8 Characterization of Torsional Vibrations: Torsional-Order Based Modal Analysis 89 8.5 Conclusions The challenge of this work is the extension of the OBMA to torsional vibrations problems (e.g. car engine). For this reason, the Torsional Order Based Modal Analysis (T-OBMA) technique has been developed. It allows the identification of torsional modes of a shaft by applying OBMA to orders obtained from the rpm measured traces. It takes into account only the measured tachometer signals. If these are measured with a good accuracy, the torsional modes identification in terms of natural frequencies and damping ratios can be performed. This tool will be helpful in the automotive domain, where the problem of torsional vibrations is quite important. The main objective is to fully understand and propose solutions (Multi-orders algorithm) to the limitations occurring when trying to apply Order Based Modal Analysis (OBMA) to rpm measurements. There are several parameters and considerations which must be taken into account when choosing the order tracking technique to apply to the acquired data. It is important to know which is the reason why an order tracking step is going to be performed. For instance, if the aim is the dynamic analysis of the rotating system by means of T-OBMA technique, then a particular care need to be reserved to the phase of the orders. In fact this is an essential part of the measurement function especially when curve-fitting methods are used afterwards (like in modal analysis). If the main scope is to analyze only at which frequencies orders are facing a resonance or at which frequency the highest order amplitude is obtained, then most of the techniques will be able to give these kind of information. Further steps to be performed in the future involve the validation of the approach on a FE simulation model and the validation in an experimental case in which the rpms are measured at several locations along the shaft (and not only at the edges of the shaft). References 1. Wu, H.L., Shao, C., Feng, Z.D.: A study of the torsional vibration of automotive power trains. In: Proceedings of 2nd International Pacific Conference on Automotive Engineering, Tokyo (1983) 2. Reik W.: Torsional vibrations in the drive train of motor vehicles. In: Proceedings of 4th LuK International Symposium, Baden-Baden (1990) 3. Centea, D., Rahnejat, H., Menday, M.T.: Non-linear multi-body dynamic analysis for the study of clutch torsional vibrations. Appl. Math. Model. 25(3), 177–192 (2001) 4. Kushwaha, M., Gupta, S., Kelly, P., Rahnejat H.: Elasto-multi-body dynamics of a multicylinder internal combustion engine. In: Proceedings of the Institution of Mechanical Engineers (2002) 5. Rajendran, S., Narasimhan, M.V.: Effect of inertia variation due to reciprocating parts and connecting rod on coupled vibration of crankshaft. J. Eng. Gas Turbines Power 119, 257–264 (1997) 6. Peeters, B., Van der Auweraer, H., Vanhollebeke, F., Guillaume, P.: Operational modal analysis for estimating the dynamic properties of a stadium during a football game. Shock Vib. 11, 395–409 (2004) 7. Janssens, K., Kollar, Z., Peeters, B., Pauwels, S., Van der Auweraer, H.: Order-based resonance identification using operational polymax. In: Proceedings of 24th International Modal Analysis Conference (IMAC), Saint Louis (2006) 8. Di Lorenzo, E., Manzato, S., Vanhollebeke, F., Goris, S., Peeters, B., Desmet, W., Marulo, F.: Dynamic characterization of wind turbine gearboxes using order-based modal analysis. In: Proceedings of 26th International Conference on Noise and Vibration Engineering (ISMA), Leuven (2014) 9. Di Lorenzo, E., Manzato, S., Peeters, B., Marulo, F., Desmet, W.: Best practices for using order-based modal analysis for industrial applications. In: Proceedings of 35th International Modal Analysis Conference (IMAC), Los Angeles (2017) 10. Heylen, W., Lammens, S., Sas, P.: Modal Analysis Theory and Testing. KU Leuven, Department Werktuigkunde, Leuven (2007) 11. Di Lorenzo, E.: Operational Modal Analysis for rotating machines: challenges and solutions. Ph.D. thesis, KU Leuven, Leuven, Belgium and University of Naples “Federico II”, Naples (2017)
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