Automotive Research & Testing Center's (ARTC) proving ... · INTRODUCTION Generally, the vehicle components or electrical devices used during transportation are easily affected by

ABSTRACTThe purpose of this paper is to apply the concept of thefrequency spectrum as derived from a Single Degree ofFreedom (SDOF) system, establish the accelerated vibrationspecification, and investigate the specification undercustomer usage with reliability analysis. The main techniqueis to convert a time domain signal, which is derived from aProving Ground or customer usage, to the frequency domain.An automotive headlamp was used in our research. The inputsignal from the Proving Ground was converted into an eight-hour bench test that is equivalent to a five-year/100,000 kmfield usage through the theory of Fatigue DamageEquivalence. The fatigue parameters of the materials werethen estimated from various vibration conditions with theMIL-STD-810F standard. The benefit of this approach is thatwe could quickly obtain the material parameters of a complexstructure made of composite plastics. Our research correlatescustomer usage with the Proving Ground and compresses the100,000 km time domain history into an eight-hourlaboratory bench test specification to accelerate the effect. Inthe end, life tests of eight headlamp pieces were conducted,and the Weibull distribution was used to perform reliabilityanalysis. The results showed that the reliability is about99.25% after the eight-hour bench test (or equivalently, after100,000 km of field usage). At a 90% confidence level, thereliability becomes about 90%.

INTRODUCTIONGenerally, the vehicle components or electrical devices usedduring transportation are easily affected by temperature,humidity, vibration, and/or shock. Therefore, environmentaltesting is important for validating the components. During theproduct development phase, environmental testing methodscan be used to increase reliability. It is very important for

manufactures and users to assess and improve reliabilitythrough the use of a life test. Accelerated Life Testing (ALT)is the most widely adopted method for environmental testingto assess product reliability.

Accelerated testing is required for vehicle components toquickly assess the life of a component and to meet the marketdemand. Therefore, market usage research must be conductedto determine the correlation between the Proving Ground andmarket research usage, and the parts must be tested in anaccelerated environment. Considering this correlation, Haq etal. [1] investigated a suspension system with rainflow cyclecounting and optimization methods and took 5 tracks ofpublic roads that added up to 100 miles and extrapolatedthem to 150,000 miles of equivalent customer miles. It wasthese 150,000 miles that were reduced to 24,000 provingground miles. Gosavi and Chavan [2] discussed powertrainsystems under customer correlated and accelerated lifetesting. Lin et al. [3] investigated the correlation between theAutomotive Research & Testing Center's (ARTC) provingground in Taiwan and 5,000 km in the Taiwan market toassess a new type of scooter durability testing. In addition tolife analysis in laboratory accelerated testing, the test loadspecifications for products have begun to be developed inrecent years. In 2006, Su [4] used the Fast FourierTransform(FFT) technique to convert time domain road loaddata to frequency domain data and established an engine-mounted product vibration test specification with equivalentfatigue damage theory. In 2006, Halfpenny [5] proposed theconcept of the Shock Response Spectrum (SRS) to calculatethe Fatigue Damage Spectrum (FDS) and, furthermore,established a vibration specification to reduce the testingtime.

Traditionally, the load specifications of vehicle componentsor electrical devices are directly given by OEMs and often are

Vibration Test Specification Design and ReliabilityAnalysis

2011-01-0491Published

04/12/2011

Wei-Lun Chang, Ken-Yuan Lin, Chin-Duo Hsueh and Jung-Ming ChangAutomotive Research & Testing Center

Copyright © 2011 SAE International

doi:10.4271/2011-01-0491

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treated as confidential information. The reasonableness of thetest specifications is unknown. Therefore, developingappropriate specifications is an important issue.

In the design and development stage for automotive products,it is important to determine the test specifications to discoverdefects early and improve reliability. In this paper, theaccelerated testing methods, which include time andfrequency domain methods, the frequency response, andother parameters of the materials, are presented. Furthermore,we construct a vibration specification from the time domainto the frequency domain. In the end, a life test of eight piecesof headlamps was conducted and the Weibull distribution wasused to perform the reliability analysis.

THEORYACCELERATED LIFE TESTING (ALT)The purpose of accelerated life testing is to use higherstresses than would normally be encountered to quicklydetermine the life of products and their reliability undernormal operating conditions. There are many kinds ofaccelerated test methods, such as frequency acceleratedmethods, compressed signal methods, increased stressmethods, etc. Frequency accelerated methods apply higherthan normal frequencies to achieve accelerated effects.Compressed signal methods edit the original signals andneglect the small amplitude signals to shorten the originalsignal histories. Increased stress methods enhance theenvironmental stresses to cause the products to fail within ashort time.

The parameters that can usually be used to controlenvironmental stress are the temperature, humidity, voltage,acceleration, stress, etc. The common temperature acceleratedmodel is the Arrhenius Model, which, when combined into atemperature-humidity mode, is known as Peck's Model. Theaccelerated testing method for acceleration and stress is theInverse Power Law [6]. This paper uses the Inverse PowerLaw to conduct a life test of headlamps to verify the damagebetween the time domain and frequency domain. The InversePower Law is given as follows :

(1)

The vibration tests conducted in laboratories typically useshakers, which means that the tests are performed in thefrequency domain. For the frequency domain, the MIL-STD-810F standard offers the vibration accelerated formulagiven below :

(2)

RAINFLOW CYCLE COUNTING ANDTHE LINEAR DAMAGE RULESignals, such as stress, strain, force or acceleration, whenmeasured over a long period of time can result in anunmanageably large amount of data. Therefore, rainflowcycle counting is used in the analysis of fatigue data to reducethe spectrum of varying stress into a set of simple stressreversals. This method also allows the application of theLinear Miner's Rule to assess the fatigue life of a structuresubject to complex loading. In a rainflow cycle countingchart, the time-history axis points downward, and one canimagine the rain flow flowing along pagoda roofs, as shownin Figure 1. According to the ASTM E 1049 standard [7], therainflow cycle counting algorithm for any set of fourconsecutive turning points is defined as three steps :Step 1. Compute the three corresponding ranges. If theamplitude changes from small to large, take half cycles.Step 2. If the middle range is smaller than the two, extract acycle of that range from the signal and proceed with the newsignal.Step 3. For the remaining ranges, when no more cycles canbe extracted, give a few additional half cycles.



Figure 1. Rainflow cycle counting[7]

Fatigue breakage is an important failure mode in the vehiclefield. When vehicles are subjected to a random vibrationenvironment, fatigue damage may accumulate. If theaccumulated fatigue damage reaches the limit of the material,failure will occur. The Linear Miner's Rule is the mostcommon method used to calculate damage. A damagefraction D is defined as the fraction of the life used up by anevent or a series of events. Failure is predicted to occur whenD ≥ 1.

(3)

SHOCK RESPONSE SPECTRUM ANDVIBRATION SPECIFICATIONThe SRS is a method used to estimate the response of an itemto an input shock, with the information presented as afrequency spectrum. The principle is that the shock signalsenter into a serial Single Degree of Freedom filter system(SDOF), as shown in Figure 2. Each filter has a specificfrequency range and specific system damping values. TheSRS is composed of the maximum response values in eachfrequency. The mathematical formula is

(4)

Figure 2. Shock Response Spectrum model

Using the Laplace Transform and assuming that the initialvalues of x(t) and u(t) are equal to zero, we can obtainanother mathematical form

(5)

The Extreme Response Spectrum (ERS) is another responsespectrum, which is similar to the SRS. The differencebetween the ERS and SRS is that the ERS is applicable tostationary processes, but the SRS is used to represent onlynon-stationary processes. Therefore, the test ERS must besmaller than the lifetime SRS to ensure that we do notaccelerate the test too much and that we apply loadsreasonably. The mathematical formula for the ERS ispresented as follows [5] :

(6)



To study the fatigue damage in the frequency domain, theconcept of the Fatigue Damage Spectrum (FDS) is used todetermine the fatigue damage directly from the PSD of thestress [5]. According to linear fatigue accumulation, we cansum up all FDSs to obtain the total desired fatigue damage.Therefore, we can get a synthesized vibration PSDspecification from the FDS, as shown below [5] :

(7)

WEIBULL RELIABILITYDISTRIBUTIONThe reliability of products can be estimated by failure dataand statistical methods. This study uses the Weibulldistribution to assess the reliability of headlamps. TheWeibull distribution is one of the most commonly useddistributions in reliability engineering. It can be used tomodel a great variety of data and life characteristics. Twopopular forms of this distribution are the two- and three-parameter Weibull distributions. The three-parameter Weibulldistribution is given as follows :

(8)

where θ, β and γ are the scale, shape and location parameters,respectively, and F is the failure rate function.

When γ =0, the distribution function of the two-parameterWeibull distribution is obtained. The parameters θ and β ofthe distribution function are estimated from observations. Themethods usually employed to estimate these parameters arethe method of linear regression, the method of maximumlikelihood, and the method of moments. This study uses theaccelerated life testing method to perform life tests on eightheadlamps. According to the failure data, we calculate theWeibull reliability distribution of the headlamps undernormal stress with the Weibull++ software of ReliaSoft.

RESEARCH AND APPLICATIONThis focus of this section is to demonstrate the conversionfrom field usage data to laboratory bench test specifications,as applied in the testing of an automotive headlamp. Thereliability was then estimated from the test data. To convertfrom the field data to the lab test, the theory of FatigueDamage Equivalence between time domain and frequencydomain data was used. The overall material parameter of theheadlamp was estimated through equation (2). The overallflowchart is shown in Figure 3. To establish the conversionfrom the field usage of 100,000 km to an eight-hourlaboratory vibration test, the data from the field and the datafrom the Proving Ground (PG), such as that from the PG roadsurfaces, were acquired. The automotive test setup andmeasurement were designed to convert the time domainsignals into the eight-hour test specification. For thereliability analysis, the stress-life method was used toevaluate the life of the headlamp. The accelerated life testdata were used to estimate the life under the specificationconditions, and the Weibull distribution was used to establishthe reliability and the characteristic life parameter.



Figure 3. The vibration specification concept flowchart

IN-VEHICLE VIBRATION SIGNALMEASUREMENT AND FIELDCORRELATIONTo measure the field usage, vehicles with 1.6 to 2.0 literengines are the main targets. Three types of data werecollected based on (1) the usage distribution according to thetype of road, (2) vehicle load distributions, and (3) drivingcharacteristics. A statistical analysis of the collected data wasperformed and could be used for the base to determine thedistribution of road measurements. The ARTC has completedabout 27,765 km of measurement in our database, including11,917 km in the northern area, 12,973 km in the central area,1,307 km in the southern area, and 1,568 km in the easternarea of Taiwan.

The measured time domain signals from the actual roads andthe PG (Belgium Road) are analyzed based on the rainflowcounting method. After the comparison total cycles of the PGand the actual road, we use a scale factor which multiply thecycles of PG to closely arrive at the market usage. Figure 4shows the correlation between PG and market.

Figure 4. Correlation between the market and the PG

We used the Belgium Road in the PG to plan for a productspecification of 100,000 km. The Belgium Road at the ARTCis 1,001 m in total length and 4 m wide, with random hillsmade of granite. Driving clockwise at speeds of 40 km/hr andabove on the front section of the road generates low-to-medium input signals. The later section of the road generateshigh input signals with speeds below 40 km/hr. As the speedincreases, the cumulative damage increases accordingly. Weplanned the test schedule based on the durability test results,as shown in Table 1.

Table 1. Test schedule plan

Figure 5 shows the full vehicle under the Belgium Road testand the test setup of the accelerometers. The accelerometersare the PCB tri-axial type and the data acquisition system is aGerman imc CRONOS-PL recorder. Figure 6 shows theacceleration signals of the three axes measured at theheadlamp.



Figure 6. Acceleration signals of the road load data

DAMAGE EQUIVALENCE OF THETIME AND FREQUENCY DOMAINSThe specifications for the automotive headlamp SAE J575 [8]were used, and a 1.81 g acceleration was applied for thevibration test in the frequency domain. Later, the accelerationwas increased to 4.81 g in accelerated testing. The test resultsare shown in Table 2. With the application of equation (2),we obtained b = 7.56 as the overall material parameter of thecomposite plastics for the headlamp. The advantage of thismethod is that we could obtain the material parameterquickly, without spending time establishing the S-N curve.

Table 2. Accelerated life testing of headlamps

Figure 7. Breakage at the reflector of headlamp

To compare the similarity of the failure modes and lifecharacteristics under both the time and frequency domains,we used a hydraulic pump for the vibration test in the timedomain. The acceleration signal was obtained from the z-axison the headlamp in the vehicle condition, as shown in Figure6. The length of the signal was about 89 seconds, and theRMS was 1.09 g. We then increased the RMS to 3.5 g intesting according to the concept described in equation (1).Using equation (2) and taking b = 7.56, we estimated the lifeto be about 13.3 hours in theory. In the real test, the failureoccurred after 12.84 hours on the weld at the reflector. It isthe same failure mode obtained in the frequency domain.Figure 8 shows the test setup and the failure location.

Figure 5. Road load data measured and the test setup



Figure 8. Time domain vibration test

The test results showed that the life from the vibration testwith the signal obtained from the time domain is similar tothat of the frequency domain-based test (12.84 hour / 13.3hour). This validates the fact that automotive electrical/electronic components could be tested using the frequencydomain-based specification that is converted from the timedomain signals taken from the field usage by using theFatigue Damage Equivalence theory. The following sectiondescribes how the conversion is made.

VIBRATION TEST SPECIFICATIONDEVELOPMENTThe measured time domain data could be converted intofrequency domain specifications with the application of theresponse concept described before and the rainflow countingmethod. From the field acceleration calculation, we estimatedthat 100,000 km is about 2,500 trips of the Belgium Road.According to the linear addition of the fatigue, the damage ofone trip could be multiplied by 2,500 to obtain the totaldamage. Figure 9 shows the results.

Figure 9. Fatigue damage spectrum

Based on the Fatigue Damage Equivalence theory, anaccelerated test can be used to simulate the total life of theheadlamp. With the application of equation (7) and the earlierderived material parameter, the eight-hour laboratoryvibration test can be developed, as shown in Figure 10.

Figure 10. Vibration specification

We take the z-axis for vertical vibration test which reduced toan eight-hour laboratory test, and it is important to ensure thatthe ERS should not greater than SRS to avoid overcompression. Figure 11 shows the result of ERS and SRS,and ERS is smaller than SRS. The vibration specification onthe z-axis can be smoothed, as in Figure 12. Table 3 showsthe vibration specification in the PSD that simulates 100,000km in the field.

Figure 11. Result of ERS and SRS

Figure 12. Smoothed vibration specification



Table 3. Vibration specification values

FATIGUE DAMAGE LIFE ESTIMATIONThis section estimates the headlamp life using the stress-lifemethod. The advantage of this method is that the product lifecan be estimated directly under the time domain. Of course,the strain gauge must be attached at the crack location toestimate the life correctly.

First, the strain gauge was attached at the upper locking areathat would crack. Then vibration tests were conducted at 2.02g, 3.5 g, and 4.68 g, respectively. The material of theheadlamp is primarily polycarbonate [9], with a Young'sModulus of 2,070 MPa. The stress amplitude is (N1, S1) =(5,000, 53 MPa) and (N2, S2) = (100,000, 18 MPa). The lifecan be calculated as shown in Table 4.

Table 4. Life predicted by the stress-life method

The life test was conducted using the developed vibrationspecification. The reliability is then estimated. Thespecification was raised from 2.02 g to 3.5 g and 4.68 g forthe accelerated tests. Table 5 shows the test results for alleight headlamp pieces. The failure modes of all eight samplesare exactly the same, i.e., they crack at the upper lockingarea. Figure 13 and 14 are the Weibull plots for the reliabilityanalysis. With an acceleration of 4.68 g, the shape parameteris 3.68 with a characteristic life of 3.39 hours. At 3.5 g, theshape parameter is 1.45 with a characteristic life of 15.28hours.

Table 5. Reliability tests

Figure 13. Reliability distribution of 4.68 g

Figure 14. Reliability distribution of 3.5 g



Figure 15. Reliability of the designed vibrationspecification (2.02 g)

The life under the normal use could be estimated from that ofthe higher stress level. Based on the data in Table 5 andequation (2), a shape parameter of 1.78 and the characteristiclife of 126.55 hours were estimated under 2.02 g. TheWeibull plot is shown in Figure 15. Figure 15 shows that thereliability is 99.25% at the end of the eight-hour vibration testin the specification. At a 90% confidence level, the reliabilityis estimated at around 90%. The B10 life (that is, the time forwhich the reliability is 90%) is 36 hours. At a 90%confidence level, the B10 life is around 20 hours.

CONCLUSIONSEnvironmental tests are used to increase product reliability.However, the testing specifications are generally confidentialin each company, and the origin of those specifications istypically unknown. The focus of this research is to explainhow the dynamic load of the field usage in the time domaincan be converted into a laboratory testing specification. Inaddition, we also demonstrate how to use the accelerated life

test and Weibull theory to analyze the reliability of theproduct under the specification.

This study used an automotive headlamp as an example toillustrate how the field usage condition of 100,000 km istransformed into an eight-hour laboratory vibration testingspecification and how a reliability estimation could be made.Laboratory vibration test are typically performed in thefrequency domain. We also show the rationale oftransforming from time domain data to a frequency domainspecification. It shows that it is possible to convert a dynamicload under the time domain into a frequency domainspecification based on the Fatigue Damage Equivalencetheory.

There are many approaches to estimate material fatigue life.The most direct method is to attach strain gauge on the crackarea to measure strain signal and apply the stress-life methodto calculate the fatigue life. In this study, strains weremeasured at 2.02 g, 3.5 g, and 4.68 g and life results wereobtained using the stress-life method. This served as apreliminary evaluation of the product life and as a referenceto the relationship between the stress and life from theaccelerated testing that was performed later.

In the reliability analysis, a total of eight headlamps werelife-tested at higher-than-normal stress levels under thespecification. The life under the normal stress was thenestimated, and the associated reliability was calculated, asshown in Figure 15. The reliability after an eight-hour test isabout 99.25%, which implies a characteristic life of 126.55hours. This means that the headlamp, after an eight-hourvibration test that is equivalent to 100,000 km in the fieldusage condition, would have a 99.25% reliability. At a 90%confidence level, this reliability is about 90%. This researchshows that there is a complete process of specificationdevelopment and reliability analysis. It can be used bycompanies as a reference in developing specifications andimproving product reliability.

REFERENCES1. Haq, S., Lee, Y., Larsen, J., Frinkle, M. et al., “Reliability-based Test Track Schedule Development for a VehicleSuspension System,” SAE Technical Paper 2007-01-1653,2007, doi:10.4271/2007-01-1653.2. Gosavi, S. and Chavan, G., “Development of CustomerCorrelated and Accelerated Driveline Durability Test Cycle,”SAE Technical Paper 2009-01-0412, 2009, doi:10.4271/2009-01-0412.3. Lin, K., Hwang, J., Chang, J., Chen, C. et al., “DurabilityAssessment and Riding Comfort Evaluation of a New TypeScooter by Road Simulation Technique,” SAE TechnicalPaper 2006-01-0730, 2006, doi:10.4271/2006-01-0730.4. Su, H., “Vibration Test Specification for AutomotiveProducts Based on Measured Vehicle Load Data,” SAE



http://www.sae.org/technical/papers/2007-01-1653

http://dx.doi.org/10.4271/2007-01-1653


http://dx.doi.org/10.4271/2009-01-0412


http://dx.doi.org/10.4271/2006-01-0730

Technical Paper 2006-01-0729, 2006, doi:10.4271/2006-01-0729.

5. Halfpenny, A., Kihm, F., “Mission Profile and TestingSynthesis Based Fatigue Damage Spectrum”, 9th

International Fatigue Congress, USA, 2006.

6. Caruso, H., Dasgupta, A., “A Fundamental Overview ofAccelerated-Testing Analytic Models”, Reliability andMaintainability Symposium, 1998. Proceedings., Annual,19-22 Jan. 1998 Page(s):389 - 393.

7. ASTM E 1049-85, “Standard Practices for Cycle Countingin Fatigue Analysis”, Reapproved 2005.

8. SAE International Surface Vehicle RecommendedPractice, “Test Methods and Equipment for Lighting Devicesand Components for Use on Vehicles Less than 2032 mm inOverall Width,” SAE Standard J575, Rev. Nov. 2006.

9. Kim, G.H., Lu, H., “Accelerated fatigue life testing ofpolycarbonate at low frequency under isothermal condition”,Polymer Testing 27, September 2007.

CONTACT INFORMATIONWei-Lun ChangAutomotive Research and Testing Center (Taiwan)http://www.artc.org.twComponent Quality DepartmentFatigue & Durability [email protected]: +886-4-7811222 ext. 2332

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Automotive Research & Testing Center's (ARTC) proving ... · INTRODUCTION Generally, the vehicle components or electrical devices used during transportation are easily affected by