Shaft Hub Fits (`shaft-hubs`)

Shaft Hub Fits

Interference fit pressure and torque capacity

Standards catalog

Validation: indicative · Method band: formula

Open calculator

Indicative method: Indicative closed-form or numerical model

Assumptions

Linear elastic material behavior unless noted otherwise.
User is responsible for load combinations and load factors per the selected design code.
Design standard (US/EU/ISO) sets unit defaults and screening check labels — not a full code worksheet.

Limitations

Professional screening / indicative workspace — does not replace a licensed PE or official code compliance review.
Where specialized evaluators are not implemented, checks map solver outputs to catalog templates for orientation only.

Engineering checks

Check	IND	US	EU	ISO
Contact pressure	implemented	—	—	—
Friction torque capacity	implemented	—	—	—

Purpose

Estimate contact pressure and friction torque capacity for interference fits between shafts and hubs. Supports press-fit and shrink-fit screening for power transmission without keys.

Physics & theory

Interference fit creates radial contact pressure $p$ at the shaft–hub interface from diametral interference $δ$ . Thick-cylinder Lamé equations relate interference to pressure based on elastic moduli, Poisson's ratios, and geometry of shaft and hub.

Friction torque capacity is $T = 2 π r^{2} μ p L$ for interface radius $r$ , friction coefficient $μ$ , and contact length $L$ . Minimum interference must overcome assembly force and operating load without slip. Maximum pressure must not exceed yield of hub or shaft at bore.

Connections transfer load through bearing, shear, tension, and friction paths depending on joint configuration. Preload in bolted joints reduces joint separation and can allow friction to carry shear; without adequate preload, bolts carry full shear in bearing against hole walls.

FEM-based bolt analysis resolves member and bolt stiffness for load sharing; VDI 2230 provides a systematic worksheet for high-fidelity preloaded joints including embedding loss and tightening scatter.

Governing equations

p = \frac{δ}{\frac{r}{E _{h}} ( 1 - ν _{h} ) + \frac{r}{E _{s}} ( 1 - ν _{s} ) + \frac{r ^{2}}{E _{h} ( r _{o}^{2} - r ^{2} )}}

T_{max} = 2 π μ p r^{2} L

σ_{θ, m a x} = p \frac{r _{o}^{2} + r ^{2}}{r _{o}^{2} - r ^{2}}

Numerical method

Lamé thick-cylinder closed-form for contact pressure from specified interference or fit tolerance. Friction torque from user $μ$ . Stress in hub bore compared to yield allowable.

Inputs

Parameter	Description
Shaft/hub diameters	Nominal and interference
Outer hub radius	Hub OD
Material $E$ , $ν$ , yield	Shaft and hub
Contact length $L$	Fit engagement length
Friction coefficient $μ$	Dry or lubricated assembly

Outputs

Contact pressure, hub hoop stress, friction torque capacity, torque utilization, minimum interference recommendation.

Design codes & checks

Indicative: Contact pressure and friction torque capacity
ISO: ISO 286 fit tolerances (with Fits module)
DIN: DIN 7190 interference fits (reference)

Assumptions & limitations

Elastic analysis; plastic deformation during press-fit not fully modeled.
Uniform pressure along length; no hub flange or step effects.
Friction coefficient highly variable with surface finish and lubricant.
Fatigue of interference joints not evaluated.

References

Shigley, J. E., & Budynas, R. G. Mechanical Engineering Design, 11th ed., Ch. 7.
DIN 7190:2017. Interference fits — Calculation and design rules.
Roark, R. J., Young, W. C., & Budynas, R. G. Formulas for Stress and Strain, thick cylinders.
ISO 286-1:2010. Limits and fits.
PhyCalcPro verification benchmarks in src/data/verification/ where available for this module.
Beer, F. P., et al. Mechanics of Materials, 8th ed. McGraw-Hill — foundational stress and deformation theory.

Maintainer note: Interference fit pressure estimate.

Shaft Hub Fits

Assumptions

Limitations

Engineering checks

Shaft Hub Fits (shaft-hubs)

Shaft Hub Fits (`shaft-hubs`)