Torsional vibration

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Torsional vibration is 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, not only the torques applied or reacted are "smooth" leading to constant speeds, but also the rotating plane where the power is generated (or 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[edit]

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:

  • Internal combustion engine: The torsional vibrations of the not continuous combustion and the crank shaft geometry itself cause torsional vibrations[1]
  • Reciprocating compressor: The pistons experience discontinuous forces from the compression.[2]
  • Universal joint: The geometry of this joint causes torsional vibrations if the shafts are not parallel.
  • Stick slip: During the engagement of a friction element, stick slip situations create torsional vibrations.
  • Lash: Drive train lash can cause torsional vibrations if the direction of rotation is changed or if the flow of power, i.e. driver vs. driven, is reversed.

Crankshaft torsional vibration[edit]

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.

  • Alternating torques are generated by the slider-crank mechanism of the crankshaft, connecting rod, and piston.
    • The cylinder pressure due to combustion is not constant through the combustion cycle.
    • The slider-crank mechanism does not output a smooth torque even if the pressure is constant (e.g., at top dead centre there is no torque generated)
    • The motion of the piston mass and connecting rod mass generate alternating torques often referred to as "inertia" torques
  • Engines with six or more cylinders in a straight line configuration can have very flexible crankshafts due to their long length.
  • 2 Stroke Engines generally have smaller bearing overlap between the main and the pin bearings due to the larger stroke length, hence increasing the flexibility of the Crankshaft due to decreased stiffness.
  • There is inherently little damping in a crankshaft to reduce the vibration except for the shearing resistance of oil film in the main and conrod bearings.

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. [3]

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.

  • Viscous dampers consist of an inertia ring in a viscous fluid. The torsional vibration of the crankshaft forces the fluid through narrow passages that dissipates the vibration as heat. The viscous torsional damper is analogous to the hydraulic shock absorber in a car's suspension.
  • Tuned absorber type of "dampers" often referred to as a harmonic dampers or harmonic balancers (even though it technically does not damp or balance the crankshaft). This damper uses a spring element (often rubber in automobile engines) and an inertia ring that is typically tuned to the first torsional natural frequency of the crankshaft. This type of damper reduces the vibration at specific engine speeds when an excitation torque excites the first natural frequency of the crankshaft, but not at other speeds. This type of damper is analogous to the tuned mass dampers used in skyscrapers to reduce the building motion during an earthquake.

Torsional vibrations in electromechanical drive systems[edit]

Torsional vibrations of drive systems usually result in a significant 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 more or less severe perturbation of the electromagnetic flux and thus additional oscillations of the electric currents in the motor windings. Then, the generated electromagnetic torque is also characterized by additional variable in time components which induce torsional vibrations of the drive system. According to the above, mechanical vibrations of the drive system become coupled with the electrical vibrations of currents in the motor windings. Such a coupling is often complicated in character and thus computationally troublesome. Because of this reason, till present majority of authors used to simplify the matter regarding mechanical vibrations of drive systems and electric current vibrations in the motor windings as mutually uncoupled. Then, the mechanical engineers applied the electromagnetic torques generated by the electric motors as ‘a priori‘ assumed excitation functions of time or of the rotor-to-stator slip, e.g. in paper [4][5][6] usually basing on numerous experimental measurements carried out for the given electric motor dynamic behaviours. For this purpose, by means of measurement results, proper approximate formulas have been developed, which describe respective electromagnetic external excitations produced by the electric motor,.[7] However, the electricians thoroughly modelled electric current flows in the electric motor windings, but they usually reduced the mechanical drive system to one or seldom to at most a few rotating rigid bodies, as e.g. in [8] In many cases, such simplifications yield sufficiently useful results for engineering applications, but very often they can lead to remarkable inaccuracies, since many qualitative dynamic properties of the mechanical systems, e.g. their mass distribution, torsional flexibility and damping effects, are being neglected. Thus, an influence of drive system vibratory behaviour on the electric machine rotor angular speed fluctuation, and in this way on the electric current oscillations in the rotor and stator windings, can not be investigated with a satisfactory precision.

Mechanical vibrations and deformations are phenomena associated with an operation of majority of railway vehicle drivetrain structures. The knowledge about torsional vibrations in transmission systems of railway vehicles is of a great importance in the fields dynamics of mechanical systems.[9] Torsional vibrations in the railway vehicle drive train are generated by several phenomena. Generally, these phenomena are very complex and they can be divided into two main parts.

  • To the first one belongs the electromechanical interaction between of the railway drive system including the: electric motor, gears, the driven part of disc clutch and driving parts of the gear clutch.[10]
  • To the second one belong torsional vibrations of the flexible wheels,[11][12] and wheelsets caused by variation of adhesion forces in the wheel-rail contact zone.[13]

An interaction of the adhesion forces has nonlinear features which are related to the creep value and strongly depends on the wheel-rail zone condition and track geometry (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 [14] This approach does not allow to analyse self-excited vibrations which have an important influence on the wheel-rail longitudinal interaction.[15] A dynamic modelling of the electrical drive systems coupled with elements of a driven machine [16][17] or vehicle is particularly important when the purpose of such modelling is to obtain an information about the transient phenomena of system operation, like a run-up, run-down and loss of adhesion in the wheel-rail zone. The modelling of an electromechanical interaction between the electric driving motor and the machine as well as to an influence of the self-excited torsional vibrations in the drive system.[18][19]

Measuring torsional vibration on physical systems[edit]

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[edit]

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:

  • AxSTREAM RotorDynamics, ( SoftInWay) - Commercial FEA-based program for performing the full scope of torsional analyses on the complete range of rotating equipment. Can be used to perform steady-state and transient, modal, harmonic and reciprocating machines analysis, and generates stability plot and Campbell diagrams quickly.
  • ARMD TORSION (Rotor Bearing Technology & Software, Inc.) - Commercial FEA-based software for performing damped and undamped torsional natural frequencies, mode shapes, steady-state and time-transient response of mechanical drive trains with inputs of various types of external excitation, synchronous motor start-up torque, compressor torques, and electrical system disturbances.

Bond Graphs can be used to analyse torsional vibrations in generator sets, such as those used aboard ships.[20]

See also[edit]


  • Nestorides, E.J., BICERA: A Handbook on Torsional Vibration, University Press, 1958, ISBN 0-521-04326-3
  • Parikyan, T. (2011). "Multi-cycle torsional vibration simulation with AVL EXCITE Designer". ASME Paper ICEF2011-60091. doi:10.1115/ICEF2011-60091. Cite journal requires |journal= (help)


  1. ^ Den Hartog, J. P. (1985). Mechanical Vibrations. Nineola, N.Y.: Dover Publications. p. 174. ISBN 0-486-64785-4.
  2. ^ Feese, Hill. "Prevention of Torsional Vibration Problems in Reciprocating Machinery" (PDF). Engineering Dynamics Incorporated. Retrieved 17 October 2013.
  3. ^ VULKAN Couplings System Competence - Torsional Vibration Calculation, retrieved 2021-06-06
  4. ^ 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.
  5. ^ A. Laschet A., Simulation von Antriebssystemen, Springer-Verlag, Berlin, Heidelberg, London, New-York, Paris, Tokio, 1988.
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  7. ^ A. Laschet A., Simulation von Antriebssystemen, Springer-Verlag, Berlin, Heidelberg, London, New-York, Paris, Tokio, 1988.
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  9. ^ 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.
  10. ^ 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.
  11. ^ 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.
  12. ^ R. Bogacz, R. Konowrocki, On new effects of wheel-rail interaction, Arch. Appl. Mech, Vol.82 (2012)1313-1323.
  13. ^ 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.
  14. ^ 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
  15. ^ 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.
  16. ^ 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, ISSN 0888-3270, Vol.49, pp.118-134, 2014
  17. ^ 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, ISSN 0888-3270, doi:10.1016/j.ymssp.2015.09.030, Vol.70-71, pp.397-413, 2016
  18. ^ Konowrocki R., Szolc T., An analysis of the self-excited torsional vibrations of the electromechanical drive system,Vibrations in Physical Systems, ISSN 0860-6897, Vol.27, pp.187-194, 2016
  19. ^ 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
  20. ^ Heeringa, T (2018-10-03). "Torsional Vibration Analysis by Bondgraph Modelling. A practical approach". Glasgow, UK. doi:10.24868/issn.2515-818X.2018.034. Cite journal requires |journal= (help)

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