George P. Gogue
Dan Jones


The brushless dc (bldc) motor is now being used in a number of high performance applications where motor speeds of 10,000 to 30,000 rpm are being achieved. The impact of iron or core losses due to eddy currents cannot be ignored and must be included in any design procedure for these high speed applications.

This paper will compare the various design tradeoffs of the internal motor losses in small bldc motors, specifically a 2.0" OD and a 3.0" OD brushless dc motor, when operating at high speeds. These losses include eddy current, hysteresis and copper losses.

The results will be presented and a number of computer simulation solutions will be shown. These will be used in optimizing different performance parameters. Some of these results will be matched to various applications in the US Market.

The impact of the motor's thermal performance will limit the actual dissipated power that the brushless dc motor can achieve. A series of thermal resistance targets will be established which will be used as practical limits to the motor's ability (or inability) to dissipate heat.


The brushless motor in this investigation uses Neodymium iron magnets. The magnets and the steel core are mounted directly on the shaft. The magnet configuration is an arc segment. 4 pole and 8 pole designs of various rotor diameters will be simulated and analyzed.

The laminated stator stack surrounds the rotor and carries the winding. Carbon steel is used in the core, and silicon steel or nickel-iron is used in the stator lamination. A 24 slot lamination pattern was selected as the "universal" pattern to achieve an integral tooth pitch for purposes of this paper. A full slot pitch skew was employed to reduce cogging only as a normal design practice. A 27 slot 8 pole lamination pattern was initially investigated as a lower cogging solution but was not used.

Different types of silicon steel and nickel-iron are used in this investigation to study the effect on the iron losses. Several winding configurations are used with the various combinations of poles and teeth. Constant adjusting of winding turns and wire size are accomplished to keep the copper volume as close to the 40% value of copper fill as possible.

The 40% value relates the actual copper wire fill of the uncoated stator slot to the

theoretical fill. There is no winding factor which relates the lay of the wire and the number of insulated copper wire crossovers. This can be accounted for by not allowing a fill factor above 50% in most designs. The 40% fill selected is a comfortable value that can be readily machine wound.


The work that follows was done using a design program written with electromagnetic formulae and electrical circuit analogies. A detailed description can be found in a previous paper (Ref. 1). This program employs a lumped reluctance model that identifies the reluctance values of each soft iron member and uses a computed value to establish iron losses. Leakage flux is estimated. The second quadrant permeance slope is computed. The magnet airgap flux is determined and then the motor's soft iron members are checked for saturation. If any silicon iron members exceed 17.5 kG (1.75 Tesla) or nickel-iron exceeds 14.0 kG (1.4 Tesla), the soft iron member cross section is increased, and the solution is rerun. The winding pattern, turns and wire size are then selected, and the motor's performance parameters are computed.

The program has since been expanded to include calculation of iron losses as well as other losses. Calculations of detent torque and inductance have also been added to the program but will not be discussed here.

The software is written for personal computers and is intended to facilitate changes in parameters. Results are either tabulated or plotted in bar or curve form. Typical solution time with PC-AT computer hardware is less than 1 minute. Total simulation time including input and printout is less than 5 minutes per run. There is also a Finite Element Methods Program (FEM) that is used to achieve greater solution accuracies. Total simulation time is between 8 to 10 hours.


The design of an electric motor is an intensely complicated affair, particularly if one wants to single out one parameter such as iron losses. It is quite possible that an unacceptable motor design will result if one does not focus on a number of motor parameters during the design phase. A number of general design parameters must be fixed in order to achieve a workable design. Figure 1 outlines these general parameters for both 2.0" OD and 3.0" OD bldc motors. There are also a number of mechanical parameters that are controlled such as the housing, tooth and back iron flux densities, magnet arc width in degrees and slot copper fill.

Figure 1

The load currents are the current limit values. This is established by developing a thermal resistance in degree C/watt while the motor is bolted to a large-aluminum heat sink. Reference (2) describes the various methods to establishing the motor's thermal resistance. The thermal resistance times the copper loss (dissipated power) establishes the temperature rise of the motor. The values established are held constant for all calculations.

Supply voltage is selected as a typical value for bldc motors used in high speed applications. The peak current values are theoretical values only. The output power values and load torque values were maximized whenever possible.


The iron losses consist of two basic components: hysteresis and eddy current. These two components vary differently with frequency and flux-density. The following equations demonstrate that:


= hysteresis loss (W/kg)

= hysteresis constant

B = flux-density (T)

= eddy current loss (W/kg)

= eddy current constant

f = frequency (Hz)

t = thickness (mm)

Catalogs on steel from US suppliers hardly ever separate the iron or core losses into hysteresis and eddy current. Instead, loss curves are usually given versus the flux density (at a fixed value of frequency). Since hysteresis loss varies with motor switching frequency (f) and eddy current loss with , it has been found that the total loss varies with where y is between 1.2 and 1.8, depending on the type of iron or steel. For ease of calculation and in order to increase the margin of safe operation, y can be assumed to be 2. Figure 2 gives the properties of some of the most popular steels used as laminations (Ref. 3).

Figure 2

The core or iron loss vs. flux density of M6 is illustrated in Figure 3 alongside the M19 through M50 silicon steels (Ref. 4). The core loss for nickel-iron, type 4750 is shown in Figure 4.

Figure 3

Figure 4

The comparison shows lower losses for the M6 material and this is not totally due to the thinner steel represented by this curve. These curves are approximated to straight lines for certain ranges of flux density. For example, between 8 and 18 kG, the core loss in W/lb for M6 is as follows:

High speed operation gives rise to additional losses which are otherwise negligible:

a. Skin effect causes an increase in the hysteresis loss at the surface of the lamination. These same effects result in an increase in the eddy-current losses by reducing the effective area.

b. Slot harmonics when one member is slotted, introduce flux-ripple. This sets up additional hysteresis losses as the amount of flux and its local path change with rotation.

c. The manufacturing process of the lamination can also increase the iron losses by 10-15%. The mechanical stresses responsible can be reduced by annealing the steel after punching.

d. Ironically, the same desirable flat-topped emf (and flux) waveforms for optimized performance of bldc motors give rise to additional eddy current losses. This is owing to the fact that the harmonic contents of the flux-waveform produce losses in addition to those caused by the fundamental waveform.

It is prudent in the course of designing a high speed bldc motor to give due attention to the above secondary issues. Any mathematical method for calculating these effects quickly becomes complicated and a victim of many assumed factors and empirical formulae.


The magnetic circuit is divided into several sections, each having a different value of flux-density. The teeth are assumed parallel sided for ease of calculation. The flux-density in all parts of the teeth is assumed constant. A refinement of thin calculation would be to calculate the loss in the tooth tip separately from the body of the tooth. This would account for the effect of higher flux-density in the tooth tips. The value of flux-density in the lamination core is much more difficult to assess. In the absence of analysis techniques such as the finite element method (FEM), the flux densities are determined by calculation at different sections of the core. This calculation requires estimating the cross-sectional areas of the path of flux. It also requires a knowledge of how flux travels through the core. This depends greatly on the combinations of poles and teeth.

The actual computer printout is divided into 3 parts. The first part computes the magnet permeance slope. The second part checks the magnetic circuit values, computes the basic winding parameters and then the motor performance parameters. Figure 5A, B, and C show a single printout format. Since over 60 simulations were done, a series of summary charts were created listing the salient parameters.

Figure 5A

Figure 5B

Figure 5C

The variables are listed below:

1. Different lamination materials; M6, M19, M36 silicon steel and 4750 nickel-iron

2. Different rotor diameters:

0.7" to 1.1" for 2" motor

1.3" to 1.7" for 3" motor

3. Different number of poles: 4 and 8.

Figures 6 through 11 are a sampling of the simulations, with Figure 6 displaying the five simulations of the M6 4 pole 3.0' OD bldc motor. Figure 7 summarizes the five simulations of the M19 4 pole 3.0" OD bldc motor. Figure 8 shows the five simulations of the M36, 8 pole, 3.0" OD bldc motor.

Figure 6

Figure 7

Figure 8

The same selection of simulations (Figures 9, 10 and 11) were selected from the simulations run on the 2.0" OD bldc motor. The 4750 simulations indicate the superiority of the 4750 material even with the lower iron saturation values. Figure 12 displays the results in terms of losses.

Figure 9

Figure 10

Figure 11

Figure 12

The various simulations will demonstrate which combinations of poles, lamination materials and rotor diameter are the best. The major design target is the lowest combination of dissipated power and core loss.


The major emphasis is on achieving the lowest possible core loss. The change in rotor OD changes the relationship of copper to iron/magnet ratio. A larger rotor OD will reduce the copper volume but will result in a larger magnet volume. Typically, a smaller rotor OD is the selection for an incremental motion application. The torque to inertia (T/J) ratio is less important for these high performance systems.

The lowest iron loss and the highest output power are the desired simulation outputs. Figure 13 defines the components of the total power loss for the 3.0" OD bldc motor. The 4 pole, 4750 simulation is by far the lowest with the 8 pole M36 the highest. The results of the 2.0" OD show the same pattern in terms of number of poles and lamination material (Figures 14A, B, C and D).

Figure 13A

Figure 13B

Figure 13C

Figure 13D

Figure 14A

Figure 14B

Figure 14C

Figure 14D

The best unit in terms of efficiency (i.e. output power divided by total input power at the current limit or load point) is the 4 pole 4750, 1.5" rotor OD version of the 3.0" OD bldc motor and the 4 pole 4750 0.9" rotor OD version of the 2.0" OD bldc motor. The M6 material in both 4 pole configurations is a somewhat distant second choice to the nickel-iron (type 4750). The directionality of the oriented M6 material will require automatic indexing of the lams to significantly reduce this effect. Figure 15 yields an excellent comparison of the core loss and copper winding loss for all lamination materials used in the 3.0" OD bldc motor. The copper loss for the various simulations was relatively fixed by the current limit condition and the motor phase resistance. The 2.0" OD motor core and winding losses are shown in Figure 16. Note the nickel-iron type 4750 performance.

Figure 15

Figure 16


The results indicate that the material selection is all important in achieving the lowest iron and copper loss combinations. The number of poles is next in importance within the silicon iron family. The lamination thickness was set at .014 and .018 inches, which are readily available in the US as standard gauge. These two thicknesses were used because there was some available core loss data from the US Suppliers. Thinner laminations were not considered because of much higher costs. The motor geometry in terms of rotor OD with a fixed magnet material and copper fill had the least effect. One can select for secondary conditions either lower copper mass (higher rotor OD values) or higher power rates and theoretical acceleration values (lower rotor OD Values).

This simulation program has been utilized for a number of designs in the area of precision laser measuring of magnetic media and high speed drilling applications where high speed, wide speed range and high performance velocity control are required.

There is one sobering condition that the authors encountered when trying to obtain further data on the various silicon steel and nickel iron lamination materials. Most information available on this material is old and of a very limited nature. We could not obtain data on most of the materials as a function of lamination thickness, beyond a few popular material thicknesses. We also found it difficult to obtain data on core or iron loss as a function of frequency. The basic motor winding switching frequencies at 8 pole and 15,000 rpm load speed will reach 1000 Hz.

It is certainly of some concern to realize that most of the data used on material magnetic performance was at least 15 years old and in many cases 20 years or older. It is hoped that soft iron and specialty steel manufacturers in the US will begin a program of testing based on a market requirement to use these materials at higher motor speeds and frequencies.

9. References

1. Dan Jones, "Motor Magnetics Design Changes in Higher Energy Rare-Earth PM dc Motors," Motorcon, Chicago, IL, October 1985.

2. An Engineering Handbook by ElectroCraft Corp. - "DC Motors Speed Controls, Servo Systems and Encoders," Sixth Edition, 1983.

3. Electrical Materials Handbook, Allegheny Ludlum Steel Corporation, Pittsburgh 22, Pennsylvania; 1961

4. TEMPEL Motor Lamination Catalog, TEMPEL STEEL, Niles, Illinois.

5. Specialty Steels Technical Data, Carpenter Technology Corp.

6. Armco Oriental Electrical Steel Handbook, Ninth Edition, Armco Inc., Middletown, Ohio; 1979.