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Torsional Vibration Analysis of a Test Rig Driveline Equipped with a Flexible Coupling MARCO TRONCOSSI 1* , EMILIANO MUCCHI 2 , ALESSANDRO RIVOLA 1 1 Department of Engineering for Industry University of Bologna Via Fontanelle 40, 47121 Forlì (FC) ITALY 2 Department of Engineering University of Ferrara Via Saragat 1, 44121 Ferrara (FE) ITALY * [email protected] * http://www.diem.ing.unibo.it/personale/troncossi Abstract: - The paper deals with a case study from the automotive industry and relative to a test rig of internal combustion engines: the output shaft of the engine transmission is connected with an electromechanical brake by means of a transmission shaft which hosts a torsional coupling with rubber elements. The engine test cell was developed several years ago; over years, the engine operations and performance have been changed, in terms of output power and torque, entailing more severe dynamic loads affecting the driveline members. In this scenario, early failures of the rubber elements of the flexible coupling have occurred. The goal is to solve the problem by bringing the fewest possible modifications to the cell layout. An experimental campaign was thus carried out, with the aim of characterizing the current system dynamic behavior and finding possible modifications able to solve the problem. In particular, torsional vibration measurements have been achieved by a coder-based technique using high-quality optical sensors and equidistantly spaced markers (zebra tape) on the rotating components. The measured data were analyzed in the Time, Frequency, Time-Frequency, and Order domains. The paper presents the experimental setup, the data processing and the results obtained from tests performed on the original system and on a modified version of the transmission driveline, after changing the elastodynamic properties of the coupling. Key-Words: Torsional Vibration; Instantaneous Angular Speed; Flexible Coupling; Experimental Test; Time- Frequency Analysis; Order Analysis 1 Introduction This work addresses the dynamic analysis of the coupling components in internal combustion engine test rigs from the experimental standpoint. In the current set up, the output shaft of the engine transmission is connected with an electromechanical brake by means of a transmission shaft which hosts a torsional coupling with rubber elements (high flexible couplings). Recently, the rising performance of engines has led to an abrupt increase of the dynamic loads affecting the driveline, particularly the elastic couplings. A negative effect has been affecting the mentioned torsional coupling, with high oscillations of its components leading to the collapse of the rubber elements (the dissipated energy overheats the rubber that undergoes to early failure). The challenge is to solve the problem by bringing the fewest possible modifications to the cell layout. Unfortunately the coupling supplier is not able to provide an off-the-shelf solution. An experimental campaign was thus carried out, with the aim of (i) characterizing the current system dynamic behavior, determining the response signature, and detecting the source of critical problems, and (ii) finding possible modifications able to solve the problem, with a low impact into the cell architecture. In particular, torsional vibration measurements have been achieved by a coder-based technique using high-quality optical sensors and equidistantly spaced markers (zebra tape) on the rotating components. The optical sensors were mounted before and after the coupling rubber elements, at the engine-side and brake-side, respectively, in order to track the torsional oscillations affecting the rubber element. The measured data were analyzed in the Time, Frequency, Time-Frequency, and Order domains. The results obtained from a first test campaign performed on the current version of the system Recent Advances in Mechanical Engineering ISBN: 978-960-474-402-2 198

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Torsional Vibration Analysis of a Test Rig Driveline Equipped with a Flexible Coupling

MARCO TRONCOSSI 1*, EMILIANO MUCCHI 2, ALESSANDRO RIVOLA 1

1 Department of Engineering for Industry University of Bologna

Via Fontanelle 40, 47121 Forlì (FC) ITALY

2 Department of Engineering University of Ferrara

Via Saragat 1, 44121 Ferrara (FE) ITALY

* [email protected] * http://www.diem.ing.unibo.it/personale/troncossi Abstract: - The paper deals with a case study from the automotive industry and relative to a test rig of internal combustion engines: the output shaft of the engine transmission is connected with an electromechanical brake by means of a transmission shaft which hosts a torsional coupling with rubber elements. The engine test cell was developed several years ago; over years, the engine operations and performance have been changed, in terms of output power and torque, entailing more severe dynamic loads affecting the driveline members. In this scenario, early failures of the rubber elements of the flexible coupling have occurred. The goal is to solve the problem by bringing the fewest possible modifications to the cell layout. An experimental campaign was thus carried out, with the aim of characterizing the current system dynamic behavior and finding possible modifications able to solve the problem. In particular, torsional vibration measurements have been achieved by a coder-based technique using high-quality optical sensors and equidistantly spaced markers (zebra tape) on the rotating components. The measured data were analyzed in the Time, Frequency, Time-Frequency, and Order domains. The paper presents the experimental setup, the data processing and the results obtained from tests performed on the original system and on a modified version of the transmission driveline, after changing the elastodynamic properties of the coupling. Key-Words: Torsional Vibration; Instantaneous Angular Speed; Flexible Coupling; Experimental Test; Time-Frequency Analysis; Order Analysis

1 Introduction This work addresses the dynamic analysis of the coupling components in internal combustion engine test rigs from the experimental standpoint. In the current set up, the output shaft of the engine transmission is connected with an electromechanical brake by means of a transmission shaft which hosts a torsional coupling with rubber elements (high flexible couplings). Recently, the rising performance of engines has led to an abrupt increase of the dynamic loads affecting the driveline, particularly the elastic couplings. A negative effect has been affecting the mentioned torsional coupling, with high oscillations of its components leading to the collapse of the rubber elements (the dissipated energy overheats the rubber that undergoes to early failure). The challenge is to solve the problem by bringing the fewest possible modifications to the cell layout. Unfortunately the coupling supplier is not able to provide an off-the-shelf solution.

An experimental campaign was thus carried out, with the aim of (i) characterizing the current system dynamic behavior, determining the response signature, and detecting the source of critical problems, and (ii) finding possible modifications able to solve the problem, with a low impact into the cell architecture. In particular, torsional vibration measurements have been achieved by a coder-based technique using high-quality optical sensors and equidistantly spaced markers (zebra tape) on the rotating components. The optical sensors were mounted before and after the coupling rubber elements, at the engine-side and brake-side, respectively, in order to track the torsional oscillations affecting the rubber element. The measured data were analyzed in the Time, Frequency, Time-Frequency, and Order domains. The results obtained from a first test campaign performed on the current version of the system

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Fig. 1: Schematic of the system under study

Fig. 2: Test rig and optical sensor setup. Fig. 3: (a) Minimal schematic of the flexible coupling;

(b) collapsed rubber element (engine-side). permitted to identify the excitation of its natural frequencies. A second test campaign was performed after changing the current rubber elements of the coupling with harder ones. The purpose was both to obtain a better response in terms of coupling speed oscillations (due to the expected higher natural frequencies) and to obtain a wider experimental database useful for the validation of numerical models of the driveline. The response proved pretty good: the smoother relative motion of the two coupling sections led indeed to smaller stress of the rubber elements, possibly providing a viable solution of the original problem with a minimum cost in terms of structural modifications. In addition, a further numerical investigation, not reported in this paper that is entirely devoted to the experimental activity, was performed in order to find out the optimal variant of the transmission driveline which both minimizes speed oscillations and requires sustainable modifications of the system components [1].

2 Materials and methods 2.1 System description A schematic of the test rig being studied is depicted

in Fig.1 and a close up picture of the flexible coupling region is reported in Fig.2. The test rig consists of a few main components: the crankshaft of the engine drives a transmission shaft by means of a gearing with a constant and fix gear ratio of about 3 (the exact value is confidential and cannot be reported); the transmission shaft is connected to the electromagnetic brake by means of the flexible coupling.

The flexible coupling is composed of two rubber elements, characterized by a hardness of 45 Sh in the Shore scale, working in series and clumped to three metallic flanges (Fig.3). 2.2 Experimental setup Torsional vibration measurements on the flexible coupling were carried out by using two optical sensors (Optel Thevon 152 G7 GP RV4), acquiring TTL signals from a zebra tape with line width of 2 mm. The two sensors were equipped with two different probes (Optel Thevon MULTI TBYO 6M HM6X100 SURG and Optel Thevon MULTI SLIT YO 6M HM6X80 SURG), both fixed to a stiff bracket. The zebra tape was mounted in the two end-sections of the flexible coupling, at the brake-side and engine-side (in Fig.2 the engine-side tape is visible), providing the instantaneous angular speed

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(IAS) measurements conventionally denoted as nbs and nes respectively. The high number of lines per revolution (94 and 78, for the brake-side and engine-side respectively) guaranteed a suitable resolution in the torsional measurements. In addition, the tacho signal from a phonic wheel with 8 teeth fixed to the engine crankshaft was acquired and the corresponding IAS will be referred to as nc in the following. Finally, in order to possibly have additional information for enforcing the data analysis, a tri-axial accelerometer (PCB 356B21) was glued to the engine block support, in a convenient location close to the transmission shaft bearings. All the data were acquired by means of LMS SCADAS MOBILE SCM05 equipped with the LMS SCM-RV4 module. The counting rate of the optical sensors was 800 MHz and the sampling frequency of the IAS and acceleration signals was 10240 Hz.

2.3 Test procedures and data processing The system was tested at different operational conditions, namely runups and stationary regimes, and for different working conditions in terms of velocity and throttle opening (50% and 75%). Runup tests were conducted in order to find out resonant bandwidths of the system for a continuous change of engine speed. In addition, stationary tests were performed to have more precise information about the natural frequencies for a number of different constant regimes. Two test campaigns were performed, corresponding to rubber elements of the flexible coupling having different hardness, namely 45 Sh and 70 Sh, respectively.

The torsional oscillations of the two coupling ends were evaluated in terms of their relative velocity, denoted as nrel and determined as nrel = nes – nbs. The data of runup tests were analyzed in the Time and Time-Frequency domains, whereas data measured for stationary tests were analyzed in the Time, Frequency, and Order domains.

Velocity signals acquired in stationary tests (each one lasting 20 s) were resampled with reference to the crankshaft angular position [2]. Therefore signal nc was taken as reference and the synchronous averaging of all the data was performed for each thermodynamic cycle (corresponding to two crankshaft revolutions). Statistical parameters of interests (e.g. mean, RMS, and peak values) were then computed on the angle-based data averages.

For the frequency analysis, the Fast Fourier Transform (FFT) of the signals was computed by

averaging blocks of data corresponding to 20 thermodynamic cycles.

In order to associate the frequency content of the acquired signals with the excitations, the order analysis is preferred to the frequency analysis [2, 3]. Since the major excitations of all the driveline components are due to the engine firing, the order tracking was performed by resampling data still referring to crankshaft tacho measure nc.

Time-frequency analyses of the runup test signals, having a duration of 44 s, were performed by computing the Short Time Fourier Transform (STFT) [4, 5], calculating the spectra in time windows of 0.1 s (thus providing a frequency resolution of 10 Hz). 3 Results Due to confidentiality agreement with the industrial partner, all the data related to the shaft velocities cannot be explicitly reported. Therefore data relative to runup tests will be shown as normalized to nc maximum value, whereas the constant speeds of the stationary tests will be conventionally referred to as Regime A, Regime B,…, being Regime A the lowest speed.

Among all the collected data, only a limited portion will be reported in the present paper. In particular, in this section the results relative to the current system will be firstly reported, aiming at highlighting the dynamic effects that likely led to the early collapse of the rubber elements. Then, the main data resulting from the substitution of the 45 Sh rubber elements of the flexible coupling with harder ones (70 Sh) will be shown and compared with the previous ones. 3.1 Tests with “45 Sh” flexible coupling The results here reported refer to tests conducted on the current test rig, where the flexible coupling has rubber elements with hardness 45 Sh. The throttle opening was 50%.

3.1.1 Runup tests A number of different tests were performed, namely runup and rundown with different levels of (constant) acceleration. The analysis of the corresponding data led to the same remarks and conclusions. In this section only the results relative to runup performed with the lowest acceleration are shown.

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In Fig. 4 the time series of the acquired IAS are plotted as scaled to the maximum value of the crankshaft velocity nc. The oscillation of the velocity nes of the engine-side flange of the coupling is significantly higher and more irregular than the brake-side one (nbs). In particular it is subjected to a very high increment after the sixteenth second of the run.

The analysis of this oscillation is the main tool to understand the dynamic phenomenon underlying the system behavior. To this aim the analysis was focused on the relative velocity between the two coupling ends, nrel, which was analyzed in the Time-Frequency domain to highlight the presence of resonant bands of the system. In Fig. 5 it can be noted that the frequency content of nrel is dominated by order 1 of the crankshaft rotation and – to a smaller extent – by order 0.5, 1.5, and 2, being order 0.5 associated with the engine thermodynamic cycle. Starting from the sixteenth second of the runup, the amplitude of nrel significantly increases with a frequency content firstly associated with the crankshaft order 0.5 (16–18 s) and then dominated by order 1 for a long time interval (18–30 s). Two natural frequencies, f1 and f2 (actual values are confident and cannot be reported), are excited in these two phases, being f2 widespread in a large bandwidth. It could be noted that the second one is excited also by the crankshaft order 1.5, with lower energy, in the interval 8–12 s. Other possible higher resonances, f3 and f4, are slightly excited by the crankshaft orders 1.5 and 2 at about 18–20 s, but with a low energy.

The RMS value of nrel computed for the entire duration of the runup is about 156 rpm.

3.1.2 Stationary tests Stationary tests at different velocities were performed and the corresponding runs will be conventionally referred to as Regime A, Regime B, …, Regime G, where Regime A and Regime G are about 30% and 95%, respectively, of the maximum speed reached during the runup tests.

After resampling and synchronously averaging the velocity signals based on the rotation of the crankshaft, the order and frequency analyses (the latter not reported for preserving data confidentiality) and the time statistics allowed for enforcing the interpretation of the system dynamic behavior retrieved for the runup tests.

In particular a more accurate estimation of the system natural frequencies was achieved. Figure 6

Fig. 4: Time data of the normalized velocity signals acquired during a runup test (45 Sh rubber elements).

Fig. 5: Time-frequency analysis of the relative velocity nrel computed for a runup test (45 Sh rubber elements).

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reports the crankshaft-angle-based trend of nrel over five thermodynamic cycles and its order-based spectral analysis for Regime D (limited to the first two crankshaft orders), which is about the 60% of the runup maximum velocity (i.e. the velocity achieved at the twentieth second of the runup in Fig.5). It appears evident the consistency with the time-frequency analysis of the runup tests: nrel signal is indeed dominated by the crankshaft orders 1 and 2, partly exciting the resonant frequency f2 and f4, and at a lower extent by orders 0.5 and 1.5 which excites the resonant frequencies f1 and f3, respectively. A minor contribution of the transmission shaft orders is also somehow appreciable (corresponding to multiples of about one third of the crankshaft order 1). It is worth noticing the presence of a low frequency resonance f0 corresponding about to 0.1 crankshaft order. This natural frequency was excited in each stationary regime, but at a negligible level since the excitation coming from the engine did not contain the corresponding harmonic content. Therefore the excitation of such a resonance was likely due to low frequency mechanical noise present in each test.

Table 1 reports the most significant statistical values of nrel computed for the stationary tests, i.e. the RMS value and the “Irregularity Ratio”, IR,

Fig. 6: (a) nrel reported over five thermodynamic cycles for Regime D stationary test; (b) Order analysis of nrel.

Table 1. Statistical parameters of nrel computed for the stationary tests performed with the 45 Sh rubber element.

nrel RMS [rpm] IR [%] Regime A 91 24.2 Regime B 115 15.4 Regime C 183 21.2 Regime D 245 25.2 Regime E 236 18.8 Regime F 173 13.2 Regime G 94 6.8

Table 2. Statistical parameters of nrel computed for the stationary tests performed with the 70 Sh rubber element.

nrel RMS [rpm] IR [%] Regime A 109 27.6 Regime B 125 17.0 Regime C 63 8.0 Regime D 42 5.2 Regime E 34 4.0 Regime F 31 3.2 Regime G 72 5.2

between the nrel peak-to-peak amplitude and the mean value of the transmission shaft velocity. Consistently with the time-frequency analysis, Regime D proved the most critical for the oscillations which the rubber elements are subjected to. It is also worth noticing that from a relative point of view, i.e. in percentile terms of IR, the slowest Regime A exhibits quite important oscillations.

From the analysis of all the data retrieved from both runup and stationary tests performed on the current test rig, it can be concluded that five natural frequencies were likely present in the bandwidth of interest (corresponding to the maximum frequency that can be excited by the crankshaft order 2 in the runup tests). In particular:

f0 was never significantly excited; f1 was excited by the crankshaft order 0.5 at a

velocity corresponding to about Regime C; f2 was excited by both orders 1 and 1.5

depending on the crankshaft speed; the medium-high frequencies f3 and f4 were

excited with low energy by the crankshaft orders 1.5 and 2.

The most important contribution to the coupling relative oscillations was provided by the natural frequency f2, which is widespread in quite a large band. Efforts to improve the dynamic response of the flexible coupling (and the entire driveline as a consequence) should be thus focused at moving these resonant bands away from the bandwidth that can be excited by the crankshaft orders 0.5 to 2 (while not introducing, at the same time, other resonances in this bandwidth).

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It is worth recalling that the performed experimental analysis did not permit to determine the vibration modes associated with the mentioned natural frequencies. In other words, it is not possible to state that only torsional modes were excited, since it cannot be excluded that a flexural mode of the transmission shaft could induce coupled oscillations in the IAS. 3.2 Tests with “70 Sh” flexible coupling A further test campaign was carried out with a flexible coupling characterized by different elastodynamic properties. In particular a coupling with rubber elements having 70 Sh hardness was used instead of the original 45 Sh rubber. The stiffening effect of the harder rubber was expected to increase the system natural frequencies with a possible benefit on the dynamic behavior of the driveline. The same kind of tests with the same operative conditions adopted in the previous campaign was performed. In this paragraph the corresponding results are reported and discussed consistently with the presentation in Section 3.1.

Figure 7 reports the IAS during the runup, scaled to the maximum value of the crankshaft velocity nc. The oscillations of the speed nes of the engine-side flange was significantly smaller than in the previous campaign (Fig. 4), whereas nbs was basically the same. As a consequence the relative velocity nrel was significantly lower, as it can be seen in Fig. 8, where the full scales of time plot and colormap are the same as in Fig. 5 in order to highlight the important reduction. The RMS value of nrel computed for the entire duration of the runup was 74 rpm, i.e. less than the half of the previous campaign value (156 rpm). Some dynamic effects were still present, though resulting in speed oscillations largely smaller than in the case of the 45 Sh rubber elements. In particular, the signal was dominated by the crankshaft order 1, which excited natural frequency f1

* at the time interval 10–14 s, corresponding to a velocity that was about 50% of the final runup velocity. Moreover, at the very beginning of the run (for a velocity of about 30% of the maximum value), order 0.5 seemed to excite resonance f0

*. The star symbol is introduced in order to have explicit reference to the 70 Sh coupling.

The analysis of the stationary test data can help to understand the different dynamic behavior of the system after the rubber change. Table 2 reports the statistical parameters computed for the stationary tests conducted with the 70 Sh rubber elements. The global decrement of the oscillation amplitudes

Fig. 7: Time data of the normalized velocity signals acquired during a runup test (70 Sh rubber elements).

Fig. 8: Time-frequency analysis of the relative velocity nrel computed for a runup test (70 Sh rubber elements).

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appears evident for Regimes C to F, for which the current coupling (with 45 Sh rubber elements) presented its critical response. In spite of this great improvement it should be noted that the new coupling response was slightly worst for the low Regimes A and B. Figure 9 reports the crankshaft-angle-based trend of nrel and its order-based spectral analysis for Regime D, for a direct comparison with the analogous analysis presented in Fig.6. Figure 10 reports the same quantities relative to Regime B, that for these new tests is more interesting since it corresponded to the speed achieved during the runup at the twelfth second when the resonant frequency f1

* was excited by the crankshaft order 1. In these figures the resonant frequencies are appreciable as quite widespread hills among the narrowband peaks corresponding to the crankshaft orders and transmission shaft orders. Since the harder rubber entails a higher stiffness of the flexible coupling, it is reasonable concluding that the natural frequencies f0 and f1 of the 45 Sh rubber coupling (corresponding respectively about to 0.10 and 0.45 crankshaft orders, for Regime D, Fig.6b) moved to the higher values f0

* and f1* for the 70 Sh

rubber coupling (corresponding about to 0.20 and 0.77 orders for Regime D, Fig.9b, and to 0.25 and 0.96 for Regime B, Fig.10b). No other natural frequencies seemed to be excited for the 70 Sh rubber coupling for any regime achieved in the runup and in the stationary tests.

Just before concluding that the substitution of the rubber elements of the coupling could be a viable low-cost solution of the original problem, it is sensible wondering if the stiffening effect of the harder rubber induced secondary effects, possibly troublesome, in other parts of the driveline. To this aim, the IAS nc of the crankshaft is compared both for the runup and stationary tests. The colormaps in Figure 11 (sharing the same full scale) report the comparison between the STFTs of nc, whereas Table 3 reports the RMS values of the crankshaft velocity oscillations, Δnc, and the IR values computed for the seven stationary tests. The data analysis reveals that the oscillations of nc were slightly higher at low-medium regimes in the case of the 70 Sh rubber, but to a negligible extent so that no problematic operations were induced on the whole system. The same conclusion could be drafted by observing the signals measured by the tri-axial accelerometer placed on the engine block support, which were basically the same for the two test campaigns (Table 4 reports data relative to the runup tests). This would suggest that the use of the hard rubber should not cause an increment of the

Fig. 9: Results relative to 70 Sh rubber elements: (a) nrel for Regime D stationary test; (b) Order analysis of nrel.

Fig. 10: Results relative to 70 Sh rubber elements: (a) nrel for Regime B stationary test; (b) Order analysis of nrel.

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dynamic forces loading the mechanical components of the driveline (in particular the gears), thus avoiding negative secondary effects.

3.3 Discussion The increment of the rubber hardness entailed a higher stiffness of the flexible coupling (and thus of the entire driveline), with an increment of the system natural frequencies and a corresponding decrement of the torsional oscillations. In particular, the low frequency resonance was subjected to an increment of about 100% passing from the 45 Sh rubber (f0) to the 70 Sh rubber (f0

*). This is a negative effect since f0

* could be excited by crankshaft order 0.5, at low velocity. The second natural frequency increases of about 70% passing from f1 for the 45 Sh rubber to f1

* for the 70 Sh rubber. The third natural frequency f2 was the most critical for the global dynamic behavior of the flexible coupling with the 45 Sh rubber elements. The introduction of the 70 Sh rubber made the third natural frequency increase to such an extent that it was not excited with sufficient energy by none of the main orders dominating the coupling response. The same can be stated for frequencies f3 and f4. This is certainly the major effect that can be observed and is definitely positive for the global dynamic behavior of the system.

As a consequence, for the coupling with 70 Sh rubber elements the first two frequencies dominated the system response in terms of torsional oscillations: the first one, f0

*, was excited by crankshaft order 0.5 at low velocities whereas the second one, f1

*, was excited by order 1 at a velocity which was about the 50% of the maximum speed achieved in the runup tests. The corresponding oscillations, in terms of relative velocity amplitude (nrel), were pretty limited, exhibiting a RMS value of nrel significantly smaller than in the case of the soft rubber (74 rpm and 156 rpm for the 70 Sh and 45 Sh rubber elements, respectively).

The only drawback provided by the rubber substitution was observed at the lowest velocities, for which the oscillations of both nc and nrel were higher for the 70 Sh rubber. On the other hand, such regimes are unfrequently kept during typical operations of the engine test rig, so that the simple substitution of the 45 Sh rubber elements with 70 Sh ones could represent a solution more than acceptable to solve the problem of the rubber collapse induced by the coupling torsional oscillations.

A further numerical investigation, reported in [1]

Fig. 11: Time-frequency analysis of crankshaft IAS nc computed for the runup tests with (a) the 45 Sh rubber and (b) the 70 Sh rubber. Table 3. Crankshaft velocity oscillations RMS value, Δnc, and irregularity ratio, IR, computed for the stationary tests performed with the two flexible couplings.

nc Δnc [rpm] IR [%]

Sh 45 Sh 70 Sh 45 Sh 70 Regime A 319 368 22.6 25.6 Regime B 177 239 7.8 10.6 Regime C 153 205 6.0 7.8 Regime D 193 182 7.0 6.2 Regime E 187 159 6.4 4.8 Regime F 176 144 5.0 4.0 Regime G 144 139 3.6 3.2

Table 4. RMS values of the three components of the engine block support acceleration (m/s2) during runup.

Vertical Transversal Longitudinal Sh 45 265 359 392 Sh 70 263 364 395

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(validated on the base of this experimental data), was performed in order to find out the optimal variant of the transmission driveline which both minimizes speed oscillations and requires an acceptable modification of the system components (in terms of complexity of intervention on the cell layout). In particular the optimal solution would consist of (i) a coupling having 60 Sh rubber elements and lightened flanges, (ii) a lighter transmission shaft, and (iii) a heavier flywheel on the engine crankshaft.

4 Conclusion The paper illustrates the investigation on the driveline of a test rig for internal combustion engines from the experimental point of view. The focus was placed on the torsional vibrations of the flexible coupling, that were supposed to be the cause of the frequent early collapse of its rubber elements. A first campaign performed on the current test rig permitted to quantify the torsional oscillations (measured in terms of relative velocity between its two ends) and to identify the main resonances dominating the system dynamic response. In particular, one of the natural frequency (f2), widespread in a pretty large bandwidth, could be excited for many engine regimes and was thus defined as the main target of possible interventions to modify the coupling elastodynamic properties. A second campaign was performed after changing the rubber elements of the flexible coupling, in particular using a harder (and consequently stiffer) rubber. The system response significantly improved,

i.e. the coupling torsional oscillations were largely lower, thus entailing limited dynamic loads acting on the critical components. The data analysis permitted to verify that the previously critical resonance f2 moved out of the bandwidth excited by the engine operations (basically by the crankshaft orders 0.5, 1, 1.5, and 2). The secondary, and possibly negative, effects of the rubber substitution resulted not troublesome, so that this simple modification could represent a viable solution to solve the original problem with a minimum cost in terms of structural modifications of the cell. References: [1] M. Cocconcelli, A. Agazzi, E. Mucchi, G.

Dalpiaz, R. Rubini, “Dynamic Analysis of Coupling Elements in IC Engine Test Rigs”, Proceedings of ISMA 2014, September 15-17, 2014, Leuven (Belgium)

[2] K.R. Fyfe, E.D.S. Munck, “Analysis of computed order tracking”, Mechanical Systems and Signal Processing, Vol. 11, No. 2, 1997, pp. 187–205.

[3] S. Gade, H. Herlufsen, H. Konstantin-Hansen, N.J. Wismer, “Order Tracking Analysis", Technical Review No. 2, Brüel & Kjær, 1995.

[4] A.V. Oppenheim, R.W. Schafer, J.R. Buck, Discrete-time signal processing, Prentice-Hall, 1999.

[5] R.X. Gao, R. Yan, “From Fourier Transform to Wavelet Transform: A Historical Perspective”, in: Wavelets - Theory and Applications for Manufacturing (Chapter 2), Springer, 2011

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