we have critical speed ranges for all the rotating equipments. During steam turbine ramp-up condition it ramps with a designed ramp-up rates as per the design and it changes at the time of critical speed ranges. But during ramp-down condition turbines doesn't follow any fast ramp-down rates during these critical speeds. Why it was designed so.
We have the facility of vacuum breaking system also, but in most of the cases we didn't use this system. Why.
madhu.yedla [at] gmail.com
Critical speed: It is the speed at which the center of mass is not equal to the center of rotation.
Normally at these critical speeds the vibration is very high i.e. deflection of the shaft is infinity i.e. angular velocity (W) of the shaft = Critical angular velocity (Wc).
Basically vibrations is expressed in the terms of displacement (mills or mm or microns), Velocity (mm/sec or inch/sec), Acceleration (mm/sec2).
Critical speed (rpm)useful to express the vibration in the terms of mm/sec.
To avoid the shaft deflection to infinity, find out the critical speed of the shaft.
Critical speed of the shaft (Nc) = 1/2(pi)*square root of (g/dl)-------(1)
Here pi= 3.14 and g= acceleration due to gravity, dl=change of elongation of the shaft.
Here dl value will change with respect to the type of the shaft and loads on the shaft.
Type of shaft-Cantilever (CL), simply supported beam (SSB) and Fixed beam (FB)
Type of loads--- Unit or point Loads (PL) and uniformly distributed loads (UDL)
Our Turbine shaft is a SSB with combination of Point loads and uniformly distributed loads.
So d= wl3/3EI (for unit loads with SSB)-----(2)(Here l3 is the L power 3)
= (5/384)*(wl3/EI) (for uniformly distributed loads with SSB)----(3)
Here w=weight, l- length of shaft, E- Young's modulus, I - Moment of inertia.
Dunkerley's formula is useful to find out the critical speed with different loads
1/ (Nc) 2 = 1/ (N1) 2+1/ (N2) 2+1/ (N3) 2 +.....
(1/ N1 square+ 1/N2 square+ 1/N3 square+......)
Here Nc= critical speed, N1, N2, N3..... Critical speeds at different type of loads
So, the critical speed calculation will give a sense to avoid the rotation of the shaft at this speed to avoid the deflection of the shaft to infinity.
There are 3 comparisons to find out the criticality of the shaft deflection :
1. Speed of the Shaft=Critical speed of the Shaft----- Deflection of the shaft is infinity
2. Speed of the Shaft<Critical speed of the Shaft----- Deflection of the shaft in the terms of +ve. So, Shaft is under hogging (Upper side bowing)
3. Speed of the Shaft>Critical speed of the Shaft----- Deflection of the shaft in the terms of -ve. So, Shaft is under sagging (Lower side bowing)
So, shaft will have different critical speeds to avoid the deflection of the shaft. Based on this calculation, ramp rate will change at this point of speed.
I am coming to the point,,
To avoid the deflection of the shaft while start up of a steam turbine, Critical speed calculation is very important.
Design ramp rate is such a way that to avoid the running of the shaft at critical speed while start-up.
But while shut-down the Turbine shaft automatically it will coast down (rotation of the shaft is due to residual kinetic Energy only while shutdown and It will never stay at critical speed).
Bowing of the Shaft will find out for a turbine shaft before start-up by using the measurement of "eccentricity"
Formation of Bowing of the Shaft will avoid by find out the critical speed while start-up.
So, "Critical speed calculation is to avoid the formation bowing"while start-up. "Eccentricity is to find out the bowing" at lower speeds before start the machine by keeping the Turbine under turning gear.
Normally before starting a turbine, Eccentricity value is very critical: Eccentricity or Rate of change of eccentricity (ROCE) high will not give permissive to start the machine.
Eccentricity will able to find out the any type of bowing like-fixed Bowing, Gravity bowing and thermal bowing(It will not distinguish the type of bowing-it will give eccentricity value only)
Eccentricity also gives a sense for the condition of the Center of mass to center of Rotation.
Normally vacuum is advisable to break in emergency situation only unless shut-down
i.e. Total Lube oil system failure and thrust bearings unable to handle load. If break the vacuum, Turbine will coast down rapidly-It is not advisable. In the normal operation, vacuum is useful to coast down the turbine properly which is based on the residual kinetic energy in the rotor.
I hope it is useful for u.
Waiting for your reply
Hi this is Lakshmaiah
I have doubt in the calculation of critical speeds
As I go with the study material in various text books, the majority of the problems are solved for uniform diameter shafts but in actual practice the turbine rotor consists of different diameter sections. hence how to consider the step sections of the rotor while calculating the critical speeds.
kindly reply back,