Friction in Machines

1. Introduction to Friction in Machines

Friction is the resisting force that opposes the relative motion (or tendency of motion) between two surfaces in contact.

Key Points

• Acts tangentially to the contact surface
• Depends on the nature of surfaces and normal reaction
• Always opposes motion

2. Types of Friction in machines

(a) Static Friction

• Acts when bodies are at rest
• Prevents motion until a limiting value is reached

(b) Kinetic (Sliding) Friction

• Acts when bodies are in motion
• Slightly less than limiting friction

(c) Rolling Friction

• Occurs when a body rolls over a surface
• Much smaller than sliding friction

(d) Fluid Friction

• Resistance offered by fluids (liquids/gases)

3. Laws of Dry Friction (Coulomb Friction)

1. Friction is proportional to normal reaction
2. Independent of contact area
3. Depends on nature of surfaces
4. Kinetic friction < limiting friction
5. Acts opposite to motion

4. Limiting Friction and Coefficient of Friction

Limiting Friction

Maximum friction before motion starts:$$F_{max} = \mu N$$Fmax​=μN

Where:

• $F_{max}$Fmax​ = limiting friction
• $\mu$μ = coefficient of friction
• $N$N = normal reaction

Coefficient of Friction

$$\mu = \frac{F}{N}$$

5. Angle of Friction and Angle of Repose

Angle of Friction (φ)

$\tan \phi = \mu$tanϕ=μ

• Angle between resultant reaction and normal reaction

Angle of Repose (θ)

• Maximum angle at which a body remains at rest on an inclined plane

$$\theta = \phi$$θ=ϕ

6. Cone of Friction

6

• The locus of resultant reaction forms a cone
• Semi-vertical angle = angle of friction
• If resultant lies inside cone → no motion
• Outside cone → motion occurs

7. Friction in Machine Elements

(a) Friction in Screws

• Used in screw jacks, bolts, and power screws
• Efficiency depends on friction
• Self-locking occurs when friction is high

(b) Friction in Bearings

6

• Occurs between shaft and bearing
• Types:
  • Sliding bearings
  • Rolling bearings
• Lubrication reduces friction

(c) Belt and Rope Drives

• Friction between belt and pulley transmits power
• Governed by:

$$\frac{T_1}{T_2} = e^{\mu \theta}$$T2​T1​​=eμθ

Where:

• $T_1$T1​ = tight side tension
• $T_2$T2​ = slack side tension
• $\theta$θ = angle of contact

8. Advantages of Friction

• Enables walking and gripping
• Power transmission (belts, clutches)
• Braking systems
• Holding fasteners (nuts & bolts)

9. Disadvantages of Friction

• Causes wear and tear
• Generates heat
• Reduces efficiency
• Requires lubrication

10. Methods to Reduce Friction

• Lubrication (oil, grease)
• Polishing surfaces
• Using ball/roller bearings
• Streamlining (in fluids)

11. Methods to Increase Friction

• Roughening surfaces
• Using friction materials (rubber, brake lining)
• Increasing normal force

12. Application in Machines

• Brakes: friction stops motion
• Clutches: friction transmits torque
• Screw jack: lifting heavy loads
• Bearings: support rotating shafts

13. Important Formulas Summary

• $F = \mu N$F=μN
• $\mu = \tan \phi$μ=tanϕ
• $T_1/T_2 = e^{\mu \theta}$T1​/T2​=eμθ
• Efficiency depends on friction

---