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Stresses in Rotating Disks (Annular Rings) of Constant Thickness Equation and Calculator

Manufacturing, Design and Engineering

Stresses in Rotating Disks (Annular Rings) of Constant Thickness Equation and Calculator

A homogeneous annular disk of uniform thickness outer radius R, and weight per unit volume d, with a central hole of radius Ro, rotates about its own axis with a uniform angular velocity of ω rad/s. At any point a distance r from the center there is a radial tensile inertia stress.

Stresses in Rotating Disks (Annular Rings) of Constant Thickness Equation and Calculator

Preview: Stresses in Rotating Disks (Annular Rings) of Constant Thickness Calculator

Radial Tensile Inertia Stress:
Radial tensile inertia stress

Tangential Tensile Inertia Stress:
Tangential Tensile Inertia Stress

Maximum Radial Stress occurs at r = ( R · Ro )0.5
Maximum Radial Stress

Maximum radial tangential stress occurs at the perimeter of the hole:
Maximum radial tangential stress

Change in outer radius:
Change in outer radius

Change in inner radius:
Change in inner radius

Where:

R = outer radius of disk,(in, m);
Ro = inner radius of disk or radius of bore (in, m);
r = tensile inertia stress at some radial distance (in, m);
δ = Mass per unit volume (lbs/in3, (kg/m3);
g = G Force (386.4 in/s2, 9.81456 m/s2)
ω = Angular rotation speed (rad/s);
rpm = revolutions per minute
E = Elastic Modulus (psi, Pa);
v = Poisson's ratio.

Conversion:

1 rad/sec = 9.549296596425384 rpm
1 rpm = 0.104719755 rad/sec

Reference: Roark's Formulas for Stress and Strain, 7th Edition

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