How is the idealized press-fit force calculated?

For the stated same-material solid-shaft/thick-ring elastic model, interface pressure is obtained from Lamé compliance and sliding force is F = p × π × d × L × μ. The fitted-ring outer diameter must describe that ring itself, not the overall outside diameter of an assembled rolling bearing.

What friction coefficient should I use?

Use a coefficient validated for the actual material pair, surface finish, lubricant, speed and contact pressure. The calculated force is directly proportional to μ, so a generic oiled or dry label is not sufficient for press sizing.

What does the thermal result mean?

The tool reports only the theoretical temperature rise δ/(αd) that expands the bore by the stated diametral interference. It contains no assembly clearance or thermal-loss allowance. Follow the component or bearing manufacturer’s mounting method and temperature limits.

Can pressing damage the bearing?

Yes, if force is applied through the wrong ring. When pressing onto a shaft, apply force ONLY to the inner ring. When pressing into a housing, apply force ONLY to the outer ring. Never transmit force through rolling elements.

Free Engineering Tool #058

Bearing Press-Fit Force Calculator

Estimate axial sliding force for an idealized same-material solid shaft and thick-walled fitted ring. This is a Lamé-model estimate, not a bearing-manufacturer mounting-force value.

Lamé EquationsAssembly ForceCold Press

Nominal Bore d (mm)

Diametral Interference δ (mm, e.g. 0.018)

Contact Length (mm, bearing width)

Fitted Ring Outer Diameter D_r (mm, ring material boundary; not bearing OD)

Sliding Friction μ (validated for the actual interface)

Young’s Modulus E (GPa; same material for shaft and ring)

Thermal Expansion α (μm/(m·K), e.g. 11.7)

Quick presets

Model boundary: valid only for a uniform elastic interference fit between a solid shaft and a concentric thick-walled ring of the same isotropic material under the simplified open-ended Lamé model. Real rolling-bearing rings, hollow shafts, dissimilar materials, short contacts and nonuniform geometry require manufacturer calculation or FEA.

Results

Press-Fit Force

—

Interface Pressure p

—

Equivalent tonne-force

—

Theoretical Minimum Temperature Rise

—

Interface Pressure (Lamé)

Press-Fit Force

μ — validated sliding-friction coefficient for the actual interface
δ — diametral interference (shaft OD − ring bore)
d — nominal interface diameter
D_r — actual outer material boundary of the fitted thick ring, not overall bearing OD
E — Young’s modulus shared by shaft and ring in this special-case equation

Hot Mounting Alternative

ℹ️ The thermal result is only ΔT_min = δ/(αd), the uniform temperature rise that expands the bore by exactly the interference. It provides zero assembly clearance and ignores heat loss to the shaft. Add an engineered clearance allowance and follow the component manufacturer’s permitted heating method and temperature limit.

Practical Example

Worked example — idealized ring geometry, δ = 0.018 mm

k = 50/80 = 0.625

p = 210000 × 0.018 / (2 × 50) × (1 − 0.625²) = 23.03 MPa

F = 23.03 × π × 50 × 18 × 0.10 / 1000 = 6.51 kN (0.66 tf)

⚠️ Critical: When pressing a bearing onto a shaft, apply force ONLY to the inner ring. Never transmit force through rolling elements — this will cause brinelling damage.

For the stated same-material solid-shaft/thick-ring elastic model, interface pressure comes from Lamé compliance and F = p × π × d × L × μ.

D_r must be the outer material boundary of the fitted ring itself, not the outside diameter of an assembled rolling bearing.

Use a value validated for the actual material pair, finish, lubricant, speed and pressure. Force is directly proportional to μ, so generic oiled/dry labels are insufficient for press sizing.

It is only δ/(αd): the uniform temperature rise that expands the bore by exactly the interference. It includes no assembly clearance or heat-loss allowance. Follow manufacturer limits.

No. Entry geometry, breakaway friction, misalignment, roughness, plasticity and edge effects are omitted. Apply an engineering process allowance backed by actual data.

Yes — apply mounting force only to the ring with the interference fit. Do not transmit mounting force through the rolling elements; use the bearing manufacturer’s mounting instructions.

The procedures described on this page were developed and field-tested by the Vibromera team using the Balanset-1A, a portable dual-channel balancer and vibration analyzer for on-site rotor balancing.