STRESSES IN ROTATING RINGS (ANNULAR DISKS)

Stresses in Rotating Rings Calculator was developed to calculate radial / tangential stresses (inertia stresses), the change of the inner and outer radiuses of a ring which rotates about its own axis with a uniform angular velocity. The calculator is valid for homogeneous annular disk of uniform thickness. It has been assumed that the effect of deformation could be ignored and the rotating ring is rigid. Rotating elements, such as flywheels and blowers, can be simplified as a rotating ring and stress calculation can be done..The formulas used for calculations are given in the List of Equations section.

If there are radial pressures or pulls distributed uniformly along either the inner or outer perimeter of the disk, these stresses shall be superimposed upon the inertia stresses calculated here. Stresses, moments, and shears due to balanced forces (including gravity) shall also be superimposed upon calculated values in here.


Calculator:

Torsional stress of solid shaft
 INPUT PARAMETERS
Parameter Symbol Value Unit
Rotation speed w rpm
Shaft outer radius R
Shaft inner radius R0
Radius to the stress element
under consideration
r
Density p
Poisson's Ratio ν ---
Elastic Modulus  E

Note: Use dot "." as decimal separator.

 


 RESULTS
Parameter Symbol Value Unit
Radial Tensile Stress  (at any point
with a distance r from the center)
σr ---
Tangential Tensile Stress (at any point
with a distance r from the center)
σt ---
Maximum Radial Stress r)max ---
Maximum Tangential Stress t)max ---
Dimensional Change in the Outer Radius ∆R ---
Dimensional Change in the Inner Radius ∆R0 ---


List of Equations:

Step Parameter/Condition Symbol Equation
1 Radial tensile inertia stress σr Radial tensile inertia stress formula for rotating ring
2 Tangential tensile inertia stress σt Tangential tensile inertia stress formula for rotating ring
3 Maximum radial stress r)max Maximum radial tensile inertia stress formula for rotating ring
4 Maximum tangential stress t)max Maximum tangential tensile inertia stress formula for rotating ring
5 Dimensional change in the outer radius ∆R Formula for dimensional change in outer radius due to inertia stress in rotating ring
6 Dimensional change in the inner radius ∆R0 Formula for dimensional change in inner radius due to inertia stress in rotating ring

Reference: