Tribology And Maintenance Engineering (ME-802 (B)) Notes

Unit 1: Fundamentals of Tribology

1.0 Introduction to Tribology

Definition: Tribology is the science and technology of interacting surfaces in relative motion. It encompasses the study of friction, wear, and lubrication.
Historical Developments:
- Ancient: Use of lubricants (water, animal fats) in chariots, pyramids.
- 15th-18th Century: Leonardo da Vinci's laws of friction; Amontons' formalization.
- 1966: The term "Tribology" was coined by Peter Jost in a UK government report, highlighting massive economic losses due to poor tribological practices.
- Modern: Expansion to include bio-tribology (joints), space tribology (vacuum), and nano-tribology.
Industrial Significance:
- Economic: Reduces maintenance costs, energy consumption, and component replacement. Jost's report estimated UK losses at ~£515 million/year (1966).
- Reliability: Enhances machine life, efficiency, and safety.
- Sustainability: Lowers emissions and resource consumption through efficient design.
[!TIP] Exam Focus: Be prepared to cite Jost's 1966 report and quantify tribology's impact (e.g., 20-30% energy savings possible via reduced friction).

2.0 Contact Mechanics

Conforming vs. Non-Conforming Contacts:

| Feature | Conforming Contact | Non-Conforming Contact | | :--- | :--- | :--- | | Geometry | Surfaces fit closely (e.g., journal bearing). | Surfaces have distinct radii (e.g., ball-on-flat, gear tooth). | | Pressure | Low, uniformly distributed. | Very high, localized (Hertzian). | | Deformation | Significant elastic/plastic deformation. | Primarily elastic (Hertzian). |
Hertzian Contact Theory:
- Assumptions in Hertzian Analysis:
  1. Both materials are homogeneous, isotropic, linear elastic.
  2. Surfaces are smooth, frictionless, and non-conforming.
  3. Stresses are within elastic limit (no plastic deformation).
  4. Bodies are semi-infinite (elastic half-spaces).
  5. Contact area is small compared to body dimensions.
- Elastic Half-Spheres Concept: Two spheres (or a sphere and a flat) are modeled as elastic half-spaces deforming under load. The contact is a circular area of radius a.
- Key Formulas (for two spheres):

$$ \frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} \quad \text{(Reduced radius of curvature)} $$

$$ a = \left( \frac{3FR}{4E^*} \right)^{1/3} \quad \text{(Contact radius)} $$

$$ p_0 = \frac{3F}{2\pi a^2} \quad \text{(Maximum contact pressure)} $$

    Where:

    *   $F$ = Normal load

    *   $R$ = Reduced radius of curvature

    *   $$\displaystyle E^* = \left( \frac{1-\nu_1^2}{E_1} + \frac{1-\nu_2^2}{E_2} \right)^{-1} $$ (Reduced elastic modulus)

    *   $$\displaystyle E_1, E_2 $$ = Elastic moduli; $$\displaystyle \nu_1, \nu_2 $$ = Poisson's ratios.

> [!TIP] **Common Pitfall:** Hertzian theory is **only valid for elastic, frictionless, non-conforming contacts**. It fails for plastic deformation, high friction, or conforming contacts.

3.0 Friction

Laws of Friction (Amonton's Laws):
1. First Law: Force of friction ($$\displaystyle F_f $$) is directly proportional to normal load ($W$): $$\displaystyle F_f = \mu W $$. ($\mu$ = coefficient of friction).
2. Second Law: Friction is independent of apparent contact area.
3. Third Law: Kinetic friction is independent of sliding velocity.
Exceptions to the Laws:
- Very low loads (adhesive forces dominate).
- Very high speeds (frictional heating).
- Boundary lubrication (third law fails).
- Very rough surfaces (second law may not hold).
Bowden and Tabor's Theory:
- Core Idea: Real area of contact ($$\displaystyle A_r $$) is much smaller than apparent area ($$\displaystyle A_a $$). $$\displaystyle A_r $$ is determined by plastic deformation of surface asperities.
- Equation: $$\displaystyle F_f = \tau \cdot A_r $$, where $\tau$ = shear strength of junction.
- Since $$\displaystyle A_r \propto W $$ (for plastic flow), $$\displaystyle F_f \propto W $$, explaining Amonton's First Law.
- Explains why $\mu$ is typically 0.1 to 0.3 for metals (shear strength $\tau$ is ~0.1-0.3 times hardness $H$).
Factors Affecting Friction:
- Material Pair: Surface energy, hardness.
- Surface Roughness: Optimal roughness for lubrication; very smooth increases adhesion.
- Normal Load: Affects real contact area.
- Sliding Velocity: Affects temperature, lubrication regime.
- Environment: Humidity, temperature, contaminants.
Stick-Slip Phenomenon:
- Definition: Cyclic oscillation between static adhesion (stick) and dynamic sliding (slip). Causes vibration, noise, and surface damage.
- Cause: Non-linear friction-velocity characteristic. Static friction coefficient ($$\displaystyle \mu_s $$) > kinetic friction coefficient ($$\displaystyle \mu_k $$). System stiffness and damping play a role.
- Prevention: Increase system damping, use lubricants, apply compliant layers, control velocity.
Friction Reduction Methods (Focus on Adhesive Component):
- Lubrication: Introduce a film to separate surfaces.
- Surface Coatings: Low shear strength materials (PTFE, MoS₂, DLC).
- Surface Texturing: Micro-dimples to trap lubricant and reduce real contact.
- Material Selection: Use materials with low surface energy or high hardness.

4.0 Wear

Definition: Progressive loss of material from a solid surface due to mechanical action.
Classification of Wear:

| Type | Mechanism | Typical Example | | :--- | :--- | :--- | | Adhesive | Material transfer due to cold welding of asperities. | Scuffing, galling. | | Abrasive | Hard protrusions or particles plough/remove material. | Two-body (grinding), three-body (sand). | | Fatigue | Cyclic stresses cause crack initiation & propagation. | Spalling in bearings, gear pitting. | | Corrosive | Chemical/electrochemical reaction with environment + mechanical action. | Oxidative wear, fretting. | | Other | Erosion (impinging particles), impact, cavitation. | Pump impeller damage. |
Factors Affecting Wear:
1. Material Properties: Hardness, toughness, ductility, microstructure.
2. Load & Contact Stress: Higher load → higher wear rate (often non-linear).
3. Sliding Distance & Velocity: Affects temperature, lubrication.
4. Environment: Corrosive media, temperature, humidity.
5. Surface Finish: Roughness can increase abrasive wear or aid lubrication.
6. Lubrication: Presence/type of lubricant film.

5.0 Lubrication

Lubrication Regimes (Based on $\lambda$ - Film Thickness Ratio):

$$ \lambda = \frac{h}{R_q} \quad \text{(Where $h$ = lubricant film thickness, $$\displaystyle R_q $$ = composite RMS roughness)} $$

| Regime | $\lambda$ | Condition | Friction Source |

Hydrodynamic Lubrication:
- Principle: Relative motion drags lubricant into a converging wedge (e.g., journal bearing), generating hydrostatic pressure that supports the load.
- Governing Equation: Reynolds Equation (simplified for 1D):

$$ \frac{\partial}{\partial x} \left( h^3 \frac{\partial p}{\partial x} \right) = 6\mu U \frac{\partial h}{\partial x} $$

    Where $h(x)$ = film thickness, $p$ = pressure, $\mu$ = viscosity, $U$ = surface velocity.

*   **Key:** Requires **relative motion** and **converging geometry**.

Elasto-Hydrodynamic Lubrication (EHL):
- Applies to highly loaded, non-conforming contacts (rolling bearings, gears).
- Key Feature: Elastic deformation of surfaces significantly affects the lubricant film shape. Viscosity of lubricant increases sharply under high pressure (Barus equation: $$\displaystyle \mu = \mu_0 e^{\alpha p} $$).
- Film thickness is much thicker than predicted by rigid-body Reynolds equation.

6.0 Bearings

Classification by Applied Load:
- Radial Bearings: Support load perpendicular to shaft axis (e.g., deep groove ball bearing).
- Thrust Bearings: Support load axial to shaft (e.g., thrust ball bearing).
- Linear Bearings: Support linear motion (e.g., guide ways, linear recirculating ball bearing).
Classification by Film Thickness (Lubrication Regime):
- Hydrodynamic Bearings: Self-acting, $$\displaystyle \lambda > 3 $$. (e.g., plain journal bearing).
- Hydrostatic Bearings: Externally pressurized oil film, supports load at zero speed. High stiffness, low friction.
- Boundary Lubricated Bearings: $$\displaystyle \lambda < 1 $$, rely on surface films/coatings. (e.g., dry bearings, bushings).
Cylindrical Roller Bearings:
- Advantages:
  - High radial load capacity.
  - Low friction (rolling elements).
  - Higher speed capability than spherical roller bearings.
- Disadvantages:
  - Poor axial load capacity (unless with flanges).
  - Sensitive to misalignment.
  - Higher noise/vibration at high speeds.

7.0 Surface Engineering

Coating Techniques:
- Physical Vapour Deposition (PVD):
  - Process: Physical process (evaporation, sputtering) in vacuum. Vaporized material condenses on substrate.
  - Diagram:
    DiagramCANVAS: Show vacuum chamber, target (cathode), substrate (anode), plasma, coating deposition
  - Coatings: TiN, TiAlN, DLC. Hard, wear-resistant, decorative.
- Electroplating:
  - Process: Electrochemical deposition from aqueous solution. Substrate is cathode, metal anode.
  - Equation: $$\displaystyle M^{n+} + ne^- \rightarrow M $$ (at cathode).
  - Coatings: Chrome, nickel, cadmium. For corrosion resistance, wear, appearance.
- Hard Facing (Weld Overlay):
  - Process: Welding process (MMA, TIG, plasma) depositing hard, wear-resistant alloy.
  - Diagram:
    DiagramCANVAS: Show welding torch, workpiece, deposited bead with high carbide content
  - Coatings: Stellite, tungsten carbide. For severe abrasive/adhesive wear.
Geometrical Parameters of Coatings:
- Thickness: Measured in microns (µm). Affects load support, fatigue life.
- Adhesion Strength: Critical for coating retention. Measured by scratch test.
- Surface Roughness: Influences friction, wear, and further coating adhesion.
- Porosity: Affects corrosion resistance and hardness.
Microstructural Treatments (Bulk Surface Modification):
- Carburizing/Nitriding: Diffuse carbon/nitrogen to form hard case.
- Induction Hardening: Rapid surface heating & quenching.
- Laser Surface Melting/Alloying: Rapid solidification, fine microstructure.
- Shot Peening: Introduce compressive residual stresses.
- Thermal Spraying: Spray molten particles (plasma, flame).
Coatings for Specific Environments:
- High Temperature Oxidation/Corrosion:
  - MCrAlY (M=Ni, Co) overlay coatings.
  - Thermal Barrier Coatings (TBCs): YSZ (Yttria-Stabilized Zirconia) via plasma spray.
- Acidic Environment Resistance:
  - Electroplated Nickel-Phosphorus (Ni-P): Amorphous, corrosion-resistant.
  - Rubber/Polymer Linings: For chemical tanks.
  - Ceramic Coatings: Al₂O₃, Cr₂O₃ via thermal spray.

8.0 Tribological Measurements

Friction Measuring Equipment (Common Types):
1. Pin-on-Disk Tribometer: Most common. Rotating disk, stationary pin.
2. Four-Ball Tester: For lubricant EP (Extreme Pressure) properties.
3. Reciprocating (Block-on-Ring) Tester: Simulates sliding contact.
4. Universal Mechanical Tester (UMT): Versatile, multiple configurations.
Detailed Method: Pin-on-Disk Tribometer
- Principle: A stationary pin (ball or flat) is loaded against a rotating disk. Friction force is measured during sliding.
- Setup:
  - Specimens: Pin (material of interest), Disk (standard material, e.g., AISI 52100 steel).
  - Loading: Dead weight or spring applies normal load ($W$).
  - Motion: Disk rotates at controlled speed ($v$).
  - Measurement: Load cell measures tangential friction force ($$\displaystyle F_f $$).
  - Environment: Can be controlled (dry, lubricated, temperature, humidity).
- Procedure:
  1. Clean specimens (solvent, ultrasonic).
  2. Mount pin and disk.
  3. Apply predetermined normal load ($W$).
  4. Start disk rotation at set speed ($v$).
  5. Record friction force ($$\displaystyle F_f $$) vs. time or sliding distance.
  6. Calculate coefficient of friction: $$\displaystyle \mu = F_f / W $$.
  7. After test, measure wear scar on pin (optical microscope) or wear track on disk (profilometer).
- Output: $\mu$ vs. time, wear volume/rate, specific wear rate: $$\displaystyle K = \frac{V}{W \cdot s} $$ (Where $V$ = wear volume, $s$ = sliding distance).
[!TIP] Exam Tip: Be able to sketch a pin-on-disk setup and list key parameters measured (F_f, W, v, s, wear scar).

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Tribology And Maintenance Engineering (ME-802 (B)) - Unit 1 Short Notes