Synthesis and Validation of Accelerated Vibration Durability Tests Marco Bonato, PhD, AMRSC, Valeo Thermal Systems David Delaux, Group Reliability Director, Valeo Management Service Key Words: Accelerated Tests, Engine Cooling Components, Fatigue Damage Equivalence Theory, Reliability Specification Design, Vibration Fatigue SUMMARY & CONCLUSIONS
validate the mechanical endurance of the components according to qualification tests that are supplied by each car constructor. Vibration specifications are commonly performed on a mono-axial dynamic tests bench, therefore the samples to be tested are loaded separately for vibration in the vertical direction (Z axis), longitudinal direction (Y axis) and latitudinal direction (X axis). The most commonly used types of vibration signals can be divided into four groups: 1) Fixed sine: a number of sinusoidal cycle loadings are conducted at a given frequency and at a certain level of acceleration (Figure1a). 2) Swept sine: as opposed to a fixed sine, the sinusoidal cycles are swept in frequency and/or amplitude (Figure1b). 3) Shocks: excitation type half-sine (also called pulsed signals): the component under validation normally undergoes a shock input on both direction (e.g. +Z ; -Z) (Figure1c). 4) Random (PSD): vibration tests used to simulate the random vibration environment encountered during driving conditions (Figure1d). A random signal is the most realistic signal for product validation.
This study illustrates a methodology used in our company (car components manufacturer) which enables to generate, starting from any given customer vibration specification, a fatigue damage equivalent Power Spectrum Density (PSD) signal. This PSD can be used to evaluate the mechanical durability of engine cooling or engine-mounted components. The methodology permits to accelerate durability bench tests, to compare the severity of different vibration specifications and to perform structural simulation. One practical example will illustrate the experimental validation of the procedure, based on strain-damage measurements. The main limitations of the methodology are related to the nature of the specified signal. In the case of specifications composed of purely random signals, the method is always applicable. 1 INTRODUCTION With the automotive market becoming more and more globalized and competitive, the importance of performing faster product development has driven our company to find new ways for make product validation more efficient, and in parallel to search for tools that guarantee a more robust and flexible approach to predictive reliability. In the framework of a global programme focussed on the improvement the reliability of our components, particular attention has been given to ameliorate the prediction of the mechanical endurance of engine cooling components undergoing vibration solicitations. 2 SPECIFICATIONS FOR ENDURANCE TESTS 2.1 Generic Specifications During driving conditions, engine cooling products are subject to different types of vibration loadings. The most common are divided into shocks (highly transient events, such as potholes, bumps, sidewalks, and in general all the unpredictable irregularities of the road) and stationary (those signals originated from “normal” driving situations, e.g. highways driving). In order to assess the durability of engine cooling products, car component manufacturers are required to 978-1-4799-6703-2/15/$31.00 ©2015 IEEE
Figure 1. Example of classical vibration signals used for validation of engine cooling components. a) fixed sine; b) swept sine; c) half sine shock; d) random PSD. 2.2 Tailored Specifications The specifications described in previous section belong to
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the type called “generic” ones. They are often calculated by carmakers from a mixture of acceleration measurements and expressed as an envelope of the signal. They are applied for different exposure duration, typically 75 or 96 hours per axis [1]. Indeed, a PSD is the vibration signal that better reproduce vibration loadings during driving conditions. Compared to sines (swept and fixed) and to pure shock, a PSD permits to excite in its defined spectrum all natural frequencies simultaneously. Note that even though most fatigue loadings come as shock signals, the response of engine cooling products exhibits a broad spectrum, characteristic of a random excitation. PSD signals are also more “practical” from a design of reliability point of view: 1. Test duration can be reduced according to equation 1 [2]: we are able to transform the original PSD of duration T test and amplitude G test to an accelerated PSD of duration T acc and amplitudes G acc . The fatigue parameter b (Basquin’s exponent) is calculated as the negative inverse of the Stress-Life (S-N) curve slope in Log-Log. A typical value for aluminium alloy engine cooling components undergoing vibration loadings [3, 4, 5] is b = 8.
Figure 2. Schematic view of the Test Tailoring Methodology. The accelerated vibration tests are based on Fatigue Damage Spectra of measured road load data. 2.3.1 Measurement and Mission Profile The first step is the acquisition of vibration measurements from sensors placed on the components mounting points (e.g. on the chassis or the siderail). The vehicle equipped with accelerometers is driven into a dedicated test track (e.g. Belgium road), where vibrations generated from both stationary and shocking events are recorded. From the set of road load data, a replication factor (number of repeats) is applied to each recorded events. The value of these coefficients is based on a statistical estimation of the occurrence of that particular excitation during the vehicle lifetime. The total time series originated from the concatenation of all the events multiplied by their repeat numbers is called Mission Profile. Both events type, duration, number of repeats are chosen by the carmaker and tailored to the type of vehicle. Hundred hours of this profile corresponds to the total life of the automobile. The next step of the procedure is the calculation of the Shock Response Spectrum (SRS) and Fatigue Damage Spectrum (FDS).
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T b (1) Gacc = Gtest test Tacc The severity of PSD signals (at iso-test time) can be easily estimated. We compare the amplitude of the spectral signal by quantification of its gRMS (root mean square acceleration), which is the area underneath the curve that represents the power of the overall signal. An accelerated PSD can be derived from road load data measured accelerations, according to the test tailoring procedure [1, 2, 3] already standardised for military and civilian use [4, 5].
2.3 Test Tailoring Approach In the past, at the design stage and the initial development stage, car manufacturers tended to rely on existing standards as guidelines for formulating the specifications. This would often cause either an over-test or an under-test with regards to the overall spectrum or in specific frequency bands [6]. To overcome this, a new approach has been developed since the end of the 1970s, which emphasised the importance of developing a correct vibration specification using the acceleration data acquired directly on the vehicle, and coupled with a robust procedure formulated for deriving the specifications out of the vibration data so obtained. The test tailoring methodology is nowadays recommended by both military and civilian standards [4, 5, 7]. In the case of engine cooling components, vibration specifications are designed and tailored on the real environment, based on acceleration measurements acquired on the mounting point of the components to validate. A schematic description of the methodology is given in Figure 2.
2.3.2 Shock Response Spectrum (SRS) The SRS is obtained from input accelerations by calculating the maximum acceleration (or displacement) seen by the component assuming a Single Degree of Freedom (SDOF) response (Figure 3). Because the natural frequencies of the component are often unknown, the SDOF filter is repeated over a given range of natural frequencies to make sure that all eventualities are taken into account. The SRS represents the curve plotting the maximum acceleration (or displacement) response depending on frequency, as shown in Figure 4. It is called Extreme Response Spectrum (ERS) when the input signal is given in the frequency domain. The typical Dynamic Amplification factor taken is Q = 10. Real world applications are seldom SDOF systems. Nevertheless, in most cases the response is dominated by a single dynamic mode and this, together with the conservatism
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most commonly used. The counted stress ranges are then used to calculate the cumulative fatigue damage (Figure 6).
of the assumption, makes this approach applicable for all practical cases.
Figure 3. Displacement response of a single degree of freedom (SDOF) system. Figure 6. Calculation of the Fatigue Damage Spectrum in the frequency domain. 2.3.4 Test Synthesis The inversion of the FDS permits to calculate an equivalent PSD signal which bears at least the same fatigue damage content of the original time series but in a reduced amount of time (Figure 2). The result of this step (called Test Synthesis) is the obtainment of the final tailored accelerated specification. The validity of the synthesised test is confirmed by a comparison between the SRS of the original acceleration time series and the ERS of the synthetic PSD. This procedure verifies that the accelerated signal does not bring any unrealistic shock. The synthetic PSD is accepted when its ERS is less than twice the SRS of measured accelerations. The tailored test methodology allows to adapt the synthetic accelerated PSD to the carmaker’s reliability targets, for a given confidence level, by applying a safety coefficient to the PSD amplitudes. This majoring factor is calculated by considering the statistic dispersion of the mechanical endurance and of the environmental solicitation, and it is related to the number of samples tested. The procedure of “Test Tailoring” has been adopted by our company since 1998. The methodology offers the advantage of being easily applicable, to be tailored to a wide range of components and practically to any type of vehicle. Internal study has shown that a testing-time reduction to maximum 30 hours permits to perform an accelerated test that causes on the component the same failure modes found on the vehicle during driving conditions without provoking unrealistic shock.
Figure 4. Calculation of the Shock Response Spectrum. 2.3.3 Fatigue Damage Spectrum (FDS) The FDS is derived using an analogous approach to the SRS but this time the SDOF transfer function response is rainflow cycles counted (deterministic approach) [1], and the related fatigue damage is calculated using the material S-N curve (Basquin’s equation) and Miner’s cumulative law (Figure 5).
2.4 New Trend in carmakers Vibrations Signals Nowadays, a new generation of vibration specifications for engine cooling components is becoming more and more common among car manufacturers. A specification might be made of, for example, as concatenation of PSD spectra, or mixture of harmonic and random signals, or as multiple shocks followed by a random PSD. While shaker controller suppliers have successfully implemented these new types of
Figure 5. Calculation of the Fatigue Damage Spectrum in the time domain. In the case of a signal given in the frequency domain, the FDS is obtained through a probabilistic approach. The stress peaks distribution is estimated statistically. Rayleigh, Lalanne and Dirlik’s formulations are the peak distribution equations 9
input signals, they cannot be adopted for structural simulation, which requires one only signal in the spectral domain. For the same reason, a direct comparison of their severity is not possible. In this context, a general procedure that allows simplifying complex specifications into a unique signal expressed as a PSD would be convenient from numerous points of view. Indeed, it offers the advantage to potentially shortening the test time, and to simplifying the conduct of bench testing. Validation tests would be time and cost effective. And, as mentioned, the possibility of reducing any vibration input to a PSD would facilitate the comparison of new specification with old ones, or the confrontation of vibration signals from different car manufacturer. Moreover, the accumulation of complex signals in a sole random PSD would permit the performance of structural simulation, therefore helping the process of design validation.
experimentally verified, in order to detect systematic errors that would result in a final synthetic PSD over- or underestimating the severity of the original specification.
3 CUMULATING VIBRATIONS SIGNALS The procedure here illustrated is based on the theory of fatigue damage equivalence. Starting from any vibration specification, we generate a final synthetic PSD that has at least the same damage potential of the original signal. The methodology involved the calculation of the Fatigue Damage Spectra associated to the customer vibratory specification, followed by the derivation of the (accelerated) synthesised PSD. A schematic view of the procedure is illustrated in Figure 7. The first step consists in the identification of the mission profile. This information is normally included in the technical description of the carmaker specification, and detailed as type, order (e.g. are they in series or in parallel?), and number of the loadings events, together with the test time. The second step is the calculation of the FDS of the signals (Figure 5). When the signal is given as a time series, the FDS can always be performed via the iterative process (deterministic approach). In the case of a signal is given in the spectral domain for a known stress cycles distribution, the FDS is calculated in the so-called “direct method” (stochastic approach) from a statistical estimation of the rainflow counted cycles. This approach is nowadays possible only for random PSD, sine-on-random and single sine sweep signal [8]. For all other types of signals, it is necessary to regenerate a time series starting from the spectral signal (time series reconstruction), and then calculate the FDS via the iterative process. Once the FDSs of all the events are obtained, we calculate the total FDS as the sum of the FDS (for events in series) according to the mission profile, and via the inversion of the FDS we generate the synthetic accelerated PSD (test synthesis). No safety coefficients are added to the PSD, because it is assumed that they have already been included in the specification by the carmaker. The PSD obtained is now ready to be applied to accelerated bench testing or structural simulations.
Figure 7. Procedure for accumulation of specification signals into one accellerated PSD. The methodology here proposed has been validated by performing strain measurements, acquired on real components during bench tests (Figure 8). To makes sure that the new synthetic PSD bears at least the same amount of fatigue damage of the customer specification, we compare the damage provoked by the original signal to the damage caused by the new synthetic PSD.
Figure 8. Experimental validation of test synthesis procedure. 5 CASE STUDY: MULTI-PSD SIGNAL A new specification for the validation of an engine cooling radiator is composed of two PSDs of different severity (PSD1 of duration Time_1, more severe than PSD2 of duration Time_2) which are run alternating PSD1 - PSD2 for an overall duration Tf (hours) = (T1+T2)*repeats number (Figure 9). 5.1 Accumulation of the Specification signal According to the methodology herein described, we have proceeded as follows (Figure 10):
4 EXPERIMENTAL VALIDATION OF THE METHOD The
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Figure 9. Multiple-PSD signal specification
Figure 11. Brazed radiator equipped with accelerometers (left) and strain gages (right). 1. 2. 3. 4.
Measurements were performed for all the input signals: Customer PSD 1 Custumer PSD 2 Iso-time accumulated PSD 30 hours accumulated PSD.
5.2.3 Relative Damage Calculations
Figure 10.Accumulation of the multi-PSD signal into an equivalent PSD.
Measured data (acceleration and strain) were post treated using anomalies detection algorithms implemented within HMB’s nCode GlyphWorks software [9]. After having verified that strain signals did not contain any corrupted data (presence of spikes or drifts that would lead to incorrect calculations), strain cycles ranges occurrence was extrapolated via rainflow cycles extraction. The relative fatigue life was calculated from a material fatigue curve typical of engine cooling products, with Basquin’s exponent value b = 8. The stress intercept was set to 2000 Mpa, to be appropriate for the needs of this relative damage calculation [10]. The relative fatigue damage was obtained by application of the linear cumulative Miner’s rule. (Figure 12).
1) Calculation of the FDS for each PSD segment. 2) Multiplication of each FDS by the number of repeats, and sum to the total FDS. 3) From the total FDS, derivation of the synthetic PSD, both as iso-test time signal and accelerated one (30 hours, according to our standard). 5.2 Validation of the methodology Vibrations tests were performed at Valeo La Verrière Research Center (France). During the process of validation, the component is solidly clamped on the shaker, using a rigid structure (no rubbers interface between frame and specimen). This permits to remove all the nonlinearity of the response. 5.2.1 Data Collection A brazed radiator was equipped in strain gauges. The sensors position was chosen according to simulation results and previously realized test up to failure. Strain gages were placed close to the traditional hot spots, near the zone of maximum stress, i.e. at the connections between the tubes and the header (Figure 11). Two accelerometers were positioned to capture the control signal (drive) injected on the jig and the responses on the component measured in the zone of maximum displacement, i.e. on the radiator centre body. 5.1.2 Measurements Several random tests of 15 minutes each were performed, only in the the Z axis direction (vertical axis), because this is the direction of displacement that generate most of the fatigue damage during real life driving. Data were recorded at 4600 samples per second giving an excellent resolution of over 40 points per cycle at the highest frequency considered. The fatigue damage was calculated and then scaled for the whole duration of the signals considered.
Figure 12. Calculation of relative damage from strain measurements. The authors decided to focus on strain results from only one strain gage, for the sake of simplicity. Similar results were obtained for all the other strain gages mounted on the component.
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In parallel, from acceleration data, we calculated the FDS for iso-test time (same length as customer’s) and the accelerated test PSD, and for both drive and response accelerometers. Because the synthetic PSD is obtained as the inversion of the FDS of the original specification, the FDS experimentally measured from acceleration of the synthetic PSD is expected to be equivalent to the FDS original customer’s specification. Note that both strain damage and FDS spectra were calculated on single measurements and then scaled to the duration of the whole testing time.
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Manoj Kumar, T. Narasirnha Rao, K. Jagadisan and K. Jayathirtha Rao, Tailoring of Vibration Test Specifications for a Flight Vehicle, Def Sci I, Vol. 52, N0.1, January 2002. 7. MIL STD 810F- Annex A, US National Defense Standard. 8. A. Halfpenny and T. C. Walton, Using the Fatigue Damage Spectrum (FDS) to determine flight qualification of vibrating components on helicopters, Astelab 2009, Paris. 9. HBM-nCode Glyphworks Accellerated Tests Users manual (2013). 10. F. Kihm and D. Delaux, Vibration fatigue and simulation of damage shaker table tests: influence of clipping the random drive signal, Procedia Engineering, 2013, 66, 549–564 . BIOGRAPHIES Marco Bonato, PhD, AMRSC Valeo Thermal Systems 8 rue Louis Lormand, 78321 La Verrière, France e-mail:
[email protected] Marco Bonato is a Reliability Engineer, in Valeo since 2012. His responsibility includes the elaboration of new vibration specifications (test tailored methodology) as well as the design of reliability studies related to engine cooling components. Marco’s broad scientific experience spans almost 10 years in applied research and optimization. He actively participates in the development and implementation of customer-based engineering and reliability issues. Marco holds a Ph.D. in Material Science from the University of Bristol (UK). Prior to this, he obtained a Master degree in Inorganic Chemistry at the University of Padua (Italy). He is currently Associate Member of the Royal Society of Chemistry.
Figure 13.Comparison of FDS (left) from customer specification (green line), 30 hours accelerated PSD (blue line) and iso-time PSD (red line). Damage results from strain measurements (right). 5.3 Results and Conclusions The results show an excellent correlation (Figure 13), in terms of FDS and strain damage, between the original customer specification and the synthetic PSDs (for both the iso-time and accelerated one). This demonstrates that the methodology of signals accumulation and testing time reduction is perfectly applicable in the case of purely random input signals. The applicability for other types of signals (e.g. swept-sines-on-random) is currently under investigation.
David Delaux, Group Reliability Director, Valeo Management Service 43 rue Bayen 75017 Paris. France
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D. Delaux and F. Kihm, Synthesis of an Engine Vibration Specification and Comparison with Existing Qualification Specification, Astelab 2010, Paris. C. Lalanne, Mechanical Vibration and Shock Analysis, Volume 1-5, Wiley, 2009. A. Halfpenny Accelerated Vibration Testing Based on Fatigue Damage Spectra, Aerospace Testing Expo, Hamburg, 2006. Ministère de la Défense, Délégation Générale pour l'Armement France. GAM EG-13 - Essais généraux en environement des matériels. Paris : Ministère de la Défense, France, 1986. AFNOR FD X07-144-2-1996, French Certification Norm: Tests - Tests Design And Realization - Tests In Environment
David Delaux (graduated from Centre Etudes Supérieures Industrielles of Paris, France) is Group Reliability Director. David joined Valeo in September 1997 in Engine Cooling branch and was responsible for Material Department (validation of all aluminum alloys and polymers) and for Reliability Department (warranty issues, reliability validations – corrosion, thermal shock, pressure pulsation, vibration). Now he is responsible for leading the global competency development and the reliability strategy for Valeo worldwide. As Reliability Senior Expert, David has been involved in different scientific organizations, such as the French Army Committee (CIN EG MECA) and ASTE (Association des Sciences et des Techniques d’Environnement).
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