Mechanical Design Data and Machine-Element Reference: Bearing Type Selection Characteristics

Bearing Type Selection Characteristics

Legend: ++ = excellent, + = good, — = poor/unsuitable, ½ = limited in one direction

Bearing Selection Procedures

Selection of Deep Groove Ball Bearings (Method 1 — Basic L₁₀ Life)

1. Determine required life in operating hours
   • Consider continuous vs intermittent operation and expected equipment life
   • Common default for mechanical design: 10 years
2. Convert design life from hours to millions of revolutions:
   • L = (60 × N × h) / 10⁶
   • Where: L = design life (millions of revolutions), N = average speed (rev/min), h = design life (hours)
3. Determine average radial load (Fr) and axial load (Fa)
   • Loads are typically shaft reaction forces at the bearing
   • Apply shock factors to steady loads where dynamic loads occur
4. Calculate the ratio Fa/Fr
5. Select a bearing from data tables for the known shaft size
   • In the absence of other knowledge, select a bearing around the mid-range of those available
   • Record the static load rating Co and dynamic load rating C
6. Calculate the ratio Fa/Co and read off the value of e from the calculation factors graph
   • For normal clearance bearings, project from the Fa/Co value to the Y line and down to the e scale
7. Calculate the equivalent dynamic bearing load P:
   • If Fa/Fr ≤ e → then P = Fr
   • If Fa/Fr > e → then P = X·Fr + Y·Fa where X = 0.56
   • Values of Y can be read from the graph by projecting across from the Fa/Co value to the Y line
   • Note: This graph is drawn for normal clearance bearings
8. Calculate the bearing L₁₀ life:
   • L₁₀ = (C / P)³
9. Compare L₁₀ to L:
   • If L₁₀ < L → bearing is too small; repeat steps 5–8 with a higher load capacity bearing
   • If L₁₀ ≈ L → bearing is acceptable
   • If L₁₀ > L → bearing may be oversized; repeat with a lower load capacity bearing
10. Calculate equivalent static bearing load Po:
    • Po = 0.6·Fr + 0.5·Fa
    • Check that Po < Co; if not, select another bearing
    • Note: If Po < Fr then set Po = Fr
11. Check minimum radial load:
    • For satisfactory operation: Fr > 0.01·C
    • More accurate methods based on lubricant viscosity and operating speed exist in manufacturer catalogues
12. Check maximum shaft speed does not exceed the speed rating of the bearing

Selection of Self-Aligning Ball Bearings (Method 1 — Basic L₁₀ Life)

• Steps 1–4 are identical to the deep groove ball procedure
• Step 5: Use bearing data tables specific to self-aligning ball bearings (with or without adaptor sleeves)
  • Record C, Co, and calculation factors: e, Y₁, Y₂, Y₀
• Step 6: Calculate equivalent dynamic bearing load P:
  • If Fa/Fr ≤ e → then P = Fr + Y₁·Fa
  • If Fa/Fr > e → then P = 0.65·Fr + Y₂·Fa
• Steps 7–8: Calculate L₁₀ life using L₁₀ = (C / P)³ and compare to required life
• Step 9: Calculate equivalent static bearing load:
  • Po = Fr + Y₀·Fa
  • Check that Po < Co
  • Note: If Po < Fr then set Po = Fr
• Step 10: Minimum radial load check: Fr > 0.01·C
• Step 11: Check maximum shaft speed
• Step 12: If tapered bore with adaptor sleeve, check axial load limit:
  • Fa < 3·B·d
  • Where: Fa = axial load (N), B = bearing width (mm), d = internal diameter (mm)

Selection of Cylindrical Roller Bearings (Method 1 — Basic L₁₀ Life)

• Steps 1–4 follow the same pattern
  • Note: Fa/Fr ratio should not exceed 0.5
• Step 5: Use cylindrical roller bearing data tables; record Co and C
• Step 6: Calculate equivalent dynamic bearing load P:
  • For bearings without flanges (type NU): P = Fr
  • For bearings with flanges:
    • If Fa/Fr ≤ e → then P = Fr
    • If Fa/Fr > e → then P = 0.92·Fr + Y·Fa
    • Where: e = 0.2, Y = 0.6 for series 10, 2, 3, and 4; e = 0.3, Y = 0.4 for series 22 and 23
• Step 7: Calculate L₁₀ using: L₁₀ = (C / P)^(10/3)
  • Note: Roller bearings use the exponent 10/3 rather than 3
• Steps 8–9: Compare life, check static load:
  • Po < Co/1.5 (for cylindrical roller bearings)
  • Note: Po = Fr for cylindrical roller bearings
• Step 10: Minimum radial load: Fr > 0.02·C
• Step 11: Check maximum shaft speed

Selection of Spherical (Self-Aligning) Roller Bearings (Method 1 — Basic L₁₀ Life)

• Steps 1–4 follow the same pattern
• Step 5: Use spherical roller bearing data tables; record Co, C, and calculation factors e, Y₁, Y₂, Y₀
• Step 6: Calculate equivalent dynamic bearing load P:
  • If Fa/Fr ≤ e → then P = Fr + Y₁·Fa
  • If Fa/Fr > e → then P = 0.67·Fr + Y₂·Fa
• Step 7: Calculate L₁₀ using: L₁₀ = (C / P)^(10/3)
  • Roller bearing exponent 10/3 applies
• Steps 8–9: Compare life, check static load:
  • Po = Fr + Y₀·Fa
  • Check that Po < Co/1.5
• Step 10: Minimum radial load: Fr > 0.02·C
• Step 11: Check maximum shaft speed

Method 2 — Adjusted Rating Life

• Uses the formula: Lna = a₁ × a₂ × a₃ × L₁₀
• Where:
  • a₁ = life adjustment factor for reliability
  • a₂ = life adjustment factor for material
  • a₃ = life adjustment factor for operating conditions

Reliability Factor (a₁)

• For the standard 90% reliability: a₁ = 1
• For higher reliability levels, manufacturer handbooks provide corresponding a₁ values (always < 1)

Material Factor (a₂)

• For standard bearing steels (as defined by international standards): a₂ = 1
• Premium manufacturer steels may have higher life properties

Operating Conditions Factor (a₃)

• Determined primarily by bearing lubrication (assuming normal operating temperatures and cleanliness)
• Some manufacturers combine a₂ and a₃ into a single factor a₂₃

Determining a₂₃

1. Calculate the mean diameter of the bearing: dₘ = 0.5 × (d + D)
   • Where d = bore diameter, D = outer diameter
2. From Diagram 1, read the required kinematic viscosity (ν₁) for adequate lubrication at the given rotational speed and mean diameter
3. Calculate the viscosity ratio: κ = ν / ν₁
   • Where ν = actual kinematic viscosity of the lubricant at operating temperature
4. From Diagram 3, read the value of a₂₃ based on κ
5. Apply: Lna = a₁ × a₂₃ × L₁₀

Notes on Viscosity and Temperature

• Viscosity and temperature of lubricants are interrelated; for liquid lubricants, viscosity decreases with temperature
• Typical pre-lubricated deep groove ball bearing grease has a viscosity of 100 mm²/s at 40°C
• Operating temperature depends on ambient temperature, bearing load, shaft speed, housing design, and similar factors
• Measurement of similar bearings under operating conditions is a good method for estimating operating temperature
• Diagram notes: shaded area on Diagram 3 is for lubricants with additives; diagrams are valid for mineral oils and greases under normal cleanliness conditions

Method 3 — New Life Theory

• Introduces the concept of a fatigue load limit (Pu) — the load below which fatigue will not occur (given adequate lubrication and cleanliness)
• For loads below Pu, the bearing theoretically lasts indefinitely
• The formula: Lnaa = a₁ × a_the bearing supplier × L₁₀
• Where:
  • a₁ = reliability factor (same as Method 2)
  • a_the bearing supplier = life adjustment factor based on new life theory

Determining a_the bearing supplier

1. Calculate the viscosity ratio κ (same as Method 2)
2. Determine the contamination factor ηc from the contamination table
3. Calculate: ηc × Pu / P
4. From Diagram 4 (ball bearings) or Diagram 5 (roller bearings), read a_the bearing supplier based on κ and ηc·Pu/P
5. Apply: Lnaa = a₁ × a_the bearing supplier × L₁₀ (assuming a₁ = 1 for 90% reliability: L_the bearing supplier = a_the bearing supplier × L₁₀)

Key insight: If κ > 4, use the κ = 4 curve. As ηc·Pu/P tends to zero, a_the bearing supplier tends to 0.1 for all values of κ

Contamination Factor (ηc) Reference Table

Worked Example — Comparing All Three Methods

Given:

• Shaft diameter: 45 mm
• Speed: 5000 rev/min
• Bearing designation: 6309 (deep groove ball)
• Radial load: 8 kN, no axial load
• Lubrication: oil with viscosity 20 mm²/s at operating temperature
• Reliability: 90% (normal)

Method 1 — Basic L₁₀ Life:

• From bearing tables for 6309 (45 mm shaft): C = 52.7 kN
• Since no axial load: P = Fr = 8 kN
• L₁₀ = (52.7 / 8)³ = 286 million revolutions

Method 2 — Adjusted Life:

• a₁ = 1 (90% reliability)
• From tables: D = 100 mm → dₘ = 0.5 × (45 + 100) = 72.5 mm
• From Diagram 1 at 5000 rpm: required viscosity ν₁ = 7 mm²/s
• Actual viscosity ν = 20 mm²/s → κ = 20/7 = 2.9
• From Diagram 3 with κ = 2.9: a₂₃ = 2
• Lna = 1 × 2 × 286 = 572 million revolutions
• The longer life is due to lubricating oil viscosity being ~3× the minimum required

Method 3 — New Life Theory:

(a) Clean conditions:

• From tables: Pu = 1.34 kN, ηc = 0.8 (normal cleanliness)
• ηc × Pu/P = 0.8 × 1.34/8 = 0.134
• From Diagram 4 with κ = 2.9: a_the bearing supplier ≈ 8
• Lnaa = 8 × 286 = 2288 million revolutions
• This is 4× higher than the adjusted life method prediction

(b) Contaminated conditions (ηc = 0.2):

• ηc × Pu/P = 0.2 × 1.34/8 = 0.0335
• From Diagram 4 with κ = 2.9: a_the bearing supplier ≈ 1.2
• Lnaa = 1.2 × 286 = 343 million revolutions
• Contamination causes a considerable reduction in predicted life

Life Calculation Methods Comparison

Bearing Exponents by Type

Equivalent Dynamic Load Formulas in the supplied reference

Equivalent Static Load Formulas in the supplied reference

Note: For all types, if Po < Fr, then set Po = Fr

Minimum Radial Load Requirements

Self-Aligning Ball Bearing Adaptor Sleeve Axial Load Limit

Bearing Selection Decision Process

flowchart TD
    A[Start: Define Operating Requirements] --> B[Determine required life in hours]
    B --> C[Convert hours to millions of revolutions<br/>L = 60·N·h / 10⁶]
    C --> D[Determine radial load Fr and axial load Fa]
    D --> E[Calculate Fa/Fr ratio]
    E --> F[Select bearing type based on<br/>load direction, speed, alignment needs]
    F --> G[Select specific bearing from data tables<br/>Record C, Co, and calculation factors]
    G --> H[Calculate equivalent dynamic load P]
    H --> I[Calculate L₁₀ = C/P raised to p<br/>p=3 ball, p=10/3 roller]
    I --> J{L₁₀ vs L?}
    J -->|L₁₀ < L| K[Bearing too small<br/>Select higher capacity]
    K --> G
    J -->|L₁₀ ≈ L| L[Bearing OK]
    J -->|L₁₀ >> L| M[Bearing oversized<br/>Select lower capacity]
    M --> G
    L --> N[Check static load Po < Co or Co/1.5]
    N --> O[Check minimum radial load]
    O --> P[Check maximum shaft speed]
    P --> Q[Bearing Selection Complete]

Three Life Calculation Methods

flowchart LR
    subgraph Method1["Method 1: Basic L₁₀"]
        M1A[Load data only] --> M1B["L₁₀ = (C/P)^p"]
    end

    subgraph Method2["Method 2: Adjusted Life Lna"]
        M2A[Load data] --> M2D
        M2B[Reliability a₁] --> M2D
        M2C[Material + Lubrication a₂₃] --> M2D
        M2D["Lna = a₁ · a₂₃ · L₁₀"]
    end

    subgraph Method3["Method 3: New Life Lnaa"]
        M3A[Load data] --> M3E
        M3B[Reliability a₁] --> M3E
        M3C[Viscosity ratio κ] --> M3E
        M3D[Contamination ηc + Fatigue limit Pu] --> M3E
        M3E["Lnaa = a₁ · a_the bearing supplier · L₁₀"]
    end

    Method1 -.->|Adds reliability,<br/>material, lubrication| Method2
    Method2 -.->|Adds fatigue limit<br/>and contamination| Method3

Factors Affecting Bearing Life

flowchart TD
    A[Bearing Life] --> B[Steel Type]
    A --> C[Lubrication]
    A --> D[Cleanliness]

    B --> B1[Standard ISO steel: a₂ = 1]
    B --> B2[Premium steels: a₂ > 1]

    C --> C1[Lubricant type: oil / grease]
    C --> C2[Additives present?]
    C --> C3[Viscosity at operating temp]
    C --> C4[Circulation and filtration method]
    C --> C5[Change interval]

    D --> D1[Environmental contaminants]
    D --> D2[Metallic particles / dirt / dust]
    D --> D3[Water contamination]
    D --> D4[Lubricant filtration quality]
    D --> D5[Sealing method effectiveness]

Viscosity Ratio (κ) Determination Process

flowchart TD
    A[Calculate mean diameter<br/>dₘ = 0.5 × d + D] --> B[Use Diagram 1:<br/>Find required viscosity ν₁<br/>from speed and dₘ]
    B --> C[Determine actual lubricant<br/>viscosity ν at operating temp]
    C --> D[Calculate κ = ν / ν₁]
    D --> E{κ value?}
    E -->|κ < 1| F[Inadequate lubrication<br/>Reduced life]
    E -->|κ ≈ 1| G[Marginal lubrication<br/>Standard life]
    E -->|κ > 1| H[Good lubrication<br/>Extended life]
    E -->|κ > 4| I[Use κ = 4 curve<br/>Maximum benefit reached]

Imperial-Metric Equivalents Reference

Key Terms Glossary

• L₁₀ Life: The rated life at which 90% of a group of identical bearings will survive under a specified load; expressed in millions of revolutions
• Basic Dynamic Load Rating (C): The constant radial load that produces a basic rating life of 1 million revolutions for a bearing
• Basic Static Load Rating (Co): The static load that produces a specified permanent deformation at the most heavily stressed rolling element/raceway contact
• Fatigue Load Limit (Pu): The load below which metal fatigue will not occur in a bearing with adequate lubrication and cleanliness (used in Method 3)
• Equivalent Dynamic Bearing Load (P): A calculated constant radial load that would produce the same life as the actual combined radial and axial loads
• Equivalent Static Bearing Load (Po): A calculated static radial load that would cause the same total permanent deformation as the actual combined loads
• Viscosity Ratio (κ): The ratio of actual lubricant kinematic viscosity to the required minimum kinematic viscosity at operating temperature (κ = ν/ν₁)
• Contamination Factor (ηc): A factor (0 to 1) representing the level of particulate contamination in the bearing operating environment
• Adjusted Rating Life (Lna): Bearing life calculated using Method 2, incorporating reliability, material, and lubrication adjustment factors
• a₁: Life adjustment factor for reliability (= 1 for 90% reliability)
• a₂: Life adjustment factor for material (= 1 for standard bearing steels)
• a₃: Life adjustment factor for operating conditions (primarily lubrication)
• a₂₃: Combined material and operating conditions factor
• a_the bearing supplier: Life adjustment factor used in the new life theory (Method 3)
• Deep Groove Ball Bearing: Most common bearing type; handles radial and moderate axial loads; low friction; high speed capability
• Self-Aligning Ball Bearing: Accommodates shaft misalignment and deflection; uses a spherical outer ring raceway
• Cylindrical Roller Bearing: Handles heavy radial loads; higher capacity than ball bearings of equivalent size; line contact between rollers and raceways
• Spherical Roller Bearing: Handles heavy radial and moderate axial loads while accommodating misalignment; uses barrel-shaped rollers
• Adaptor Sleeve: A tapered sleeve used to mount bearings with tapered bores onto cylindrical shafts
• Shock Factor: A multiplier applied to steady loads to account for dynamic/impact loading conditions

Quick Revision

• Design life equation: L = (60 × N × h) / 10⁶ — converts hours to millions of revolutions
• Ball bearing life: L₁₀ = (C/P)³
• Roller bearing life: L₁₀ = (C/P)^(10/3)
• Average bearing life ≈ 5 × L₁₀ life
• Three life methods: Basic L₁₀ (load only) → Adjusted Lna (+ reliability, material, lubrication) → New Life Lnaa (+ fatigue limit, contamination)
• Adjusted life formula: Lna = a₁ × a₂₃ × L₁₀
• New life formula: Lnaa = a₁ × a_the bearing supplier × L₁₀
• Viscosity ratio: κ = ν/ν₁ — higher κ means better lubrication and longer life (cap at κ = 4)
• Contamination factor ηc: 1 = very clean, 0.8 = sealed/greased for life, 0.5 = shielded, 0.1–0.5 = contaminated, 0 = heavily contaminated
• If Fa/Fr ≤ e: simpler formula applies (usually P = Fr or P = Fr + Y₁·Fa)
• If Fa/Fr > e: more complex formula with combined load factors applies
• Static load checks: Deep groove ball: Po < Co; Roller bearings: Po < Co/1.5
• Minimum radial load: Ball bearings Fr > 0.01·C; Roller bearings Fr > 0.02·C
• Always check: shaft speed does not exceed bearing speed rating
• 37 standard bearing types — selection based on load direction, speed, accuracy, noise, friction, self-alignment
• Key factors affecting life beyond load: steel type, lubrication quality, and cleanliness

Journal Bearings, Belt Drives & Bearings Reference

Overview

• This document consolidates key mechanical design reference data covering three foundational topics in machine element design: rolling element bearings, journal (plain) bearings, and belt drives
• The material is drawn from a technical education data manual used in mechanical engineering coursework
• It provides selection procedures, design formulas, worked examples, comparison tables, and catalogue reference data for practical design applications
• Understanding these components is essential for designing rotating machinery, power transmission systems, and general mechanical assemblies

Key Concepts

• Rolling Element Bearings — bearings that use balls or rollers to reduce friction between rotating and stationary parts; include cylindrical roller bearings and spherical roller bearings
• Journal Bearings — also known as plain bearings or bushes; rely on a lubricant film between the shaft (journal) and the bearing surface rather than rolling elements
• Thick-Film Lubrication — a condition in journal bearings where the lubricant film is thick enough that the journal does not contact the bearing surface, resulting in minimal wear
• Bearing Modulus (M) — a dimensionless parameter used to assess whether thick-film lubrication will occur in a journal bearing
• Belt Drives — power transmission systems that use flexible belts running over pulleys to transfer rotational energy between shafts
• Wedge Belts — V-shaped cross-section belts (including vee, wedge, banded, multi-pull, link, cogged raw edge, and synchronous types) used in modern power transmission
• Service Factor — a multiplier applied to the normal running power to account for the type of driven machine, prime mover, and operating hours

Rolling Element Bearings

Cylindrical Roller Bearings (Single Row)

• Bore diameter ranges covered: 30–55 mm
• Key parameters listed for each bearing designation:
  • Principal dimensions: bore diameter (d), outer diameter (D), width (B)
  • Basic load ratings: dynamic (C) and static (C₀) — measured in Newtons (N)
  • Fatigue load limit (Pᵤ) — threshold below which fatigue life is theoretically infinite
  • Speed ratings: reference speed for grease and oil lubrication (r/min)
  • Mass — in kilograms
  • Bearing dimensions: inner ring (d₁, d₂), outer ring (D₁), fillet radii (r₁₂ min, r₃₄ min), and abutment dimensions (dₐ min, Dₐ max, rₐ max)
• Bearing type designations include NU, NJ, NUP, and N series — each denoting a specific internal configuration of rollers and flanges
• Angle rings are listed separately with their own designation codes, masses, and dimensions (B₁, B₂)

Spherical Roller Bearings (Single Row)

• Bore diameter ranges covered: 20–55 mm
• Available bore types: cylindrical bore, tapered bore (designated with "K" suffix)
• Designation codes: CC, E, EK — indicating different internal designs and load capacities
• Key parameters are the same as cylindrical roller bearings plus additional calculation factors:
  • e — a limiting value for the ratio of axial to radial load
  • Y₁, Y₂ — axial load factors used in equivalent dynamic load calculations
  • Y₀ — static axial load factor
• Abutment and fillet dimensions include: dₐ (min), Dₐ (max), rₐ (max), plus additional dimensions for shoulder diameters and chamfer limits
• A footnote indicates that permissible axial displacement from the normal position of one bearing ring relative to the other is specified in manufacturer catalogues

Journal (Plain) Bearings

Definition and Construction

• A journal bearing (also called a bush or plain bearing) consists of a bearing surface surrounding a rotating shaft (the journal), housed within a stationary housing
• The journal is not necessarily larger in diameter than the shaft — it is often the same diameter
• Two main types of journal bearings:
  • Pressure-lubricated type — lubricant is pumped into the bearing under pressure (e.g., automotive engine bearings); requires complex design and is outside the scope of standard data manuals
  • Non-pressure-lubricated type — relies on self-lubrication or simple oil/grease supply; suitable for off-the-shelf selection
• Flange-type bearings have a flange on one side to accommodate thrust loads in addition to radial loads

Bearing Materials

• Journal material: typically a hard material with a fine, smooth, ground or lapped finish
• Bearing material: a dissimilar, softer material with a relatively open and porous finish
• Why dissimilar materials are required:
  • Prevents localised welding and seizure
  • Soft material allows embeddability of foreign particles
  • Porous, open finish retains lubricant
• Common bearing materials:
  • Metallic: bronze (copper-tin alloy), white-metal alloys (lead-tin-aluminium-antimony-copper), cast iron (historically used, now rare)
  • Non-metallic: nylon, phenolics, PTFE (polytetrafluoroethylene)
• Common lubricants: oils and greases; some special bearings use water or even air (dry operation)

Porous Bronze Bearings

• Manufactured using powder metallurgy — pure copper and tin powders are sintered together
• Self-lubricating: pre-impregnated with a standard lubricating oil (approximately 30% oil by volume)
• Under many operating conditions, no additional lubrication is required
• In some cases, auxiliary lubrication is recommended to extend bearing life

Performance Factors for Good Operation

• Surface finish of the shaft (journal):
  • Should be a fine ground finish, preferably lapped
• Surface hardness of the shaft:
  • Recommended minimum: steel with 0.35–0.45% carbon content (equivalent to a medium carbon grade)
  • For heavy-duty applications, the shaft should be hardened
• Grade of lubricant:
  • Higher viscosity → longer bearing life
  • However, higher viscosity → greater friction
  • High-viscosity lubricants should only be used with high loads
  • Bearing life can be extended by cutting a grease groove into the bearing and pumping grease in
  • Standard pre-impregnation uses a light machine oil (approximately 20 centipoise at 65°C)
• Heat dissipation:
  • Friction generates heat, which reduces lubricant viscosity and increases wear
  • Housing material and design should promote heat dissipation
  • Example: a thermosetting plastic housing will not dissipate heat as readily as a metallic housing
• Shock loads:
  • Porous bronze bearings handle moderate radial shock loads due to oil-cushioned operation
  • Excessive prolonged radial shock increases metal-to-metal contact and reduces bearing life
  • Large out-of-balance forces in rotating members also reduce life
• Clearance:
  • Bearings are typically a light press fit in the housing
  • A shouldered tool is usually used for installation via an arbour press
  • Running clearance between journal and bush: rule-of-thumb is 1/1000 of the journal diameter
  • Example: 25 mm journal → 0.025 mm running clearance
• Length-to-diameter ratio (L/d):
  • Recommended range: 0.5 to 1.5
  • Too small → high bearing pressure, difficult lubricant retention, side leakage
  • Too large → high friction, potential misalignment causing metal-to-metal contact

Advantages of Journal Bearings (vs. Rolling Element Bearings)

• Low cost
• Quiet operation with minimal noise
• Little radial space required
• High speed capability
• Can operate with non-oil lubricants (water, grease, or even dry/air)

Disadvantages of Journal Bearings (vs. Rolling Element Bearings)

• Relatively low radial load carrying capacity
• Zero thrust load capability (unless a flange type is used with a stepped shaft)
• Low misalignment capability (self-aligning types exist in small sizes but require the misalignment to be taken up between the outer bearing surface and the housing)
• Shaft material and surface finish are critical to performance
• Large sizes (above ~50 mm) are generally not available off-the-shelf

Summary of Best Applications

• Journal bearings are most suitable for relatively high-speed shafts with moderate radial loads and low or zero thrust loads, particularly when cost, noise, and space are important considerations

Thick-Film Lubrication Theory

Lubrication Regimes

• Boundary lubrication: at rest or very low speeds, the journal contacts the lower face of the bearing; considerable wear occurs
• Thin-film (transition) lubrication: as speed increases, oil is dragged around by the shaft, the shaft begins to "float" on a thin oil film; the journal may occasionally contact the bearing (especially during shock loads); moderate wear may occur
• Thick-film lubrication: at high speed, the oil film becomes thick enough that no contact occurs between journal and bearing; no wear occurs because there is no metal-to-metal contact

Frictional Torque vs. Speed

• At rest/low speed: high friction due to metal-to-metal contact (boundary lubrication)
• As speed increases: friction decreases as metal contact diminishes
• Once floating (thick-film regime): friction increases again because fluid friction increases with velocity (as with any fluid flow)
• The most desirable operating point is the region around the onset of thick-film lubrication — below this point, wear occurs and frictional torque is high

Bearing Modulus (M)

• Defined as:

$$M = \frac{\mu \cdot v}{p}$$

• Where:
  • μ = dynamic viscosity of the lubricant (centipoise, cp) at operating temperature
  • v = linear (surface) velocity of the journal (m/s)
  • p = bearing pressure calculated on the projected area (MPa)
• Note: 1 cp = 1000 Pa·s (i.e., 1 centipoise = 0.001 Pa·s)
• Design rule-of-thumb: thick-film lubrication onset occurs at a bearing modulus of approximately 75
  • If M > 75 → thick-film lubrication is likely
  • If M < 75 → consider increasing lubricant viscosity or other design changes to raise M
  • If M >> 75 → thick-film lubrication is assured, but friction will be high — consider reducing lubricant viscosity

Selection Procedure for Porous Bronze Journal Bearings

1. Obtain relevant data: journal (shaft) diameter, running speed, and radial load
2. Select a bearing length from the standard size table; as a first trial, assume L/d = 1 (i.e., bearing length equals shaft diameter)
3. Calculate bearing pressure (p):

$$p = \frac{F}{A} = \frac{F}{d \times L}$$

• Where: p = bearing pressure (MPa), F = radial bearing load (N), d = journal diameter (mm), L = bearing length (mm)

4. Calculate surface velocity (v):

$$v = r \cdot \omega = \frac{d}{2000} \times \frac{2\pi N}{60}$$

• Where: N = rotational speed (rev/min), d = diameter (mm), v = surface velocity (m/s)

5. Check bearing pressure against maximum allowable:

   • For velocities ≤ 1 m/s, use the velocity vs. maximum pressure table
   • For velocities > 1 m/s, use the maximum bearing pressure vs. shaft speed chart (which provides curves for different shaft diameters)
   • If the calculated pressure exceeds the maximum, try a longer bearing to reduce pressure

6. Calculate the p·v factor:

   • Multiply bearing pressure (MPa) by surface velocity (m/s)
   • If p·v > 0.53 → auxiliary lubrication is needed
   • If p·v slightly exceeds 0.53, it may be possible to reduce p·v below 0.53 by increasing the bearing length (which reduces pressure)

7. Check for thick-film lubrication:

   • Calculate the bearing modulus M
   • Standard porous bronze bearings are pre-impregnated with a light machine oil having a viscosity of approximately 20 cp at 65°C
   • If M > 75 → thick-film operation is likely
   • If M < 75 → consider increasing viscosity or other design modifications
   • If M >> 75 → thick-film operation is assured but friction is high; consider reducing viscosity

8. Record the catalogue number and relevant design data for the selected bearing