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发布日期:2021年04月14日



TORSIONAL VIBRATION CALCULATION OF A SHAFT

Torsional vibration calculation of a shaft to find natural frequency of a uniform shaft with a concentrated end mass. Shaft is fixed from one end and the other end is free (cantilevered shaft).

Torsional Vibration Calculator of a Shaft:

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Torsional Vibration Calculator of a Shaft
 INPUT PARAMETERS
Parameter Value
Density of shaft [ps]
Shaft outer diameter [do]
Shaft inner diameter [di]
Shaft length [l] 全程露脸东北老女 全程露脸东北老女 ,星球大战克隆人战争第五季 星球大战克隆人战争第五季
Modulus of rigidity [G]
Mass moment of inertia of end mass [J]

Note: Use dot "." as decimal separator.


 RESULTS
Parameter Value全程露脸东北老女 全程露脸东北老女 ,星球大战克隆人战争第五季 星球大战克隆人战争第五季
Polar second moment of area of uniform shaft [K] ---
Mass moment of inertia of uniform shaft [Js] ---
First torsional natural frequency of the system [f1] --- Hz


Definitions:

Modulus of rigidity (modulus of elasticity in shear): The rate of change of unit shear stress with respect to unit shear strain for the condition of pure shear within the proportional limit. Typical values Aluminum 6061-T6: 24 GPa, Structural Steel: 79.3 GPa.

Polar Moment of Inertia: A geometric property of cross section. Measure of ability how a beam resists torsion.

Torsional Vibration Equations:

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Equation
Polar second moment of area of a hollow shaft [K]
$$K=\frac { 1 }{ 2 } \pi \left( { r }_{ o }^{ 4 }-{ r }_{ i }^{ 4 } \right) $$
Mass moment of inertia of a hollow shaft [Js]
$${ J }_{ s }=\frac { 1 }{ 2 } { m }_{ s }\left( { r }_{ i }^{ 2 }+{ r }_{ o }^{ 2 } \right) $$
First torsional natural frequency of the system (Approximately) [f1]
 $${ f }_{ 1 }=\frac { 1 }{ 2\pi } \sqrt { \frac { GK }{ (J+{ J }_{ s }/3)l } }  $$

ms - Shaft mass, J - Mass moment of inertia of the point mass, l - Length of the shaft,  ri- Hollow shaft inner radius, ro - Shaft outer radius

Supplements:

Reference:

  • Young, W. C., Budynas, R. G.(2002). Roark's Formulas for Stress and Strain . 7nd Edition, McGraw-Hill, Chapter 16 , pp 767 - 768
  • 全程露脸东北老女 全程露脸东北老女 ,星球大战克隆人战争第五季 星球大战克隆人战争第五季