a sample durability study of a circuit board under random vibration and design optimization

8/8/2019 A Sample Durability Study of a Circuit Board Under Random Vibration and Design Optimization

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Advanced CAEAll contents Copyright Ahmad A. Abbas , All rights reserved.

A Sample Durability Study of a Circuit Board underRandom Vibration and Design Optimization

By: MS.ME Ahmad A. Abbas

[email protected]

www.AdvancedCAE.com

Sunday, March 07, 2010
mailto:[email protected]:[email protected]://www.advancedcae.com/http://www.advancedcae.com/http://www.advancedcae.com/mailto:[email protected]


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CAE Studies By: Ahmad A. Abbas Page 2

Table of ContentsIntroduction ......................................................................................................................... 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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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 1 -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 1 -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 1 -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 itssubjected to an acceleration PSD (Power Spectral Density) profile, the aim of the study is to test thehardware 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 beenreported about the screw holes. There are many overlapping vibration waves that are applied to thiscomponent, therefore and because of the mathematical complexity of working with these overlappingvibrations statistical random vibration was used.

A random vibration was considered since the movement of this vehicle component was a randommotion with erratic manner which contained many frequencies in a particular frequency band; withmotion nature that was not repeatable.

Statistical random vibration method is a more efficient way of dealing with random vibrations todetermine 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 probabilitydistribution. 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 providesa more practical process for characterizing random vibrations than analyzing an unimaginably largeset 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 +1 and the-1 valu e 68.3 percent of the time. It will be between the +2 and the -2 values 95.4 percent of thetime. It will be between t he +3 and the -3 values 99.73 percent of the time. The Gaussian

probability distribution does not indicate the random signals frequen cy content. That is the functionof 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 wireson the base of the board. The insulator may consist of one or numerous layers of material glued into asingle entity. These additional layers may serve a number of purposes, including providing groundingto 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 thecomponent assembly, the main to materials are Copper Alloy and General Purpose PBT Plastic. InFigure 4 the material assignment of the assembly is illustrated, the Copper Alloy materials are markedwith 1 and PBT Plastic components are indicated with number 2.

Figure 4 Material assignments of the model

Copper Alloy

Density: 8800-8940 kg/m 3 Elastic Modulus: 117 GPaPoisson's Ratio: 0.34Tensile Strength: 220 MPaYield Strength: 89 MPaPercent Elongation: 50%Hardness: 45 (HB)

Table 1 Copper Alloy mechanical properties

General Purpose PBT Plastic

Density: 1300 kg/m 3

Elastic Modulus: 193 GPaPoisson's Ratio: 0.3902Tensile Strength: 56.5 MPaPercent 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 screwsmounting locations (Surfaces).

This will apply that:

= 0 (Translation along x-axis) = 0 (Translation along y-axis) = 0 (Translation along z-axis)

= 0 (Rotation about x-axis) = 0 (Rotation about y-axis) = 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 geometricalinfluence 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 aninput PSD level of describes in Table 3 and Figure 5 for a period of 20.0 hours.

Breakpoint Frequency (Hz) Magnitude ( 2 / ) 10 .01

250 .02500 .04750 .04

1000 .022000 .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 inFigure 6 , which shows a maximum 1 stress of 4.63 MPa and the full results is presented in Table 4 .

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

Standard Deviation Bending Stress Percentage of Occurrence

Standard Deviation Maximum Stress Percentage of Occurrence1 stress 4.63 MPa 68.3%2 stress 9.26 MPa 27.1%3 stress 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 usedin conjunction with the standard fatigue analysis procedure. The Three- Band Technique using MinersCumulative 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 wehave 4 screw holes near to the edge of the bored, the computed alternating stress has to account forstress concentration effects. The stress concentration factor K can be used in the stress equation or indefining the slope b of the S-N fatigue curve for alternating stresses. For this sample problem, a stressconcentration factor K = 3 will be used in the S-N fatigue curve as it was estimated from Figure 7 andFigure 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 forthe 1, 2 and 3 stresses can be obtained from the following equation:

1 = 2 (2

1)

Where:

2= 49.9 MPa (stress to fail at S1000 reference point)

2 = 1000 ( 1000 reference point)

1 = 4.63 (1 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

= [ (49.910 6 4.6610 6

10 3 10 8 )] 1 =4.856

1 1 = 1000 49.94.63

4.856

= 1.03 10 8

2 2 = 1000 49.99.26

4.856

= 3.6 10 6

3 3 = 1000 49.9

13.89

4.856

= 5.02 10 5

Node at root having maximum stress at the systems first natural frequency of about 120 Hz thus, t heactual number of fatigue cycles (n) accumulated during 20 hours of vibration testing can be obtainedfrom the percent of time exposure for the 1 , 2 and 3 values:

1 1 = 120 203600

.683 = 5.90 106

2 2 = 120 203600

.271 = 2.34 106

3 2 = 120 203600

.0433 = .376 106

0

5000000

10000000

15000000

20000000

25000000

30000000

35000000

40000000

45000000

50000000

55000000

60000000

1 10 100 1000 10000 1000001000000 100000001000000001E+09 1E+10

k=1

k=2

k=3


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Miners cumulative fatigue damage ratio is based on the idea that every stress cycleuses up part of the fatigue life of a structure, whether the stress cycle is due tosinusoidal vibration, random vibration thus the damage can be written as:

Therefore for the original model the damage will be:

5.9010 6 1.0310 8

+2.3410 6

3.610 6+

.37610 6

5.0210 5= 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 contourplot shown in Figure 12 , which shows a maximum 1 stress of 3.11 MPa and the full results ispresented in Table 5.

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


Standard Deviation Maximum Stress Percentage of Occurrence1 stress 3.11 MPa 68.3%2 stress 6.22 MPa 27.1%3 stress 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 optimizedmodel for the 1, 2 and 3 s tresses will be:

1 1 = 1000 49.93.11

4.856

= 7.19

108

2 2 = 1000 49.96.22

4.856

= 24.8 10 6

3 3 = 1000 49.99.33

4.856

= 3.47 10 6

Therefore for the first optimized model the damage will be:

5.90106

7.1910 8+

2.34106

24.810 6+

.376106

3.4710 6= 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 besuggested:

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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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 1 stress of 2.42 MPa, aslo the full results ispresented in Table 6 .

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


Standard Deviation Maximum Stress Percentage of Occurrence

1 stress 2.42 MPa 68.3%2 stress 4.84 MPa 27.1%3 stress 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 optimizedmodel for the 1, 2 and 3 stresses will be:

1 1 = 1000 49.92.42

4.856

= 24.3

108

2 2 = 1000 49.94.84

4.856

= 86.0 10 6

3 3 = 1000 49.97.26

4.856

= 11.7 10 6

Therefore for the first optimized model the damage will be:

5.90106

24.310 8+

2.34106

86.010 6+

.376106

11.7 10 6= 6.2%

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


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Conclusion

This study shows that the original design did not meet the minimum requirements to undergo suchvibration condition.145% damage was calculated in the original model, this means that the failureexceeded the possible life by 45 percent, with the expected life of the structure obtained from thefollowing calculation:

Total life = Used life + Remaining life

While fatigue life evaluation under a random process is highly complicated, Miners Rule provide s areasonably good prediction. In the case-study, the safety factor of 2 calculated from structural stressvalues 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 bechanged to provide a fatigue life of approximately 40 hours, amounting to a safety factor of 2 on thefatigue life.

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


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Advanced CAE

*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
mailto:[email protected]:[email protected]://www.advancedcae.com/http://www.advancedcae.com/http://www.advancedcae.com/mailto:[email protected]

a sample durability study of a circuit board under random vibration and design optimization

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