Short Answer:

Coulomb damping, also called dry friction damping, occurs when two solid surfaces in contact move against each other and friction opposes their motion. The damping force produced is constant in magnitude and always acts opposite to the direction of motion.

In simple terms, Coulomb damping reduces vibration by converting mechanical energy into heat through dry friction. It is commonly found in mechanical joints, sliding parts, and bearings where metal surfaces rub against each other during motion.

Detailed Explanation :

Coulomb Damping

Coulomb damping is a type of damping that results from dry friction between two solid surfaces that slide or rub against each other. It is named after Charles-Augustin de Coulomb, who first explained the law of dry friction. Unlike viscous damping, where the damping force depends on velocity, in Coulomb damping, the damping force remains constant in magnitude but opposite in direction to the motion of the vibrating body.

Whenever two dry surfaces come into contact and relative motion occurs, frictional resistance develops. This resistance converts part of the mechanical energy of vibration into heat, leading to a gradual reduction in the vibration amplitude. Coulomb damping is widely observed in mechanical systems where parts are in contact without lubrication, such as linkages, joints, and bearings.

Principle of Coulomb Damping

The working principle of Coulomb damping is based on dry friction. When a vibrating body moves in one direction, the frictional force acts in the opposite direction. When it moves back, the direction of friction reverses, but the magnitude remains constant. This repeated resistance during each cycle of vibration leads to energy loss.

The energy lost per cycle of vibration depends on the amount of frictional force and the distance traveled during one vibration. Since the damping force does not depend on speed, the vibration amplitude decreases linearly with time, unlike viscous damping, where it decreases exponentially.

Mathematically, the damping force in Coulomb damping is given by:

Where:

•  = Damping (frictional) force
•  = Coefficient of friction between the two surfaces
•  = Normal reaction force between the surfaces

This equation shows that the damping force depends only on the friction coefficient and the normal force, not on velocity.

Behavior of Coulomb Damping

In a system with Coulomb damping, the motion gradually slows down and stops after a few cycles because the friction force continuously opposes the motion. The amplitude of vibration reduces by a fixed amount in each half-cycle, resulting in a linear decay of motion.

For example, if a block slides on a rough surface after being given an initial push, it experiences Coulomb damping. The block moves back and forth due to vibration, but each oscillation becomes smaller until it stops completely due to frictional resistance.

Characteristics of Coulomb Damping

1. The damping force is constant in magnitude and opposite in direction to motion.
2. It is independent of velocity of vibration.
3. The amplitude decreases linearly with time.
4. The energy lost per cycle is constant.
5. It occurs mostly in systems with dry surface contact and no lubrication.

These characteristics make Coulomb damping very different from viscous damping, where damping depends on velocity and results in smooth, exponential decay.

Factors Affecting Coulomb Damping

1. Coefficient of Friction:
   The amount of damping depends directly on the coefficient of friction between the surfaces. A higher coefficient means more damping.
2. Surface Roughness:
   Rougher surfaces increase friction and therefore increase damping.
3. Normal Force:
   The contact pressure or normal force between surfaces affects the damping magnitude.
4. Material Type:
   Materials like rubber and leather provide more frictional damping compared to smooth metals.
5. Lubrication:
   The presence of lubrication reduces dry friction, thereby reducing Coulomb damping significantly.

Applications of Coulomb Damping

1. Machine Joints and Bearings:
   Found in mechanical joints, pivots, and bearings where surfaces slide over each other.
2. Vibration Testing Equipment:
   Used to study the effect of dry friction on damping.
3. Metal Cutting and Machining Tools:
   Friction between tool and workpiece contributes to damping during cutting operations.
4. Building and Structural Components:
   In some structures, friction at joints provides natural damping during vibrations or earthquakes.
5. Braking Systems:
   Coulomb damping principle is used in friction brakes, where dry friction between brake pad and disc reduces motion.

Advantages of Coulomb Damping

• Simple and naturally present in many systems.
• Does not require fluids or external damping devices.
• Effective for large vibration amplitudes.
• Works even at low speeds or slow vibrations.

Limitations of Coulomb Damping

• Not suitable for small or precision systems because the damping force is not adjustable.
• Causes wear and tear due to dry surface contact.
• Generates heat, leading to material damage over time.
• Damping is not smooth or uniform like viscous damping.

Comparison with Viscous Damping

Property	Coulomb Damping	Viscous Damping
Damping Force	Constant (independent of velocity)	Proportional to velocity
Type of Friction	Dry friction	Fluid friction
Energy Loss	Constant per cycle	Varies with speed
Amplitude Reduction	Linear	Exponential
Common Example	Sliding surfaces, joints	Dashpot, shock absorber

(Though presented in points here, the comparison helps understand key differences clearly without using tables or graphs.)

Practical Example

A practical example of Coulomb damping can be seen in a pendulum with a rough hinge. As it swings, dry friction at the hinge resists motion, and with each swing, the pendulum loses energy. The amplitude gradually decreases linearly until it stops completely. This is a clear example of energy loss due to constant frictional resistance.

Conclusion

In summary, Coulomb damping or dry friction damping occurs due to constant frictional resistance between two solid surfaces in contact. It is independent of velocity and leads to linear reduction in vibration amplitude. The energy is dissipated as heat due to friction, eventually bringing the system to rest. Though simple and naturally present in many systems, it can cause wear and is less controlled than viscous damping. Still, Coulomb damping plays a crucial role in understanding and controlling vibrations in many mechanical systems.