b 
The first mode natural frequency is based upon the Young’s Modulous, thickness,

poisson’s ration, which is the plate stiffness D, the density and the length and width; a
and b respectively. The second equation is to solve for the displacement of the PWB
based off the first mode natural frequency at the center of the board. :
G

2
* P * Q* f n [3]
Z RMS 

9.81* G
[3]
fn2
The displacement is really a dynamic single amplitude response based on the first mode

natural frequency and G, or GRMS. GRMS is the response of the PWB based off the
4
transmissibility, Q, first mode natural frequency, and the power spectral density value
where the first mode is. The transmissibility is then calculated through the random
analysis. These results are then compared for accuracy based on the FEM. Although the
displacement calculated is accurate, it does not give you the worst case. Steinberg uses a
3 band method approach to determine max displacements of the PWB which is used for
the high cycle fatigue life. This is the point where maximum damage will occur in the
electrical components. Although based on this statistical approach will only occur 4.33%
of the time, it must be considered in the overall damage calculations.
Figure 2-1-3: Gaussian Distribution for Stienberg 3 Band Method
The basic idea is that when the number of cycles reaches the number of allowed or
calculated cycles, the part will ideally fail. Traditionally, this calculation is used to
ensure that this never happens for any electrical component; BGA’s do not always
follow the same “simple calculations” and have relatively short cycle lives. There is a lot
that can go wrong with a single BGA: improper installation, solder joint failures due to
thermal or structural inputs, and for each of these failures, every solder ball can be
slightly different. Controlling this environment is crucial as well as the processes
involved in assembling the BGA’s to PWB’s.
2.2 Finite Element Model: Random Vibration
The FEM will be created in PATRAN with MD enabled version 2010 and solved with
MD NASTRAN 2008. The FEM is composed of a few different types of elements to try
and decrease the model size. The PWB consists of 2-D Hex-8 shell elements, as well as
the BGA body. The Solder balls in the BGA will be modeled with 3-d Hex-20 elements
for detail and accuracy. All of the elements are tied together using a glue constraint for
5
deformable bodies through PATRAN. The Glue constraint makes it much easier to
connect multiple bodies and greatly reduce the number of user input REB2 or REB3
Multi point constraints.
The method that is used to solve the problem of ball grid arrays and common aerospace
random vibration environments is composed of multiple independent steps. The first is
to simply run a modal analysis of the PWB with no BGA attached. Having the BGA
attached to the PWB will not affect the stiffness to a degree of concern and the model
can now be much smaller. The modal analysis should line up with the calculated results;
this is the success criterion for this step. The next step involves developing a model for
random vibration cases. Again the simple PWB model used for the modal analysis is
used to keep the model size down during dynamic analysis. The result that is desired
here is to find the max displacement of the PWB and then compare this to the hand
calculations, again which should line up for each vibration case. The difference here is
that for each random vibration case, although the natural frequencies are going to be the
same as long as the boundary conditions are the same, the transmissibility will not be.
This is the term that is calculated from the room mean square (RMS) of the vibration
response of the board. From the modal analysis, it is easy to narrow down the area where
the Q will be the highest and thus the highest displacement. The hand calculations are
modified and again compared with the FEM results to validate this step. In the idea of
keeping the model as light as possible and the iterations as few as possible, it was not
possible to run the full model with the BGA on the PWB. Instead, taking the results from
the random acceleration analysis, determining the max displacement, it is just as easy to
run a static inertial analysis on the full FEM. This dramatically reduces the computation
time for the study at hand. Although this deviates slightly from the original plan of
running dynamic simulation for each case, the results are very close to one another. This
is a standard industry practice that is creative and very time forgiving.
Now that the thought process is given for how the FEM will be solved, the boundary
conditions must be analyzed. The most important boundary condition or load case is of
6
course the random vibration environments that are analyzed. The figure below from
RTCA DO-160F shows the vibration curves for fixed wing aircraft:
Figure 2.2-1: RTCA DO-160 Vibration Levels for Fixed Wing Aircraft [1]
The PWB boundary conditions are simple as described in Steinberg for the 3 fixed edge
case. This approach is chosen after a popular robust design in aerospace rack card
assemblies. This design includes the use of wedge lock card guides. Below is a picture
representation of what they are and how they work:
7
Figure 2.2-2: Wedge Lock Card Guides [3]
The wedge lock card guide essential keeps the board edge fixed (all 6 degrees of
freedom). In turn this gives the designer a much more stiffness that will have less
displacement at the board center due to higher first modes. The last edge that is fixed
comes from connectors on the daughterboard connecting to the motherboard as seen in
Figure 2.1-2. Although this connection may not always be completely fixed due to
tolerances in the rack assembly and improper mating with the interconnect board, it is
assumed that the mating conditions are fixed.
The last boundary condition for this model is the mating condition of the solder balls to
the PWB and the solder balls to the BGA package. There are several ways to do this
which include user defined Multi Point Constraints (MPCs), REB2 or REB3, Mesh
matching, or lastly the Glue constraint. The REB2 MPC is used as a rigid or bolted
connection which would be far to stiff for this application. The REB3 element would be
idea but very cumbersome, about 968 connections to match the solder balls to the PWB
and the BGa body. Mesh matching is typically a very good option, although for this
case, the mesh is very fine, .008 inches, which results in a model too large to solve for
either dynamic or static modeling with the computer hardware available. Lastly the Glue
boundary can be applied to the solid geometry to which the mesh is associated. This
boundary sets up the model with REB3 connections that are ideal for this analysis case.
These REB3 connections are created when the solution is solved in NASTRAN rather
than PATRAN. The tolerances of these connections are set within PATRAN and are
usually a percentage of the smallest shell or solid element. More detail will be discussed
in the results chapter about these boundary conditions.
8
Lastly the elements have all been chosen for a reason. The hex-8 shell elements are used
for all shell elements. The hex-8 elements allow the mesh on the PWB and the BGA
body to be much more course due to the larger number of nodes. This is necessary to
keep the model size down. For the 3-d solid solder balls, the mesh was done by taking a
section view of the solder ball and doing a surface mesh seed. This 2-d mesh seed was
then revolved to get the spherical shape of the solder ball. Hex-8 elements were used for
the 2-d mesh seed so a more course mesh could be used and the element edges that are
along the spherical edge actually resemble a sphere and map to the surface much better.
A very fine hex-4 can be used to get the same result, but is much heavier in the model. A
detailed description of the FEM will be described in the results section.
2.3 FEA Model Optimization
FEA model optimization is crucial for this problem as the model size is a few hundred
thousand elements and many more nodes. Since there are only three different bodies in
this analysis, the PWB, BGA solder balls, and the BGA body, there are a few different
mesh optimization ideas. Firstly the solder balls must be detailed and accurate, but
cannot slow down the model and have such a fine mesh that the model will not even
converge in a reasonable time. This will be done by looking at static cases of single
solder balls under static loading conditions. Displacement and stress gradients are
observed to get the most course mesh yet highly accurate results. The second option is to
refine the mesh size of the PWB and the BGA body that best connect to the BGA balls
with the very small tolerances applied to the Glue boundary condition.
9
3. RESULTS AND DISCUSSION
3.1
Analytical Results
The analytical section for the results is not intended to exactly calculate results but to
validate the FEA model. This is talked about in section chapter 2.1 under the analytical
model methodology. The first step is to calculate the first mode natural frequency of the
PWB. This is calculated using Steinberg’s equation for a thin plate with three fixed
edges. This solution is derived using the Raleigh method and shown as equation 1. Note
that the length and width are not the 9in by 6in as stated above. This is due to the wedge
lock card guides and the constraints that are made on the FEM. The length and width
match the FEM exactly.
PWB length, a = 8.85 in
PWB width, b = 5.7 in
Thickness, h = .1 in
Adjusted Weight, W = .9819 lbs
Gravity, g = 386.4 in/sec2
Poisson’s Ratio, v = .3
PWB Stiffness, D = 265.57 Lbs in
Adjusted Density, p (W/gab) = 5.0375e-5 lbs s2/in3
fn = 266.4 Hz
The next hand calculation is to calculate the maximum board displacement at the center
of the PWB. For this model, this is not the maximum displacement due to the fact that
only 3 edges are fixed. If 4 edges were fixed or simply supported, the maximum
displacement would be directly at the center. The maximum displacement will really
reside at the center of the unsupported edge. This value will be found through the
random analysis of the PWB. To calculate the displacement at the center of the board,
the GRMS must be calculated. This is something that is usually calculated with the
random analysis tool, so it may have to be modified after to validate the results. Also the
transmissibility, Q, will need to be modified after the random analysis is run, so an initial
value of 20 will be used. For each random category, there is a different value for GRMS
and Z, displacement, will be different. The calculations for each of the other cases will
10
be shown in Appendix 1. The calculation shows below is based on Curve C in RTCA
DO-160.
PSD, Power Spectral Density, P = .2 (at first resonance)
Transmissibility, Q = 20
fn= 266.4
Equation 3, GRMS= 12.94
Equation 4, ZRMS= .0018 in
The first mode natural frequency is found from doing a modal analysis on the PWB and
compared to the calculated value above. The transmissibility is recalculated using the
FEM to adjust this calculation and recalculate the single amplitude displacement
response from the random analysis tool and finally used to validate the accuracy of the
finite element model.
3.2
FEA Model Optimization
Optimization of the FEM is important to ensure accuracy yet reduce calculation time.
This is especially important in this analysis, as there are 484 balls with a very fine mesh.
3.3
Finite Element Model
3.3.1
Finite Elements
The finite element model is intended to be very detailed. The solder balls on the BGA
are the focus of the analysis. Discuss different element types quad 8, quad 4. REB2 vs
REB3 etc
3.3.2
Material Properties
3.3.3
Finite Element Model
3.3.4
Natural Frequencies
The first analysis that was done is the to calculate the first mode natural frequency. This
analysis was done without the BGA for the reason that the BGA does not have enough
mass to impact the analysis. The FEA was meshed with a Quad 8 shell element. The
PCB was modeled as 2-D and considered a thin plate. The small displacements and .1
inch thickness makes this a smart modeling decision. This could have been done with
11
quad 4 elements, but would not have made any noticeable calculation time savings. The
following figures below show the first 3 modes for the PCB. The PCB was constrained
with a 6 degree of freedom MPC that is constrained by a single node in space. This node
has the 6 DOF constraint applied.
Figure 3.3.4-1: First Mode 266.59 Hz
It is obvious to see that this first mode natural frequency nearly exactly matches the hand
calculations from chapter 3.1. Although the following modes are not directly calculated,
the following figures show what the next two mode shapes look like. The remaining
natural frequencies are calculated using MSC PATRAN and located in Appendix 2.
Figure 3.3.4-2: Second Mode 341.07 Hz
12
Figure 3.3.4-3: Third Mode 511.18 Hz
The second mode and third mode are not used for the calculations in this paper. The
intent is to use the first mode as the basis of comparison for a few reasons; the first being
that the initial natural frequency will give the largest displacements and thus the most
curvature to the board. This more than anything is the primary reason for looking at the
first mode. Board curvatures and displacements are the name of the game for electronics
packaging engineers as we try to optimize the Ball Grid Array’s. The later modes, 2 and
on, are not of concern due to their displacements. As shown in the hand calculations, the
displacements expected are to be around .002 inches at the center of the PWB. The
second mode, at a much higher frequency, will yield much less displacement and less
curvature. Of course when doing RMS, or room mean square, calculations, it does take
into account the entire spectrum of results, which for this is 10-2000 Hz. This is talked
about in the next chapter about the Random Analysis.
3.3.5
Random Analysis
3.3.6
Inertial Analysis
3.4
Miner's Damage Index Calculations
3.5
Fatigue Life
13
4. CONCLUSIONS
4.1
Future Work and Model Improvement
14
Literature Cited
[1] RTCA, Incorporated. “Environmental Conditions and Test Procedures for Airborne
Equipment.” RTCA, Incorporated., Washington, DC. SC-135, Dec. 2007.
[2] Pierce, David M., and Sheri D. Sheppard. Fatigue Life Prediction Methodology for
Lead-Free Solder Alloy Interconnects: Development and Validation. Tech.
Stanford, CA: Stanford University. Print.
[3] Steinberg, Dave S. Vibration Analysis for Electronic Equipment. New York: John
Wiley & Sons, 2000. Print.
[4] Chen, Y. S. "Combining Vibration Test with Finite Element Analysis for the
Fatigue Life Estimation of PBGA Components." (2007): 638-644. Science
Direct. Web. Aug.-Sept. 2010.
[5] Amy, Robin A. “Accuracy of Simplified Printed Circuit Board Finite Element
Models.” (2009): 1-12. Science Direct. Web. Aug-Sept. 2010.
[6] Bieler, T. R. “Lead Free Solder.” (2010): 1-12. Science Direct. Web. Aug-Sept
2010.
[7] Arulvanan, P., Zhong, Z. W. “Assembly and reliability of PBGA packages on FR-4
PCBs with SnAgCu solder.” (2006): 2462-2468. Science Direct. Web. AugSept. 2010.
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