Fatigue of a Circuit Board Under Random Vibration

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Advanced CAE All contents © Copyright Ahmad A. Abbas , All rights reserved. A Sample Durability Study of a Circuit Board under Random Vibration and Design Optimization By: MS.ME Ahmad A. Abbas [email protected] www.AdvancedCAE.com Sunday, March 07, 2010

Transcript of Fatigue of a Circuit Board Under Random Vibration

Page 1: Fatigue of a Circuit Board Under Random Vibration

Advanced CAE

All contents © Copyright Ahmad A. Abbas , All rights reserved.

A Sample Durability Study of a Circuit Board under

Random Vibration and Design Optimization

By: MS.ME Ahmad A. Abbas

[email protected]

www.AdvancedCAE.com

Sunday, March 07, 2010

Page 2: Fatigue of a Circuit Board Under Random Vibration

CAE Studies By: Ahmad A. Abbas Page 2

Table of Contents

Introduction ......................................................................................................................... 4

Analysis Information .......................................................................................................... 5

Original Model Geometry ............................................................................................... 5

Material Properties .......................................................................................................... 6

Boundary Condition ........................................................................................................ 7

Vibration Profile ............................................................................................................. 8

Original Model Results and Analysis ................................................................................. 9

Stress Results .................................................................................................................. 9

Fatigue Analysis.............................................................................................................. 9

Optimized model 1 ............................................................................................................ 13

First optimized model Results and Analysis ..................................................................... 14

Stress Results ................................................................................................................ 14

Fatigue Analysis............................................................................................................ 15

Optimized model 2 ............................................................................................................ 16

Second optimized model Results and Analysis ................................................................ 17

Stress Results ................................................................................................................ 17

Fatigue Analysis............................................................................................................ 18

Conclusion ........................................................................................................................ 19

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CAE Studies By: Ahmad A. Abbas Page 3

Table of Illustrations

FIGURE 1 THE ORIGINAL MODEL OF THE CIRCUIT BOARD ....................................................................... 4 FIGURE 2 THE ORIGINAL MODEL OF THE CIRCUIT BOARD 3D VIEWS ...................................................... 5 FIGURE 3 SIMPLIFIED 2D DRAWING OF THE ORIGINAL MODEL ............................................................... 5 FIGURE 4 MATERIAL ASSIGNMENTS OF THE MODEL ............................................................................... 6 FIGURE 5 VIBRATION PROFILE FREQUENCY VS. MAGNITUDE .................................................................. 8 FIGURE 6 1Σ-RMS VALUES OF NODAL STRESSES OF THE ORIGINAL GEOMETRY...................................... 9 FIGURE 7 TENSION STRESS CONCENTRATION PETERSON PLOT ............................................................. 10 FIGURE 8 BENDING STRESS CONCENTRATION PETERSON PLOT ............................................................ 10 FIGURE 9 S-N CURVE FOR PBT PLASTIC WITH A STRESS CONCENTRATION OF 1, 2 AND 3 ................... 11 FIGURE 10 FIRST OPTIMIZED MODEL OF THE CIRCUIT BOARD 3D VIEWS ............................................... 13 FIGURE 11 SIMPLIFIED 2D DRAWING OF THE FIRST OPTIMIZED MODEL ................................................. 13 FIGURE 12 1Σ-RMS VALUES OF NODAL STRESSES OF THE FIRST OPTIMIZED MODEL .............................. 14 FIGURE 13 SECOND OPTIMIZED MODEL OF THE CIRCUIT BOARD 3D VIEWS ........................................... 16 FIGURE 14 SIMPLIFIED 2D DRAWING OF THE SECOND OPTIMIZED MODEL ............................................ 16 FIGURE 15 1Σ-RMS VALUES OF NODAL STRESSES OF THE SECOND OPTIMIZED MODEL ......................... 17

Index of Tables

TABLE 1 COPPER ALLOY MECHANICAL PROPERTIES ................................................................................... 6 TABLE 2 GENERAL PURPOSE PBT PLASTIC MECHANICAL PROPERTIES ....................................................... 6 TABLE 3 VIBRATION PROFILE TABLE ........................................................................................................... 8 TABLE 4 RESPONSE PSD OF STRESS DISTRIBUTION OF THE ORIGINAL PBT PLASTIC BOARD ...................... 9 TABLE 5 RESPONSE PSD OF STRESS DISTRIBUTION OF THE FIRST OPTIMIZED MODEL ............................ 14 TABLE 6 RESPONSE PSD OF STRESS DISTRIBUTION OF THE SECOND OPTIMIZED MODEL ....................... 17

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Introduction

The objective of the study is to evaluate the response of a circuit board to a harsh vibration situation,

and determine the root cause of reported failures and suggest new model with suitable capability.

The circuit board under study shown in Figure 1 is part of a ground vehicle engine control box and it’s

subjected to an acceleration PSD (Power Spectral Density) profile, the aim of the study is to test the

hardware for harsh road condition qualification.

Figure 1 The original model of the circuit board

The circuit board is subjected to an intense vibration environment and the durability failures have been

reported about the screw holes. There are many overlapping vibration waves that are applied to this

component, therefore and because of the mathematical complexity of working with these overlapping

vibrations statistical random vibration was used.

A random vibration was considered since the movement of this vehicle component was a random

motion with erratic manner which contained many frequencies in a particular frequency band; with

motion nature that was not repeatable.

Statistical random vibration method is a more efficient way of dealing with random vibrations to

determine the probability of the occurrence of particular amplitudes of stresses for fatigue analysis.

The random vibration can be characterized using a mean, the standard deviation and a probability

distribution. Individual vibration amplitudes are not determined. Rather, the amplitudes are averaged

over a large number of cycles and the cumulative effect determined for this time period. This provides

a more practical process for characterizing random vibrations than analyzing an unimaginably large

set of time–history data for many different vibration profiles.

The results of this analysis the represented by Gaussian process, which are described in terms of

standard deviation of the distribution. The instantaneous acceleration will be between the +1σ and the

-1σ value 68.3 percent of the time. It will be between the +2σ and the -2σ values 95.4 percent of the

time. It will be between the +3σ and the -3σ values 99.73 percent of the time. The Gaussian

probability distribution does not indicate the random signal’s frequency content. That is the function

of the power spectral density analysis.

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Analysis Information

Original Model Geometry

The original model shown in Figure 2 and Figure 3 is a small circuit board with the main thickness of

.01 m. This circuit board consist of an insulator, with threads of conductive material serving as wires

on the base of the board. The insulator may consist of one or numerous layers of material glued into a

single entity. These additional layers may serve a number of purposes, including providing grounding

to the board.

Figure 2 The original model of the circuit board 3D views

Figure 3 Simplified 2D drawing of the original model

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Material Properties

For simplification the circuit board was modeled using the two main isotropic materials in the

component assembly, the main to materials are Copper Alloy and General Purpose PBT Plastic. In

Figure 4 the material assignment of the assembly is illustrated, the Copper Alloy materials are marked

with 1 and PBT Plastic components are indicated with number 2.

Figure 4 Material assignments of the model

Copper Alloy

Density: 8800-8940 kg/m3

Elastic Modulus: 117 GPa

Poisson's Ratio: 0.34

Tensile Strength: 220 MPa

Yield Strength: 89 MPa

Percent Elongation: 50%

Hardness: 45 (HB)

Table 1 Copper Alloy mechanical properties

General Purpose PBT Plastic

Density: 1300 kg/m3

Elastic Modulus: 193 GPa

Poisson's Ratio: 0.3902

Tensile Strength: 56.5 MPa

Percent Elongation: 15%

Table 2 General Purpose PBT Plastic mechanical properties

1

2

1

1

2

2

2

2

1

2

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Boundary Condition

The complete assembly will be assembled in the engine control box using 4 screws, as shown below:

The boundary condition is fixed, that would mean there are zero degrees of freedom at the screws

mounting locations (Surfaces).

This will apply that:

𝑑𝑥 = 0 (Translation along x-axis) 𝑑𝑦 = 0 (Translation along y-axis) 𝑑𝑧 = 0 (Translation along z-axis) 𝑑𝑟𝑥 = 0 (Rotation about x-axis) 𝑑𝑟𝑦 = 0 (Rotation about y-axis) 𝑑𝑟𝑧 = 0 (Rotation about z-axis)

For more advance analysis spring B.C model could be used to account for a small elasticity affect of

the screws, in this case-study the fixed support will be considered for simplification.

Mounting points to vehicle –

rigidly mounted using screws

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Vibration Profile

This system has an overall damping ratio was assumed to be 5 percent. Due to the geometrical

influence the assembly will have a uniform bases excitation restricted to only the z-axis direction.

The assembly must be capable of operating in a white-noise random vibration environment with an

input PSD level of describes in Table 3 and Figure 5 for a period of 20.0 hours.

Breakpoint Frequency (Hz) Magnitude ( 𝑔2/𝐻𝑧)

10 .01

250 .02

500 .04

750 .04

1000 .02

2000 .01

Table 3 Vibration profile table

Figure 5 Vibration profile frequency vs. magnitude

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Original Model Results and Analysis

Stress Results

Now the challenge is to determine the approximate dynamic stress and the expected fatigue life of the

assembly.

Analysis of the assembly under the given vibration profile will results in a stress contour plot shown in

Figure 6, which shows a maximum 1σ stress of 4.63 MPa and the full results is presented in Table 4.

Figure 6 1σ-RMS values of nodal stresses of the original geometry

Standard Deviation Bending Stress Percentage of Occurrence

Standard Deviation Maximum Stress Percentage of Occurrence

1stress 4.63 MPa 68.3%

2stress 9.26 MPa 27.1%

3stress 13.89 MPa 4.33%

Table 4 Response PSD of stress distribution of the original PBT Plastic board

Fatigue Analysis

For fatigue life calculation in the sample problem, root mean square (RMS) stress quantities are used

in conjunction with the standard fatigue analysis procedure. The Three-Band Technique using Miner’s

Cumulative Damage Ratio will be used for this fatigue analysis.

The first step is to determine the number of stress cycles needed to produce a fatigue failure. Since we

have 4 screw holes near to the edge of the bored, the computed alternating stress has to account for

stress concentration effects. The stress concentration factor K can be used in the stress equation or in

defining the slope b of the S-N fatigue curve for alternating stresses. For this sample problem, a stress

concentration factor K = 3 will be used in the S-N fatigue curve as it was estimated from Figure 7 and

Figure 8.

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Figure 7 Tension Stress concentration Peterson Plot

Figure 8 Bending Stress concentration Peterson Plot

The approximate number of stress cycles N required to produce a fatigue failure in the component for

the 1σ, 2σ and 3σ stresses can be obtained from the following equation:

𝑁1 = 𝑁2(𝑆2

𝑆1)𝑏

Where:

𝑆2 = 49.9 MPa (stress to fail at S1000 reference point)

𝑁2 = 1000 (𝑆1000 reference point)

𝑆1 = 4.63 (1σ RMS stress)

b (Slope of fatigue line with stress concentration K = 3 as shown in figure 9 )

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Figure 9 S-N curve for PBT Plastic with a stress concentration of 1, 2 and 3

𝑏 = [𝑎𝑏𝑠(𝑙𝑜𝑔 49.9∗106 −𝑙𝑜𝑔 4.66∗106

𝑙𝑜𝑔 103 −𝑙𝑜𝑔 108 )]−1=4.856

1𝜎 𝑁1 = 1000 49.9

4.63

4.856

= 1.03 ∗ 108

2𝜎 𝑁2 = 1000 49.9

9.26

4.856

= 3.6 ∗ 106

3𝜎 𝑁3 = 1000 49.9

13.89

4.856

= 5.02 ∗ 105

Node at root having maximum stress at the system’s first natural frequency of about 120 Hz thus, the

actual number of fatigue cycles (n) accumulated during 20 hours of vibration testing can be obtained

from the percent of time exposure for the 1, 2and 3values:

1𝜎 𝑛1 = 120𝑐𝑦𝑐𝑙𝑒𝑠

𝑆𝑒𝑐 ∗ 20ℎ𝑟

3600𝑆𝑒𝑐

ℎ𝑟 ∗ .683 = 5.90∗ 106 𝑐𝑦𝑐𝑙𝑒𝑠

2𝜎 𝑛2 = 120𝑐𝑦𝑐𝑙𝑒𝑠

𝑆𝑒𝑐 ∗ 20ℎ𝑟

3600𝑆𝑒𝑐

ℎ𝑟 ∗ .271 = 2.34∗ 106 𝑐𝑦𝑐𝑙𝑒𝑠

3𝜎 𝑛2 = 120𝑐𝑦𝑐𝑙𝑒𝑠

𝑆𝑒𝑐 ∗ 20ℎ𝑟

3600𝑆𝑒𝑐

ℎ𝑟 ∗ .0433 = .376∗ 106 𝑐𝑦𝑐𝑙𝑒𝑠

0

5000000

10000000

15000000

20000000

25000000

30000000

35000000

40000000

45000000

50000000

55000000

60000000

1 10 100 1000 10000 1000001000000100000001000000001E+09 1E+10

k=1

k=2

k=3

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Miner’s cumulative fatigue damage ratio is based on the idea that every stress cycle

uses up part of the fatigue life of a structure, whether the stress cycle is due to

sinusoidal vibration, random vibration thus the damage can be written as:

Therefore for the original model the damage will be:

5.90 ∗ 106

1.03 ∗ 108+

2.34 ∗ 106

3.6 ∗ 106+

. 376 ∗ 106

5.02 ∗ 105= 145.6%

Thus it is clear why high rate of failure were occurring in the component.

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Optimized model 1

Since the damage in the original model exceeds the maximum level, optimization will be necessary,

Figure show the first optimized model:

Figure 10 First optimized model of the circuit board 3D views

Figure 11 Simplified 2D drawing of the first optimized model

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First optimized model Results and Analysis

Stress Results

Analysis of optimized the assembly under the given vibration profile will results in a stress contour

plot shown in Figure 12, which shows a maximum 1σ stress of 3.11 MPa and the full results is

presented in Table 5.

Figure 12 1σ-RMS values of nodal stresses of the first optimized model

Standard Deviation Bending Stress Percentage of Occurrence

Standard Deviation Maximum Stress Percentage of Occurrence

1stress 3.11 MPa 68.3%

2stress 6.22 MPa 27.1%

3stress 9.33 MPa 4.33%

Table 5 Response PSD of stress distribution of the first optimized model

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Fatigue Analysis

The approximate number of stress cycles N required to produce a fatigue failure in the first optimized

model for the 1σ, 2σ and 3σ stresses will be:

1𝜎 𝑁1 = 1000 49.9

3.11

4.856

= 7.19 ∗ 108

2𝜎 𝑁2 = 1000 49.9

6.22

4.856

= 24.8 ∗ 106

3𝜎 𝑁3 = 1000 49.9

9.33

4.856

= 3.47 ∗ 106

Therefore for the first optimized model the damage will be:

5.90 ∗ 106

7.19 ∗ 108+

2.34 ∗ 106

24.8 ∗ 106+

. 376 ∗ 106

3.47 ∗ 106= 21.1%

Thus the damage to the component will be much lower.

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Optimized model 2

Based on the insight obtained from the two previous simulations the following optimization will be

suggested:

Figure 13 Second optimized model of the circuit board 3D views

Figure 14 Simplified 2D drawing of the second optimized model

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CAE Studies By: Ahmad A. Abbas Page 17

Second optimized model Results and Analysis

Stress Results

Analysis of optimized the assembly under the given vibration profile will results in a stress contour

plot shown in Figure 15, which shows a maximum 1σ stress of 2.42 MPa, aslo the full results is

presented in Table 6 .

Figure 15 1σ-RMS values of nodal stresses of the second optimized model

Standard Deviation Bending Stress Percentage of Occurrence

Standard Deviation Maximum Stress Percentage of Occurrence

1stress 2.42 MPa 68.3%

2stress 4.84 MPa 27.1%

3stress 7.26 MPa 4.33%

Table 6 Response PSD of stress distribution of the second optimized model

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Fatigue Analysis

The approximate number of stress cycles N required to produce a fatigue failure in the first optimized

model for the 1σ, 2σ and 3σ stresses will be:

1𝜎 𝑁1 = 1000 49.9

2.42

4.856

= 24.3 ∗ 108

2𝜎 𝑁2 = 1000 49.9

4.84

4.856

= 86.0 ∗ 106

3𝜎 𝑁3 = 1000 49.9

7.26

4.856

= 11.7 ∗ 106

Therefore for the first optimized model the damage will be:

5.90 ∗ 106

24.3 ∗ 108+

2.34 ∗ 106

86.0 ∗ 106+

. 376 ∗ 106

11.7 ∗ 106= 6.2%

Thus the damage to the component will be much lower than both cases.

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CAE Studies By: Ahmad A. Abbas Page 19

Conclusion

This study shows that the original design did not meet the minimum requirements to undergo such

vibration condition.145% damage was calculated in the original model, this means that the failure

exceeded the possible life by 45 percent, with the expected life of the structure obtained from the

following calculation:

Total life = Used life + Remaining life

While fatigue life evaluation under a random process is highly complicated, Miner’s Rule provides a

reasonably good prediction. In the case-study, the safety factor of 2 calculated from structural stress

values is not adequate to ensure fatigue life of the component for the chosen environment.

When it comes to design for manufacturing, it would be recommended that the circuit board design be

changed to provide a fatigue life of approximately 40 hours, amounting to a safety factor of 2 on the

fatigue life.

Therefore, it is highly recommended to adopt the second optimization for engineering design change

purposes.

Page 20: Fatigue of a Circuit Board Under Random Vibration

Advanced CAE

All contents © Copyright Ahmad A. Abbas , All rights reserved.

*The geometry was taken from a standard part library and modified for this study; also all data are

assumptions for proof of concept only.

By: MS.ME Ahmad A. Abbas

[email protected]

www.AdvancedCAE.com