* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Power engineering wikipedia, lookup

Electrical ballast wikipedia, lookup

Electrical substation wikipedia, lookup

Electric motor wikipedia, lookup

Commutator (electric) wikipedia, lookup

History of electric power transmission wikipedia, lookup

Brushed DC electric motor wikipedia, lookup

Power inverter wikipedia, lookup

Three-phase electric power wikipedia, lookup

Current source wikipedia, lookup

Distribution management system wikipedia, lookup

Switched-mode power supply wikipedia, lookup

Surge protector wikipedia, lookup

Resistive opto-isolator wikipedia, lookup

Power electronics wikipedia, lookup

Pulse-width modulation wikipedia, lookup

Buck converter wikipedia, lookup

Stepper motor wikipedia, lookup

Voltage optimisation wikipedia, lookup

Stray voltage wikipedia, lookup

Opto-isolator wikipedia, lookup

Power MOSFET wikipedia, lookup

Mains electricity wikipedia, lookup

Alternating current wikipedia, lookup

Induction motor wikipedia, lookup

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