Interference, Shrink, and Press Fit Design Suite

Screen cylindrical and tapered interference fits, thermal mounting changes, and thin-wall plastic press-fit capacity.

Engineering screening tool—verify inputs and results independently. Use at your own risk.

Fit inputs

Choose a mode, enter positive geometry and verified material properties, then compare stresses and capacity with project allowables.

Elastic fit result

Contact pressure—MPa

Friction force—kN

Torque capacity—N·m

Inner equivalent stress at fit—MPa

Outer equivalent stress at fit—MPa

Idealized axisymmetric fit. The equations use uniform interface pressure and nominal friction capacity.

How to use

Select Elastic cylindrical for a straight elastic press/shrink fit, Tapered connection for axial seating on a cone, Thermal mounting for the separate cooling/heating change needed to clear an interference ratio, or Thin-wall plastic for a yielded thin member in a rigid bore.
Enter all required dimensions in mm, moduli in GPa, strengths in MPa, thermal coefficients in µm/m·K, and dimensionless Poisson, friction, taper, or interference ratios. Inputs are unsigned magnitudes.
For elastic modes, use effective interference after roughness flattening and require dᵢ < d < dₒ; enter dₒ = 0 only to represent an unbounded outer body. Keep −1 < ν < 0.5.
Select Calculate, or edit a field for immediate updating. Reset restores the displayed example values for the active mode.
Read contact pressure as the canonical elastic/tapered result, required outer heating as the thermal result, and deterministic torque range as the plastic result. Supporting force, torque, stress, and central-95% values are shown separately.
Correct any red warning before interpretation. Outputs follow two-decimal display rounding; calculations retain full floating-point precision.
Compare elastic equivalent stresses with verified elastic limits and capacity with design load plus safety factors. In thermal mounting, add practical assembly clearance and account for heat transfer; the two temperature results are alternatives, not simultaneous requirements.
Do not use the models for non-axisymmetric geometry, partial contact, combined plasticity and elasticity, transient thermal gradients, yielding in an elastic mode, creep, fatigue/fretting life, safety-critical release, or fits outside validated material and manufacturing data.

Worked example

1. Select Elastic cylindrical and use dᵢ = 20 mm, d = 23 mm, dₒ = 80 mm, L = 20 mm, Eᵢ = 100 GPa, Eₒ = 210 GPa, νᵢ = νₒ = 0.3, δ = 0.023 mm, and μ = 0.12. 2. Calculate to obtain p = 13.15 MPa, F = 2.28 kN, and T = 26.22 N·m. 3. Compare the reported interface equivalent stresses with verified yield limits. 4. Correct δ for roughness and tolerance before treating the capacity as a design value.

Equations used

Elastic compliance: nₒ = {[(dₒ²+d²)/(dₒ²−d²)] + νₒ}/Eₒ; nᵢ = {[(dᵢ²+d²)/(dᵢ²−d²)] + νᵢ}/Eᵢ

Elastic pressure: p = (δ/d)/(nₒ − nᵢ)

Friction capacity: F = πdLμp; T = Fd/2

Lamé stresses at each radius: σt,i(dᵢ)=2p/[(dᵢ/d)²−1], σt,i(d)=p[(dᵢ/d)²+1]/[(dᵢ/d)²−1], σt,o(d)=p[(dₒ/d)²+1]/[(dₒ/d)²−1], σt,o(dₒ)=2p/[(dₒ/d)²−1]; σr = 0 at free surfaces and −p at the interface; σe = √(σt²+σr²−σtσr).

Tapered mode: δ = Cz; d₁ = dₘ + CL/2; d₂ = dₘ − CL/2; Fp = p(π/4)(d₁²−d₂²). The self-locking screen is μ ≥ C/2.

Thermal mounting: ΔTᵢ = −(δ/d)/αᵢ; ΔTₒ = +(δ/d)/αₒ.

Thin-wall plastic: p = 2sRₘ/d; F = μpπdL; T = Fd/2. Each deterministic minimum uses all listed minima except dmax in the pressure denominator; each maximum uses the opposite bounds. For a stated ±3σ range, x̄=(xmin+xmax)/2, σ=(xmax−xmin)/6, and the displayed central interval is x̄±1.96σ.

Here dᵢ, d, dₒ, dₘ, d₁, d₂, L, δ, z and s are geometric quantities; E is Young’s modulus; ν is Poisson’s ratio; μ is friction coefficient; C is taper ratio; α is linear expansion coefficient; p is compressive contact-pressure magnitude; σt and σr are signed hoop and radial stresses (compression negative); σe is von Mises equivalent stress; F is axial friction force; Fp is axial pressure force; T is torque; and Rₘ is tensile strength. MPa and mm are used consistently for force and torque conversion.

Theory and method

The elastic modes apply Lamé thick-cylinder compliance to two concentric members and equate their combined radial deformation to the effective diametral interference. Nominal Coulomb friction over area πdL then screens axial slip force and torque. The tapered mode converts seating travel to interference and compares friction with taper geometry. Thermal mounting uses free linear expansion separately for cooling the inner part or heating the outer part. The plastic mode assumes a thin wall carries approximately Rₘ hoop stress while the mating bore is rigid.

Assumptions and limits: axisymmetry, uniform interference and pressure, homogeneous isotropic materials, small elastic strain in elastic modes, quasi-static loading, no keyway/spline, no edge-pressure distribution, and constant μ. Typical δ/d is near 0.001. Roughness flattening may be estimated as Δδrough ≈ 0.2(Rz1+Rz2), with Rz≈6Ra as a screening rule; subtract it from measured diametral interference. Approximate μ ranges include dry steel/steel 0.10–0.15, lubricated steel/steel 0.05–0.10, and dry steel/yellow-metal 0.05–0.10. Verify current standards and surface data.

References: Lamé thick-cylinder equations; A. van Beek, Advanced Engineering Design: Lifetime Performance and Reliability, interference-fit calculation collection; ISO 6336-2 is cited only for the archived roughness relation Rz≈6Ra, not as a complete interference-fit design standard. Use current fit/tolerance, material, assembly, and safety requirements for final design.

Continue in TriboSolver to refine contact pressure, local stress, friction, thermal assembly, fatigue, and tolerance effects.

Adhesive Slip-Fit Shaft Joint Calculator screens bonded joints; Probabilistic Fit Tolerance Calculator evaluates dimensional overlap probability.