- Email: [email protected]
New methodology for accelerating the four-post testing of tractors using wheel hub displacements
b i o s y s t e m s e n g i n e e r i n g 1 2 9 ( 2 0 1 5 ) 3 0 7 e3 1 4
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/issn/15375110
Research Paper
New methodology for accelerating the four-post testing of tractors using wheel hub displacements Michele Mattetti a, Giovanni Molari a,*, Andrea Vertua b a b
Department of Agricultural and Food Sciences, Bologna University, viale G. Fanin, 50, 40127, Italy CNH Italia, viale delle Nazioni 55, Modena, Italy
article info
Durability tests of tractor prototypes need substantial financial and time commitments.
Article history:
The duration and cost of tests could be reduced using accelerated tests able to reproduce
Received 24 July 2014
on the structural part of the tractor, the same damage produced on the tractor during its
Received in revised form
real life but over a reduced time period. It has been recently demonstrated how it is
4 October 2014
possible to speed up the tests using automotive proving grounds. However a complete
Accepted 26 October 2014
prototype with all its components is necessary to perform tests on proving grounds, but to
Published online
test only the structural durability is possible the use of a 4-post bench. A 4-post bench is able to reproduce a specific vehicle response, with the possibility of applying fatigue editing
Keywords:
techniques to remove the non-damaging portions of the load signals. These techniques are
Durability
usually applied to load signals measured with strain gauges during tests on proving
Tractor
grounds. However, strain gauge installations and data validation of the acquired signals are
4 post bench
time-consuming. Here a new method, able to calculate the displacements on the wheel
Accelerated test
hub starting with acceleration measurements, applying fatigue editing techniques and defining drive files to command the actuators of a 4-post bench is described. The method proposed has an acceleration factor for the test of 5.3 together with a more rapid procedure to fit the transducers and to analyse the data obtained from the accelerometers compared to those obtained from the strain gauges. © 2014 IAgrE. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
The tractor producers are increasingly trying to reduce the time-to-market whilst increasing product reliability (Hughes, Jones, & Burrows, 2005; Strutt & Hall, 2003). One of the more onerous activities in the approval process of new vehicles is durability approval. This activity consists in the application of a load sequence, able to reproduce a damage equivalent to
that obtained during the real use by customers, to the whole vehicle or to a specific component (Oelmann, 2002). In agricultural vehicles these tests can be performed on a bench, on tracks with bumps or by field tests. A bench is usually used for early stage prototypes, the tracks with bumps for advanced prototypes and the field test as final verification before the vehicle is released onto the market. The field tests are preferable due to the possibility of reproducing the real use of the machine, but recently the
* Corresponding author. DISTAL, University of Bologna, via G. Fanin 50, 40127 Bologna, Italy. Tel.: þ39 051 2096191; fax: þ39 051 2096178. E-mail address: [email protected] (G. Molari). http://dx.doi.org/10.1016/j.biosystemseng.2014.10.009 1537-5110/© 2014 IAgrE. Published by Elsevier Ltd. All rights reserved.
308
b i o s y s t e m s e n g i n e e r i n g 1 2 9 ( 2 0 1 5 ) 3 0 7 e3 1 4
Nomenclature a A d F F 1 FFTfilt ni PD RF Si T Tm Te
acceleration Fourier transform of the acceleration displacement Fourier transform inversion of the Fourier transform FFT (fast Fourier transform) filter cycle number of the loading history pseudo-damage reduction factor load amplitude Tukey window function duration of the measured signal duration of the edited signal
producers have been reducing the amount of field testing because of difficulties in the control and reproducibility of the tests and to the strong dependence on weather and field conditions which do not easily fit in with development programming. Recently a method able to reproduce the real loads on tractors has been successfully defined using automotive proving grounds permitting tests to be accelerated by a factor of 3 (Mattetti, Molari, & Sedoni, 2012). To perform this test is necessary for a tractor prototype to be completed with all the components. However, to test the structural durability of the tractor it is useful to verify only the structural part of the tractor using a 4-post bench, without waiting for all the components. Four-post benches consist of 4 hydraulic actuators installed to reproduce a specific dynamic response on the vehicle. The drive files used to command the actuators are calculated from the signals reproduced from system identification techniques (Kelly, Kowalczyk, & Oral, 2002). Four-post benches have been used for many years in the automotive sector for different uses such as durability assessment and suspension tuning (Dodds, 1974; Kowalczyk, 2002; Londhe, Kangde, & Karthikeyan, 2012). In the agricultural sector 4-post benches have been used only to reproduce the vibrations transmitted to the driver (Anthonis, Vaes, Engelen, Ramon, & Swevers, 2007; Hostens, Anthonis, Kennes, & Ramon, 2000). The advantages of using a 4-post bench with respect to the proving grounds are numerous; it can be used continuously in any weather condition, tests are repeatable and fatigue editing techniques can be used. Editing techniques have been used to modify strain gauge signals reproduced at the bench by removing portions of the signal not likely to cause damage (El-Ratal, Bennebach, Lin, & Plaskitt, 2002). Although there are three types of fatigue editing technique (Abdullah, 2009; Conle & Topper, 1979; Lubinski, Guynn, Simms, & Woerner, 2001), only editing in the time domain can be used for a 4-post test because it maintains the synchronicity of the different signals. Fatigue editing techniques are more frequently used on external loads applied to components to define a test valid not only for the vehicle under examination but also for similar vehicles. To perform the procedure the damage is calculate using a pseudo stress-life curve which differs with respect to the real curve for the material but has the same damage exponent (Ledesma, Jenaway, Wang, & Shih, 2005).
As the vertical wheel hub loads in a vehicle are proportional to the vertical displacements caused by the road surface (Awate, Panse, & Dodds, 2007) a method to directly derive the drive files using proving ground digitised profiles tailored for a specific vehicle has been developed (Scime, 2011). Although the procedure permits drive files to be defined without any measurement, it requires time consuming preparatory work to convert the roughness of the road surface into displacements of the wheel hub and it does not permit the use of fatigue editing techniques. It is therefore necessary to measure the vertical displacements of the wheel hub during drive tests on proving grounds. These displacements can be measured with specific laser sensor (Gillespie, Sayers, & Segel, 1980) or more simply calculated through a double integration of the vertical accelerations of the wheel hub measured by accelerometers. However, due to the small zero output acceleration bias in the accelerometer signals, the integrated signals have a drift (Han, 2010) which is usually deleted using a high pass filter (Halfpenny, Hussain, McDougall, & Pompetzki, 2010). The roll-off and the phase delay caused by the IIR (infinite impulse response) and FIR (finite impulse response) filters on the signal, distort the not damaging portions making fatigue editing impossible (El-Ratal et al., 2002). The objective of this paper is the definition of a methodology to integrate the accelerations measured on the wheel hub by removing the signal drift and allowing the application of fatigue editing techniques on the signals to be used to calculate the drive files, allowing a 4-post bench test to be carried out.
2.
Materials and methods
A four wheel drive tractor with 80 kW PTO (power take off) power and a mass of 3500 kg was used for the test. The tractor was instrumented with 4 monoaxial accelerometers (Measurment Specialities 4630 with full scale of ±50 g, Measurement Specialities Inc., Hampton, Va) and two half-bridge strain gauges (HBM K-216.61-2064, HBM, Marlboro, MA), calibrated to measure the axle forces. The measured channels are reported in Table 1 and the position of some transducers is shown in Fig. 1, the others not shown were in similar positions on the other semi-axles.
Table 1 e Measured channel list. Channel 1 2 3 4 5 6
Measured channel Axle left hand front (LHF) vertical load Axle right hand front (RHF) vertical load Axle left hand front (LHF) vertical acceleration Axle right hand front (RHF) vertical acceleration Axle left hand rear (LHR) vertical acceleration Axle right hand rear (RHR) vertical acceleration
b i o s y s t e m s e n g i n e e r i n g 1 2 9 ( 2 0 1 5 ) 3 0 7 e3 1 4
309
in different time windows and calculating for each window the pseudo-damage (PD) (Socie & Pompetzki, 2004): PD ¼
X
ni S4i
(2)
i
where Si is the load amplitude derived and ni is the cycle number counted in the loading history both computed with the rainflow algorithm (Downing & Socie, 1982; Rychlik, 1987). The signals were edited maintaining the 99% of the total damage, removing the not damaging portions and finally combining the not contiguous portions with a half-sine function with a duration of 0.3 s. For each signal set to be edited, to maintaining the relative phases among them, a window was only removed only if all the corresponding windows could be removed. Fatigue editing was applied firstly to the channels 1 and 2 and then separately to the displacements obtained from the integration of the channels 3 and 4. After verification that the signal portions identified as not damaging were contemporary, the reduction factor (RF) was calculated for each edited signal defined as:
Fig. 1 e Position of the strain gauge (A), and the accelerometer (B), in the right side of the front axle.
The tractor was driven on 6 different proving grounds (PG 1, PG 2, PG 3, PG 4, PG 5 and PG 6) and in two field operations (FO1 and FO2) with specific testing conditions defined in a previous work (Mattetti, 2012). The data were acquired with a data logger (Somat Edaq, Darmstadt, Germany) sampled at 500 Hz and filtered with a low-pass filter to remove the high frequency noise. The strain gauge signals were manipulated to delete spikes, clippings and drifts, and the accelerations were doubled integrated using the following characteristic of the Fourier transform (Yang, 2009): F
Aðf Þ) aðtÞTðtÞ F
1
dðtÞ )
1 2
ð2pf Þ
Aðf ÞFFTfilt ðf Þ
(1)
where a(t) is acceleration, T(t) is the Tukey window function, A(f) is the Fourier transform of the acceleration, FFTfilt(f) is a FFT (fast Fourier transform) filter, d(t) is displacement, F is a Fourier transform, and F 1 the inversion of the Fourier transform. The Tukey window function was used for tapering to zero each side of the signals so as to reduce the leakage that smears out the signal energy over a wide frequency range. The drift of the integrated signal was removed using the FFT filtering with a cutting frequency equal to 0.8 Hz (Press, Teukolsky, Vetterling, & Flannery, 2007). The integration process of the signals was verified by establishing that the vertical displacements of a wheel hub and the correspondent vertical loads on the axle were linearly and frequency correlated. Linear correlation was evaluated through the joint-frequency calculation verifying that large frequencies of occurrence were on the diagonal, whilst the correlation on the frequency domain was verified with values of the coherence function higher than 0.8 in the presence of peaks of the cross-spectrum of the two signals (Awate et al., 2007). Subsequently, using the commercial software nCode Glyphworks™ (www.ncode.com), fatigue editing was applied in the time domain. The process consisted of dividing signals
RF ¼
ðTm Te Þ 100 Tm
(3)
where Tm (s) is the duration of the measured signal, and Te (s) duration of the edited signal. After the fatigue editing process was applied, the displacement integrated from the signals obtained from the channels 3, 4, 5 and 6 and the FFT of the original displacement signals were compared with the edited ones to verify that the editing process had not introduced anomalous peaks. The edited signals of the displacements were then used to calculate the drive files of the hydraulic actuators of the 4-post bench (Kelly et al., 2002). The obtained signals were applied to a spindle coupled 4-post bench, with the characteristics indicated on Table 2. Each test configuration was reproduced a defined number of times to realise the whole test using the methodology introduced by Mattetti et al. (2012).
3.
Results and discussion
The load signals obtained from the channel 1, and the displacement signals obtained from the integration of the signals obtained from the channel 3 for a defined test condition on proving ground were chosen as example (PG3) for the left hand front axle (LHF) and are reported in Fig. 2. The drift of the displacement signal was shown to be correctly removed and the signal shows few oscillations due to the low-pass filtering effect of the integration process that emphasises the lower frequencies by reducing the higher.
Table 2 e 4 post bench specifications. Maximum vehicle weight [kg] Actuator max force [kN] Actuator amplitude displacement [mm] Operating system pressure [MPa]
6000 63 350 22
310
b i o s y s t e m s e n g i n e e r i n g 1 2 9 ( 2 0 1 5 ) 3 0 7 e3 1 4
Fig. 2 e LHF load (a) and LHF displacement (b) for the testing condition PG 3. A detailed comparison between the force and displacement signals displayed in Fig. 3 shows how the phase delay between the two signals introduced by the filters was negligible with the alignment of the peaks. The joint frequency distribution between the LHF loads and the LHF displacement for the chosen test condition was mainly distributed along the main diagonal indicating a linear relationship between displacements and forces (Fig. 4). The linearity between forces and displacements of the wheel hub was possibly due to the simple kinematics of the front pivoting axle and of the rear axle that was part of the tractor driveline. The cross-spectrum and the coherence function between LHF loads and LHF displacements for the testing condition chosen are reported in Fig. 5. It was possible to detect a high correlation in the frequency domain, with a value of the coherence function equal to 1 in correspondence of the two higher peaks at the frequency of 1.2 and 2.5 Hz. This correlation confirms that the cutting frequency of the filter, chosen as 0.8 Hz, is sufficiently high to correctly delete
Fig. 3 e Time history zoom of LHF vertical load (
drift without reducing the frequencies of interest. The optimal cutoff frequency was found to be 0.8 Hz, equivalent to 2/3 of the frequency of the first peak in the frequency spectrum of the acceleration. The portion of the signal deleted by the fatigue editing of the test conditions is reported in Fig. 6. The portions deleted are contemporaneous confirming the applicability of the fatigue editing techniques to the displacement signals integrated from the acceleration signals, if they are suitably processed to delete the drift. The original displacement signal was similar to the edited one from the PG3 (Fig. 7), indeed the peak series and their entities were the same but the edited signal was 24% shorter. The edited signal and the original had the same spectral behaviour (Fig. 8) however the original signal had a PSD value very low for frequency lower than 0.8 Hz due to the FFT filter. This was not present in the edited signal due to the joining function introduced to join the two non-contiguous portions of the signal. The reduction factors from displacement and load signals for all the testing conditions are reported in Table 3.
) and LHF vertical displacement (
) for the testing condition PG 3.
b i o s y s t e m s e n g i n e e r i n g 1 2 9 ( 2 0 1 5 ) 3 0 7 e3 1 4
311
Fig. 4 e Joint frequency distribution between LHF vertical displacement and LHF vertical load for the testing condition PG 3. Fatigue editing from the displacement signals produced a reduction factor similar to that obtained from the load signals in all the testing conditions with a maximum difference in the reduction factor of 8%. This demonstrated that the fatigue editing can be correctly applied to the displacement signals. Between the different testing conditions, the FO2 presented a higher difference between the two RFs, probably due to the longitudinal load transfer during the work that caused a slow variation of load on the axles. These oscillations were not
present in the displacement signal due to the FFT filter; therefore some portions of the signal may have been wrongly evaluated as not damaging. This caused an RF slightly higher for the displacement editing with respect to the load one. The duration of the drive files and the number of repetitions for each testing condition are reported on Table 4. The use of the 4-post bench together with the fatigue editing techniques permitted a reduction of the total time of the test to only 601 h (Table 4) instead of the 1100 h obtained
Fig. 5 e Cross spectrum of the LHF vertical load and of the LHF vertical displacement (a) and correspondent coherence function (b) for the testing condition PG 3.
312
b i o s y s t e m s e n g i n e e r i n g 1 2 9 ( 2 0 1 5 ) 3 0 7 e3 1 4
Fig. 6 e Fatigue editing applied to the LFH vertical load (a) and to the LFH vertical displacement (b) for the testing condition PG 3. The green parts were not damaging and therefore deleted. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 7 e Comparison between the original (a) and edited signals (b) for the LHF vertical displacement and testing condition PG3.
Fig. 8 e Comparison between the power spectrum density of the LHF vertical displacement signal ( one ( ) for the testing condition PG3.
) and the edited
b i o s y s t e m s e n g i n e e r i n g 1 2 9 ( 2 0 1 5 ) 3 0 7 e3 1 4
Table 3 e Reduction factor (RF) comparison for load and displacement signals for each testing condition. Testing condition
RF from load data [%]
RF from displacement data [%]
51 26 24 24 24 24 60 52
51 32 21 24 20 22 62 60
PG 1 PG 2 PG 3 PG 4 PG 5 PG 6 FO 1 FO 2
by Mattetti et al. (2012) who used proving grounds and field operations to obtain the same damage as field usage lasting 3200 h, giving an acceleration factor of 5.3 for the data. Using this methodology it is also possible to reduce the time required for testing since it can be performed continuously without any delays due driver changes or unfavourable weather conditions. The 4-post bench also permits structural durability analysis to be carried out without requiring a completed tractor further reducing the time-to-market of new models. In addition, the development of a test starting from measures performed with accelerometers permits the frequent updating of the test specifications thereby increasing the reliability of the product. The more rapid mounting of the accelerometers rather than strain gauges, and not having to identify and remove anomalies in the signals (i.e. spikes, drifts and clippings) further reducing the time for the tests. Also, computing the drive files of the actuators starting from displacement is faster than starting from the accelerations, or from loads measured on specific points of the vehicle. The methodology applies only to vertical loads with the 4-post bench test. Testing still requires some field operations to replicate the life time damage induced by the horizontal loads.
4.
Conclusions
A methodology to allow accelerated structural tests to be performed on tractors using 4-post benches has been presented and shown with test data to accelerate bench tests by
Table 4 e Duration of tests for the different testing conditions. Testing conditions
Repetition Drive file Testing number duration [s] condition (Mattetti et al. 2012) duration [h]
PG 1 PG 2 PG 3 PG 4 PG 5 PG 6 FO 1 FO 2
181 32 107 7 675 2050 7008 8412
132 309 331 313 340 372 50 89
7 3 10 1 64 212 98 207
Total
e
e
601
313
a factor greater than five. Starting with the accelerations measured on wheel hubs during driving tests on proving grounds, vertical displacements were calculated and fatigue editing techniques applied to delete the not damaging signal portions. Drive files to control the actuators of the 4-post bench test were defined. It has been shown that FFT filtering can effectively remove the drift induced by the numerical integration of the signal with a minimum introduction of a phase delay and that the reduction in amplitude caused by filter roll-off that could alter the evaluation of the damaging portions of the signal during the fatigue editing process has been verified. However, the choice of the cutting frequency of the filter is a crucial for the method reliability because too high a cutting frequency causes attenuation of the frequencies of interest and too low a cutting frequency does not completely reduce the frequencies induced by the integration process. The results obtained suggest the opportunity to continue in the development of innovative methodologies that permit the reduction and simplification of data acquisition and data analysis to define the loads to apply in the tests. The methodology to reduce and simplify the testing procedures will also help increase the reliability of the developed machines.
references
Abdullah. (2009). A study of fatigue data editing using the ShortTime Fourier Transform (STFT). American Journal of Applied Sciences, 6(4), 565e575. http://dx.doi.org/10.3844/ ajassp.2009.565.575. Anthonis, J., Vaes, D., Engelen, K., Ramon, H., & Swevers, J. (2007). Feedback approach for reproduction of field measurements on a hydraulic four poster. Biosystems Engineering, 96(4), 435e445. http://dx.doi.org/10.1016/j.biosystemseng.2006.11.015. Awate, C., Panse, S., & Dodds, C. (2007). Validation of an accelerated test on a 4-Post road simulator. SAE Technical Paper, 1e8, 2007-26-070. Conle, A., & Topper, T. H. (1979). Evaluation of small cycle omission criteria for shortening of fatigue service histories. International Journal of Fatigue, 1(1), 23e28. http://dx.doi.org/ 10.1016/0142-1123(79)90041-0. Dodds, C. J. (1974). The laboratory simulation of vehicle service stress. Journal of Engineering for Industry, 96(2), 391e398. http:// dx.doi.org/10.1115/1.3438342. Downing, S. D., & Socie, D. (1982). Simple rainflow counting algorithms. International Journal of Fatigue, 4, 31e40. El-Ratal, W., Bennebach, M., Lin, X., & Plaskitt, R. (2002). Fatigue life modelling and accelerated test for components under variable amplitude loads. In Symposium on Fatigue Testing and Analysis Under Variable Amplitude Loading Conditions. Gillespie, T. D., Sayers, M. W., & Segel, L. (1980). Calibration of response-type road roughness measuring systems. NCHRP Report, (228). Halfpenny, A., Hussain, S., McDougall, S., & Pompetzki, M. (2010). Investigation of the durability transfer concept for vehicle prognostic applications. Presentato al 2010 NDIA Ground Vehicle Systems Engineering and Technology Symposium, MI, USA. Han, S. (2010). Measuring displacement signal with an accelerometer. Journal of Mechanical Science and Technology, 24(6), 1329e1335. http://dx.doi.org/10.1007/s12206-010-0336-1. Hostens, I., Anthonis, J., Kennes, P., & Ramon, H. (2000). PMdpower and machinery: six-degrees-of-freedom test rig design for simulation of Mobile agricultural machinery
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vibrations. Journal of Agricultural Engineering Research, 77(2), 155e169. http://dx.doi.org/10.1006/jaer.2000.0571. Hughes, S., Jones, R. P., & Burrows, A. J. (2005). Application of system Modeling to road load data synthesis for automobile product development. In ASME International Mechanical Engineering Congress and Exposition. Orlando (FL). http:// dx.doi.org/10.1115/IMECE2005-79253. Kelly, J., Kowalczyk, H., & Oral, H. A. (2002). Track simulation and vehicle characterization with 7 Post testing. SAE Technical Paper, 1e9, 2002-01-3307. Kowalczyk, H. (2002). Damper tuning with the use of a seven post shaker rig. SAE Technical Paper, 1e14, 2002-01-0804. Ledesma, R., Jenaway, L., Wang, Y., & Shih, S. (2005). Development of accelerated durability tests for commercial vehicle suspension components. SAE Technical Paper, 1e13, 2005-01-3565. Londhe, A., Kangde, S., & Karthikeyan, K. (2012). Deriving the compressed accelerated test cycle from measured road load data. SAE Technical Paper, 1e12, 2012-01-0063. Lubinski, P. J., Guynn, E. G., Simms, C. M., & Woerner, D. R. (2001). Effects of fatigue calculation parameters on the resulting tests generated from fatigue-based editing. SAE Technical Paper, 1e12, 2001-01-0833. Mattetti, M. (2012). Accelerated structural tests on agricultural tractors (PhD). Bologna: University of Bologna.
Mattetti, M., Molari, G., & Sedoni, E. (2012). Methodology for the realisation of accelerated structural tests on tractors. Biosystems Engineering, 113(3), 266e271. http://dx.doi.org/ 10.1016/j.biosystemseng.2012.08.008. Oelmann, B. (2002). Determination of load spectra for durability approval of car drive lines. Fatigue & Fracture of Engineering Materials & Structures, 25(12), 1121e1125. Press, W. H., Teukolsky, S. A., Vetterling, T. W., & Flannery, B. P. (2007). Numerical recipes: The art of scientific computing. Cambridge: Cambridge Univ. Press. Rychlik, I. (1987). A new definition of the rainflow cycle counting method. International Journal of Fatigue, 9(2), 119e121. http:// dx.doi.org/10.1016/0142-1123(87)90054-5. Scime, S. (2011). Conducting tire-coupled (4-Post) durability simulations without road load data acquisition. SAE Technical Paper, 2011-01-0225. Socie, D., & Pompetzki, M. (2004). Modeling variability in service loading spectra. Journal of ASTM International, 1(2), 46e57. Strutt, J. E., & Hall, P. L. (2003). Global vehicle reliability: Prediction and optimization techniques. Suffok (UK): Professional Engineering Pub. Yang, W. (2009). Signals and systems with MATLAB. London, UK: Springer.
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/issn/15375110
Research Paper
New methodology for accelerating the four-post testing of tractors using wheel hub displacements Michele Mattetti a, Giovanni Molari a,*, Andrea Vertua b a b
Department of Agricultural and Food Sciences, Bologna University, viale G. Fanin, 50, 40127, Italy CNH Italia, viale delle Nazioni 55, Modena, Italy
article info
Durability tests of tractor prototypes need substantial financial and time commitments.
Article history:
The duration and cost of tests could be reduced using accelerated tests able to reproduce
Received 24 July 2014
on the structural part of the tractor, the same damage produced on the tractor during its
Received in revised form
real life but over a reduced time period. It has been recently demonstrated how it is
4 October 2014
possible to speed up the tests using automotive proving grounds. However a complete
Accepted 26 October 2014
prototype with all its components is necessary to perform tests on proving grounds, but to
Published online
test only the structural durability is possible the use of a 4-post bench. A 4-post bench is able to reproduce a specific vehicle response, with the possibility of applying fatigue editing
Keywords:
techniques to remove the non-damaging portions of the load signals. These techniques are
Durability
usually applied to load signals measured with strain gauges during tests on proving
Tractor
grounds. However, strain gauge installations and data validation of the acquired signals are
4 post bench
time-consuming. Here a new method, able to calculate the displacements on the wheel
Accelerated test
hub starting with acceleration measurements, applying fatigue editing techniques and defining drive files to command the actuators of a 4-post bench is described. The method proposed has an acceleration factor for the test of 5.3 together with a more rapid procedure to fit the transducers and to analyse the data obtained from the accelerometers compared to those obtained from the strain gauges. © 2014 IAgrE. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
The tractor producers are increasingly trying to reduce the time-to-market whilst increasing product reliability (Hughes, Jones, & Burrows, 2005; Strutt & Hall, 2003). One of the more onerous activities in the approval process of new vehicles is durability approval. This activity consists in the application of a load sequence, able to reproduce a damage equivalent to
that obtained during the real use by customers, to the whole vehicle or to a specific component (Oelmann, 2002). In agricultural vehicles these tests can be performed on a bench, on tracks with bumps or by field tests. A bench is usually used for early stage prototypes, the tracks with bumps for advanced prototypes and the field test as final verification before the vehicle is released onto the market. The field tests are preferable due to the possibility of reproducing the real use of the machine, but recently the
* Corresponding author. DISTAL, University of Bologna, via G. Fanin 50, 40127 Bologna, Italy. Tel.: þ39 051 2096191; fax: þ39 051 2096178. E-mail address: [email protected] (G. Molari). http://dx.doi.org/10.1016/j.biosystemseng.2014.10.009 1537-5110/© 2014 IAgrE. Published by Elsevier Ltd. All rights reserved.
308
b i o s y s t e m s e n g i n e e r i n g 1 2 9 ( 2 0 1 5 ) 3 0 7 e3 1 4
Nomenclature a A d F F 1 FFTfilt ni PD RF Si T Tm Te
acceleration Fourier transform of the acceleration displacement Fourier transform inversion of the Fourier transform FFT (fast Fourier transform) filter cycle number of the loading history pseudo-damage reduction factor load amplitude Tukey window function duration of the measured signal duration of the edited signal
producers have been reducing the amount of field testing because of difficulties in the control and reproducibility of the tests and to the strong dependence on weather and field conditions which do not easily fit in with development programming. Recently a method able to reproduce the real loads on tractors has been successfully defined using automotive proving grounds permitting tests to be accelerated by a factor of 3 (Mattetti, Molari, & Sedoni, 2012). To perform this test is necessary for a tractor prototype to be completed with all the components. However, to test the structural durability of the tractor it is useful to verify only the structural part of the tractor using a 4-post bench, without waiting for all the components. Four-post benches consist of 4 hydraulic actuators installed to reproduce a specific dynamic response on the vehicle. The drive files used to command the actuators are calculated from the signals reproduced from system identification techniques (Kelly, Kowalczyk, & Oral, 2002). Four-post benches have been used for many years in the automotive sector for different uses such as durability assessment and suspension tuning (Dodds, 1974; Kowalczyk, 2002; Londhe, Kangde, & Karthikeyan, 2012). In the agricultural sector 4-post benches have been used only to reproduce the vibrations transmitted to the driver (Anthonis, Vaes, Engelen, Ramon, & Swevers, 2007; Hostens, Anthonis, Kennes, & Ramon, 2000). The advantages of using a 4-post bench with respect to the proving grounds are numerous; it can be used continuously in any weather condition, tests are repeatable and fatigue editing techniques can be used. Editing techniques have been used to modify strain gauge signals reproduced at the bench by removing portions of the signal not likely to cause damage (El-Ratal, Bennebach, Lin, & Plaskitt, 2002). Although there are three types of fatigue editing technique (Abdullah, 2009; Conle & Topper, 1979; Lubinski, Guynn, Simms, & Woerner, 2001), only editing in the time domain can be used for a 4-post test because it maintains the synchronicity of the different signals. Fatigue editing techniques are more frequently used on external loads applied to components to define a test valid not only for the vehicle under examination but also for similar vehicles. To perform the procedure the damage is calculate using a pseudo stress-life curve which differs with respect to the real curve for the material but has the same damage exponent (Ledesma, Jenaway, Wang, & Shih, 2005).
As the vertical wheel hub loads in a vehicle are proportional to the vertical displacements caused by the road surface (Awate, Panse, & Dodds, 2007) a method to directly derive the drive files using proving ground digitised profiles tailored for a specific vehicle has been developed (Scime, 2011). Although the procedure permits drive files to be defined without any measurement, it requires time consuming preparatory work to convert the roughness of the road surface into displacements of the wheel hub and it does not permit the use of fatigue editing techniques. It is therefore necessary to measure the vertical displacements of the wheel hub during drive tests on proving grounds. These displacements can be measured with specific laser sensor (Gillespie, Sayers, & Segel, 1980) or more simply calculated through a double integration of the vertical accelerations of the wheel hub measured by accelerometers. However, due to the small zero output acceleration bias in the accelerometer signals, the integrated signals have a drift (Han, 2010) which is usually deleted using a high pass filter (Halfpenny, Hussain, McDougall, & Pompetzki, 2010). The roll-off and the phase delay caused by the IIR (infinite impulse response) and FIR (finite impulse response) filters on the signal, distort the not damaging portions making fatigue editing impossible (El-Ratal et al., 2002). The objective of this paper is the definition of a methodology to integrate the accelerations measured on the wheel hub by removing the signal drift and allowing the application of fatigue editing techniques on the signals to be used to calculate the drive files, allowing a 4-post bench test to be carried out.
2.
Materials and methods
A four wheel drive tractor with 80 kW PTO (power take off) power and a mass of 3500 kg was used for the test. The tractor was instrumented with 4 monoaxial accelerometers (Measurment Specialities 4630 with full scale of ±50 g, Measurement Specialities Inc., Hampton, Va) and two half-bridge strain gauges (HBM K-216.61-2064, HBM, Marlboro, MA), calibrated to measure the axle forces. The measured channels are reported in Table 1 and the position of some transducers is shown in Fig. 1, the others not shown were in similar positions on the other semi-axles.
Table 1 e Measured channel list. Channel 1 2 3 4 5 6
Measured channel Axle left hand front (LHF) vertical load Axle right hand front (RHF) vertical load Axle left hand front (LHF) vertical acceleration Axle right hand front (RHF) vertical acceleration Axle left hand rear (LHR) vertical acceleration Axle right hand rear (RHR) vertical acceleration
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309
in different time windows and calculating for each window the pseudo-damage (PD) (Socie & Pompetzki, 2004): PD ¼
X
ni S4i
(2)
i
where Si is the load amplitude derived and ni is the cycle number counted in the loading history both computed with the rainflow algorithm (Downing & Socie, 1982; Rychlik, 1987). The signals were edited maintaining the 99% of the total damage, removing the not damaging portions and finally combining the not contiguous portions with a half-sine function with a duration of 0.3 s. For each signal set to be edited, to maintaining the relative phases among them, a window was only removed only if all the corresponding windows could be removed. Fatigue editing was applied firstly to the channels 1 and 2 and then separately to the displacements obtained from the integration of the channels 3 and 4. After verification that the signal portions identified as not damaging were contemporary, the reduction factor (RF) was calculated for each edited signal defined as:
Fig. 1 e Position of the strain gauge (A), and the accelerometer (B), in the right side of the front axle.
The tractor was driven on 6 different proving grounds (PG 1, PG 2, PG 3, PG 4, PG 5 and PG 6) and in two field operations (FO1 and FO2) with specific testing conditions defined in a previous work (Mattetti, 2012). The data were acquired with a data logger (Somat Edaq, Darmstadt, Germany) sampled at 500 Hz and filtered with a low-pass filter to remove the high frequency noise. The strain gauge signals were manipulated to delete spikes, clippings and drifts, and the accelerations were doubled integrated using the following characteristic of the Fourier transform (Yang, 2009): F
Aðf Þ) aðtÞTðtÞ F
1
dðtÞ )
1 2
ð2pf Þ
Aðf ÞFFTfilt ðf Þ
(1)
where a(t) is acceleration, T(t) is the Tukey window function, A(f) is the Fourier transform of the acceleration, FFTfilt(f) is a FFT (fast Fourier transform) filter, d(t) is displacement, F is a Fourier transform, and F 1 the inversion of the Fourier transform. The Tukey window function was used for tapering to zero each side of the signals so as to reduce the leakage that smears out the signal energy over a wide frequency range. The drift of the integrated signal was removed using the FFT filtering with a cutting frequency equal to 0.8 Hz (Press, Teukolsky, Vetterling, & Flannery, 2007). The integration process of the signals was verified by establishing that the vertical displacements of a wheel hub and the correspondent vertical loads on the axle were linearly and frequency correlated. Linear correlation was evaluated through the joint-frequency calculation verifying that large frequencies of occurrence were on the diagonal, whilst the correlation on the frequency domain was verified with values of the coherence function higher than 0.8 in the presence of peaks of the cross-spectrum of the two signals (Awate et al., 2007). Subsequently, using the commercial software nCode Glyphworks™ (www.ncode.com), fatigue editing was applied in the time domain. The process consisted of dividing signals
RF ¼
ðTm Te Þ 100 Tm
(3)
where Tm (s) is the duration of the measured signal, and Te (s) duration of the edited signal. After the fatigue editing process was applied, the displacement integrated from the signals obtained from the channels 3, 4, 5 and 6 and the FFT of the original displacement signals were compared with the edited ones to verify that the editing process had not introduced anomalous peaks. The edited signals of the displacements were then used to calculate the drive files of the hydraulic actuators of the 4-post bench (Kelly et al., 2002). The obtained signals were applied to a spindle coupled 4-post bench, with the characteristics indicated on Table 2. Each test configuration was reproduced a defined number of times to realise the whole test using the methodology introduced by Mattetti et al. (2012).
3.
Results and discussion
The load signals obtained from the channel 1, and the displacement signals obtained from the integration of the signals obtained from the channel 3 for a defined test condition on proving ground were chosen as example (PG3) for the left hand front axle (LHF) and are reported in Fig. 2. The drift of the displacement signal was shown to be correctly removed and the signal shows few oscillations due to the low-pass filtering effect of the integration process that emphasises the lower frequencies by reducing the higher.
Table 2 e 4 post bench specifications. Maximum vehicle weight [kg] Actuator max force [kN] Actuator amplitude displacement [mm] Operating system pressure [MPa]
6000 63 350 22
310
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Fig. 2 e LHF load (a) and LHF displacement (b) for the testing condition PG 3. A detailed comparison between the force and displacement signals displayed in Fig. 3 shows how the phase delay between the two signals introduced by the filters was negligible with the alignment of the peaks. The joint frequency distribution between the LHF loads and the LHF displacement for the chosen test condition was mainly distributed along the main diagonal indicating a linear relationship between displacements and forces (Fig. 4). The linearity between forces and displacements of the wheel hub was possibly due to the simple kinematics of the front pivoting axle and of the rear axle that was part of the tractor driveline. The cross-spectrum and the coherence function between LHF loads and LHF displacements for the testing condition chosen are reported in Fig. 5. It was possible to detect a high correlation in the frequency domain, with a value of the coherence function equal to 1 in correspondence of the two higher peaks at the frequency of 1.2 and 2.5 Hz. This correlation confirms that the cutting frequency of the filter, chosen as 0.8 Hz, is sufficiently high to correctly delete
Fig. 3 e Time history zoom of LHF vertical load (
drift without reducing the frequencies of interest. The optimal cutoff frequency was found to be 0.8 Hz, equivalent to 2/3 of the frequency of the first peak in the frequency spectrum of the acceleration. The portion of the signal deleted by the fatigue editing of the test conditions is reported in Fig. 6. The portions deleted are contemporaneous confirming the applicability of the fatigue editing techniques to the displacement signals integrated from the acceleration signals, if they are suitably processed to delete the drift. The original displacement signal was similar to the edited one from the PG3 (Fig. 7), indeed the peak series and their entities were the same but the edited signal was 24% shorter. The edited signal and the original had the same spectral behaviour (Fig. 8) however the original signal had a PSD value very low for frequency lower than 0.8 Hz due to the FFT filter. This was not present in the edited signal due to the joining function introduced to join the two non-contiguous portions of the signal. The reduction factors from displacement and load signals for all the testing conditions are reported in Table 3.
) and LHF vertical displacement (
) for the testing condition PG 3.
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311
Fig. 4 e Joint frequency distribution between LHF vertical displacement and LHF vertical load for the testing condition PG 3. Fatigue editing from the displacement signals produced a reduction factor similar to that obtained from the load signals in all the testing conditions with a maximum difference in the reduction factor of 8%. This demonstrated that the fatigue editing can be correctly applied to the displacement signals. Between the different testing conditions, the FO2 presented a higher difference between the two RFs, probably due to the longitudinal load transfer during the work that caused a slow variation of load on the axles. These oscillations were not
present in the displacement signal due to the FFT filter; therefore some portions of the signal may have been wrongly evaluated as not damaging. This caused an RF slightly higher for the displacement editing with respect to the load one. The duration of the drive files and the number of repetitions for each testing condition are reported on Table 4. The use of the 4-post bench together with the fatigue editing techniques permitted a reduction of the total time of the test to only 601 h (Table 4) instead of the 1100 h obtained
Fig. 5 e Cross spectrum of the LHF vertical load and of the LHF vertical displacement (a) and correspondent coherence function (b) for the testing condition PG 3.
312
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Fig. 6 e Fatigue editing applied to the LFH vertical load (a) and to the LFH vertical displacement (b) for the testing condition PG 3. The green parts were not damaging and therefore deleted. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 7 e Comparison between the original (a) and edited signals (b) for the LHF vertical displacement and testing condition PG3.
Fig. 8 e Comparison between the power spectrum density of the LHF vertical displacement signal ( one ( ) for the testing condition PG3.
) and the edited
b i o s y s t e m s e n g i n e e r i n g 1 2 9 ( 2 0 1 5 ) 3 0 7 e3 1 4
Table 3 e Reduction factor (RF) comparison for load and displacement signals for each testing condition. Testing condition
RF from load data [%]
RF from displacement data [%]
51 26 24 24 24 24 60 52
51 32 21 24 20 22 62 60
PG 1 PG 2 PG 3 PG 4 PG 5 PG 6 FO 1 FO 2
by Mattetti et al. (2012) who used proving grounds and field operations to obtain the same damage as field usage lasting 3200 h, giving an acceleration factor of 5.3 for the data. Using this methodology it is also possible to reduce the time required for testing since it can be performed continuously without any delays due driver changes or unfavourable weather conditions. The 4-post bench also permits structural durability analysis to be carried out without requiring a completed tractor further reducing the time-to-market of new models. In addition, the development of a test starting from measures performed with accelerometers permits the frequent updating of the test specifications thereby increasing the reliability of the product. The more rapid mounting of the accelerometers rather than strain gauges, and not having to identify and remove anomalies in the signals (i.e. spikes, drifts and clippings) further reducing the time for the tests. Also, computing the drive files of the actuators starting from displacement is faster than starting from the accelerations, or from loads measured on specific points of the vehicle. The methodology applies only to vertical loads with the 4-post bench test. Testing still requires some field operations to replicate the life time damage induced by the horizontal loads.
4.
Conclusions
A methodology to allow accelerated structural tests to be performed on tractors using 4-post benches has been presented and shown with test data to accelerate bench tests by
Table 4 e Duration of tests for the different testing conditions. Testing conditions
Repetition Drive file Testing number duration [s] condition (Mattetti et al. 2012) duration [h]
PG 1 PG 2 PG 3 PG 4 PG 5 PG 6 FO 1 FO 2
181 32 107 7 675 2050 7008 8412
132 309 331 313 340 372 50 89
7 3 10 1 64 212 98 207
Total
e
e
601
313
a factor greater than five. Starting with the accelerations measured on wheel hubs during driving tests on proving grounds, vertical displacements were calculated and fatigue editing techniques applied to delete the not damaging signal portions. Drive files to control the actuators of the 4-post bench test were defined. It has been shown that FFT filtering can effectively remove the drift induced by the numerical integration of the signal with a minimum introduction of a phase delay and that the reduction in amplitude caused by filter roll-off that could alter the evaluation of the damaging portions of the signal during the fatigue editing process has been verified. However, the choice of the cutting frequency of the filter is a crucial for the method reliability because too high a cutting frequency causes attenuation of the frequencies of interest and too low a cutting frequency does not completely reduce the frequencies induced by the integration process. The results obtained suggest the opportunity to continue in the development of innovative methodologies that permit the reduction and simplification of data acquisition and data analysis to define the loads to apply in the tests. The methodology to reduce and simplify the testing procedures will also help increase the reliability of the developed machines.
references
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