.. _sphx_glr_api_gallery_mechanical_engineering_rotordynamics:

Rotordynamics
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Unbalanced rotors and critical speeds.


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    <div class="sphx-glr-thumbcontainer" tooltip="Rankine (1869) had argued that a shaft could not run stably above its whirling speed, yet de Laval&#x27;s steam turbines of the 1880s and 1890s did exactly that. Henry Jeffcott (1919) explained why with the simplest model: a disk whose centre of mass sits a small distance e from a flexible massless shaft. The shaft centre whirls in step with the spin at radius e r^2/\sqrt{(1 - r^2)^2 + (2\zeta r)^2}, with r the speed over the critical speed \sqrt{k/m} (~engineeringkit.mechanical_engineering.jeffcott_response). Through resonance the whirl swings round by half a turn. Far above it the heavy side of the disk faces inward and the disk spins about its own centre of mass, so the whirl radius settles at e. The force that reaches the bearings is the unbalance force (~engineeringkit.mechanical_engineering.rotating_unbalance_force) times the transmissibility (~engineeringkit.mechanical_engineering.transmissibility).">

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  .. image:: /api/gallery/mechanical_engineering/rotordynamics/images/thumb/sphx_glr_plot_01_jeffcott_rotor_thumb.png
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  :doc:`/api/gallery/mechanical_engineering/rotordynamics/plot_01_jeffcott_rotor`

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      <div class="sphx-glr-thumbnail-title">Jeffcott's rotor and the critical speed (1919)</div>
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   /api/gallery/mechanical_engineering/rotordynamics/plot_01_jeffcott_rotor