ROTORDYNAMICS and the KGB

An analogy by John M. Vancewww.vavco.comCopyright 2011

What is the KGB? (Question for youngsters)

The KGB was the notorious Russian secret spy agency during the “Cold War”(1954-1991). Vladimir Putin was an important member. American CIA and FBI agents often had to deal with KGB agents in foreign countries and in the USA. There was a great deal of deception and intrigue on both sides, if movies and magazine articles can be believed. Some agents were called “double agents”because they were working for both sides at the same time. According to Wikipedia: “The KGB classified its spies as agents (intelligence providers) and controllers (intelligence relayers). The false-identity legend assumed by a USSR-born illegal spy was elaborate, the life of either a "live double" (participant to the fabrication) or a "dead double" (whose identity is tailored to the spy). The agent then substantiated his or her legend by living it in a foreign country, before emigrating to the target country; thus the sending of US-bound illegal residents via the Soviet residency in Ottawa, Canada. Tradecraft included stealing and photographing documents, code-names, contacts, targets, and dead letter boxes, and working as "friend of the cause" agents provocateur who infiltrate the target's group to sow dissension, influence policy, and arrange kidnappings and assassinations.”

THE KGB DOUBLE AGENT

You can’t trust him

but you can’t ignore him, either

He is one of your few sources of information

and

He might be telling the truth!

IN ROTORDYNAMICS TESTING AND ANALYSIS

THE KBG AGENT IS

INTUITION

What is “intuition”

•Divine inspiration?

•A talent unique to women?

Intuition to most engineers and managers is an expectation that they know what will happen because they have seen something similar before

AN EXAMPLE WHERE INTUITION WOULD FAIL(except for one who has seen a spinning top)

the solid cone will fall down

unless it is spinning

r

m

k

m2r

kr

RANKINE’S CONTRIBUTION TO ROTORDYNAMICSIn 1869 Rankine published an article that influenced the design of rotating machinery for years. He gave a correct equation for the critical speed but incorrectly predicted that machines could not run at speeds above a critical speed. His free-body diagram of a whirling rotor is shown below. A “centrifugal force” mω2r is shown pulling the rotor outward from the whirl orbit. Many people including some engineers have an intuitive “feel” for centrifugal force, but it is not a real force. The correct conclusion from the free-body diagram is that the spring force kracts on the rotor mass to produce the centripetal acceleration ω2r. The centrifugal force is not really there and should be removed from the diagram. Many machines today run at speeds well above one or two critical speeds.

kr = m2r

Critical Speed = [k/m]1/2

RANKINE’S MISTAKE (intuition instead of math)“At very high speeds, centrifugal force will overcome the restoring elastic force, and the whirl amplitude will become unbounded” (Engineer, 1869)

r

m

k

m2r

kr

The truth is: The centrifugal force mω2r does not exist.

Intuition told Rankine: “Centrifugal force will break the rotor at supercritical speeds”Intuition also says: “Centrifugal force will pull the unbalance mass on a rotor to the outside of the whirl orbit and hold it there”

The truth is: The unbalance comes around to the inside of the whirl orbit at high speed and stays there

r

JEFFCOTT’S ANALYSIS (1919) REVEALED THE TRUTH

Jeffcott’s simplified rotor model has a disk that is unbalanced (by an added mass in the picture above). The disk is located at mid-span of the flexible shaft (even steel is flexible). Jeffcott’s mathematical analysis shows that the most common whirling motion has the whirling speed equal to the shaft spin speed with the unbalance phase angle βholding constant. The angle β changes only if the speed changes. At high speed, the angle β approaches 180° (all the way to the inside). This is called the “critical speed inversion” and has been verified by countless numbers of experiments. The graphs on the following page show how the whirl amplitude and phase angle change with shaft speed ω. This would not be true if there was really a “centrifugal force”.

r

The graphs are from Dr. Vance’s book Rotordynamics of Turbomachinery

“TO REDUCE DESTRUCTIVE ROTOR VIBRATION, COAT THE SHAFT WITH AN ENERGY-ABSORBING MATERIAL TO RAISE ITS DAMPING COEFFICIENT”

The truth is:

EXPERIMENTS AND MATHEMATICAL ANALYSIS HAVE SHOWN THAT DAMPING IN ROTATING ASSEMBLYS CAN CAUSE ROTORDYNAMIC INSTABILITY (ROTOR WHIRLING) AT SUPERCRITICAL SPEEDS

INTUITION TOLD SOME PHYSICISTS ATTENDING A NASA-LEWIS WORKSHOP ON PREVENTING ENGINE FAILURES IN COMMERCIAL AIRLINERS:

KIMBALL-1924 identified internal damping as destabilizing

To be effective, damping must be in non-rotating parts such as bearings and seals. Damping in the rotor can drive the whirl.

Sub-synchronous whirl has the rotor spin speed faster than the whirl speed.

The dark-shaded stresses on the right are from rate of strain. They drive the whirl.

INTUITION SAYS:“IF THE VIBRATION AMPLITUDE IS TOO LARGE, STIFFEN IT UP”

The truth is:ALTHOUGH STIFFENING THE ROTOR ASSEMBLY IS USUALLY GOOD DESIGN PRACTICE, STIFFENING THE BEARINGS OR BEARING SUPPORTS REDUCES THE EFFECTIVENESS OF DAMPING AND INCREASES THE VIBRATION AMPLITUDE AT THE CRITICAL SPEED. THIS IS ESPECIALLY TRUE FOR LONG ROTORS AS FOUND IN MULTI-STAGE CENTRIFUGAL COMPRESSORS (SEE BELOW).

The shaft bending stiffness is inversely proportional to the cube of the length (1/L3).

To illustrate the concept of a flexible rotor on flexible supports, a Jeffcott rotor is mounted on flexible bearing supports with stiffness KB and damping CB in the drawing above. Damping is force that opposes vibratory velocity. Damping dissipates vibratory energy, converting it to heat. The damping becomes less effective as KB is made stiffer. Poor design practice (all too common) has stiffness KB ten (or more) times the shaft bending stiffness, which leads to very large unbalance response at the critical speeds along with susceptibility to sub-synchronous instability. Squeeze film dampers are effective to reduce vibration mainly because they incorporate soft bearing supports (reducing KB). They don’t add damping; they just make it more effective.

INTUITION SAYS:

“DAMPING IS ALWAYS GOOD IN A ROTATING MACHINE. GET AS MUCH YOU CAN”

The truth is:

MANY MODERN HIGH SPEED MACHINES OPERATE AT SUPERCRITICAL SPEEDS WHERE DAMPING INCREASES THE DYNAMIC BEARING LOADS

Damping at high speeds is especially undesirable in machines with ball bearings, since their life is inversely proportional to the cube of the dynamic load. The ball bearing life will increase eight times if the dynamic load is cut in half. The next page shows how the dynamic load FB varies with speed ω for two different values of damping in a stiff rotor that runs above its first critical speed. . A good design will have operating speeds to the far right on the graph with low damping.

Bearing force transmissibility vs. shaft speed ratio for two values of damping, with a rigid rotor and soft supports (from Vance, Rotordynamics of Turbomachinery)

INTUITION SAYS: MOUNTING THE TILT-PAD BEARINGS IN A COMPRESSOR ON SQUEEZE FILM DAMPERS REDUCES THE VIBRATION BY INCREASING THE DAMPING.

In this case the predicted result is correct but the perceived reason is wrong.

Damping comes from the oil films. The original oil film is between the shaft and the bearing, and the added one is in the land between the two O-rings. Two dampers in series always have a smaller damping coefficient than either one. But the O-rings provide a low stiffness support that allows motion to dissipate energy.

INTUITION SAYS: “A FOUR BLADED DAMPER SEAL WOULD HAVE DOUBLE THE DAMPING OF A TWO BLADED DAMPER SEAL”

The truth is:

DAMPING FROM ONE TYPE OF POCKET DAMPER SEAL IS SHARPLY REDUCED AS MORE BLADES ARE ADDED IN THE SAME AXIAL LENGTH ALONG THE SHAFT

IN A POCKET DAMPER SEAL (TAMSEALTM) THE CIRCUMFERENTIAL CAVITY BETWEEN THE TEETH IS DIVIDED BY PARTITION WALLS INTO DISCRETE POCKETS. THE SEAL ABOVE IN A CENTRIFUGAL COMPRESSOR HAS ONLY TWO TEETH TO MAXIMIZE THE DAMPING.

TWO BLADES

The graph shows how two types of seals reduced the vibratory response to unbalance in a laboratory rotor. The two-bladed pocket damper seal completely eliminates the critical speed. More information on damper seals can be found in the book Machinery Vibration and Rotordynamics by Vance, Zeidan, and Murphy.

CONCLUSION

INTUITION BASED ON PREVIOUS OBSERVATIONS WILL ALWAYS BE VALUABLE TO ENGINEERS AND MANAGERS.

BUT BE AWARE THAT ROTATING MACHINERY CAN SOMETIMES GENERATE SURPRISES, WHICH CONTRADICT INTUITION AND WHICH CAN BE UNDERSTOOD ONLY THROUGH RIGOROUS ANALYSIS, COMPONENT TESTING, AND REALISTIC COMPUTER SIMULATIONS.