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This is the author's version of an extended abstract that has been submitted to the 72
nd
edition of STLE Annual Meeting
& Exhibition (21-25 May 2017, Atlanta, Georgia)
CAPACITANCES AND LUBRICANT FILM THICKNESSES OF GREASE AND OIL
LUBRICATED BEARINGS
Rolling Element Bearings II: Rolling Element Bearing Dynamics
N. Bader
1
, A. Furtmann
1
, H. Tischmacher
2
and G. Poll
1
1
Institute of Machine Design and Tribology (IMKT), Leibniz Universitaet Hannover, Germany
2
Siemens AG, Process Industries and Drives Division, Large Drives, Nuremberg, Germany
INTRODUCTION
The electrical capacitance of lubricated contacts and bearings is a parameter that has been investigated for many years [1–3].The
focus of these investigations was to examine the film-thickness of the elastohydrodynamic contact between the rolling elements and the
raceways. Nowadays the capacitance is not only of interest for the field of lubrication but also for a drive system behavior and the
occurrence of bearing currents and electrical erosive wear. Modern drive systems can be characterized more and more by variable-speed
operation that comes with many advantages like an increased efficiency but also some disadvantages. One of these is the occurrence of
so called parasitic currents which are a result of the common-mode voltage U
cm
that is inherent in the widely used voltage source
inverters. The capacitance of drive system bearings – and other parts like gears [4, 5] – combined with motor inherent capacitances
creates a capacitance voltage divider. As a result, a voltage U
b
that is proportional to the common-mode voltage occurs at the motor
bearings. Possible arc discharges in the lubricant gap can melt or vaporize material in the bearing raceways. This leads to a normally
grey-frosted raceway with no influence on the bearing lifetime, or to so-called corrugated patterns (see Figure 1 a), which reduce the
bearing lifetime. Furthermore, the discharges damage the lubricant due to the high temperature in the discharge arcs (see Figure 1 b).
Unscheduled maintenance and therefore higher costs are the result. There are three main types of bearing currents. One of them is the
so called EDM-current (Electrical Discharge Machining) which depends on the breakdown effects inside the lubrication gap of the
rolling element bearing. In contrast to the two other types of bearing currents (circulating and rotor ground currents), the occurrence of
EDM currents is strongly influenced by the common-mode voltage and the parasitic capacitance network behind the motor terminals
which consists of the stator winding-to-frame capacitance C
wf
, the stator winding-to-rotor capacitance C
wr
, the rotor-to-frame capacitance
C
rf
and the capacitances C
b
of the rolling bearings at the drive end and non drive end of the motor. Equation 1 gives the ratio between
the common-mode-voltage and the bearing voltage – the so called Bearing Voltage Ratio BVR – depending on the capacitance network.
( 1 )
a) b)
Fig. 1: Fluting on a bearing raceway (a) and charred lubricant due to EDM-currents (b) [4]
This is the author's version of an extended abstract that has been submitted to the 72
nd
edition of STLE Annual Meeting & Exhibition
(21-25 May 2017, Atlanta, Georgia)
BASICS
A prediction of EDM-currents requires the knowledge of the bearing capacitances to calculcate the voltage across the bearing and
the minimum film-thickness in a bearing to determine the critical breakdown voltage. Each EHL-contact can be described as a system
of three parallel capacitances as shown in Figure 2. The capacitance of the Hertzian contact can be calculated quite well, however the
inlet and outlet zone of the Hertzian contact also contribute to the total capacitance [2, 6]. The influence of these areas is often described
by a constant factor (usually 3.5) while in reality the factor depends on geometry and film-thickness. For a better understanding
measurements and calculations for a single contact on a two-disc-testrig and for a multi contact in a bearing are conducted in this work.
Fig. 2: Left: Equivalent model for capacitance in an EHL-Contact (according to [2, 3]); Right: Twin disc test rig used
With knowledge of the Hertzian contact area A
Hertz
, the central film-thickness h
0
and the dielectric behavior of the lubricant ε
r
,
equation 2 can be used to determine the Hertzian capacitance C
Hertz
. These parameters are all dependant on factors like the pressure p,
temperature ϑ, contact force F
N
, curvature radius R, combined Young’s Modulus E’, hydrodynamic speed v and viscosity η.
⋅
, ⋅
,,
,
,,,
( 2 )
The total capacitance of a contact can be calculated by equation 3 if the capacitance of the entry and exit zone are known or if one
assumed or calculated a value for k
C
= C
total
/C
Hertz.
⋅
( 3 )
SINGLE CONTACT MODEL
To allow for a comparison of the single EHL contact capacitance model measurements were conducted using a twin disc test
rig shown in Figure 2 right. Here, a single EHL contact is investigated. The contact is established between a cylindrical and a crowned
disc which are pushed together with a defined normal force. The load, speed, oil temperature, and slide to roll ratio (SRR) can be variied.
The use of insulating bearings and couplings, allows for a defined path only through the EHL contact. During the experiments the
capacitance of the contact was measured using a measurement system which was applied to the shafts. The shafts were contacted using
copper brushes. Subsequently a voltage step V
step
was applied over a charing resistor R. The Voltage of the EHL contact V
EHL
was
measured. From the time constant of the V
EHL
the capacitance of the EHL contact could be determined. As only one contact is present
Equation 3 can be used to describe the total capacitance C
total
. Furthermore, the Hertzian contact area and the film thickness can be
acurately calculated thus allowing for the determinitaion of C
Hertz
. Therefore, the factor k
c
can be accurately determined and compared
to theoretically expected value resulting from simulations of the capacitance of the contacting geometries.
BEARING AS MULTI CONTACT MODEL
Contrary to the single-contact model of the two-disc testrig, a bearing consists of multiple contacts with different capacitances.
These capacitances can be combined to a single bearing capacitance. However, for this the cage design is important as it influences the
way the contact capacitances are combined. For a bearing with a conducting cage and by assuming that there is no separating fluid film
between the balls and the cage, the equivalent circuit is shown in Figure 3. All contacts at one ring are in parallel with each other and
then in series with the other rings’ capacitances. For a bearing with N rolling elements Equation 4 can be used to calculate the bearing
capacitance C
b
from the inner-ring capacitances C
i
and the outer-ring capacitances C
o
.
C
Entry
C
Hertz
C
Exit
Hertzian
contact range Exit rangeEntry range
U
1
U
2
h
min
h
0
ε
r
2b
This is the author's version of an extended abstract that has been submitted to the 72
nd
edition of STLE Annual Meeting & Exhibition
(21-25 May 2017, Atlanta, Georgia)
Fig. 3: Equivalent model for a ball bearing with a conducting cage
∑
,
⋅∑
,
∑
,
∑
,
( 4 )
A bearing test-rig as described in [7, 8] was used to measure the capacitance behavior of ball bearings 6008 for different operating
conditions like temperature, speed, load and various lubricants using an oil bath as lubrication method. The measurements – examples
are given in Figure 4 – show a few characteristic effects:
- increasing speed leads to lower capacitances due to the higher film-thickness
- increasing load leads to higher capacitances due to the bigger Hertzian contact area
- increasing temperature leads to higher capacitances due to the decrease in viscosity and therefore film-thickness
- at high speed and high viscosity (low temperature) the capacitance increases again due to starvation effects
- the influence of the Hertzian contact capacitance decreases with higher film-thickness
Fig. 4: Measured capacitances for ball bearing 6008 by various axial loads and speed (left diagram) and for different temperatures (right diagram)
To determine the effect of inlet and outlet zone of the EHD-contact the ratio between the calculated Hertzian capacitance and the
measured capacitance is plotted over the calculated film-thickness (Figure 5 left). In this diagram different lubricants, viscosity and
speeds were used. It can be seen that regardless of the parameters that create the film, a comparable behavior between measured and
calculated capacitance exists. The resulting curve can be used to determine the total capacitance of a ball bearing (Figure 5 right) and is
a confirmation to the results of Jablonka et. al. [6] and their tests with a ball on disc contact. Similar analysis for systems with axial load
show comparable results but with reduced values for k
C
as the Hertzian contact is larger due to the increased number of loaded balls.
However, the often used value k
C
= 3.5 is part of this curve in an area with where many measuremts are performed.
This is the author's version of an extended abstract that has been submitted to the 72nd edition of STLE Annual Meeting & Exhibition
(21-25 May 2017, Atlanta, Georgia)
Fig. 5: Ratio kC for a radial load of 1000 N (500 N per bearing) using different oils and temperatures (left
diagram) and a comparison of calculated and measured capacitance for the same load condition (right diagram).
SHC320: PAO oil ISO VG 320. MIN20: Mineral oil ISO VG 320, Alvania: Grease base oil ISO VG 100
ACKNOWLEDGMENTS
The authors wish to thank the Siemens AG for partially funding and supporting in this project.
REFERENCES
[1] A. W. Crook, “The Lubrication of Rollers II. Film Thickness with Relation to Viscosity and Speed,”
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.
254, no. 1040, pp. 223–236, 1961.
[2] P. Brüser, “Untersuchungen über die elastohydrodynamische Schmierfilmdicke bei elliptischen Hertzschen
Kontaktflächen,” Dissertation, Fakultät für Maschinenbau und Elektrotechnik, Technische Universtität
Braunschweig, Braunschweig, 1972.
[3] A. Dyson, H. Naylor, and A. R. Wilson, “The Measurement of Oil-Film Thickness in Elastohydrodynamic
Contacts,” Proceedings of the Institution of Mechanical Engineers, Conference Proceedings, vol. 180, no.
2, pp. 119–134, 1965.
[4] H. Tischmacher, I. P. Tsoumas, and A. Furtmann, “Extended probability model for discharge activities in
the drive train of converter-fed electric motors,” in 2015 17th European Conference on Power Electronics
and Applications (EPE'15 ECCE-Europe): IEEE, 2015, pp. 1–10.
[5] A. Furtmann, H. Tischmacher, and G. Poll, “Extended HF equivalent model of a drive train,” in 2016 XXII
International Conference on Electrical Machines (ICEM): IEEE, 2016, pp. 2244–2250.
[6] K. Jablonka, R. Glovnea, and J. Bongaerts, “Evaluation of EHD films by electrical capacitance,” J. Phys.
D: Appl. Phys., vol. 45, no. 38, p. 385301, 2012.
[7] E. C. Wittek et al., “Capacitances and lubricant film thicknesses of motor bearings under different
operating conditions,” in 2010 XIX International Conference on Electrical Machines (ICEM), 2010, pp. 1–
6.
[8] E. C. Wittek et al., “Capacitance of bearings for electric motors at variable mechanical loads,” in 2012
XXth International Conference on Electrical Machines (ICEM), 2012, pp. 1602–1607.
KEYWORDS
EHL: EHL (General), Rolling Bearings: Rolling Element Bearings, General, Wear: Electrical Erosive Wear.
0
5
10
15
20
25
30
35
40
0,0E+00 2,0E-07 4,0E-07 6,0E-07 8,0E-07 1,0E-06 1,2E-06
k
C
Calcu late d film-th ickness in m
Ratio k
C
over film -thickness for a r adial load of 500 N
SHC320 20 °C
SHC320 40°C
SHC320 60 °C
SHC320 80 °C
MIN320 20 °C
MIN320 40 °C
MIN320 60 °C
MIN320 80 °C
Alv ania 20 °C
Alv ania 40 °C
