Tribology for Engineers: Friction, Wear Mechanisms, the Stribeck Curve, and Lubrication Regimes
Tribology — the science of interacting surfaces in relative motion — governs the performance and longevity of virtually every mechanical system, from rolling element bearings and gear trains to hip implants and metal-cutting tools. This article provides a rigorous, quantitative treatment of friction coefficients, the principal wear mechanisms (adhesive, abrasive, surface fatigue, and corrosive), the Archard wear equation, the Stribeck curve, hydrodynamic and elastohydrodynamic lubrication, and material selection strategies for wear resistance.
✓ Key Takeaways
- Friction is not an intrinsic material property — it depends on surface roughness, contact geometry, environment, sliding speed, and load. Amontons’ Laws are empirical approximations valid over limited ranges.
- The Archard wear equation (V = K·W·L / H) shows wear volume scales linearly with load and sliding distance, and inversely with hardness — the primary basis for hardness-based material selection in tribological applications.
- Four primary wear mechanisms operate in engineering contacts: adhesive, abrasive, surface fatigue (delamination/spalling), and corrosive/oxidative wear. Mixed-mode wear is the rule, not the exception.
- The Stribeck curve maps three lubrication regimes — boundary, mixed, and hydrodynamic (or elastohydrodynamic) — against the Hersey number (η·N/P). Optimum bearing design targets full-film hydrodynamic or EHL operation.
- Elastohydrodynamic lubrication (EHL) is sustained by the piezoviscous effect (Barus equation) and elastic deformation of the contacting surfaces, enabling sub-micrometre film thickness at GPa-level contact pressures in gears and bearings.
- Wear-resistant microstructures combine high hardness (to resist cutting and adhesion) with sufficient toughness (to resist sub-surface fatigue); case-hardened steels, hard-faced overlays, and ceramic coatings each address different tribological environments.
1. Fundamentals of Friction
1.1 Amontons’ Laws and Their Limitations
The classical description of dry sliding friction rests on Amontons’ two empirical laws (1699), subsequently extended by Coulomb (1781): (1) the friction force F is proportional to the applied normal load W, and (2) friction is independent of the apparent contact area. These yield the familiar expression:
F = μ × W
where: μ = coefficient of friction (dimensionless)
F = friction force (N)
W = normal load (N)
The physical basis, developed by Bowden and Tabor (1950), lies in the real contact area Ar. When two surfaces are brought into contact, load is borne by asperity junctions. The real contact area is far smaller than the apparent contact area and scales with load: Ar = W / py, where py is the yield pressure of the softer material (~3×H for hardness H in Pa). Friction arises from the shear strength τs of these junctions:
F = τ‑s × A‑r = (τ‑s / p‑y) × W
∴ μ = τ‑s / p‑y
This model correctly predicts that μ is independent of load and apparent area for plastically deforming asperity contacts. However, Amontons’ laws break down at very low loads (elastic contacts, where Ar ∝ W2/3 per Hertz theory), at very high velocities (thermally softened junctions), in the presence of lubricants (film strength, not asperity shear, dominates), and for viscoelastic materials. For practical engineering calculations, μ is treated as a system property determined experimentally under representative conditions.
Typical Friction Coefficient Values
| Contact Pair | Condition | μstatic | μkinetic |
|---|---|---|---|
| Steel / steel | Dry | 0.74 | 0.57 |
| Steel / steel | Lubricated (mineral oil) | 0.11 | 0.08 |
| Steel / PTFE | Dry | 0.04 | 0.04 |
| Steel / bronze | Dry | 0.36 | 0.22 |
| Cast iron / cast iron | Dry | 0.44 | 0.32 |
| WC-Co cermet / steel | Dry | 0.35 | 0.28 |
| Al₂O₃ / steel | Dry | 0.61 | 0.45 |
| Rubber / concrete | Wet | 0.45–0.75 | 0.40–0.65 |
1.2 Velocity, Temperature, and Load Dependence
At elevated sliding velocities, frictional heating raises the interfacial temperature. For unlubricated metal contacts, the flash temperature ΔT at an asperity junction is approximated by:
ΔT = 0.31 × μ × W × v / (a × (k₁ + k₂))
where: v = sliding velocity (m/s)
a = contact radius (m)
k₁, k₂ = thermal conductivities (W/m·K)
Flash temperatures can reach hundreds of degrees Celsius at asperity contacts even when the bulk temperature is modest. This localised heating softens asperities (reducing H and increasing Ar), promotes oxidation (often forming protective oxide glazes that reduce μ), and can cause phase transformations in the subsurface. At sufficiently high speeds and loads, the transition from mild (oxidative) to severe (metallic transfer) wear is driven primarily by the flash temperature exceeding the oxide decomposition or softening temperature.
2. Wear Mechanisms
Wear is the progressive loss of material from a solid surface due to mechanical action. In engineering components, four primary mechanisms operate, and real tribosystems commonly exhibit mixed-mode behaviour:
2.1 Adhesive Wear
When clean metallic surfaces contact under load, strong adhesive bonds (cold welds) form at asperity junctions. As sliding continues, these junctions are sheared — but fracture does not always occur at the original interface. When shear occurs within the softer body, material transfers to the harder surface as a transfer layer, which may subsequently detach as loose debris. The progression from mild (transfer layer formation) to severe adhesive wear (gross metallic transfer, surface damage, seizure) is governed by the ratio of interface shear strength to material shear strength, material compatibility (similar crystal structure and lattice parameter promote strong adhesion), and surface contamination (oxides and lubricant boundary films inhibit adhesion).
2.2 Abrasive Wear
Abrasive wear involves material removal by hard particles or hard surface asperities. Two distinct modes are recognised:
- Two-body abrasion: A hard, rough surface slides against a softer material, with asperities acting as micro-cutting tools (e.g., file on metal, grinding wheel on workpiece). Material removal occurs by micro-ploughing, micro-cutting, or micro-fatigue.
- Three-body abrasion: Hard particles are introduced between two surfaces, rolling and sliding to abrade both (e.g., sand ingestion in machinery, contaminated lubricants). Three-body abrasion rates are typically 10× lower than two-body because particles can roll rather than cut continuously.
A critical parameter in abrasive wear resistance is the ratio Hmaterial / Habrasive. When this ratio exceeds ~0.8, the abrasive cannot effectively penetrate the surface and wear rate drops sharply. Below this threshold (soft material / hard abrasive regime), wear rate scales with hardness per the Archard equation. Common abrasives in engineering: silica (H ≈ 1100 HV), alumina (H ≈ 1800–2000 HV), silicon carbide (H ≈ 2200–2500 HV). Only ceramics, cemented carbides, and hard coatings can approach or exceed abrasive hardness.
2.3 Surface Fatigue Wear (Delamination and Contact Fatigue)
In rolling or rolling-sliding contacts — rolling element bearings, gears, cams — the dominant failure mechanism is sub-surface initiated fatigue. Cyclic Hertzian contact stresses create alternating shear stresses that peak at a depth of approximately 0.47a below the surface (where a is the Hertz contact radius). Cracks nucleate at this depth, often at non-metallic inclusions, segregation bands, or carbide interfaces, and propagate parallel to the surface before turning upward to produce spalls (surface pitting) or delaminations (thin sheet wear).
The contact fatigue life (L10) for rolling element bearings is governed by the Lundberg-Palmgren equation, refined as the ISO 281 modified rating life:
L₁₀m = a₁ × aᵢˣ × (C/P)ᴩ
where: C = dynamic load rating (N)
P = equivalent dynamic bearing load (N)
p = load-life exponent (3 for ball, 10/3 for roller bearings)
a₁ = reliability factor (1.0 for 90% reliability)
aᵢˣ = integrated life modification factor (lubrication, contamination, fatigue limit)
2.4 Corrosive and Oxidative Wear
In corrosive wear, chemical reaction with the environment (oxidation in air, chemical attack in corrosive fluids) produces a reaction product layer on the surface. If this layer is hard and adherent, it may act as a protective glaze (mild wear regime); if brittle and weakly adherent, repeated mechanical removal followed by re-oxidation produces a steady-state corrosive wear rate. Oxidative wear is the predominant mechanism in unlubricated or inadequately lubricated steel contacts at moderate temperatures (150–600°C), where Fe₃O₄ and Fe₂O₃ glazes form and reduce metallic adhesion. The transition from mild (oxidative) to severe (metallic) wear as a function of load and speed — the Lancaster wear map — is a key design tool.
3. The Archard Wear Equation
The Archard equation (1953) provides the quantitative framework for predicting adhesive and abrasive wear rates in engineering:
V = K × W × L / H
Rearranged as specific wear rate:
k = V / (W × L) = K / H [m²/N or mm³/N·m]
where: V = volume of material removed (m³)
K = dimensionless wear coefficient
W = normal load (N)
L = total sliding distance (m)
H = hardness of softer surface (Pa)
k = specific wear rate (m²/N)
The wear coefficient K is determined experimentally for each tribological system and condition. Representative values are:
| Wear Mode | Material System | K (dimensionless) |
|---|---|---|
| Severe adhesive | Steel/steel, unlubricated | 10⁻² – 10⁻¹ |
| Mild adhesive | Steel/steel, boundary lubricated | 10⁻⁶ – 10⁻⁵ |
| Mild adhesive | Brass/steel, lubricated | 10⁻⁷ – 10⁻⁶ |
| Two-body abrasion | Steel abraded by SiC | 10⁻³ – 10⁻² |
| Three-body abrasion | Steel with SiC particles | 10⁻⁴ – 10⁻³ |
| Abrasion | WC-Co cermet / SiC | 10⁻⁶ – 10⁻⁵ |
| Surface fatigue | Bearing steel (through-hardened) | 10⁻⁶ – 10⁻⁷ |
4. The Stribeck Curve and Lubrication Regimes
4.1 The Hersey Number
The Stribeck curve — independently developed by Stribeck (1902) and reformulated by Hersey (1914) — plots friction coefficient against the dimensionless group known as the Hersey number:
Hs = (η × N) / P
where: η = dynamic viscosity of lubricant (Pa·s)
N = rotational speed (rev/s)
P = bearing pressure = W / (L·D) (Pa)
L = bearing length, D = shaft diameter (m)
The Stribeck curve identifies three distinct lubrication regimes based on the ratio of film thickness to composite surface roughness, characterised by the film parameter Λ (lambda ratio):
Λ = hₘᵢₙ / σᵉ*
where: hₘᵢₙ = minimum film thickness (m)
σ* = composite surface roughness = √(σ₁² + σ₂²) (m)
σ₁, σ₂ = RMS roughness of surfaces 1 and 2
4.2 Boundary Lubrication (Λ < 1)
At low speeds, high loads, or with very viscous lubricants, the film thickness is insufficient to separate the surfaces. Asperity contacts carry the load and friction is controlled by the shear strength of boundary layers — adsorbed films of lubricant molecules, oxide layers, and the reaction products of extreme-pressure (EP) additives. Friction coefficients are typically 0.1–0.4. Boundary additives (fatty acids, zinc dialkyldithiophosphate — ZDDP, molybdenum disulphide — MoS2) are critical to maintaining acceptable wear rates in this regime. The temperature stability of the boundary film is paramount: ZDDP anti-wear films form and maintain integrity up to ~200°C, above which EP additives such as sulphur-phosphorus compounds are required.
4.3 Mixed Lubrication (1 < Λ < 3)
In the mixed regime, a partial fluid film reduces asperity contact stress but does not provide complete separation. Both asperity load-sharing and hydrodynamic pressure contribute to load support. Friction coefficient decreases with increasing Hersey number as more load is transferred to the fluid film. This is the operating regime of many journal bearings at start-up and shutdown, most gear tooth contacts during sliding, and many cam-follower systems. The proportion of load carried by asperities decreases from ~100% at Λ = 1 to ~0% at Λ = 3.
4.4 Hydrodynamic Lubrication (HDL, Λ > 3–5)
In hydrodynamic lubrication, the relative motion of the surfaces and the viscosity of the lubricant generate sufficient pressure to completely support the load on a converging fluid film, with no asperity contact. Reynolds’ equation governs the pressure distribution in the fluid film:
∂/∂x [ h³ ∂p/∂x ] = 6η U ∂h/∂x
where: h = local film thickness (m)
p = film pressure (Pa)
U = surface velocity (m/s)
η = dynamic viscosity (Pa·s)
x = coordinate in sliding direction
The Sommerfeld number, S = (ηN/P)×(R/c)2, where R is the shaft radius and c is the radial clearance, determines the eccentricity ratio and minimum film thickness in journal bearings. In the full-film HDL regime, friction arises entirely from viscous dissipation in the shearing fluid, and friction coefficient rises with increasing Hersey number (viscosity×speed). There is no wear in a well-maintained hydrodynamic bearing.
4.5 Elastohydrodynamic Lubrication (EHL)
Elastohydrodynamic lubrication applies to non-conformal contacts (ball on race, gear tooth on tooth, cam on follower) where the nominal contact area is very small and Hertzian contact pressures reach 0.5–3.5 GPa. Under these pressures, two effects distinguish EHL from classical HDL:
- Piezoviscous effect: Lubricant viscosity increases exponentially with pressure, described by the Barus equation: η = η0 × eαp, where α is the pressure-viscosity coefficient (typically 1–3 × 10-8 Pa-1 for mineral oils) and p is the contact pressure. At 1 GPa, mineral oil viscosity increases by factors of 104 to 107, effectively solidifying the lubricant within the contact.
- Elastic deformation: Both surfaces deform under pressure, flattening the Hertzian contact zone and creating a near-parallel exit constriction that traps the pressurised lubricant film.
hₘᵢₙ = 3.63 R' (U*)⁰·⁷¹ (G*)⁰·⁵⁶ (W*)⁻⁰·₁3 (1 - e⁻⁰·⁶8k)
where: R' = reduced radius of curvature
U* = dimensionless speed parameter = η₀U / (E'R')
G* = dimensionless materials parameter = αE'
W* = dimensionless load parameter = W / (E'R'²)
k = ellipticity parameter
E' = reduced elastic modulus
EHL film thicknesses are typically 0.1–1 μm. The lambda ratio Λ for rolling element bearings operating under EHL is typically 1.5–5, meaning operation is often in the mixed-to-full-film EHL regime rather than pure HDL. Surface hardness of bearing races is critical to minimising abrasion in the mixed regime and to providing fatigue resistance in the sub-surface stress field.
5. Lubrication Theory — Beyond the Stribeck Curve
5.1 Lubricant Viscosity and the Viscosity-Temperature Relationship
Dynamic viscosity (η, Pa·s) is the primary lubricant property governing hydrodynamic film thickness. The viscosity-temperature relationship for mineral oils is described by the Walther equation (basis for ASTM D341 viscosity-temperature charts) or, for engineering purposes, by the Vogel equation:
η = A × exp[ B / (T - C) ]
where: T = temperature (K)
A, B, C = empirically determined constants for the specific oil
Typical for ISO VG 46 mineral oil: A=0.0141 mPa·s, B=1000 K, C=140 K
The Viscosity Index (VI, ASTM D2270) quantifies the sensitivity of viscosity to temperature change: a high VI oil (VI > 120, typical of Group III base oils or polyalphaolefins) maintains viscosity better across the operating temperature range than a low VI oil (VI ≈ 0–60, typical of Group I mineral oils). Corrosion inhibitors, anti-wear additives (ZDDP), and VI improvers (polyisobutylene, polymethacrylate) are blended into base oils to produce commercial lubricant formulations.
5.2 Extreme-Pressure (EP) Additives and Boundary Film Chemistry
In gear and hypoid axle lubricants operating under high contact pressures and flash temperatures, boundary films must be regenerated rapidly. EP additives — sulphurised fats, phosphate esters, dithiocarbamates — react with the metal surface at elevated temperature to form inorganic iron sulphide or iron phosphate reaction layers (15–100 nm thick). These layers are harder than the oil film but shear more easily than the base metal, reducing the wear coefficient by 102–104 relative to unlubricated contact. The trade-off is that EP additives are corrosive to copper alloys (brass bearings, bronze bushings) at elevated temperatures; additive compatibility with the full bearing system must be verified.
6. Material Selection for Wear Resistance
6.1 Steels: Heat Treatment and Microstructure
Through-hardened tool steels (e.g., D2, M2 HSS) achieve 60–66 HRC via heat treatment, providing an excellent combination of high hardness (for abrasion resistance) and moderate toughness (for impact loads). Case-hardened steels (e.g., 8620, 18CrNiMo7-6) provide a hard, wear-resistant case (58–64 HRC) over a tough, fatigue-resistant core. The case microstructure — tempered martensite with finely dispersed retained austenite — is tailored for contact fatigue applications such as gears and bearings.
For martensitic microstructure optimisation in bearing steels (e.g., 52100 / EN31), retained austenite (RA) content must be controlled. Excessive RA (beyond ~15 vol%) can transform to martensite under contact stress cycling, causing volume expansion, residual stress reversal, and dimensional instability. Sub-zero treatment (-80°C for 1–2 h after quenching) converts RA to fresh martensite, which is subsequently tempered to restore toughness.
6.2 Hard Facing and Surface Engineering
For severe abrasive wear applications (mining, dredging, earthmoving), hardfacing by SMAW, FCAW, or PTA deposition applies high-hardness alloys to base metal surfaces. Key hardfacing alloy systems:
| Hardfacing System | Hardness Range | Primary Wear Mode | Typical Application |
|---|---|---|---|
| Martensitic Cr steel (Fe-Cr-C) | 55–65 HRC | Low-stress abrasion | Bucket lips, dozer blades |
| High-Cr white iron (Fe-Cr-C, >25% Cr) | 60–70 HRC | Abrasion + moderate impact | Slurry pump liners, mill liners |
| Tungsten carbide composite (WC in Ni matrix) | 900–1500 HV | High-stress abrasion | Drill bits, oil sand wear components |
| Cobalt-base (Stellite 6) | 38–46 HRC | Adhesion + high-temperature | Valve seats, hot extrusion dies |
| Nickel-base (Colmonoy 56) | 56–60 HRC | Corrosive abrasion | Chemical pump shafts, plungers |
6.3 Hard Coatings: PVD and CVD
Physical vapour deposition (PVD) and chemical vapour deposition (CVD) apply thin hard coatings (1–15 μm) to cutting tools, dies, and precision components. TiN (hardness 2300 HV) was the first commercial PVD coating; subsequent development has produced TiAlN (3000 HV, oxidation-resistant to 800°C), CrN (1800 HV, superior corrosion resistance), and diamond-like carbon (DLC, 2000–8000 HV, very low μ ≈ 0.05–0.15). The low friction coefficient of DLC makes it particularly effective in boundary-lubricated contacts where it reduces both wear and energy losses. Coating adhesion (critical scratch load Lc by nanoindentation and scratch testing per ISO 20502) and coating thickness are the primary quality control parameters.
6.4 Ceramics and Cermets
Engineering ceramics (Al2O3, Si3N4, SiC, ZrO2) offer very high hardness (1500–2500 HV) and excellent chemical stability, but low fracture toughness (KIc = 3–8 MPa·m1/2) limits their application to smooth, steady-contact environments. Silicon nitride (Si3N4) hybrid ceramic bearings have largely replaced steel bearings in high-speed machine tool spindles due to their 40% lower density (reducing centrifugal loading on raceways), higher hardness, lower coefficient of thermal expansion, and electrical insulation. Cemented tungsten carbide (WC-Co) combines the hardness of WC (~2400 HV) with the toughness conferred by the cobalt binder phase, making it the dominant material for mining drill bits, metal-forming dies, and precision wear components.
7. Wear Testing Standards
Standardised wear testing allows comparison between materials and lubricants under controlled, reproducible conditions:
| Standard | Test Configuration | Wear Mode Simulated | Key Output |
|---|---|---|---|
| ASTM G99 | Pin-on-disc | Sliding adhesive / mild abrasive | Specific wear rate k (mm³/N·m), μ |
| ASTM G133 | Ball-on-flat reciprocating | Boundary lubrication, fretting | Wear scar width, k, μ vs. cycles |
| ASTM G65 | Dry sand rubber wheel | Low-stress three-body abrasion | Volume loss (mm³) |
| ASTM G76 | Solid particle erosion | Erosive wear by particle impact | Erosion rate (g/kg of erodent) |
| ASTM G77 | Block-on-ring | Sliding, high contact pressure | Wear scar, mass loss, μ |
| ISO 6336 | FZG gear rig | Gear tooth scuffing and pitting | Scuffing load stage, micropitting |
8. Industrial Applications
8.1 Rolling Element Bearings
Rolling element bearing steels (52100, M50, M62, CSS-42L) operate in the EHL regime under normal conditions (Λ ≈ 2–5). Bearing failure modes — spalling, micropitting, false brinelling (fretting), and electric erosion — are directly related to tribological conditions. The ratio of lubricant film to surface roughness (Λ) is the primary design parameter; achieving Λ > 2 at minimum operating speed requires lubricant selection, preload optimisation, and surface finish specification (Ra target < 0.1 μm for precision bearings). Toughness requirements and cleanliness standards (ASTM A295, ISO 683-17) for bearing steel define maximum inclusion density for contact fatigue life.
8.2 Gear Tooth Contacts
Involute gear tooth contacts operate in a combination of rolling and sliding EHL. At the pitch point, pure rolling occurs; away from the pitch point, sliding increases, with maximum sliding velocities and boundary conditions at the tooth tip and root. Gear failure modes include: micropitting (grey staining) in the mixed EHL regime at low Λ, macropitting (spalling) from sub-surface fatigue, scuffing (adhesive failure under extreme temperature), and abrasive wear from contaminants. Gear lubricants (ISO VG 68–460) contain EP additives specifically formulated to provide boundary protection at the tooth tip and root without excessive corrosion of bronze synchroniser rings.
8.3 Metal-Cutting Tool Contacts
Cutting tool wear involves a complex tribological system at the tool-chip interface and tool-workpiece interface. At the rake face, temperatures of 600–1000°C and contact pressures of 500–2000 MPa create severe adhesive and diffusive wear conditions — particularly problematic for HSS tools on austenitic stainless steels and titanium alloys. Tool wear mechanisms include: crater wear (diffusive dissolution of carbides at high temperature — governed by Fick’s law), flank wear (abrasive removal of tool material by hard inclusions in the workpiece — governed by Archard equation), and built-up edge (BUE) formation from adhesive transfer of workpiece material. The Taylor tool life equation, VTn = C (where V is cutting speed, T is tool life, n and C are empirical constants), remains the primary practical tool for cutting parameter optimisation.
9. FAQ — Tribology for Engineers
What is the Archard wear equation and what does the wear coefficient K represent?
The Archard wear equation is V = K × W × L / H, where V is the volume of material removed, W is the applied normal load, L is the sliding distance, H is the hardness of the softer surface, and K is the dimensionless wear coefficient. K represents the probability that a given asperity contact will produce a wear particle. For mild adhesive wear (well-lubricated metals), K ranges from 10-8 to 10-5; for severe adhesive wear (unlubricated, same-material pairs), K can reach 10-2 to 10-1. A low K value indicates a tribological system with low wear propensity.
What are the three regimes on the Stribeck curve?
The Stribeck curve plots friction coefficient against the Hersey number (η·N/P). Three regimes: (1) Boundary lubrication — film thickness insufficient to separate surfaces; friction controlled by surface chemistry and boundary additives (μ = 0.1–0.4); (2) Mixed lubrication — partial film formation with both asperity contact and fluid film contributions, friction decreasing with increasing speed; (3) Hydrodynamic or elastohydrodynamic lubrication — full fluid film separates surfaces, friction rises slowly with speed due to viscous drag. The minimum friction coefficient marks the mixed-to-full-film transition.
What is the difference between adhesive wear and abrasive wear?
Adhesive wear occurs when two sliding surfaces form adhesive junctions at asperity contacts; as sliding continues, material transfers from one surface to the other or forms loose debris. It is dominant in metal-on-metal contacts without adequate lubrication. Abrasive wear occurs when hard particles or asperities plough through a softer surface by micro-cutting or micro-fatigue. Two-body abrasion involves a hard surface directly abrading a soft one; three-body abrasion involves loose particles between the surfaces. Abrasive wear produces directional scratches and typically exhibits higher wear rates than adhesive wear under equivalent contact conditions.
How does surface hardness affect wear resistance?
The Archard equation shows wear volume is inversely proportional to hardness (V ∝ 1/H). Increasing hardness by heat treatment, case hardening, or hard coating directly reduces wear rate. This relationship breaks down when hardness is achieved by sacrificing toughness — brittle surfaces can fail by sub-surface fatigue and spalling under cyclic contact stresses. The optimum tribological microstructure combines a hard wear-resistant surface with a tough substrate. For abrasive wear, material hardness must exceed approximately 0.8× the hardness of the abrasive for effective resistance.
What is elastohydrodynamic lubrication (EHL) and where does it apply?
EHL applies to highly loaded non-conformal contacts (rolling element bearings, gears, cams) where contact stresses reach 0.5–3.5 GPa. In EHL, lubricant viscosity increases dramatically under pressure (Barus equation: η = η0·eαp), enabling a coherent film at pressures that would expel a conventional lubricant. Simultaneously, elastic deformation of both surfaces creates a near-parallel film exit that traps pressurised lubricant. Minimum film thickness is typically 0.1–1 μm, calculated using the Hamrock-Dowson equation.
What is the specific wear rate and how is it used in material comparison?
Specific wear rate (k) is volume of material removed per unit sliding distance per unit normal load: k = V / (L × W), with units of m2/N or mm3/(N·m). Values range from ~10-15 m2/N for hard ceramics in well-lubricated conditions to ~10-10 m2/N for unlubricated metals. It normalises the Archard K coefficient by hardness and is the primary parameter for ranking materials in tribological databases. ASTM G99 pin-on-disc is the standard test configuration for measuring specific wear rate.
How is the Hersey number used to predict lubrication regime in journal bearings?
The Hersey number (Hs = η·N/P) is a dimensionless group characterising the lubrication regime: η is dynamic viscosity (Pa·s), N is rotational speed (rev/s), and P is projected bearing pressure (Pa). At low Hersey numbers the bearing operates in the boundary regime; increasing Hs passes through the Stribeck minimum into hydrodynamic operation. The Sommerfeld number S = (η·N/P)·(R/c)2 (R = bearing radius, c = radial clearance) determines film thickness and eccentricity ratio for design calculations.
What is surface fatigue wear and what microstructural factors govern it?
Surface fatigue wear (delamination/contact fatigue) occurs in rolling contacts when cyclic Hertzian stresses initiate sub-surface cracks that propagate parallel to the surface and emerge as thin wear sheets (delaminations) or pits (spalls). Microstructural factors governing resistance: inclusion density (oxide/sulphide inclusions act as stress raisers — vacuum-degassed steels show superior life), retained austenite content (excess RA causes dimensional instability under cyclic stress), carbide morphology (fine spheroidised carbides preferred over coarse angular carbides), and compressive residual stress profile from case hardening or shot peening.
How is the coefficient of friction measured experimentally?
Friction coefficient (μ = Ffriction/Fnormal) is measured using standardised tribometers. The pin-on-disc (ASTM G99) and ball-on-flat configurations apply a known normal load while measuring tangential force with a strain gauge or load cell during controlled sliding. Reciprocating tribometers (ASTM G133) simulate boundary-lubricated conditions. In all cases, temperature, humidity, surface roughness (Ra), and sliding speed must be precisely controlled and reported for reproducibility. Running-in transients and steady-state values are recorded separately.
Recommended Technical References
Engineering Tribology — Stachowiak & Batchelor
The definitive graduate-level text on tribology: friction, lubrication, wear mechanisms, EHL, and surface engineering. Essential reference for bearing and gear designers.
View on AmazonWear: Materials, Mechanisms and Practice — Stachowiak
Comprehensive coverage of wear mechanisms, materials testing standards, hard coatings, and industrial case studies. Aligns directly with ASTM G99, G65, and ISO tribology standards.
View on AmazonIntroduction to Tribology — Bhushan
From asperity contact mechanics to MEMS tribology, Bhushan’s text covers nanoscale through macroscale friction and wear, including modern coatings and MEMS/NEMS applications.
View on AmazonASM Handbook Vol. 18 — Friction, Lubrication and Wear Technology
The ASM practitioner’s reference for tribology: wear testing, lubricant selection, failure analysis, and materials data. Indispensable for industrial failure investigation.
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