A key is a crucial machine element designed to connect a rotating component, such as a gear or pulley, to a shaft. Its fundamental purpose is to transmit torque and prevent any relative rotational motion between the shaft and the attached component, ensuring they function as a single unit.

Key Role in Power Transmission

In a gear train, a key plays a vital role in transmitting power from the shaft to the gear, or vice versa. The key fits into a groove (known as a keyway) cut into both the shaft and the hub of the gear. When the shaft rotates, it exerts a force on the key, which in turn transmits this force to the gear, causing it to rotate. This mechanism ensures synchronized movement and efficient power transmission.

Forces Experienced by a Key

When a key is actively transmitting power in a gear train, it is subjected to two primary types of forces due to the torque being transferred. These forces are:

• Shear Force
• Crushing Force (also known as bearing force)

Shear Force on the Key

Shear force acts tangentially across the cross-section of the key. Imagine the torque from the shaft trying to rotate the gear. This action creates a tendency for the key to be cut or sheared along its length. The shaft applies a force on one side of the key, and the gear's hub applies an equal and opposite force on the other side. This results in shearing stress primarily across the horizontal plane of the key. The area resisting this shearing is typically the product of the key's length and width.

Mathematically, the shear stress ($\tau$) on the key can be expressed as:

\(\tau = \frac{F_s}{A_s}\)

Where:

• \(F_s\) is the shear force transmitted by the key.
• \(A_s\) is the shear area of the key (length \(\times\) width).

Crushing Force on the Key

Crushing force, or bearing force, acts perpendicularly to the contact surfaces between the key and the keyways in both the shaft and the gear hub. As the key transmits torque, it presses against the material of both the shaft and the gear hub. This compressive action causes a crushing or bearing stress on the surfaces in contact. If this stress exceeds the material's permissible limit, it can lead to plastic deformation or crushing of the key or the keyway material.

The crushing stress ($\sigma_c$) on the key can be expressed as:

\(\sigma_c = \frac{F_c}{A_c}\)

Where:

• \(F_c\) is the crushing force exerted on the key's bearing surface.
• \(A_c\) is the crushing area (length \(\times\) half the key's thickness, as the force is distributed over half the key's thickness on each side).

Key Design Considerations

For safe and effective power transmission, a key must be designed to withstand both the shear force and the crushing force without failure. If the shear force is too high, the key might break across its cross-section. If the crushing force is excessive, the key or the keyway material might deform, leading to loosening of the connection or failure to transmit power efficiently. Therefore, engineers consider both failure modes during the design process to select appropriate key dimensions and materials.