SIMULATION MODEL AND LABORATORY TESTS OF SWITCHED

SIMULATION MODEL AND LABORATORY TESTS OF SWITCHED

Nr 62
Prace Naukowe Instytutu Maszyn, Napędów i Pomiarów Elektrycznych
Politechniki Wrocławskiej
Nr 62
Studia i Materiały
Nr 28
2008
switched reluctance motor , rolling rotor,
simulation model, laboratory tests
Antero ARKKIO* Adam BIERNAT**, Bogdan BUCKI**,
Grzegorz KAMIŃSKI**, Andrzej SMAK**, Paweł STASZEWSKI**
SIMULATION MODEL AND LABORATORY TESTS OF
SWITCHED RELUCTANCE MOTOR WITH ROLLING ROTOR
In the report measurements of Rolling Rotor Switched Reluctance Motor (RRSRM) laboratory
model for large torque/small speed applications are presented. Laboratory model shortly described is
constructed on base of the best design determined after calculations of several different motor constructions. The static torque, no-load, load and thermal characteristics of prototype motor are presented. Laboratory measurements are verified by simulated characteristics.
1. INTRODUCTION
Rolling rotor electrical machines [5] based on reluctance principles can be considered as a volume saving alternative [4] to conventional frequency converter-induction
motor-gear box torque delivering system. The lack of excitation in the rotor gives the
flexibility in adaptation of motor shape to specific requirements. Since the torque
produced depends on the current and the actual rotor position motor operation requires strict phase excitation strategy. Thus no load and load tests are crucial to
evaluate RRSRM performance while parallel investigation based on simulation model
allows for easy comparison of different control strategies and to determine one that
best suit peculiar application requirements.
2. LABORATORY MODEL OF RRSRM
No load and load tests were carried over RRSRM model [11] which construction is
presented on Fig. 1. Motor stator contains 5 salient poles with concentrated winding.
__________
*
Helsinki University of Technology, Otakaari 5a str., 02015 Espoo, FI, [email protected]
** Warsaw University of Technology, pl. Politechniki 1, 00-661 Warszawa, PL,
[email protected]
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Fig. 1. Construction of tested RRSRM. 1 – stator,
2 – concentrated winding, 3– rotor iron, 4 – torque
transmitting “fork” system; one sided crankshaft
system is invisible.
Rys. 1. Konstrukcja badanego RRSRM. 1 – stojan,
2 – uzwojenie koncentryczne, 3– rdzeń wirnika,
4 – system “fork” przeniesienia momentu; jednostronny system „crankshaft” jest niewidoczny.
Rotor made of ring iron sheets, mounted on bearings of one sided crankshaft system is able to perform rolling movement on smooth internal stator surface filled with
epoxy material. Non-slippery rotation [7] is secured by special rubber rings attached
to rotor surface. Sequential activation of motor phase winding leads to development
of reluctance type force due to minimization of the energy stored in the air gap. Force
developing between rotor and stator extorts successively rotor roll and crankshaft
rotation. Gear factor depends on crankshaft eccentricity ε and rotor diameter dr as
follows:
gf =
dr
ε
(1)
For the test purpose high torque produced is transmitted outside with help of simple “fork” type mechanical system (chosen point of rotor performs movement of hypocycloidal shape [8, 9]). In the prototype simple one key per phase drive system is
adapted as shown on Fig.2. Code disc mounted on crankshaft end together with sensor
works as an absolute shaft position encoder. Mechanical mounting secures change of
sensor position during motor operation resulting in change of phase “switch on” angle.
RRSRM is a torque delivering machine, operating with low rotational speed [10], thus
simple single switch system was adapted. Low switching frequency makes possible to use
freewheeling phase current to produce useful torque for adequate switch “on” angle.
3. SYMULATION MODEL OF RRSRM
Electrical equation of the machine can be described as follows:
∂ψ (i, ϑ ) di ∂ψ (i,ϑ ) dϑ
+
+ Ri = u (t ) ,
∂i
dt
∂x
dt
(2)
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∂ψ (i,ϑ ) di
di
= Ld (i,ϑ ) – transformation voltage in the phase winding,
∂i
dt
dt
∂ψ (i,ϑ ) dϑ
dϑ
– rotation voltage in the phase winding, Ψ – flux
= k E (i, x)
∂ϑ
dt
dt
were:
linkage, ϑ – angle of rotation, R – phase winding resistance, u(t) – supply voltage.
Fig. 2. Drive system adapted for test of RRSRM
Rys. 2. Układ napędowy badanego silnika RRSRM
Fig. 3. RRSRM phase inductance as a function
of rotor angle position and phase current
Rys. 3. Indukcyjność fazy silnika w zależności
od położenia kątowego wirnika
i prądu fazowego
Torque produced in the machine can be calculated as follow:
i
∂ ∫ψ (i,ϑ )di
0
∂ϑ
= M e (i,ϑ ) .
(3)
In consequence to be able to simulate machine behavior in dynamic state it is necessary to know the flux for all rotor positions and for all current densities. In case of
laboratory model both measurements of flux or phase inductance as a function of rotor angle and phase current can be performed. A set of characteristics of phase inductance is presented on Fig. 3.
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Due to the specific motor construction typical mechanical equation should be
modified [2] by adding gravity influence if rotor is unbalanced and noticeable preload
linked with anti-slip rubber rings and possible inaccurate crankshaft mechanical fitting:
J
dω
+ Dω + M g (ϑ ) + M 0 + M f (ϑ ) = M e (i, ϑ )
dt
(4)
were: D – rubber ring dumping coefficient, M g = mgε cos(ωt + ϑ g ) – torque of
gravity force origin, m – unbalanced mass, g – gravity factor, ϑ g –gravity force phase
shift), M0 – preload linked with rubber rings compression,
M f = M f max (1 + cos(ωt + ϑ f ) – torque of inaccurate crankshaft fitting origin.
4. MEASUREMENTS
Experimental results are limited to the only one type of phase switch “on/off”
strategy, and one type of torque transmission system due to hardware limitations.
Having simulation results compared with measurements and thus satisfactory level of
similarity confirmed for extended testing of RRSRM behavior simulation model can
be used [3]. The exemplary measurement results are presented below.
Fig. 4. Static synchronous torque of RRSRM
Rys. 4. Moment synchronizujący RRSRM
Measurement of static synchronous torque on the crankshaft end was preformed
for 1st and 3rd phase for two values of current – 1.6 A, and 2 A. Results of measurements are presented on Fig. 4. Differences result of inaccurate crankshaft mechanical
fitting. Synchronous static torque produced on torque end of the shaft can be calculated based on transmission factor gf of RRSRM assuming non-slippery roll of rotor.
Measurement of static synchronous torque on the crankshaft end was preformed
for 1st and 3rd phase for two values of current – 1.6 A, and 2 A. Results of measurements are presented on Fig. 4. Differences result of inaccurate crankshaft me-
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chanical fitting. Synchronous static torque produced on torque end of the shaft can be
calculated based on transmission factor gf of RRSRM assuming non-slippery roll of
rotor.
Fig. 5. Experimental dependence of rotational
frequency of crankshaft end and motor current on
supply voltage in respect to switch “on” angle for
72 deg switch “on” span
Rys. 5. Zależność częstotliwości obrotowej wału
i prądu od napięcia zasilania w funkcji kąta
załączenia pasma dla kąta przewodzenia 72°
Fig. 6. Trajectory of electromagnetic torque projected on electromagnetic torque plane captured for
5 subsequent crankshaft full 360 deg rotations
Rys. 6. Trajektoria pracy silnika na powierzchni
odzwierciedlającej moment elektromagnetyczny
zarejestrowana podczas symulacji dla 5 pełnych
obrotów wału
Fig. 7. Temperature rise of phase 3 winding
during load test. Thermal sensors placed in
the frontal and groove part of winding
Rys. 7. Przyrost temperatury uzwojenia 3 pasma fazowego podczas obciążenia. Czujnik
temperatury został umieszczone na dnie żłobka
i w czole uzwojenia
No load tests were performed for three different values of supplying voltage (20 V,
25 V and 30 V). Exemplary results of measurements of rotational frequency of crankshaft end and mean value of motor current for fixed angular “switch on” span and
different supply voltages are presented on Fig. 5. Due to high torque ripples for the
well advanced and delayed switch “on” angles (close to –30 deg and +40 deg) witch
can be regarded as a torque pulses swaying of shaft rotational speed can be noticed
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both during experiment and simulation. Additionally a phenomenon of shaft sway of
electromechanical resonant nature can be observed. Simulated trajectory of electromagnetic torque produced in one chosen phase during several full 360 deg rotations of
crankshaft end is shown on Fig. 6. Different trajectory path for each subsequent full
shaft rotation evokes chaotic behavior. During tests the motor was cooled only in
natural way, no forced cooling in any kind was adapted. Thermal test was performed
for 9.5 Nm load, angular switch “on” span 72°, supply voltage 30 V. Test results are
presented on Fig. 7.
5. CONCLUSIONS
Analysis of measurements allows checking correctness of motor design and formulating several remarks that help to improve motor construction:
a) over sized winding grove cross section (linked with assumed current density) resulting in comparatively low winding temperature gives the room for making the stator and frame motor thinner;
b) to avoid appearance of torque originating in inaccurate crankshaft fitting demands of very high quality of mechanical treatment should be secured;
c) application of modified system of torque reception from rolling rotor is necessary to assure smooth shaft rotation.
d) simple “one key per phase drive system” impose supply voltage level/switch
“on” phase control strategy for lowest torque ripple level operation;
e) in case of battery operation requirements and torque ripples permissible the
switch “on” span control strategy is recommended.
The satisfactory similarity between simulation results laboratory measurements allows using the simulation model for testing different control strategies [1, 6] and motor dynamic behavior forced by operation cycles and load change.
REFERENCES
[1] BIERNAT A., Regulacja momentu w silniku reluktancyjnym z toczącym się wirnikiem. [Torque control of Rolling Rotor Switched Reluctance Motor]. International Symposium on Electrical Machines –
SME, 2003, p. 297–305
[2] BIERNAT A., Identyfikacja wpływu parametrów węzłów mechanicznych na dynamikę przełączalnego
silnika reluktancyjnego z toczącym się wirnikiem. [Identification of mechanical nodes parameters influence on dynamics of Rolling Rotor Switched Reluctance Motor]. Prace Naukowe Politechniki
Warszawskiej, rok 2001, Elektryka z. 116, pp. 49–60
[3] BIERNAT A., KAMIŃSKI G., Dynamika przełączalnego silnika reluktancyjnego z toczącym się
wirnikiem, Prace Naukowe Politechniki Warszawskiej, 2001, Elektryka Nr. 117, p. 5–16
[4] BORZIAK J.G., ZAJKOW M.A, NANII W. P., Elektrodwigatieli s katiaszczimsia rotorom, Kijew
Tehnika, 1983;
[5] KAMIŃSKI G., Silniki elektryczne z toczącymi się wirnikami, WPW 2003
58
[6] REINERT J., ENSLIN J.H.R., SMITH E.D. Digital Control and Optimization of a Rolling Rotor
Switched Reluctance Machine, IEEE Transactions on Industry Applications, Vol. 31, No. 2,
March/April 1995
[7] SCHON R., Elektrische Wälzmaschinen, Elektrotechnik und Maschinenbau. No3, 1961
[8] VIVIANI A., Experimental and theoretical study of hypocycloidal motors with two-harmonic field
windings, IEEE Transactions on Power Systems, 1980, p. 292–300
[9] WILLIAMSON A.C., SPOONER E., BELARBI M., Improvements in hypocycloidal machines, Proceedings of the International Conference on Electrical Machines, Pisa, Italy, Sept. 12–14, 1988, Vol. 3,
p. 351–356
[10] Wójcik M., Silniki wolnobieżne o wirniku toczącym się, Przegląd Elektrotechniczny nr 2, 1978
[11] Rolling-rotor electrical machine, Grant N0 40125/06 conducted in collaboration by Helsinki University of Technology and Warsaw University of Technology, sponsored by finish Academy of Technology Sciences TEKES, WARTSILA Oy and ABB/Finland, 2005–2007