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vibration. The results are given in the last two columns of Fig. 18. The second and
third columns give the most and least favorable amplification factors from Fig. 19,
based on knowing only the inertias of the system components. From these it appears
that this mill is basically well designed torsionally, since test torques are not much
greater than for the most favorable system.
The fourth column gives the result using the Snively and Black formula based on
knowing only the first three natural frequencies of the system.
Test torques are as much as 28 to 51 percent higher than the column 6 calculated
values, and this will be discussed later.
While damping has a minor effect on peak torques resulting from suddenly
applied torques, we at Elliott are vitally concerned with the magnitude of torsional
damping. We occasionally encounter a system in which the natural frequencies cannot
adjusted to avoid resonance with an operating speed. We then must be able to
estimate the typical magnitudes of damping as well as of exciting torques that can be
expected for the various system elements, in order to calculate factors of safety.
The authors have considered only damping torques defined as a function of the
difference in velocity between adjacent inertias, as indicated by their equations (2-5).
This represents material damping in shafts, which is negligible since shaft material
has a log decrement in the order oi 0.002, whereas the tests indicate an overall log
decrement in this system of about 0.32. This can also represent damping due to loose
coupling fits, which is unlikely except for the roll couplings where rapid wear of
clearances suggests abnormally high damping. Calculations show that if all damping
were generated by the roll couplings, their damping ratio would have to be about 0.3
to 0.5 (Q — 1 to 1.7), which appears too high to be likely, so other or additional
damping sources must be found.
Material damping may also be generated in the material being rolled, which may
be greater than for shaft material due to elevated temperature and greater plasticity.
Slippage between work and rolls, and between work rolls and backup rolls would
also produce damping, but the absence of chatter does not point to this source. The
torsional model used by the writer does not permit the use or study of this source of
damping, since infinite stiffness was assumed between rolls.
Main test phase T max, Table 2 of 71VIBR-95, design
arance.
Most favorable single degree of freedom system.
Very unfavorable system.
From equation (7) of Snively & Black, 33 Mar. 1964 issue.
Pollard approx. method - undamped,
Pollard approx, method - damped.
Branch in system neglected.
Backlash neglected.
Damping neglected except in last column. the steel being rolled, due to the nonuniform velocity rather than to a hysteresis loop
in shear.
Assuming no damping other than due to varying roll velocity, the damping
contributed by the rolls would correspond to about Q = 7 (damping ratio = 0.072),
which does not appear unreasonable.
Fig. 20 shows the calculated transient torque corresponding to this value of roll
damping plus the indicated damping assumed motors and gear. Comparison with the
authors' test curves shows that vibration in the second critical does not attenuate as
rapidly as in the tests, and since calculations show the second critical to be relatively
insensitive to any but motor damping, indicates greater motor damping is present.