BIZOMAT MAKEOS · Strength
Press and Shrink Fit Pressure and Holding Torque
What contact pressure, hub stress and holding torque does this interference give?
Interface pressure of a hub on a solid or hollow shaft from the diametral interference (Lamé), hub bore stresses, torque and axial holding capacity, and the hub temperature rise for a shrink fit.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Interface diameter | mm | Nominal diameter of the fit. |
| Hub outside diameter | mm | Outside diameter of the hub around the fit. |
| Shaft bore (0 = solid) | mm | Bore of a hollow shaft; 0 for solid. |
| Diametral interference | mm | Shaft diameter minus hub bore diameter; use the minimum for holding capacity and the maximum for stress. |
| Engagement length | mm | Length of the fitted contact. |
| Coefficient of friction at interface | Friction coefficient for the assembled fit, from tests or your design guide (assembly method and surface finish affect it). | |
| Materials | ||
| Hub elastic modulus | GPa | Hub material modulus. |
| Hub Poisson’s ratio | Hub Poisson’s ratio. | |
| Shaft elastic modulus | GPa | Shaft material modulus. |
| Shaft Poisson’s ratio | Shaft Poisson’s ratio. | |
| Hub yield strength | MPa | Minimum yield strength of the hub material. |
| Required safety factor on hub | Factor of safety required by your design code, customer specification or company standard. | |
| Shrink fitting | ||
| Hub expansion coefficient | µm/(m·K) | Linear expansion coefficient of the hub material over the heating range. |
| Assembly clearance wanted when hot | mm | Extra clearance needed to slide the hot hub on (often about 0.001 × d). |
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: Interface diameter
- What it is
- The nominal diameter at the fitted surface, where the shaft and hub bore meet.
- 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 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the nominal fit size, not the shaft or bore limit sizes.
What this means: Hub outside diameter
- What it is
- The outside diameter of the hub around the fit: the outer boundary of the material that grips the shaft.
- 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 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must be larger than the fit diameter; a thin hub gives low pressure and high hoop stress.
What this means: Shaft bore (0 = solid)
- What it is
- The bore of a hollow shaft at the fit. Zero means a solid shaft.
- 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 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must be smaller than the fit diameter; a bore makes the shaft more flexible and lowers the contact pressure.
What this means: Diametral interference
- What it is
- The diametral interference: how much larger the shaft diameter is than the hub bore before assembly.
- 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 0.04 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Contact pressure, hub stress and holding torque rise in proportion to it.
- Get it right
- Use the diameter difference, not the radial one. Run the minimum for holding capacity and the maximum for hub stress.
What this means: Engagement length
- What it is
- The axial length over which the shaft and hub are actually in contact.
- 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 60 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Holding torque and axial force rise in proportion to it.
- Get it right
- Exclude chamfers, grooves and any part of the hub that overhangs the shaft.
What this means: Coefficient of friction at interface
- What it is
- The coefficient of friction between the shaft and hub surfaces in the assembled fit, which turns contact pressure into holding force.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 to 2. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.15 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Holding torque and axial force rise in proportion to it.
- Get it right
- Take it from tests or your design guide; assembly method, lubrication and surface finish change it.
Materials
What this means: Hub elastic modulus
- What it is
- The elastic modulus (Young’s modulus) of the hub material, from the material data sheet.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 1000 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter GPa, not MPa: 1 GPa is 1000 MPa.
What this means: Hub Poisson’s ratio
- What it is
- Poisson’s ratio of the hub material, from the material data sheet.
- 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 dimensionless ratio, not a percentage.
What this means: Shaft elastic modulus
- What it is
- The elastic modulus (Young’s modulus) of the shaft material, from the material data sheet.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 1000 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter GPa, not MPa: 1 GPa is 1000 MPa.
What this means: Shaft Poisson’s ratio
- What it is
- Poisson’s ratio of the shaft material, from the material data sheet.
- 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 dimensionless ratio, not a percentage.
What this means: Hub yield strength
- What it is
- The minimum yield strength of the hub material, from the material certificate or specification. The hub’s von Mises stress at the bore is compared with it.
- 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 350 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, not a typical value.
What this means: Required safety factor on hub
- What it is
- The minimum ratio of hub yield strength to hub von Mises stress the fit must achieve, from your design code, customer specification or company standard.
- 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 1.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- This is a requirement you set; the tool only compares the calculated factor with it.
Shrink fitting
What this means: Hub expansion coefficient
- What it is
- The coefficient of linear thermal expansion of the hub material over the heating range, used to work out how much the hub must be heated to slide on.
- Units and format
- Enter a number in µm/(m·K): micrometres per metre per kelvin. The form accepts 0.000001 µm/(m·K) to 100 µm/(m·K). Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 11.5 µm/(m·K) as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher coefficient lowers the heating temperature needed.
- Get it right
- Enter µm/(m·K), which is the same number as ×10⁻⁶ per K.
What this means: Assembly clearance wanted when hot
- What it is
- The extra diametral clearance wanted between the heated hub bore and the shaft so the hub slides on freely before it cools.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.03 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It is added to the interference when calculating the heating temperature.
Method and formulas
- p = δ ÷ [d((D² + d²) ÷ (D² − d²) + νh) ÷ Eh + d((d² + di²) ÷ (d² − di²) − νs) ÷ Es].
- Hub hoop at bore σθ = p(D² + d²) ÷ (D² − d²); von Mises with σr = −p.
- Torque T = μ p π d² L ÷ 2; axial force F = μ p π d L.
- Temperature rise ΔT = (δ + clearance) ÷ (α d).
- Example: 0.04 mm interference on a 50 mm steel fit in a 100 mm hub gives p = 60 MPa and holds 2,120.6 N·m.
Limitations
- Elastic, plane-stress Lamé solution for equal-length hub and shaft; hub ends and keyways raise local stresses.
- Surface smoothing reduces effective interference on rough surfaces.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check gears, couplings and pulleys pressed on shafts
- Find the heating temperature for a shrink fit
- Compare interference with torque requirement
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Interface pressure
- Hub hoop and von Mises stress at the bore
- Holding torque and axial force
- Hub temperature rise for shrink fitting
Interpreting the result
- Check holding capacity at minimum interference and hub stress at maximum interference.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 631–634. 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
Interference fits on hollow shafts
In Stress Transformation by the Numbers
What it covers: How a hub shrunk onto a shaft creates pressure and stress in both parts, how to design the fit from the torque, why a hollow shaft's bore needs checking, and how to check the limits.
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Open the Press and Shrink Fit Pressure and Holding Torque calculator