BIZOMAT MAKEOS · Mechanics
Centrifugal Load on a Bolted Attachment (Overspeed and Bolt Stress)
What pull does centrifugal force put on the bolts holding this mass to a rotor, does it stay within the bolt allowable at overspeed, and at what speed would it reach the limit?
Check of a mass bolted to a rotating arm, hub or drum: centrifugal force at the running speed (as the centrifugal force tool), the force at your overspeed factor, the tension per bolt for bolts loaded radially, the bolt stress on the thread stress area, the safety factor against the allowable, and the speed at which the bolts would reach the allowable.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Attached mass | kg | Mass of the part held by the bolts. |
| Radius to its centre of gravity | mm | Radius from the axis to the part’s centre of gravity. |
| Running speed | rpm | Normal running speed. |
| Overspeed factor | Highest speed the rotor can reach as a multiple of running speed (governor or trip setting). | |
| Bolts carrying the pull | Number of bolts sharing the outward pull. | |
| Bolt diameter | mm | Bolt diameter. |
| Thread pitch | mm | Thread pitch. |
| Allowable bolt tensile stress | MPa | Allowable tensile stress in the bolts (your value; allow for preload and fatigue). |
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: Attached mass
- What it is
- The mass of the part bolted to the rotating arm, hub or drum, which the bolts must hold against the outward pull at speed.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0.000001 kg to 100000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Centrifugal force and bolt stress rise in direct proportion to mass.
- Get it right
- Include clamps, counterweights and anything else held by the same bolts.
What this means: Radius to its centre of gravity
- What it is
- The radial distance from the axis of rotation to the centre of gravity of the attached part, not to its bolts or its outer edge.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Force and bolt stress rise in direct proportion to this radius.
- Get it right
- For a long or offset part, measure to its centre of gravity, not to the bolt circle.
What this means: Running speed
- What it is
- The normal rotational speed of the arm, hub or drum carrying the part in service, before any overspeed.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 100000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1500 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Force rises with the square of speed, so 10 % more speed gives 21 % more pull.
What this means: Overspeed factor
- What it is
- The highest speed the rotor could reach, as a multiple of running speed, set by the governor, trip or drive limit. The bolts are checked at this speed.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 3. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The force at overspeed grows with the square of this factor.
- Get it right
- A multiplier, not a percentage: 10 % overspeed is entered as 1.1.
What this means: Bolts carrying the pull
- What it is
- The number of bolts that share the outward pull equally, each loaded in tension along the radius.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 100. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Stress per bolt falls in proportion to the number of bolts.
- Get it right
- Count only bolts that the pull loads in tension; bolts in shear or off the load path carry less.
What this means: Bolt diameter
- What it is
- The nominal (major) diameter of each bolt. With the thread pitch it gives the tensile stress area used for the bolt stress.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Bolt stress falls roughly with the square of the diameter.
- Get it right
- Use the nominal size, for example 10 for M10, not the minor diameter.
What this means: Thread pitch
- What it is
- The axial distance between neighbouring thread crests of the bolt, used with the diameter for the tensile stress area.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.25 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Coarse and fine metric threads have different pitches; for inch threads, pitch = 25.4 ÷ TPI.
What this means: Allowable bolt tensile stress
- What it is
- The tensile stress you allow in each bolt at overspeed, set from the bolt grade’s proof or yield strength with your own margin for preload and fatigue.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 2000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- A stress in MPa, not a load per bolt.
Method and formulas
- F = m ω² r (as the centrifugal force tool); at overspeed F × factor².
- Load per bolt = F ÷ bolts; stress = load ÷ A_s with A_s = π ÷ 4 (d − 0.9382P)².
- Speed at the allowable = running speed × √(allowable ÷ running stress).
- Example: 2 kg at 150 mm pulls 7,402.2 N at 1500 rpm and 10,659 N at overspeed, 72.792 MPa in each bolt.
Limitations
- Bolts loaded in pure tension; shear and bending from acceleration need separate checks.
- The rotor itself must be checked for the overspeed too.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check the bolts on a counterweight, beater or blade
- Set an overspeed trip for a rotating attachment
- Choose bolt size for a rotor fitting
Who it is for
- Design engineers
- Maintenance engineers
- Safety engineers
What you get
- Centrifugal force at running and overspeed
- Load and stress per bolt
- Safety factor and limiting speed
Interpreting the result
- Force rises with the square of speed: a 20% overspeed gives 44% more pull.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 187–190, 1521–1535. Topic reference; no source tables or recommended settings are reproduced.
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Open the Centrifugal Load on a Bolted Attachment (Overspeed and Bolt Stress) calculator