Torsional vibration explained

Torsional vibration is the angular vibration of an object - commonly a shaft - along its axis of rotation. Torsional vibration is often a concern in power transmission systems using rotating shafts or couplings, where it can cause failures if not controlled. A second effect of torsional vibrations applies to passenger cars. Torsional vibrations can lead to seat vibrations or noise at certain speeds. Both reduce the comfort.

In ideal power generation (or transmission) systems using rotating parts, the torques applied or reacted are "smooth" leading to constant speeds, and the rotating plane where the power is generated (input) and the plane it is taken out (output) are the same. In reality this is not the case. The torques generated may not be smooth (e.g., internal combustion engines) or the component being driven may not react to the torque smoothly (e.g., reciprocating compressors), and the power generating plane is normally at some distance to the power takeoff plane. Also, the components transmitting the torque can generate non-smooth or alternating torques (e.g., elastic drive belts, worn gears, misaligned shafts). Because no material can be infinitely stiff, these alternating torques applied at some distance on a shaft cause twisting vibration about the axis of rotation.

Sources of torsional vibration

Torsional vibration can be introduced into a drive train by the power source. But even a drive train with a very smooth rotational input can develop torsional vibrations through internal components. Common sources are:

Crankshaft torsional vibration

Torsional vibration is a concern in the crankshafts of internal combustion engines because it could break the crankshaft itself; shear-off the flywheel; or cause driven belts, gears and attached components to fail, especially when the frequency of the vibration matches the torsional resonant frequency of the crankshaft. Causes of the torsional vibration are attributed to several factors.

If torsional vibration is not controlled in a crankshaft it can cause failure of the crankshaft or any accessories that are being driven by the crankshaft (typically at the front of the engine; the inertia of the flywheel normally reduces the motion at the rear of the engine). The couplings turn the vibration energy into heat. Therefore, and to ensure that the coupling is not damaged due to this (temperature could be very high, depending on the load), this is verified through torsional vibration calculation.

This potentially damaging vibration is often controlled by a torsional damper that is located at the front nose of the crankshaft (in automobiles it is often integrated into the front pulley). There are two main types of torsional dampers.

Torsional vibrations in electromechanical drive systems

Torsional vibrations of drive systems usually result in a fluctuation of the rotational speed of the rotor of the driving electric motor. Such oscillations of the angular speed superimposed on the average rotor rotational speed cause perturbations of the electromagnetic flux, leading to additional oscillations of the electric currents in the motor windings. Then, the generated electromagnetic torque is also influenced by additional time-varying electromechanical interactions, which lead to further torsional vibrations of the drive system. According to the above, mechanical vibrations/oscillations of the drive system become coupled with the electrical oscillations of the motor windings' currents. Such coupling is typically nonlinear and presents a high computational burden.

Due to the highly nonlinear and coupled nature of electromechanical oscillations, approximations are often used, enabling such oscillations to be characterized analytically. To simplify the characterization of the oscillations between mechanical and electric systems, it is common to assume the mechanical and electrical components are uncoupled. Then, by holding either the mechanical or electrical aspect in steady-state, the characteristic of the other can be calculated. A common method is to apply electromagnetic torques generated by the electric motors as assumed excitation functions of time or of the rotor-to-stator slip,[3] [4] [5] which are usually based on numerous experimental measurements carried out for a given electric motor's dynamic behaviour. For this purpose, by means of measurement results, i.e., empirically, formulas have been developed that provide good approximations for the electromagnetic external excitations produced by the electric motor.[6] Although the electric currents flowing in the electric motor windings are accurate, the mechanical drive system is typically reduced to one or seldom to at most a few rotating rigid bodies. [7] In many cases, such simplifications yield sufficiently useful results for engineering applications, but they can lead to inaccuracies since many qualitative dynamic properties of the mechanical systems, e.g., their mass distribution, torsional flexibility, and damping effects, are neglected. Thus, an influence of the oscillatory behaviour of drive systems on the electric machine rotor angular speed fluctuations, and in this way on the electric current oscillations in the rotor and stator windings, cannot be investigated with a satisfactory precision, excepting numerical methods, which can provide arbitrarily high accuracy.

Mechanical vibrations and deformations are phenomena associated with the operation of the majority of railway vehicle drivetrain structures. The knowledge about torsional vibrations in transmission systems of railway vehicles is of a great importance in the field of mechanical system dynamics.[8] Torsional vibrations in railway vehicle drivetrains are generated by many coupled mechanisms, which are very complex and can be divided into two main parts:

  1. The electromechanical interactions within the railway drivetrain system, including the electric motor, gears, and the driven parts of the disc and gear clutches.[9]
  2. Torsional vibrations of the flexible wheels[10] [11] and wheelsets caused by variations of the adhesion forces in the wheel-rail contact zone.[12]

An interaction of the adhesion forces has nonlinear features which are related to the creep value and strongly depend on the wheel-rail zone conditions and the track geometry (especially when driving on a curve section of the track). In many modern mechanical systems, torsional structural deformability plays an important role. Often the study of railway vehicle dynamics using the rigid multibody methods without torsionally deformable elements are used [13] This approach does not enable analysis of the self-excited vibrations, which have an important influence on the wheel-rail longitudinal interaction.[14] A dynamic modelling of the electrical drive systems coupled with elements of a driven machine [15] [16] or vehicle is particularly important when the purpose of such modelling is to obtain an information about the transient phenomena of system operation, like run-up, run-down, and the loss of adhesion in the wheel-rail zone. The modelling of an electromechanical interaction between the electric driving motor and the machine also influence the self-excited torsional vibrations in the drive system.[17] [18]

Measuring torsional vibration on physical systems

The most common way to measure torsional vibration is the approach of using equidistant pulses over one shaft revolution. Dedicated shaft encoders as well as gear tooth pickup transducers (induction, hall-effect, variable reluctance, etc.) can generate these pulses. The resulting encoder pulse train is converted into either a digital rpm reading or a voltage proportional to the rpm.

The use of a dual-beam laser is another technique that is used to measure torsional vibrations. The operation of the dual-beam laser is based on the difference in reflection frequency of two perfectly aligned beams pointing at different points on a shaft. Despite its specific advantages, this method yields a limited frequency range, requires line-of-sight from the part to the laser, and represents multiple lasers in case several measurement points need to be measured in parallel.

Torsional vibration software

There are many software packages that are capable of solving the torsional vibration system of equations. Torsional vibration specific codes are more versatile for design and system validation purposes and can produce simulation data that can readily compared to published industry standards. These codes make it easy to add system branches, mass-elastic data, steady-state loads, transient disturbances and many other items only a rotordynamicist would need. Torsional vibration specific codes:

Bond Graphs can be used to analyse torsional vibrations in generator sets, such as those used aboard ships.[19]

See also

Bibliography

External links

Notes and References

  1. Book: Den Hartog, J. P.. Mechanical Vibrations. 1985. Dover Publications. Nineola, N.Y.. 0-486-64785-4. 174.
  2. Web site: Feese, Hill. Prevention of Torsional Vibration Problems in Reciprocating Machinery. Engineering Dynamics Incorporated. 17 October 2013. 19 October 2013. https://web.archive.org/web/20131019133556/http://turbolab.tamu.edu/proc/turboproc/T38/ch18_Feese.pdf. dead.
  3. B. F. Evans, A. J. Smalley, H. R. Simmons, Startup of synchronous motor drive trains: the application of transient torsional analysis of cumulative fatigue assessment, ASME Paper, 85-DET-122, 1985.
  4. A. Laschet A., Simulation von Antriebssystemen, Springer-Verlag, Berlin, Heidelberg, London, New-York, Paris, Tokio, 1988.
  5. P. Schwibinger, R. Nordmann, Improvement of a reduced torsional model by means of parameter identification, Transactions of the ASME, Journal of Vibration, Acoustics, Stress and Reliability in Design, 111, 1989, pp. 17-26.
  6. A. Laschet A., Simulation von Antriebssystemen, Springer-Verlag, Berlin, Heidelberg, London, New-York, Paris, Tokio, 1988.
  7. L. Harnefors, Analysis of subsynchronous torsional interaction with power electronic converters, IEEE Transactions on power systems, Vol. 22, No. 1, 2007, pp. 305-313.
  8. R. Bogacz, T. Szolc, H. Irretier, An application of torsional wave analysis to turbogenerator rotor shaft response, J.Vibr. Acou. -Trans. of the Asme, Vol. 114-2 (1992) 149-153.
  9. O. Ahmedov, V. Zeman, M. Byrtus, Modelling of vibration and modal properties of electric locomotive drive, Eng. Mech., Vol. 19: 2/3 (2012) 165–176.
  10. S. Noga, R. Bogacz, T. Markowski, Vibration analysis of a wheel composed of a ring and a wheel-plate modelled as a three-parameter elastic foundation, J.Sound Vib., Vol. 333:24, (2014) 6706-6722.
  11. R. Bogacz, R. Konowrocki, On new effects of wheel-rail interaction, Arch. Appl. Mech, Vol.82 (2012)1313-1323.
  12. 5. V. Zeman, Z. Hlavac, Dynamic wheelset drive load of the railway vehicle caused by shortcircuit motor moment, App. & Comp. Mech., Vol.3, No.2 (2009)423–434.
  13. B.S. Branislav, Simulation of torsion moment at the wheel set of the railway vehicle with the traction electromotor for wavy direct current, Mech. Trans. Com., Issue 3 (2008) 6-9
  14. J. Liu, H. Zhao, W. Zhai, Mechanism of self-excited torsional vibration of locomotive driving system, Front. Mech. Eng.China, Vol.5:4 (2010,) 465-469.
  15. Szolc T., Konowrocki R., Michajłow M., Pręgowska A., An investigation of the dynamic electromechanical coupling effects in machine drive systems driven by asynchronous motors, Mechanical Systems and Signal Processing,, Vol.49, pp.118-134, 2014
  16. Konowrocki R., Szolc T., Pochanke A., Pręgowska A., An influence of the stepping motor control and friction models on precise positioning of the complex mechanical system, Mechanical Systems and Signal Processing,,, Vol.70-71, pp.397-413, 2016
  17. Konowrocki R., Szolc T., An analysis of the self-excited torsional vibrations of the electromechanical drive system, Vibrations in Physical Systems,, Vol.27, pp.187-194, 2016
  18. Konowrocki R., Analysis of electromechanical interaction in an electric drive system used in the high speed trains, ART Conference 2016, ADVANCED RAIL TECHNOLOGIES - 5th International Conference, 2016-11-09/11-11, Warsaw (PL), pp.1-2, 2016
  19. Book: Heeringa, T. Proceedings of the International Naval Engineering Conference and Exhibition (INEC). 2018-10-03. Torsional Vibration Analysis by Bondgraph Modelling. A practical approach. 14. https://zenodo.org/record/2530805. Glasgow, UK. 10.24868/issn.2515-818X.2018.034. free.