Chapter 15 : Fritction & Its Concept - Diploma in Mechanical Engineering

 

Chapter 15 : Friction & Its Concept

Friction is a force that opposes the relative motion or tendency of such motion between two surfaces in contact. It plays a crucial role in our daily lives, influencing how objects move or come to a stop. In this chapter, we will explore the concept of friction, its applications, and its specific role in the engineering principle of banking roads.

Concept of Friction

Types of Friction

1. Static Friction:

ü  Static friction is the force that prevents the relative motion between two surfaces when they are at rest.

ü  It varies based on the force attempting to cause motion and is capable of reaching a maximum value before motion occurs.

2. Kinetic Friction:

ü  Kinetic friction, also known as dynamic or sliding friction, opposes the motion between two surfaces in contact.

ü  Once an object is in motion, kinetic friction comes into play, and its magnitude is generally less than the maximum static friction.

3. Rolling Friction:

ü  Rolling friction occurs when one object rolls over another.

ü  It is generally less than sliding friction and is observed in scenarios involving wheels or spherical objects.

4. Fluid Friction:

ü  Fluid friction, also known as viscous or air resistance, is experienced by objects moving through a fluid (liquid or gas).

ü  The magnitude of fluid friction depends on the object's shape and speed.

Factors Affecting Friction

Several factors influence the magnitude of friction between two surfaces:

• Nature of Surfaces:
• Rough surfaces exhibit higher friction than smooth surfaces.
• Normal Force:
• The force exerted by a surface perpendicular to the contact area affects friction. Higher normal forces often result in higher friction.

Applications of Friction

1. Vehicle Brakes:

• Friction between brake pads and the wheels is crucial for slowing down or stopping vehicles.
• By increasing friction through materials and design, effective braking systems are achieved.

2. Footwear Traction:

• Shoes with high friction soles provide better traction, preventing slips and falls.
• Cleats or treads increase the contact area, enhancing friction between shoes and the ground.

3. Belt and Pulley Systems:

• Friction between belts and pulleys is essential for the transfer of motion and power in machines.
• Proper tension and material selection ensure efficient energy transfer.

Application to Banking of Roads

1. Principle of Road Banking:

• The concept of road banking involves tilting the road surface to help vehicles negotiate turns more safely.
• Banking reduces the reliance on friction alone to prevent slipping.

2. Components of Banked Roads:

• Banking Angle (θ):
• The angle of inclination of the road surface from the horizontal.
• It is designed to counteract the effects of friction and provide a component of the normal force that contributes to centripetal force.
• Friction:
• Friction between the tires and the road surface is still essential for maintaining control.
• However, it is not the sole factor preventing slipping.

3. Balancing Forces:

• When a vehicle turns on a banked road, it experiences two horizontal forces: the frictional force and the horizontal component of the normal force.
• The sum of these forces provides the centripetal force required for circular motion.

4. Optimizing Banking for Safety:

• Properly designed banking reduces the reliance on friction, allowing for safer turns, especially at higher speeds.
• Overbanking or underbanking can lead to undesirable consequences, emphasizing the importance of precise design.

Laws of Friction

The laws of friction describe the relationship between the force required to overcome friction and the normal force acting between two objects in contact. The most common representation of these laws is attributed to the work of French scientist Guillaume Amontons and Charles-Augustin de Coulomb.

1. Amontons' First Law:

• The force of friction is directly proportional to the applied load or normal force.
• Mathematically, it can be expressed as F_f = μ_s⋅N, where F_f is the force of friction, μ_s is the coefficient of static friction, and NN is the normal force.

2. Amontons' Second Law:

• The force of friction is independent of the apparent area of contact between the two surfaces.
• This means that, regardless of the size of the contact area, the force of friction remains constant for a given normal force and coefficient of friction.

3. Coulomb's Law of Friction:

• Coulomb expanded on Amontons' work and introduced the concept of kinetic or sliding friction.
• The force of kinetic friction (F_k​) is proportional to the normal force (N) and is expressed as F_k=μ_k⋅N, where μ_k is the coefficient of kinetic friction.
• The coefficient of kinetic friction is generally less than the coefficient of static friction (μ_s​).

4. Direction of Frictional Force:

• The force of friction always acts opposite to the direction of motion or the impending motion of the object.

Coefficients of Friction:

• Coefficients of friction (μ) are dimensionless values that represent the ratio of the force of friction to the normal force.
• There are two main coefficients: μ_s for static friction and μ_k​ for kinetic friction.

Concept of Friction Cone

The concept of the friction cone is particularly relevant in the study of multibody dynamics, robotics, and mechanical engineering. It is used to describe the possible directions in which a force can be applied to an object in contact with a surface while still maintaining static equilibrium.

Static Friction Cone:

• For an object in static equilibrium (not moving), the static friction cone represents all the possible directions in which a force can act without causing motion.
• The static friction force can act in any direction within this cone.

Dynamic Friction Cone:

• In the case of an object in motion, the dynamic friction cone represents all the possible directions for the kinetic friction force to act.
• This cone is generally narrower than the static friction cone, reflecting the fact that the force of kinetic friction is usually less than the force of static friction.

Use in Robotics and Mechanics:

• Understanding the friction cone is crucial in the design and control of robotic systems, especially those with multiple contact points.
• It is employed in algorithms that calculate and optimize the distribution of forces on the contact points to achieve stable and efficient motion.

Limitations and Challenges:

• The friction cone model assumes idealized conditions and may not fully capture the complexities of real-world friction.
• Surface irregularities, material properties, and other factors can influence the actual behavior of friction.

Conclusion

The laws of friction, as formulated by Amontons and Coulomb, provide fundamental insights into the nature of frictional forces and their relationships with normal forces. The concept of the friction cone is a valuable tool in mechanics and robotics, allowing engineers and researchers to model and predict the behavior of objects in contact with surfaces. As we continue to advance in the understanding and application of friction, these principles contribute to the design of systems that optimize performance, stability, and safety in various fields of engineering and technology.

Conclusion

Friction is a fundamental force that both hinders and enables motion in various contexts. Understanding the concept of friction, its types, and the factors influencing it is crucial for designing systems where friction is either a beneficial or limiting factor. The application of friction in road banking exemplifies the careful balance required to optimize safety and efficiency in engineering. As we continue to explore and utilize friction in diverse scenarios, the principles discussed in this chapter provide a foundation for innovative and effective design in transportation, machinery, and everyday applications.