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1.1.7 Accelerated and Decelerated Shafts

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Consider a shaft carrying a gas turbine rotor or piston engine flywheel with the moments and torques acting as shown in Figure 1.4. A heat engine is usually started by means of an external driver such as starting motor by accelerating the driving shaft from rest to the required speed. The driving torque required to accelerate the shaft Td is balanced by the inertia couple Mi = (α is angular acceleration) and resistance couple MR, which is mainly due to friction in the bearings, as shown in Figure 1.4a. The governing equation is

(1.16)

To stop an engine, a braking torque Tb is applied, which is assisted by the resistance moment Mr to decelerate the shaft from the rated speed to rest, as shown in Figure 1.4b The governing equation is

(1.17)

The engine can be brought to rest without applying a braking torque by cutting off the fuel supply and allowing the resistance couple to decelerate the shaft to rest. Note that when the shaft is decelerating, the angular acceleration vector is counter to the direction of rotation of the shaft.

Fundamentals of Heat Engines

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