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:
- Pure dry sliding — No lubricating medium between surfaces (e.g., nylon or PTFE bearings running dry)
- Hydrodynamic lubrication — A wedge-shaped film of lubricant builds up naturally from shaft rotation, partially or fully separating the surfaces
- Hydrostatic lubrication — Lubricant is introduced under external pressure, forcing surfaces apart regardless of speed
- 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:
- Type of operation (full, mixed, or boundary film)
- Surface speed (RPM)
- 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:
- Journal (shaft) — The rotating member
- Bushing (bearing) — The stationary member
- 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:
- Establish and maintain an efficient lubricant film between moving surfaces
- 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
- Single inlet hole — Simplest design; oil enters through a single drilled hole in the unloaded region
- Circular groove — Circumferential groove divides bearing into two halves; length l for design purposes is one-half the total bearing length
- Straight axial groove — Runs parallel to the shaft axis in the unloaded region
- Straight axial groove with feeder groove — Axial groove with circumferential feed channels for better distribution
- 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
Where:
- = Heat-radiating capacity (ft-lb/min)
- = Total length of bearing (inches)
- = Bearing diameter (inches)
- = Constant (determined by O. Lasche)
- = Temperature rise (°F)
The product varies based on bearing ventilation conditions:
| Condition | at 60°F Rise | 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)
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:
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)
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′)
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)
Step 12: Friction Horsepower (P_f)
Step 13: Factor X
Can be obtained from the table below or calculated:
| 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)
Step 15: Bearing Capacity Number (C_n)
Step 16: Flow Factor (q)
Obtained from design charts using C_n.
Step 17: Hydrodynamic Flow (Q_1)
Step 18: Pressure Flow (Q_2)
Where K = 1.64 × 10⁵ for single oil hole; K = 2.35 × 10⁵ for central groove.
Step 19: Total Flow (Q)
Step 20: Bearing Temperature Rise (Δt)
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:
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.
