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Ring Fit Calculator

Analyze cylindrical press fits and shrink fits using elastic shaft-hub compliance, Lamé stresses, torque and axial slip capacity, operating-temperature fit loss, and thermal assembly temperatures. Minimum, nominal, and maximum interference are evaluated together so the tool reflects real tolerance spread instead of a single optimistic number.

Tool Purpose & README

What this tool is for

Use this tool when you need to size or verify a straight cylindrical interference fit between a shaft and a hub. It is meant for quick design analysis, tolerance studies, and assembly planning.

  • Elastic interface pressure at reference and operating temperature
  • Hub and shaft von Mises stress from Lamé radial and hoop stresses
  • Friction-based torque and axial load capacity
  • Fit retention or loss with thermal expansion mismatch
  • Hub heating and shaft cooling temperatures for assembly
  • Interference sensitivity plots so min/nom/max fits can be compared directly

This is a classical axisymmetric calculator. It does not model yielding, keyways, grooves, split hubs, taper fits, fretting fatigue, or local stress raisers.

Inputs

Expert Mode Show custom material properties, limits, and sweep controls.
Length & Stress
Temperature

Geometry and interference inputs follow the selected display units. Custom material properties remain entered in MPa, dimensionless Poisson ratio, and microstrain per degree C.

Geometry

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Interference Range

Minimum, nominal, and maximum interference are all evaluated in v1. The minimum operating fit governs retention; the maximum fit often governs stress.

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Materials

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Service Conditions

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Requirements & Sweep Controls

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Enter the fit geometry and press Calculate to see pressure, stress, slip capacity, and thermal assembly results.

Pressure and Capacity vs Interference

Reference and operating pressure are plotted against interference, with torque capacity shown on the secondary axis. The min/nom/max interference band is marked so you can see whether tolerance spread is materially changing the joint behavior.

Stress vs Interference

Hub and shaft von Mises stress grow with interference. This plot makes it easy to see whether the maximum interference case is consuming yield margin.

Temperature Effect on Nominal Fit

Operating interference and operating pressure for the nominal fit are shown over temperature. Mixed-material fits can lose pressure quickly when the hub expands more than the shaft.
Contents
  1. What this model assumes
  2. Pressure from interference
  3. Hub and shaft stress
  4. Operating temperature and fit loss
  5. Assembly temperatures
  6. Limits of the model

1. What This Model Assumes

The calculator models a straight cylindrical shaft and hub as elastic, axisymmetric members. The fit pressure comes from the combined radial compliance of the two cylinders. Slip capacity is based on uniform pressure and a single friction coefficient over the full contact length.

Interpretation Use the minimum operating interference case to judge fit retention and service slip margin. Use the highest-pressure case to judge stress and assembly effort.

2. Pressure From Interference

The classical interference-fit relationship can be written as combined compliance:

Equation (1)
$$ \delta_d = p d \left(C_h + C_s\right) $$
  • \delta_d: diametral interference
  • p: interface pressure
  • d: fit diameter
  • C_h: hub radial compliance
  • C_s: shaft radial compliance

For thick hubs and hollow shafts, the compliance factors depend strongly on diameter ratio. That is why hub wall thickness and shaft bore size matter even before yield is considered.

3. Hub and Shaft Stress

The interface produces radial compression and hoop stress. The calculator evaluates the bore-side Lamé stresses and reports a plane-stress von Mises equivalent.

Equation (2)
$$ \sigma_{vm} = \sqrt{\sigma_\theta^2 - \sigma_\theta \sigma_r + \sigma_r^2} $$
  • \sigma_\theta: hoop stress at the interface
  • \sigma_r: radial stress at the interface

4. Operating Temperature and Fit Loss

The nominal reference interference is adjusted for free differential expansion. When the hub grows more than the shaft, interference falls. If it falls to zero, the idealized model reports full loss of contact pressure.

Equation (3)
$$ \delta_{d,op} = \delta_{d,ref} - d(\alpha_h - \alpha_s)\Delta T $$
  • \alpha_h: hub thermal expansion coefficient
  • \alpha_s: shaft thermal expansion coefficient
  • \Delta T: operating minus reference temperature

5. Assembly Temperatures

For thermal assembly, the required temporary diameter change must exceed the worst-case interference plus a user-entered assembly clearance. The tool reports hub-only heating, shaft-only cooling, and an equal-temperature combined strategy.

Assembly caution Heating or cooling temperatures alone are not proof of metallurgical safety. Temper, coatings, lubricant, condensation, and handling practice still need engineering judgment.

6. Limits of the Model

This calculator is not appropriate for plastic fits, tapered joints, split hubs, keyed hubs, grooved bores, fretting life analysis, or cases where local stress concentration dominates. Use testing, design codes, or FEA when the classical axisymmetric assumptions stop being representative.

Do not over-claim A classical interference-fit calculator is a strong screening tool, not a substitute for detailed design verification when fit geometry or material behavior is outside the elastic thick-cylinder assumptions.