Bearing Internal Load Distribution and Stiffness Calculator
Use at your own risk. Independently verify screening results before making design decisions.
Bearing and load inputs
Results update automatically. Use operating clearance and effective contact data for the installed bearing.
Equilibrium result
The plot follows the rolling-element sequence from the radial load line.
Method, assumptions and engineering use
The radial modes solve discrete force equilibrium at every rolling-element azimuth, including operating clearance or interference. The angular-contact mode iterates the operating contact angle under concentric thrust. The double-row mode solves coupled radial and axial equilibrium across both spherical-roller rows.
- Positive diametral clearance narrows the active load zone; a negative value represents radial interference.
- Contact coefficients must represent the selected bearing geometry and the two race contacts acting in series.
- Rigid-ring, static equilibrium is assumed. Ring ovalization, fits, temperature, misalignment, edge stress, lubrication traction and fatigue life are outside this screening calculation.
Use the calculated maximum load and tangent stiffness as inputs to a documented bearing-system model, and compare loads only against current manufacturer limits for the exact bearing and operating condition.
Input definitions
| Input | Meaning | Units |
|---|---|---|
| Radial load (F_r) | Static radial load applied through the bearing center. | N |
| Axial load (F_a) | Static thrust carried by the bearing. | N |
| Rolling-element count (Z) | Number of equally spaced balls or rollers. | elements |
| Elements per row (Z) | Number of equally spaced rollers in each spherical-bearing row. | rollers/row |
| Diametral clearance (P_d) | Positive for clearance and negative for radial interference or preload. | mm |
| Effective contact stiffness (K_n) | Combined element/race contact coefficient for Q = K_n delta^n. | N/mm^n |
| Ball diameter (D) | Ball diameter used by the angular-contact geometry relation. | mm |
| Initial contact angle (alpha_0) | Mounted contact angle before thrust deformation. | deg |
| Row contact angle (alpha) | Nominal spherical-roller row angle to the radial plane. | deg |
| Raceway geometry factor (B) | Dimensionless angular-contact conformity/geometry parameter. | dimensionless |
| Contact coefficient (K) | Angular-contact coefficient in the dimensionless thrust relation. | N/mm² |
How to obtain and interpret stiffness
Select a bearing mode, enter the operating load and contact data, and calculate. Radial ball and roller modes display radial tangent stiffness; angular-thrust mode displays axial tangent stiffness. Double-row spherical mode displays both radial and axial tangent stiffness, with the other applied load held constant. All stiffness values are in N/mm.
Tangent stiffness is the local slope dF/dδ at the calculated operating point, so a small load change gives Δδ ≈ ΔF/k. Secant stiffness F/δ is the slope from the origin and is generally different. The input contact coefficient K_n in Q = K_n δ^n is not the bearing stiffness: its units are N/mm^n, and geometry, clearance and the active rolling elements determine the assembled result.
For radial modes, δ_j = max(δ_r cos ψ_j − P_d/2, 0), F_r = Σ K_n δ_j^n cos ψ_j, and k_r = Σ n K_n δ_j^(n−1) cos² ψ_j over loaded elements. The exponent n is 3/2 for balls or 10/9 for rollers. For zero clearance the model gives k_r = n F_r/δ_r.
The angular-thrust stiffness uses a 0.01% positive load increment, including the resulting contact-angle change. The double-row model forms the coupled tangent matrix J = ∂(F_r,F_a)/∂(δ_r,δ_a). Its displayed free-coupling values are k_r = det(J)/J_aa at fixed F_a and k_a = det(J)/J_rr at fixed F_r. These differ from the diagonal terms for a constrained displacement in the other direction.
Worked example: Radial ball mode with 8,900 N, 9 balls, 0.015 mm diametral clearance and K_n = 373,500 N/mm^1.5 gives displacement 0.0602701 mm and tangent stiffness 259,841 N/mm. A small extra 10 N therefore predicts about 0.0000385 mm additional displacement. The secant value is about 147,669 N/mm; it should not replace the tangent value for small perturbations.
These estimates assume rigid rings apart from contact compliance, equally spaced elements and quasi-static loading. Housing, shaft and mounting flexibility are excluded. Verification compares exact zero-clearance stiffness with the power-law relation and central load perturbations of 1% and 0.1% in all modes; the stiffness comparisons agree within 0.02%. Recalculate if load, clearance or the active contact set changes substantially.
For detailed tribological simulation, see TriboSolver.
Reference
Harris, T. A. and Kotzalas, M. N. (2006), Advanced Concepts of Bearing Technology: Rolling Bearing Analysis, Fifth Edition, CRC Press, Chapters 7–8. doi:10.1201/9781420006582.
Related tools: high-speed bearing effects, bearing kappa factor, and the TriboNet calculator directory.
