Spiral-Groove Bearing Design Suite Calculator

How to use

1. Select Journal bearing, Spiral thrust, or Herringbone thrust.
2. Enter the required geometry, operating load or speed, and dynamic viscosity in the units shown. Positive rotation denotes the groove pumping direction.
3. Select Calculate or edit a field to update the one canonical result panel. Reset restores that mode’s worked defaults.
4. Interpret maximum load for journal mode or required speed for thrust modes together with torque, power, and the secondary coefficients.
5. Correct any inline warning before using a result. Treat h₀/R ≤ 5×10⁻⁵ as outside the recommended thin-film screening range, even though the historical air-bearing example lies slightly below it.
6. Do not use this model for transient start-up, cavitation, compressible-gas corrections, thermal viscosity change, elastic deformation, roughness-scale films, or unstable groove geometries.

Input definitions

Journal-bearing inputs

• L/D is bearing length divided by shaft diameter; it is dimensionless and must be greater than zero.
• D is the positive shaft diameter in mm.
• c/R is radial clearance divided by shaft radius; enter a value greater than zero and less than one.
• n is positive shaft speed in rpm. Positive rotation denotes the intended groove-pumping direction.
• η is positive lubricant dynamic viscosity in Pa·s at operating temperature.
• S′ is a positive dimensionless stiffness coefficient selected from a validated groove-geometry correlation; it is not derived by this calculator.
• εmax is the permitted eccentricity divided by radial clearance; enter a value greater than zero and less than one, selected for the allowed operating orbit.

Thrust-bearing inputs

• F is the positive compressive axial load in N; tensile loading and load reversal are outside this model.
• D=2R is the positive outer bearing diameter in mm.
• h₀ is the positive minimum land-film thickness in µm. Independently assess designs at h₀/R ≤ 5×10⁻⁵.
• η is positive dynamic viscosity at operating temperature: µPa·s for Spiral thrust and Pa·s for Herringbone thrust.
• h₂ is groove depth measured from the land surface and must exceed h₀; both dimensions are entered in µm.
• λ = rᵢ/rₒ is the inner-to-outer groove-radius ratio; enter a value greater than zero and less than one.
• α is the groove angle in degrees between the groove tangent and local surface velocity; enter a value greater than 0° and less than 90°.
• k is a positive integer groove count for equally spaced grooves. The groove orientation must pump toward the loaded film.

Equations used

Journal bearing

Let R=D/2, L=(L/D)D, radial clearance c=(c/R)R, and ω=2πn/60. The implemented stiffness and limiting load are

S = S′ηωR⁴/c³;   Fmax = S εmax c.

Surface speed V=ωR, shear stress τ=ηV/c, friction force Ff=τπDL, torque M=FfD/2, and power P=FfV=Mω. S′ and εmax are dimensionless geometry inputs; η is Pa·s, dimensions are converted to metres, and positive n is the pumping direction.

Spiral and herringbone thrust bearings

For both thrust modes, R=D/2, δ=h₀/h₂ is the land-to-groove film-depth ratio, H=δ/(1+δ) is its bounded transformed film parameter, and q=cot α is the groove-angle factor. The coefficient g₁ is the dimensionless hydrodynamic pumping coefficient; for the intended groove orientation it must combine with the coupling factor to produce a positive load coefficient. The coefficient g₂ is the dimensionless viscous-shear coefficient.

g₁ = H²q(1−H)(1−H³) / [(1+H³)²+4H³q²]
g₂ = (1+H)/2 + 3H(1−H)² / [2(1+H³+4H³q²)].

φ₁ and φ₂ are dimensionless finite-groove attenuation parameters that combine groove angle and groove count. C₁ and C₂ are dimensionless finite-groove coupling factors that combine attenuation with the inner-to-outer radius ratio. F* is the dimensionless load coefficient relating applied load to viscosity, speed, radius, and film thickness. μ* is the dimensionless friction coefficient supplied by the groove correlation; μ without a star is the physical thrust-bearing friction coefficient used for torque.

For a one-sided spiral thrust bearing, φ₂=2π(1−2α/π)tanα/k, C₂=[exp(−φ₂)−λ⁴exp(φ₂)]/(1−λ⁴), F*=3π(1−λ⁴)g₁C₂/2, μ*=δg₂/(3g₁C₂), and μ = μ* h₂/R. For the herringbone thrust bearing, φ₁=π(1−2α/π)tanα/k, C₁=[exp(−φ₁)−λ²exp(φ₁)]/(1−λ²), F*=3π(1−λ²)²g₁C₁²/4, μ*=[2(1+λ²)/(3(1−λ²))]g₂/(g₁C₁²), and μ = μ* h₀/R.

ω = Fh₀²/(ηR⁴F*);   n=60ω/(2π);   T=μFR;   P=Tω.

Here λ=rᵢ/rₒ, α is in radians inside equations, k is an integer groove count, F is N, η is Pa·s after conversion, and h₀/h₂/R are metres. Calculations retain full precision; displayed values use locale formatting with up to five to seven decimals.

Theory and method

Spiral grooves generate hydrodynamic pumping as one bearing surface rotates. Journal mode uses a geometry-supplied stiffness number and maximum eccentricity to estimate radial support and viscous loss. The thrust modes use finite-groove dimensionless pumping and shear coefficients to solve the speed needed to support a specified axial load at a chosen film thickness.

Assumptions include steady laminar isoviscous flow, rigid smooth parallel surfaces, uniform film thickness, fully flooded grooves, the intended pumping direction, and negligible thermal, elastic, inertial, edge-leakage, and compressibility corrections. S′ and εmax must come from a geometry correlation or validated analysis. The thrust correlations require 0<λ<1, 0<α<90°, h₂>h₀, and positive load and viscosity. Check thin gas films with a compressible Reynolds-equation model.

Worked example

1. Journal: L/D=1, D=6 mm, c/R=0.001, n=600 rpm, η=0.04 Pa·s, S′=4.4, εmax=0.36 gives S≈33.2 MN/m, Fmax≈35.8 N, M≈0.853 mN·m, and P≈0.05358 W.
2. Spiral thrust: F=10 N, D=150 mm, h₀=3 µm, η=18.1 µPa·s, h₂=8 µm, λ=0.5, α=15°, k=15 gives n≈4.151 rpm and P≈0.00003915 W. The unusually low speed reflects the large air-bearing diameter; independently assess compressibility and the h₀/R limit.
3. Herringbone thrust: F=10 N, D=14 mm, h₀=1 µm, η=0.02 Pa·s with the same groove geometry gives n≈46.459 rpm and P≈0.001134 W.

References

Equations follow the spiral-groove bearing correlations in A. van Beek, Advanced Engineering Design: Lifetime Performance and Reliability, chapter on hydrodynamic bearings. For design refinement, solve the Reynolds equation with actual groove geometry, lubricant rheology, thermal balance, and deformation.

Continue in TriboSolver to refine film pressure, load, and thermal behavior with a numerical bearing model.