BIZOMAT MAKEOS · Strength
Shrink or Press Fit Design from Required Torque
What interference does a hub need to transmit this torque and thrust, will the hub survive it, and how hot must it be to assemble?
Design of a cylindrical interference fit working backwards from the duty: the interface pressure needed for the torque and axial load with a safety factor, the diametral interference that produces it (Lamé thick-cylinder theory, solid or hollow shaft), hub bore stresses with a von Mises check, the press-in force, and the hub heating temperature for a shrink fit with assembly clearance.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Duty | ||
| Torque to transmit | N·m | Torque the fit must carry. |
| Axial load to transmit | kN | Axial force the fit must carry. |
| Safety factor on slip | Safety factor against slip. | |
| Geometry and materials | ||
| Interface diameter | mm | Nominal diameter at the interface. |
| Shaft bore (0 = solid) | mm | Bore of a hollow shaft. |
| Hub outside diameter | mm | Outside diameter of the hub. |
| Engaged length | mm | Length of the fit. |
| Friction coefficient at the interface | Coefficient of friction at the interface (about 0.1–0.2 for dry steel press fits; shrink fits often higher). | |
| Hub modulus | GPa | Elastic modulus of the hub. |
| Hub Poisson’s ratio | Poisson’s ratio of the hub. | |
| Shaft modulus | GPa | Elastic modulus of the shaft. |
| Shaft Poisson’s ratio | Poisson’s ratio of the shaft. | |
| Hub yield strength | MPa | Yield strength of the hub material. |
| Assembly | ||
| Hub expansion coefficient | µm/m·K | Linear expansion coefficient of the hub. |
| Assembly clearance wanted (diametral) | mm | Clearance needed to slide the hot hub on. |
| Shaft (ambient) temperature | °C | Starting temperature of the parts. |
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.
Duty
What this means: Torque to transmit
- What it is
- The torque the fit must transmit by friction between shaft and hub without slipping.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0 N·m to 100000000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 500 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- With no axial load, the required pressure and interference rise in proportion to torque.
- Get it right
- Use the peak torque in service, not the average; the slip safety factor is applied on top.
What this means: Axial load to transmit
- What it is
- Any axial force the fit must carry at the same time as the torque; the tool combines the two as a vector at the interface.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0 kN to 1000000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- In kilonewtons; enter 0 if the fit carries torque only.
What this means: Safety factor on slip
- What it is
- The factor by which the friction capacity of the fit must exceed the torque and axial duty, as protection against slip.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 10. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Required pressure and interference rise in direct proportion to it.
Geometry and materials
What this means: Interface diameter
- What it is
- The nominal diameter where shaft and hub meet: the shaft outside diameter and the hub bore at the fit.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5000 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.
What this means: Shaft bore (0 = solid)
- What it is
- The bore of a hollow shaft at the fit. A hollow shaft is less stiff, so it needs more interference for the same pressure.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 5000 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
- 0 means a solid shaft; the bore must be smaller than the interface diameter.
What this means: Hub outside diameter
- What it is
- The outside diameter of the hub over the length of the fit.
- 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 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger hub diameter lowers the hub hoop stress and the interference needed.
What this means: Engaged length
- What it is
- The axial length over which shaft and hub are actually in contact.
- 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 60 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Required pressure falls in proportion to the engaged length.
- Get it right
- Leave out chamfers and relief grooves.
What this means: Friction coefficient at the interface
- What it is
- The coefficient of friction between the shaft and hub surfaces at the fit.
- Units and format
- Enter a plain number with no unit. The form accepts 0.01 to 1. 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
- Required pressure and interference are inversely proportional to it.
- Get it right
- Use a value for the actual finish, lubrication and assembly method (press or shrink), from test data or a design standard.
What this means: Hub modulus
- What it is
- The elastic modulus of the hub material, from its data sheet; a stiffer hub needs less interference for the same pressure.
- 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 206 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- In GPa, not MPa.
What this means: Hub Poisson’s ratio
- What it is
- Poisson’s ratio of the hub material, used in the hub’s share of the interference.
- 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.
What this means: Shaft modulus
- What it is
- The elastic modulus of the shaft material, from its data sheet, used in the shaft’s share of the interference.
- 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 206 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- In GPa, not MPa.
What this means: Shaft Poisson’s ratio
- What it is
- Poisson’s ratio of the shaft material, used in the shaft’s share of the interference.
- 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.
What this means: Hub yield strength
- What it is
- The yield strength of the hub material, compared with the von Mises stress at the hub bore.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 5000 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.
- Effect on the result
- It does not change the interference; it sets the pass or fail stress check.
- Get it right
- Use the minimum yield strength for the hub material and heat treatment from the material standard or certificate.
Assembly
What this means: Hub expansion coefficient
- What it is
- The coefficient of linear thermal expansion of the hub material, used to find how hot the hub must be to slide over the shaft.
- Units and format
- Enter a number in µm/m·K: micrometres per metre per kelvin. The form accepts 0.000001 µm/m·K to 50 µm/m·K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 11.7 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
- The hub temperature rise needed is inversely proportional to it.
- Get it right
- µm per metre per kelvin; a value given as 10⁻⁶/K is the same number.
What this means: Assembly clearance wanted (diametral)
- What it is
- The extra clearance you want between the heated hub bore and the shaft so the hub slides on freely during assembly.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 5 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.02 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More clearance raises the hub heating temperature.
- Get it right
- Diametral, not radial; it is added to the interference when working out the heating temperature.
What this means: Shaft (ambient) temperature
- What it is
- The temperature of the shaft during assembly, which is also the hub’s starting temperature before heating.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -50 °C to 200 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The hub temperature result moves up one for one with it.
Method and formulas
- Pressure for the duty: p = n √[(2T ÷ d)² + F_a²] ÷ (π d L μ).
- Interference δ = p d {[(D² + d²) ÷ (D² − d²) + ν_h] ÷ E_h + [(d² + d_i²) ÷ (d² − d_i²) − ν_s] ÷ E_s}.
- Hub bore hoop stress σ_t = p (D² + d²) ÷ (D² − d²); von Mises with the radial −p: √(σ_t² + σ_t p + p²).
- Press force = π d L μ p; hub temperature rise = (δ + clearance) ÷ (α d).
- Example: 500 N·m on a 50 mm fit 60 mm long needs 18.313 µm of interference.
Limitations
- Uniform pressure over the length; hub ends and keyways raise local stresses.
- Surface smoothing reduces effective interference; add roughness allowance.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Specify the interference for a gear, coupling or sleeve on a shaft
- Check that the hub can take the interference needed
- Set the induction or oven temperature for assembly
Who it is for
- Design engineers
- Mechanical engineers
- Engineering managers
What you get
- Required pressure and interference
- Hub stress check
- Press force and shrink-fit temperature
Interpreting the result
- Specify the minimum interference from this result and check the maximum interference against hub yield.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 631–633, 2442–2444. 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.
Method explained here · BIZOMAT original book
Thermal Expansion by the Numbers
What it covers: Calculate how parts, pipes, liquids and gases change with temperature: growth, measuring at 20 °C, thermal stress, pipe loops, shrink fits, expansion vessels, gas pressure and machine design.
Useful alongside · BIZOMAT original book
Shrink fitting with liquid nitrogen
In Cryogenic Liquids by the Numbers
What it covers: Check a fit against its torque, find a shaft’s real contraction from NIST’s integrated data, the temperature it needs and the time to assemble, and a constant-coefficient mistake.
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.
Open the Shrink or Press Fit Design from Required Torque calculator