IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 38, NO. 4, JULY/AUGUST 2002
1027
Impact of Stator Windings and End-Bells on
Resonant Frequencies and Mode Shapes of
Switched Reluctance Motors
Wei Cai, Senior Member, IEEE, Pragasen Pillay, Senior Member, IEEE, and Zhangjun Tang, Student Member, IEEE
Abstract—One of the main drawbacks of switched reluctance
motors (SRMs) is vibration and acoustic noise, which limits their
application. An accurate predication of the modal vibration frequencies of the SRM stator is essential in order to design a lowvibration motor and operate it quietly. Electronic techniques for
noise reduction also depend on knowledge of the resonant frequencies, which depend on the mechanical structure surrounding the
laminations. This paper examines the effects of the stator windings
and end-bells on stator modal vibration frequencies. The error in
the calculation of the resonant frequencies can be up to 20% if the
influence of end-bells is neglected. The numerical computations of
the stator mode shapes and resonant frequencies are validated with
experimental results.
Index Terms—Modal analysis, switched reluctance motor, vibrations and acoustic noise.
I. INTRODUCTION
T
HE switched reluctance motor (SRM) has many advantages over the induction motor and brushless dc motors,
but is inferior with respect to vibration and acoustic noise. It
is widely accepted that the stator vibration at the turn-off of a
phase is a dominant source of acoustic noise [1]–[3], [13], [14].
The vibration and resulting acoustic noise is particularly severe
when stator resonance occurs, i.e., when the frequencies and
waveforms of the excitation (usually radial magnetic forces) coincide with the normal mode shapes and natural frequencies [1],
[3], [13]. It is important to accurately predict the resonant frequencies and vibration characteristics of the SRM stator in order
to design quiet electrical machines [10], [11] and for quiet operation [3].
The contribution of the stator poles and ribs has been investigated with numerical computations in previous papers [4], [13],
[14]. Generally, the poles and ribs of the SRM stator cannot
be treated as an extra mass (an acceptable effect in induction
motors) [4], [11], [12] although the analytical formulas using
the assumption of “extra mass” showed a good estimation of
the frequencies of the low order modes. Many mode shapes are
Paper IPCSD 01–094, presented at the 1999 IEEE International Electric Machines and Drives Conference, Seattle, WA, May 9–12, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Electric
Machines Committee of the IEEE Industry Applications Society. Manuscript
submitted for reviewAugust 1, 2000 and released for publication April 25, 2002.
W. Cai is with Delco Remy America, Anderson, IN 46013 USA (e-mail:
Caiw@delcoremy.com).
P. Pillay and Z. Tang are with the Department of Electrical and Computer
Engineering, Clarkson University, Potsdam, NY 13699-5720 USA (e-mail:
pillayp@clarkson.edu).
Publisher Item Identifier 10.1109/TIA.2002.800594.
Fig. 1. Stator disassembly of a 4-kW SRM with four phases and 8/6 poles.
hidden under the “extra mass” assumption and the poles and ribs
play a “stiffness” role on the resonant frequencies of high-order
modes [4], [13], [14].
Previous work [4]–[6] on the effect of phase windings has
concentrated on the induction motor. There is some controversy
concerning the contribution of the phase windings. Some investigators treated windings as additional mass [4], [6], [11] while
others did not account for them [2], [7], [8], [12] in the resonant
frequency calculations. It was believed that the windings have
effects of both additional mass and vibration damping in induction motors [5].
The contribution of the windings to the resonant frequencies of the SRM stator is investigated in this paper. There is
no previous work on the effect of SRM end-bells on the stator
resonant frequency characteristics. Modeling the end-bells and
computing their influence on the SRM stator vibrations is the
new contribution in this paper. A shaker–accelerometer measurement system is employed to measure the resonant frequencies of the first several mode shapes. Experimental results validate the three–dimensional (3-D) numerical computations with
the finite-element method.
II. FINITE-ELEMENT MODELS FOR MODAL ANALYSIS
OF THE SRM STATOR
A commercial 4-kW SRM with four phases and 8/6 poles
is used as the basis of the calculations with the stator components shown in Fig. 1. For the encased stator of the SRM, the
end-bells are tightly mounted on both sides of the stator frame
in order to support the rotor assembly. Bolts are used to connect
the frame and the end-bells. The dimensions of the laminations
of the stator and rotor are given in the Appendix. The height
0093-9994/02$17.00 © 2002 IEEE
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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 38, NO. 4, JULY/AUGUST 2002
(a)
(b)
(d)
(c)
(e)
Fig. 2. Finite-element model of the SRM stator assembly. (a) Model without end-bells. (b) Elements of end-bells. (c) Model with end-bells. (d) Half a model of
the stator assembly. (e) Elements of half a model.
from the shaft center line to mounting feet is 112 mm; the thickness of stator frame is 10.2 mm and frame length is 190 mm plus
a 5-mm lip on each side to support the end-bells. Three trapezoidal strengthening keys with height 13 mm and length 190 mm
are seated on the frame 120 from each other. Two groups of tall
trapezoidal ribs of height 23.2 mm are evenly distributed on the
left and right side of the top-strengthening key, respectively. Six
short ribs of height 8 mm are evenly distributed between the
mounting feet. The horizontal and vertical wall thickness of the
terminal box with dimensions of 190 mm 85 mm 60 mm
are 7 and 8 mm, respectively. The whole stator is supported on
two feet of dimensions 190 mm 47 mm 12 mm. The stator
laminations are stacked with common 0.5 mm silicon steel sheet
and the frame is die-cast iron. The lamination stack is pressed
into the smooth bore of the ribbed frame so that a frictional contact is maintained. The material properties can be found in the
Appendix.
The mathematical model of the finite-element method for
modal analysis is given in previous papers [14], [15]. Two basic
finite-element models are built to investigate the effects of windings and end-bells. A stator skeleton, as shown in Fig. 2(a), includes the details of a ribbed frame structure with terminal box
and mounting feet. The mass of the phase windings is treated as
an increase of the mass density of the pole to which the winding
is attached. This model can be extended to consider the influ-
ence of the frame overhang length on stator vibration by increasing frame length.
The end-bell with bearing housing is modeled in Fig. 2(b).
Two meshed end-bells are attached to the stator skeleton, as
shown in Fig. 2(c). The connections between the end-bells and
stator frame can be expressed by merging different node sets at
the contact surface of the frame and end-bells. The correct finite-element model to reflect the actual contact at the interface
between frame and end-bell is investigated in Section IV. The
element distributions of the stator components are revealed in
Fig. 2(d) and (e), which reflects the procedure for generating
the whole finite element model of the SRM stator. The winding
mass is evenly distributed on the stator poles.
III. IMPACT OF WINDINGS ON THE RESONANT FREQUENCY OF
THE STATOR ASSEMBLY WITHOUT END-BELLS
The concentrated windings of the SRM are installed on the
stator poles. There is insulation between a pole and winding.
For conventional motors, the contact between pole and winding
assembly is tight enough to allow the windings to move with
the pole, but cannot add an extra stiffness due to the existence
of the insulation. Although the windings may contribute to stiffness if the slot fill factor is high, the increase in the stiffness
is low when compared to the mass added by the windings to
CAI et al.: RESONANT FREQUENCIES AND MODE SHAPES OF SRMs
1029
(a)
(a’)
(a”)
(b)
(b’)
(c)
(d)
(e)
(e’)
=
Fig. 3. Modes and frequencies of lamination stack and ribbed frame plus windings. (a) f
992Hz (sub
(sub 11). (b) f
2495 Hz (sub 17). (b’) f
2615 Hz (sub 18. (c) f
3562 Hz (sub 21). (d) f
(e’) f
5528 Hz (sub 35).
=
=
=
=
=
=
=
=
the stator assembly. Therefore, the effect of the windings is
equated to an increase of the pole mass. As a result, the geometrical model for finite-element computation is the same as the
model without end-bells in Fig. 2(a), but the poles are treated
as the third material with the same Young’s modulus, the same
Poisson’s ratio, but a different specific mass (18 590 kg/m ). For
this 4-kW SRM, selected computational results of the quasi-inplane flexural modes are given in Fig. 3. A detailed examination of the mode shapes of the SRM is given in [13] and, therefore, not repeated here. While the second and third mode shapes
in a smooth cylinder are well defined, several additional mode
shapes are created in a frame with ribs between the standard
second and third mode shapes. A comparison between computations with and without the effects of windings is given in Table I.
Measurements were performed with the rotor assembly and
the stator end-bells removed from the SRM (details of the tech-
=
= 7). (a’) f = 1040 Hz (sub =8). (a”) f = 1466 Hz
= 5091 Hz (sub = 31). (e) f = 5459 Hz (sub = 33).
nique are in Section V). The computed results with the model
including the winding influence, in columns (a′), (b′), and (d)
of Table I, have an error of less than 5%, compared to the
measured modal frequencies of corresponding mode shapes,
shown in Section V. Obviously, unacceptable results with errors
of more than 40% may be produced when neglecting the effects
of windings when the resonant frequencies are computed for
the SRM stator.
It is possible for the windings to constrain the motion of
the pole at high frequencies of the in-plane flexural modes or
in bending modes, torsional modes and out-of-plane flexural
modes. In these cases, the windings may lead to an increase of
the corresponding mode frequencies, and is equivalent to additional stiffness applied to the stator assembly. This is left for
future investigation, with the emphasis in this paper being on the
lower frequencies, which dominate acoustic noise production.
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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 38, NO. 4, JULY/AUGUST 2002
(e”)
(e”’)
(f’)
(g)
(f)
(h)
(i)
(i’)
=
=
=
=
Fig. 3. (Continued.) Modes and frequencies of lamination stack and ribbed frame plus windings. (e”) f
5683 Hz (sub 37). (e”’) f
5866 Hz (sub 38).
(f) f
6073 Hz (sub 41). (f’) f
6121 Hz (sub 42). (g) f
6238 Hz (sub 44). (h) f
6316 Hz (sub 46). (i) f
6533 Hz (sub 50). (i’) f
6798 Hz (sub 52).
=
=
=
=
=
=
=
=
=
=
=
=
TABLE I
COMPARISON OF COMPUTED MODAL FREQUENCIES WITH AND WITHOUT WINDINGS
IV. IMPACT
OF
END-BELLS ON NORMAL VIBRATIONS
OF THE SRM STATOR
Up to now, the effects of the windings on the resonant frequencies have been considered. The effect of the end-bells on
the resonant frequency has been determined experimentally. A
“shaker–accelerometer” test system was employed to perform
the test. The resonant frequency of the second-order mode of the
stator without end-bells is 1060 Hz, which becomes 1325 Hz
after adding the two end-bells. The error of the resonant frequency approaches 25% if the end-bell effects on the secondorder mode are ignored. Therefore, the effects of the end-bells
CAI et al.: RESONANT FREQUENCIES AND MODE SHAPES OF SRMs
1031
(a)
(a’)
(a”)
(a”’)
(b)
(b’)
(c)
(d)
(e)
=
=
Fig. 4. Mode shapes of the whole stator assembly with end-bell contact, case 3). (a) Mode at 1241 Hz (sub 7, second). (a’) Mode at 1340 Hz (sub 8, second).
(a”) Mode at 1480 Hz (sub 9, second). (a”’) Mode at 1556 Hz (sub 10, second). (b) Mode at 2589 Hz (sub 19). (b’) Mode at 2810 Hz (sub 22). (c) Mode
at 3663 Hz (sub 32). (d) Mode at 5199 Hz (sub 49). (e) Mode at 5734 Hz (sub 53).
=
=
=
=
on the normal vibration of the SRM stator cannot be omitted.
The question that needs to be answered is the determination of
the correct modeling procedure.
The modeling of the end-bells using finite elements is nontrivial. Three modes of contact between frame and end-bells
are examined and compared with experimental results in order
to model the stator assembly for natural vibration analysis correctly.
(i) The frame and end-bells are in perfect contact with each
other, i.e., these surfaces will move together.
(ii) Only the nodes on the periphery are merged together
while the cross-sectional surfaces are left to vibrate
freely.
(iii) The local areas around the connection bolts are assumed
to have identical motion while the rest of the areas on the
surfaces vibrate independently.
=
=
=
The three models have the same geometrical dimensions of a
real 4-kW SRM, as shown in Fig. 2(c). The windings are treated
as extra mass and added to the poles since in-plane flexural
mode shapes are the main concern in this dissertation. The finite element models are shown step by step in Fig. 2(b), (d),
and (e).
The mode shape and resonant frequencies for case iii) above,
which is validated by experimental results, are given in Fig. 4.
The resonant frequencies of selected mode shapes for all three
cases are listed in Table II. To clearly show the deformation
inside the stator at each mode, one end-bell is removed to show
the mode shapes. Of course, both end-bells are included in the
modal analysis by finite-element computations.
Compared to the numerical results in Fig. 3, the resonant
frequencies corresponding to the same mode shapes are raised
after the end-bells are added to the stator assembly of the SRM,
as shown in Fig. 4 and Table II. The mode shapes in Fig. 4,
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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 38, NO. 4, JULY/AUGUST 2002
(f)
(g)
(h)
(i)
Fig. 4. (Continued.) Mode shapes of the whole stator assembly with end-bell contact, case 3). (f) Mode at 6105 Hz (sub
(h) Mode at 6332 Hz (sub 63). (i) Mode at 6544 Hz (sub 69, zeroth).
=
=
= 59). (g) Mode at 6253 Hz (sub = 61).
TABLE II
RESONANT FREQUENCY VARIATION DUE TO INSTALLATION PATTERN OF END-BELLS
(where the end-bells are included) should be compared to the
corresponding mode shapes in Fig. 3, where the end-bells are
omitted. For example, the frequency of the second-order mode
shape will increase 20% with end-bells, compared to the one
without including the end-bell effects. It appears that the effect
of the end-bells is to compensate for the frequency decrease
caused by the windings. This observation explains a phenomenon: some measurement results of resonant frequencies are
close to the computed values when both windings and end-bells
are neglected in the model. However, this cancellation will not
always be exact, since the positive contribution of the end-bells
to the SRM stator vibration will not always cancel out the neg-
CAI et al.: RESONANT FREQUENCIES AND MODE SHAPES OF SRMs
(a)
1033
(b)
(c)
Fig. 5. Some mode shapes possibly excited by electromechanical origins. (a) 2646 Hz (sub
6467 Hz (sub 67, 0val) (oval). (d) 7278 Hz (sub 81) (axial).
=
=
ative contribution of the windings exactly. It is necessary to
consider the winding influence and the end-bell impact on the
vibration of the SRM separately. End-bells should not be removed from the physical model for finite-element analysis of
SRM stator vibrations.
The correct method to add end-bells to the numerical model
is important for accurate computation of the stator vibration.
The mounting surfaces of the end-bells would have perfect contact with the frame faces if manufacturing and installation are
ideal. In the finite-element model, this corresponds to merging
all nodes at the contact areas. Error in the computed results,
based on this assumption, occurs for the second-order mode
shape and their frequencies when compared to experimental results. In fact, it is impossible to mount the end-bells perfectly
at the well-machined ends of the stator frame. In practice, only
local areas on contacting surfaces make proper contact, which
can be easily found if the end-bells are removed from the SRM.
These local areas are concentrated around the bolt holes. Therefore, only the nodes around the bolt areas are merged with the
rest left to move freely. This model, called “bolt area merged,” is
validated by the “shaker–accelerometer” test. For instance, the
error of the resonant frequencies produced with this model is
less than 2% for the second and fourth mode shapes (1304 and
5199 Hz). The selected mode frequencies are given in the last
column of Table II. Generally, the predicted resonant frequency
increases as one models the end-bells in terms of bolt merged to
perifery merged to all nodes in the end-bell being merged to the
frame. This is expected because of the corresponding increase
in stiffness.
Comparing the frequencies under “Periphery merged (ii)” to
the results from “Bolt area merged (iii)” in Table II, the frequencies corresponding to selected in-plane flexural modes are of
similar accuracy, except for the second order mode shapes. This
means that the two models are acceptable for high-frequency
models but not in the low-frequency range. The mode sequence
in terms of the frequencies is changed, and the modes related
to the end-bell motion, the torsional modes, bending modes,
and the out-of-plane modes are all different from each other.
The reason for this is the differing constraints in the end-bell
mounting.
In Fig. 5(a), the bearing housing moves up and down. This
mode can be excited by an eccentric air gap or rotor bend. A
mode describing the swinging of the bearing housing is shown
in Fig. 5(b), which can be excited by an unbalanced rotor. The
bearing itself may stimulate the mode corresponding to oval de-
(d)
= 20 (up and down). (b) 3047 Hz (sub = 26) (housing swing). (c)
Fig. 6. Vibration-experimental bench assembly (testing stator without
end-bells).
formation of bearing housing, such as the mode of Fig. 5(c). The
end-bells behave like thin plates and deform in the axial direction, as shown in Fig. 5(d). Any end thrust caused by the rotor
may excite this mode.
V. EXPERIMENTAL VALIDATION
In Fig. 7, the acceleration outputs of channels 2, 3, and 4 from
an oscilloscope correspond to accelerometers spaced 90 apart
around the SRM (Fig. 6) and which, therefore, correspond to the
top, sides, and bottom of the SRM. The accelerometer outputs
in Fig. 7 are processed to determine the resonant frequencies,
which are shown in Table III. The experimental results clearly
show the difference in the resonant frequency as a result of the
end-bell and also shows the correlation with the theoretical results with the “bolt area merged” model.
Fig. 8 shows the measured force and acceleration spectra
(stator with end-bells) under white-noise excitation using a
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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 38, NO. 4, JULY/AUGUST 2002
Oscilloscope output of the second-order mode of the SRM stator with end-bells.
TABLE III
TESTED RESONANT FREQUENCIES FOR THE SRM WITH AND WITHOUT END-BELLS
connecting the shaker and the stator of the SRM, and four ropes
holding the motor to a solid bench), which can be confirmed
by looking at the peak of the force spectrum. The peak caused
by the experimental setup disappeared in the transfer function
plot, however, another peak around 2500 Hz is shown in the
transfer function plot, which is the third mode frequency.
The measured second and third mode resonant frequencies
(1320 and 2500 Hz) using white-noise excitation for the stator
with end-bells are fairly close to the results of the other methods
mentioned above, which confirms the validity of both methods.
VI. CONCLUSIONS
Fig. 8. Force and acceleration spectrums under white-noise excitation (stator
with end-bells, no rotor).
shaker, together with the transfer function. It can be seen
from the white-noise excitation results that the second mode
resonant frequency is 1320 Hz for the stator with end-bells.
Another peak in the acceleration spectrum (around 2020 Hz),
is caused by the experimental system (there is a steel push rod
A knowledge of the resonant frequencies of the SRM is
important for producing low-vibration and low-noise designs.
Electronic techniques for the reduction of acoustic noise
depend on a knowledge of the resonant frequencies. Previous
work has examined the effects of the laminations and a frame
on the resonant frequencies. This paper extends that work to
include the effects of the windings and the end-bells. Among
the findings of this research, are the following.
1) Windings influence the resonant frequencies significantly
and their effects are different depending on the particular
resonant frequency. Errors of over 40% in the estimation
of the resonant frequency can occur for some of the resonant frequencies.
CAI et al.: RESONANT FREQUENCIES AND MODE SHAPES OF SRMs
1035
REFERENCES
Fig. 9. Dimensions of a 4-kW SRM with 8/6 poles and four phases.
TABLE IV
GEOMETRICAL PARAMETERS AND MATERIALS PROPERTIES OF SRM STATOR
2) The end-bells must be included in the model for determining the resonant frequencies. Errors in excess of 25%
can exist if they are neglected.
3) Windings tend to reduce the resonant frequencies, while
end-bells increase the resonant frequencies. Hence, they
tend to offset each other, but not completely, depending
on the design.
4) The finite-element model which gives the best results is
that where the elements around the bolts of the end-bell
are merged, and not all the elements where the end-bell
meets the frame.
5) Shaker tests with sinusoidal and white-noise excitation
validate some of the results.
APPENDIX
See Fig. 9 and Table IV.
[1] D. E. Cameron, J. H. Lang, and S. D. Umans, “The origin and reduction
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[2] R. S. Colby, F. Mottier, and T. J. E. Miller, “Vibration modes and acoustic
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Annu. Meeting, vol. 1, Orlando, FL, Oct. 8–12, 1995, pp. 441–447.
[3] C. Y. Wu and C. Pollock, “Analysis and reduction of acoustic noise and
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vol. 31, pp. 91–98, Jan./Feb. 1995.
[4] S. P. Verma and R. S. Girgis, “Resonance frequencies of electrical machines stator having encased construction, Part I: Derivation of the general frequency equation,” IEEE Trans. Power App. Syst., vol. PAS-92,
pp. 1577–1585, Sept./Oct. 1973.
[5] R. K. Singal, K. Williams, and S. P. Verma, “The effect of windings,
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[6] C. Yongxiao, W. Jianhua, and H. Jun, “Analytical calculation of natural frequencies of stator of switched reluctance motor,” in Proc. 8th
Int. Conf. Electrical Machines and Drives, Cambridge, U.K., Sept. 1–3,
1997, pp. 81–85.
[7] Y. Tang, “Characterization, numerical analysis and design switched reluctance motor for improved material productivity and reduced noise,”
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6–10, 1996, pp. 715–722.
[8] J. Mahn, D. Williams, P. Wung, G. Horst, J. Lloyd, and S. Randall, “A
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Meeting, vol. 1, San Diego, CA, Oct. 6–10, 1996, pp. 779–785.
[9] F. Camus, M. Gabsi, and B. Multon, “Prediction des vibrations du stator
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[10] M. Besbes, C. Picod, F. Camus, and M. Gabsi, “Influence of stator geometry upon vibratory behavior and electromagnetic performances of
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[11] A. Ellison and S. Yang, “Natural frequencies of stators of small electric
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[12] E. Erdelyi and G. Horvay, “Vibration modes of stators of induction motors,” Trans. ASME, vol. 24(E), pp. 39–45, 1957.
[13] P. Pillay and W. Cai, “An investigation into vibration in switched
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[15] M.
Petyt,
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Wei (William) Cai (S’99–M’00–SM’01) received
the B.Sc. and M.Sc. degrees from Harbin Institute
of Electrical Technology (HIET), Harbin, China,
and the Ph.D. degree from Clarkson University,
Potsdam, NY.
He was an Instructor and then Associate Professor
in the Department of Electrical Engineering, HIET,
from 1985 to 1994. He was an Honorary Research
Fellow at WEMPEC, University of Wisconsin,
Madison, from 1994 to 1995. He was an Electrical
Engineer in the Institute of Electrical Machines,
ETH-Zurich, Switzerland, in 1996. Since 1999, he has been an Electrical
Specialist with Delco Remy America, Anderson, IN. His interests include
design, control, and modeling of electrical machines and drives, numerical
computation of electromagnetic fields and mechanical structures, and vibration
and noise of electrical machines. He is currently working on the design
of hybrid vehicle drive systems, integrated starter alternator dampers, and
high-power alternators, as well as starters and alternators in 42-V systems.
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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 38, NO. 4, JULY/AUGUST 2002
Pragasen Pillay (S’84–M’87–SM’92) received
the Bachelor’s degree from the University of
Durban-Westville, Durban, South Africa, in 1981,
the Master’s degree from the University of Natal,
Durban, South Africa, in 1983, and the Ph.D.
degree from Virginia Polytechnic Institute and State
University, Blacksburg, in 1987.
From January 1988 to August 1990, he was with
the University of Newcastle-upon-Tyne, U.K. From
August 1990 to August 1995, he was with the University of New Orleans. Currently, he is with Clarkson
University, Potsdam, NY, where he is a Professor in the Department of Electrical
and Computer Engineering and holds the Jean Newell Distinguished Professorship in Engineering. His research and teaching interests are in modeling, design,
and control of electric motors and drives for industrial and alternate energy applications.
Dr. Pillay is a member of the IEEE Power Engineering, IEEE Industry Applications (IAS), IEEE Industrial Electronics, and IEEE Power Electronics Societies. He is a member of the Electric Machines Committee and Chairman of
the Industrial Drives Committee of the IAS and Chairman of the Induction Machinery Subcommittee of the IEEE Power Engineering Society. He has organized and taught short courses in electric drives at IAS Annual Meetings. He is
a member of the Institution of Electrical Engineers, U.K., and a Chartered Electrical Engineer in the U.K. He was also a recipient of a Fulbright Scholarship.
Zhangjun Tang (S’00) received the B.S. degree in
1994 from Harbin Institute of Technology, Harbin,
China, and the M.S. degree in 1997 from Beijing Institute of Control Devices, Beijing, China. He is currently working toward the Ph.D. degree at Clarkson
University, Potsdam, NY.
From April 1997 to July 1999, he was an Electrical
Engineer at Beijing Institute of Control Devices.
His research interests include design, control,
and modeling of electrical machines and drives,
numerical computation of electromagnetic fields
and mechanical structures, and vibration and noise of electrical machines. He
is currently working on his Ph.D. dissertation on vibration and acoustic noise
in switched reluctance motors.