A spur gear transmitting power is connected to the shaft with a key of...
Stresses developed in a key of rectangular section
When a spur gear transmitting power is connected to the shaft with a key of rectangular section, different types of stresses are developed in the key. The key is a machine element that is used to transmit torque between a shaft and a component mounted on it. The types of stresses developed in the key are:
1. Shear stress - Shear stress is the stress that is developed in the key due to the shear forces acting on it. Shear forces are the forces that act parallel to the surface of the key. Shear stress is calculated by dividing the shear force by the cross-sectional area of the key. In the case of a rectangular key, the shear stress is maximum at the corners of the key.
2. Bearing stress - Bearing stress is the stress that is developed in the key due to the compressive forces acting on it. Compressive forces are the forces that act perpendicular to the surface of the key. Bearing stress is calculated by dividing the compressive force by the contact area between the key and the shaft. In the case of a rectangular key, the bearing stress is maximum at the edges of the key.
3. Bending stress - Bending stress is the stress that is developed in the key due to the bending moment acting on it. Bending moment is the moment that is produced when a force is applied perpendicular to the axis of the shaft. Bending stress is calculated by dividing the bending moment by the moment of inertia of the key. In the case of a rectangular key, the bending stress is maximum at the center of the key.
Conclusion
In conclusion, when a spur gear transmitting power is connected to the shaft with a key of rectangular section, both shear and bearing stresses are developed in the key. The magnitude of these stresses is dependent on several factors, such as the dimensions of the key, the torque transmitted, and the material properties of the key and shaft. It is important to design the key properly to ensure that it can withstand the stresses developed during operation.
A spur gear transmitting power is connected to the shaft with a key of...
As the shear stress will generate on the upper and lower end of key, it will tend to shear.Similarly the key is bearing a unit amount of load(P) due to which it is also subjected to bearing.