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Transcript
IEEE APEC Conference
San Jose, CA
March 1996
System Electrical Parameters and Their Effects on Bearing Currents
Doyle Busse, Jay Erdman, Russel J. Kerkman, Dave Schlegel, and Gary Skibinski
Allen Bradley Company
6400 W. Enterprise Drive
Mequon, WI 53092
(414) 242 - 8263 FAX (414) 242 - 8300
Abstract - This paper examines ac motor shaft voltages and resulting bearing currents when operated under Pulse Width
Modulation (PWM) voltage source inverters. The paper reviews
the electrical characteristics of bearings and motors that cause
shaft voltages and bearing currents. A brief review of previous
work is presented, including a system model for electrical analysis
of bearing currents. Relying on the work of a companion paper,
the propensity for Electric Discharge Machining (EDM) is determined by a design equation that is a function of system components. Pertinent machine parameters and their formulas are
presented and values calculated for machines from 5 to 1000 Hp.
The effects of system elements on shaft voltages and bearing currents are evaluated experimentally and the results compared to
theory. Finally, the paper will present quantitative results for one
solution to the shaft voltage and bearing current problem.
I. Introduction
Drive systems engineers typically concern themselves
with the distribution of developed motor torque. An analysis
of mechanical components (e.g., motor bearings) seldom is
of interest. However, the presence of Insulated Gate Bipolar
Transistors (IGBTs) and higher carrier frequencies require
the design engineer to be aware of the effects of Pulse Width
Modulation (PWM) waveforms on the system mechanical
components.
Recently, investigators observed the existence of significant shaft voltages induced by PWM voltage source inverters.
The values exceed those associated with magnetic dissymetries reported on by Alger and others over three quarters
of century ago [1]. The effect these voltages can have on the
bearing race surfaces is shown in Fig. 1[2]. With the continuing increase in bearing life through improvements in mechanical design and lubrication, the fluting of Fig. 1 is
troubling because recent bearing failures have shown to be
the result of Electrostatic Discharge Machining (EDM); voltage breakdown of the lubricant with coincident gap
discharge.
More recent investigators include Costello and Lawson
[3,4]. They reported on shaft voltage and bearing current
problems, but were primarily concerned with magnetically
induced bearing currents. Possible mechanisms for bearing
damage when operating on Variable Frequency Drives
(VFD) are dv/dt or electrostatically induced currents, oil film
dielectric breakdown causing EDM currents, and current
causing chemical changes within the lubricant. A recent investigation was conducted by Chen, et al., on this EDM phenomenon [5]. Recently, the authors presented their findings
on EDM and its relationship to PWM inverter operation
[6,7]. The authors suggested the sources for Rotor Shaft to
Ground Voltage (Vrg) include electrostatic charge build up
and capacitive coupling. These studies resulted in an electrical model of the inverter, motor, and bearing system, and the
development of an Electrostatic Shielded Induction Motor
(ESIM), a solution to the electrostatically induced bearing
damage.
The electrical model accurately predicted the Vrg and
bearing currents measured when operating with PWM Voltage Source Inverters (VSI). The electrical system model consists of a balanced three phase source with a common mode
or zero sequence source from neutral to ground and two sets
of balanced three phase impedances coupled by an equivalent
π network of machine capacitances. The zero sequence or
common mode equivalent circuit is shown in Fig. 2. The
bearing model combines a bearing resistance in series with
the parallel combination of the Bearing Capacitance (Cb)
and a nonlinear device; the device accounts for the random
charging and discharging of the rotor shaft.
This paper further examines the zero sequence model and
explains the electrical factors driving the shaft voltage coupling mechanism. Motor capacitance formulas are presented
and values calculated for a range of horsepower ratings. Effects of machine parameters and interface components (e.g.,
common mode chokes, cables) are examined analytically and
Fig. 1 Surface Roughness of a Ball Bearing Race
due to Electrical Fluting [2].
IEEE APEC Conference
Vsource
i(t)
Vsng
Zseries
Vsg
Lo
Csr
Zparallel
Csf
Crf
March 1996
A. Capacitance Calculations for the Shaft Voltage and
Bearing Current Model
Vrg
ro
San Jose, CA
Ib
Mechanical Components - Cb
Rb
Cb
Z
Gnd
The occurrence of Vrg and bearing currents depends on the
existence of Cb. Furthermore, the bearing impedance becomes capacitive only when a lubricant film occurs in the
contact regions between the balls or rollers and the raceways
[8]. The minimum film thickness is given by:
Fig. 2 Common Mode Equivalent Model.
H 0 = 2.65U 0.7 g 0.54 / Q 0.13
compared with experimental results. The paper shows second
and third order reduced models accurately predict the frequency response and damping factor of the Vrg and system
current. Experimental results suggest bearing current densities with PWM VSI drives can exceed bearing life thresholds.
Finally, results employing an ESIM and identical system interface components show the efficacy of the ESIM in reducing rotor voltage build up.
where U is a function of the fluid velocity and viscosity, g a
function of the pressure coefficient of viscosity and modulus
of elasticity, and Q the force or load acting on the ball or
roller [9]. Other factors influencing the Cb include the temperature (T), viscosity (η), additives (λ), lubricant film thickness relationship to the rms value of the contact surface (Λ),
and dielectric strength of the lubricant (εr) [8].
The dielectric strength of lubricants is determined by
static tests [10]. Data provided by lubricant vendors indicates
dielectric strengths range from 1 to 30 kV/mm. These values
reflect dielectric strengths of films on the order of millimeters. However, typical bearing loads together with (1) and
measured data indicate lubricant film thickness ranges from
0.2 to 2.0 microns. These values are significantly lower than
those employed by the static tests. Based on tests, the authors
conclude that 15 Vpk/µm dielectric strength is reasonable.
This suggests shaft voltages from 3 to 30 volts can produce
EDM currents [6]. Furthermore, tests performed on the 15
Hp induction motor of [6] showed a maximum withstand
voltage of 30 volts peak at pulse duration's of 10 µsecs. Thus,
Cb becomes a complicated function of all the above variables
(Cb(Q, εr,U,T,η,λ,Λ)) [8].
II. The Common Mode Equivalent Circuit
For purposes of investigating Vrg buildup, dv/dt current,
and EDM discharge, the common mode or zero sequence
equivalent circuit of Fig. 2 provides accurate results without
the complexity of the distributed system. The common mode
models for the ac machine, cable, common mode chokes,
transformers, and line reactors are included in the figure. Although greatly simplified, the equivalent circuit provides a
useful tool for the analysis of system parameters and their effect on Vrg and bearing current.
From Fig. 2, it is clear the existence of dv/dt and EDM
bearing currents with PWM VSI drives depends on the following three conditions: (1) a source of excitation (Vsg),
which is transferred by the zero sequence or common mode
components to the Stator Neutral to Ground Voltage (Vsng),
(2) a capacitive coupling mechanism, accomplished by the
Stator to Rotor Capacitance (Csr), and (3) sufficient Vrg
buildup, a random occurrence depending on the existence of
Cb. All three of these conditions must simultaneously exist
for EDM currents to occur.
This section of the paper will explore the system factors
contributing to the development of Vrg buildup. Part A develops the machine components of Fig 2, with Cb calculations based on results by researchers in Tribology. Following
the presentation of relevant mechanical properties, machine
capacitance formulas are derived for the components in Fig.
2. Part B examines experimental evaluations of the model
parameters and compares the values to the design
calculations.
(1)
Electrical Components - Lo, Ro, Csf, Csr, Crf
Although a distributed parameter system, lumped parameters adequately model the system as shown in Fig. 2.
This system consists of the stator winding zero sequence impedance (Lo and Ro), the Stator winding to Frame Capacitance (Csf), Csr, the Rotor to Frame Capacitance (Crf), and
Cb. A formula for each capacitance follows, together with
calculations for machines from 5 to 1000 horsepower. These
formulas assume the geometrical shapes depicted in Fig. 3. A
comparison with experimental values for the 15 Hp machine
of [6] is presented in part B.
Calculation of Csf: The Csf model consisted of Ns parallel
capacitors, where Ns is the number of stator slots. Each slot
consisted of a conductor Ls meters long, Wd meters deep,
and Ws meters wide centered within a rectangular conduit
IEEE APEC Conference
San Jose, CA
March 1996
C sf = K sf N s εr εo ( W d + W s )L s / d
Frame
( Wr ) - Rotor
Conductor Width
( g ) - Air
Gap
a) Stator to Rotor
and
Rotor to Frame
Capacitance
Stator
Winding
Rotor
( Rr ) - Rotor
Radius
( Rs ) - Stator Radius
( Ws ) - Stator
Slot Width
( d ) - Dielectric
Thickness
Calculation of Csr: The stator to rotor coupling capacitance,
shown in Fig. 3, consists of Nr sets of parallel conducting
plates. The area of each plate equals the product of the length
of the rotor (Lr) and the width of the rotor conductor near the
rotor surface (Wr). This capacitance is given by (3); where
the distance between the parallel plates (g) is the air gap of
the machine [11]. Fig. 4 shows calculated Csr for induction
machines from 5 to 1000 Hp.
C sr = K sr N r εo W r L r / g
(3)
( Rc ) - Radial
Clearance
Conductor
( Rb ) - Ball
Radius
( Wd ) - Stator Slot
Depth
b) Stator to Frame
Capacitance
(2)
c) Bearing
Capacitance
Fig. 3 Capacitance System Models.
with all sides at the same potential. A dielectric material
separates the conductor and conduit by d meters with a relative permittivity of εr (slot paper). Equation (2) provides the
Csf for Ns slots [11]. Fig. 4 shows calculated values of Csf
for induction machines from 5 to 1000 Hp.
Calculation of Crf: The capacitive coupling between the rotor and frame, shown in Fig. 3, is determined as the capacitance of two concentric cylinders or a coaxial capacitor. In
this case, the effective gap between the cylinders must compensate for the effect of the stator slot widths. If the inside
radius of the outer cylinder (stator) is Rs and the outer radius
of the inner cylinder (rotor) Rr, then the capacitance is given
by (4) [11]. Fig. 4 shows calculated Crf for induction machines from 5 to 1000 Hp.
C rf = K rf πεo L r / ln ( R s / R r )
Calculation of Cb: The bearing capacitance depends on the
geometrical configuration of the bearing, load, speed, temperature, and characteristics of the lubricant. Each bearing
type - ball, roller, journal, etc. - yields a capacitance model,
with the capacitance value a function of physical and operating parameters. For example, a journal bearing's capacitance
increases with increasing eccentricity and length/diameter
ratio [12]. The capacitance of all bearings depends on the
load angle and relative permittivity of the lubricant.
The model selected for ball bearings, shown in Fig. 3, assumes a set of Nb pairs of concentric spheres, where Nb is
the number of balls. Each capacitor pair includes an inner
sphere (modeling the balls) within an outer sphere (modeling
the raceways). Equation (5) provides the mathematical formula for this capacitance [11]. The radius of the inner sphere
(Rb) corresponds to the radius of the ball; the radius of the
equivalent outer sphere equals the radius of the inner sphere
plus the radial clearance (Rb + Rc), the distance to the outer
raceway. The bearing capacitance varies with the shaft diameter and radial clearance and is plotted in Fig. 4.
C b = N b 4 πεo εr / ( 1 / R b − 1 / (R b + R c ))
Fig. 4 Calculated Motor and Bearing Capacitance Values.
(4)
(5)
Fig. 4 shows with increasing machine size Cb decreases;
the machine capacitances, however, increase with increasing
horsepower [7]. These calculations are based on design data
for four pole, 460 Vac induction machines and associated
bearing dimensions.
IEEE APEC Conference
B. Experimentally Determined System Capacitances
The machine zero sequence inductance and parasitic capacitances were measured on the induction machine of [6].
Measurement results and methodology for each element of
the system model follow. Table 1 lists measured and calculated capacitance values for the machine of [6]. The measured capacitance values were made with the rotor externally
driven at controlled speeds when appropriate.
Lo and Ro: The common mode or zero sequence impedance
of the machine equals one third of the stator resistance in series with one third of the stator leakage inductance. They
were obtained by connecting the three stator lines and measuring the impedance line-to-neutral with a Hewlett-Packard
4284A LCR meter. A value of 300 µH and 59.8 Ω was measured at 100 KHz.
Csf: For the 15 Hp machine of [6], the Csf obtained by LCR
measurement with the rotor removed was 11.1 nF. By removing the rotor, the effects of Csr, Crf, and Cb are eliminated.
The 11.1 nF compares well with the calculated value 7.7 nF
in Fig. 4, which is based on a different stack length than the
motor of [6].
Csr: Measurement of Csr was achieved by shorting the rotor
shaft to frame and connecting a LCR meter to the three commonly connected stator terminals and the machine frame. To
obtain Csr, the value of Csf is subtracted from the capacitance reading of the LCR meter. For the 15 Hp machine of
[6], the measured value was 100 pF; Fig. 4 shows a value of
123 pF. Fig. 4 suggests an increasing Csr with increasing
horsepower, which is consistent with the increasing machine
length and number of slots of higher power machines.
Cb: The bearing capacitance is a function of dielectric characteristics, resistivity, and temperature of the lubricant, geometrical construction, dynamics of the asperity contact of the
balls with the race, and speed of the rotor. The Cb, therefore,
is dynamic and dependent on the operating conditions of the
machine. Tests were performed with a segmented bearing
and a pressure contact between the race, film, a known insulator, and the ball. For the 15 Hp machine of [6], a Cb of 200
Table 1. Capacitance Values for 15 Hp machine of [6].
15 Hp Machine [6]
Calculated 15 Hp Machine
Csf
11 nF
7.7 nF
Crf
1.1 nF
1.0 nF
Csr
100 pF
123 pF
Cb
200 pF
225 pF
San Jose, CA
March 1996
pF was measured. This compares favorably with the calculated value of 225 pF of Fig. 4, predicted by the bearing
model.
Crf: An indirect measurement of Crf is possible once Csf,
Csr, and Cb are known. By placing a LCR meter to measure
the impedance from rotor to frame, the dominance of Csf can
be reduced. The value obtained for the 15 Hp induction machine of [6] was 1.1 nF; Fig. 4 indicates 1.0 nF for a 15 Hp
machine, which compares favorably with the measurement.
III. Effect of Drive Variables on Motor Shaft Voltage and
Bearing Current
This section examines drive variables - common mode
chokes, line reactors, long cables - and their effect on Vrg
and bearing current. These passive elements often provide
the impedance necessary for proper functioning of AC drive
systems. For example, common mode chokes reduce conducted noise and series line reactors control voltage reflection at a motor's terminals. Therefore, the effects these
elements have on Vrg and bearing currents are important to
quantify. To accomplish this, first a design equation - the
Bearing Voltage Ratio (BVR) - establishes a machine design
criterion for evaluating the potential for Vrg and bearing current. Next, the common mode circuit above is reduced in
complexity and a simple analysis tool is presented.
A. System Model and Analysis
With the common mode model for the drive established,
an analysis of the effects of system parameters on Vrg and
bearing currents is possible. Fig. 2 allows for the investigation of common mode chokes or transformers, line reactors,
and long cables through the modification of the series and
parallel impedance elements; it provides a model capable of
examining PWM modulation techniques and power device
rise times; and it allows for an investigation of source to
ground voltage levels.
Steady State Shaft Voltage Level: With PWM frequencies
much less than the natural frequency of the system zero sequence network impedance, the capacitors divide Vsng and
yield the following algebraic relationship for the BVR.
BVR = V rg / V sng = C sr / (C sr + C b + C rf )
(6)
This relationship, although simple, provides substantial
information about bearing charge and discharge phenomena
and potential improvements. For example, a value of Vrg,
the bearing Threshold Voltage (Vth), exists for each value of
film thickness below which dielectric breakdown EDM does
not occur. This threshold depends on pulse duration and
IEEE APEC Conference
Bearing Voltage Ratio
Breakdown
BVR
0.15
0.1
0.05
0
1
10
100
1000
Motor Horsepower
Fig. 5 Bearing Voltage Ratio.
characteristics of the lubricant. However, (6) provides an estimate of Vrg. This estimate when compared to Vth determines the likelihood of EDM discharge. For example, with a
dielectric strength of 15 Vpk/µm and lubricant film thickness
varying between 0.2 and 2 µm, Vth ranges from 3 to 30 Vpk.
With a BVR of 0.1 (Fig. 5), Vrg is in the neighborhood of 35
Vpk for a 460 volt system having a Vsng equal to one half
bus voltage or 350 Vdc. A Vrg of this magnitude is sufficient
to cause EDM discharge.
Equation (6) also suggests a large Cb reduces the bearing
voltage; thus, to maintain bearing or shaft voltage below Vth
- the maximum sustainable voltage without dielectric breakdown EDM - increase the relative permittivity of the lubricant. This expression also shows how the ESIM eliminates
the potential for bearing or shaft static voltage build up: for
an ESIM, the Csr in (6) is zero. In addition, the capacitive
voltage divider indicates inserting an insulating sleeve or
barrier may exacerbate the bearing charging since this reduces the effective Cb.
Using (6) and combining it with results of the capacitance
curves of the previous section, the BVR as a function of
San Jose, CA
March 1996
horsepower was derived with the results shown in Fig. 5.
From Fig. 5, the machine of [6] has a predicted BVR of
0.074. Fig. 6 shows a typical sequence of Vsng, bearing current, and Vrg traces. It shows three different shaft voltage
phenomena occurring in the bearing. Region A depicts the
shaft and bearing charging according to the capacitor divider
action of (6) followed by an EDM discharge. Region B represents a charging and discharging of the bearing without
EDM current. Finally, region C shows the rotor and bearing
charging, but to a much lower voltage level before EDM discharge [7]. The BVR is obtained by dividing Vrg by the Vsng
at a point where the machine's rotor rides the lubricant, region A for example. The experimental value (0.064) is in
good agreement with the theoretical calculation of 0.074.
A Second Order Model Approximation: The common mode
model of Fig. 2 adequately describes most of the observed
phenomena associated with shaft voltages and common mode
currents. However, the complexity of this model often obscures the cause and effect of PWM voltage source inverters
on shaft voltages and bearing currents. A reduced order
model, if applied correctly, would have a distinct advantage
to the circuit of Fig. 2. Common mode chokes, line reactors,
and output filters, for example, often are employed to reduce
Electromagnetic Interference (EMI) from PWM voltage
source inverters. Also, many applications require long cable
lengths between the inverter and load. The reduced order
model of Fig. 7, therefore, provides a simple model retaining
the important effects of these elements on the Vsng of the
machine [11,13].
The second order system of Fig. 7 has the following general solution for a step input:
V sng = V sg (1 −
1
1− ζ 2
i(t) =
e − ζ ω n t sin( ω n 1 − ζ 2 t + ψ )) (7)
V sg
1− ζ
2
Zo
e − ζ ω n t sin ω n 1 − ζ 2 t .
(8)
Where
Vrg
C
A
B
ωn =
1
L o C eq
, ζ =
ro
2
C eq
Lo
, Zo =
Lo
C eq
, ψ = A tan (
1− ζ
2
ζ
Ib
Vsng
i (t)
Zcm
ro
Vsg
Lo
Ceq
Gnd
Fig. 6 Examples of Bearing Breakdown Mechanisms
due
to Film Breakdown, dv/dt Currents and Asperity Contacts with an IGBT Drive.
Vsng
Fig. 7 Second Order Model.
Gnd
)
IEEE APEC Conference
and ω n is the undamped natural frequency, ζ is the damping
ratio, Zo is the characteristic impedance, and Ψ is the phase
angle of Vsng. The equivalent capacitance, (Ceq), equals
[Csf // ( Csr + Crf // Cb)] - the Csf in parallel with the series
combination of the Csr and the parallel combination of the
Crf and Cb.
This formulation of the system equations also allows for
an easy analysis of the rise time of the forcing function Vsg,
the effect of the PWM frequency, and influence of the system
parameters on damping, natural frequency, and overshoot. If
the rise time of the stepped Vsng is longer than one half of
the oscillation period, the zero sequence current is reduced
substantially; thus reducing the dv/dt current through the
bearing and frame. Furthermore, increasing the common
mode inductance - with common mode chokes and line reactors - without considering the effect on the damping factor
can raise the Q of the circuit. The higher Q and lower natural frequency may result in a near resonance condition with
the stepped waveform of the forcing function's PWM carrier.
Fig. 8 shows system time constant (ζ ω n ) and damped
natural frequency (ω n 1 − ζ 2 ) as functions of common
mode inductance (Lcm) for the 15 Hp induction motor of [6].
Both quantities have been converted into hertz or 1/seconds,
for easy comparison with typical carrier frequencies employed by IGBT inverters. IGBT VSI s often incorporate
common mode chokes to reduce the dv/dt current. Fig. 8 indicates damped natural frequency and time constant decrease
with increasing common mode inductance. For typical common mode inductances, the damping in the system decreases
and the damped natural frequency is well within the dominant frequencies of the common mode voltage source of
IGBT inverters, setting up a potential resonance condition.
San Jose, CA
March 1996
Vsource
i (t)
Vsng
ro
Lo
req'
Vsg
Csf
'
Ceq
Gnd
Fig. 9 Third Order System Model.
A Third Order Model - The EDM Discharge Current: The
second order system, very useful for voltage and common
mode analysis, fails to describe the EDM discharge phenomena. The full order model of Fig. 2 is too complex. However,
the third order system of Fig. 9 is manageable and accurately
describes the common mode and EDM discharge. In this figure, the Ceq of Fig. 7 is resolved into Csf in parallel with an
equivalent circuit for the Csr in series with the parallel combination of the Crf and Cb. This can also be expressed as:
Csf || [ Csr + ( Crf || Cb)].
An eigenvalue analysis of this third order system with parameters corresponding to the conditions of Fig. 6 showed a
pair of complex poles at 95.7 KHz with a time constant of
8.57 µsec. The third pole, associated with the bearing voltage
and current, is located on the negative real axis with a time
constant of 0.01 picosec., accurately modeling the response
observed following an EDM discharge (Region A Fig. 6).
B. Model Evaluation and Component Analysis
Damped Natural Frequency
Time Constant
Fig. 8 Inverter Time Constant and Damped Natural
Frequency as a Function of Common
Mode Inductance.
Evaluation of the second order model requires experimental results that allow a comparison of the natural frequency and damping factors with the predicted values based
on Fig. 7. The response of the stator neutral voltage, rotor
shaft voltage, and bearing current to a PWM VSI with various
system components inserted between the inverter and motor
provides data for model evaluation and demonstrates the effect of system components on bearing currents.
Effects of Common Mode Components, Line Reactors, and
Cable Lengths: With the appearance of IGBT inverter
drives, common mode noise presents a significant challenge
to drive design. Common mode chokes and transformers, inserted between the inverter output and load motor, provide
additional impedance to common mode current without affecting the fundamental component. Another approach inserts a three phase line reactor, but at the price of reduced
fundamental voltage at the terminals of the machine.
IEEE APEC Conference
San Jose, CA
March 1996
Vrg
Vrg
Ib
Ib
Vsng
Fig. 10 Common Mode Choke Response.
Fig. 10 shows the response of Vsng, Vrg, and bearing current with a common mode choke of 270 µH and 2.6 Ω inserted between inverter output and load motor. The Vsng
oscillates at 60 KHz with a damping ratio of 0.12. Using the
model of Fig. 7, the calculated values are 62.7 KHz and a
damping factor of 0.12. Adding the common mode choke to
reduce dv/dt current also affects the response of Vsng and
Vrg. The reduced damping causes the machine's Vsng to
overshoot considerably the nominal steady state value for
each switching instant. The decreased damping also provides
the rotor the opportunity to charge once the bearing rides the
lubricant film.
To examine the effects of reduced damping in more detail,
a three phase series reactor with a common mode reactance
of 600 µH was inserted between the inverter output and load
motor. The theoretical frequency and damping factor were
Vrg
Ib
Vsng
Fig. 11 Series Reactor Response.
Vsng
Fig. 12 Long Cable Length Response.
50.3 KHz and 0.0158 respectively. Experimental results for a
15 Hp induction machine (Fig. 11) show a lightly damped 50
KHz oscillation. The decrease in damping increases the
probability of Cb charging. This is because the system capacitance never achieves the steady state charge associated
with the forcing function. Each time the bearing rides the
film, the presence of Cb alters the system topology and the
voltage distribution must change to reflect the change in impedance. Thus with relatively light damping, Vsng is excited
and rings to an excessively large value. In the case of Fig.
11, Vsng exceeds 590 Vpk, which is 280 Vpk larger than one
half Vbus.
A cable's length also affects dv/dt current, shaft voltage
buildup, and bearing current discharge. Fig. 12 shows the
Vsng, Vrg, and bearing current with a 600 foot cable. At the
frequencies of interest, the cable presented an equivalent series impedance of 3.2 Ω and 80 µH, and a parallel resistance
of 3.0 Ω in series with 22 nF of capacitance. The Thévenin
equivalent equals a resistance of 10.9 Ω in series with 129
µH. The calculated damped natural frequency and damping
ratio for the model of Fig. 7 are 71.7 KHz and 0.18. These
compare well with the experimental values of 76.0 KHz and
0.19 respectively.
The transient response of the long cable system shows the
Vsng rings up to over 600 Vpk, with a nominal 630 Vdc
bus. The bearing rides the lubricant film and charges to 25
Vpk just before the ring up of Vsng. Once the stator begins to
ring up to the 600 Vpk level, Vrg responds with a slight delay and achieves almost 65 Vpk before an EDM of 3.2 Apk
occurs. Experimental results similar to these confirm excessive Vsng and Vrg are possible with long cable lengths. The
resulting current densities - 2.48 to 5.16 Apk/mm2 - are in
the region to reduce bearing life.
IEEE APEC Conference
San Jose, CA
March 1996
Standar
d
Standar
d
ESIM
Fig. 13 Common Mode Choke Response with a
Standard Motor and an ESIM.
IV. System Performance of an ESIM
The three conditions necessary for the existence of bearing current outlined in section II provide the basis for investigations into solutions to the problem. One solution
proposed, prototyped, and tested by the authors is the ESIM.
The ESIM essentially decouples the stator and rotor by inserting a Faraday shield between the stator and rotor. The
prototype reported on in [6,7] proved effective in eliminating
EDM current and in reducing dv/dt current to acceptable
levels.
To examine the effectiveness of the ESIM, tests were performed using typical system components reported in section
ESIM
Fig. 15 Long Cable Length Response with a
Standard Motor and an ESIM.
III. Figures 13-15 show experimental results of a 4 pole, 460
volt, 15 Hp ESIM with a common mode choke, series reactor,
and long cable respectively. Each figure shows traces of the
rotor voltage with and without the Faraday shield active. As
discussed earlier, the magnitude of rotor voltage is a measurement of the potential for EDM discharge.
In each case, the ESIM reduces the rotor voltage; the rotor voltage ranges from approximately 10% to 25% of the
value without the Faraday shield. This demonstrates the universality of the ESIM as a solution to the shaft voltage and
bearing current problem. Furthermore, the results without
the Faraday shield are consistent with those reported in section III and [7] for a standard induction motor. Note the reduced damping for the case of the series reactor; this
correlates well with the generalized damping and frequency
results of Fig. 8. In addition, point A of Fig. 14 corresponds
to an EDM discharge (note the abrupt discharge and lack of
oscillation). In contrast, the ESIM revealed no EDMs.
V. Conclusions
Standar
d
A
ESIM
Fig. 14 Series Reactor Response with a
Standard Motor and an ESIM.
The paper reviewed the cause for recently reported bearing failures and examined the important system parameters
and their relationship to EDM and dv/dt bearing current.
Models and formulas were presented for the major system
elements influencing rotor shaft voltage and bearing current
Parameters were calculated for machines from 5 to 1000 Hp
based on machine design data and correlated with tests on a
15 Hp machine. The effects of system components on bearings were evaluated through reduced order models and experimental results. Finally, test results for an ESIM
IEEE APEC Conference
demonstrated its ability to attenuate dv/dt current and eliminate EDM current for all system components tested.
VI. References
[1] Alger P., Samson H., "Shaft Currents in Electric Machines" A.I.R.E. Conf.
,Feb. 1924
[2] Tallian, T., Baile, G., Dalal, H., and Gustafsson, O., "Rolling Bearing
Damage - A Morphological Atlas", SKF Industries, Inc., Technology Center,
King of Prussia, PA.
[3] Costello, M., "Shaft Voltage and Rotating Machinery", IEEE Trans. IAS,
March 1993
[4] Lawson, J. ,"Motor Bearing Fluting", CH3331-6/93/0000-0032 1993-IEEE
[5] Chen, Shaotang, Lipo, Thomas A., Fitzgerald, Dennis, "Modeling of Motor
Bearing Currents in PWM Inverter Drives," IEEE IAS Annual Conference Records, October 8-12, 1995, Vol. 1, pp. 388-393.
[6] Erdman, Jay, Kerkman, Russel J., Schlegel, Dave, and Skibinski, Gary,
"Effect of PWM Inverters on AC Motor Bearing Currents and Shaft Voltages,"
APEC '95, Tenth Annual Applied Power Electronics Conference and Exposition, March 5-9, 1995, Vol. 1, pp. 24-33.
[7] Busse, Doyle, Erdman, Jay, Kerkman, Russel J., Schlegel, Dave, and Skibinski, Gary, "Bearing Currents and Their Relationship to PWM Drives,"
IECON '95, IEEE 21st Annual Industrial Electronics Conference, November 6 10, 1995, Vol. 1, pp. 698-705.
[8] Busse, Doyle, Erdman, Jay, Kerkman, Russel J., Schlegel, Dave, and Skibinski, Gary, "The Effects of PWM Voltage Source Inverters on the Mechanical
Performance of Rolling Bearings," to be presented at APEC '96, Eleventh Annual Applied Power Electronics Conference and Exposition, March 3-7, 1996.
[9] Harris, T., Rolling Bearing Analysis, Wiley, 3rd edition, 1991
[10] Alston, L., High Voltage Technology, Oxford Press, 1968
[11] Hayt, William H., Engineering Electromagnetics, McGraw-Hill, 5th Edition, 1989.
[12] Prashad, H., "Theoretical Evaluation of Capacitance, Capacitive Reactance, Resistance and Their Effects on Performance of Hydrodynamic Journal
Bearings," Trans. of the ASME, Oct. 1991, Vol. 113, pp. 762-767.
[13]Melsa, James L., Schultz, Donald G., Linear Control Systems, McGrawHill, 1969.
San Jose, CA
March 1996