Restrictor-Compensated Hydrostatic Thrust Bearing Calculator

Engineering screening tool—verify inputs and results independently. Use at your own risk.

Bearing and supply inputs

Positive pressure is above the selected absolute ambient pressure; all radii are measured from the bearing axis.

Screening result

Ideal incompressible, isothermal performance at the entered operating point.

Load capacity—kN

How to use

Select Capillary, Orifice, or Fixed flow. Capillary and orifice modes size equal parallel restrictors; fixed flow evaluates an ideal constant-flow feed without a bore size.
Enter outer radius R₀ and central-pocket radius R₁ in mm, requiring 0 < R₁ < R₀.
Enter uniform film thickness h₀ in µm and absolute supply and ambient pressures in MPa. Supply must exceed ambient.
Enter positive dynamic viscosity η and density ρ. The model treats both as constant.
Enter pressure factor β=(pᵣ−pₐ)/(pₛ−pₐ), strictly between 0 and 1. It sets the recess pressure and therefore load and flow.
For capillaries, enter integer count n and l/d. For orifices, enter n and Cᴅ. These values size each feed passage; they do not change the required total land flow.
Select Calculate. Correct any red geometry or range warning before interpreting results.
Read load, stiffness, flow, hydraulic power, restrictor size, and Reynolds diagnostics. Low film Reynolds number supports the laminar-land assumption; restrictor regime must also suit the selected feed law.
Select Reset example to restore the demonstrated oil-fed 60/42 mm-radius case.
Do not use this model for compressible gas films, turbulent lands, cavitation, thermal/elastic distortion, dynamic stability, misalignment, roughness contact, or safety-critical final design.

Worked example

1. Select Capillary and use R₀=60 mm, R₁=42 mm, h₀=30 µm, pₛ=2 MPa abs, pₐ=0 MPa abs, η=0.02 Pa·s, ρ=870 kg/m³, β=0.7, n=1, and l/d=20.

2. Select Calculate. Expected results are about 11.320 kN load, 339.60 MN/m stiffness, 2.7745 mL/s flow, 5.549 W hydraulic power, and 0.4224 mm capillary diameter.

3. Reᶠ≈0.457 supports laminar land flow. Reᵣ≈364 is a screening diagnostic; verify entrance, manufacturing, contamination, and stability effects independently.

Input definitions and signs

Radii and film thickness are positive. Pressure is absolute at the entries; Δp=pₛ−pₐ and recess pressure pᵣ=pₐ+βΔp. Load is reported as positive compressive support capacity. Stiffness is the positive magnitude opposing a film-thickness reduction. Flow is positive from supply through the pocket to ambient.

Theory and method

The calculator treats a rigid circular thrust land surrounding a central constant-pressure pocket. The film is steady, laminar, incompressible, isoviscous, axisymmetric, and parallel. Ambient pressure acts at R₀. Define x=R₁/R₀, Δp=pₛ−pₐ, β=(pᵣ−pₐ)/Δp, and A=πR₀².

Equations used

Aₑ/A = (x²−1)/(2 ln x); C_f = −π/(6 ln x)

F*=β(Aₑ/A); Q*=βC_f; F=F*ΔpA; Q=Q*h₀³Δp/η; P=QΔp

Capillary: S*=3(1−β)F*; d=[(Q/n)128η(l/d)/(πΔp(1−β))]^(1/3)

Orifice: S*=6F*(1−β)/(2−β); Aᵣ=(Q/n)Cᴅ⁻¹[ρ/(2Δp(1−β))]^(1/2); d=(4Aᵣ/π)^(1/2)

Fixed flow: S*=3Aₑ/A. All modes: S=S*AΔp/h₀; V_f=Q/(2πR₁h₀); Re_f=ρV_fh₀/η; Reᵣ=ρVᵣd/η.

Here F is load, S axial stiffness, Q total volumetric flow, P ideal hydraulic power, d each equal feed-passage diameter, n passage count, Cᴅ discharge coefficient, η viscosity, and ρ density. In fixed-flow mode β still defines the operating recess pressure and land flow; no feed diameter or Reᵣ is inferred.

Assumptions, limits, and references

Applicable to rigid, flat, coaxial liquid-lubricated thrust bearings with a deep central pocket and negligible pocket pressure loss. It excludes compressibility, inertia in the land, thermal viscosity change, elastic deformation, tilt, grooves/pads, transient restrictor dynamics, cavitation, surface contact, and pump efficiency. Reynolds values are diagnostics, not automatic validity guarantees. Reference: A. van Beek, Principles of Tribology, hydrostatic thrust-bearing relations C11.3, C11.4, and P11.2.

Continue in TriboSolver to refine geometry, pressure distribution, deformation, or operating-condition sensitivity with a more detailed analysis workflow.