The formula to calculate the deflection of a shaft is:
\[ D = \frac{F \cdot L^3}{3 \cdot E \cdot I} \]
Where:
Let's say the applied force (\( F \)) is 1000 N, the length of the shaft (\( L \)) is 2 m, the modulus of elasticity (\( E \)) is 200 GPa (which is \( 200 \times 10^9 \) Pa), and the moment of inertia (\( I \)) is \( 0.0001 \) m^4. Using the formula:
\[ D = \frac{1000 \cdot 2^3}{3 \cdot 200 \times 10^9 \cdot 0.0001} \]
We get:
\[ D = \frac{1000 \cdot 8}{600 \times 10^9} = \frac{8000}{600 \times 10^9} \approx 1.33 \times 10^{-5} \text{ m} \]
So, the shaft deflection (\( D \)) is approximately \( 1.33 \times 10^{-5} \) meters.
Shaft deflection refers to the degree to which a structural element is displaced under a load. It is a critical factor in mechanical engineering and structural design, as excessive deflection can lead to failure of the component or the entire system. In the context of a rotating shaft, such as in an engine or transmission, deflection can cause misalignment, vibration, and increased wear on bearings and other components. This can result in decreased performance, increased maintenance costs, and potential catastrophic failure. Therefore, engineers must carefully consider and calculate expected shaft deflection during the design process to ensure the integrity and longevity of the system. Factors influencing shaft deflection include the material properties of the shaft, the magnitude and direction of the applied load, the length of the shaft, and the method of support at the ends of the shaft.
