Vibration Test Specification Design and Reliability Analysis

Vibration Test Specification Design and Reliability 2011-01-0491 Published Analysis 04/12/2011

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

manufactures and users to assess and improve reliability ABSTRACT through the use of a life test. Accelerated Life Testing (ALT) The purpose of this paper is to apply the concept of the is the most widely adopted method for environmental testing frequency spectrum as derived from a Single Degree of to assess product reliability. Freedom (SDOF) system, establish the accelerated vibration specification, and investigate the specification under Accelerated testing is required for vehicle components to customer usage with reliability analysis. The main technique quickly assess the life of a component and to meet the market is to convert a time domain signal, which is derived from a demand. Therefore, market usage research must be conducted Proving Ground or customer usage, to the frequency domain. to determine the correlation between the Proving Ground and An automotive headlamp was used in our research. The input market research usage, and the parts must be tested in an signal from the Proving Ground was converted into an eight- accelerated environment. Considering this correlation, Haq et hour bench test that is equivalent to a five-year/100,000 km al. [1] investigated a suspension system with rainflow cycle field usage through the theory of Fatigue Damage counting and optimization methods and took 5 tracks of Equivalence. The fatigue parameters of the materials were public roads that added up to 100 miles and extrapolated then estimated from various vibration conditions with the them to 150,000 miles of equivalent customer miles. It was MIL-STD-810F standard. The benefit of this approach is that these 150,000 miles that were reduced to 24,000 proving we could quickly obtain the material parameters of a complex ground miles. Gosavi and Chavan [2] discussed powertrain structure made of composite plastics. Our research correlates systems under customer correlated and accelerated life customer usage with the Proving Ground and compresses the testing. Lin et al. [3] investigated the correlation between the 100,000 km time domain history into an eight-hour Automotive Research & Testing Center's (ARTC) proving laboratory bench test specification to accelerate the effect. In ground in Taiwan and 5,000 km in the Taiwan market to the end, life tests of eight headlamp pieces were conducted, assess a new type of scooter durability testing. In addition to and the Weibull distribution was used to perform reliability life analysis in laboratory accelerated testing, the test load analysis. The results showed that the reliability is about specifications for products have begun to be developed in 99.25% after the eight-hour bench test (or equivalently, after recent years. In 2006, Su [4] used the Fast Fourier 100,000 km of field usage). At a 90% confidence level, the Transform(FFT) technique to convert time domain road load reliability becomes about 90%. data to frequency domain data and established an engine- mounted product vibration test specification with equivalent INTRODUCTION fatigue damage theory. In 2006, Halfpenny [5] proposed the concept of the Shock Response Spectrum (SRS) to calculate Generally, the vehicle components or electrical devices used the Fatigue Damage Spectrum (FDS) and, furthermore, during transportation are easily affected by temperature, established a vibration specification to reduce the testing humidity, vibration, and/or shock. Therefore, environmental time. testing is important for validating the components. During the product development phase, environmental testing methods Traditionally, the load specifications of vehicle components can be used to increase reliability. It is very important for or electrical devices are directly given by OEMs and often are Gratis copy for Wei-Lun Chang Copyright 2011 SAE International E-mailing, copying and internet posting are prohibited Downloaded Thursday, March 24, 2011 06:34:15 AM

treated as confidential information. The reasonableness of the test specifications is unknown. Therefore, developing appropriate specifications is an important issue.

In the design and development stage for automotive products, it is important to determine the test specifications to discover defects early and improve reliability. In this paper, the accelerated testing methods, which include time and frequency domain methods, the frequency response, and other parameters of the materials, are presented. Furthermore, we construct a vibration specification from the time domain to the frequency domain. In the end, a life test of eight pieces of headlamps was conducted and the Weibull distribution was used to perform the reliability analysis. The vibration tests conducted in laboratories typically use shakers, which means that the tests are performed in the THEORY frequency domain. For the frequency domain, the MIL- STD-810F standard offers the vibration accelerated formula ACCELERATED LIFE TESTING (ALT) given below : The purpose of accelerated life testing is to use higher stresses than would normally be encountered to quickly determine the life of products and their reliability under normal operating conditions. There are many kinds of accelerated test methods, such as frequency accelerated (2) methods, compressed signal methods, increased stress methods, etc. Frequency accelerated methods apply higher than normal frequencies to achieve accelerated effects. Compressed signal methods edit the original signals and neglect the small amplitude signals to shorten the original signal histories. Increased stress methods enhance the environmental stresses to cause the products to fail within a short time.

The parameters that can usually be used to control RAINFLOW CYCLE COUNTING AND environmental stress are the temperature, humidity, voltage, acceleration, stress, etc. The common temperature accelerated THE LINEAR DAMAGE RULE model is the Arrhenius Model, which, when combined into a Signals, such as stress, strain, force or acceleration, when temperature-humidity mode, is known as Peck's Model. The measured over a long period of time can result in an accelerated testing method for acceleration and stress is the unmanageably large amount of data. Therefore, rainflow Inverse Power Law [6]. This paper uses the Inverse Power cycle counting is used in the analysis of fatigue data to reduce Law to conduct a life test of headlamps to verify the damage the spectrum of varying stress into a set of simple stress between the time domain and frequency domain. The Inverse reversals. This method also allows the application of the Power Law is given as follows : Linear Miner's Rule to assess the fatigue life of a structure subject to complex loading. In a rainflow cycle counting chart, the time-history axis points downward, and one can imagine the rain flow flowing along pagoda roofs, as shown in Figure 1. According to the ASTM E 1049 standard [7], the (1) rainflow cycle counting algorithm for any set of four consecutive turning points is defined as three steps : Step 1. Compute the three corresponding ranges. If the amplitude changes from small to large, take half cycles. Step 2. If the middle range is smaller than the two, extract a cycle of that range from the signal and proceed with the new signal. Step 3. For the remaining ranges, when no more cycles can be extracted, give a few additional half cycles. Gratis copy for Wei-Lun Chang Copyright 2011 SAE International E-mailing, copying and internet posting are prohibited Downloaded Thursday, March 24, 2011 06:34:15 AM

(4)

Figure 1. Rainflow cycle counting[7]

Fatigue breakage is an important failure mode in the vehicle field. When vehicles are subjected to a random vibration environment, fatigue damage may accumulate. If the accumulated fatigue damage reaches the limit of the material, failure will occur. The Linear Miner's Rule is the most common method used to calculate damage. A damage fraction D is defined as the fraction of the life used up by an event or a series of events. Failure is predicted to occur when D ≥ 1. Figure 2. Shock Response Spectrum model

Using the Laplace Transform and assuming that the initial values of x(t) and u(t) are equal to zero, we can obtain (3) another mathematical form

(5)

The Extreme Response Spectrum (ERS) is another response SHOCK RESPONSE SPECTRUM AND spectrum, which is similar to the SRS. The difference VIBRATION SPECIFICATION between the ERS and SRS is that the ERS is applicable to The SRS is a method used to estimate the response of an item stationary processes, but the SRS is used to represent only to an input shock, with the information presented as a non-stationary processes. Therefore, the test ERS must be frequency spectrum. The principle is that the shock signals smaller than the lifetime SRS to ensure that we do not enter into a serial Single Degree of Freedom filter system accelerate the test too much and that we apply loads (SDOF), as shown in Figure 2. Each filter has a specific reasonably. The mathematical formula for the ERS is frequency range and specific system damping values. The presented as follows [5] : SRS is composed of the maximum response values in each frequency. The mathematical formula is (6) Gratis copy for Wei-Lun Chang Copyright 2011 SAE International E-mailing, copying and internet posting are prohibited Downloaded Thursday, March 24, 2011 06:34:15 AM

(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-parameter Weibull distribution is obtained. The parameters θ and β of the distribution function are estimated from observations. The methods usually employed to estimate these parameters are the method of linear regression, the method of maximum To study the fatigue damage in the frequency domain, the likelihood, and the method of moments. This study uses the concept of the Fatigue Damage Spectrum (FDS) is used to accelerated life testing method to perform life tests on eight determine the fatigue damage directly from the PSD of the headlamps. According to the failure data, we calculate the stress [5]. According to linear fatigue accumulation, we can Weibull reliability distribution of the headlamps under sum up all FDSs to obtain the total desired fatigue damage. normal stress with the Weibull++ software of ReliaSoft. Therefore, we can get a synthesized vibration PSD specification from the FDS, as shown below [5] : RESEARCH AND APPLICATION This focus of this section is to demonstrate the conversion from field usage data to laboratory bench test specifications, as applied in the testing of an automotive headlamp. The reliability was then estimated from the test data. To convert (7) from the field data to the lab test, the theory of Fatigue Damage Equivalence between time domain and frequency domain data was used. The overall material parameter of the headlamp was estimated through equation (2). The overall flowchart is shown in Figure 3. To establish the conversion from the field usage of 100,000 km to an eight-hour laboratory vibration test, the data from the field and the data from the Proving Ground (PG), such as that from the PG road surfaces, were acquired. The automotive test setup and measurement were designed to convert the time domain signals into the eight-hour test specification. For the reliability analysis, the stress-life method was used to evaluate the life of the headlamp. The accelerated life test data were used to estimate the life under the specification conditions, and the Weibull distribution was used to establish the reliability and the characteristic life parameter.

WEIBULL RELIABILITY DISTRIBUTION The reliability of products can be estimated by failure data and statistical methods. This study uses the Weibull distribution to assess the reliability of headlamps. The Weibull distribution is one of the most commonly used distributions in reliability engineering. It can be used to model a great variety of data and life characteristics. Two popular forms of this distribution are the two- and three- parameter Weibull distributions. The three-parameter Weibull distribution is given as follows : Gratis copy for Wei-Lun Chang Copyright 2011 SAE International E-mailing, copying and internet posting are prohibited Downloaded Thursday, March 24, 2011 06:34:15 AM

Figure 4. Correlation between the market and the PG

We used the Belgium Road in the PG to plan for a product specification of 100,000 km. The Belgium Road at the ARTC is 1,001 m in total length and 4 m wide, with random hills made of granite. Driving clockwise at speeds of 40 km/hr and above on the front section of the road generates low-to- medium input signals. The later section of the road generates high input signals with speeds below 40 km/hr. As the speed increases, the cumulative damage increases accordingly. We planned the test schedule based on the durability test results, as shown in Table 1.

Table 1. Test schedule plan

Figure 3. The vibration specification concept flowchart

IN-VEHICLE VIBRATION SIGNAL MEASUREMENT AND FIELD CORRELATION To measure the field usage, vehicles with 1.6 to 2.0 liter engines are the main targets. Three types of data were collected based on (1) the usage distribution according to the type of road, (2) vehicle load distributions, and (3) driving Figure 5 shows the full vehicle under the Belgium Road test characteristics. A statistical analysis of the collected data was and the test setup of the accelerometers. The accelerometers performed and could be used for the base to determine the are the PCB tri-axial type and the data acquisition system is a distribution of road measurements. The ARTC has completed German imc CRONOS-PL recorder. Figure 6 shows the about 27,765 km of measurement in our database, including acceleration signals of the three axes measured at the 11,917 km in the northern area, 12,973 km in the central area, headlamp. 1,307 km in the southern area, and 1,568 km in the eastern area of Taiwan.

The measured time domain signals from the actual roads and the PG (Belgium Road) are analyzed based on the rainflow counting method. After the comparison total cycles of the PG and the actual road, we use a scale factor which multiply the cycles of PG to closely arrive at the market usage. Figure 4 shows the correlation between PG and market. Gratis copy for Wei-Lun Chang Copyright 2011 SAE International E-mailing, copying and internet posting are prohibited Downloaded Thursday, March 24, 2011 06:34:15 AM

Figure 5. Road load data measured and the test setup

Table 2. Accelerated life testing of headlamps

Figure 6. Acceleration signals of the road load data

DAMAGE EQUIVALENCE OF THE Figure 7. Breakage at the reflector of headlamp TIME AND FREQUENCY DOMAINS The specifications for the automotive headlamp SAE J575 [8] To compare the similarity of the failure modes and life were used, and a 1.81 g acceleration was applied for the characteristics under both the time and frequency domains, vibration test in the frequency domain. Later, the acceleration we used a hydraulic pump for the vibration test in the time was increased to 4.81 g in accelerated testing. The test results domain. The acceleration signal was obtained from the z-axis are shown in Table 2. With the application of equation (2), on the headlamp in the vehicle condition, as shown in Figure we obtained b = 7.56 as the overall material parameter of the 6. The length of the signal was about 89 seconds, and the composite plastics for the headlamp. The advantage of this RMS was 1.09 g. We then increased the RMS to 3.5 g in method is that we could obtain the material parameter testing according to the concept described in equation (1). quickly, without spending time establishing the S-N curve. Using equation (2) and taking b = 7.56, we estimated the life to be about 13.3 hours in theory. In the real test, the failure occurred after 12.84 hours on the weld at the reflector. It is the same failure mode obtained in the frequency domain. Figure 8 shows the test setup and the failure location. Gratis copy for Wei-Lun Chang Copyright 2011 SAE International E-mailing, copying and internet posting are prohibited Downloaded Thursday, March 24, 2011 06:34:15 AM

Figure 8. Time domain vibration test

The test results showed that the life from the vibration test with the signal obtained from the time domain is similar to Figure 10. Vibration specification that of the frequency domain-based test (12.84 hour / 13.3 hour). This validates the fact that automotive electrical/ electronic components could be tested using the frequency We take the z-axis for vertical vibration test which reduced to domain-based specification that is converted from the time an eight-hour laboratory test, and it is important to ensure that domain signals taken from the field usage by using the the ERS should not greater than SRS to avoid over Fatigue Damage Equivalence theory. The following section compression. Figure 11 shows the result of ERS and SRS, describes how the conversion is made. and ERS is smaller than SRS. The vibration specification on the z-axis can be smoothed, as in Figure 12. Table 3 shows VIBRATION TEST SPECIFICATION the vibration specification in the PSD that simulates 100,000 km in the field. DEVELOPMENT The measured time domain data could be converted into frequency domain specifications with the application of the response concept described before and the rainflow counting method. From the field acceleration calculation, we estimated that 100,000 km is about 2,500 trips of the Belgium Road. According to the linear addition of the fatigue, the damage of one trip could be multiplied by 2,500 to obtain the total damage. Figure 9 shows the results.

Figure 11. Result of ERS and SRS

Figure 9. Fatigue damage spectrum

Based on the Fatigue Damage Equivalence theory, an accelerated test can be used to simulate the total life of the headlamp. With the application of equation (7) and the earlier derived material parameter, the eight-hour laboratory vibration test can be developed, as shown in Figure 10. Figure 12. Smoothed vibration specification Gratis copy for Wei-Lun Chang Copyright 2011 SAE International E-mailing, copying and internet posting are prohibited Downloaded Thursday, March 24, 2011 06:34:15 AM

Table 3. Vibration specification values Table 5. Reliability tests

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

First, the strain gauge was attached at the upper locking area that would crack. Then vibration tests were conducted at 2.02 Figure 13. Reliability distribution of 4.68 g g, 3.5 g, and 4.68 g, respectively. The material of the headlamp is primarily polycarbonate [9], with a Young's Modulus of 2,070 MPa. The stress amplitude is (N1, S1) = (5,000, 53 MPa) and (N2, S2) = (100,000, 18 MPa). The life can be calculated as shown in Table 4.

Table 4. Life predicted by the stress-life method

The life test was conducted using the developed vibration specification. The reliability is then estimated. The specification was raised from 2.02 g to 3.5 g and 4.68 g for the accelerated tests. Table 5 shows the test results for all Figure 14. Reliability distribution of 3.5 g eight headlamp pieces. The failure modes of all eight samples are exactly the same, i.e., they crack at the upper locking area. Figure 13 and 14 are the Weibull plots for the reliability analysis. With an acceleration of 4.68 g, the shape parameter is 3.68 with a characteristic life of 3.39 hours. At 3.5 g, the shape parameter is 1.45 with a characteristic life of 15.28 hours. Gratis copy for Wei-Lun Chang Copyright 2011 SAE International E-mailing, copying and internet posting are prohibited Downloaded Thursday, March 24, 2011 06:34:15 AM

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

This study used an automotive headlamp as an example to illustrate how the field usage condition of 100,000 km is transformed into an eight-hour laboratory vibration testing specification and how a reliability estimation could be made. Laboratory vibration test are typically performed in the frequency domain. We also show the rationale of transforming from time domain data to a frequency domain specification. It shows that it is possible to convert a dynamic load under the time domain into a frequency domain specification based on the Fatigue Damage Equivalence theory.

There are many approaches to estimate material fatigue life. The most direct method is to attach strain gauge on the crack area to measure strain signal and apply the stress-life method to calculate the fatigue life. In this study, strains were measured at 2.02 g, 3.5 g, and 4.68 g and life results were obtained using the stress-life method. This served as a preliminary evaluation of the product life and as a reference to the relationship between the stress and life from the accelerated testing that was performed later.

In the reliability analysis, a total of eight headlamps were life-tested at higher-than-normal stress levels under the specification. The life under the normal stress was then estimated, and the associated reliability was calculated, as shown in Figure 15. The reliability after an eight-hour test is about 99.25%, which implies a characteristic life of 126.55 hours. This means that the headlamp, after an eight-hour Figure 15. Reliability of the designed vibration vibration test that is equivalent to 100,000 km in the field specification (2.02 g) usage condition, would have a 99.25% reliability. At a 90% confidence level, this reliability is about 90%. This research shows that there is a complete process of specification The life under the normal use could be estimated from that of development and reliability analysis. It can be used by the higher stress level. Based on the data in Table 5 and companies as a reference in developing specifications and equation (2), a shape parameter of 1.78 and the characteristic improving product reliability. life of 126.55 hours were estimated under 2.02 g. The Weibull plot is shown in Figure 15. Figure 15 shows that the REFERENCES reliability is 99.25% at the end of the eight-hour vibration test in the specification. At a 90% confidence level, the reliability 1. Haq, S., Lee, Y., Larsen, J., Frinkle, M. et al., “Reliability- is estimated at around 90%. The B10 life (that is, the time for based Test Track Schedule Development for a Vehicle which the reliability is 90%) is 36 hours. At a 90% Suspension System,” SAE Technical Paper 2007-01-1653, confidence level, the B10 life is around 20 hours. 2007, doi:10.4271/2007-01-1653. 2. Gosavi, S. and Chavan, G., “Development of Customer CONCLUSIONS Correlated and Accelerated Driveline Durability Test Cycle,” SAE Technical Paper 2009-01-0412, 2009, doi: Environmental tests are used to increase product reliability. 10.4271/2009-01-0412. However, the testing specifications are generally confidential 3. Lin, K., Hwang, J., Chang, J., Chen, C. et al., “Durability in each company, and the origin of those specifications is Assessment and Riding Comfort Evaluation of a New Type typically unknown. The focus of this research is to explain Scooter by Road Simulation Technique,” SAE Technical how the dynamic load of the field usage in the time domain Paper 2006-01-0730, 2006, doi:10.4271/2006-01-0730. can be converted into a laboratory testing specification. In 4. Su, H., “Vibration Test Specification for Automotive addition, we also demonstrate how to use the accelerated life Products Based on Measured Vehicle Load Data,” SAE Gratis copy for Wei-Lun Chang Copyright 2011 SAE International E-mailing, copying and internet posting are prohibited Downloaded Thursday, March 24, 2011 06:34:15 AM

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CONTACT INFORMATION Wei-Lun Chang Automotive Research and Testing Center (Taiwan) http://www.artc.org.tw Component Quality Department Fatigue & Durability Laboratory [email protected] Tel: +886-4-7811222 ext. 2332

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