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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 31, NO. 4, JULYIAUGUST 1995 933 Interactive Computer Aided Design of Permanent Magnet DC Motors David A. Staton, Malcolm I. McGilp, and Timothy J. E. Miller, Senior Member, IEEE Abstract-A summary of the design theory associated with dc commutator motors is presented. This is followed by a detailed description of a Computer Aided Design program written specifically for this class of motor. Tbe software engineering content is extremely important: Once the engineering design equations are developed and validated, the productivity of the design engineer depends critically on the efficiency and user-friendliness of the software itself. The program described in the main text permits the integration of the motor design with the design of the electronic controller, together with the simulation of the wbole system. When sizing motors for a particular application, speed of execution and the flexibility to evaluate a wide range of design options and parameter variations are essential, while absolute accuracy is only of secondary importance. I. INTRODUCTION B EFORE the wide availability of inexpensive computing facilities, motor design was carried out using simplified analytical and lumped circuit calculation techniques, consolidated by empirical and experimental data to account for saturation, leakage, etc. [ 11-[5]. The original Computer Aided Design (CAD) programs developed for motor design were direct translations of the traditional procedures. However, it was soon realized that the greater calculation speed could be more fully utilized by developing improved lumped circuit models to account directly for saturation and flux leakage paths [6]-[ 101. Over the last decade, there has been a massive increase in the amount of research carried out on developing CAD software for the design of electrical machines. Much of this research has been dedicated to improving the accuracy of the machine models used in the packages, with particular emphasis being placed on the use of finite element analysis. Powerful programs based on the finite-element method, capable of electromagnetic, thermal, and mechanical analysis are increasinglyused to improve old designs or generate new ones. Generic simulation packages complement these tools with the simulation of the power electronic and digital or analog controllers. In this environment, there is an important role for simpler “sizing” software to prepare preliminary designs, and it is all to the good if such sizing programs integrate a range of capabilities covering electromagnetic, thermal, and control aspects. While accuracy is not the primary requirement, speed of execution is paramount, together with the flexibility Paper IPCSD 95-08, approved by the Electric Machines Committee of the IEEE Industry Applications Society for presentation at the 1993 IEEE Industry Applications Society Annual Meeting, Toronto, Ontario, Canada, October 3-8. Manuscript released for publication January 20, 1995. The authors are with the SPEED Laboratory, Department of Electrical and Electronic Engineering, University of Glasgow, Glasgow G I 2 8LT, Scotland. IEEE Log Number 941 I 123. to evaluate a wide range of design options and parameter variations. In this paper, a sizing package for dc commutator motors, PC-DCM, will be described. PC-DCM is the newest of the family of CAD packages written specifically to run on a PC [ 111, [ 121, the other packages being for the design of switched reluctance motors (PC-SRD) and brushless dc motors (PC-BDC). All the packages have similar user-interfaces, file-handling, and use common databases. This makes it straightforward for a designer to move from one package to the next. The software engineering content is extremely important: Once the engineering design equations are developed and validated, the productivity of the design engineer depends critically on the efficiency and user-friendliness of the software itself. The CAD packages developed take full advantage of the latest graphical interface and file handling techniques. 11. DESIGNTHEORY A. The D 2 L Equation The fundamental design equation for many types of machine is the so-called D 2 L equation, which relates the gross output torque of a motor to the armature volume, specific magnetic loading (B), and specific electric loading ( Q ) T =T / ~ D ~ L , Q B where T gross output torque (Nm), Q specific electric loading (Nm), B specific magnetic loading (T), D, armature diameter (m), La armature length (m). This expression holds the key relationships between the mechanical, electrical, and magnetic design variables. For a given torque (or power at a set speed), the armature volume can only be reduced if the values of B or Q are increased. Alternatively, for a given motor frame, the torque can only be increased if B , Q. or the armature volume is increased. Specific Magnetic Loading (B): The specific magnetic loading is the mean flux density in the airgap, and is equal to where B, is the airgap flux density beneath a magnet pole, and ,Om is the magnet arc (electrical radians). 0093-9994/95$04.00 0 1995 IEEE IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS. VOL. 31, NO. 4, JULYIAUGUST 1995 934 6) MAGNET MAGNET 1 Fig. 1. Magnetic lump circuit (two-pole motor). FLUX INCREASE DUE TO MAGNET OVERHANG 60 50 1 - -MULLARDS DATA _ _ _ _ 3-D FE DATA \ Dab \ ARMATURE 1) 6 40- 2B 30- 8% m- - 3.14 157 1.13 P Fig. 3. 3-d finite element model of magnetlframe overhang [ 6 ] . 1.c4 s 0.78 LINEAR NON-LINEAR 10 - 1 1.2 1A 1.6 1.8 2 DEMAGNETISATIONCURVE MAGNET/ARMATURE LENGTH RATIO Fig. 2. Flux increase due to magnet overhang. The value of B, is related to the average flux density in the magnets (B,) by the ratio of the magnet to airgap crosssectional area. In order to account for flux focusing within the magnet, the magnet area is calculated at a radius one third the distance from the inner surface of the magnet (i.e., a radius equal to D,/2 1, lm/3).The magnet area is also adjusted to account for magnet leakage flux. I, is the radial magnet thickness and I, is the radial airgap length. In order to calculate the average flux density within the magnet, the lumped-circuit shown in Fig. 1 must be solved. Due to the low remanence of ferrite materials, it is common practice to let the magnet overhang the armature by around 20% in order to increase the flux-per-pole by up to 15%. Fig. 2 plots the increase in flux due to a magnet overhanging the armature. This data was compiled by Mullards Ltd. [4] from measurements on a range of ferrite motors. In order to substantiate this data, a series of three-dimensional finite element calculations have been carried out [6], [7]. Fig. 3 shows a typical mesh and flux plot taken from the analysis. While the use of magnet overhang is usually cost effective for low-priced ferrite materials, it is not normally used with more expensive rare earth magnets. It is also common to let the magnetic section of the frame overhang the magnet and armature in the axial plane as shown in Figs. 3 and 8. The overhanging frame is used to relieve the flux density in the active section of the frame, as shown in Fig. 3. This allows a thinner frame section to be used. It is also beneficial for mounting the brush gear, provides space for the end windings, and allows less bulky end shields to be fitted to the motor. + + H w Hk MAGNETISING FORCE (Nm) Fig. 4. PM demagnetization characteristic and load-line. A permanent magnet is characterized by its demagnetization characteristic (see Fig. 4), i.e., its B-H characteristic in the second quadrant. The equation for the linear section of the B-H characteristic is Bm = P o P v H m + B, (3) where B, magnet remanent flux density, B, magnet working flux density, H, magnet working magnetizing force, and p, magnet recoil permeability. If the iron sections of the magnetic circuit are not heavily saturated, the magnet flux can be calculated using a simple linear-load line technique. The load line is plotted on the demagnetizationcharacteristic of Fig. 4. It has a gradient equal to (4) where 1; is the extended airgap, A , is the airgap area beneath a magnet pole, and A, is the magnet area. 935 STATON et al. : INTERACTIVE COMPUTER AIDED DESIGN OF P E R M A ~ N TMAGNET DC MOTORS 1 The extended airgap is used to account for the fact that the effective reluctance of a slotted airgap is larger than the actual airgap and is taken in to account by applying the analytical work of Carter to calculate an airgap extension factor [l], [ 131. The intercept of the load-line with the demagnetization characteristic is given by 1mAgIAm B , = Br prlb lmAg/Am ' + l.W 9 0.80 t o.60 (5) m 0.40 0.w For a given magnet material, in order to calculate the specific magnetic loading ( B ) it is necessary to know the magnet arc, H (k") airgap length, and magnet thickness. In order to maximize B , the magnet arc should be as large as possible, although Fig. 5. Typical PM demagnetization characteristics. an upper limit will usually be set (typically 120' to 140') by the need to allow a sufficiently wide neutral zone such that the conductors undergoing commutation have no induced small, the armature teeth will usually be thin and there will rotational EMF. The airgap length is usually determined by be large slots. This results in a comparatively low value of B mechanical tolerances and is typically 0.5 to 1.O mm. The main and a high value of Q. In a rare earth magnet motor, whose factors that affect the choice of magnet thickness are demag- remanence is large, the armature teeth will usually be wide netization withstand (see later section), mechanical constraints and small slots. This results in a comparatively large value of (i.e., the magnet arc will be fragile if 1, is too small) and cost B and a low value of Q. (rare earth magnets are extremely expensive, therefore 1, will usually be small). B. Magnet Materials If the iron sections of the magnetic circuit become saturated, Fig. 5 compares typical demagnetization characteristics of the load-line is no longer linear as depicted in Fig. 4, which the major magnet material types available today. The metal results in a reduction in B m . In this case, the simple formula alloy materials are seldom used in motors of this type, since given in (5) is no longer valid, and an iterative technique must their highly nonlinear demagnetization characteristics and low be used in order to solve the magnetic circuit. coercivities give them a low resistance to demagnetization.The Specijc Electric Loading (Qj: The specific electric loading essentially linear demagnetizationcharacteristicsand relatively is the ampere-conductors per meter of armature periphery high coercivities of ferrite and rare earth magnets make them ideally suited to motor applications. There has been continuous Q = - ZIa development of ferrite materials since their introduction in xaD, 1953, such that they are nearing their theoretical optimum [14] where Ia is the armature current (amperes), a is the number and are well established as the most cost effective material for of armature winding parallel paths, and Z is the total number many types of motors. A new generation of potentially lower of conductors in the armature. cost rare earth Neodymium-Iron-Boron (Nd-Fe-B) materials The allowable specific electric loading can either be esti- has recently emerged, having a larger energy-densitythan older mated by the designer from previous experience, or calculated Samarium-Cobalt (Sm-CO) materials. Current grades of Ndfrom an assessment of the achievable conductor current den- Fe-B have a limited operating temperature range due to their sity, J , based on thermal considerations, and the total copper large temperature coefficients of remanence and coercivity. area Currently Nd-Fe-B is still much more costly than ferrite. SmCOis even more expensive and will continue to find use only in the most technically demanding applications requiring precise performance over extended temperature ranges. where A c U is the total copper area in rotor slots and KFF is the current form factor. The area available for copper in the slotted armature usually C. Additional Design Constraints only amounts to 30% of the actual slot area due the conductor Thermal Constraints: The specific torque is limited ultiand slot liner insulation and wedges and a realizable packing mately by the permitted temperature rise of the most temdensity. The current form factor is included in the equation to perature sensitive element within the motor which is usually account for the fact that torque is dependent upon the average determined by the winding insulation class. The major sources armature current but the losses, and thus thermal aspects are of heat are copper losses in the windings, eddy current and dependent on the rms current. hysteresis losses in the rotor steel, friction and windage losses, Relationship Between B and Q: The values of B and Q are and brush contact losses. The subsequent temperature rise is not independent, since, in general, higher levels of B demand determined by the thermal dissipation of the motor frame more iron to carry the flux while higher levels of Q demand ( K D P ) In . PC-DCM: Friction (PFR)and windage (PwI) increased slot areas, both competing for space, particularly in losses must be estimated on the basis of previous experience; the armature. In a ferrite magnet motor, whose remanence is iron loss (PFE) is calculated using specific loss curves for 0 -900 -800 -700 -6W -500 -4W -3W -2W -IC0 0 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 31, NO. 4. JULYIAUGUST 1995 936 the lamination material (curves resident in the steel database) and component flux density levels output by the magnetic lump circuit model; brush loss calculated (PBR)from the brush current and brush voltage drop (taken from the brush database); and copper loss (Pc,,) calculated from the rms value of armature current and winding resistance (Ra).The total frame surface area available for dissipation (ADP)is calculated and the winding temperature rise (TR)estimated using the equation TR = + (Pcu+ PFE+ PBR PFR+ PWI) . KDPADP I 26th t h y 1993 .?!:I3 I M o r cross-sation editor 2 lun t i u i a t i o n 11 3- 4 Output deslgn sheet 5 Steel aat.b& 6 lbgnet database 7 b u s h database T TorquefSpced charactcrist i c G Simulation graphs U Uinding design S Sizing roitine I h i n t laminations and grnphs I 8 User preferences (8) PFR is calculated from the input value of TFR (friction loss torque). Pm71 is calculated from the input values of WFO,RPMo, NWF and the speed at which the calculation is performed (WM) according to the equation 9 Return to DOS Fig. 6 . PC-DCM main menu screen. (9) RPMo is the speed at which the windage power loss W,, is specified. Demagnetization Constraints: Under a load condition, the load-line is displaced as shown in Fig. 4. The trailing pole tips of the magnets are subject to a demagnetizing field and the leading pole tips to a promagnetizing field. Solving Ampere's Law for the magnet circuit results in the following expression, which calculates the maximum level of armature current (Iddm) which can be supplied to the motor before the magnet working point at the trailing edge of the magnet is driven beyond the linear section of the demagnetization characteristic (specified by Hk in Fig. 4) I I I Fig. 7. Cross-section editor (radial). Commutation Constraints: The value of reactance voltage is the main parameter used to judge the ability of a motor to commutate satisfactorily. This is the voltage induced in a coil undergoing commutation, when the current is reversed, which opposes the change in current. The magnitude of the generated EMF is proportional to rate of change of current (speed and current magnitude dependent) and the inductance (dependent upon the number of turns and the magnetic circuit associated with a coil in a slot) of the coil undergoing commutation. A design rule is that this EMF should not be greater than 3 V for satisfactory commutation. The easiest solution that can be implemented to reduce the reactance voltage is to increase the commutator segments (subdivide the coil into sections). This can be achieved in PC-DCM by increasing the number of coil sides per layer, but remembering to reduce the turns per coil proportionally. In addition to this transformer EMF, there may also be a rotational induced EMF due to the leakage flux on the neutral axis of the machine. The rotational EMF is minimized by limiting the magnet arc to between 120" and 140". The combined transformer and rotational EMF can cause poor commutation, and lead to arcing at the brush contacts and rapid brush wear, or in severe cases commutation failure. Mechanical Constraints: Mechanical limitations are imposed by manufacturing considerations, and application requirements. Typically, manufacturing limitations will set minimum and maximum magnet thicknesses, maximum armature length, minimum tooth thickness, etc. Typical application limitations are standard shaft heights, limits on the rotor inertia, and overall frame diameterflength constraints. 111. THE PC-DCM DESIGN PACKAGE A. General Procedure for Using PC-DCM On entering PC-DCM, the main menu options listed in Fig. 6 are available to the user. The general procedure for using the package is to define the motor geometry using a cross-section editor. This is not only used to define the geometry, but also to view and edit the motor cross section, both in the radial and axial planes (Figs. 7 and 8 show radial and axial cross sections for a small 120 W, 3000 r/min ferrite motor). This geometry can also be input using the template editor (see Fig. 9), which is used to set the winding STATON er al.: INTERACTIVE COMPUTER AIDED DESIGN OF PERMANENT MAGNET DC MOTORS 937 m.m cam I0.m a.m 2o.m 6.030 1o.m 0.W 1a 3.m m 2 I 72.391 l.Oo0 Fig. 8. Fig. 10. PC-DCM winding editor. Cross-section editor (axial). Tu SORng hrn Width LCon SD 3.508 28.008 68.008 6.808 lotTypc Sericirc LPrane Lend1 kndt 15.808 StP 0.958 CSL 1 1 ILcyth 40.800 10.008 2.008 109.808 39.808 SOD Lnafnet Lend3 8.400 78.808 20.000 n 1i ndi nf Paraneterr t UpIypc tap PronlRcg Prow 1 TC YDia 62 8.458 lhrou HBrush b 2 ontrol Parmeters RPll D U C ~ VSupply 1268.809 5e.808 108.908 HrChop 2869.808 29.008 Pisptn nur 18.00B 2 Xlnd 1.809 Drive Chopper 2. bo 6bo am 12:1 ser option Parameters Haplnp 28.808 1.808 Ydplmp me zsomoe 1.990 XPe 1.808 XLenk IOUnits Losrlr XSht Hctric 9.820 1.8W 1 . m Fig. 9. PC-DCM template editor. (the graphical winding editor must be used if the winding is nonstandard), control, and other parameters. A graphical winding editor, shown in Fig. 10, is provided to generate and display winding layouts. The winding is generated automatically if it has a standard lap or wave format. Alternatively, custom windings can be "wound" using a cursor. The program automatically builds a coil list table as the "winding" proceeds, and during the simulation phase it calculates the back-EMF waveform, resistance, and inductance of the complete winding and the waveforms of flux-density in the teeth and yoke as the rotor rotates. The latter waveforms are used for the computation of core-losses. The run simulation option is used to calculate the performance at a singly defined operating point on the torque-speed characteristic. A view simulation graph facility is provided to view the waveforms of supply voltage, back-EMF, and armature voltage and current (see Figs. 11 and 12). An outpur design sheet facility is used to examine the performance in fine detail. All the input and calculated design parameters are listed. In all, over 120 parameters are included and are divided into Dimensional. Winding, Control, Material Fig. 11. Simulation v-z wavefonns (Z-kHzchopper drive). I U60 I 1.m 1.m 2.M xm 3.m I Fig. 12. Simulation v-i waveforms (semi-converter drive). Data, Magnet Design, Simulation Output and Miscellaneous categories. Fig. 13 shows an example of a small section of a typical output design sheet. IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 31, NO. 4, JULYIAUGUST 1995 938 In the initial stages of a design it may be beneficial to carry out a sizing exercise based on the D 2 L equation and calculations of B and Q. A sizing option is provided for this purpose. ----___--- krlgn: 2 e . w Dcp.c Lia 0.33 T d Q.219 T x 1.WT cw k 1.B9Q B. Databases wlrtion Output:-----td 8 . ~ 1HM 2.380 II 18.851 dim ron) 4.273 U rush) 1.681 U d a l 3667.882 rpm I1 18.124 13 sh 2.3W A pRirc 19Q.232 Dep.C MF RPH lrms err UWrict) U(Totrl) 2714.088 rpm 102.216 U 73.211 X 5.684 U 17.024 U 28.149 U 5.118 U 7 . 2 ~n m ^ z 2.w m Tnl TStsll kckUlF Idcmg 8.w nm 5.w nu 85.761 U 28.253 A i.em iemo U urns 108.088 U 2.3@ A L m 98.088 U isccllancaur:---------- Fig. 13. PC-DCM output design sheet. Four databases are used within PC-DCM. There is a main design database and three material databases. The design database files contain all the dimensional, winding, and control parameters required to specify a design. The file also stores information required to form a link to the appropriate material databases and the selected material datafiles. The three material databases contain steel, magnet, and brush data. The steel datafiles contain B / H and iron loss curve-fit data. The magnet database contains data required to model the demagnetization curve together with a limiting value of magnetizing force ( H k ) beyond which irreversible demagnetization will result. The brush database contains a curve fit of the variation in brush voltage drop with brush current density. All material data is input via specific template editors and graphical routines are provided for viewing the appropriate curve fits. A feature of all the databases is that they contain version information and future releases of PC-DCM will be able to read old datafiles and make the relevant changes to the data. C. Calculations Perlformed by PC-DCM A variety of drive types are integrated into the package, which are: a) dc voltage source b) PWM chopper c) Semi-converter phase controller d) Full-converter phase controller In calculating the performance of the motor and drive Fig. 14. Torque-speed characteristic (2-kHz chopper drive). combination, the following general calculations are performed: 1) Calculate Motor Dimensions: The important dimensional parameters such as airgap length and slot area are calculated. 2 ) Calculate Airgap Extension: Carter’s coefficient is used to calculate the effective airgap taking into account slotting. 3 ) Solve Magnetic Circuit: The magnet working point is calculated, accounting for the nonlinear magnet circuit, end effects (magnet and frame overhang) and leakage (see Section 11-A). The flux-per-pole and component flux density levels are also calculated. 4) Calculate Winding Parameters: The mean-length-pertum, armature resistance, armature inductance, and inductance of the commutating coils are calculated. 5) Back-EMF Calculation: This is calculated from a knowledge of the winding design, flux-per-pole, and speed. Fig. 15. Torque-speed characteristic (semi-converter drive). 6) Calculate Voltage and Current Waveforms: The supply voltage is dependent upon the selected drive type (dc, Rather than just calculating the performance at a singly chopper, or phase control). The armature current is caldefined point on the torque-speed characteristic, it is possible culated knowing the drive details, back-EMF waveform, to calculate and display the entire torque-speed characteristic armature resistance and inductance, and the speed of as shown in Figs. 14 and 15. rotation. STATON er al.: INTERACTIVE COMPUTER AIDED DESIGN OF PERMANENT MAGNET DC MOTORS 7 ) Calculate Copper Loss: This is calculated from the armature rms current and winding resistance. 8 ) Calculate Component Weights: The iron, copper, and magnet weights are calculated. The individual weights of the armature teeth and core are also calculated and are used in the iron loss calculation. 9) CaZculate Iron Loss: This is calculated from a knowledge of the component weights, flux density levels and speed. The variation in wattskilograms with flux density and frequency is modeled and the relevant coefficients for the selected steel type are held in the steel database files. 10) Calculate Friction and Windage Loss: The friction loss torque is an input variable in the template editor. The windage loss ( W W I )is calculated using (9). 11) Calculate the Performance: The torque, power, and efficiency are calculated at the defined speed (RPM). 12) CaEculate the Demagnetization Withstand: The maximum value of current that can be supplied to the armature before the onset of irreversible demagnetization is calculated using (10). 13) Predict the Temperature Rise: The temperature rise of the armature winding is estimated from a knowledge of the total loss, the frame surface area and a value of dissipation ( K D ~Ultimately, ). the temperature rise limits the continuously rated output torque of the motor. 14) Analyze the Commutation Performance: The commutation performance is analysed by calculating the reactance voltage of the coil undergoing commutation (Section 11-C). D. Performance at a Singly Defined Operating Point The Run Simulation option is used to calculate the performance at singly defined operating point on the torque-speed characteristic. The armature voltage and current waveforms are calculated and can be viewed. Fig. 11 shows voltage and current waveforms for the motor shown in Fig. 7, when driven from a 2-kHz chopper running at 50% duty cycle. The two characteristics shown in the top section of the graph are the 50% duty cycle supply voltage waveform and the back-EMF waveform. The characteristic shown in the central section of the graph is the armature voltage waveform, which is identical to the supply voltage waveform in this case. This is because the armature current is continuous with time (no zero component), which is shown in the bottom section of the graph. If the armature current is discontinuous with time (having a zero component), the armature voltage is equal to back-EMF during periods when both the supply voltage and armature current are zero. This is in fact the case in Fig. 12, which shows the voltage and current waveforms for the motor shown in Fig. 7, operating from a semi-converter phase controller. The phase controller has a 90" firing angle (turn-on angle) and the same average voltage and speed as the previous chopper calculation. E. The Torque Speed Characteristic When calculating the torque-speed characteristic of the motor and drive, a range of voltages (dc supply), duty cycles 939 (chopper), or firing angles (converters) can be selected and multiple characteristics plotted on the same graph. Fig. 14 shows the torque-speed characteristic for the motor shown in Fig. 7 when supplied from a 100-V, 2-kHz chopper drive with the duty cycle ranging from 50% to 100% in 10% increments. The characteristics are virtually linear and equally spaced. The slight deviation from a purely linear characteristic is due to the fact that friction, windage, and iron losses vary with speed, and brush loss varies with armature current. In order to account for armature reaction, a magnetic lumped circuit much more complex than that shown in Fig. 1 is required, and this results in a multi-fold increase in computation time. Armature reaction is not calculated in the present version of PC-DCM as the speed of response must be fast enough for true interactive use. However, with the increased availability of high-speed 486 E ' s , it may be possible to include a more complex lumped circuit model in the future. In Fig. 14, there is a discontinuity near no-load due to the armature current becoming discontinuous [ 151. Fig. 15 shows the torque-speed characteristics for the same motor as used in Fig. 14, but operated from a 157 V-Peak (100 V-Mean at 0" firing angle), 50-Hz Semi-converter phase controller. Calculations were performed at firing angles equal to O", 15", 30°, 4 5 O , 60°, 75", and 90". In this case, the torque-speed characteristics are far from linear over much of their section. This is due to the fact that the armature current is discontinuous over much of the torque-speed characteristic [15], as shown in Fig. 12. The discontinuous current is mainly due to the low frequency of the drive, but is also a function of the armature inductance, which is relatively low in permanent magnet motors due to the large effective airgap. The spacing between individual torque-speed characteristics is also far from constant and is due to the nonlinear variation in average voltage with firing angle. F. The Sizing Routine When starting a completely new design, the designer has the option of running a sizing routine. A sizing template editor is used to define the parameters required by the routine. These include: the required torque and speed, the frame diameter and length constraints, the allowable temperature rise, the frame dissipation, component flux density levels, frame and magnet overhang factors, expected full-load current form-factor, and demagnetization constraints. The appropriate magnet, steel, and brush materials must also be selected. The sizing algorithm is then run. The sizing routine is a nested-loop iterative solver, with the outer loop setting current loading, itself dependent upon the allowable temperature rise, total losses, and the frame dissipation figure. Central to the operation of the routine is the D 2 L equation. In the first iteration, rough estimates of B and Q are made. Using (1) and a value of D,/L,, the first estimates of D, and L, are calculated. The magnetic circuit shown in Fig. 1 determines the tooth to slot width ratio and the frame dimensions. The magnet thickness is determined by the demagnetization constraints. Once the motor dimensions have been set, the winding design and losses can be calculated. IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 31, NO. 4, JULYIAUGUST 1995 940 Gowing the total loss, an estimate of the temperature rise is then made. If this is larger than the specified requirement, Q is adjusted appropriately- In the second iteration, the calculated values of B and Q are fed into (1) and the new values of D~ and L, calculated (with account taken for the frame constraints). Within a few iterations, a stable solution should be obtained. At this stage, the user should check the design using the full computational capabilities of PC-DCM. [ l l ] T. J. E. Miller and M. I. McGilp, “Nonlinear theory of the switched reluctance motor for rapid computer-aided design,” Proc. IEE, vol. 137, Pt.B, no. 6, pp. 337-347, Nov. 1990. “High-speed CAD for brushless motor drives,” EPE Firenze, [12] -, vol. 3, pp. 435439, 1991. 1131 G. Qishan and G . Hongzaan, “Slotted permanent magnet machines,” Electrical Machines and Power Syst., pp. 273-284, Oct. 1985. (141 J, Banige, G , m i t e , and C, Tufts, ‘ m e design and application of ceramic magnets for dc permanent magnet motors,” Magnets In-YourFuture, Oct. 1986. [ 151 P. C. Sen, Thyristor DC Drives. New York: Wiley-Intencience, I98 I . Iv. DISCUSSION AND CONCLUSION The software-engineeringcontent of motor design continues to expand. Powerful programs based on the finite-element method, capable of electromagnetic, thermal, and mechanical analysis are increasingly used to improve old designs or generate new ones. Generic simulation packages complement these tools with the simulation of the power electronic and digital or analog controllers. In this environment there is an important role for simpler “sizing” software to prepare preliminary designs, and it is all to the good if such sizing programs integrate a range of capabilities covering the electromagnetic as well as the control aspects. While accuracy is not the primary requirement, speed of execution is paramount, together with the flexibility to evaluate a wide range of design options and parameter variations. The dc commutator motor design program PC-DCM includes many of the basic design calculations normally performed in preparing a new design. The speed and ease with which design variations can be undertaken gives a completely new dimension to the design process, and it compresses the time to produce a design from days into hours. REFERENCES [I] M. G. Say, Direct Current Machines. New York: Pitman, 1980. [2] A. F. Puchstein, The Design of Small DC Motors. New York: Wiley, 1961. [3] A. E. Clayton, The Performance and Design of DC Machines. New York: Pitman, 1959. [4] I. J. Williams, “Why permanent magnet? An introduction to a new range of permanent magnet dc motors,’’ G.E.C.J. for Ind., vol. 7, no. 3, Oct. 1983. J. R. Ireland, Ceramic Permanent Magnet Motors-Electrical and Magnetic Design and Applications. New York McGraw-Hill, 1968. D. A. Staton, “CAD of permanent magnet dc motors for industrial drives,” Ph.D. thesis, University of Sheffield, England, Aug. 1988. I. J. Williams, T. S. Birch, D. Howe, and D. A. Staton, “Computeraided design of permanent magnet dc motors,” Contr./Morors/Drives Con&, 1985, pp. 29-35. 181 D. A. Staton, M. I. McGilp, T. J. E. Miller, and G. Gray, “High-speed PC-based CAD for motor design,” EPE Brighton, vol. 6, pp. 2 6 3 1 , 1993. M. A. Jabbar, “Design and operational aspects of high-speed appliance motors using ceramic magnets, electric machines and drives,” IEE Cof, London, Publication no. 282, pp. 311-315, Nov. 1987. D. B. Jones, “Computer simulations compare brush and brushless dc motor designs for high power density applications,” PCIM, pp. 20-34, June 1988. David A. Staton was born in Chesterfield, England, on July 29, 1961. He received the B.Sc. (Hons.) degree in electrical and electronic engineering from Trent Polytechnic, Nottingham, England, in 1983, and the Ph.D. degree from the University of Sheffield, England, in 1988. From 1977 to 1984, he was employed by British Coal, who sponsored him while he was undertaking the B.Sc. degree. While at the University of Sheffield, he developed CAD software for permanent-magnet dc motors in collaboration with GEC Electromotors Ltd. From 1988 to 1989, he was with Thorn EM1 Central Research Laboratories, and was engaged in the design of motors for the Kenwood range of food processors. Since 1989, he has been employed as a research fellow in the SPEED Laboratory, University of Glasgow, Scotland. His research interests are in the computer-aided design of permanent-magnet and reluctance motors. Malcolm I. McGilp was born in Helensburgh, Scotland, on March 12, 1965. He received the B.Eng. (Hons.) degree in electronic systems and microcomputer engineering from the University of Glasgow, Scotland, in 1987. He has been a research assistant in the SPEED Laboratory, University of Glasgow, since 1987, mainly working on computer-aided design of electric drives and power electronic circuit analysis. %?’ Currently, he is working on creating engineercomputer interfaces for SPEED software and for interfacing SPEED software to other engineering applications. Timothy J. E. Miller (M’7&SM’82) ) is a native of Wigan, U.K. He was educated at Atlantic College, and the University of Glasgow and the University of Leeds. . He had a student apprenticeship with Tube Investments Ltd. From 1979 to 1986, he was an Electrical Engineer and Program Manager at General Electric Corporate Research and Development, Schenectady, NY. His industrial experience includes periods with GEC (UK), British Gas, ana International Research and Development. He is currently Lucas Professor in Power Electronics, and founder and Director of the SPEED Laboratory, University of Glasgow, Scotland. He is the author of 105 publications in the fields of motors, drives, power systems, and power electronics. Dr. Miller is a Fellow of the Royal Society of Edinburgh, Fellow of the IEE, and a member of Ivy CC, Glasgow.