Paired Rolling-Bearing Preload and Axial Load Sharing Calculator

Inputs

Results update automatically. Use the sign convention shown below.

Unloaded angle α₀degBall diameter Dmm Curvature factor B—Load constant KN/mm² Ball count ZelementsInitial preload F_pN External axial load F_aN

Axial load sharing

Solved compressive axial loads and mode-specific diagnostics.

Bearing loads—

Axial load by bearing (N)

Equations used

Duplex angular-contact preload

For unloaded contact angle α₀, ball diameter D [mm], curvature factor B [dimensionless], load constant K [N/mm²], ball count Z, and contact angle α:

F(α) = K Z D² sin(α)[cos(α₀)/cos(α) − 1]^3/2

δ(α) = B D sin(α − α₀)/cos(α)

The preload angle satisfies F(α_p)=F_p. Under signed load F_a [N], the solver enforces F(α₁)−F(α₂)=F_a and δ(α₁)+δ(α₂)=2δ(α_p). Positive load increases bearing 1 load.

Radial-load-induced thrust

S₁ = Fr₁/(2Y₁); S₂ = Fr₂/(2Y₂)

Fa₁ = max(S₁, S₂ − P_a); Fa₂ = Fa₁ + P_a

Fr, S, Fa and signed P_a use N; Y is a positive user-entered catalog factor. Positive P_a acts toward bearing 2.

General power-law pair

δ_0,i=(F₀/C_i)^1/nᵢ; δ̄_i=δ_0,i+Δs/2

F₁=C₁max(δ̄₁+x,0)^n₁; F₂=C₂max(δ̄₂−x,0)^n₂; F₁−F₂=F_a

k_pair=k₁+k₂; k_i=n_iC_iδ_i^nᵢ−1 [N/mm]

The unloading threshold occurs when one compression reaches zero. The angle estimate is α_i=atan[(A_isinα_0,i+δ_i)/(A_icosα_0,i)].

Assumptions and limits

All modes are quasistatic and assume rigid rings/supports; tandem sets, moments, dynamics, centrifugal effects, lubrication and fatigue life are excluded.
The duplex model is for angular-contact ball bearings with validated internal geometry and load constant.
The radial mode is a catalog-factor screening relation, not detailed rolling-element contact analysis.
The power-law mode requires validated coefficients and uses average—not maximum—load per element.

How to use

Select Duplex preload, Radial load sharing, or Power-law pair. Do not use these opposed-pair models for tandem sets.
For duplex preload, enter unloaded angle in degrees, ball diameter in mm, dimensionless curvature factor, load constant in N/mm², ball count, preload in N and signed external load in N.
For radial load sharing, enter both radial reactions in N, positive catalog Y factors and signed external load P_a in N; positive acts toward bearing 2.
For the power-law pair, choose back-to-back or face-to-face and enter preload, signed load, coefficients in N/mmⁿ, exponents, interference in mm, geometry and element counts.
Results calculate automatically after every valid edit; there is no separate Calculate button.
Use Reset example to restore the benchmark example for the selected mode.
Read the two bearing loads with contact angles or induced minima, displacement, tangent stiffness, residual and unloading warning where shown. The plot compares axial load in N.
Correct any red validation warning. A duplex load above its unloading threshold is outside the opposed-contact solution; a power-law unloaded state means preload sharing has been lost.
Use manufacturer or otherwise validated internal geometry, stiffness constants and Y factors. Do not infer them from a designation or transfer them between unlike bearings.
Do not use this calculator for detailed rolling-element/raceway stresses, radial/moment coupling, dynamic or thermal prediction, bearing rating, reliability, or fatigue-life decisions.

Reference and validation

Equations were independently implemented and benchmarked against Harris and Kotzalas (2006), Rolling Bearing Analysis, Fifth Edition, Volume I Chapter 8 Example 8.3 and Volume II Chapter 9 Examples 9.1–9.2. doi:10.1201/9781482275148.