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# Essais & Simulations n°122

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• Septembre
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Accompagner la croissance de l’automobile par les essais

## dossier automobile First

dossier automobile First assumption of the FDS is to simulate the component as a simple model mass-spring with one degree of freedom (1 DOF). Figure 7. simple model representative of capacitor In this case, we need to fix the damping ratio ξ (ξ=1/2Q with Q: factor of over-tension). For our case, we fixed the damping ratio ξ at 5% (or Q=10). Second assumption is to use afatigue curve with Basquin’s approximation (N.σ b =Cwith N: number of cycle to failure, σ:stress in MPa, C: constant, bisthe inverse of the slope). Figure 8. Basquin’s law representation Third assumption is to suppose an elastic behavior defined by the formula: σ =K.ε (σ: stress K: proportionality factor ε: strain) We need to estimate 3following parameters ,for the part which is submitted to adynamic work: i. the b and C coefficients of the Basquin relation: Nσ b =C ii. the K coefficient of proportionality between the stress and the deformation in the part which is submitted to adynamic work Find below abrief description of the capacitor failed during the HALTtest at 45 gRMS. Figure 9. Sketch of acapacitor The welding is arrounded in red, weight lower 6g, solder join supposed SAC305 (Tin ,3%of silver and 0.5% of Copper) i. Estimation of Basquin’s coefficient Noguchi’s paper  has described an interesting study of fatigue electronic component with asolder join SAC305. Figure 10. solder SAC305 fatigue curve Considering the Basquin relation: N.σ b =C N1 =10 4 cycles at σ1 =4MPa N2 =10 7 cycles at σ2 =2MPa It comes: b=10 Now let’s estimate Cvalue: 10 4 .(4.10 6 ) 10 = 1070 =C j. Evaluation of K Proportionality coefficient The absolute calculation of FDS (Fatigue Damage Spectrum) requires knowledge of the coefficient of proportionality between the stress and strain of the form: σ =K.ε ( σ= stress; ε= strain or deformation) The factor Kshould not be confused with stiffness k(from the relation F=k.Z with Zthe relative displacement). How to adjust the value of K? We will seek, by gradual approach, the value of Ktoobtain adamage close to 1 in the critical frequency bandwidth (reflecting the fact that the component is failed). In our case, the Kvalue was tuned in order to obtain adamage of 1inthe FDS for the band 250-400 Hz. The corresponding value of Kis 2.10 10 N.m-3 d. Absolute Fatigue Damage Spectrum Step #1 of the methodology (Figure 1). The component has been ejected during aHALT test with an gRMS acceleration of 45 g. The test during which was recorded the data considered here, representing the input of the capacitor along in plane direction has been measured during the 20 gtest. We will assume proportionality; and thus increase the measurement by 2.25 to get the value that should expect in aHALT test at 45 g. The absolute FDS has been calculated with the following parameters: b=10; K=2.10 10 N.m-3; C=10 70 Computation done with Q=10 (ratio damping ξ=5%); from 1Hzto10 kHz; 48 pts per octave. The measurement point used in the FDS computation is the closest point of measurement on the PCB to the capacitor; it is therefore considered to be the input applied to the capacitor. Essais & Simulations • SEptEmbrE 2015 • pAGE 48

dossier automobile In our case, the criteria would be: Criteria =(Env. X Prod.) b =(2x2) 10 =4 10 Figure 11.FDS of HALT 45gRMS and 20gRMS Step #2 of the methodology (Figure 1). The vehicle stress is supposed representative of 2 PSD specifications which describe: • Shipping phase: during 50 hours • Operation phase: during 8550 hours It is supposed that the product will be submitted to the cumulative damage by fatigue (Miner’s rule) of the two shipping and operating situations, and will be represented by one FDS curve (the summation of the 2previous ones) Step #3 of the methodology (Figure 1). In the case of capacitor that stands out at an RMS acceleration of 45 g, if we assume adynamic work in the range 250-400 Hz, the FDS of the 45g HALT test is 1011 times higher than the one of life profile. 5. fatigue Criteria What should be the fatigue criteria to judge adesign change? Step #4 of the methodology (Figure 1). We propose the new criteria: With: b: Basquin’s coefficient. According the figure 10, we use b=10. Prod.: coefficient for variability of the Product strength (robustness margin) Env.: coefficient for variability of the Environment (stress, uncertainty of the measurement, ….) These coefficients are in the same spirit of the stress-strength approach that is described in details in Pierrat and Delaux’s paper . In other words, we might consider that if afailure (accountable to fatigue damage accumulation) is precipitated during HALT itcould be considered as assignable (i.e. should be corrected), if the ratio of the HALT test FDS to the life profile FDS isn’t not exceeding (Env. xProd.) b =(2x2) 10 =4 10 As seen before with the figure 12, the ratio is: FDSHalt /FDSLife Profile = 1011 ≥ criteria = 410 So in our case, the Design Change of the defect having rushed the capacitor is not necessary. 6. Conclusion This paper has proposed an innovative methodology to interpret afailure occurred in HALT test as avehicle risk or not for amechatronic system. Aconcrete case has been presented to illustrate the pedagogy. The rigorous methodology follows this procedure: Step #1: calculation of the absolute FDS of the HALT repetitive shock stimuli Step #2: calculation of the absolute FDS of the life profile sequence to which is expected to be applied to the product Figure 12. ratio FDS of HALT and Life Profile As refuge values, we recommend to use Env.Coef egal to 2and Prod. Coef egal to 2. These values are used in our concrete case study. If we have a better confidence and knowledge of the Environment, the Env.Coef can be closed to 1.2 and 1.4. Idem for the Prod. Coef value, if we have abetter knowledge of the Product strength distribution, Product value can be closed to 1.2 and 1.6. Step #3: comparison of the 2above FDS, in the range of frequencies concerned bythe precipitated defect. Step #4: application of criteria to conclude onthe relevance of the failure to be corrected. The new criteria is: Essais & Simulations • SEptEmbrE 2015 • pAGE 49

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