TORSIONAL VIBRATION OF A SHAFT

Torsional vibration of a shaft calculator was developed to calculate 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). The formulas used for vibration of unifrom shaft calculations are given in the "List of Equations" section.


Calculator:

Torsional stress of solid shaft
 INPUT PARAMETERS
Parameter Symbol Value Unit
Density of shaft ps
Shaft outer diameter do
Shaft inner diameter di
Shaft length l
Modulus of rigidity G
Mass moment of inertia of end mass J

Note: Use dot "." as decimal separator.

 


 RESULTS
Parameter Symbol Value Unit
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.


List of Equations:

Parameter/Condition Symbol Equation
Polar second moment of area of a hollow shaft K Equation for polar second moment of area of a hollow shaft
Mass moment of inertia of a hollow shaft Js Equation for mass moment of inertia of a hollow shaft
First torsional natural frequency of the system (Approximately) f1 Equation for first torsional natural frequency of the torsional vibration

Symbol Parameter
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

Reference: