APEC96 Elect Libs

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Abstract - This paper examines ac motor shaft voltages and re-

sulting 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 analysisof bearing currents. Relying on the work of a companion paper,

the propensity for Electric Discharge Machining (EDM ) is deter-

mined by a design equation that is a function of system compo-nents. 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 cur-

rents 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 signifi-

cant shaft voltages induced by PWM voltage source inverters.

The values exceed those associated with magnetic dissy-

metries 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 con-

tinuing increase in bearing life through improvements in me-

chanical 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 ); volt-

age breakdown of the lubricant with coincident gapdischarge.

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 in-

vestigation was conducted by Chen, et al., on this EDM phe-

nomenon [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 electri-

cal model of the inverter, motor, and bearing system, and the

development of an Electrostatic Shielded Induction Motor

( ESIM ), a solution to the electrostatically induced bearingdamage.

The electrical model accurately predicted the Vrg and

bearing currents measured when operating with PWM Volt-

age Source Inverters (VSI ). The electrical system model con-

sists 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 cou-

pling mechanism. Motor capacitance formulas are presented

and values calculated for a range of horsepower ratings. Ef-

fects of machine parameters and interface components (e.g.,

common mode chokes, cables) are examined analytically and

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

Fig. 1 Surface Roughness of a Ball Bearing Race

due to Electrical Fluting [2].



compared with experimental results. The paper shows second

and third order reduced models accurately predict the fre-

quency response and damping factor of the Vrg and system

current. Experimental results suggest bearing current densi-

ties with PWM VSI drives can exceed bearing life thresholds.

Finally, results employing an ESIM and identical system in-

terface components show the efficacy of the ESIM in reduc-ing rotor voltage build up.

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. Al-

though greatly simplified, the equivalent circuit provides a

useful tool for the analysis of system parameters and their ef-

fect 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 fol-

lowing 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 de-velops the machine components of Fig 2, with Cb calcula-

tions 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.

A. Capacitance Calculations for the Shaft Voltage and

Bearing Current Model

Mechanical Components - Cb

The occurrence of Vrg and bearing currents depends on the

existence of Cb. Furthermore, the bearing impedance be-comes 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:

H 0 = 2.65U 0.7 g 0.54 / Q0.13 (1)

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 tem-

perature (T ), viscosity (η), additives (λ), lubricant film thick-

ness 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 millime-

ters. 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].

Electrical Components - Lo, Ro, Csf, Csr, Crf

Although a distributed parameter system, lumped pa-

rameters adequately model the system as shown in Fig. 2.

This system consists of the stator winding zero sequence im-

pedance ( Lo and Ro), the Stator winding to Frame Capaci-

tance (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. Theseformulas 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


Csr

Vsg

Zseries

Csf

Crf

Cb

Rb

Z

Lo

Zparallel

r o

i( t )

Vsource Vsng Vrg

Ib

Gnd

Fig. 2 Common Mode Equivalent Model.



with all sides at the same potential. A dielectric material

separates the conductor and conduit by d meters with a rela-

tive 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.

C sf = K sf N s εr εo (W d + W s) L s / d (2)

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 therotor 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 εoW r Lr / g (3)

Calculation of Crf : The capacitive coupling between the ro-

tor and frame, shown in Fig. 3, is determined as the capaci-

tance of two concentric cylinders or a coaxial capacitor. In

this case, the effective gap between the cylinders must com-

pensate for the effect of the stator slot widths. If the inside

radius of the outer cylinder (stator) is Rs and the outer radiusof the inner cylinder (rotor) Rr, then the capacitance is given

by (4) [11]. Fig. 4 shows calculated Crf for induction ma-

chines from 5 to 1000 Hp.

C rf = K rf πεo Lr / ln ( R s / Rr ) (4)

Calculation of Cb: The bearing capacitance depends on the

geometrical configuration of the bearing, load, speed, tem-

perature, 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 operat-

ing 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, as-

sumes 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 for-

mula 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 di-ameter and radial clearance and is plotted in Fig. 4.

C b = N b 4 πεo εr / ( 1 / Rb − 1 / ( Rb + Rc)) (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.


Fig. 4 Calculated Motor and Bearing Capacitance Values.

( Wr ) - Rotor

Conductor Width

Rotor Stator

Winding

Frame

( g ) - Air

Gap

( Rr ) - Rotor

Radius

( Rs ) - Stator Radius

( Wd ) - Stator Slot

Depth

( d ) - Dielectric

Thickness

Conductor

( Ws ) - Stator

Slot Width

b) Stator to Frame

Capacitance

c) Bearing

Capacitance

a) Stator to Rotor

and

Rotor to Frame

Capacitance

Fig. 3 Capacitance System Models.

( Rc ) - Radial

Clearance

( Rb ) - Ball

Radius



B. Experimentally Determined System Capacitances

The machine zero sequence inductance and parasitic ca-

pacitances 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 calcu-lated capacitance values for the machine of [6]. The meas-

ured 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 se-

ries with one third of the stator leakage inductance. They

were obtained by connecting the three stator lines and meas-

uring the impedance line-to-neutral with a Hewlett-Packard

4284A LCR meter. A value of 300 µH and 59.8 Ω was meas-

ured 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 remov-

ing 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 com-

monly connected stator terminals and the machine frame. To

obtain Csr , the value of Csf is subtracted from the capaci-

tance 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 char-

acteristics, resistivity, and temperature of the lubricant, geo-

metrical 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 insu-

lator, and the ball. For the 15 Hp machine of [6], a Cb of 200

pF was measured. This compares favorably with the calcu-

lated 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 ma-

chine 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 con-

ducted noise and series line reactors control voltage reflec-tion 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 cur-

rent. 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 investiga-

tion 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 se-

quence 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


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

Table 1. Capacitance Values for 15 Hp machine of [6].



characteristics of the lubricant. However, (6) provides an es-

timate of Vrg . This estimate when compared to Vth deter-

mines 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 break-

down EDM - increase the relative permittivity of the lubri-

cant. 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 re-

duces the effective Cb.

Using (6) and combining it with results of the capacitancecurves of the previous section, the BVR as a function of

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 cur-

rent, 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 repre-sents 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 dis-

charge [7]. The BVR is obtained by dividing Vrg by the Vsng

at a point where the machine's rotor rides the lubricant, re-

gion 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 ob-

scures the cause and effect of PWM voltage source inverterson 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 gen-

eral solution for a step input:

V sng = V sg (1 − 1

1−ζ2e−ζωn t sin( ωn 1 − ζ2 t + ψ )) (7)

i(t ) =V sg

1−ζ2 Z oe−ζωn t sin ωn 1 − ζ2 t . (8)

Where

ωn = 1

LoC eq

, ζ =r o

2

C eq

Lo, Z o =

Lo

C eq, ψ = A tan (

1−ζ2

ζ )


BC A

Vrg

Vsng

I b

Fig. 6 Examples of Bearing Breakdown Mechanisms

due to Film Breakdown, dv/dt Currents and Asper-

ity Contacts with an IGBT Drive.

Bearing Voltage Ratio

0

0.05

0.1

0.15

1 10 100 1000

Motor Horsepower

B r e a k d o w n

B V R

Fig. 5 Bearing Voltage Ratio.

Vsg

Zcm

Ceq

Lor oi ( t )

Gnd

Vsng

Gnd

Fig. 7 Second Order Model.



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 reac-

tors - without considering the effect on the damping factor

can raise the Q of the circuit. The higher Q and lower natu-

ral 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 (ζωn ) and damped

natural frequency ( ) as functions of commonωn 1 − ζ2

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 em-

ployed by IGBT inverters. IGBT VSI s often incorporate

common mode chokes to reduce the dv/dt current. Fig. 8 in-

dicates damped natural frequency and time constant decrease

with increasing common mode inductance. For typical com-

mon mode inductances, the damping in the system decreases

and the damped natural frequency is well within the domi-

nant frequencies of the common mode voltage source of

IGBT inverters, setting up a potential resonance condition.

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 phenom-

ena. The full order model of Fig. 2 is too complex. However,

the third order system of Fig. 9 is manageable and accuratelydescribes the common mode and EDM discharge. In this fig-

ure, the Ceq of Fig. 7 is resolved into Csf in parallel with an

equivalent circuit for the Csr in series with the parallel com-

bination of the Crf and Cb. This can also be expressed as:

Csf || [ Csr + ( Crf || Cb)].

An eigenvalue analysis of this third order system with pa-

rameters 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

Evaluation of the second order model requires experi-

mental results that allow a comparison of the natural fre-

quency 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 ef-

fect 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, in-

serted between the inverter output and load motor, provide

additional impedance to common mode current without af-

fecting the fundamental component. Another approach in-

serts a three phase line reactor, but at the price of reduced

fundamental voltage at the terminals of the machine.


Fig. 9 Third Order System Model.

Vsource

Vsng

Gnd

i( t )

Vsg

Csf

Lo

r o

r eq'

Ceq'

Damped Natural FrequencyTime Constant

Fig. 8 Inverter Time Constant and Damped Natu-

ral Frequency as a Function of Common

Mode Inductance.



Fig. 10 shows the response of Vsng, Vrg , and bearing cur-rent with a common mode choke of 270 µH and 2.6 Ω in-

serted 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 reactanceof 600 µH was inserted between the inverter output and load

motor. The theoretical frequency and damping factor were

50.3 KHz and 0.0158 respectively. Experimental results for a15 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 ca-

pacitance 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 im-

pedance. 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 theVsng , Vrg , and bearing current with a 600 foot cable. At the

frequencies of interest, the cable presented an equivalent se-

ries 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 de-

lay and achieves almost 65 Vpk before an EDM of 3.2 Apk

occurs. Experimental results similar to these confirm exces-

sive Vsng and Vrg are possible with long cable lengths. The

resulting current densities - 2.48 to 5.16 Apk/mm 2 - are in

the region to reduce bearing life.


Fig. 10 Common Mode Choke Response.

Vrg

I b

Vsng

Fig. 11 Series Reactor Response.

Vrg

I b

Vsng

Fig. 12 Long Cable Length Response.

Vrg

I b

Vsng



IV. System Performance of an ESIM

The three conditions necessary for the existence of bear-

ing current outlined in section II provide the basis for inves-

tigations 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 in-

serting 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 per-formed using typical system components reported in section

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 meas-

urement of the potential for EDM discharge.

In each case, the ESIM reduces the rotor voltage; the ro-

tor voltage ranges from approximately 10% to 25% of the

value without the Faraday shield. This demonstrates the uni-

versality 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 sec-tion III and [7] for a standard induction motor. Note the re-

duced 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 EDM s.

V. Conclusions

The paper reviewed the cause for recently reported bear-

ing 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 bear-

ings were evaluated through reduced order models and ex-

perimental results. Finally, test results for an ESIM


Fig. 13 Common Mode Choke Response with a

Standard Motor and an ESIM .

Standar d

ESIM

Fig. 14 Series Reactor Response with a


A

Standar

d

ESIM

Fig. 15 Long Cable Length Response with a


Standar

d

ESIM



demonstrated its ability to attenuate dv/dt current and elimi-

nate 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 BearingDamage - 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 Re-

cords, 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 Exposi-

tion, March 5-9, 1995, Vol. 1, pp. 24-33.[7] Busse, Doyle, Erdman, Jay, Kerkman, Russel J., Schlegel, Dave, and Skib-

inski, 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 Skib-

inski, Gary, "The Effects of PWM Voltage Source Inverters on the Mechanical

Performance of Rolling Bearings," to be presented at APEC '96, Eleventh An-

nual 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 Edi-

tion, 1989.[12] Prashad, H., "Theoretical Evaluation of Capacitance, Capacitive Reac-

tance, Resistance and Their Effects on Performance of Hydrodynamic JournalBearings," Trans. of the ASME, Oct. 1991, Vol. 113, pp. 762-767.

[13]Melsa, James L., Schultz, Donald G., Linear Control Systems, McGraw-

Hill, 1969.


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