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Fig. 21 shows the effect of increasing motor damping together with somewhat
reduced roll damping. This matches the tests well enough to establish that motor
damping corresponds to about Q = 20 and roll damping to about Q = 10.
Dimensionless expressions such as Q, damping ratio, and logdecrement relate
"inertial" damping to the inertia of the systehi element involved. However, the inertia
per se does not generate the damping, which is a power loss more logically related to
the power being absorbed or generated by the system element involved.Consequently,
it is unwise to assume that a test value of Q obtained for one machine is valid for a
different design of that type of machine. For example, suppose the back-up roll
diameter were increased such that the total idealized roll inertia were doubled. The
work done by the rolls is the same, the power expended in damping is the same, but
the Q of the rolls required to represent the same damping would be doubled. ;
Consequently, a better expression than Q is needed to compare damping of, say,
compressors of different size and design.
It is therefore proposed that Q/H, or alternatively damping ratio multiplied by H,
be adopted as the figure of merit for inertial torsional damping of turbines and
compressors, where H is the ratio of the energy in HP sec stored in the inertia at test
speed, to the HP of the machine under test conditions. For AC generators and motors
H should be based on rated HP and speed. Our tests to date indicate that gear damping
is independent of H, and that Q alone is a good figure of merit for gears with
acceptable noise and lateral vibration. One test on a system with an unusually rough
gear indicated several times the gear damping that we normally find.
Returning to the discrepancy between calculated and maximum test torques shown
in Fig. 18, several explanations are possible. Coupling backlash in the new unworn
condition may be sufficient to cause this increase above the step torque calculations. It
is also possible that the torque required as the work enters the rolls and comes up to
full speed is that much greater than the steady rolling torque, and hence the initial step
of torque is correspondingly greater. Another possibility is that the forcing function is
the sum of a step of torque plus a Dirac impulse function. This possibility is explored
in Fig. 22 where the additional sine terms represent the impulse. The impulse was
chosen to result in about the maximum test value of peak torque and causes a phase
shift toward zero time for both natural frequencies, and an excursion above zero
torque for the second and fourth half cycles. Since neither of these effects is typical of
the authors' test results, it appears that the forcing function does not contain a pure
impulse effect of significant magnitude
Authors' Closure
We agree that a shock sensitive system can respond violently to the correct torque
time input function irrespective of the initial state of clearance. We wanted to
demonstrate the need for "off design" analysis by showing that a drive system that
was sound dynamically when operating under design clearances exhibited large
torsional amplification factors as the available clearances increased.
We have found that the areas Mr. Pollard neglects can be very critical in certain
systems, e.g., backlash has proven to be one of the most sensitive parameters relative
to torque amplifications in rolling mill drive systems; the shock propagation can be
quite nonsynchronous in branched systems (this was measured to be a function of bar
entry conditions); motor torque in the system can effect torque amplification factors