6. Friction in Machines free study note

1. Introduction to Friction in Machines

Friction in machines is the resistive force that opposes the relative motion or tendency of motion between two surfaces in contact. It is an unavoidable phenomenon in all mechanical systems and plays a crucial role in machine performance, efficiency, wear, and energy consumption.

While friction causes energy loss and wear in many applications, it is also essential for the proper functioning of components such as brakes, clutches, belt drives, and fasteners.

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)

The Laws of Dry Friction, also known as Coulomb’s Laws of Friction, describe the behavior of friction between two dry, unlubricated surfaces in contact. These laws were established by the French physicist Charles-Augustin de Coulomb in the 18th century and form the basis for the analysis of friction in engineering mechanics and machine design.

Dry friction is the resisting force that acts between two solid surfaces in contact when they tend to move or move relative to each other without lubrication.It always acts parallel to the contact surface and opposite to the direction of motion or impending motion.

These laws are applicable to dry contact surfaces where lubrication is absent and are widely used in the design of brakes, clutches, bearings, screws, and other machine elements.

4. Limiting Friction and Coefficient of Friction

Limiting Friction

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

Where:

$F_{max}$ = limiting friction
$\mu$ = coefficient of friction
$N$ = normal reaction

Coefficient of Friction

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

5. Angle of Friction and Angle of Repose

Angle of Friction (φ)

$\tan \phi = \mu$

Angle between resultant reaction and normal reaction

Angle of Repose (θ)

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

$\theta = \phi$

6. Cone of Friction

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

Friction in screws is the resistance encountered between the mating threads of a screw and a nut when one moves relative to the other. This friction significantly affects the torque required to lift or lower loads, the efficiency of power screws, and the self-locking ability of screw mechanisms.

Power screws are widely used to convert rotary motion into linear motion in devices such as screw jacks, presses, vices, clamps, lead screws, and lifting mechanisms. Understanding thread friction is essential for designing safe and efficient machine elements.

(b) Friction in Bearings

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:

$\frac{T_1}{T_2} = e^{\mu \theta}$