Analysis And Characterization Of Switched Reluctance Mot (1)

IEEE TRANSACTIONS ON MAGNETICS, VOL. 41, NO. 4, APRIL 2005

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Analysis and Characterization of Switched Reluctance Motors: Part II—Flow, Thermal, and Vibration Analyses K. N. Srinivas1 , Member, IEEE, and R. Arumugam2 , Member, IEEE Electrical and Electronics Engineering Department, Crescent Engineering College, Chennai 600 048, India Electrical Engineering Department, Anna University, Chennai 600 025, India This paper presents new approaches for certain mechanical characterizations, such as thermal and vibration analyses, of switched reluctance motors (SRMs). The paper presents, in three parts, the modeling and simulation procedure for three-dimensional (3-D) finiteelement analysis (FEA)-based flow analysis, flow-analysis-based thermal analysis, and a realistic vibration analysis. Section I documents a computational fluid dynamics (CFD) flow analysis procedure for the evaluation of the air velocity distribution inside the SRM at any speed. Section II presents a prediction method for steady-state and transient thermal characteristics of an SRM, using 3-D FEA. The convection coefficient at various heat-dissipating surfaces inside SRM, which is not a material property, but a quantity that solely depends on the air velocity at the respective surfaces, is the major parameter to be evaluated for an accurate simulation of heat distribution. The results of CFD analysis are used, for the first time on SRM, for this purpose. Windage loss calculation, one of the other applications of CFD, is introduced. Vibration in electric motors is an inevitable, at the same time undesirable, property that originates from four major sources: mechanical, magnetic, applied loads and, to a smaller extent, the associated electronic devices. Section III presents: 1) a thorough numerical study of vibration analysis in SRMs, using 3-D FEA methodology, covering all the above vibration sources except the electronics; 2) a 3-D modal analysis of SRMs including stator and rotor structures, shaft, end shields, bearings, and housing; 3) an unbalanced rotor dynamics analysis; 4) associated harmonic analysis; and 5) a stress analysis under various loading conditions. The 3-D vibration analyses presented in this paper to examine the vibration in SRM as a whole are new additions to SRM vibration analysis. Section IV concludes the paper. Future work in every section is highlighted. Index Terms—Air velocity, computational fluid dynamics, switched reluctance motors, thermal characterization, 3-D finite-element analysis, vibration analysis.

I. FLOW ANALYSIS IN SRM

I

N switched reluctance motors (SRMs), a progressive switching of stator coils in a clockwise direction produces a magnetic field that enables steady motion of the rotor in a counter-clockwise direction. The aim is now to trace the path and velocity of the air in the interpolar regions (regions between two adjacent poles, called air pockets) of both stator and rotor during the rotation of the rotor. Let the application of the knowledge of air velocity be considered for thermal analysis, in which this will help in the accurate evaluation of convection heat coefficient at different heat dissipating iron surfaces inside the machine, which is not a material property, but a quantity that solely depends on the air velocity. A. Computational Fluid Dynamics (CFD) 1) Introduction: CFD (for a good treatment, refer to [1]–[3]) is predicting what will happen, quantitatively, when fluid flows, often with the complications of simultaneous flow of heat and mass transfer, mechanical movement (in the case of electric machines, the rotor), and stresses in and displacement of immersed or surrounding solids. The “fluid” that flows inside a rotating electric machine is the air, which is highly turbulent when the rotor rotates. In the great majority of fluid flow problems, precise analytical determinations of fluid velocities are not possible, owing to the complex effects upon the flow of fluid vis-

Digital Object Identifier 10.1109/TMAG.2004.843349

cosity, and a proper assumption and modeling would yield realistic solutions of the complicated numeric equations of CFD. Throughout this paper, air gap means the gap between the rotor and stator when they are aligned and air pocket means the air region at the stator or rotor interpolar region (Fig. 1). 2) Governing Equation: The following are the major assumptions made. a) The flow is turbulent since the operating speed is 3000 rpm. b) The air is steady inside the machine. c) Incompressible fluid analysis is sufficient. Analysis for the determination of the air velocity involves the determination of the pattern (whirl and turbulence) of the fluid flow. The governing equation is the two-dimensional (2-D) Laplace equation given by the following: (A1) This Laplace equation is solved by finite-element analysis (FEA) procedures for evaluating the net velocity vector distriin three dimensions (3-D). With the density bution of the whirling fluid being , the governing equation in 3-D becomes, , that is, (A2) 3) Preprocessing: The fluid (that is the dry air) has a density of 1.21 kg/m and kinematic viscosity of 17.6 10 . These are set as the material properties. Fig. 2 shows the meshed model

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Fig. 1.

IEEE TRANSACTIONS ON MAGNETICS, VOL. 41, NO. 4, APRIL 2005

The FEA model of SRM.

Fig. 3.

Meshed model of the subdivided rotor interpolar air region.

Fig. 2. Meshed model of the stator interpolar air region.

of air pocket in the stator interpolar region. The velocity of air according to the operating speed is set as the boundary condition at the outer periphery of the air pocket. Consider the air boundary in the rotor interpolar region, which is an arc, as shown in Fig. 3. When velocity of the air is set at the rotor interpolar region, care must be exercised to account for this lengthier curvature of the air boundary. The rotor interpolar arc is divided into suitable equal segments. The arc is divided into ten segments. The velocity is set at each segment depending on the angle subtended. The velocities in the and directions (Fig. 3) will be respectively and , where is the rotor velocity at rpm, given , in m/s. is the diameter excluding the air gap by length when velocity is calculated for the rotor and is including the air gap length when velocity is calculated for the stator. These velocities are set on each segment of the rotor interpolar arc. This exercise does not arise with the stator interpolar air modeling because of the smaller curvature of the air boundary due to six stator poles. Since the curvature is almost a straight line, velocity in direction alone is specified. Also, it is important to note that the air at the rotor and stator pole surface moves in opposition. The air velocity vector at these surfaces are accordingly set as the boundary conditions.

Fig. 4. Flow analysis results indicating the air turbulence and its velocity at different places in the stator interpolar air region at 3000 rpm (5.0265 m/s).

4) Determination of Air Velocity: The interpolar regions of stator and rotor are modeled separately in order to evaluate the air velocity at different surfaces of SRM for a particular speed. The command FLDATA will perform the flow evaluation using (A2) to get the whirl and turbulence of the air velocity vector at the considered air pocket. The command PLVECT, V will plot the velocity vector as per its whirl and turbulence directions. /CVAL is a useful command in flow analysis to select a particular range of velocities. For instance, consider /CVAL, 5, 7. This will display air velocity regions between 5 and 7 m/s anywhere inside the SRM. The results of simulation of CFD is shown in Figs. 4 and 5. For the operating speed of 3000 rpm, the air velocity is 5.172 m/s. It is observed from the simulation results that at the surfaces s4, s5, s6, and s7 the air velocity is between 2.299 and 3.448 m/s, which is equivalent to the whirl of air between speed 1200 and 2000 rpm. A similar observation in the air pocket at the rotor interpolar region shows that the iron surfaces s8 and s9 are dissipating heat at the air velocities 2.234 and 3.351 m/s.

SRINIVAS AND ARUMUGAM: ANALYSIS AND CHARACTERIZATION OF SWITCHED RELUCTANCE MOTORS

Fig. 5. Flow analysis results indicating the air turbulence and its velocity at different places in the rotor interpolar air region at 3000 rpm (5.0265 m/s).

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analysis, which dates back to early 1920 [4]. An equivalent thermal circuit for induction motor has been reported in [5], in which different parts of the motor have been represented as lumped parameters of thermal resistors and capacitors interconnected. The steady-state temperature is calculated based on the thermal resistances representing the different sections of the motor. Namburi et al. [6] showed how temperature rise is dependent on motor loading by fitting curves with different time constants and different values of output power. Adopting [6]–[8], Faiz et al., in [9] and [10] determined heat distribution in SRM for natural and forced cooling using the thermal equivalent circuit model. The thermal analysis for SRM presented in this section is novel in introducing computational fluid dynamics for determining the air velocity distribution inside SRM. The results of CFD will help to precisely evaluate the convection coefficient at all the heat dissipating iron surfaces of SRM resulting in a realistic thermal simulation. This section is organized as follows: The necessary calculations for thermal analysis using FEA are given in Section II-B. In Section II-C, implementation of CFD for thermal analysis is presented. FEA procedure for steady-state thermal analysis is given in Section II-D, and the same procedure for transient thermal analysis considering various duty cycles is elaborated in Section II-E. This section also presents transient thermal characteristics including eddy-current loss distribution and radial fins. Section II-F introduces, in basic terms, application of flow analysis for windage loss calculation. B. Fundamentals of Thermal Analysis 1) Preprocessing: The governing equation for 2-D finite-element thermal analysis involving respectively heat dissipation processes by convection and conduction, in 3-D, is given in the following:

Fig. 6. Result of 3-D FEA flow analysis indicating air velocity distribution on the whole SRM model.

Velocities less than 2 m/s may be ignored as they are not near the iron surfaces and oriented at the midregion of the air pocket. Turbulence of air is inherently 3-D, and hence, air flow analysis in 3-D can only be helpful in predicting the turbulence of air inside SRM. Results of such a 3-D flow analysis are shown in Fig. 6. It has to be noted that in a 3-D flow analysis, results can also indicate varying pressures at various air pockets. This is obvious as the velocity of air is not constant. As the pressure of air is not of analysis interest, say for thermal analysis, the analyst can safely omit it. The option of animating the air turbulence when the rotor rotates is possible. II. FLOW-ANALYSIS-BASED THERMAL ANALYSIS IN SRM A. Review of Previous Works Thermal modeling using thermal equivalent circuit of electric motors has been extensively done in the past for thermal

(B1) where unknown temperature distribution in degrees kelvin; heat conductivity in degrees kelvin per square meter; heat source in watts per square meter; heat transfer coefficient; ambient temperature in degrees kelvin. Fig. 1 shows the model of SRM. The material properties of each component of the machine, such as thermal conductivity, resistivity, density, Poisson’s ratio, specific heat, etc., are specified. The stator and rotor are chosen to be steel and the perfect conductor option is given for the windings. The density was assigned to be 7866 kg/m . For a steady-state analysis or for a transient analysis, major material properties necessary are the thermal conductivity and the electric conductivity of the materials. Thermal conductivity is set as 445 K/m , the resistivity is set as 0.021 m/mm , and the ambient temperature is initially set as 298 K. After assigning such material properties, the model is meshed, and the next stage is to fix the boundary conditions.

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The values for all the above data for dry are W m K

and

m s b) For the surface s2 (the surface which dissipates the heat upward by natural convection): (B3) (area/perimeter) . where c) For the surface s3 (the surface which dissipates the heat downward by natural convection: (B4) Fig. 7. Location of boundary conditions.

2) Heat Source and the Boundary Condition: In SRM, when one of the phases is conducting, the ( ) copper loss produced is dissipated as heat. The value of heat flux , evaluated as power loss in watts per square meter of the surface, is set as the surface heat source at four vertical sides of the excited stator pole. However, mechanical losses are not considered. The developed heat is dissipated mainly through the air trapped in between the stator and rotor poles, other iron surfaces in the vicinity of the excited phase which are considerably heated, rotor body, and partly by the outward facing cylindrical yoke. Neglecting the other iron surfaces in the vicinity of the excited phase, the heat will be dissipated out by the natural convection process through the surfaces s1, s2, and s3, as shown , and in Fig. 7. The respective convection coefficients are specified at these surfaces. The convection coefficient is to be found out for different dissipating surfaces depending on the shape of the surface and the velocity of the air in contact with the surface of heat dissipation. There are various formulas available for the evaluation of convection coefficients depending on the shape of the heat-dissipating surface [11]–[13]. The convection coefficient for the surfaces s1, s2, and s3 are evaluated using the following formulas. a) For the surface s1: The conduction coefficient for the surface s1 is given in the following: (B2) where thermal conductivity of dry air, W/m K; diameter of the stator up to the stator pole arc, m; Reynold’s number angular velocity which is, at a speed of rpm, , rad/s; 2 kinematic viscocity, m /s; Prandtl number; where

The value of convection coefficient at the heat dissipating surfaces other than s1, s2, and s3 is usually neglected, which is not true in practice. The heat-dissipating surfaces in the interpolar regions, that is the regions of air between the adjacent stator poles and the adjacent rotor poles, do participate in convecting heat depending on the velocity of air with which they are in contact. Therefore, the convection coefficient at different wall portions is to be evaluated using (B2) at the respective air velocities. The results of air flow analysis are used to find out air velocity, and hence the convection coefficients, at different sur, and faces in the machine. The application of , and are shown in Fig. 7. C. Tracing Air Velocity Vector in Interpolar Regions A detailed CFD [14] methodology to get the distribution of the air velocity vector in the interpolar air pockets has to be performed earlier. The various air velocities at the surfaces in the air pocket regions are identified. The respective convection are calculated using (B2). All such ’s are coefficients specified as boundary conditions. The steady-state and transient thermal characterization is then carried out. D. Steady-State Thermal Analysis Once the preprocessing, as explained in Section II-B1 is completed, then the analysis mode can be either selected as steady-state or transient, respectively, by using commands post-processing—analysis—thermal—steady-state or postprocessing—analysis—thermal—transient. The ambient temperature was set to be 25 C (298 K) using tamb, 298. and the convection coefficients at the surThe heat flux faces s1–s9 are specified and the steady-state simulation is run. The primary data obtainable from the steady-state heat run is the nodal temperature. The data which can be derived out of nodal temperatures are the nodal and element thermal fluxes and the nodal and element thermal gradients. To start with, the ambient temperature was set as 25 C and a finite-element heat run was carried out. The simulation resulted in a steady-state temperature of 30 C. The steady-state simulation is repeated again with 30 C as the ambient temperature. The process is repeated until two successive steady-state temperatures are the same. The settlement was achieved at a temperature of 35 C. The model with boundary conditions, results of steady-state

SRINIVAS AND ARUMUGAM: ANALYSIS AND CHARACTERIZATION OF SWITCHED RELUCTANCE MOTORS

Fig. 10.

Isotherm plot showing the different temperature zones in SRM.

Fig. 11.

Pattern of the intermittent load.

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Fig. 8. Meshed 3-D model of SRM in FEA scenario with the boundary conditions specified.

Fig. 9.

Steady-state temperature distribution.

simulation, and thermal gradients under steady-state conditions are shown in Figs. 8–10. E. Transient Thermal Analysis 1) Simulation Procedure and Results: The transient thermal analysis, in which the temperature varies with respect to time, is simulated for different duty cycles. The setting up of boundary conditions has certain steps to be followed using “load step” (LS) files. The value of is set on the meshed model of excited stator poles according to the load pattern. For instance, consider the intermittent load as shown in Fig. 11. The load step (LS) files are sequentially created to take care of the changes in and the respective time period, using solution—time-step—sub-step command. The execution of this command will require the respective values of changing load and time, which has to be systematically input. Finally, write LS command will be used to

write the above sequence of LS files as a single file to perform transient thermal analysis. The command outres, all, all must be given before simulation to make the final result of th LS th LS file. file as the starting values for the An example of intermittent load is considered for illustration (Fig. 11). The ON and OFF periods are 900 s each. The heat flux, in W/m , is proportional to 7 A at all the ON periods. It is zero at all the OFF periods. This alternative variation of heat flux and the respective time duration are is sequentially stored in an LS file, and the transient thermal simulation is run. The results of simulation showing temperature rise from 0 to 10 000 s at stator is shown in Fig. 12. 2) Thermal Analysis Considering Eddy-Current Loss: The core loss distribution in SRM is another considerable factor for heat production. Before the boundary conditions are set as detailed in this paper for thermal analysis, an iron loss analysis has to be performed to take into account the core loss distribution. Fig. 13 depicts the results of eddy-current loss distribution as obtained by FEA [15]. The thermal analysis made on this model will be a simulation considering copper loss and eddy-current loss. The results of simulation conducted on this model, showing temperature rise from 0 to 7200 s at stator, for the continuous load of 7 A, is shown in Fig. 14, which indicate that the steady-state temperature is attained at 356 K, whereas without considering the eddy-current loss, it was 350 K.

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Fig. 12.

IEEE TRANSACTIONS ON MAGNETICS, VOL. 41, NO. 4, APRIL 2005

Transient temperature-time curve of stator body for the intermittent load.

temperature rise is usually selected for the end product. Table I is the summary of steady-state thermal analysis performed on varying fin dimensions. The fin with a thickness of 2 mm and a length of 3.5 mm is declared for the end product as it produced the least steady-state temperature of 329.893 K. Figs. 16 and 17 respectively represent the results of steady-state and transient thermal analyses on the SRM with radial fins. F. Another Application of Flow Analysis

Fig. 13.

Eddy-current distribution model for thermal analysis.

3) Thermal Analysis Considering Fins: The temperature rise of the electric machines is kept under permissible limits by providing fins. It is possible to increase the heat energy transfer between the outer surface of the machine and the ambient air by increasing the amount of the surface area in contact with the air. Fins are the corrugations provided throughout the outer surface of the frame. When fins are provided on the outer frame of the machine, as shown in Fig. 15, the surface area of heat dissipation gets increased, thus effecting the heat dissipation. It is of the kind called radial fin with rectangular profile. In order to increase the fin effectiveness, various possible combinations of fin dimensions are to be considered. Steadystate thermal analysis has to be carried out for each combination. The fin dimension which produces the least steady-state

One another major application of flow analysis is windage loss calculation. Windage or air friction is the term generally used to denote the loss due to fluid drag on a rotating body. The accurate prediction and reduction of windage loss is becoming more important with the growing development of high-speed machinery. Information published in the open literature is sparse and addresses cases of large machinery at lower speeds. This section attempts to introduce a flow analysis based procedure, to calculate the windage loss in high-speed SRM. Two approaches available in the reference for the evaluation of air friction, that is the windage, loss are used. In the first method (complete derivation in [16]), the air friction loss is calculated using watts where the friction factor

(B5)

is determined as (B6)

Equation (B5), termed as head loss in fluid dynamics, is equivalent to the fluid friction (that is windage) loss. Air friction loss is evaluated individually at all the heat dissipating walls of the air pockets at the respective air velocities. The summation will then yield the total windage loss. In the second method (full derivation of the formula in [17]), the formula of (B7) is used to determine the air friction loss

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Fig. 14.

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Transient heat distribution in stator considering copper loss and eddy-current loss distribution.

TABLE I STEADY-STATE THERMAL ANALYSIS RESULTS DIMENSIONS OF RADIAL FINS

FOR

VARIOUS

Fig. 15. Model of SRM with fins and terminal box.

at various wall portions in the air pockets, at the respective air velocities. The summation of all the air friction losses at the walls of the air pockets at the respective air velocities will give the total windage loss

watts

(B7)

However, this is an overall introduction to emphasize that the knowledge of air velocity at every air portion of a machine will yield windage loss which will be far from approximations. Ultimately, from an electrical point of view, all of the windage loss results in drag on the rotor. A careful prediction of forces on the rotor to get the drag, in conjunction with the air-velocity-based

calculations mentioned in this section, will help to fine-tune the results. This can be considered as a future work to elevate this section. Similarly optimizing the insulations used in various parts of the machine, which depends on the heat dissipating capacity of the machine and which in turn is an air-velocity-dependent, is also a notable extension of air flow analysis.

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(a)

sidering the stator frame alone. Although the stator is the major portion of noise production, there are contributions from other parts such as rotor core, end rings, bearings, shaft, and applied loads which were believed to be negligible in the above earlier attempts. A 3-D FEA is capable of accounting for all these parts. Section III-B describes the modal analysis on SRM in 3-D considering the rotor, shaft, end shields, bearings, and housing. Section III-C records the simulation procedure for unbalanced rotor dynamic analysis on SRM, which is essential to verify whether the vibration of rotor including housing is within the acceptable limits. This section also reports on the harmonic analysis to identify the frequencies at which the vibration is maximum due to the rotor eccentricity. Vibration due to machine coupling with a load, pulley, and belt tension, and mounting of SRM on foundation is examined in Section III-D. This is simulation of load test on SRM. Modeling of different auxiliaries and consideration of different loads are the highlights of the section. B. Modal Analysis Including Housing The SRM model under consideration and the meshes formed during FEA are shown in Fig. 18. The length of the stator stack is 90 mm. The end shield has thickness of 10 mm. The shaft has a diameter of 25 mm. The main values set during simulation N/m ; specific mass of are: The Young’s modulus kg/m ; total mass density kg/m ; winding Poisson’s ratio . In the SRM, it is found that resonance occurs if the phase frequency or add harmonics coincides with the stator natural frequency, resulting in a peaking of the stator frequency. The is given by [25] phase frequency (C1) is the speed in radians/s and is the number of rotor where poles. Vibration is maximum if any of the frequencies (C2)

(b) Fig. 16 (a) Steady-state temperature distribution in SRM with fins (a) at full load and (b) at twice the full load.

are coincident with the natural frequency of the machine given by [25] (C3)

III. 3-D VIBRATION ANALYSES OF SRM A. Introduction When a phase is excited, the magnetic flux from the excited stator pole crosses the air gap in a radial direction producing large radial forces on the excited stator poles, which deform the stator into an oval shape, called ovalization. It is imperative to know the frequencies (called the modal frequencies) at which the radial forces are induced, as the coincidence of the natural frequency of the stator with any of the modal frequencies will cause resonance resulting in vibration and noise. A modal study will yield the possible frequencies (and hence the respective speeds) to be skipped for a quiet operation of the machine. There are major papers available in the literature to investigate vibrations in SRM, from the machine’s side and also from the controller’s side [18]–[24], based on 2-D modal analysis con-

is the stator iron thickness in meters, is the mass where density of the material in kilograms/cubic meter, and is the mean radius of the stator shell in meters given by where is the outer diameter of the stator. The governing Laplace equation that is solved iteratively to find the modal frequencies is (C4) where is the modal vector, and is the frequency of vibration. The solution is the th mode shape and is the corresponding natural frequency. The 3-D modal analysis reveals certain modes which are producing vibration (and the associated acoustic noise) in SRM due to rotor and housing structures. The mode frequency of 231.154 Hz (3467 rpm), shown in Fig. 19(a), is observed to produce twist of rotor. Modal frequency of 160 Hz

SRINIVAS AND ARUMUGAM: ANALYSIS AND CHARACTERIZATION OF SWITCHED RELUCTANCE MOTORS

Fig. 17.

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Transient temperature distribution in SRM with fins for a continuous load.

Fig. 19. 3-D modal analysis results at mode frequencies (a) 231.154, (b) 160, (c) 364.5, and (d) 231.134 Hz. Fig. 18. 3-D model of SRM with stator, rotor, shaft, end shield, housing, and bearing.

[Fig. 19(b)] causes shaft bend with a severity at the shaft-rotor edge. Frequency of 364.5 Hz causes rotor structure and rear shaft vibration [Fig. 19(c)] and at 231.15 Hz [Fig. 19(d)], the rotor deforms at an angle. At modal frequencies of 3089 Hz

[Fig. 20(a)], 1910 Hz [Fig. 20(b)], and 161 Hz [Fig. 20(c)], the housing also gets involved in contributing vibration. The rotor rocks up and down causing it to strike against the stator, transmitting the vibration till housing and foundation. The shaft bends. The drive may not be able to handle any load at these speeds. At 900 Hz [Fig. 20(d)], the housing with foundation undergoes vibration.

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Fig. 20.

IEEE TRANSACTIONS ON MAGNETICS, VOL. 41, NO. 4, APRIL 2005

3-D modal analysis results at mode frequencies (a) 3089, (b) 1910, (c) 161, and (d) 900 Hz.

C. Unbalanced Rotor Dynamics A harmonic frequency analysis has been performed to identify whether the vibration of rotor and housing is within safe range. The aim is to obtain the SRM structure response at several frequencies with respect to displacement. Peak responses are identified and plotted as a graph. Stresses are reviewed at these frequencies. The weight of the rotor (w) is 3.75 kg. The balancing quantity ( ) and the damping ratio ( ) were assumed to be 2.5 and 0.02, respectively, which are the usual standard values for high-speed machines. The rated speed is 3000 rpm. The centrifugal force is calculated using the formula (C5) As all the units are in millimeters, the g used is 9810, which gives the centrifugal force, , as 0.3. This is applied to the center node of the rotor, as a lateral load. Arresting the nodes at the foundation forms one of the boundary conditions to model that the SRM is bolted to the foundation. In case of SRM, is set the whole housing also sit on the bearings. So, the

throughout the outer housing surface and to the front and rear bearings. This is a constant force applied over a frequency range. The frequency range was assumed to be 400, which is on the upper side. The “harmonic analysis” to identify the possible high vibrating and noise producing speed bandwidth which is skipped fast during accelerations, is performed on this model using the FE package. The unbalance force , at a frequency , is . But, the force which the FE package finds will be at . It , using a small program. has to be converted as The result of the simulation is shown in Fig. 21. It can be observed that the rotor eccentricity reaches a maximum of 6 m only, that is, 6 10 mm whereas that of outer frame is 1 10 mm. As this eccentricity is of negligible micrometers, it is conclusive that the rotor dynamics of the considered SRM is in acceptable limits. D. Static Stress Analysis 1) Methodology: Static analysis is simulating a load test on SRM for observations in limit violations of stress and deformation at different places. Additional models required are bearings

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kg; belt prestress and housing kg. weight of pulley The full load of 3.63 N m is considered. As the assignment of load, etc., are in force units, the equivalent kgf m is kgf m. Using the radius of the shaft and converting all kg. quantities to a single unit, the force is This force is spread over all the finite-element nodes at the shaft end. It is observed that there are 12 nodes. Thus, the equivadirection is lent force applied to each of the 12 nodes in 5.1. Further, the sum of the weight of pulley and belt loading mechanism, belt’s prestress and the housing with stator, which amounts to 7.85 kg, is divided to all the 12 nodes in a similar direction, as they act downwards. way and applied at the At this full-load model, a “stress analysis” is run whose output is shown in Fig. 22. Winding weight is considered as net mass along with the weight of the stator. The material considered has a maximum tensile stress of 45 kg/mm . The stress in the SRM on full load is simulated to be 21 kg/mm . It can readily be observed that the factor of for the full-load case. Thus, the SRM safety is can be operated at full load without any mechanical threat. This analysis can be extended for any load by a suitable application of boundary conditions. Fig. 21.

Results of unbalanced rotor dynamic analysis.

IV. CONCLUSION

Fig. 22.

Result of static stress analysis at full load.

and pulley. Bearing is the element in SRM to hold the housing and the rotor mass at the shaft. So, bearing is simulated as four springs attached to the housing from the bearing locations (front and rear). The node at the front bearing location and four nodes at the housing each displaced by 90 in and axes are selected and joined. A similar procedure is repeated at the rear side of the shaft. The spring stiffness (21 000) is assigned and bearing is thus modeled. The pulley is modeled by assigning its weight at the end of the front shaft. mm; outer The required data are: the radius of the shaft mm; thickness of pulley mm; diameter of pulley

This paper, made up of three parts, discussed respectively, flow analysis, flow-analysis-based thermal analysis, and vibration analysis, all by 3-D FEA procedure (using FEA package ANSYS v. 6.0), for the first time for SRM. A procedure to trace the velocity distribution inside SRM is presented in Section I of the paper. Section II presented a procedure to simulate steadystate and transient thermal characterization using the knowledge of air velocity distribution inside the machine obtained using the air flow analysis. It may be noted that an accurate thermal analysis would not have been possible had the air flow analysis been not conducted because, in such a nonflow analysis, could only be specified at air gap the convection coefficient regions, and not in the interpolar air regions, which will approximate the simulation results to a greater extent. The fact of laminated stator and rotor is neglected. The results were presented by considering the excitation of one phase. The temperature internal to SRM is uniform and that all of the temperature rise is from the ambient air surrounding the machine inside to the stator’s outer surface. It has been observed that the steady-state temperature is 350 K considering only copper loss, whereas it reaches 359 K considering the eddy loss also. Provision of fins enhances the heat dissipation; the steady-state temperature is then 333 K. Notable future works are inclusion of iron and mechanical losses, fine tuning the analysis by considering the laminations and, on these improvements, a dynamic heat run. In Section III, the stator, stator frame, rotor, end-rings, bearings, shaft, pulleys, and applied loads have been modeled in 3-D to study the vibration in SRM as a whole [26], [27]. The eccentricity in the SRM rotor including housing is found to be much less from the rotor dynamic study. From the static stress analysis, the reviewed stresses reveal that the stresses are under safe limit at full load.

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Manuscript received October 8, 2004; revised November 4, 2004.

K. N. Srinivas (M’03) received the Diploma in electrical and electronics engineering (DEEE) from Chengalvarayan Polytechnic, Chennai, India, in 1985 with high first class honors, the M.E. degree from Annamalai University, India, in 1993 with first class with distinction, and the Ph.D. degree from Anna University, India, in 2004. He is currently an Assistant Professor in the Electrical Engineering Department at Crescent Engineering College, Chennai, India. He visited Japan, Singapore, Malaysia, Thailand, and the United States during his research period to present his findings at IEEE international conferences. His contribution in the IEEE international conference, IECON 2000, held in Japan, and IECON 2003, held in the USA, received the best contribution award by the IEEE industrial electronics society which includes a citation and fellowship. He has more than 19 international journal and conference publications. His technical interests are electric machines and drives and their performance evaluation through simulations and power system state estimation, unit commitment, and contingency analysis.

R. Arumugam (M’03) received the B.E. degree and the M.Sc. degree (Engg.) in power systems engineering from the College of Engineering, Guindy, Chennai, India, in 1969 and 1971, respectively, and the Ph.D. degree in electric machine analysis and design from Concordia University, Montreal, QC, Canada, in 1987. He is a Professor of Electrical Engineering at Anna University, Chennai, India. He is currently the Director of the Electrical and Electronics Engineering Department, where he leads a team of engineers in electric machines and drives. He is actively involved in industrial consultancy with major Indian industries such as TVS Luacs Ltd., BPL Telecom Ltd., and Tamilnadu electricity board.