Thrust pad bearing to ISO 12131: film thickness, friction, temperature

What does the ISO 12131 thrust bearing calculation deliver?

ISO 12131 is the calculation standard for hydrodynamic thrust bearings with pads whose sliding faces form a wedge – fixed pads with a machined wedge or tilting pads that adjust themselves to the load-carrying wedge depth. The thrust collar drags the oil into the converging gap of each pad and builds up the pressure that carries the axial load. The standard describes load capacity, friction and flow with dimensionless characteristic values that depend only on the ratio of film thickness to wedge depth hmin/Cwed and on the width ratio B/L; ISO 12131-2 supplies closed-form approximations. Because the viscosity depends on the bearing temperature and the temperature on the friction power, the operating state is found iteratively. In the design sequence the calculator comes after the choice of ring diameters, number of pads and material: it answers whether film and temperature are permissible at rated load and speed and how much oil must be supplied.

Where the calculator sits in the design sequence

Thrust bearings are designed from the axial thrust of the machine: first the thrust ring diameters, number of pads and material are fixed and the specific load p = F/(B·L·Z) is checked against the material; ISO 12131-3 quotes 5 to 7 MPa as usual limits and requires a hydrostatic jacking check above 3 MPa at start-up. Then an oil is chosen – viscosities come from the data sheet, if necessary via dynamic/kinematic viscosity conversion or lubricant viscosity vs temperature. Only then does the hydrodynamic calculation of this tool begin, chaining film thickness, friction, flow and temperature. For the journal bearing on the same shaft the hydrodynamic journal bearing to DIN 31652 calculator follows the same scheme.

Typical questions: is unpressurised lubrication with heat dissipation through the housing enough? Which wedge depth or pad profile gives the largest film thickness? How much oil has to be pumped with recirculating lubrication so that the outlet temperature stays below the limit?

Where the inputs come from

Load and speed: axial thrust from the machine calculation (pressure difference times area for a fan, residual thrust of a pump) at rated speed; ISO 12131-1 recommends investigating the thermally most unfavourable operating point with high speed and load. Geometry: Do, Di and Z from the design; L follows from the circumference minus the oil recesses, square pads (B/L ≈ 1) are standard; lwed/L = 0.75 is the reference value of the characteristic functions. Wedge depth: the machined wedge for fixed pads, or the wedge depth resulting from pivot position and load for tilting pads – usual values 20 to 100 µm. Oil: viscosities at two temperatures from the data sheet, ρ·cp ≈ 1.8 MJ/(m³·K) for mineral oil. Heat dissipation: housing surface from the drawing or the approximations of the standard, kA = 15 to 20 W/(m²·K); for recirculating lubrication the cooler outlet temperature, ΔT = 10 to 30 K and M = 0.4 to 0.6. Guide values: material group per ISO 12131-3 Table 3, Fst/F from the start-up behaviour, Rz of the thrust collar from the drawing.

Formula and variables

FB* = F · Cwed² / (U · ηeff · L² · B · Z) → hmin/Cwed = f⁻¹(FB*, B/L) → hmin

• D = (Do + Di)/2, B = (Do − Di)/2, U = π · D · N, p = F/(B · L · Z) (ISO 12131-1 eq. 30)
• fB* = f(hmin/Cwed, B/L) (ISO 12131-2 eq. 2) · Pf = fB* · U² · ηeff · B · L · Z / Cwed (eq. 7)
• Convection: Teff = fB* · U² · ηeff / (k · Cwed) + Tamb, k = kA · A / (B · L · Z) (eq. 15, 16)
• Recirculating: Q = Pf / (ρ · cp · ΔT), Q* = Q / Q₀, Q₀ = B · hmin · U · Z (eq. 12, 24)
• ΔT₂ = ΔT · Q* / (Q₁* − 0.5 · Q₃*) (eq. 27) · ΔT₁ = (Q₁* − Q₃*) / (M · Q* + (1 − M) · Q₃*) · ΔT₂ (eq. 22)
• Teff = Ten + ΔT₁ + 0.5 · ΔT₂ (eq. 28) · TB = T₂ = Ten + ΔT₁ + ΔT₂ (eq. 29)
• Re = ρ · U · hmin / ηeff ≤ Recr (eq. 2) · hlim,tr = D · Rz / 3000 (ISO 12131-3 eq. 1)

Choose the inputs correctly

Axial load F, thrust collar speed, outside and inside diameter of the sliding face, pad length L, wedge length lwed and wedge depth Cwed, number of pads Z, the dynamic viscosity at two temperatures, and the heat dissipation: housing surface, heat transfer coefficient and ambient temperature for convection, or oil inlet temperature, chosen oil temperature rise and mixing factor for recirculating lubrication. For the checks the material group, the load ratio at start-up and optionally roughness and custom limits.

How to use the calculator

Enter axial load and speed, the ring diameters, pad length, wedge length and wedge depth and the number of pads, plus the two viscosity points of the oil. First choose convection with housing surface and ambient temperature to check whether unpressurised lubrication is enough; if the bearing temperature exceeds the limit, switch to recirculating lubrication and enter inlet temperature, desired oil temperature rise and mixing factor. Set the material group, the load ratio at start-up and, if available, roughness or custom limits. After calculating, the assessment shows whether film thickness, load, temperature and flow regime meet the guide values; the oil flow is the design value for pump and cooler.

Worked example

Example A.1 of ISO 12131-1 (thrust bearing of an axial fan): Do = 340 mm, Di = 280 mm, L = 30 mm, lwed = 22.5 mm, Cwed = 50 µm, Z = 24, F = 20 kN, N = 10 s⁻¹, ISO VG 68, convection with A = 1.25 m², kA = 20 W/(m²·K), Tamb = 20 °C. The calculator converges at TB = 70.1 °C, hmin = 21.7 µm, fB* = 1.76, Pf = 1.25 kW, Re = 10.9 and p = 0.93 MPa; the standard finds 69.1 °C, 21.3 µm, 1.73, 1.23 kW and 10.8 by reading charts. Example A.2 (F = 40 kN, N = 16.67 s⁻¹, Cwed = 55 µm, ISO VG 46) gives 110 °C with convection (standard 104.6 °C) – not permissible – and with recirculating lubrication, Ten = 40 °C, ΔT = 12 K, M = 0.5, Teff = 54.6 °C, hmin = 22.0 µm, Pf = 4.27 kW and Q = 11.9 l/min (standard Table A.3: 54.5 °C, 21.5 µm, 4.13 kW, 11.5 l/min).

How to read characteristic values, film thickness and temperature

The load characteristic value FB* combines load, speed, viscosity and pad geometry: large values mean high relative load and lead, through the characteristic function, to a small relative film thickness hmin/Cwed. The minimum film thickness at the outlet edge must exceed the ISO 12131-3 guide value hlim – tabulated by sliding diameter and speed, depending on whether the full load is present at start-up. With convection the bearing temperature equals the effective temperature; with recirculating lubrication the oil outlet temperature T₂ lies ΔT₁ + ΔT₂ above the inlet temperature, and the calculator reports both parts separately: the rise from mixing in the oil recess and the rise in the gap. The oil flow follows from the chosen temperature rise – a smaller ΔT lowers the temperature but needs more oil. Reynolds number and specific load complete the check.

Force in N, speed in min⁻¹, diameters and lengths in mm, wedge depth in µm, viscosity in mPa·s, temperatures in °C, housing area in m², heat transfer coefficient in W/(m²·K), oil temperature rise in K, heat capacity in MJ/(m³·K); outputs in µm, W, l/min and MPa. Internally the core works in SI units with the rotational frequency N in s⁻¹.

Heat balance and mixing model of the oil recesses

With convection, ISO 12131-1 equates the friction power with the heat dissipated through housing and surroundings, kA·A·(TB − Tamb); conduction through the shaft is neglected. The bearing temperature then follows in closed form from eq. (16) but must be iterated because it changes the viscosity and hence fB*. With recirculating lubrication the balance is finer: the oil leaving a pad at its end (Q₂ = Q₁ − Q₃) mixes in the following recess with freshly supplied oil. How complete this mixing is, is described by the empirical mixing factor M – M = 0 means the hot oil runs unmixed into the next pad and additional fresh oil would be ineffective; M = 1 means complete mixing. From M, the relative flow Q* and the characteristic values Q₁*, Q₃* follow the temperature rise in the recess ΔT₁ and in the gap ΔT₂, from these the effective temperature for the viscosity and the outlet temperature T₂ as bearing temperature.

The calculator starts 60 K above ambient for convection and 40 K above the inlet temperature for recirculating lubrication, averages the assumed and computed temperature after each step and stops at 0.01 K – like the standard, which quotes 2 K as the hand-calculation threshold. If Q* is smaller than Q₃*, the mixing model is outside its validity; choose a smaller temperature rise and thus more oil.

Typical applications

Thrust bearings of fans, pumps, compressors, hydro turbines and generators, ship thrust blocks, thrust bearings in gearboxes; deciding between unpressurised and recirculating lubrication; determining oil flow and cooler capacity; assessing wedge depth, number of pads and oil choice for film thickness and temperature.

Assumptions, limits and common mistakes

ISO 12131-1:2020 (clause 6.2 eq. 3, 4; 6.3 eq. 5–7; 6.4 eq. 8–12; 6.5 eq. 13–29; 6.6 eq. 30; Annex A examples A.1 and A.2 with Table A.3 as reference test), ISO 12131-2:2023 (eq. 1–3 approximation functions for FB*, fB*, Q₁*, Q₃* with Tables 2–5 as cross-check, eq. 4 Vogel viscosity), ISO 12131-3:2020 (eq. 1 hlim,tr, Tables 1–4). Limits: wedge pads with flat land, lwed/L = 0.5 … 1 (functions tabulated for 0.75), 0.5 ≤ B/L ≤ 2, 0.1 ≤ hmin/Cwed ≤ 10, laminar flow, steady load, rigid pads without thermal or elastic deformation; the closed-form approximations deviate from the standard's charts by a few percent. Hydrostatic jacking, tilting-pad pivot position and dynamic loads are not covered.

Common mistake: Do not confuse the wedge depth with the film thickness – Cwed is a geometric dimension of the pad, hmin the result. Enter the pad length L in the circumferential direction at the mean diameter, not the chord or the angle; Z pads must fit on the circumference. For tilting pads the wedge depth is not a fixed quantity but adjusts itself – calculate with a realistic value and check the sensitivity. The oil temperature rise ΔT is a choice, not a result: it sets the flow, and too large a ΔT can leave the mixing model. For loads above 3 MPa at start-up consider hydrostatic jacking.