Abstract - This paper investigates AC induction motor shaft voltage problems, current flow thru motor bearings and electric discharge current problems within bearings when operated under both pure sinewave and Pulse Width Modulated (PWM) inverter sources. Recent experience suggests that PWM voltage sources with steep wavefronts especially increase the magnitude of the above electrical problems, leading to motor bearing material erosion and early mechanical failure. Previous literature suggests that shaft voltage -bearing current problems under 60 Hz sinewave operation are predominantly electromagnetically induced. It is proposed that under PWM operation these same problems are now predominantly an electrostatic phenomenon. A system model to describe this phenomenon is characterized and developed. Construction and test of a new Electrostatic Shielded Induction Motor (ESIM) verifies this model and is also a possible solution to the bearing current problem under PWM operation.
I. Introduction
Bearing currents and shaft voltages under 60 Hz sinewave operation has been a recognized problem since 1924 [1-3]. The bearing impedance characteristic largely determines the resulting bearing current that will flow for a given shaft voltage magnitude and waveform present. A number of surveys have indicated that 30 % of all motor failures operated with 60 Hz sinewave voltage are due to bearing current damage [4]. All rotating machines potentially have a bearing current problem whether it is DC or AC, and either large or small horsepower in size. These rotating machines have three basic sources of shaft voltage - electromagnetic induction, electrostatic coupled from internal sources or electrostatic coupled from external sources.
Electromagnetic induction from the stator winding to the rotor shaft was recognized by Alger [1] and is more prevalent in long axial machines. The shaft voltage is due to small dissymmetries of the magnetic field in the air gap that are inherent in a practical machine design. Most induction motors are designed to have a maximum shaft voltage to frame ground of < 1 Vrms with recommended practice limits stated in [5]. The induced shaft voltage s cause bearing current flow in a circulating path from the shaft, thru side A grounded bearing, thru the stator frame, thru side B grounded bearing and back to the shaft. The induced shaft voltage, although low in magnitude, results in a high circulating current thru both motor bearings since the impedance of the circulating path is low. Modern day induction motors less than 250 horsepower have grounded bearings but have minimized steady state shaft voltage to extremely small values. However, during transient start and stop conditions across the AC line, magnetic dissymmetries appear as increased shaft voltage, resulting in bearing current flow and reduced life [4]. This transient bearing current flow for line started motors was experimentally verified. The traditional electromagnetic solution to induced shaft voltage on larger frames is to insulate the non drive end bearing. This does not mitigate shaft voltage but rather the resulting bearing current.
Electrostatic induced shaft voltage may be present in any situation where rotor charge accumulation can occur. Examples are belt driven couplings, ionized air passing over rotor fan blades or high velocity air passing over rotor fan blades as in steam turbine [6]. The electrostatic solution is to keep the shaft and frame at the same potential by installing a shaft grounding brush to reduce electrostatic build up and reduce shaft voltage to 70 - 400 mV. This value is not enough to cause damaging bearing current to flow.
Electrostatic coupled shaft voltage from external rotor sources, such as a static exciter in a turbine generator, is possible and historically solved with the application of a shaft grounding brush [6]. Electrostatic coupled shaft voltage from external stator sources, such as a PWM inverter, is investigated in this paper.
A. Present Theory of Bearing Current with AC Line
The shaft voltage magnitude measured is commonly used as an indicator of the possible bearing current that results. It is the magnitude and passage of electrical current thru the bearing that results in ultimate mechanical damage [7]. Bearing damage caused by electrical current is characterized by the appearance of either pits or transverse flutes burnt into the bearing race. Electrical pitting continues until the bearing loses its coefficient of friction, further increasing the losses and breaking up bearing surface. Typical fluting results in a washboard like formation that appears on the race as shown in
Effect of PWM Inverters on AC Motor Bearing Currents and Shaft Voltages Jay Erdman, Russel J. Kerkman, Dave Schlegel, and Gary Skibinski
Allen Bradley Drives Division
6400 W. Enterprise Drive P.O Box 760
Mequon, WI 53092
(414) - 242 - 7151 (414) - 242 - 8300 Fax
Fig. 1. It has been proposed that the current density of the ball bearing contact area with the race is a better identifying factor for permissible peak amps allowed without pitting or fluting.However, this contact area is difficult to analyze since it varies with bearing speed and load, vibration, method of installation,viscosity and temperature of the lubricant. It is known that the contact area increase is proportional to the bearing load raised to approximately the 1/2 power [8].
Thus, it is important to characterize the impedance of the bearing under different loading conditions to determine the problem severity. Surface contact is made in three ways: metal to metal, quasi-metallic surface contacts and metal point contact thru electrically insulating surfaces between the ball surface roughness and race roughness.
The actual bearing contact zone area in a slow moving or non-rotating bearing is large and consists mostly of
quasi-metallic surfaces. The lubricant film is only 50
Angstroms (1 A o = 10-10 m) while quasi-metallic surfaces have metallic oxides of 100-120 A o . Quantum mechanical tunneling effects enable the current to pass thru the contact zone with series resistances < 0.5 ?. This is evidenced by the low
bearing resistance measurement made at low speeds in Fig. 2.Reference [7] suggests that large current may pass thru non-rotating bearings without damage.
The actual bearing contact zone area in a rotating bearing is smaller and depends on bearing surface roughness. The contact area comprises primarily of asperity point-like contact of ball metal to race metal as shown in Fig. 3a for low speed operation. High speed operation in Fig 3b has fewer asperity contact points. Asperity contact duration is typically 100 μs at low speed and 33 μs at high speed. The increased bearing resistance with rotation shown in Fig. 2 suggests that the lubricant is introducing a partially insulating film between ball and race at speeds greater than 10% of rated. Typical surface roughness of the race and ball from Fig. 4 is seen to be in the 1 - 10 micron (1 micron = 1 μm) range while the typical lubricating film of 0.1 - 2 micron depends on speed, lubricant characteristics and to a lesser extent on load [7]. Fig. 5 shows the relationship between oil film and surface roughness in a
bearing [8]. Percent film is the time percentage during which the "contacting " surfaces are fully separated by an oil or lubricant film while Gamma is the relationship of lubricant film thickness to rms value of contacting surface roughness.Most bearing applications operate in the Gamma = 1 to 2
region. This implies that high quality bearings look like a high resistive impedance 80 % of the time with the oil film acting as a capacitor ready to charge to breakdown potential. A lower quality bearing will have low resistance metal to metal contact a majority of the time and in the presence of high resistivity lubricant acts as a race to ball junction capacitor that may charge only randomly during non contact peak to valley points.
The magnitude of the shaft voltage will determine the bearing current present in lower quality bearings having asperity contacts the majority of the time or high quality bearings that use low resistivity lubricants. A high shaft voltage causes increased current and pits or craters to form since bearing current flows thru a number of points. Heating can occur at point contact to such a degree that the material melts creating craters, thus liberating wearing metal particles into the lubricant. A low shaft voltage has lower current amplitudes but has been found to still cause corrosive type of pitting due to grease decomposition.
In high quality bearings with high resistance grease, the junction bearing capacitor may discharge into a low impedance circuit when the electric field exceeds the breakdown strength in the lubricant asperity points . The
bearing breakdown voltage threshold is 0.4 volts since mineral oil field strength is 106 v/m, a typical oil film is 0.2 microns and there are two films in series. On occasion the bearing capacitor voltage, charged by the shaft voltage present, becomes high enough ( > 0.4 volts) to break down the grease and a short (nanoseconds) high current impulse flows from the charged oil film capacitor within the bearing as shown in Fig.6. This discharge current pulse, if it occurs, is a prime source of bearing erosion and is commonly referred to as fluting or Electric Discharge Machining (EDM ). The washboard craters
of Fig. 1 are formed from the microscopic pits that soften
under repetitive heating of the race to its melting temperature.Several authors suggest that shaft voltage < 0.3 volts is safe, while 0.5 - 1.0 volts may develop harmful bearing
currents, and shaft voltages > 2 volts may destroy the bearing.The rotating bearing breakover threshold voltage (when
bearing current starts to flow) was measured under DC source voltage to be 700 mv peak.
B. Proposed Theory of Bearing Current with PWM Inverters
The preceding analysis was based on steady state, low
frequency and low dv/dt shaft voltage sources. However, PWM inverter modulation causes high frequency step-like voltage source waveforms and high dv/dt's to be impressed across the stator neutral to frame ground. It is shown that a portion of this waveform is also present as rotor shaft voltage to ground due to capacitor divider action. The preceding sinewave analysis applies to PWM operation but with the change that the experimental static breakdown threshold voltage on the rotor shaft increases to 8-15 volts ( Fig. 6) vs. 700 mv for the same bearing monitored under 60 Hz sinewave operation (Fig.10). This increase is explained using dielectric breakdown theory for pulsed sources [9]. Fig. 7 shows that the impulse breakdown strength of hexane (1.1 106 v/m) increases dramatically over the static value for short step-like pulse durations. The bearing voltage breakdown threshold also increases as a function of shaft voltage rate of change [10].This increased breakdown level under PWM operation is
undesirable since during bearing discharge the resulting EDM bearing currents are much higher than with sinewave
operation. Fig. 8 shows that rough surfaces typically seen in bearings will have a statistical time lag of 3 us prior to breakdown, which agrees with measured value of Fig 6.It is theorized that the high quality bearings of Fig. 5(Gamma = 2 ) give long mechanical life when used under sinewave operation but may lead to premature bearing current
failure under inverter operation due to the bearing junction capacitor being impulse charged 80 % of the time to higher impulse shaft voltages. This will result in higher destructive EDM discharge currents. The low quality bearings of Fig. 5 (Gamma =1) give low mechanical life bearings when used under sinewave operation but may actually be better for inverter operation since the destructive capacitive EDM currents only occur 5 % of the time due to asperity contact resistance shorting the bearing.
Test results of a 15 HP motor ( with grounded motor bearings) under 60 Hz steady state sinewave operation showed no evidence of EDM current occurring, except on across the line starting. Test results on the same motor under Bipolar Junction Transistor (BJT) and Insulated Gate Bipolar Transistors (IGBT) PWM inverter sources however did show evidence of EDM and fluting on a continuous basis.
II. Effect of PWM Drives on Bearing Current A. Test Structure and Instrumentation
The measurement of the contributors to bearing roughness induced by PWM voltage source inverters requires detecting signals within a noisy environment. The identification of the contributors requires an experimental structure with test instruments that provide isolation, but adequate sensitivity. Fig. 9 shows the test fixture and instrumentation employed for the investigation presented in this paper. The motor was a 15 Hp, 460 volt, 8 pole, induction motor. The drive and non drive bearings were insulated. A grounding strap simulated normal grounded bearings. A carbon brush sensed the rotor shaft voltage. The stator neutral was available for measuring the stator neutral to ground voltage. High voltage probes with an isolation amplifier performed voltage measurements and a current probe detected the current through the grounding strap. A digital sampling oscilloscope with mass storage provided a tracking of the desired signals. A spectrum analyzer detected the frequency and phase content of the voltages and current.
B. Sine Wave Operation of the Induction Motor
Bearing and shaft currents are not specific to motors operating from PWM voltage source inverters. Alger investigated shaft and bearing currents in the 1920's. Exciting the induction motor with sine waves provided a reference condition. Measurements of the stator neutral to ground and rotor to ground voltages and rotor current were made while operating the induction machine at no-load and 60 Hz. The
results of those tests are shown in Fig. 10. EDM currents were not detected. The 60 volt stator neutral voltage induced a 1 volt rotor voltage, a 60 to 1 reduction. This rotor shaft voltage level is at the upper end of the standards.
C. Evidence of Electric Discharge Machining (EDM) Limiting the number of variables is essential in preventing unjustifiable conclusions from experimental results, especially when investigating the effects of high frequency IGBT inverters. To accomplish this: The power cable was fixed to a length of ten feet with four conductors and the braided shield grounded at the drive end. A 4 KHz carrier frequency was selected. Common mode chokes were not inserted in the input or output of the drive.
Tests were performed on the drive system of Fig. 9. The stator neutral to ground voltage, rotor shaft to ground voltage, and bearing strap current were monitored. Fig. 11 shows experimental results when operating the AC drive at rated volts per hertz and 48 Hz. The stator neutral to ground voltage displays the typical per carrier cycle waveform associated with PWM voltage source inverters. The rotor voltage, however, shows a quite different profile. For a majority of the time, the rotor is grounded, but occasionally the rotor tracks the stator neutral to ground voltage. Then quite suddenly, the rotor voltage collapses, producing a current pulse. Fig. 6 is an expanded plot of an EDM discharge. As the stator to neutral voltage increases, the rotor voltage responds with a capacitive charging characteristic. In fact, the rotor voltage rises to a value fifteen times larger than the measured value when operating on sine waves. At the instant of discharge, an impulse of current occurs with the rotor voltage simultaneously collapsing.
A number of bearings were removed from motors operating on AC drives and the AC mains. The bearings were examined for evidence of EDM fluting. Fig. 1 shows examples of bearings from motors operated on AC drives after being sectionalized. The fluting is quite pronounced. The outer bearing race on the left shows a random EDM discharge. The outer race on the right shows a continuous etching of the race surface.
The normal dv/dt switching current is in the hundreds of milli-amp range and occurs with the rise in rotor potential. A review of the technical literature does not indicate a consensus on the effects of this relatively small current. However, the large current following the rapid collapse of the larger rotor voltage is believed to cause EDM. The value of the EDM shown is limited by the inserted grounding strap and its surge impedance. A standard drive system's bearing current would be limited by the bearing short circuit impedance. This current, its cause, modeling, and control, are the focus of the remainder of this paper.
III. An Equivalent Circuit for Bearing
Displacement and EDM Currents
A. The Model
Fig. 12 shows the physical construction of the test motor. Both the drive and non drive ends of the rotor were outfitted with an insulated bearing support sleeve, which isolated the rotor bearings from the motor frame. This provided a measurement of the rotor open circuit voltage, and when shorted by the grounding strap, simulates an actual bearing mounting. In addition, the grounding strap provides a mechanism for measuring the bearing to ground current. Fig.
12 shows a carbon brush for measuring the rotor voltage and investigating solutions to the EDM bearing current problem. The motor had 48 stator slots and 64 rotor bars. Fig. 13 depicts the capacitive coupling relevant to the development of the model. The stator to frame capacitance (C
sf
) is a distributed element representing the capacitive coupling to frame along the length of the stator conductors. For most investigations, magnetic coupling of the stator and rotor is sufficient. But with the high dv/dt present with modern power
devices, capacitive coupling considerations cannot be ignored.Therefore, the stator to rotor capacitance (C sr ) and the rotor to frame capacitance (C rf ) are included.
The bearings, lubricating film, and insulating sleeve present a combination of capacitances, resistances, and a nonlinear impedance, Fig. 14. First there exists an inner and outer race resistance. Then, depending on the physical construction, the bearing consists of n balls in parallel; each ball having an effective resistance (R ball,i ). In addition, each ball is immersed in the lubricating film; thus, each ball develops two
capacitances (C ball,i ) linking the ball to the inner and outer
races. The ball portion of the bearing model, therefore,consists of n parallel combinations of (C ball,i ) and (R ball,i ).Between balls, the inner and outer races are separated by the lubricant, which forms a dielectric barrier. Therefore, a capacitance (C gap,i ) is formed between each pair of balls,resulting in n parallel capacitors. The nonlinear impedance (Z l,i ) accounts for the mechanical and electrical abnormalities and randomness of the bearing.
Combining the individual components results in a reduced order bearing model, which is compatible with the motor drive models employed in simulations and analyses. The reduced order model consists of a resistance (R b ) in series with the parallel combination of an effective capacitance (C b ) and a nonlinear impedance (Z l ). Finally, the insulating sleeve adds a series capacitance (C sleeve ) that is shorted when the grounding strap is employed.
Combining the bearing model with a simple inverter/motor model yields the model of Fig. 15. Here, the inverter is modeled as three line to neutral voltages with a neutral to
ground zero sequence source. This model allows the inverter's voltages to be examined as positive, negative, and zero
sequence sets. The motor is represented as two sets of three phase windings; one each for the stator and rotor windings.The capacitive coupling from stator to frame is lumped at the neutral of the stator winding and the capacitive coupling
n Balls
in Parallel
C gap,i
,i
Z
Per Ball Model
Fig. 14 Motor Bearing Models
Fig. 12 Physical Construction of the Test Motor
between the stator and rotor connects the stator and rotor zero sequence networks. Finally, the rotor to frame capacitance and bearing provide the paths to ground from the rotor shaft,here represented by the neutral of the rotor.
B. An Explanation of the Cause of Bearing Displacement and EDM Currents
Examining the bearing model in the context of the
experimental results shown in Fig. 11, the significance of the nonlinear impedance Z l is apparent. Because the bearing capacitor normally exhibits a dv/dt or displacement current when the stator voltage changes, the nominal dv/dt current is limited by the impedance given by the model of Fig. 15 with Z l equal to a low non zero value. This corresponds to the bearing in a position of low impedance between outer and inner race.However, occasionally the bearing rides the lubricating film,which allows the rotor to track the source voltage with a
random duration. This condition corresponds to a substantial increase in Z l . When Z l collapses, reflecting the preferred bearing position or the breakdown of the film, the capacitor C b is discharged and an EDM current occurs, with the current through the bearing limited by the zero sequence or common mode impedance. Thus, the bearing's impedance is statistical in nature and depends on the position of the balls, the condition of the bearing and its lubricant.C. Model Parameter Values
Inputs to the model of Fig. 15 include relevant bearing and motor parameters, and the zero sequence forcing function.Calculations and tests provided parameter values and the source voltage. To calculate the stator to rotor capacitance,two parallel conductors were analyzed with a separation equal to the distance between the centers of the conductors. This value was modified to reflect the number of stator slots and slot opening area. To establish the rotor to frame capacitance,the rotor and stator were considered to be parallel cylinders with an air gap. Fig. 16 shows the C rf as a function of
horsepower for 4 and 6 pole motors. The bearing film
capacitance was calculated assuming a spherical construction for the ball with respect to the race surface. A typical value for the ball bearing capacitance is 190 pf [11]. The calculated values for the test motor and bearing are contained in Table 1.Tests were performed to establish the accuracy of the above calculations. With the stator unexcited and the rotor coupled to a drive motor, measurements of the effective capacitance from rotor to frame were made with a RLC meter at various speeds. The tests consistently produced a capacitance of 1400pf. This value represents the equivalent of C sr // ( C sf + (C rf //C b )). Although the C b depends on the speed of rotation, the invariance of the measurement suggests C rf dominates. The C sf is obtained by measuring the capacitance from the stator terminals to frame with the rotor removed. To establish the C sr , measurements were made of the effective capacitance from stator terminals to frame with rotor shaft and frame connected.The C sr is obtained by subtracting C sf . Fig. 17 shows C sr for the test motor as a function of frequency. Finally, the bearing impedance Z l was measured as a function of rotational speed,the results of which are shown in Fig. 2. This in combination with the measured value of C b allowed for the determination of C rf . The measured values are included in Table 1.
Verification of the parameter values consisted of tests with the insulating sleeve grounding strap open circuited and the drive operating at various frequencies at no-load. The stator neutral to ground voltage and rotor voltage to ground were measured; the stator voltage from the neutral of the stator windings and the rotor voltage from the rotor brush
Calculated
Measured Csr 100 pF 100 pF Csf -----11 nF Crf
1 nF 1.1 nF Cb
200 pF
200 pF
Table 1 Motor Model Capacitances
attachment. Typical results of the tests are displayed in Fig.18. With the grounding strap open, the rotor voltage is
strikingly different from the rotor voltage of Fig. 11, where the grounding strap was in place. The tracking of the stator to neutral voltage by the rotor voltage confirms the existence of zero sequence paths as indicated by the model of Fig. 15. The stator to rotor voltage ratio confirmed the relative weighting of the capacitors C sr and C rf in Table 1.D. Simulation Results
For simulation and analysis purposes, the model of Fig. 15was reduced to a zero sequence approximation, which is the shaded portion of Fig. 15. A simulation was developed with the parameters of Table 1 for the bearing model. The simulation provided an analytical tool for examining the effects of PWM waveforms, verifying the system model and parameters by correlating simulation results with experimental data, and for evaluating various solutions to EDM. Fig. 19shows an expanded portion of Fig. 11 and a simulation
employing the zero sequence model. The forcing function for the simulation was the stator neutral to ground voltage from the experimental results. The outputs include the rotor voltage and probe current as shown.
Comparing the simulation results to the experimental results shows good agreement. The dv/dt and EDM currents are representative of experimental results. The rapid rise in rotor voltage at the point of EDM discharge is in very good agreement with the data. To obtain this accuracy, an estimate of the nature of Z l is necessary. For the results presented
above, Z l was modeled as a diac (Fig. 2); high impedance until the voltage threshold is met; thereafter it is voltage limited.The threshold voltage was experimentally determined. The value of the impedance while voltage tracking, determined from the rate at which the experimental rotor voltage of Fig.19 decayed, was found to be in good agreement with the results of Fig. 2.
One area where the simulation fails to predict the observed response occurs in the transient response of the dv/dt and EDM currents. Close examination of the experimental results shows a 12.5 MHz oscillation in the measured current;however, the oscillation does not appear in the simulation results. One explanation for this discrepancy is the
measurement technique. Inserting a grounding strap modifies the system impedance. The characteristic impedance of the grounding strap alters the natural frequency and establishes an oscillation in the dv/dt and EDM currents.
IV. The Electrostatic Shielded Induction Motor: A Solution to EDM Bearing Currents
The previous section's experimental results suggest electrical discharge as a principal contributor to bearing roughness. A bearing model was developed and interfaced with the model for the electrical source and interconnecting network. The model reflects the observed electrical behavior,which suggests the source of PWM induced bearing roughness is the common mode or zero sequence voltage.
Using the model developed above, the task of proposing solutions to EDM discharge becomes simply one of disrupting the discharge either through the source voltage,
interconnecting impedance, or the bearing design. Thus three design areas are available for investigation.
Because of the capacitive coupling from stator to rotor, the most likely candidate is the coupling mechanism from stator to
rotor - the C
sr in Fig. 15. If an electrostatic shield is inserted
between the stator and rotor, the coupling capacitance from stator to rotor is defeated; thus reducing the dv/dt and preventing voltage tracking by the rotor. Because the induction machine generates torque through magnetic induction, the presence of the shield will not affect motor output ratings. A shield was constructed by inserting 1 inch adhesive backed copper foil tape strips to cover the stator slot area. The shield was grounded to the motor frame.
Fig. 20 shows the stator neutral to ground and shaft voltage for an identical operating condition as shown in Fig. 18. With the shield in place, a rotor voltage of 18 volts peak exists when the outer race grounding strap is open circuited - a 56% reduction when compared to the 40 volts peak of Fig. 18. With the strap grounded (Fig. 21), the dv/dt currents were reduced from 500 ma to 50 ma. No EDM currents were detected.
Employing the copper foil strips as indicated above reduced the rotor exposure to the stator windings in the precise proportion by which the rotor voltage is reduced. By extending the Faraday shield to enclose the stator end windings and duplicating the tests above, a near complete shielding of the rotor voltage was observed. As results of Fig.
22 show, the rotor voltage with grounding strap open is reduced 98% when compared to the unshielded case. Connecting the grounding strap (Fig. 23), virtually zero dv/dt current was measured and no EDM current detected.
The experimental results presented above confirm bearing currents, both dv/dt and EDM, are induced primarily by electrostatic coupling. The stator to rotor capacitance couples the zero sequence or common mode source from stator to rotor. The bearing provides a return path for the common mode source, thus allowing dv/dt and EDM discharge currents.
V. Conclusions
The paper presented a review of electrically induced bearing roughness for AC machines under low frequency sine wave operation. A theory was proposed for lubricant dielectric breakdown under PWM excitation. Electrostatic coupled discharge or displacement (dv/dt) and electric discharge
machining (EDM) currents were identified and experimentally measured. Electrical models were developed and experimentally verified for the source voltage, coupling network, and bearing. An electrostatic shielded induction motor was described and experimentally demonstrated as a solution to the bearing current problem.
The technical literature and experience show unloaded motors at high speed provide the worst case scenario for bearing currents. In addition, applications with coupled loads tend not to exhibit the problem because of parallel paths for electrostatic discharge.
ACKNOWLEDGMENT
The authors wish to thank Mr. Steve Stretz for his research assistance in the bearing current phenomenon from a motor design point of view.
REFERENCES
[1] Alger P., Samson H., "Shaft Currents in Electric Machines" A.I.R.E. Conf. , Feb 1924
[2] Costello, M., "Shaft Voltage and Rotating Machinery", IEEE Trans. IAS, March 1993[3] Lawson, J. ,"Motor Bearing Fluting", CH3331-6/93/0000-0032 1993-IEEE
[4] Prashad, H., "Theoretical Analysis of Capacitive Effect of Roller Bearings on Repeated Starts and Stops of a Machine Under the Influence of Shaft Voltages", Journal of Tribology, Jan. 1991
[5] NEMA MG-1 Specification Part 31, Section IV , 1993
[6] Ammann, C. , Reichert,K., Joho, R., Posedel, Z., "Shaft Voltages in Generators with Static Excitation Systems-Problems and Solutions", 1987 IEEE Power Eng. Society Summer Mtg.
[7] Andreason, S. "Passage of Electrical Current thru Rolling Bearings", SKF Gothenburg
[8] Harris,T. Rolling Bearing Analysis, Wiley, 1984
[9] Alston,L., High Voltage Technology, Oxford Press ,1968
[10] Prashad, H., "Theoretical Evaluation of Capacitance, Resistanace and their Effects on Performance of Hydrodynamic Journal Bearings , Journal of Tribology, Oct. 1990
[11] Prashad, H. "Theoretical Analysis of the Effects of Instantaneous Charge Leakage On Roller Bearings Lubricated with High Resistivity Lubricants under the Influence of Electric Current", Journal of Tribology Jan.1990.