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Rotating Discs and Cylinders
The Stresses and Strains generated in a rotating disc or cylinder.
Contents
Introduction
The rotation of a fast moving disc or cylindrical member can set up axial, circumferential and radial stresses. For instance, in the turbine section of an aircraft gas turbine engine, the rotor disc frequently turns at speeds in the region of 10000 r.p.m. This generates large amounts of stresses and strains on the material of the rotor disc. Similar loads are bourne by the cylindrical turbine rotor shafts that transmit the rotational movement from the turbine to the compressor section. To design a disc or shaft that can withstand these stresses without catastrophic failure in flight, it is important to understand the loads acting on them. This section analyses the stress and strains acting on rotating discs and cylinders.
Discs Of Uniform Thickness.
For a "thin" disc it can be assumed that the Stress in the Axial direction is zero. Due to the rotation of the disc, Circumferential







A Solid Disc
Since the Stresses can not be infinite at the centre of a solid Disc, B must be zero. If R is the outside radius of the disc then rewriting equations (14) and (15): From Which: At the centre r = 0 and so: This is the Maximum Stress. At the outside :

A Disc With A Central Hole
The Radial Stress is Zero at both the inner and outer radii. If the value of these is




Example:
[imperial]
Example - Stress in a hollow uniform disc
Problem
A thin uniform disc of 10 in. diameter with a central hole of 2 in. , runs at 10,000 r.p.m. Calculate the maximum Principal Stress and the maximum Shear Stress in the disc. Take
and Density = 0.28 lb.in.-3

Workings
The maximum Principal Stress will be at the inside and is given by equation (31)
The maximum Shearing Stress at any radius is given by:
It can be seen from the diagram that the greatest Stress difference occurs at and the Maximum Shearing Stress is:
Solution
The maximum Principal Stress = 16,500 lb.in-2
The maximum Shear Stress = 8250 lb.in.-2
Long Cylinders
Assume that the Longitudinal Stress is



A Disc Of Uniform Strength
Consider the condition of equal stress at all radii, i.e.





Example:
Example - A Disc Of Uniform Strength
Problem
A Turbine rotor Disc is 24 in. Diameter at the blade ring and is keyed to a 2 in diameter shaft. If the minimum thickness is 3/8 in. what should be the thickness at the shaft for a uniform stress of 30,000 lb./in2. aqt 10,000 r.p.m.? Density of material = 0.28 lb./in3.
Workings
Solution
The required thickness = 2.5 inches