A Sample Durability Study of a Circuit Board under Random Vibration and Design Optimization By: MS.ME Ahmad A. Abbas Ahmad.Abbas@AdvancedCAE.com www.advancedcae.com Sunday, March 07, 2010 Advanced CAE All contents Copyright Ahmad A. Abbas, All rights reserved.
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 CAE Studies By: Ahmad A. Abbas Page 2
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 CAE Studies By: Ahmad A. Abbas Page 3
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. CAE Studies By: Ahmad A. Abbas Page 4
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 CAE Studies By: Ahmad A. Abbas Page 5
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. 1 2 2 1 1 2 2 2 Figure 4 Material assignments of the model Copper Alloy 1 Density: 8800-8940 kg/m 3 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 2 Density: 1300 kg/m 3 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 CAE Studies By: Ahmad A. Abbas Page 6
Boundary Condition The complete assembly will be assembled in the engine control box using 4 screws, as shown below: Mounting points to vehicle rigidly mounted using screws 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 dy = 0 dz = 0 (Translation along x-axis) (Translation along y-axis) (Translation along z-axis) dr x = 0 (Rotation about x-axis) dr y = 0 (Rotation about y-axis) dr z = 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. CAE Studies By: Ahmad A. Abbas Page 7
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 ( g 2 /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 CAE Studies By: Ahmad A. Abbas Page 8
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 1 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 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. CAE Studies By: Ahmad A. Abbas Page 9
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: N 1 = N 2 ( S 2 S 1 ) b Where: S 2 = 49.9 MPa (stress to fail at S1000 reference point) N 2 = 1000 (S 1000 reference point) S 1 = 4.63 (1σ RMS stress) b (Slope of fatigue line with stress concentration K = 3 as shown in figure 9 ) CAE Studies By: Ahmad A. Abbas Page 10
60000000 55000000 50000000 45000000 40000000 35000000 30000000 25000000 20000000 15000000 10000000 5000000 0 1 10 100 1000 10000 100000100000010000000 1000000001E+09 1E+10 k=1 k=2 k=3 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 10 6 log 10 3 log 10 8 )] 1 =4.856 1σ N 1 = 1000 49.9 4.63 2σ N 2 = 1000 49.9 9.26 4.856 4.856 = 1.03 10 8 = 3.6 10 6 3σ N 3 = 1000 49.9 13.89 4.856 = 5.02 10 5 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, 2 and 3 values: 1σ n 1 = 120 cycles Sec 2σ n 2 = 120 cycles Sec 3σ n 2 = 120 cycles Sec 20hr 3600Sec hr 20hr 3600Sec hr 20hr 3600Sec hr.683 = 5.90 10 6 cycles.271 = 2.34 10 6 cycles.0433 =.376 10 6 cycles CAE Studies By: Ahmad A. Abbas Page 11
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 10 6 2.34 106. 376 106 + + 1.03 108 3.6 106 5.02 10 5 = 145.6% Thus it is clear why high rate of failure were occurring in the component. CAE Studies By: Ahmad A. Abbas Page 12
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 CAE Studies By: Ahmad A. Abbas Page 13
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 1 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 CAE Studies By: Ahmad A. Abbas Page 14
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 N 1 = 1000 49.9 3.11 2σ N 2 = 1000 49.9 6.22 3σ N 3 = 1000 49.9 9.33 4.856 4.856 4.856 = 7.19 10 8 = 24.8 10 6 = 3.47 10 6 Therefore for the first optimized model the damage will be: 5.90 10 6 2.34 106. 376 106 + + 7.19 108 24.8 106 3.47 10 6 = 21.1% Thus the damage to the component will be much lower. CAE Studies By: Ahmad A. Abbas Page 15
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 CAE Studies By: Ahmad A. Abbas Page 16
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 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 CAE Studies By: Ahmad A. Abbas Page 17
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 N 1 = 1000 49.9 2.42 2σ N 2 = 1000 49.9 4.84 3σ N 3 = 1000 49.9 7.26 4.856 4.856 4.856 = 24.3 10 8 = 86.0 10 6 = 11.7 10 6 Therefore for the first optimized model the damage will be: 5.90 10 6 2.34 106. 376 106 + + 24.3 108 86.0 106 11.7 10 6 = 6.2% Thus the damage to the component will be much lower than both cases. CAE Studies By: Ahmad A. Abbas Page 18
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. CAE Studies By: Ahmad A. Abbas Page 19
*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 Ahmad.Abbas@AdvancedCAE.com www.advancedcae.com Advanced CAE All contents Copyright Ahmad A. Abbas, All rights reserved.