Rotating Solid Disk

Description

A solid disk of radius 9" and thickness 1" rotates about its center with angular velocity ω = 25 rad/sec. Determine the stress distribution in the disk.

File Name

Browse to drive letter:\Users\Public\Public Documents\SOLIDWORKS\SOLIDWORKS version\samples\Simulation Examples\Verification\Static_18.SLDPRT and open the file.

Study Type

Static.

Mesh Type

Solid mesh.

Meshing Parameters

Use a Global Size of 0.25 in.

Material Properties

Modulus of elasticity = 3 X l07 psi, Poisson's ratio = 0.3, Density = 7.7244 lb/in3.

Modeling Hints

Due to symmetry, only a 45º wedge is analyzed.

Results

   

Theory

SOLIDWORKS Simulation
Location (r = 0.5") Radial stress (SX), psi 416.37 404.3
Tangential stress (SY), psi 416.91 415.8
Location ( r = 8.5") Radial stress (SX), psi 45.12 44.74
Tangential stress (SY), psi 203.16 202.8
To obtain the above results, define the SX and SY plots using Axis1 as a reference then use the Probe tool to probe these plots at the desired locations (X = ~ 0.35" and X = ~ 6.01").

Analytical Solution

s

Radial stress: SX = (3 + v / 8) * ρ* ω2 * (b2 - r2 )

Tangential stress: SY = (3 + v / 8) * ρ * ω2 * b2 - ( 1+ 3 v / 8 ) *ρ * ω2 * r2

where:
  • v: Poisson's ratio
  • ρ: Mass per unit volume
  • ω: Angular velocity
  • b: Disk radius
  • r: Radial distance

Reference

S. P. Timoshenko and J. N. Goodier, “Theory of Elasticity,” McGraw-Hill, New York, l970, p. 80.