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GuidePublished 14 Aug 202623 min readBy Kevin JoginMachine DesignBearingsPlain and Journal Bearings: MaterialsDesign and Lubrication

Engineering · Machine Design · Bearings

Plain and Journal Bearings: Materials, Design and Lubrication: What Exactly Are Plain Bearings? The Three...

Engineering handbook for plain and journal bearings: materials, design and lubrication, covering what exactly are plain bearings? the three classes you must...

Executive summary

This handbook section converts the supplied engineering material into a practical, source-controlled reference. It concentrates on the following learning outcomes.

What Exactly Are Plain Bearings? The Three Classes You Must Know
Four Modes of Relative Motion
Plain Bearings vs. Rolling Contact Bearings: The Trade-Off
Types of Journal Bearings: Nine Configurations Every Engineer Should Recognize
. Circumferential-Groove Bearings
. Short Cylindrical Bearings

What Exactly Are Plain Bearings? The Three Classes You Must Know

Plain bearings—also called sliding bearings or sleeve bearings—provide sliding contact between mating surfaces. Unlike rolling element (anti-friction) bearings that use balls or rollers, plain bearings rely on a thin film of lubricant to separate moving surfaces.

Every plain bearing falls into one of three classes:

  • Radial bearings — Support rotating shafts or journals. These are the most common type, often called sleeve bearings or journal bearings
  • Thrust bearings — Support axial loads on rotating members
  • Guide or slipper bearings — Guide moving parts in a straight line (such as machine tool ways)

Within radial bearings, the two most common configurations are:

  • Full journal bearings — 360-degree contact with the mating journal
  • Partial journal bearings — Less than 180-degree contact; used when load direction is constant, offering simplicity, ease of lubrication, and reduced frictional loss

Four Modes of Relative Motion

The sliding surfaces in a plain bearing can operate under any of four conditions:

  1. Pure dry sliding — No lubricating medium between surfaces (e.g., nylon or PTFE bearings running dry)
  2. Hydrodynamic lubrication — A wedge-shaped film of lubricant builds up naturally from shaft rotation, partially or fully separating the surfaces
  3. Hydrostatic lubrication — Lubricant is introduced under external pressure, forcing surfaces apart regardless of speed
  4. Hybrid lubrication — A combination of hydrodynamic and hydrostatic action

Plain Bearings vs. Rolling Contact Bearings: The Trade-Off

Before you choose a bearing type, you need to understand what you're gaining—and what you're giving up.

Advantages of plain bearings over rolling contact bearings:

  • Require less space — Critical in compact assemblies
  • Quieter in operation — No rolling elements generating noise
  • Lower cost — Especially in high-volume production
  • Greater rigidity — No deflection from rolling element compliance
  • Life is generally not limited by fatigue — Unlike ball bearings with finite L10 life

Disadvantages of plain bearings:

  • Higher frictional properties — Result in higher power consumption
  • More susceptible to damage from foreign material in the lubrication system
  • More stringent lubrication requirements — Film must be continuously maintained
  • More susceptible to damage from interrupted lubrication supply — Even brief oil starvation can be catastrophic

The takeaway: Plain bearings a desktop spreadsheet application where space, noise, cost, and rigidity matter. Rolling bearings win where low friction, simple lubrication, and predictable fatigue life are priorities.



Types of Journal Bearings: Nine Configurations Every Engineer Should Recognize

the practitioner's mistake wasn't just ignorance about lubrication. He also didn't understand that different bearing geometries solve different problems. Here are the configurations that matter:


. Circumferential-Groove Bearings

An oil groove extends circumferentially around the bearing, dividing it into two shorter bearings that tend to run at slightly greater eccentricity. The stability advantage is slight, but the design is most commonly used in reciprocating-load main and connecting-rod bearings because of its uniform oil distribution.


. Short Cylindrical Bearings

A better solution than circumferential-groove bearings for high-speed, low-load service. The bearing is shortened to increase unit loading, forcing the shaft to ride at substantial eccentricity. Instability rarely results when shaft eccentricity exceeds 0.6. Very short bearings are avoided because they lack temporary rotating-load capacity if rotor unbalance develops during service.


. Cylindrical-Overshot Bearings

Used where surface speeds of 10,000 fpm or more exist and additional oil flow is needed for cooling. A wide circumferential groove extends across the upper half of the bearing between two axial oil grooves. The elimination of shearing action over the upper half, combined with the flow of cool oil, produces cooler operation.


. Pressure Bearings

Employ a groove over the top half that terminates at a sharp dam about 45 degrees beyond vertical in the direction of rotation. At high speed, the shaft's shear action pumps oil into this groove, where it's stopped by the dam, creating high pressure over the upper half. This self-generated load increases shaft eccentricity and stability.


. Elliptical (Lemon-Bore) Bearings

The bore is machined circular, then the bearing is assembled with shims at the split line. Removing the shims produces an elliptical bore with the major axis at the split. The increased clearance at the sides reduces the "cross-coupling" forces that cause oil whip instability. The most common geometry for fixed-geometry journal bearings in turbomachinery.


. Offset-Half Bearings

The upper half-bearing center is shifted in the direction of shaft rotation, creating a converging film in the upper half that generates a downward force to help stabilize the shaft. Used in high-speed, light-load applications where stability is critical.


. Three-Lobe Bearings

Three arcs, each with a center well outside the clearance circle, create three converging wedge regions. These are highly effective anti-oil-whip bearings but are more difficult to manufacture because the bore must be machined in three parts with shims between each part.


. Pivoted-Shoe (Tilting Pad) Bearings

One of the most stable bearing configurations. The bearing surface is divided into three or more individually pivoted segments. Each shoe tilts to form a wedge-shaped film, creating forces that push the shaft toward the center. For single-direction rotation, shoes may be pivoted near one end and spring-loaded.


. Nutcracker Bearings

Two cylindrical half-bearings with the upper half free to move vertically, forced toward the shaft by a hydraulic cylinder. The pressure can come from an external source or be tapped from the high-pressure film in the lower half (self-loading). Used to increase eccentricity to the point where stable operation is achieved.



Hydrostatic Bearings: When Hydrodynamics Isn't Enough

Hydrostatic bearings are used when operating conditions require full-film lubrication that cannot be developed hydrodynamically—typically at very low speeds or zero speed under heavy load.

The hydrostatically lubricated bearing is supplied with lubricant under pressure from an external source. The pressurized oil lifts the shaft off the bearing surface before rotation begins.

Key advantages of hydrostatic bearings:

  • Low friction — Even at zero speed
  • High load capacity — Independent of shaft speed
  • High reliability — No metal-to-metal contact at any operating condition
  • High stiffness — Excellent for precision applications
  • Long life — No wear under normal operating conditions

Successful applications include:

  • Machine tools (precision spindles)
  • Rolling mills
  • Heavily loaded, slow-moving machinery
  • Telescope mounts and radar antennas

Designer's warning: Hydrostatic bearing design requires specialized techniques and a thorough understanding of hydraulic components external to the bearing package. Do not specify this type of bearing without full knowledge of all aspects of the system, including pumps, flow control valves, pressure regulators, and filtration.



The Three Modes of Bearing Operation: Understanding the Friction Curve

This is where the practitioner's story gets instructive. He knew his bearings ran hot. He didn't understand why—because he didn't understand the Stribeck curve and the three modes of lubrication.


Mode 1: Full-Film (Hydrodynamic) Lubrication

Complete physical separation of sliding surfaces. This is the ideal operating condition, producing low friction and long, wear-free service life.

Requirements for achieving full-film lubrication:

  • Lubricant with correct viscosity for the proposed operation
  • Proper lubricant flow rates maintained
  • Proper design methods and considerations utilized
  • Surface velocity in excess of 25 feet per minute

Coefficient of friction: 0.001 to 0.005


Mode 2: Mixed-Film Lubrication

A transitional mode between full-film and boundary conditions. There is partial separation of the sliding surfaces by the lubricant film, but metal-to-metal contact still occurs intermittently.

Requirements:

  • Surface velocity in excess of 10 feet per minute

Coefficient of friction: 0.02 to 0.08


Mode 3: Boundary Lubrication

The sliding surfaces rub together with only an extremely thin film of lubricant present. This is acceptable only for oscillating or slow rotary motion.

Characteristics:

  • Oscillatory or rotary motion usually less than 10 feet per minute
  • Usually grease lubricated or periodically oil lubricated

Coefficient of friction: 0.08 to 0.14


The Critical Startup Sequence

Every journal bearing passes through all three modes during startup. At rest, the journal and bearing are in contact (boundary). As the shaft begins to rotate, operation transitions through mixed-film. When design speeds and loads are reached, a properly designed bearing achieves full-film lubrication.

Mode Surface Velocity Coefficient of Friction Film Condition
Full-Film > 25 fpm 0.001–0.005 Complete separation
Mixed-Film > 10 fpm 0.02–0.08 Partial separation
Boundary < 10 fpm 0.08–0.14 Rubbing contact

This is why startup and shutdown are the most dangerous moments for a plain bearing. The bearing must survive boundary and mixed-film conditions every time the machine cycles. Material selection, surface finish, and lubricant properties must account for these transient conditions—not just the steady-state design point.



Methods of Retaining Bearings: Keeping Them in Place

A bearing that moves in its housing is a bearing that fails. Several methods ensure bearings remain properly seated.


Press or Shrink Fit

The most common and satisfactory technique. The bearing is pressed or shrunk into the housing with an interference fit, permitting uniform wall thickness over the entire length.

Key specifications for stock bushings:

OD Size OD Oversize (Nominal)
≤ 3 inches 0.002–0.003 inch over nominal
> 3 inches 0.003–0.005 inch over nominal

Critical note: As a result of press or shrink fit, the bearing bore "closes in" by approximately 70 to 100 percent of the interference fit amount. Do not attempt to predict this reduction precisely to avoid final clearance machining—always machine after installation.

Shrink fit methods:

  • Dry ice in alcohol: Temperature of −110°F
  • Liquid air: Boils at −310°F
  • Chilling the bearing is easier and preferred over heating the housing

When pressing a bearing into the housing:

  • Apply driving force uniformly to the end of the bearing
  • Mating surfaces must be clean, smoothly finished, and free of machining imperfections

Keying Methods

When a press fit alone isn't sufficient, keying methods fix the bearing's position relative to the housing:

  • Set screws — Simple, but creates a stress concentration in the bearing wall
  • Woodruff keys — Good axial and rotational positioning
  • Bolted bearing flanges — Excellent for heavy-duty applications requiring frequent access
  • Threaded bearings — Bearing screwed directly into housing
  • Dowel pins — Precise rotational positioning
  • Housing caps — Clamp bearing in place axially

Factors to consider when selecting a keying method:

  • Maintain uniform wall thickness in the load-carrying region
  • Provide maximum contact area between bearing and housing for heat transfer
  • Prevent local deformation from the keying method—machine after keying
  • Consider thermal distortion effects on the keying method


Methods of Sealing: Containing the Lubricant, Excluding Contaminants

Every sealed bearing application has two jobs: prevent escape of fluid and prevent migration of foreign matter from outside.


Static vs. Dynamic: The First Decision

  • Static seal: No relative motion between joining parts or between seal and mating part
  • Dynamic seal: Any relative motion between parts—the seal must be selected accordingly

Dynamic Seals

Positive Contact (Rubbing) Seals:

Used where positive containment of liquids or gases is required or where the seal area is continuously flooded. When properly selected and applied, they can provide zero leakage for most fluids.

Cautions:

  • Sensitive to temperature, pressure, and speed
  • Improper application causes early failure
  • Applicable to both rotating and reciprocating shafts

Controlled Clearance (Noncontact) Seals:

Representative types include throttling bushings and labyrinths, which work by fluid-throttling action in narrow annular or radial passages.

Advantages:

  • Frictionless
  • Insensitive to temperature and speed
  • No wear or distortion during equipment life

Disadvantages:

  • Limited use when leakage rates are critical
  • Can become costly as configuration becomes elaborate

Static Seals

Cover a broad range of designs and materials:

  • Molded packings: Lip type and squeeze-molded
  • Simple compression packings
  • Diaphragm seals
  • Nonmetallic gaskets
  • O-rings
  • Metallic gaskets and O-rings


Hardness and Surface Finish: The Details That Make or Break Your Design

Even in well-lubricated full-film bearings, momentary contact between journal and bearing occurs during starting, stopping, or overloading. In mixed-film and boundary bearings, continuous metal-to-metal contact is the norm.


The Hardness Rule

The journal must always be harder than the bearing material. This ensures scoring and wear occur on the bearing (which is cheaper and easier to replace) rather than the shaft.

General rule: Recommended Brinell hardness of the journal is at least 100 points harder than the bearing material.

Specific hardness requirements by material:

Bearing Material Required Journal Hardness
High-lead, low-tin bronze (soft) Standard — adequate for boundary/mixed-film
High-tin, low-lead bronze (hard) Higher hardness required
Aluminum bronze 550–600 Bhn
Cast iron bearings 150–250 Bhn journal
Carbon-graphite bearings Cast iron ≥ 400 Bhn or hard chrome-plate steel; phosphor-bronze ≥ 135 Bhn

The harder the bearing material:

  • The better the alignment required
  • The more reliable the lubrication must be
  • The more carefully abrasives must be excluded

Surface Finish Requirements

Peak surface variations must be less than the expected minimum film thickness. Otherwise, asperity peaks will contact each other, producing high friction and temperature rise.

Surface roughness by finishing method:

Method Surface Roughness (microinches, rms)
Boring, broaching, reaming 32–64
Grinding 16–64
Fine grinding 4–16

Surface finish by operating mode:

Operating Mode Bearing (µin rms) Journal (µin rms)
Full-Film 6–16 8–20
Mixed-Film 12–32 16–32
Complete Boundary 16–63 20–63

Rules of thumb:

  • Smoother finishes are required for harder materials, high loads, and high speeds
  • Full-film bearings at high eccentricity ratios need the best surface finishes
  • Boundary and mixed-film bearings can tolerate rougher finishes because wear-in will eventually smooth the surfaces


Machining Journal Bearing Bores: Four Methods Compared

The method you use to finish the bearing bore determines your achievable tolerances, alignment, and surface quality.


Boring

The gold standard. Provides the best concentricity, alignment, and size control. It is the finishing method of choice when close tolerances and clearances are desirable.


Broaching

A rapid finishing method with good size and alignment control when adequate piloting is possible. Particularly compatible with soft babbitt materials.


Reaming

Facilitates good size and alignment control when piloting is utilized. Can be accomplished manually or by machine—machine method is preferred.


Burnishing

A fast sizing operation with good alignment control but not as good size control as cutting methods. Not recommended for soft materials such as babbitt.

Special benefit: Burnishing has an ironing effect that gives added seating of the bushing OD in the housing bore. It is often used for this purpose on thin-wall (1/32-inch) bushings, even when a further sizing operation follows.

Method Size Control Alignment Control Speed Best For
Boring Excellent Excellent Moderate Close tolerances
Broaching Good Good Fast Babbitt, production runs
Reaming Good Good Moderate General purpose
Burnishing Fair Good Fast Thin-wall bushings, added seating


Methods of Lubrication: Choosing the Right Delivery System

The lubrication method you choose determines your bearing's load capacity, operating temperature, and reliability. Here is every major method, ranked from most to least effective.


. Pressure Lubrication (Best)

Oil is fed abundantly to the bearing from a central groove, single or multiple holes, or axial grooves. The moving oil:

  • Flushes dirt from the bearing
  • Removes heat faster than any other method
  • Permits thinner oil films and unimpaired load capacities

Oil supply pressure is directly proportional to shaft speed, but for most installations, 50 psi is adequate.


. Oil Bath Lubrication

The bushing is submerged in oil. The most reliable method except pressure lubrication. Practical if:

  • The housing can be made oil-tight
  • Shaft speed is not so great as to cause excessive churning

. Oil Ring Lubrication

A ring in contact with the shaft picks up oil and delivers it to the bearing. Within reasonable limits, it brings enough oil to maintain hydrodynamic lubrication.

Optimal operating range: Peripheral speed of shaft between 200 and 2,000 feet per minute.

Load capacity limitations:

  • Safe load for hydrodynamic lubrication: one-half that of pressure-fed bearings
  • Unless load is light, hydrodynamic lubrication is doubtful
  • Safe load then becomes one-quarter that of pressure-fed bearings

Failure modes:

  • Speed too low → insufficient oil delivered
  • Speed too high → ring can't keep pace; centrifugal force throws oil off ring

. Splash Fed Lubrication

Covers a variety of intermittently lubricated bushings, from bearings spattered by other moving parts to bearings regularly dipped in oil. Practical when housing can be made oil-tight and moving parts don't churn the oil. Requires engineering judgment for load capacity determination.


. Wick or Waste Pack Lubrication

Oil is delivered by capillary action. The amount delivered is proportional to the size of the wick or pack. Suitable for light-duty applications.


. Grease Lubrication

Grease packed in a cavity surrounding the bushing is less adequate than oil but has the advantage of being semi-permanent. Although hydrodynamic lubrication is possible under very favorable circumstances, boundary lubrication is the usual state.

Coefficients of friction for grease-lubricated bearings: 0.08 to 0.16

Average design value: 0.12



Lubricant Selection: Matching Oil to Operating Conditions

The value of an oil as a lubricant depends mainly on its film-forming capacity—its ability to maintain a continuous film between bearing surfaces. This depends largely on viscosity.

Critical principle: An oil of the lowest viscosity that will retain an unbroken oil film is the most suitable lubricant. Higher viscosity than necessary wastes power by overcoming internal fluid friction.


The Selection Method

Three factors drive lubricant selection:

  1. Type of operation (full, mixed, or boundary film)
  2. Surface speed (RPM)
  3. Bearing loading (light or heavy)

General lubricant selection guide:

Journal Speed (RPM) Light Load (100 psi) Full-Film Heavy Load (250 psi) Full-Film Boundary/Mixed (Light) Boundary/Mixed (Heavy)
10–60 SAE 20–30 SAE 30–50 Grease Grease
60–200 SAE 10–20 SAE 20–40 SAE 40–50 SAE 50
200–1,000 SAE 10 SAE 20–30 SAE 30 SAE 40
1,000–4,000 SAE 5–10 SAE 10–20 SAE 20 SAE 30
4,000–10,000 SAE 5 SAE 10 SAE 10 SAE 20

Rule of thumb: Heavier oils for high loads; lighter oils for high speeds.


Oil Viscosity Unit Conversion

When working across international standards, you'll need to convert between viscosity units:

Convert From To Centipoise (Z) To Reyn (µ)
Poise (P) × 100 × 1.45 × 10⁻⁵
Centipoise (Z) × 1.45 × 10⁻⁷
Reyn (µ) × 6.9 × 10⁶
Centistoke (v) × ρ (specific gravity) × 1.45 × 10⁻⁷ × ρ


Greases and Solid Lubricants: When Oil Isn't Practical

There are valid engineering reasons to use greases or solid lubricants instead of oil:

  • Lengthen the period between relubrication
  • Avoid contaminating surrounding equipment with leaking oil
  • Extreme temperature ranges where oils fail
  • Contaminating atmospheres where oils degrade
  • Extreme unit pressures that would destroy boundary lubricating films

Grease Types and Operating Limits

Grease Type Max Operating Temperature Load Range Notes
Calcium (lime soap) 160°F Moderate
Sodium soap 300°F Wide Good for wide speed range
Aluminum soap 180°F Moderate
Lithium soap 300°F Moderate Good low-temperature performance
Barium soap 350°F Wide

NLGI Grease Consistency Classification

NLGI No. Consistency Typical Application Method
0 Semifluid Brush or gun
1 Very soft Pin-type cup or gun
2 Soft Pressure gun or centralized system
3 Light cup grease Pressure gun or centralized system
4 Medium cup grease Pressure gun or centralized system
5 Heavy cup grease Pressure gun or hand
6 Block grease Hand, cut to fit

Grease groove note: Grooves for grease should generally be up to 1.5 times wider than those for oil.


Solid Lubricants

For extreme conditions where neither oil nor grease will work:

Lubricant Operating Temperature Load Range
Graphite Up to 1,000°F Wide
Molybdenum disulfide (MoS₂) −100°F to 750°F Wide


Journal Bearing Anatomy: The Three Essential Components

No matter the shape, every journal bearing has three basic components:

  1. Journal (shaft) — The rotating member
  2. Bushing (bearing) — The stationary member
  3. Lubricant — The separating medium

Key Nomenclature

  • W = Applied load
  • N = Revolutions per minute
  • e = Eccentricity (offset of journal center from bearing center)
  • θ = Attitude angle (angle between applied load and point of minimum film thickness)
  • d = Journal diameter
  • c_d = Diametral clearance (bearing diameter minus journal diameter)
  • h_o = Minimum film thickness
         ┌─────────────────────┐
         │      Bearing        │
         │   ┌─────────────┐   │
         │   │   Lubricant  │   │
         │   │  ┌───────┐   │   │
         │   │  │Journal │   │   │
         │   │  │   ●    │ e │   │
         │   │  └───────┘   │   │
         │   │   ← ho →     │   │
         │   └─────────────┘   │
         └─────────────────────┘
              d ──────────
           d + cd ──────────────

The journal does not sit concentrically in the bearing. Under load, it shifts to one side, creating a converging wedge of lubricant that generates the hydrodynamic pressure to support the load.



Grooving and Oil Feeding: Getting Lubricant Where It Matters

Grooving in a journal bearing serves two purposes:

  1. Establish and maintain an efficient lubricant film between moving surfaces
  2. Provide adequate bearing cooling

The only practical location for introducing lubricant is in a region of low pressure. In a loaded bearing, the high-pressure zone is on the loaded side where the film converges. Oil must enter from the unloaded side.


Five Common Grooving Configurations

  1. Single inlet hole — Simplest design; oil enters through a single drilled hole in the unloaded region
  2. Circular groove — Circumferential groove divides bearing into two halves; length l for design purposes is one-half the total bearing length
  3. Straight axial groove — Runs parallel to the shaft axis in the unloaded region
  4. Straight axial groove with feeder groove — Axial groove with circumferential feed channels for better distribution
  5. Straight axial groove in shaft — Groove is machined into the journal itself rather than the bearing


Heat Radiating Capacity: Preventing Thermal Runaway

In a self-contained lubrication system, the heat generated by bearing friction must be removed to prevent continued temperature rise.


The Heat Radiation Formula

HR=LdCtRH_R = L \cdot d \cdot C \cdot t_R

Where:

  • HRH_R = Heat-radiating capacity (ft-lb/min)
  • LL = Total length of bearing (inches)
  • dd = Bearing diameter (inches)
  • CC = Constant (determined by O. Lasche)
  • tRt_R = Temperature rise (°F)

The product CtRC \cdot t_R varies based on bearing ventilation conditions:

Condition CtRC \cdot t_R at 60°F Rise CtRC \cdot t_R at 120°F Rise
Thin bearing ~200 ft-lb/min/in² ~700 ft-lb/min/in²
Unventilated ~250 ft-lb/min/in² ~600 ft-lb/min/in²
Well ventilated ~350 ft-lb/min/in² ~1000 ft-lb/min/in²

This is where the practitioner went wrong. His No. 4 dryer bearing was in an unventilated enclosure. The heat radiation capacity was far lower than he assumed. The bearing couldn't shed heat fast enough, oil viscosity dropped, film thickness collapsed, and the bearing entered mixed-film operation. From there, it was a slow spiral to seizure.



Journal Bearing Design: The Complete Step-by-Step Lubrication Analysis

This is the heart of journal bearing engineering. The following procedure leads to a complete lubrication analysis that forms the basis for bearing design.


Design Notation

Symbol Definition Units
c Specific heat of lubricant Btu/lb/°F
c_d Diametral clearance inches
C_n Bearing capacity number
d Journal diameter inches
e Eccentricity inches
h_o Minimum film thickness inches
K Constants (1 for single oil hole; 2 for central groove)
l Bearing length (as defined by groove type) inches
L Actual overall length of bearing inches
m Clearance modulus (c_d / d)
N Shaft speed rpm
p_b Unit load psi
p_s Oil supply pressure psi
P_f Friction horsepower hp
P′ Bearing pressure parameter
q Flow factor
Q_1 Hydrodynamic flow gpm
Q_2 Pressure flow gpm
Q Total flow gpm
Q_R Total flow required gpm
r Journal radius inches
Δt Actual temperature rise °F
Δt_a Assumed temperature rise °F
t_b Bearing operating temperature °F
t_in Oil inlet temperature °F
T_f Friction torque in-lb/in
T′ Torque parameter
W Load pounds
X Factor (from Table or calculation)
Z Viscosity centipoises
ε Eccentricity ratio
α Oil density lb/in³

The 23-Step Procedure

Step 1: Journal Diameter (d)

Determined by shaft strength and/or deflection requirements using strength of materials principles. The bearing bore is designed around the shaft—not the other way around.

Step 2: Bearing Length (L)

Determined by an assumed l/d ratio. Bearing pressure and the possibility of edge loading from shaft deflection and misalignment must be considered.

Alignment rule: Shaft misalignment from location tolerances and/or deflections should be maintained below 0.0003 inch per inch of length.

Step 3: Bearing Pressure (p_b)

pb=WKldp_b = \frac{W}{K \cdot l \cdot d}

Where K = 1 for single oil hole, K = 2 for central groove.


Allowable Sleeve Bearing Pressures

Type of Service Pressure (psi)
Electric motor & generator bearings 100–200
Turbine & reduction gears 100–250
Heavy line shafting 100–150
Locomotive axles 300–350
Light line shafting 15–35
Diesel engine, main 800–1,500
Diesel engine, rod 1,000–2,000
Diesel engine, wrist pins 1,800–2,000
Automotive, main bearings 500–700
Automotive, rod bearings 1,500–2,500
Centrifugal pumps 80–100
Aircraft rod bearings 700–3,000

Step 4: Diametral Clearance (c_d)

Selected on a trial basis from recommended ranges based on shaft diameter and speed:

  • Above 600 rpm: Tighter clearance range
  • Below 600 rpm: Wider clearance range

These are hot or operating clearances—thermal expansion of journal and bearing must be accounted for when establishing machining dimensions.

Clearance modulus:

m=cddm = \frac{c_d}{d}

Step 5: Length-to-Diameter Ratio (l/d)

Usually between 1 and 2, though modern high-speed compact designs use ratios as low as 0.3.


Representative l/d Ratios

Type of Service l/d Ratio
Gasoline and diesel engine main bearings & crankpins 0.3–1.0
Generators and motors 1.2–2.5
Turbogenerators 0.8–1.5
Machine tools 2.0–3.0
Light shafting 2.5–3.5
Heavy shafting 2.0–3.0
Steam engine main bearings 1.5–2.5
Steam engine crank and wrist pins 1.0–1.3

Step 6: Assumed Operating Temperature (t_b)

tb=tin+Δtat_b = t_{in} + \Delta t_a

An initial assumption of Δt_a = 20°F is standard.

Step 7: Viscosity of Lubricant (Z)

The viscosity in centipoises at the assumed bearing operating temperature is found from viscosity-temperature curves for SAE grade oils.

Step 8: Bearing Pressure Parameter (P′)

P=6.9×1000×m2×pbZ×NP' = \frac{6.9 \times 1000 \times m^2 \times p_b}{Z \times N}

Step 9: Eccentricity Ratio (ε)

Using P′ and l/d, the value of 1/(1 − ε) is determined from design charts. From this, ε is calculated.

Step 10: Torque Parameter (T′)

Obtained from design charts using 1/(1 − ε) and l/d.

Step 11: Friction Torque (T_f)

Tf=T×r2×Z×N6900×1000×mT_f = \frac{T' \times r^2 \times Z \times N}{6900 \times 1000 \times m}

Step 12: Friction Horsepower (P_f)

Pf=K×Tf×N×l63,000P_f = \frac{K \times T_f \times N \times l}{63{,}000}

Step 13: Factor X

Can be obtained from the table below or calculated:

X=0.1837α×cX = \frac{0.1837}{\alpha \times c}

Temperature (°F) X Factor
100 12.9
150 12.4
200 12.1
250 11.8
300 11.5

Step 14: Total Flow Required (Q_R)

QR=X×PfΔtaQ_R = \frac{X \times P_f}{\Delta t_a}

Step 15: Bearing Capacity Number (C_n)

Cn=(l/d)260×PC_n = \frac{(l/d)^2}{60 \times P'}

Step 16: Flow Factor (q)

Obtained from design charts using C_n.

Step 17: Hydrodynamic Flow (Q_1)

Q1=N×l×cd×q×d294Q_1 = \frac{N \times l \times c_d \times q \times d}{294}

Step 18: Pressure Flow (Q_2)

Q2=K×ps×cd3×d×(1+1.5ϵ2)Z×lQ_2 = \frac{K \times p_s \times c_d^3 \times d \times (1 + 1.5\epsilon^2)}{Z \times l}

Where K = 1.64 × 10⁵ for single oil hole; K = 2.35 × 10⁵ for central groove.

Step 19: Total Flow (Q)

Q=Q1+Q2Q = Q_1 + Q_2

Step 20: Bearing Temperature Rise (Δt)

Δt=X×PfQ\Delta t = \frac{X \times P_f}{Q}

Step 21: Comparison of Actual and Assumed Temperature Rise

If Δt_a and Δt differ by more than 5°F, repeat Steps 7–20 using a new Δt halfway between the former Δt_a and Δt.

Step 22: Minimum Film Thickness (h_o)

When the temperature iteration converges:

ho=cd2×(1ϵ)h_o = \frac{c_d}{2} \times (1 - \epsilon)

Step 23: Iterate for Clearance Optimization

Assume a new diametral clearance c_d and repeat Steps 4–22. When sufficient values have been calculated, plot the full lubrication study showing:

  • Minimum film thickness vs. c_d
  • Oil temperature rise vs. c_d
  • Friction horsepower vs. c_d
  • Oil flow vs. c_d

From these curves, determine the optimum operating clearance range.


Engineering use and verification

Begin with load paths, motion, interfaces and credible failure modes. Define duty cycle, environment, alignment, lubrication, manufacturing variation and maintenance access before choosing a component. Check static strength, fatigue, stiffness, heat, wear and fastening together because improving one constraint can worsen another. Record assumptions and verify the assembled system, not just catalogue ratings for isolated parts.

  • Confirm scope, assumptions, interfaces and required outcome.
  • Use one controlled unit system and show every conversion.
  • Identify current project, customer and regulatory requirements.
  • Separate source examples from mandatory acceptance criteria.
  • Check calculations, tables and selections by an independent method.
  • Verify safety, maintainability and credible failure modes.
  • Record evidence, revisions, approvals and unresolved limitations.
  • Validate the result under representative operating conditions.

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