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ELECTRIC MACHINE DESIGN USING SPEED AND MOTOR-CAD T.J.E. Miller and D.A. Staton


Authors' Note Electric Machine Design is one of the key engineering skills in the modern world, essential in the generation of electricity and its use in appliances, vehicles of all kinds, industrial machinery, and many other applications. Yet the art is taught in very few colleges; there is a worldwide scarcity of designers; and the theoretical background is difficult to acquire without years of specialized study. In this book two of the most experienced authors in the field have combined to present a practical guide to the design of electric machines using the SPEED and Motor-CAD software packages, which were written to work together, one for the electromagnetic and the other for the thermal aspects. No fewer than ten different machine types are introduced, starting in each case from a simple specification and proceeding through to a credible prototype. Rules of thumb and basic engineering principles are used throughout, to guide and inform the design process, and ample reference is made to the extensive documentation of both SPEED and Motor-CAD for a deeper theoretical understanding. The book has been used and tested in training classes in the United States, Japan, and Europe. It can be used as a course text, either in intensive sessions covering up to 10 days of instruction; or as a self-study text in conjunction with the SPEED and Motor-CAD software. We have chosen the "print-on-demand" route with wire-binding to ensure that Electric Machine using SPEED and Motor-CAD fits comfortably on the desk beside your computer, and is readily updated as the software itself develops.

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This book is dedicated to Jimmy Kelly

As a technician in the mechanical engineering workshop at the University of Glasgow, Jimmy Kelly built most of the test rigs and prototype motors on which SPEED was built over a 25-year period. The workshop is in the James Watt building, and anyone visiting the university may see the huge carved relief on the south wall facing the Clyde, celebrating the practical art of the craftsman and engineer. This fine monument is a tribute to those whose genius is expressed through their hands, and perhaps a reminder that engineering is about making things.

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Preface This book is a primer for engineers learning to design electric machines using SPEED and Motor-CAD. It can be used in two ways: •

SPEED and Motor-CAD are designed to work together. They were written by the same family of engineers. The authors understand the main requirements in this type of design software:

as part of a SPEED or Motor-CAD training course. Individual chapters can be used for the design sessions that are so popular in the training courses. If you have the book in advance, you can prepare the example on your lap-top for each day of the training. This is the best way. It means you will arrive at the class with momentum and questions. When the class is prepared, it becomes possible to go into more detail on the advanced features of the programs, and to take the design examples further.

it must be fast

it must rely on the engineering theory, — not just the physics

it must be documented and supported almost without limit.

The book is not a reference book where you can “look something up”; that is the rôle of the reference manuals. (SPEED tutorials fall somewhere in the middle: they provide step-bystep instructions to particular procedures, but they contain no design guidance and they do not form a coherent approach to design).

for self-study. The book is designed for this. You can therefore use it as a substitute for the training course. However, please recognize that the book is short and introductory. It prepares the ground for more advanced work. If you prefer to work alone, you will find plenty of advanced documentation in the tutorials, the reference manuals, and SPEED’s Electric Machines to take you further into the capabilities of SPEED and Motor-CAD.

The book is an introduction, covering only the most elementary aspects of each design. Many advanced concepts, parameters, and methods available in SPEED and Motor-CAD are not mentioned here; some of them will be covered in training courses, but ultimately the reader should refer to SPEED’s Electric Machines (SEM) and the reference manuals, and interact with the original SPEED/Motor-CAD authors.

The book is organized as a collection of short “design stories”. Each design example is developed from scratch in the same step-by-step way we use in the SPEED training classes. Each chapter is self-contained, and you can read lineby-line while executing the program.

The book provides a little theory, but it is not a substitute for proper training in the theory of electrical machines. Engineers who are qualified in this field will recognize the theoretical principles described here, and they will see the logic of the calculations more clearly. For a fuller account of machine and drive theory, consult SPEED’s Electric Machines (SEM), or the Green Book (GB), [1].

You should achieve the same results as those displayed in the book, and soon you’ll be able to improve on them. Most of the keystrokes for the SPEED part of each chapter are tabulated in the Appendix. You can use these tables to recover quickly if something goes wrong. Instructors can use them for the same purpose.

For the SPEED interface, the WinSPEED manual is recommended. Parenthetic interjections are irresistible in a technical book, so we use references [], footnotes, and doubly-indented paragraphs like the next one. Some of these are introduced with the somewhat precocious words “Design wisdom”. Here are two examples:

Each chapter except chapter 11 has a thermal section. Once the design is established with SPEED, we pass it to Motor-CAD to begin the design for cooling and heat transfer.

Design wisdom — e = L di/dt is not Faraday’s law. It’s only half of it. If that was all there was to Faraday’s law, we wouldn’t have any electric machines, or even any transformers. (We might have a few chokes and rinky-dink inductors).

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Design wisdom — Minor variations in results may arise with different versions. They will generally be unimportant. But it is also possible for one incorrect parameter to ruin the entire calculation or even prevent the program from working. Computer programs are inflexible and curmudgeonly, and always contain errors, so if there is a problem and you are sure your data is correct, contact your technical support engineer. The units used in this book are predominantly metric (mm, Nm, etc), as a reluctant concession to the metric majority, and as a mark of respect for the unarguable virtue of conformity in engineering units. However, TJEM’s preference is the English or Imperial system of units, (partly because of the familiar appropriateness of scale, and partly because of the power of fractions.

For example, 1½ pounds per square inch seems easier than 20,700 newtons per square metre). So inches and other English units appear here and there, often in places where points can be scored against the awkwardness of SI units. Alas, the shaku is not used in this book, but it would be fun to try it.

Design wisdom — In a mathematical equation, units are strictly superfluous. In an engineering equation, units are a sine qua non. modulation), RMS (root-mean-square), and p.u. (per-unit). But PM (permanent-magnet) is used sparingly (to avoid confusion with Prime Minister, or post meridiem. The TEMPLATE EDITOR is referred to as Ted (though Hid might be more descriptive), and individual pages by the form Ted/Electrical, etc. Latin phrases such as mutatis mutandis, ad hoc, etc. are used wherever possible— the Romans were engineers too, and they are still around.

The SPEED part of the book refers to the program functions using short-cut keys, and only occasionally spells out the full menu item. For example, Static design is executed using [Ctrl+2], which is more concise and efficient than the cumbersome menu descriptor [Analysis | Static design]. It is recommended to learn the short-cut keys, especially the main ones. The WinSPEED manual provides a list of them, but they appear on the menus, so the only excuse for not using them is laziness.

Notation: Parameter names in SPEED are generally limited to 8 characters. There is no consistent naming convention, and there are significant differences in nomenclature between the individual SPEED programs (mainly because the originals were written at different times). T can mean torque or temperature; R can mean radius or resistance. W is often used for losses in watts (having a connotation of “waste”); but it might also mean width. Both prefixes and suffices are used, often inconsistently: for example, you might find wSlot or SlotWid both referring to the width of a slot.

Fonts: This work is set in 10pt Nimrod MT to save paper, and because of its kerning qualities in equations. Boldface is used for parameters appearing in the SPEED programs, such as Rad1 or Tph. The equivalent mathematical descriptor may be written in the classical form, so Tph becomes Tph. Non-numerical parameter values are written in ordinary type, as for example in Drive = Square. In this example, Drive is the parameter name, and “Square” is the value which will appear in the edit field in the TEMPLATE EDITOR, Ted. Menu items are written in boldface sans-serif, e.g., Analysis | Static design. Short-cut keys are written in boldface enclosed in brackets: [Ctrl+1]. Italics are used for emphasis or for special terms like Dynamic design, which is a complete process, not simply a menu item. Main SPEED windows are in small caps, e.g., DESIGN SHEET, WINDING EDITOR.

Learn the parameter names (and their meanings, which are given in the reference manuals). Don’t guess. A smart programmer might be tempted to rationalise it all, creating even greater chaos, for the SPEED documentation will never be rationalised in this way. The mathematical conventions are followed more faithfully: for example, lower-case letters are used for instantaneous quantities like v or i, while boldface is used for phasors, which are complex: thus V or I.

Abbreviations: Generally acronyms are deprecated, except classical ones, e.g. “i.e.”. It would be churlish not to use common engineering abbreviations like PWM (pulse-width

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Upper-case italic is generally used for average quantities such as T for torque, but one cannot rely solely on the notation and one must get the detailed meaning of parameters from the equations and the context (or from SEM or the manuals).

In the Motor-CAD sections, menu items are set in the same sans-serif font as in the SPEED sections; e.g., Geometry | Radial. Likewise the parameter names are set in boldface type ; e.g., Slot Opening. In Motor-CAD the parameter names are not restricted to 8 characters, and they may even appear more like phrases with a small degree of abbreviation, e.g., Housing Outer Cooling = Natural Convection, or Housing  Ohang [F/R] = 0. The abbreviation [F/R] means “front” or “rear”. The front end generally is the drive end, and it appears at the left-hand side of the window in Geometry | Axial.

In SPEED, the parameters are entered and then a specific calculation is deliberately executed from the Analysis menu or one of the other utility menus such as the Tools menu. In Motor-CAD, the calculation is executed automatically when the relevant “results tab” is opened, for example, Temperatures or Transient.

Blind cornering — Electric machine design involves guesswork and rules of thumb, techniques well known to engineers (in spite of their often-quoted sardonic disapproval). Anyone who loves motorcycles will know about blind cornering, but it is part and parcel of the creative engineering process : venturing into the unknown. So to keep this in mind, we will occasionally refer to certain design decisions as blind cornering. With a new design, or a new type of motor, or even a new engineer, we may have no idea of the design procedure (or even if one exists). We can often get started by running SPEED to see what we get, and then use engineering common-sense and well-established principles to modify the design in the right direction.

The “engineering common-sense and wellestablished principles” are learned by analysis of test data and calculations. The computer helps with the calculations, but we must do the rest. Almost certainly this book contains errors. If you find any, please let us know.

Acknowledgements SPEED and Motor-CAD form part of the electric machine design community. This is a close-knit worldwide community, and anyone who uses this book will be a part of that community. Particular recognition should be given to Malcolm McGilp, the software engineer who designed the SPEED software architecture; Dougie Hawkins (Motor-CAD software manager); and Mircea Olaru, the author of PC-FEA.

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CONTENTS 1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Rules of thumb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Fundamental laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3 Guiding principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.4 SPEED and Motor-CAD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.5 How this book works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.6 The SPEED system — basic design process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.7 The SPEED system — features, functions, and auxiliaries . . . . . . . . . . . . . . . . . . 5 1.8 Motor-CAD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.9 SPEED and Motor-CAD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.10 SPEED and Finite-Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.11 Scripting, automation, optimization, and links . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.12 Documentation, help, training, support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2

Brushless DC Permanent-Magnet Motor with Squarewave Drive . . . . . . . . . . . 9 2.1 Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Initial sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Starting PC-BDC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4 The numbers of slots and poles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.5 Dimensions again . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.6 The winding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.7 Selecting materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.8 Setting the controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.9 Performance calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.10 Static design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.11 The design sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.12 Custom output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.13 Dynamic design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.14 Next steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.15 Finite-element analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.16 Effect of temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.17 Demagnetization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.18 Cogging torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.19 Setting up the thermal analysis with Motor-CAD . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.20 Thermal calculations using Motor-CAD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

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Interior-Permanent-Magnet Motor (IPM) with Sinewave Drive . . . . . . . . . . . 37 3.1 Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.2 Initial sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.3 Starting PC-BDC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.4 Engineering changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.5 Winding editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.6 Selecting materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.7 Estimating the number of turns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.8 Setting up the performance calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.9 Initial performance calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.10 Estimating the power available at 6,000 rpm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.11 Some of the many things we have not done . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.12 Setting up the thermal analysis with Motor-CAD . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.13 Steady-state thermal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.14 Transient Duty-Cycle Thermal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.15 Conduction Heat Transfer in Slot Using Finite-Element Analysis . . . . . . . . . . . 60 -ix-


4

Synchronous Reluctance Motor with Sinewave Drive . . . . . . . . . . . . . . . . . . . 63 4.1 Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.2 Initial sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.3 Starting PC-BDC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.4 No magnets! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.5 The stator winding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.6 Estimating the number of turns per coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.7 Wire size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.8 Selecting materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.9 Setting up the first calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.10 Setting up the thermal analysis with Motor-CAD . . . . . . . . . . . . . . . . . . . . . . . . . 75 4.11 Steady-State Thermal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

5

3-Phase Induction Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.1 Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.2 Initial sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.3 Starting PC-IMD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.4 Initial sizing and dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 5.5 Rotor design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.6 Stator winding layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.7 Determining the number of turns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.8 Selecting materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.9 Setting up the first test calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 5.10 Operation at high speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.11 Checking the flux-densities with PC-FEA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.12 Other parameters to consider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.13 Setting up the thermal analysis with Motor-CAD . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.14 Steady-State Thermal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 5.15 Fin Spacing Optimisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

6

Single-Phase Induction Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6.1 Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6.2 Starting PC-IMD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6.3 Stator winding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6.4 Estimating the number of turns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6.5 Selecting materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.6 Setting up the operating point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.7 Torque/speed characteristic and steady-state operation . . . . . . . . . . . . . . . . . . 102 6.8 Further aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 6.9 Setting up the thermal analysis with Motor-CAD . . . . . . . . . . . . . . . . . . . . . . . . 105 6.10 Steady-State Thermal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 6.11 Further Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

7

PM DC Commutator Motor (Brush motor) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 7.1 Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 7.2 Initial sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 7.3 The armature winding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 7.4 Determining the turns/coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 7.5 Selecting materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 7.6 Initial calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 7.7 Engineering changes required to meet the specification . . . . . . . . . . . . . . . . . . 120 7.8 Precise kE, or the simple formula? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 7.9 Nominal performance calculation (still with high friction) . . . . . . . . . . . . . . . 121 7.10 Calculation and graphical display of the torque/speed characteristic . . . . . . 122 7.11 Setting up the thermal analysis with Motor-CAD . . . . . . . . . . . . . . . . . . . . . . . . 123 -x-


7.12 7.13 7.14

Steady-State Thermal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 Transient thermal analysis (Stall) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Rating test using a flange-mounted plate as a heatsink . . . . . . . . . . . . . . . . . . . 127

8

AC Universal Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 8.1 Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 8.2 Initial sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 8.3 Preliminary changes to the geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 8.4 The armature winding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 8.5 Selecting materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 8.6 Setting the controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 8.7 Setting up the first test calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 8.8 Torque/speed characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 8.9 Operation at 1,500 rpm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 8.10 Setting up the thermal analysis with Motor-CAD . . . . . . . . . . . . . . . . . . . . . . . . 143 8.11 Transient heating of the rotor winding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

9

Switched Reluctance Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 9.1 Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 9.2 Initial sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 9.3 Initial performance calculation — low speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 9.4 Calculation at the high-speed point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 9.5 Checking the low-speed operation again . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 9.6 Setting up the thermal analysis with Motor-CAD . . . . . . . . . . . . . . . . . . . . . . . . 156 9.7 Duty-cycle analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

10

Salient-Pole Wound-Field Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 10.1 Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 10.2 Initial sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 10.3 Starting PC-BDC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 10.4 Engineering changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 10.5 The armature winding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 10.6 Determining the number of turns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 10.7 The field winding and the excitation current . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 10.8 Selecting materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 10.9 Setting up the controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 10.10 First calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 10.11 Harmonic analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 10.12 Generator characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 10.13 Load calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 10.14 Finite-element calculation — the single-load-point GoFER . . . . . . . . . . . . . . . . 176 10.15 Adding a damper (amortisseur) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 10.16 Short-circuit calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 10.17 Setting up the thermal analysis with Motor-CAD . . . . . . . . . . . . . . . . . . . . . . . . 179 10.18 Steady-state temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

11

Axial-flux machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 11.1 Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 11.2 Initial sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 11.3 Starting PC-AXM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 11.4 The winding editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 11.5 Selecting materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 11.6 Control settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 11.7 Static design calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 11.8 Dynamic design calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

-xi-


Appendix I : Main short-cut keys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 Appendix II : Summary of keystrokes and changes for each chapter . . . . . . . . . . . 205 Keystrokes Chapter 2 — Brushless PM Motor with Squarewave Drive . . . . . . . . . . . . 205 Keystrokes Chapter 3 — IPM Motor with Sinewave Drive . . . . . . . . . . . . . . . . . . . . . . . 207 Keystrokes Chapter 4 — Synchronous Reluctance Motor with Sinewave Drive . . . . 209 Keystrokes Chapter 5 — 3-Phase Induction Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 Keystrokes Chapter 6 — Single-Phase Induction Motor . . . . . . . . . . . . . . . . . . . . . . . . . 212 Keystrokes Chapter 7 — PM DC Commutator Motor (Brush Motor) . . . . . . . . . . . . . . . 213 Keystrokes Chapter 8 — AC Universal Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 Keystrokes Chapter 9 — Switched Reluctance Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 Keystrokes Chapter 10 — Wound-field AC Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 Appendix III : Typical values of TRV and airgap shear stress . . . . . . . . . . . . . . . . . 220 Appendix IV : Numbers of stator and rotor slots for small induction machines . . . 221 Appendix V : Options | General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 References and Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

-xii-


Electric Machine Design using SPEED and Motor-CAD

1

Introduction

1.1

Rules of thumb

There are many “rules of thumb” for designing electric machines, but no such rule applies in all cases. As an example, we have the idea that the pole-face of a synchronous machine should be roughly square.

Page 1

This idea has deep theoretical roots. It can sometimes be observed in production, though there are many more exceptions. It is an old idea, as we can see in Fig. 1.1.

Fig. 1.1 Crompton alternator, Walmsley

However, a square pole-face would not be suitable in a down-hole drilling motor, which must produce a huge torque with a severely limited diameter. Such motors may have a rotor diameter of a few inches, with an axial length measured in metres, so that with two poles the ratio of the axial length to the pole-arc is of the order of ten times the value that would give a “square pole”.

1.2

Fundamental laws

At the same time, there are fundamental physical laws that do apply rigorously in all cases, though not necessarily in an obvious way. One of the most basic laws of electric machines is Faraday’s law. A general form of it is expressed in terms of flux-linkage 5: v 

05 , 0t

(1.1)

but an engineer designing an AC machine is more likely to use

E  4#44 kw1 Tph 0m1 f

[V

RMS] .

(1.2)

Even the units of eqns. (1.1) and (1.2) are not the same. Eqn. (1.1) is in instantaneous volts, whereas eqn. (1.2) is in RMS volts. Moreover, eqn. (1.1) is always true in all circumstances, whereas eqn. (1.2) is true only when the flux-linkage of the winding is varying sinusoidally with time. The form of eqn. (1.1) is of limited use to the practical design engineer, even though eqn. (1.2) is derived from it. Conversely eqn. (1.2) is utterly useless outside the AC machine, or when the time variation of the winding flux-linkage is not sinusoidal. SPEED must use both forms: (1.1) for time-stepping simulation and for the underlying theory, and (1.2) for calculating E in a form that can readily be checked by the expression 4#44 * kw1 * Tph * PhiM1 * Freq1 which can be entered exactly in that format in the CALCULATOR, [F4].


Page 2

1.3

Electric Machine Design using SPEED and Motor-CAD

repeatedly and questioningly to the examples one encounters in the course of one’s work as a designer.

Guiding principles

The design engineer is thus faced with rules of thumb that don’t always work, and equations that may be applicable only in special cases. Nowadays s/he is also faced with software that may require a considerable learning period, making the overall learning process even more complicated. Additional complexities can arise because of interactions with power-electronics, control, protection, heat transfer, failure modes, manufacturability, production issues, material properties, costs, and many other factors.

Collect rules of thumb. Only experience will tell whether or not they are reliable. Some rules of thumb may yield their secrets to scientific analysis; but others will defy analysis, and in such cases they may be risky. They must necessarily be broken in many cases, but with scientific justification or experimental proof when this is possible.

What guidance can be given to design engineers (especially young design engineers) facing these complex challenges? The authors can do no more than offer a few points of advice based on their own experience, which covers 45 years of engagement in industrial companies and in the SPEED laboratory:

Measure and test everything in the lab. Spend as much time as possible on the factory floor.

Keep in shape. Do lots of practice. Read a lot. Study. Keep asking questions.

1.4

SPEED and Motor-CAD

Keep company with experienced engineers. This is by far the most valuable external source of wisdom and know-how. While personal experience and initiative is also important, no-one can encompass the subject alone, and “only a fool learns by his own mistakes”.1 Keep a firm grip on the fundamental physical principles such as Faraday’s law, and many others. In the authors' experience it seems that the top engineers always have an unshakeable grasp of the basics. They are rarely the ones who use sophisticated theories. They seem to be characteristically skilled in dealing with a mosaic of interacting factors, while being able to see the essential physical laws at work behind them. Often when something isn’t right, they will notice a conflict with one of the essential physical laws. For example, when one thing goes up, another goes down (especially when it shouldn’t). Such observations appear to be based on an almost intuitive grasp of the essential physical laws. But these laws are not actually intuitive. For centuries, great minds were frustrated searching for the “simple” laws of mechanics and electromagnetism. Therefore it is necessary to learn them, and to go on learning them, by applying them

1

This maxim should be relaxed for engineers. “Nothing ventured, nothing gained”.

SPEED and Motor-CAD are designed to help engineers who follow these principles. They collect many of the methods and calculations that designers do every day. These calculations are commonly done thousands of times during a design exercise, as different combinations of dimensions and parameters are changed in the search for an “optimum” design or even one that simply meets the requirements. For this reason SPEED and Motor-CAD are designed to be fast. Primarily one should think of SPEED and MotorCAD as a numerical and theoretical companion. In skilled hands, SPEED and Motor-CAD are capable of accurate and sophisticated design calculations. Both programs are primarily analytical, supported by PC-FEA for 2dimensional magnetostatic and thermal calculations. They can be used in conjunction with other specialist software — for example, FLUX™ for finite-element analysis, or STARCCM+™ for fluid flow. SPEED and Motor-CAD can be used for selflearning about electric machines, or as a tool in the teaching of electric machine performance and design. Until the publication of this book, the use of SPEED and Motor-CAD for these educational purposes was not documented, so this book is intended as a “grand tutorial” for most of the basic steps. Of course, much more can be found in the extensive internal documentation and the theory references and books.


Electric Machine Design using SPEED and Motor-CAD

Page 3

It teaches how to use SPEED and Motor-CAD, and it does this by example.

The narrative also contains elements of theory, by way of support for the design function without overwhelming it. For some calculations, the designer must know the theory.

In every example the objective is to design a machine to a specification. So the steps are set out in “do-this-do-that” fashion. The narrative includes a few comments about manufacturing practice, usually to explain or justify design decisions. Manufacturing practice varies widely, and it is beyond the scope of SPEED or MotorCAD to make pronouncements about it. The important thing is to recognize the interaction between theory on the one hand, and practical manufacturability on the other.

In each chapter, the SPEED marker appears in the margin at the point where the data is ready for export to Motor-CAD. If you are following the instructions step-by-step, this is where the export to Motor-CAD should be executed. Alternatively, save the file at this point for later use in MotorCAD.

1.5

How this book works

Fig. 1.2 The basic design process in SPEED

1.6

The SPEED system — basic design process

The SPEED system is shown in Fig. 1.2. At its core is the design loop process. We start with a Motor performance requirement, or a generator performance requirement. Design parameters are defined. These begin with physical dimensions, so there is an OUTLINE EDITOR where the dimensions can be specified. The OUTLINE EDITOR displays the cross-section in the transverse or longitudinal plane, and gives instant visualization of the design. Design parameters include electrical details of windings, and of the power supply and the controls. To assist in the layout and specification of the windings, the WINDING EDITOR provides immediate visualization of the winding layout.

The WINDING EDITOR also has many powerful analytical functions to help obtain a winding of the right quality and characteristics, and to analyze its winding factors, MMF harmonics, and phase sequence. Materials must be specified. To assist in material selection, a MATERIAL SELECTION DIALOG provides access to the materials databases (for steels, permanent magnets, and brushes). These databases can be populated and edited by the user, using the materials database editors on the Tools menu. Finally the TEMPLATE EDITOR is provided for design parameters related to the drive and control, and other program settings.

Design wisdom — the SPEED OUTLINE EDITOR helps to develop an eye for suitable proportions. We often refer to this as the “designer's eye”.


Page 4

Electric Machine Design using SPEED and Motor-CAD

Design wisdom — At the beginning of a design, a complete set of design parameters must be specified. A complete set of design parameters is just sufficient to define the machine and to run it at one or more more operating points.

The Performance calculation is the next main contribution that SPEED makes to the design process. We will see that there are many different types of performance calculation, but in all cases there is a definite Result in the form of a DESIGN SHEET and SIMULATION GRAPHS. The DESIGN SHEET is a complete set of data describing the performance at one operating point. It often contains several hundred numbers, collected into numbered sections.

In principle we have defined the basic design process : •

Machine specification

Definition of parameters

Performance calculation

However, it is extremely unlikely that the calculated performance will match the machine specification after only one pass. For this reason it is common to repeat the whole process, changing parameters in an orderly way, until the calculated performance does meet the machine specification. “In an orderly way” sounds simple. But there are so many parameters, and the relationships between them are often nonlinear or discontinuous. Some parameters can be varied continuously, while others can take only integer values. All parameters are subject to practical limits or constraints.

In fact the DESIGN SHEET is the complete collection of all input and output parameters, often far exceeding the few that are of immediate interest. SIMULATION GRAPHS include waveforms of current, voltage, torque, and other time-varying quantities. There are also numerous distributions (for example, flux-density in the airgap); special graphs such as energy-conversion loops and other operating loci; and graphical representations of equivalent circuits.

SPEED does nothing more than the performance calculation itself, so it falls to the designer, the user, to make the decisions about parameter changes. “In an orderly way” is really a paraphrase for the skill of the designer, in knowing what parameters to change, and by how much. “Repeat the whole process” also sounds simple, if tedious. SPEED provides two methods to assist the process of repetition : Ranging and Scripting. Ranging is a straightforward matter of varying one or more parameters synchronously, so that a graph can be plotted showing the variation of one or two parameters with each other. Scripting is much more powerful because it can employ SPEED as the calculating “engine” in a search or optimization process written in an external environment such as Excel™ or MATLAB.™ However, there is a danger that scripting can create data that is impractical or beyond the analysis capability of the program, so it should be used only by skilled designers.

Design wisdom — It is helpful to make up a CUSTOM DESIGN SHEET, or a CUSTOM OUTPUT panel, containing only the parameters of interest. See p. 21. The same applies to the TEMPLATE EDITOR; see p. 22. This is a good way to simplify the appearance of the program, and to collect all the parameters of immediate interest in one place.


Electric Machine Design using SPEED and Motor-CAD

FC-IV CONTROLLER

MACHINE INVERTER

Page 5

LOAD INVERTER

Gate drives Current

SPEED Reference

Resolver TORQUE

SPEED

Test Machine

Load Machine

Ldc iLdc Vs

iDC

Q1

ICdc 0

D1

Vt

VCdc

D3 Q3

D5 Q5

Cdc Q4

Q6

Q2

D4 Rdc

R_s

D6

D2

iRec iB

iA

iC

Lac Leads Rac v1

A i1

vAB B

C

i2

i3

Lph

Rph e1

e2

e3

Frame

Fig. 1.3 The SPEED system

1.7

The SPEED system — features, functions, and auxiliaries

In Fig. 1.3 the basic design process of Fig. 1.2 is illustrated with some of the features already mentioned, such as the OUTLINE EDITOR, the WINDING EDITOR, the DESIGN SHEET, and the GRAPHS. At the lower left of Fig. 1.3 is a condensed figure of a dynamometer and a circuit diagram for an inverter-fed AC machine, referring to the simulation of the drive and its digital control found in many SPEED programs. Fig. 1.3 also shows a number of important auxiliary functions and links. The finite-element GoFER — this is a closely linked finite-element program (PC-FEA) which is provided to assist with electromagnetic field calculations. “GOFER” stands for “Go to FiniteElements and Return”. The data transfer from SPEED to PC-FEA is automatic, although it can be controlled and modified by the user at all stages of the process.2 “Return” refers to data that can be passed back to SPEED for directly improving the design calculations in several different ways. 2

The FLUX™ finite-element software by CEDRAT can read SPEED datafiles of type .bd4, .im1 and .srd directly. Thereafter FLUX™ can be used flexibly for a wide range of finite-element calculations. Moreover, FLUX™ has excellent facilities for modifying the geometry with holes, flats, notches, and imperfections such as eccentricity.

The finite-element process is also used internally in some SPEED programs as an embedded solver. In this case the finite-element results are incorporated in the design calculations without displaying the flux-plot or other graphics available with the GOFER. Some calculations require this solver. The material property databases are important repositories for material property data in a form that is readable by the SPEED programs. Given the critical importance of material property data, it is essential that users prepare their own data records for materials used in their products. This data is often proprietary, particularly when it has been hard-won by painstaking efforts in the test laboratory, or by negotiation with suppliers. The material data supplied with the SPEED programs is generic and unqualified. It should only be used as a “starter”, or as representative of certain general classes of material, for example, “highsilicon steel”, or “neodymium-iron-boron”. There is an important link to Motor-CAD™ for heat-transfer analysis and cooling calculations. Finally there are facilities for linking SPEED data to manufacturing design databases such as those used with product inventories.


Page 6

1.8

Electric Machine Design using SPEED and Motor-CAD

Motor-CAD

Motor-CAD is a unique software for thermal analysis of electric machines and generators, closely linked to SPEED. The Motor-CAD solver is based on analytical network (lumped-circuit) analysis. Nodes at which temperatures will be predicted are set at important points throughout the machine geometry, e.g., the stator bore, halfway down a stator tooth, halfway through the stator back iron, at the winding hotspot, etc. The nodes are joined by thermal resistances to predict heat transfer due to conduction, radiation and convection. Power is injected at nodes at which losses occur, e.g. winding copper loss, tooth iron loss, stator yoke iron loss, etc. The network is solved to calculate the steady-state thermal performance. Results appear as node temperatures and heat-flows through resistances. Thermal capacitances are also defined at nodes to account for heat storage, so that the transient thermal response can also be calculated, e.g. temperature vs. time at the nodes. Transient calculations include the thermal response to intermittent operation and user-defined load duty-cycles. Several cooling systems are modelled, including Natural Convection, Forced Convection, Liquid Cooling, Submersible, and Through Ventilation. All thermal parameters such as conduction thermal resistances, convection and radiation heat transfer coefficients are calculated automatically. The solver quickly calculates the thermal performance, instantaneously for steadystate results and within a few seconds or minutes for the transient response (depending on the length of the transient to be calculated). Motor-CAD also has inbuilt multi-parametric sensitivity analysis capabilities. The sensitivity analysis is useful for gaining an in-depth understanding of the main constraints to dissipation, allowing informed design decisions to be made to improve the cooling. Sensitivity analysis is often run on manufacturing processdependent parameters such as the “goodness of fit” between stator lamination and housing, or the goodness of the impregnation system. The parameters are defined in Motor-CAD using descriptions and units that are designed to produce accurate results with confidence.

Details are provided for parameters based on a vast amount of testing and numerical analysis performed on various machines to gain a detailed knowledge of typical minimum, maximum and normal values. Default values are set to typical values to give realistic temperature predictions. Subsequent calibration will improve accuracy and allow for particular manufacturing processes.

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SPEED and Motor-CAD

One thing we find when we run Motor-CAD using SPEED design data is that the temperature distribution is not quite what we assumed or expected during the SPEED phase of the design process. Sometimes the temperatures are lower, but more usually they are higher. Motor-CAD not only draws our attention to the importance of the cooling and the temperature distribution ; it generally suggests improvements in the design, and increases confidence in it. What Motor-CAD has that SPEED does not have: •

Loss scaling with speed or torque, without changing the datafile

Sensitivity analysis

Vast database of materials and data on heat transfer and fluid flow

Thermal equivalent circuit with large number of nodes and steady-state schematic

Axial variation of temperatures

Temperatures overlaid on the crosssection

A wide range of housing configurations with fins, water-cooling jackets, ducts, etc.

Finite-element thermal diffusion model

Layered diffusion model for heat transfer across windings in slots

Duty-cycle editor (including duty-cycles imported from files).

Slot geometry editor showing the spacing of conductors .


T.J.E. Miller

www.speedlab.co.uk

D.A. Staton

www.motor-design.com


Electric Machine Design using SPEED and Motor-CAD, by T.J.E. Miller & D.A. Staton