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No shaft can ever be perfectly straight or perfectly balanced. When an element of mass is offset from the axis of rotation, centrifugal force will tend to pull the mass outward. The elastic properties of the shaft will act to restore the “straightness”. If the frequency of rotation is equal to one of
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will occur. In order to save the machine from failure, operation at such whirling speeds must be avoided. Whirling is a complex phenomenon that can include harmonics but we are only going to consider
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is used in mechanical engineering to determine the critical speed of a shaft-rotor system. Other methods include the
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353:{\displaystyle {\frac {1}{N_{N}^{2}}}={\frac {1}{N_{A}^{2}}}+{\frac {1}{N_{B}^{2}}}+\cdots +{\frac {1}{N_{n}^{2}}}}
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The whirling frequency of a symmetric cross section of a given length between two points is given by:
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Philosophical
Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
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A shaft with weights added will have an angular velocity of N (RPM) equivalent as follows:
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234:, m = mass of the shaft, L = length of the shaft between points.
220:{\displaystyle N=94.251{\sqrt {EI \over mL^{3}}}\ {\text{RPM}}}
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443:"NPTEL: Mechanical Engineering - Mechanical Vibrations"
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395:"On the Whirling and Vibration of Shafts"
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117:Learn how and when to remove this message
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145:the resonant frequencies of the shaft,
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55:adding citations to reliable sources
157:Dunkerley’s formula (approximation)
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230:where: E = Young's modulus, I =
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134:Rayleigh–Ritz method
18:Dunkerley's Method
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420:10.1098/rsta.1894.0008
393:Dunkerley, S. (1894).
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381:Notes and references
375:Mechanical resonance
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66:"Dunkerley's method"
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405:: 279–360.
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370:Vibration
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107:June 2015
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364:See also
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