Transient Analysis – Speed Profile
In many applications, there are needs to study the rotor motion during startup, shutdown, going through critical speeds, or rotor drop when the magnetic bearings failure occurred. In these situations, the angular velocity (speed) is no longer a constant and is a function of time. Two more terms introduced in the governing equations due to the speed variation are: circulatory matrix and forcing function. The details of the equations are documented in the DyRoBeS Theoretical Manual.
Transient Speed Profile
In DyRoBeS, two types of speed profiles can be considered.
1. Linear Profile
Linear profile gives a constant acceleration during startup and deceleration during shutdown.
Note that numerical time integration starts from ts (zero) and ends at tf. OMEGA-1 is the initial speed from ts to t1 and OMEGA-2 is the final speed after t2. The angular acceleration, velocity and displacement are:
2. Exponential Profile
In some industrial application, the rotor speed increases fast initially during startup and then gradually increases the speed as the rotor speed approaches the operating speed.
The value of 2% (0.02) was used in Lalanne and Ferraris. The larger delta value is, the straight the curve becomes. The coastdown curve is :
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