BIZOMAT MAKEOS · Strength
Rotating Disc Stress and Burst Margin
What stress does spinning cause in this solid or bored disc, and how fast can it run before yield?
Maximum centrifugal stress in a rotating solid disc or a disc with a central bore, its rim speed, safety factor against yield and the speed at which yield is reached.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Outside diameter | mm | Outside diameter of the disc. |
| Bore diameter (0 = solid) | mm | Diameter of the central bore; 0 for a solid disc. |
| Speed | rpm | Highest running speed, including overspeed conditions. |
| Density | kg/m³ | Material density. |
| Poisson’s ratio | Poisson’s ratio. | |
| Yield strength | MPa | Minimum yield strength from the material certificate or specification. |
| Required safety factor | Factor of safety required by your design code, customer specification or company standard. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Outside diameter
- What it is
- The outside diameter of the flat rotating disc, such as a flywheel, saw blade blank or grinding disc body.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 500 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Stress rises with the square of the outside radius, so a larger disc at the same speed is far more highly stressed.
What this means: Bore diameter (0 = solid)
- What it is
- The diameter of the central hole for the shaft; a value of zero treats the disc as solid.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Even a small bore roughly doubles the peak stress compared with a solid disc, so do not enter zero for a bored disc.
What this means: Speed
- What it is
- The rotational speed of the disc, which should be the highest it can reach, including overspeed or runaway conditions.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 1000000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3000 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Stress rises with the square of speed, so 10 % more speed gives about 21 % more stress.
- Get it right
- Use revolutions per minute, not rad/s. Design for the maximum speed, not the normal running speed.
What this means: Density
- What it is
- The density of the disc material, which sets the centrifugal load on each element of the disc.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 50000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7850 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Stress rises in direct proportion to density.
- Get it right
- Enter kilograms per cubic metre, not grams per cubic centimetre.
What this means: Poisson’s ratio
- What it is
- Poisson’s ratio of the disc material, which enters the elastic stress distribution in the spinning disc.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 0.5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It is a ratio, not a percentage; take it from the material data sheet.
What this means: Yield strength
- What it is
- The minimum yield strength of the disc material, compared with the peak centrifugal stress to give the safety factor and the yield speed.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 250 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the specified minimum or certificate value, not a typical value.
What this means: Required safety factor
- What it is
- The minimum ratio of yield strength to peak stress that your design code or specification requires for this rotating part.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 20. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from your code or customer specification, not from the example.
Method and formulas
- ω = 2πn ÷ 60; outer radius b, bore radius a.
- Solid disc: σmax = (3 + ν) ÷ 8 × ρ ω² b² (at the centre).
- Bored disc: hoop stress at the bore σmax = (3 + ν) ÷ 4 × ρ ω² (b² + (1 − ν) ÷ (3 + ν) a²).
- Stress rises with speed squared: yield speed = n √(S_y ÷ σmax).
- Example: a 500 mm steel disc with a 50 mm bore at 3000 rpm reaches 40.034 MPa at the bore.
Limitations
- Uniform-thickness flat disc; holes, keyways and blades add stress concentrations.
- Elastic stress; burst occurs above yield but the margin depends on ductility.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check flywheels, saw blades, pulleys and impellers for overspeed
- Find the yield speed of a disc
- Compare solid and bored discs
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Maximum stress and its location
- Rim speed
- Safety factor
- Speed at which yield is reached
Interpreting the result
- A small central bore roughly doubles the peak stress compared with a solid disc.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 187–190, 3000–3010. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Spinning safely
In Inertia and Flywheels by the Numbers
What it covers: How to check a rotating disc's stress, rim speed and speed margin, why a central hole doubles the stress, what an overspeed does, and how much energy a guard must contain if a rotor fails.
Method explained here · BIZOMAT original book
Centrifugal loads on discs and hammers
In Whirling Shafts by the Numbers
What it covers: The loads that speed itself puts on a rotor: centrifugal force on hammers and pins, hoop stress in rotating discs, why both rise with the square of speed, and a mill run 20% fast on a drive.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.