Dry Friction - Theory & Concepts

In the previous topics, surfaces were often idealized as "smooth" or frictionless. In reality, whenever two surfaces are in contact and tend to move relative to one another, a resisting force develops at the contact surface. This force is called friction.

Dry friction (or Coulomb friction) occurs between the unlubricated surfaces of two contacting solid bodies. When a horizontal force $P$ is applied to a block resting on a rough horizontal surface, the block will not move immediately. The surface exerts an equal and opposite static friction force $F_s$ that balances $P$.

• Static Friction ($F_s$): As the applied force $P$ increases, the friction force $F_s$ increases proportionally to maintain equilibrium ($F_s = P$). The block remains at rest.
• Impending Motion: There is a limit to how large the static friction force can be. When $P$ reaches this maximum value, the block is on the verge of slipping. This maximum static friction force is proportional to the normal force $N$.
• Kinetic Friction ($F_k$): If $P$ slightly exceeds the maximum static friction, the block begins to move. The friction force drops slightly to a constant value called kinetic friction.

Instead of components $N$ and $F$, the contact forces can be represented by a single resultant force $\mathbf{R}$.

Friction is not always a hindrance; it is frequently utilized in engineering mechanisms to transmit power, hold objects in place, or decelerate motion. Common applications include wedges, belts, screws, and bearings.

A wedge is a simple machine used to transform an applied force into much larger forces, directed at approximately right angles to the applied force. They are used to lift heavy blocks, adjust elevations, or split materials.

The transmission of power through belts and pulleys, or the braking of a rotating drum using a band brake, relies entirely on friction over a curved surface. When a flexible belt is wrapped around a rough cylinder and motion is impending (the belt is about to slip), the tension on the pulling side ($T_2$) is greater than the tension on the yielding side ($T_1$).

Unlike flat belts that sit on a cylindrical drum, a V-belt sits in a wedged groove with an angle $2\alpha$. The normal force is magnified by the wedge effect, which significantly increases the friction force without requiring more tension on the belt.

A square-threaded screw is essentially a wedge wrapped around a cylinder. When a moment $M$ is applied to tighten the screw against an axial load $W$, impending motion is upward along the thread. To loosen the screw, impending motion is downward. If $\theta \le \phi_s$, the screw is self-locking, meaning it will not unscrew under the axial load $W$ without an applied moment.

Friction resists the rotation of a shaft within its bearing. When motion is impending, the reactive force shifts slightly to create a resisting couple moment.

Thrust bearings provide axial support to a rotating shaft. The resisting frictional moment acts on the flat circular area.

When a cylinder or wheel rolls on a surface, deformation of both bodies occurs, shifting the normal reaction force slightly forward in the direction of motion by a distance $a$. This creates a resisting moment that must be overcome to maintain constant speed.

When a force $P$ is applied to a rigid body resting on a rough surface, two failure modes are possible: the body might slide (slip), or it might rotate (tip over). An engineer must always determine which will occur first.

Consider a block of weight $W$, height $h$, and base width $b$. A horizontal force $P$ is applied at a height $y$ from the base. The actual force $P$ required to cause motion is the smaller of $P_{\text{slip}}$ and $P_{\text{tip}}$. The smaller value determines the dominant failure mode.