A key is a crucial machine element designed to establish a positive connection between a rotating component, such as a flange coupling, and a shaft. Its primary role is to transmit torque without any relative motion (slippage) between the connected parts.

Key Function in Flange Couplings

When a flange coupling is assembled onto a shaft, a key is inserted into a precisely cut groove known as a keyway. This keyway is present on both the shaft and the internal bore of the flange coupling hub. As the shaft rotates to transmit torque, the key is subjected to forces that attempt to slide or deform it. The effective transmission of power relies on the key's ability to withstand these forces.

Shear Failure in Keys

The most common and critical mode of failure for a key connecting a flange coupling to a shaft is shear failure. Here's why:

• When torque is applied to the shaft, it creates a tangential force at the interface between the shaft and the key, and similarly between the key and the flange coupling hub.
• This tangential force acts parallel to the cross-sectional area of the key, attempting to slice or shear it along its length. If this force exceeds the shear strength of the key material, the key will break or deform permanently in shear.
• The shear stress ($\tau$) experienced by the key can be conceptually understood by considering the force ($F$) acting over the shear area ($A$) of the key: $$\tau = \frac{F}{A}$$ Here, \(A\) typically refers to the product of the key's length and width, representing the area resisting the shearing action.
• In many designs, the key is intentionally made to be the weakest link. This ensures that in the event of an excessive overload or shock, the relatively inexpensive key will fail in shear first, protecting the more costly shaft and flange coupling from damage.

For example, if a torque \(T\) is transmitted by a shaft of diameter \(d\), the tangential force \(F\) acting on the key at the shaft's surface is approximately:

$$F = \frac{2T}{d}$$

This force \(F\) directly causes shear stress in the key.

Comparison with Other Failure Modes

While a key might experience other forms of stress, shear failure is the predominant and most likely mode in this application:

• Torsion: The key itself does not undergo a twisting motion (torsion) about its own axis. Instead, it resists the torsional motion of the shaft relative to the flange coupling by being subjected to tangential forces, which induce shear.
• Tension: A key in this configuration is not primarily subjected to direct pulling (tensile) forces. Its main role is to resist tangential forces, not to be stretched.
• Bending: While some minor bending moments might arise due to clearance or misalignment, especially if the key is long, the primary design consideration and the most critical failure mode for transmitting torque is the direct shear force. The key is specifically designed to resist the shearing action caused by the transmitted torque.

Therefore, when connecting a flange coupling to a shaft, the key is most susceptible to failure due to shear stress resulting from the transmitted torque.