Avoiding Stick-Slip Chatter in Low-Speed Bearings
Page 1 of 6
Published on Machine Design (http://machinedesign.com)
Avoiding Stick-Slip Chatter in Low-Speed Bearings
by
Created 04/10/2008 - 03:00
Flexible rotors and thin lubricant films lead to noise and vibration.
M. M. Khonsari Professor
Dept. of Mechanical Engineering
Louisiana State Univ.
Baton Rouge, La.
E. R. Booser
Engineering Consultant
Vero Beach, Fla.
Stick-slip chatter commonly shows up on initial start of a machine when static friction in the bearings
temporarily restrains shaft rotation. As the shaft then winds up, torsional force rises until it exceeds the
restraining static friction. At this point, friction drops to its kinetic value as rotation initiates and the rotor
“jumps ahead” as it dissipates its stored elastic energy.
Repetition of this sequence during slow-speed rotation often produces a stop-start jerking pattern, as
illustrated in the accompanying figure. A system with a long, limber shaft is particularly susceptible to
this behavior.
Many rotating machines such as turbines, compressors, oil-well drill shafts, and water-lubricated ship
stern-tube bearings can be reduced to the concept of a disk driven by a turning gear through a flexible
shaft. Similar effects are also encountered with slow-speed sliding contacts in machine tools, metal
cutting, squealing automobile brakes, household appliances, and shaft seals.
The main culprits of stick-slip are low oil-film thickness and torsional vibration, both of which are
described next.
Low oil-film thickness
Friction characteristics with oil-film bearings are shown in the accompanying graph. The coefficient of
friction reaches a minimum at the low oil-film thickness limit corresponding to the “lift-off ” speed at
which a full oil film is first formed. Above this lift-off speed, the influence of surface asperities on bearing
performance is practically nil.
Once journal surface speed again drops below this lift-off, asperity peaks on the mating shaft and
bearing surfaces will begin again to interlace, restrain shaft rotation with increased friction, and build up
torsional elastic energy.
When this rising torsional force overcomes the static bearing friction with the slowed or halted shaft, the
shaft will unwind and jump ahead. As the wind-up torque is then relieved, the shaft may then stick again
http://machinedesign.com/print/67364
11/3/2010
Avoiding Stick-Slip Chatter in Low-Speed Bearings
Page 2 of 6
in a repeating stick-slip vibration.
The negative slope associated with the drop of the friction coefficient from boundary to mixed lubrication
sometimes gives rise to a related type of self-excited vibration. As the surface of a lubricated machine
element moves from boundary lubrication to mixed lubrication where the friction coefficient drops with
increasing speed (∂f/∂V <0), this negative equivalent damping gives rise to self-excited oscillatory
system response.
A similar phenomenon takes place in bearings of tracking devices when the mechanism must swing
back and forth to zero in on a desired target. This is a major problem in satellite systems in which ball
bearings operate under ultralow speeds. Feedback control loops are often necessary to compensate for
friction. The accompanying table gives lift-off speeds needed to generate a full oil film in a journal
bearing, speeds below which stick-slip vibration becomes a possibility. The following example can be
modified to perform lift-off calculations for specific machines. Consider an industrial steam turbine with a
bearing radial load (W) of 8,000 lb. The bearing has a journal diameter (D) of 6.0 in., a bearing length
(L) of 6.0 in., an internal bearing radial clearance (Cr) of D/1000 or 0.006 in. and a journal surface finish
(R) of 0.000020-in. rms. The viscosity of the oil at a bearing temperature of 40°C ( µ) is 4 10-6 lb-sec/in.2
Applying Reynolds hydrodynamic equation as modified for low speeds and small oil-film thicknesses to
obtain lift-off speed N0 revolutions/sec:
N0 = (h0P/Cr)/{4.678µ [(L/D)^1.044] [(D/2Cr)^2]}
where P = bearing radial unit load (P = W/LD), 222 psi, and h0 = lift-off film thickness, defined as 3 R or
60 µin.
This h0 assumes lift-off is completed when the oil film thickness rises to three times the rms journal
finish R as mated with a soft bearing surface polished smooth by initial operation. This corresponds in
the graph to a composite film parameter at breakaway of:
Λ= h0/[(Rjrnl^2 + Rbrg^2)^0.5]
or 60 µin./20 µin. = 3
Applying the Reynolds equation:
N0 =[(6E-5 in. x 222 lb/sq. in.)/6E-3 in.]/
{4.678 x 4E-6 lb-sec/sq. in. x (6.0 in./6.0 in.)^1.044 x [6.0 in./(2 x 6E-3 in.)]^2}
Torsional vibration
On start-up of a machine, initial rotor acceleration at breakaway may induce a cycle of torsional
vibration: torsional windup of the shaft to overcome static bearing friction, followed by unwinding as
shaft speed jumps ahead of the turning gear drive speed. At the completion of such a cycle, journal
surface velocity in its bearing drops and a new “stick” cycle may be initiated if the bearing is devoid of its
full film. This repetition of sticking can usually be expected only following completion of at least to of a
full torsionalvibration cycle.
Torsional-shaft displacement, ø radians, after the shaft breaks free involves harmonic vibration at ω
radians/ sec superimposed on turning gear displacement α radians/sec to give a response pattern as
http://machinedesign.com/print/67364
11/3/2010
Avoiding Stick-Slip Chatter in Low-Speed Bearings
Page 3 of 6
illustrated in the first graph. Neglecting damping effects:
dø/dt = α + [(T0ω sin(t-t0))/k]
To avoid a repetition of sticking from loss of torsional- shaft velocity within the bearing, dø/dt must be
kept above zero when sin (t – t0) = –1 at the extreme unwinding of the harmonic vibration. That
requires:
a > T0ω/k
That is, the drive gear rotational velocity α must remain significantly above the oscillating journal
velocity. This torsional low-speed limit is calculated in the following example for the previously
mentioned industrial steam turbine.
As the second criterion for avoiding low-speed stick-slip behavior, the gear drive should be set above
the oscillating journal velocity:
a > T0ω/k
where α0 = minimum turning gear rotational speed in radians/ sec, k = the shaft’s torsional stiffness, and
ω = the torsional natural frequency. T0 is the breakaway torque, f (D/2) W, lb-in., where the coefficient
of breakaway friction, f, is 0.25.
If k is 7.5 106 lb-in./rad and ω is 188.5 rad/sec (30 Hz), minimum turning gear rotational speed α0 then
becomes:
α0 = (0.25 3 in. 8,000 lb) (188.5 rad/sec)/(7.5 106 lb-in./rad) = 0.151 radians/sec = 1.4 rpm.
To avoid stick-slip vibration, both this 1.4-rpm torsional requirement and the earlier 28-rpm film lift-off
requirement must be exceeded. The designer should calculate both to ensure that minimum
requirements are satisfied.
Significant secondary effects may also be introduced in some cases either by rotor system damping or
by partial preservation of an oil film as the journal velocity passes through zero.
Once established, this calculated minimum speed will also assist in sizing system components. With
large turbines, for instance, turning gear drives have been typically set at five to 10 times their required
minimum speed with corresponding excess size and power requirements.
On the other hand, increasingly large turbines were once supplied with the same size turning-gear
motor used on existing turbines, but with a higher gear ratio to overcome the greater breakaway torque
with the heavier bearing loads. As turning-gear speed dropped below 2 rpm, chatter developed along
with fatigue damage.
Means for avoiding stickslip and chatter
Any of the following steps can be considered as possibilities for eliminating stick-slip vibration in lowspeed bearings:
http://machinedesign.com/print/67364
11/3/2010
Avoiding Stick-Slip Chatter in Low-Speed Bearings
Page 4 of 6
1. 1. Boost oil viscosity, either by using a more viscous grade of oil or lowering the oil-feed
temperature.
2. 2. Idle faster as with a turning-gear device.
3. 3. Use externally pressurized oil lifts to generate a full oil film for starting and at low speeds.
4. 4. Use a bearing material that gives a lower static coefficient of friction such as filled PTFE or filled
nylon.
5. 5. Apply ball bearings with their low friction at breakaway and at very low speeds.
Further Reading
Khonsari, M.M. and E.R. Booser. Applied Tribology — Bearing Design and Lubrication, Wiley Book Co.,
2001.
Lu, X. and M.M. Khonsari. “On the lift-off speed in journal bearings,” Tribology Letters, Vol. 20, Nos. 3-4,
pp. 299-305, 2005.
Michalopoulos, D. and A. Dimarogonas. “Stick-Slip of Rotors in Fluid Bearings at Very Low Speeds,”
Wear, Vol. 70, No. 3, pp. 303-309, 1981.
Steam turbines like this one can exhibit noisy and damaging stick-slip behavior at low speeds.
http://machinedesign.com/print/67364
11/3/2010
Avoiding Stick-Slip Chatter in Low-Speed Bearings
Page 5 of 6
Below its fluid-film lift-off speed, a shaft can display a characteristic stick-slip response such as the one
shown here. Over time, this type of chatter can lead to fatigue damage and early failure.
The Stribeck curve denotes various lubrication regimes. Below bearing lift-off speed, bearings can
demonstrate stick-slip behavior.
http://machinedesign.com/print/67364
11/3/2010
Avoiding Stick-Slip Chatter in Low-Speed Bearings
Page 6 of 6
This model of a disk driven by a turning gear through a flexible shaft is representative of many systems,
including turbines, compressors, and drill shafts.
Lift-off speeds at the low end of these ranges are to be expected with a ground surface finish of 20-µin.
rms or better, a VG 68 viscosity grade (68 cSt at 40°C) or higher viscosity industrial oil, and bearing
loading below 150 to 200 psi. The high end of these ranges is representative for a 32 VG light
industrialgrade oil, 32-µin. rms or rougher finish and loads above 200 to 300 Performance of industrial
steam and gas turbines and rotary compressors can be expected to be near the middle of these ranges.
Source URL: http://machinedesign.com/article/avoiding-stick-slip-chatter-in-low-speed-bearings-0410
http://machinedesign.com/print/67364
11/3/2010