electric motor integration with a rotary on/off valve

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Electric Motor Integration with a Rotary ON/OFF Valve Christopher Phaneuf, The Cooper Union for the Advancement of Science and Art, New York, NY Faculty Advisor: Professor Perry Li, University of Minnesota, Mechanical Engineering

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Page 1: Electric Motor Integration with a Rotary ON/OFF Valve

Electric Motor Integration with a Rotary ON/OFF Valve

Christopher Phaneuf, The Cooper Union for the Advancement of Science and Art, New York, NY

Faculty Advisor: Professor Perry Li, University of Minnesota, Mechanical Engineering

Page 2: Electric Motor Integration with a Rotary ON/OFF Valve

ABSTRACT

Electric motoring is explored as a means of improving the performance of a rotary pulse width

modulated ON/OFF valve used in a novel system for hydraulic control. From analysis of the

current design, a faster, more selective speed profile could vastly improve the efficiency and

response time of the system by reducing throttling losses experienced during valve transition.

The current self-spinning geometry theoretically operates at a PWM frequency of 84 Hz. Electric

actuation can potentially spin the valve at the target frequency of 200 Hz with the required

torque. Exploring various electric motor types and assessing respective compatibilities, the most

feasible configuration was realized. A permanent magnet interior-rotor brushless DC topology

was selected for its overall compatibility, especially the ease of mechanical integration with the

valve. By coupling the valve spool with a section of steel laminations with surface-mounted

magnets, embedding a star-wound stator in the valve sleeve, and wiring a controller and inverter

to electrically commutate the current to the stator windings, the valve can be driven faster and,

with design refinement, rotate at a variable speed. An experimental demonstration was conducted

as a proof-of-concept for the electronic control of a brushless motor. A CD-ROM motor was

interfaced with MATLAB using xPC Target and driven through a simple inverter circuit. From

the study conducted, brushless motor technology appears to be a viable option for the further

development of the rotary ON/OFF valve.

Page 3: Electric Motor Integration with a Rotary ON/OFF Valve

INTRODUCTION

A promising innovation for the hydraulics industry has emerged from the University of

Minnesota's Center for Compact and Efficient Fluid Power. The high speed rotary pulse width

modulated ON/OFF valve (Figure 1) is a device that, when paired with a fixed displacement

pump, provides the functionality of a variable displacement pump while outperforming current

ON/OFF valve designs. Due to the bulk, slow response, and expense of variable displacement

pumps, an efficient alternative in a compact package is desirable [1].

Figure 1. Current design for rotary ON/OFF valve [1]

Preceding the novel rotary valve design was the initial motivation for a high speed, efficient

ON/OFF mechanism. The idea for a variable displacement pump equivalent originated as a

hydro-mechanical adaptation of the power electronics system known as a switch-mode power

supply, or more specifically, a DC-DC boost converter [2]. The analogous hydraulic system

consists of a fixed displacement pump, a check valve, an accumulator, and an ON/OFF valve. An

experimental study of this application using an off-the-shelf linear ON/OFF valve demonstrated

Page 4: Electric Motor Integration with a Rotary ON/OFF Valve

the feasibility of the system and highlighted the areas for improvement. Among them, the most

notable was the design of a faster ON/OFF valve to reduce the energy lost during valve transition

time.

The inception of the PWM rotary ON/OFF valve has introduced an advanced means of ON/OFF

(digital) control as an alternative to throttling valves as well as an enabler for a more effective

variable displacement pump equivalent. By overcoming drawbacks in current, conventional

valves such as the power required to switch between ON and OFF in a linearly actuated design,

this valve is a step forward in the progress toward improved hydraulic systems [1]. Currently,

certain limitations restrict the valve's performance and leave room for improvements.

The most critical benefit of digital control is that power loss is minimal while flow is channeled

to either the load or tank, as opposed to the common alternative of bleeding off excess flow

through a throttling valve. It is the portion of the cycle between the openings for flow that

presents the greatest limitation on performance. This transition period occurs when the helical

barriers cross the rhombus-shaped inlet, resulting in a large pressure drop (Figure 2). This

throttling loss is a consequence of the narrowing orifice through which the fluid must travel,

which occurs four times each cycle. In addition, the accumulator limits the systems speed of

response. Without increasing the magnitude of the output pressure ripple, the response time will

improve with an increased PWM frequency [2]. Addressing these drawbacks is the focus of this

research. A higher efficiency and faster system response can be achieved by reducing the effects

of the transition event and increasing the PWM frequency of the valve.

Page 5: Electric Motor Integration with a Rotary ON/OFF Valve

Figure 2. Transition period

This study will follow the series of processes guided toward selecting, designing, and testing a

viable option for improving the rotary ON/OFF valve. From describing the general theory and

construction of the basic motor types to clarifying confusing terminology of specific

configurations, a logical progression will demonstrate the findings leading up to the eventual

selection. Following this breakdown will be a brief description of the experimental prototype

built for the purpose of a proof-of-concept. Concluding remarks will summarize the research and

provide several recommendations for future work.

Page 6: Electric Motor Integration with a Rotary ON/OFF Valve

METHODS AND RESULTS

Approaching this research objective was first a matter of choosing a direction. Several different

options offer the potential for an effective solution; however, the primary contingencies are as

follows: hydraulic actuation, electric actuation, or a refinement of the spool geometry.

Considering both my unfamiliarity with hydraulic motors and the considerably large desired

jump in performance that would not likely be met by improved contours, electric motor actuation

stood out as the most plausible solution. The research aimed at integrating an electric motor into

the ON/OFF valve occurred in three phases: selection, design, and testing. The order was not

exactly linear but each was carried out in succession.

Selecting the best motor was an extensive process consisting of reading, weighing, and

discussing. Prior to delving into the vast quantity of motor-related literature, it was important to

become familiar with the valve and associated system components and establish a flexible set of

criteria to direct the selection process. Having obtained an understanding of the valve and its

various functions and features, a general design was formulated. Initial thoughts included the

straight-forward approach of coupling a DC motor to the spool by fixing the motor shaft to one

end of the spool. A compact, custom-built motor could fit in the sleeve and slide along one or

more keyways to keep the motor in a stationary angular position while driving the spool. This

would be a simple solution that maintained the current method of linear actuation in which a

gerotor pump transfers hydraulic fluid between two end chambers on both sides of the spool to

change the linear position and, in turn, change the duty ratio. This idea served as a means of

entering the frame of thinking about this problem. Its flaws are numerous, including the question

Page 7: Electric Motor Integration with a Rotary ON/OFF Valve

of proper seals, the paths for electrical connections, and the scalability. Under the advisement to

avoid completely redesigning the valve and attempt to reconcile as many of the current design

features as possible, most notably the mechanism for linear actuation, a simple and even

previously considered but uninvestigated approach was tentatively chosen. For this design, the

spool is converted into a rotor and a stator is incorporated into the sleeve. To determine the

feasibility of this concept, research into the different electric motor types was aimed at finding

one of sufficient performance and maximum mechanical compatibility.

Electric motors are typically lumped into two broad categories based on their power source: AC

and DC. The general categories that follow are brushed DC, induction, and synchronous. For a

complete classification, see Figure 3 [3]. For the purpose of this study, only common types will

be considered. For any motor, two components are present: the stator and the rotor. As their

names imply, the stator is the stationary part and the rotor rotates. The interaction between these

parts is what separates the different motor types.

Figure 3. Electric motor classifications

Page 8: Electric Motor Integration with a Rotary ON/OFF Valve

Brushed DC motors are some of the most commonly used and understood electric drive systems;

therefore, this is the best place to begin the overview. Depending on the size and application, the

stator can either consist of windings (wound-field) or permanent magnets. For smaller DC

motors, permanent magnets are more commonly used for field excitation. The rotor acts as the

armature. Current is drawn through brushes that contact the commutator, which mechanically

switches the direction of the current passing through the rotor windings [4]. The basic

construction is depicted in Figure 4. The mechanical simplicity extends to their control. Speed is

changed by varying terminal voltage, which is usually implemented in the form of an adjustable

voltage supply, either linear or pulse-width modulated [4]. Torque depends on the armature

current. Brushed commutation is well-proven, reliable, and generally forgiving and

developments in electronics have kept brushed DC motors competitive with AC drives. They are

found most often in automotive and aircraft auxiliaries and small servo and speed-control

systems [5]. Evaluating this motor in the context of integration with the valve exposes numerous

incompatibilities. The most critical disparity is the arrangement of mechanical parts. Although

the general interior rotor orientation is desired, a rotor containing windings and requiring a

mechanical commutator would not operate immersed in hydraulic fluid. Additionally, brushes

limit speed, create friction, sparks, noise, and RFI, and eventually wear out [5].

Figure 4. Brushed DC motor construction [6]

Page 9: Electric Motor Integration with a Rotary ON/OFF Valve

A greater variety and degree of versatility is found among AC motors. The two basic types are

asynchronous, or induction, and synchronous. This nomenclature refers to the relationship

between the rotating magnetic fields of the stator and rotor. Induction motors are rugged and

efficient in large applications and operate asynchronously. As their name indicates, they work

under the principle of induction. The rotating magnetic field of the surrounding stator induces a

current in the conductors of the rotor, generating a secondary magnetic field and the subsequent

force required for rotation. Since the rotor must always interact with a moving magnetic field for

torque production, its speed must lag behind the surrounding rotating field; this essential

condition is known as slip [7]. Both single and polyphase induction motors are common. Many

are line-fed, running on 60 Hz AC. These motors dominate the domestic appliance industry, as

well as drive applications for pumps, fans, blowers, and compressors [5]. Induction motors don't

require commutation and are technically "brushless." The resulting geometry is superficially

compatible with the ON/OFF valve (Figure 5). Although simple and well-established, a myriad

of weaknesses make the induction motor a poor fit for this application. These motors typically

run at a fixed speed, depending on the frequency of the current fed to the windings. Variable

speed drives are available but tend to be complex and expensive, especially for the dynamic

performance and high efficiency that this application demands [5]. Scaling presents another

major limitation. Induction motors suffer from an insufficient magnetic flux-density at small

sizes due to copper losses. This is known as ‘excitation penalty’ or ‘magnetization penalty’ and

serves to highlight the advantage of permanent magnets in small motors [5].

Page 10: Electric Motor Integration with a Rotary ON/OFF Valve

Figure 5. Induction motor cross section [6]

Synchronous motors introduce an even more diverse collection of configurations and

applications. The two types that fall within the focus of this research are stepper (or step) motors

and three-phase, radial-flux brushless DC motors. Conventional synchronous motors operate

with field windings on the rotor and slip rings to commutate current. Generally superior to this

type is the permanent magnet synchronous motor, which replaces the field windings and slip

rings with permanent magnets mounted to the rotor. In terms of cost per unit power input, these

are some of the lowest of all electric motors [4]. It is this classification that encompasses the

relevant motor types.

Stepper motors, although typically implemented in positioning applications, have the potential to

provide the selective speed profile that the ON/OFF valve could benefit from. While most

electric motors, especially those with permanent magnets and slotted stators, are designed and

controlled to run as smoothly as possible, minimizing the often undesirable but unavoidable

occurrence of cogging, stepper motors are made to cog and are sometimes referred to as 'pulsed-

torque machines' [5]. With the proper design, this motor could step into discrete positions along

the circumference of the spool's inlet stage. With an altered helical pattern and careful alignment

to synchronize the fast transition between steps with the barriers, the stepper motor would

Page 11: Electric Motor Integration with a Rotary ON/OFF Valve

provide an effective solution to the design goal. Drawbacks in the operation of a stepping motor

are the limitations on speed and efficiency, disqualifying this option.

Brushless DC motors are a type of permanent magnet synchronous motor, often confused with

its close relative, the brushless AC or sinewave synchronous motor. To clarify the distinction, the

difference lies in the method of controlling the motor and the corresponding winding pattern. To

outline the construction of a brushless permanent magnet motor, the two main elements are a

stator, often slotted, with windings and a rotor with permanent magnets (Figure 6). The advent of

strong rare-earth permanent magnets has given the brushless motor the advantage of high power

density, providing the opportunity for scaling down motor dimensions while maintaining

adequate flux-density [3].

Figure 6. Brushless motor construction

To convert electrical energy into a rotating magnetic field in a stationary array of iron teeth, a

means of electronic commutation is required. This can come in several forms of various levels of

complexity, each suiting a different purpose or standard for performance. The commutation

Page 12: Electric Motor Integration with a Rotary ON/OFF Valve

results in a rotating magnetic field that can be thought of as a circularly arranged set of

electromagnets energized, in the general case of three-phase power, two phases at a time,

creating magnetic poles for the poles of the rotor to follow. Brushless AC motors are controlled

with a sinusoidal current waveform and generate a sinusoidal back EMF, which is a voltage

induced by the current flow that it opposes as a result of a changing electromagnetic field [7].

When variable speed is needed, the AC from the mains is rectified then inverted at the desired

frequency and rating. The windings are distributed sinusoidally, enabling the option of operation

at a constant synchronous speed without the need for commutation [5]. These motors possess a

very smooth torque profile (i.e. low torque ripple). This is at the cost of an expensive, absolute

position sensor and low inverter efficiency due to the particular sequence of switching [7].

Analogous to the label of sinewave synchronous motor, brushless DC motors are called either

squarewave or trapezoidal-type motors, referring to the current or back EMF shape, respectively.

These operate from an inverted DC supply in conjunction with inexpensive, low resolution rotor

position sensing. This is the type of electric motor selected as the most viable option for

integration with the ON/OFF valve.

For a fast, efficient, low power, variable speed drive compatible with the valve geometry, the

brushless DC motor meets the selection criteria. While the mechanical parts are simple, the

electronics needed for commutation are relatively complicated. All brushless DC motors require

an inverter as displayed in Figure 7. The common three-phase brushless motor is the

configuration considered here. These implement a three-phase bridge inverter to convert direct

current to the current waveform illustrated in Figure 8. A technique known as six-step

commutation is a common and powerful approach to commutation. This bipolar drive scheme

Page 13: Electric Motor Integration with a Rotary ON/OFF Valve

requires six power semiconductors, usually MOSFETs (Metal Oxide Semiconductor Field Effect

Transistors) or IGBTs (Insulated Gate Bipolar Transistors), two dedicated to each phase (Figure

7). To produce the proper sequence based on rotor position, a method of sensing is used. The

most common topology implements Hall Effect sensors to directly read the rotor position and

send the resulting signals to a controller to trigger the inverter in the correct sequence. An

alternative to the use of sensors is known as “sensorless” control, a method in which the back

EMF induced in the stator windings is measured from the nonenergized (floating) phase and the

position is estimated. This could be a feature more compatible with the valve since the use of

sensors poses the potential for placement issues and dangerous environmental conditions such as

high temperatures. Whichever method is used, brushless DC motors are extremely controllable,

capable of high speeds at high efficiencies, and geometrically compatible with the valve, making

them an ideal candidate for the motor integration.

Figure 7. Simplified brushless DC motor electronics

Page 14: Electric Motor Integration with a Rotary ON/OFF Valve

Figure 8. Ideal brushless DC motor current (solid) and back EMF (dashed) waveforms [5]

With an understanding of both the ON/OFF valve and brushless DC motors, designing was an

exercise in adaptation. In studying the many permutations of brushless designs found outside of

the literature in real applications, one of the quickly realized trends is the predominance of

exterior rotor brushless motors, known as outrunners (Figure 9). This term likely spawned from

remote-control aircraft enthusiasts / hobbyists, since this type of motor is a preferred means of

propulsion and a common format for home-built motors. This is possible because of the many

available devices that employ exterior rotor brushless motors for actuation, including hard drives,

cooling fans, and CD drives. Internal rotor, or inrunner, configurations are also found but

scarcely compared to the outrunner. More torque is generated with the magnets spread out

around the stator of an outrunner while higher speeds are obtained with inrunners. Both operate

Page 15: Electric Motor Integration with a Rotary ON/OFF Valve

under the same principles and are driven with identical controlling/driving systems. The limited

practical information regarding inrunner construction allowed only a simple conception of the

design. The spool-to-rotor conversion would require an additional section attached to one end of

the spool. Maximum performance would demand custom, rare earth arc magnets arranged in a

peripheral distribution around the rotor yoke, which would likely consist of steel laminations to

conduct the magnetic field and reduce eddy current losses (Figure 10). Sizing would depend on

the desired air gap, which is the space between the outer surface of the rotor and the inner

circumference of the stator. This dimension is an essential parameter in determining the

operation of the motor. A larger air gap reduces cogging torque and windage losses, which is a

mechanical form of power loss due to the frictional force between the air and the rotor [4].

Conversely, larger air gaps reduce the operating flux-density and require permanent magnets

with a higher coercive force [5]. While induction motors require an extremely small air gap with

a high tolerance, brushless DC motors are more flexibly designed, especially with the availability

of powerful permanent magnets like neodymium iron boron rare-earth magnets. The stator would

be most easily incorporated into the sleeve in the slotted style (Figure 11). This element is

composed of bonded steel laminations to form a stack. Teeth, most often designed with shoes

(see detail in Figure 11), hold the windings or coils. The most efficient and easily accomplished

form of winding is the star configuration, also referred to as a Y or wye connection (simplified in

Figure 7). The length of the stator stack is another important dimension, especially for this

application. The stator must span enough of the sleeve to surround the magnetic rotor segment in

any linear position. With its outer position exposed to circulating air, the stator can be cooled

more easily than other motor types. As the brushless design allows, all electronic components are

external, away from the high heat and the flow of hydraulic fluid. This general design, along

Page 16: Electric Motor Integration with a Rotary ON/OFF Valve

with several questions posed later in the paper for the purpose of future development, should

provide a basis for the motor integration.

Figure 9. Outrunner brushless DC motor (without controller)

Figure 10. Current spool design and permanent magnet rotor segment

Figure 11. Current sleeve / pump cover design and slotted stator lamination

Page 17: Electric Motor Integration with a Rotary ON/OFF Valve

Testing the control of a brushless motor was the final phase of the research. This experimental

hardware prototype required two computers, one host and one target equipped with a data

acquisition (DAQ) board, a screw terminal to send and receive signals through the DAQ board, a

DC power supply with a negative voltage terminal, basic electrical components such as

transistors, wire, resistors, and operational amplifiers, and most importantly, a brushless motor.

An early idea based on the recommendation of Professor Paul Imbertson was to convert an

induction motor into a brushless DC motor by modifying the rotor to hold surface mounted

magnets. This approach was eventually abandoned due to the lack of three phase induction

motors of any manageable size and power rating. All of the induction motors acquired through a

local surplus store operated on single phase AC. For use as a brushless motor, the number of

teeth would have to be a multiple of three and the stator would have to be rewound with three

wires for each phase. The labor and knowledge required for such a task exceeds my

qualifications. Instead, an outrunner brushless motor was salvaged from the spindle of an old

CD-ROM (Figure 13). Although not of the same physical configuration desired for the valve

integration, the operation is identical. The traces visible along the PCB are connections for the

three motor phases (the thickest ones) and the power, ground, and signals for three Hall Effect

sensors. Since the inverter was controlled manually, only three wires for the three phases were

soldered to the exposed areas of the traces. A three phase bridge inverter was constructed on a

breadboard using NPN transistors paired with diodes (Figure 14). The gate of each transistor was

connected to the digital outputs of the DAQ board. With the help of graduate student Mike

Rannow, operational amplifiers were wired between the inverter and the computer to protect

against voltage spikes. Another op-amp paired with a 10 ohm resistor was wired between the

positive and negative terminals of an adjustable power supply and the inverter. This maintained a

Page 18: Electric Motor Integration with a Rotary ON/OFF Valve

roughly constant current level to the motor. Six signal generators were used to trigger the

inverter from MATLAB using xPC Target. For the waveforms depicted in Figure 8, six signals,

each 60 electrical degrees out of phase with another, turn the transistors ON and OFF at a duty

ratio of 1/3, generating the sequence needed for a proper rotating magnetic field (Figure 15). At

any moment, two different phases are conducting, one in the HI or positive state and the other in

the LO or negative state. The third phase is in the floating state. With minimal debugging, the

motor was run at a low speed, exhibiting a great deal of oscillation, often referred to as

resonance, since the system acts like a spring mass system driven near its natural frequency. By

defining the time-related parameters of the signals with a variable called 'period,' the speed of the

signal could be altered by changing only this value. With subsequently smaller period values

tested, the motor ran smoother and faster. The power of MATLAB should allow for creative

manipulation of the signals to produce interesting results in future experiments.

Figure 12. Experimental setup

Page 19: Electric Motor Integration with a Rotary ON/OFF Valve

Figure 13. CD-ROM spindle motor

Figure 14. Brushless motor and inverter circuit

Page 20: Electric Motor Integration with a Rotary ON/OFF Valve

Figure 15. Six-step commutation signals

Page 21: Electric Motor Integration with a Rotary ON/OFF Valve

SUMMARY AND CONCLUSION

To solve the problem of driving a rotary valve spool at a faster, selective speed profile, a study of

electric motors and the potential for a creative means of integration was conducted. Examining

the construction and principle theory of operation behind each motor allowed a systematic

elimination of incompatible drive systems, leaving the brushless DC motor as the configuration

best suited for the valve and motor combination. A unique AC motor powered with inverted

direct current, brushless drives offer the geometric requirement of an interior rotor free of

electrical connections or windings. The outer stator holds a set of windings through which

current is electrically commutated using basic power electronics. Testing this motor type with an

experimental setup demonstrated the ease of control and flexibility that will be useful in

determining the most ideal driving scheme.

Working at the convergence of fluid power and electronics, there are still many mysteries and

questions to be answered by further modeling and analysis. Three primary directions are left

open from this study. As a first step toward better valve performance, a brushless electric drive

could spin the spool at a constant rate in the desired range around 4000 RPM. This would be the

most easily accomplished upgrade. The second option would involve exploiting the natural

rotational characteristic of a permanent magnet motor with a slotted stator. If the cogging could

be harnessed to move the spool in the manner described in the section on stepper motors and also

run efficiently at a high rate, selective speed without intensive electronics would be achieved.

The third and most desirable direction would be the most complex. Implementing a fast-

responding variable speed drive to directly control the rotation with an ideal reference speed

Page 22: Electric Motor Integration with a Rotary ON/OFF Valve

profile would execute the aim of the motor integration most effectively. Unfortunately, this

method would be limited by the precision and response time of the electric drive system, which

may end up requiring a lower average rotational speed. Another major obstacle in the search for

a means of a fluctuating speed that is aligned with the spool barriers is the change that occurs as

the spool is moved linearly when varying the duty ratio. This is where an alternative barrier

pattern such as the one proposed in the past by the project team and pictured in Figure 16 could

be more applicable. Moving beyond brushless motors to study some of the rare varieties that

were not thoroughly examined in this research could be beneficial. Reluctance motors, which

resemble brushless motors without magnets, might be a source of an even better, more feasible

solution.

Figure 16. Alternative barrier shape

In the case that a brushless motor is selected for integration into the ON/OFF valve, specific

design variables and possibilities would require exploring. The optimal feedback circuitry is an

important factor. As previously described, the controller outputs are based on the rotor position.

This measurement is either derived from sensors or estimated from the back EMF. The less

invasive implementation of sensorless control seems to be the superior choice for this application

but may not achieve the necessary accuracy for high precision timing. One possibility worth

investigating is the use of the rotary encoder located on the spool end. Another avenue for

exploration is the potential for scaling. Since a more compact valve is a current goal, the high

Page 23: Electric Motor Integration with a Rotary ON/OFF Valve

power density of a permanent magnet drive could enable the reduction of size. Less magnetic

material would also be cost effective. Other issues related to the rotor include the temperature of

the oil, since magnets undergo changes in their magnetic properties when exposed to temperature

above a limit known as the Curie point [7]. Also, the high speed rotation may necessitate a

retention system for the magnets more substantial than simple adhesive. Kevlar jackets/sleeves

are one of the newest and most effective forms of retaining structure. Rotor and stator

interactions may present problems due to the longer stator. Axial forces were qualitatively

observed when handling brushless motors from the CD-ROM, a hard drive, and a small cooling

fan. A noticeable resistance was felt while pulling the rotor from the non-energized stator. This

axial force could potentially disrupt the linear actuation of the spool. The details of further

mechanical design hinge not only on the answers to the questions posed here but also the

evolution of the valve components and an understanding of the manufacturing techniques

necessary to devise a buildable concept. If nothing else, this research should demonstrate that

nearly any rotary device requiring a reliable, efficient, and high performance means of actuation

can benefit from brushless motor technology.

Page 24: Electric Motor Integration with a Rotary ON/OFF Valve

REFERENCES

[1] H. Tu, M. Rannow, J. Van de Ven, M. Wang, P. Li and T. Chase, “High Speed Rotary Pulse

Width Modulated ON/OFF Valve” Proceedings of the 2007 ASME-IMECE, no.IMECE2007-

42559, 2007.

[2] M. Rannow, H. Tu, P. Li and T. Chase, “Software Enabled Variable Displacement Pumps –

Experimental Studies” Proceedings of the 2006 ASME-IMECE, no. IMECE2006-14973, 2006.

[3] D. Hanselman. Brushless Permanent-Magnet Motor Design. McGraw Hill, 1994.

[4] S.A. Nasar, I. Boldea, L.E. Unnewehr. Permanent Magnet, Reluctance, and Self-Synchronous

Motors. CRC Press, 1993.

[5] T. J. E. Miller. Brushless Permanent-Magnet and Reluctance Drive Motors. Oxford

University Press, 1989.

[6] Oriental Motors. Feb. 2007. Accessed 5 Aug. 2007.

<http://www.orientalmotor.com/in_motion/february_2007.htm>

[7] P. C. Sen. Principles of Electric Machines and Power Electronics. John Wiley & Sons, 2nd

ed., 1997.