Authored by:
E.R. Booser
Engineering Consultant
Vero Beach, Fla.
M.M. Khonsari
Dow Chemical Endowed Chair and Professor,
Dept. of Mechanical Engineering
Louisiana State University
Baton Rouge, La.
Edited by Jessica Shapiro
jessica.shapiro@penton.com
Key points:
• Sleeve bearings in moderate service can operate on 50% or less of the oil feed required for a full hydrodynamic oil film.
• Lower oil-feed rates mean engineers can simplify oil-delivery systems.
• Ring-oiling, wick-oiling, and mist or droplet-oiling systems can often supply enough oil to sleeve bearings at low speeds or loads.
Resources:
Louisiana State University
Bearings that Don’t Seize,” Machine Design, January 8, 2004
Connors, H.J. “An Analysis of the Effect of Lubricant Supply Rate on the Performance of the 360 Journal Bearings,” STLE Transactions, V. 5, pp. 404-417, 1962.
Elwell, R.C. 1994. “Self-Contained Bearing Lubrication: Rings, Disks, and Wicks,” Handbook of Lubrication and Tribology, Vol. 3. CRC Press, Boca Raton, FL, pp. 515–533.
Elwell, R.C. 1997. “Ring and Wick-Oiled Starved Journal Bearings,” Tribology Data Handbook. CRC Press, Boca Raton, FL, pp. 708–718.
Fuller, D.D. 1984. Theory and Practice of Lubrication for Engineers, 2nd edn. John Wiley & Sons, New York.
Khonsari, M.M. and E.R. Booser, Applied Tribology – Bearing Design and Lubrication, 2nd Ed., John Wiley & Sons, West Sussex, 2008.

It’s surprising how little lubricant oil-film sleeve bearings really need. Millions of bearings in electric motors, machine tools, pumps, and industrial fans run without a hitch on lubricant feeds that can’t develop full hydrodynamic films of oil. In fact, at low loads and speeds, less oil cuts power loss and simplifies oil-feed-system designs. Often ring oiling, oil mist, wicks, or droplet feed will work in sizable slow-speed machines.

However, engineers need to understand load and speed limits and the damping characteristics of starved bearings to ensure safe operation. A good starting point is to follow manufacturers’ guidelines. Engineers should also know how to calculate minimum oil-film thickness and power loss, as well as predict temperature rise from reduced oil supplies.

Minimum feed consequences
What’s the worst that can happen to a lubricantstarved sleeve bearing? If the lubricant film doesn’t separate bearing surfaces, they will wear and scuff, leading to surface destruction and bearing failures.

Even in cases where lubricant film is just below the minimum thickness, bearings can overheat and even seize if loads or speeds stray above the bearings’ design limits. And starved bearings are less able to damp vibration from external components or misalignments.

In his 1984 book, Theory and Practice of Lubrication for Engineers, D.D. Fuller gave the following expression for a general estimate of the minimum oil feed, Q, (in.3/sec) necessary to lubricate a 360° sleeve bearing:

Q = (0.0043 + 0.0000185 P) × UCL

where P = radial unit loading, psi; U = surface velocity, in./sec; C = radial clearance, in.; and L = bearing length, in.

So a 5-in.-diameter, 5-in.-long bearing operating under a 100-psi unit load at 500 rpm (U = (500  rpm/60 sec/min) × 5 in. × π = 131 ips), needs an oil-feed Q of    0.00015 in.3/sec. This is equivalent to one 0.008-in.3 drop of oil every 13 sec, 2 to 3% of the full feed rate.

Field observations further prove little oil is needed at low to moderate speeds: A 16-in. journal bearing ran without failure under load at 3,600 rpm for 15 min after it lost its supply of ISO VG 32 oil; and a 9-in. railway propulsion bearing ran at 600 rpm for an hour after oil feed stopped.

While these examples show bearings can operate with limited oil supplies if there’s some preexisting “oiliness” on contact surfaces, such extreme starvation isn’t good general practice. Truly dry bearings, such as those in compressors out of service for several months, quickly seize if started without lubrication.

Engineers can use empirically derived charts (such as those shown here) to predict how specific bearings will perform with less than full oil feeds.

To determine the specifics of bearing performance at a percentage of full oil feed, calculate the dimensionless Sommerfeld number from the bearing characteristics:

S = (C/R)-2μN/P

where C/R = clearance ratio; μ = oil viscosity, reyns
(lbf-sec/in.2); N = speed, rev/sec; and P = unit load, psi.

Next, determine the input flow characteristics by dividing the oil-flow rate by bearing radius, speed, clearance, and length:

Input flow variable = Q/RNCL
where Q = oil feed, in.3/sec; R = radius, in.; N = speed, rev/sec; C = clearance, in.; and L = length, in.

On the accompanying graphs, find the approximate minimum film height as a function of bearing clearance, hm/C, and the friction factor as a function of clearance ratio, f(R/C), at the intersection of the Sommerfeld and input flow numbers.

Using the friction factor, an engineer can calculate the bearing’s power loss and temperature rise at a given lubrication state:

E = fWU

where E = power loss, in.-lb/sec; f = friction, dimensionless; W = force, lb; and U = surface speed, in./sec. And

Δ T = E/(Q cp)

where Δ T = temperature rise, °F; Q = oil feed, in.3/sec; = oil density, lbm/in.3; and cp = oil heat capacity, in.-lb/(lbm-°F). In general, 50% feed provides satisfactory operation. Oil-feed rates 20 and 10% of full feed are enough for mild loads and speeds as oil film thickness in the load zone drops below 0.001 in.

So how do engineers design the feed system for partial supply? Actually, the feed arrangements are significantly simpler when delivery is less than full feed of lubricating oil. Some typical arrangements — ring oiling, wick oiling, and oil mists or drops — are covered below.

Ring-oiled bearings
Some sleeve bearings, especially those on large machines such as electric motors, pumps, and fans, are lubricated by a ring that rides on the shaft. The ring usually has an inner diameter 1.5 to 2.0 times that of the shaft diameter. It carries oil from a lower reservoir up to the bearing. Most bearings lubricated by this type of feed have length/diameter ratios, L/D, between 0.6 and 1.1.

In ring-oil setups, the amount of oil delivered to the bearing depends on the ring’s speed. At low speeds, frictional drag keeps the ring moving at the same surface velocity as the rotating shaft. This no-slip range ends as shaft speed increases and the from the rotating shaft.

Tests show that the speed at which slipping first occurs can be calculated by:

NS = 0.00048 w/(μDR2)

where NS = slip speed, rpm; w = ring weight, lb; = oil viscosity, centistokes (cSt); and DR = ring bore, in.

As shaft speed increases, the ring transitions toward being driven by the film of oil it carries. Full fluid-film drive begins at about 2.9 times NS.

Oil rings in most small machines operate in this fullfilm region with ring speed, NR , reflecting a balance between viscous drive on the ring bore by the rotating shaft and viscous drag on the lower portion of the ring by oil in the reservoir.

NR = 1.67 v0.2 (N × D2)0.8/(DR2)

where v = kinematic viscosity of the oil, in.2/sec, N = shaft speed, rev/sec; and D = shaft diameter, in.

With rising ring speed NR, oil delivery Q (in.3/sec) from a conventional ring with trapezoidal cross section at low and normal operating speeds is given by:

Q = 0.14 bv0.65(DRNR)1.5

where b = width of the ring bore riding on the journal, in. and NR = ring rotational speed, rev/sec.

One way to ensure increased oil delivery and greater reliability is to use two oil rings. Engineers should also keep in mind that, at high speeds, the ring loses oil by centrifugal throw-off and windage. At shaft surface speeds above 46 fps, the oil delivery can drop to the point that it is not enough to safely operate the bearing. Keep shaft speeds below this level or use another lubrication technique.

Wick-oiled bearings
In small machines like electric motors, fans, and pumps, wicks commonly lift oil less than 2 in. But in applications like railway journal bearings, they can raise oil 5 in. or more.

Early wicks were mostly wool felt or, in railroad bearings, waste packing. Now, synthetic fibers and injectable oil-fiber wicking mixtures are common, allowing closer integration of wick-oiled bearings with machines. For instance, the end shield of a fractionalhorsepower motor may incorporate a pocket reservoir filled with injectable oil-fiber wicking material.

The rate of mineral-oil delivery by a typical wick (in centimeters3/second) can be approximated by:

Q = kwAF0(hu – h) ÷ (μLw)

where A = cross-sectional area of the wick, cm2; Lw = distance through which oil is carried, cm; F0 = volume fraction of oil in the saturated wick (often about 0.75);
hu = ultimate wicking height, cm (about 18 cm for SAE Grade F-1 felt); h = height above the reservoir surface where oil is delivered, cm; and μ = oil viscosity at the wick temperature, cP. The empirical constant, kw, depends on capillary spacing in the wick and oil-surface tension. It is approximately 4.6 for mineral oil wicking in SAE Grade F-1 felt.

Wicks in general carry little oil. Engineers need to be careful to limit surface speeds for wick-oiled bearings to 13 fps or less because the small quantity of oil can’t carry away significant heat. But, with proper attention to surface finish and manufacturing details, wick-oiled bearings can carry surprisingly heavy loads.

Mist and drop-oiled bearings
Oil-mist and oil-droplet lubrication is predominantly seen with rolling-element bearings, but sleeve bearings operating under relatively mild conditions can also be lubricated by oil supplied as mist, air-oil delivery of evenly placed droplets, or drop oilers.

When lubricating this way, engineers should consult equipment suppliers for detailed requirements. However, two rules of thumb can provide additional guidance. First, aim for an oil-feed rate Q (in.3/hr) that would replace an oil layer 0.1-mm thick between a sleeve bearing and its journal every hour.

Second, the following expression is representative for bearings in moderate service:

Q = 0.005 LD

where L = bearing axial length, in. and D = diameter, in. Bump the 0.005 factor to 0.008 for heavy service and to 0.017 where oil is lost in high volumes. Assume that a standard oil mist delivers 0.5 in.3/min/ft3 and a drop oiler delivers about 0.0020 in.3/drop.

Example 1:
Full sleeve bearing

Estimate power loss, temperature rise, and minimum lm thickness at 50% feed for a 5-in.-diameter, 5-in.-long bearing with C/R = 0.002 and unit load P = 150 psi. The bearing runs at 1,800 rpm with VG 32 oil fed at 120°F. Assuming a 20°F temperature rise, ISO VG 32 oil at 140°F has viscosity = 1.9 × 10-6 reyns, density p = 0.0307 lbm/in.3, and heat capacity cp = 4,535 in.-lb/(lbm-°F).

First, calculate the Sommerfeld number S and input flow variable Q/(RNCL) for 50% ow (100% = 5.6 in.3sec):
S = (C/R)-2 μ N / P
S = (1/0.002)2 (1.9 × 10-6 reyns) [1,800 rpm/(60 sec/min)] /150 psi = 0.095
Q/(RNCL) = ½ (5.6 in.3/sec)/(2.5 in. × 30 rps × 0.005 in. × 5 in.) = 1.49
On the “Finding friction” graph, the intersection of S and Q/(RNCL) is f(R/C) = 2.2. Then:
f = 2.2 (C/R) = 2.2 (0.002) = 0.0044
Calculate power loss and temperature rise:
E = fWU
E
= 0.0044 (150 psi × 5 in. × 5 in.) ( × 5 in. × 30 rps)
E = 7,775 in.-lb/sec = 1.18 hp @ 1 hp/6,600 in.-lb/sec
Δ T = E/(Qpcp)
Δ T = 7,775/[0.5 × 5.6 in.3/sec × 0.0307 lbm/in.3 × 4,535 in.-lb/(lbm-°F)]
Δ T = 19.9°F (close to the assumed 20°F rise)
On the “Finding lm thickness” graph, the intersection of S and Q/(RNCL) is hm/C = 0.32. Then:
hm = hm/C × C = 0.32 × 0.005 in. = 0.0016 in.

A film of this thickness is adequate to protect from friction and wear. Only below 10 to 20 times the typical journal surface roughness of 0.000016 to 0.000032 in. would the bearing contact and wear on surface asperities.

Example 2:
Ring-oiled bearing

Consider a ring-oiled sleeve bearing with the same dimensions as in the previous example. The ISO VG 32 oil in the reservoir is at 120°F and has kinematic viscosity, = 22 cSt or 0.034 in.2/sec at 1.55 × 10-3 in.2/cSt-sec. The bronze oil ring has a bore diameter, DR = 8 in., width, b = 0.75 in., and weight, w = 2.5 lb. Determine oil delivery rate, Q, to the bearing at the 1,800-rpm running speed.

While the surface speed of the ring bore and journal are equal at low speeds, the ring is carried on a full oil lm on a shaft rotating at 1,800 rpm (30 rev/sec). Ring speed NR is then:

NR = 1.67 v0.2 (ND2)0.8/(DR2) = 1.67 (0.034 in.2)/sec)0.2[(30 rev/sec)(5 in.)2]0.8/(8 in.)2 = 2.65 rev/sec

The rate of oil delivery to the bearing, Q, is then given by:
Q = 0.14 bv 0.65 (DRNR)1.5 = 0.14 (0.75 in.) (0.034 in.2/sec)0.65 [(8 in.)(2.65 rev/sec)]1.5 =1.14 in.3/sec.

This lubrication level is about 20% of the full oil-feed rate of 5.6 in.3/sec and should be reserved for low speeds and light duty. The shaft surface speed in this case is 30 rev/sec × 5 in. × π = 39 fps, which approaches the typical maximum 46 fps for ring-oiled bearings. Consider adding a second ring to boost reliability.

Example 3:
Wick-oiled bearing

What if an engineer used wick feeding instead of an oil ring for the bearing in the previous example? Assume a wick with cross-section A = 5 cm2, length Lw= 3.5 cm, and ultimate wicking height hu = 18 cm. Oil lift above the reservoir is h = 4 cm and mineral oil wicking in SAE Grade F-1 felt provides a constant kw = 4.6, oil viscosity μ = 22 cP, and volume fraction F0 = 0.75.

The oil-feed rate in a wick-oiled bearing is determined by:

Q = kwAF0(hu h)/( μLw)
Q = 4.6 × 5 cm2 × 0.75 × (18 cm – 4 cm)/(22 cP × 3.5 cm)
Q = 3.14 cm3/sec = 0.192 in.3/sec

To get a full hydrodynamic lm of oil, 5.6 in.3/sec is required. Even the amount of oil supplied by a ring in the previous example is greater than what wicks can achieve. If the engineer did go with the wick, he would have to restrict maximum journal surface speed to about 13 fps, or 596 rpm for this 5-in. journal.

Example 4:
Mist oiling

Estimate the appropriate oil-feed rate for a 5-in.-long sleeve bearing on a 5-in.-diameter shaft under a steady load of 1,000 lb at 100 rpm.

For a sleeve bearing in moderate service like this one, the required oil-feed rate can be estimated from:

Q = 0.005 LD = 0.005 × 5 in. × 5 in. = 0.125 in.3/hr

Or, to ensure hourly replacement of an oil layer 0.1-mm thick between the bearing bore and shaft surface:

Q = πLDhm/t = π × 5 in. × 5 in. × (0.1 mm × 1 in./25.4 mm)/1 hr = 0.31 in.3/hr.

The range from 0.125 to 0.31 in.3/hr re ects the general uncertainty involved. One approach would start by setting oil-feed rate 0.31 in.3/hr and gradually reducing it until excessive oil loss, bearing temperature, or vibration are noted. Alternately, start low and raise the feed rate if there are mechanical or thermal problems.

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