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INPUT   DATA

♥ EXAMPLE Of Input/Output

Title

Inside Radius, ri		m
Outside Radius, ro		m
Modulus of elasticity, E		109N/m2
Poisson's ratio, υ
Density of disk, ρ		kg/m3
Angular velocity, ω		rpm

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OUTPUT   VARIABLES   &   GRAPHS

VARIABLES	Values	Units	Graphs:  Stresses Vs Radial Distance
♦  Max Radial Stress, σr		N/m2
♦  Max Tangential Stress, σt		N/m2
♦  Increase in inner radius, Δri		10-6m
♦  Increase in outer radius, Δro		10-6m

Stresses In A Spinning Thin Disk

Engineering components that can be modelled as a thin rotating disc include the rotor of a turbine engine, saw blades, grinding wheels, and computer magnetic recording disks. A disk is usually considered thin if its thickness is less than 1/25 of its outer radius. Consider an homogeneous annular disk of uniform thicknesss and density, rotating about its own axis with a uniform angular velocity. The disk may be solid (r_i=0) or have a central circular hole (r_i>0) cut out. The resulting stresses and expansion of the disk are described by the following equations:

where
     σ_t = tangential stress variation within the material of the disc
     σ_r = stress variation in the radial direction
     r_i = inside radius
     r_o = ouside radius
     Δr = increase in radius
     E = modulus of elasticity of the material
     υ = Poisson's ratio of the material
     ρ = Density of the material

Tips

    ◊ Use link EXAMPLE Of Input/Output  to demo data entry expectations and results; you may edit & use it as starting point

BIBLIOGRAPHY

• Young WC & Budynas RG; Roark's Formulas for Stress and Strain; 7th Edition, McGraw Hill, New York, 2002, Chapter 16.
• Brown TH; Marks' Calculations for Machine Design; McGraw Hill, New York, 2005, Chapter 3.
• Moulton A, Grosjean J & Owen G; The Moulton Formulae and Methods - directly usable for calculations in mechanical engineering; Professional Engineering Publishing Ltd, London, UK, 2005.