BIZOMAT MAKEOS · Strength
Interference Fit at Operating Temperature (Different Materials)
If the hub and shaft are different materials, how much interference is left at the operating temperature, does the fit still hold the torque hot, and is the hub overstressed at its tightest?
Check of an interference fit between a hub and shaft of different materials (aluminium on steel, bronze on steel): the interference at the operating temperature from the difference in expansion, contact pressure, holding torque and hub stress at assembly and at operating temperature (as the press and shrink fit tool), the torque against the required torque times the slip factor at the weaker condition, and the hub safety factor at the tighter one.
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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. |
| Shaft bore (0 = solid) | mm | Bore of a hollow shaft. |
| Diametral interference at assembly temperature | mm | Diametral interference at the assembly temperature. |
| Engagement length | mm | Length of the fit. |
| Coefficient of friction at interface | Friction coefficient at the interface. | |
| Materials | ||
| Hub elastic modulus | GPa | Elastic modulus of the hub. |
| Hub Poisson’s ratio | Poisson’s ratio of the hub. | |
| Hub expansion coefficient | µm/(m·K) | Expansion coefficient of the hub. |
| Hub yield strength | MPa | Yield strength of the hub. |
| Shaft elastic modulus | GPa | Elastic modulus of the shaft. |
| Shaft Poisson’s ratio | Poisson’s ratio of the shaft. | |
| Shaft expansion coefficient | µm/(m·K) | Expansion coefficient of the shaft. |
| Duty | ||
| Assembly temperature | °C | Temperature at which the interference is measured. |
| Operating temperature | °C | Temperature of the joint in service (both parts at the same temperature). |
| Torque to transmit | N·m | Torque the fit must transmit. |
| Safety factor on slip | Safety factor against slipping. | |
| Required safety factor on hub | Safety factor you need on hub yield. | |
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 where the hub bore and the shaft meet; it sets the contact pressure, the holding torque and the thermal change in interference.
- 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.
What this means: Hub outside diameter
- What it is
- The outside diameter of the hub around the fit; together with the interface diameter it sets how stiff the hub is in the radial direction.
- 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.
- Effect on the result
- A larger hub outside diameter stiffens the hub and raises the contact pressure for the same interference.
- Get it right
- If the hub is not plain, use the smallest outside diameter over the fit length, for example at a groove.
What this means: Shaft bore (0 = solid)
- What it is
- The diameter of the hole through 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.
- Effect on the result
- A larger bore makes the shaft more flexible and lowers the contact pressure for the same interference.
- Get it right
- Enter 0 for a solid shaft; a bore must be smaller than the interface diameter.
What this means: Diametral interference at assembly temperature
- What it is
- The shaft diameter minus the hub bore diameter, measured at the assembly temperature, taken on the diameter rather than per side.
- 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 0.08 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, holding torque and hub stress all rise in proportion to the interference.
- Get it right
- Enter the diametral value in millimetres: an interference of 50 µm is 0.05 mm.
What this means: Engagement length
- What it is
- The axial length over which shaft and hub are in contact, excluding chamfers and relief grooves.
- 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 rises in direct proportion to engagement length; pressure and hub stress do not change.
What this means: Coefficient of friction at interface
- What it is
- The friction coefficient between the shaft and hub surfaces at the joint, which converts the contact pressure into holding torque.
- 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 is proportional to the friction coefficient.
- Get it right
- Take it from test data or a design standard for your surfaces and assembly method; press fits and shrink fits can differ.
Materials
What this means: Hub elastic modulus
- What it is
- The elastic (Young’s) modulus of the hub material, from its data sheet; a stiffer hub produces more pressure from the same 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 70 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: the tool multiplies by 1000 internally.
What this means: Hub Poisson’s ratio
- What it is
- The Poisson’s ratio of the hub material, lateral strain divided by axial strain, from the material data sheet; it enters the hub term of the pressure formula.
- 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 0.33 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Hub expansion coefficient
- What it is
- The linear thermal expansion coefficient of the hub material, from its data sheet; it sets how much the hub bore grows as the joint warms.
- 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 23 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 hub that expands more than the shaft loses interference as the joint warms.
- Get it right
- µm/(m·K) is the same number as 10⁻⁶/K: type 12 for 12 × 10⁻⁶/K, not 0.000012.
What this means: Hub yield strength
- What it is
- The yield strength of the hub material, from the material certificate or data sheet; the hub’s von Mises stress at the tighter condition 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 250 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Shaft elastic modulus
- What it is
- The elastic (Young’s) modulus of the shaft material, from its data sheet; with the hub modulus it sets how much pressure the interference produces.
- 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: the tool multiplies by 1000 internally.
What this means: Shaft Poisson’s ratio
- What it is
- The Poisson’s ratio of the shaft material, from its data sheet; it enters the shaft term of the pressure formula.
- 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 expansion coefficient
- What it is
- The linear thermal expansion coefficient of the shaft material; the difference between the shaft and hub coefficients drives the change in interference.
- 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 11.5 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
- If the shaft coefficient exceeds the hub’s, heating tightens the fit; if it is lower, heating loosens it.
- Get it right
- µm/(m·K) is the same number as 10⁻⁶/K: type the number in front of 10⁻⁶, not the decimal fraction.
Duty
What this means: Assembly temperature
- What it is
- The temperature of both parts when the interference was measured or specified, normally workshop temperature, not the heating temperature used to shrink the hub on.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -100 °C to 500 °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.
What this means: Operating temperature
- What it is
- The temperature of the joint in service, taken as the same for hub and shaft; the change from assembly temperature alters the interference.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -100 °C to 500 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The tool assumes hub and shaft are at one temperature; transient heating of the hub alone is not modelled.
What this means: Torque to transmit
- What it is
- The working torque the fit must transmit in service without slipping, before the slip safety factor is applied.
- 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 300 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter the working torque only; the tool multiplies it by the slip safety factor, so do not include the factor twice.
What this means: Safety factor on slip
- What it is
- The multiplier on the torque to transmit; the fit must hold the torque times this factor at the weaker of the assembly and operating conditions.
- 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 1.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Required safety factor on hub
- What it is
- The least ratio of hub yield strength to hub von Mises stress you accept, checked at the tighter of the assembly and operating conditions.
- 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 1.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- Interference hot = δ₀ + d (α_shaft − α_hub)(T_op − T_a).
- At each interference: p = δ ÷ {d [(k_h + ν_h) ÷ E_h + (k_s − ν_s) ÷ E_s]}; torque = μ p π d² L ÷ 2; hub von Mises stress (as the press and shrink fit tool).
- Grip checked at the smaller interference; hub stress at the larger.
- Example: the interference drops from 80 to 34 µm at 100 °C, so the fit holds 750.48 N·m hot.
Limitations
- Both parts at the same uniform temperature; transient heating of the hub alone loosens the fit further.
- Thick-cylinder theory; stress concentrations at the hub ends are not included.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check an aluminium pulley or hub pressed on a steel shaft
- Check a bronze bush in a steel housing hot
- Choose interference for a fit that runs hot or cold
Who it is for
- Design engineers
- Machine designers
- Maintenance engineers
What you get
- Interference at operating temperature
- Pressure, torque and hub stress cold and hot
- Checks at the weaker and tighter conditions
Interpreting the result
- An aluminium hub on a steel shaft loosens as it warms: choose the interference for the hottest running condition.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 631–634, 375–376. 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
Compatibility, thermal restraint and locked-in stress
In Stress Transformation by the Numbers
What it covers: Why stresses need compatibility as well as equilibrium: restrained thermal expansion and buckling, a fit between different metals as temperature changes, and locked-in stress.
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Open the Interference Fit at Operating Temperature (Different Materials) calculator