BIZOMAT MAKEOS · Strength
Interference Fit Limits Check (IT Grades, Least and Most Interference, Torque, Stress)
With the hole and shaft tolerances I have chosen, will the fit still hold the torque at its least interference, and will the hub be overstressed at its most?
Check of an interference fit over its full tolerance range: the hole and shaft tolerances from the IT grades for the size (as the ISO tolerance grade tool), with a basic hole and your shaft lower deviation; the least and most interference; contact pressure and holding torque at the least interference against the torque times your slip factor; hub stress and safety factor at the most interference; press-in force and heating temperature for assembly at the most (as the press and shrink fit tool).
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Nominal interface diameter | mm | Nominal diameter of the fit. |
| Hole tolerance grade (basic hole, lower deviation 0) | choice | IT grade of the hole (basic hole: the hole’s lower deviation is zero). |
| Shaft tolerance grade | choice | IT grade of the shaft. |
| Shaft lower deviation (your fit) | µm | Lower deviation of the shaft from nominal for the fit you want (positive for an interference fit; from your fit standard). |
| Hub, shaft and materials | ||
| Hub outside diameter | mm | Outside diameter of the hub. |
| Shaft bore (0 = solid) | mm | Bore of a hollow shaft. |
| Engagement length | mm | Length of the fit. |
| Coefficient of friction at interface | Friction coefficient at the interface. | |
| Hub elastic modulus | GPa | Elastic modulus of the hub. |
| Hub Poisson’s ratio | Poisson’s ratio of the hub. | |
| Shaft elastic 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. |
| Required safety factor on hub | Safety factor you need on hub yield. | |
| Hub expansion coefficient | µm/(m·K) | Expansion coefficient of the hub for shrink assembly. |
| Assembly clearance when heated | mm | Clearance wanted when the heated hub is slid on. |
| Duty | ||
| Torque to transmit | N·m | Torque the fit must transmit. |
| Safety factor on slip | Safety factor against slipping. | |
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: Nominal interface diameter
- What it is
- The nominal diameter where the shaft and hub meet, the basic size the tolerance grades and deviations are applied to.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 500 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.
- Effect on the result
- Sets the size step for the IT tolerances; pressure, holding torque and press force all depend on it.
What this means: Hole tolerance grade (basic hole, lower deviati…
- What it is
- The IT tolerance grade of the hub bore on a basic-hole system: the hole is made from nominal size up to nominal plus the IT value.
- Units and format
- Choose one of 12 options from the list: IT5; IT6; IT7; IT8; IT9; IT10; IT11; IT12; IT13; IT14; IT15; IT16.
- Example
- The form opens with “IT7” selected as a worked example. Choose the option that matches your case.
- Get it right
- Only the grade number is chosen; the hole’s lower deviation is always zero here (an H hole).
What this means: Shaft tolerance grade
- What it is
- The IT tolerance grade of the shaft, which sets how far its size may vary above its lower deviation.
- Units and format
- Choose one of 12 options from the list: IT5; IT6; IT7; IT8; IT9; IT10; IT11; IT12; IT13; IT14; IT15; IT16.
- Example
- The form opens with “IT6” selected as a worked example. Choose the option that matches your case.
What this means: Shaft lower deviation (your fit)
- What it is
- How far the smallest permitted shaft is above the nominal size for the fit you want, the shaft’s lower deviation, from your fit standard or drawing.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts -1000 µm to 5000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 45 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger deviation raises both the least and most interference, so more grip and more hub stress.
- Get it right
- Enter micrometres, not millimetres; it is positive for an interference fit.
Hub, shaft and materials
What this means: Hub outside diameter
- What it is
- The outside diameter of the hub, gear or collar that is pressed or shrunk onto 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.
- Effect on the result
- A thicker hub is stiffer, giving more pressure for the same interference and a lower hoop stress factor.
- Get it right
- Use the smallest outside diameter over the fit length, such as the root of gear teeth.
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.
- Effect on the result
- A larger bore makes the shaft more flexible and lowers the contact pressure.
What this means: Engagement length
- What it is
- The axial length over which the shaft and hub are 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 press force rise in proportion to the length.
- Get it right
- Deduct chamfers and grooves from the hub length.
What this means: Coefficient of friction at interface
- What it is
- The coefficient of friction between the shaft and hub surfaces at the interface, which depends on materials, finish, lubrication and whether the fit is pressed or shrunk.
- 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 press force rise in proportion to it.
- Get it right
- Take it from test data or a fits reference for your assembly method; a lubricated press fit grips less than a dry shrink fit.
What this means: Hub elastic modulus
- What it is
- The elastic (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.
- Effect on the result
- A stiffer hub gives more contact pressure for the same interference.
- Get it right
- Enter gigapascals; cast iron and aluminium hubs are much less stiff than steel.
What this means: Hub Poisson’s ratio
- What it is
- Poisson’s ratio of the hub material: the ratio of lateral to axial strain, 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
- A dimensionless ratio between zero and one half, not a percentage.
What this means: Shaft elastic modulus
- What it is
- The elastic (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.
- Effect on the result
- A stiffer shaft gives more contact pressure for the same interference.
- Get it right
- Enter gigapascals, not megapascals.
What this means: Shaft Poisson’s ratio
- What it is
- Poisson’s ratio of the shaft material, the ratio of lateral to axial strain, 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
- A dimensionless ratio between zero and one half, not a percentage.
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 bore carries the highest stress in the fit.
- 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.
- Effect on the result
- The hub safety factor at most interference is this strength divided by the von Mises stress.
What this means: Required safety factor on hub
- What it is
- The least factor you accept between the hub yield strength and the hub stress at the most interference, from your design rules.
- 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: Hub expansion coefficient
- What it is
- The coefficient of linear thermal expansion of the hub material, used to find 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 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
- A higher coefficient lowers the heating needed for assembly.
- Get it right
- The unit is micrometres per metre per kelvin (×10⁻⁶ per K), not a decimal fraction.
What this means: Assembly clearance when heated
- What it is
- The extra diametral clearance you want between the heated hub bore and the largest 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.
- Effect on the result
- More clearance raises the temperature rise needed.
- Get it right
- Enter millimetres on diameter, not micrometres.
Duty
What this means: Torque to transmit
- What it is
- The torque the fit must carry in service without slipping, from the drive’s rated or peak torque.
- 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
- Multiplied by the slip safety factor and compared with the holding torque at least interference.
What this means: Safety factor on slip
- What it is
- The factor you need between the holding torque at least interference and the torque to transmit, to cover shocks and uncertainty in friction.
- 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
- IT values from the standard tolerance unit i = 0.45 ∛D + 0.001 D for the size step (as the ISO tolerance grade tool); hole 0 to +IT_h; shaft ei to ei + IT_s.
- Least interference = ei − IT_h; most = ei + IT_s.
- p = δ ÷ {d [(k_h + ν_h) ÷ E_h + (k_s − ν_s) ÷ E_s]}; holding torque = μ p π d² L ÷ 2; hub von Mises stress, press force and heating ΔT = (δ + clearance) ÷ (α d) (as the press and shrink fit tool).
- Example: interference 20.02–60.612 µm; it holds 1,061.4 N·m at the least and the hub has a factor of 1.6498 at the most.
Limitations
- Thick-cylinder theory; long hubs and stepped shafts concentrate stress at the hub ends.
- Surface smoothing reduces the effective interference slightly; allow for it with fine finishes ignored.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Choose a shaft tolerance for a press-fitted gear or coupling
- Check a fit over its whole tolerance band
- Set the heating temperature for shrinking on
Who it is for
- Design engineers
- Machine designers
- Maintenance engineers
What you get
- Hole and shaft limits, least and most interference
- Pressure and holding torque at least interference
- Hub stress, press force and heating temperature at most interference
Interpreting the result
- The tolerance band must keep both ends working: enough grip at the least interference and no yield at the most.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 631–634, 635–668. Topic reference; no source tables or recommended settings are reproduced.
- ISO 286-1:2010 Geometrical product specifications (GPS) — ISO code system for tolerances on linear sizes
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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