Contactless Single-Section DC Micromotor
Abstract Generated abstract
This paper examines a contactless single-section DC micromotor intended for microfan drives, where the fan load permits the use of intermittent rather than continuous electromagnetic torque. It describes a design combining a single-phase motor, rotor position sensor, semiconductor commutator, and permanent-magnet holding device, and derives practical expressions for pulsed electromagnetic torque, average torque, rotor speed, and starting conditions under an adopted duty factor of 3. Tests on prototype micromotors showed close agreement between calculated and measured torque and speed, suggesting that the proposed formulas are suitable for engineering calculations at commutation frequencies up to about 500 Hz.
Full Text
CONTACTLESS SINGLE-SECTION DC MICROMOTOR
E. T. Dikii, G. A. Parkhomenko
(Presented by the scientific seminar of the Department of Electrical Machines and General Electrical Engineering)
At present, in a number of areas of technology there has arisen a need for micromotors to drive microfans powered from a DC source [1]. The use of commutator micromotors, as well as contactless DC micromotors with continuous electromagnetic torque [2], for driving fans is in some cases irrational because of certain disadvantages inherent in them.
Since, when a motor with a fan load is started, the torque produced on the motor shaft by the fan varies smoothly from zero to the steady-state value, it is possible to use, for driving microfans, a contactless DC micromotor with intermittent or pulsed electromagnetic torque, which in terms of weight and overall dimensions more closely approaches commutator DC micromotors, while at the same time being free of their main disadvantage—the presence of mechanical contact in the brush–commutator assembly.
The article presents theoretical and experimental investigations of contactless DC micromotors with pulsed electromagnetic torque. Structurally, the contactless electric motor under consideration consists of a single-phase electric motor, a rotor position sensor, and a semiconductor commutator. To ensure starting of the electric motor, a special device is provided which holds the rotor in a prescribed position. The holding device and the motor rotor are made using permanent magnets. The semiconductor commutator may be implemented either together with the motor or separately from it, depending on the technical requirements imposed on the drive.
The rotor position sensor generates signals that automatically control the operation of the semiconductor commutator in such a way that the motor winding is connected to the DC source at definite positions of the motor rotor relative to the stator.
When the drive is in the non-operating state, the holding device fixes the rotor relative to the stator in such a position that, at the moment the electric motor is connected to the power source, the power transistor of the commutator is open and a starting current flows through the stator winding; interacting with the magnetic flux of the rotor, this current creates a starting pulsed torque.
During acceleration of the electric motor, the stator winding is supplied by unipolar pulses of variable frequency. Theoretical and experimental studies show that the magnitude of the pulse duty factor substantially affects the energy performance of the electric motor. In order to obtain a sufficiently high efficiency and good starting properties in the micromotor under consideration, a duty factor equal to 3 is adopted.
In deriving expressions for the electromagnetic torque and the rotational speed of the rotor of the micromotor under consideration, we adopt the following conditions:
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The turn-on and turn-off time of the transistor switch, because of its smallness in comparison with the period, is not taken into account.
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The emf induced in the stator winding of the motor during rotation of the rotor is practically sinusoidal.
The instantaneous value of the emf in the stator winding is determined by the expression:
\[ e = E_m \sin \omega t, \]
where
\[ E_m = \sqrt{2}\cdot 4.44 \cdot W_{\phi}\cdot K_o \cdot p \cdot n \cdot \Phi \cdot 10^{-8} \]
\(W_{\phi}\) — number of rotor revolutions per sec,
\(K_o\) — winding coefficient of the first harmonic,
\(p\) — number of pairs of motor poles,
\(n\) — number of rotor revolutions per sec,
\(\Phi\) — useful magnetic flux of a pair of poles in Mx.
In the micromotor under consideration, the sensing elements of the rotor-position sensor are oriented relative to the stator in such a way that the stator winding is connected to the power source at those instants of time when the emf induced in the winding by the rotor field retains one sign, and its curve is symmetrically located with respect to the rectangular pulses, as shown in Fig. 1.
Fig. 1. Diagram of the emf and motor supply voltage
Since, for each rotation of the rotor through \(2\pi\) electrical degrees, the commutation process in the micromotor is periodically repeated, for analysis of its operation it is sufficient to consider the electromagnetic processes during the time in which the indicated rotation of the rotor occurs.
For practical calculations it is convenient to use the mean values of the pulsed electromagnetic torque developed by the motor. We obtain the expression for the mean value of the pulsed electromagnetic torque by using the expression for the mean pulsed value of the emf and the electromagnetic power. The mean pulsed value of the emf induced in the winding during commutation, with rotation of the rotor in the electric motor under consideration, is equal to
\[ E_{\text{av. p.}}= \frac{1}{\frac{\pi}{6}-\left(-\frac{5\pi}{6}\right)} \int_{-\frac{\pi}{6}}^{\frac{5\pi}{6}} E_m \cdot \sin \omega t\,dt =0.827\,E_m . \]
After substituting the value of \(E_m\), we obtain:
\[ E_{\text{av p}}=5.18\cdot k_0\cdot W_\phi\cdot p\cdot n\cdot \Phi\cdot 10^{-8}, \]
or
\[ E_{\text{av p}}=C_e\cdot n\cdot \Phi, \]
where
\[ C_e=5.18\cdot k_0\cdot W_\phi\cdot p\cdot 10^{-8}. \]
If the micromotor consumes an average current \(I_{\text{av}}\), then the average pulse current \(I_{\text{av p}}\), for the adopted duty ratio, is equal to
\[ I_{\text{av p}}=3\cdot I_{\text{av}}, \]
and the pulse-average electromagnetic power and the average electromagnetic power over a rotation through \(2\pi\) electrical degrees are, respectively,
\[ P_{\text{em p}}=3\cdot I_{\text{av}}\cdot E_{\text{av p}}, \qquad P_{\text{em av}}=I_{\text{av}}E_{\text{av p}}. \]
The average value of the pulsed electromagnetic torque and the average electromagnetic torque are obtained from the expressions for the average pulsed electromagnetic power and the average electromagnetic power:
\[ M_{\text{av. p}}=\frac{P_{\text{em. p}}}{\Omega}, \qquad M_{\text{av}}=\frac{P_{\text{em. av}}}{\Omega}, \]
where \(\Omega=2\pi n\) is the angular velocity of rotation of the rotor. After transformations, we finally obtain
\[ M_{\text{av p}}=0.84\cdot k_0\cdot W_\phi\cdot p\cdot I_{\text{av}}\cdot \Phi\cdot 10^{-9}\quad (kgm) \]
\[ M_{\text{av}}=0.84\cdot k_0\cdot W_\phi\cdot p\cdot I_{\text{av}}\cdot \Phi\cdot 10^{-9}\quad (kgm) \]
The expression for the average rotational speed of the rotor is obtained by using the emf equation of the electric motor. If single-polarity voltage pulses of amplitude \(u_m=\text{const}\) are applied to the terminals of the electric motor at a certain frequency, then a pulsed electromagnetic torque acts on the rotor, bringing the rotor into rotation. During the pauses, the motion of the rotor continues by inertia due to the change in the kinetic energy of the rotating parts of the drive. In the general case the electric motor operates in a transient mode, in which the back emf, the pulse current in the stator, and the rotational speed of the rotor vary continuously. In this case, a self-induction emf arises in the stator winding, \(L\dfrac{di}{dt}\), where \(L\) is the inductance of the stator circuit. The emf equation of the electric motor takes the form
\[ u-\Delta u-e-L\frac{di}{dt}=iR. \]
In practical calculations the self-induction emf may be neglected, owing to the smallness of \(L\), and the emf equation of the electric motor may be represented in the form
\[ u-\Delta u-E_{\text{av p}}=I_{\text{av p}}\cdot R, \]
where \(R\) is the resultant ohmic resistance of the stator circuit, \(\Delta u\) is the voltage drop across the collector-emitter junction of the power transistor. Substituting the value of \(E_{\text{av p}}\), we obtain the expression for the average rotational speed of the rotor of the electric motor:
\[ n=\frac{u-\Delta u-3I_{\mathrm{av}}R}{C_e\cdot \Phi}\ \text{rev/sec}. \]
For successful starting of the micromotor it is necessary to satisfy the following conditions:
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The holding device must reliably hold the motor rotor in a strictly defined position relative to the stator.
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The kinetic energy of the rotating parts of the drive, obtained during the action of the first pulse of electromagnetic torque at start-up, must be greater than the energy required to overcome the braking forces of the rotor during the subsequent pause.
The first condition can easily be fulfilled by providing one or two permanent magnets in the micromotor design. It should be noted here that, when the rotor is rotating, the holding device practically does not create additional losses in the motor, since the mean value of the torque produced during rotation of the rotor through \(2\pi\) electrical degrees is equal to zero.
The second condition may be represented by the following inequality:
\[ A_1-A_2>A_3, \]
where \(A_1\) is the work of the driving forces applied to the rotor during the action of the first pulse of electrical energy at start-up;
\(A_2\) is the work of the braking forces during the same time;
\(A_3\) is the work of the braking forces during the first pause at start-up.
For the accepted duty factor, equal to 3, the above-mentioned works may be represented by the following expressions:
\[ A_1=M_{\mathrm{av}\,p}\frac{2}{3}\pi\cdot k_1, \]
\[ A_2=\frac{2}{3}\pi\cdot k_1\left(M_{\mathrm{av}\,t}+M_{\mathrm{av}\,h}\right), \]
\[ A_3=\frac{4}{3}\pi\cdot k_2\cdot M_{\mathrm{av}\,t}. \]
After substitution, the inequality takes the following form:
\[ k_1\left(M_{\mathrm{av}\,p}-M_{\mathrm{av}\,t}-M_{\mathrm{av}\,h}\right)>2k_2\cdot M_{\mathrm{av}\,t} \]
\(k_1\) is a coefficient taking into account the circumstance that the action of the first pulse of electrical energy at start-up will cease before the rotor turns through an angle of 120 electrical degrees;
\(k_2\) is a coefficient taking into account the increase in the forces resisting rotation of the rotor due to the appearance of load as the rotor rotational speed appears.
\(M_{\mathrm{av}\,p}\) is the starting torque of the motor when the first pulse is applied.
\[ M_{\mathrm{av}\,p}=0.84\cdot k_0\cdot W_{\phi}\cdot p\cdot I_p\cdot \Phi\cdot 10^{-9}, \]
where
\[ I_p=\frac{u-\Delta u}{R}; \]
\(M_{\mathrm{av}\,h}\) is the mean torque of the holding device during rotation through 120 electrical degrees;
\(M_{\mathrm{av}\,t}\) is the mean torque of the rotor braking forces during its rotation through \(2\pi\) electrical degrees, consisting of the bearing friction torque and additional reactive torques arising because of nonuniformity of the magnetic resistance of the stator around the circumference of the air gap.
Table 1
| Motor type | \(U\), V | \(I_{\mathrm{dv}}\), A | \(M\), g cm | \(M_{\mathrm{em}}\), g cm | \(n\), rpm | \(\eta\), % | \(M_{\mathrm{em}}\) calc., g cm | \(n\) calc., rpm | \(2p\) |
|---|---|---|---|---|---|---|---|---|---|
| MBI-1 | 27 | 0.2 | 30 | 53.5 | 7500 | 42.6 | 54.6 | 7900 | 4 |
| MBI-2 | 24 | 0.41 | 100 | 172 | 4300 | 44.8 | 165 | 4130 | 4 |
For practical verification of the expressions given above, prototype models of micromotors were manufactured; their tests showed good agreement between the calculated and actual parameters. The test and calculation data are given in Table 1.
Theoretical studies and experimental tests of prototype samples of contactless direct-current micromotors with pulsed electromagnetic torque make it possible to draw the following conclusions:
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In designing electric drives with a fan load, in some cases a contactless direct-current microelectric motor with pulsed electromagnetic torque has substantial advantages over commutator direct-current micromotors and contactless direct-current micromotors with continuous electromagnetic torque.
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The expressions given for the electromagnetic torque and rotational speed of the micromotor under consideration are acceptable for practical engineering calculations at commutation frequencies of approximately up to 500 Hz.
REFERENCES
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E. A. Lodochnikov, V. G. Sheminov, A. G. Parkhomenko et al. “A series of microelectric drives of the MB type.” Elektrotekhnika, 1966, No. 2.
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I. E. Ovchinnikov, N. I. Lebedev, Contactless Direct-Current Motors for Automatic Devices. Nauka, 1966.