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1. Single-phase motors
Many industrial and domestic applications, computers, office equipment and instruments require small single-phase auxiliary electric motors rated up to 200W fed from 50 or 60 Hz single-phase mains. Applications, such as fans, sound equipment and small water pumps were a decade ago the exclusive domain of the very low-efficiency shaded pole induction motor. Owing to cost-effective magnets and power electronics, PM brushless motors can successfully replace cage induction motors. Higher efficiency and smaller sizes of PM brushless motors reduce the energy consumption, volume and mass of apparatus.
1.1 Single-phase two-pole motors with nonuniform air gap
A salient pole PM synchronous motor can be designed with nonuniform air gap as a self-starting motor. With regard to the stator magnetic circuit, two types of construction can be identified: U-shaped, two-pole asymmetrical stator magnetic circuit (FIG. 1) and two-pole symmetrical stator magnetic circuit (FIG. 2). In both asymmetrical and symmetrical motors, the nonuniform air gap can be smooth (Figs 1a and 2a) or stepped (Figs 1b and 2b). The leakage flux of a U-shaped stator is higher than that of a symmetrical stator. Nonuniform air gap, i.e., wider at one edge of the pole shoe than at the opposite edge, provides the starting torque as a result of misalignments of the stator and rotor field axes at zero current state.
The rest angle θ0 of the rotor is the angle between the center axis of the stator poles and the axis of the PM rotor flux. These motors are self starting only when, with the armature current Ia = 0, the angle θ0 > 0. The largest starting torque is achieved when the rest angle θ0 =90 deg. The motor constructions shown in FIG. 1 limit the rest angle to θ0 = 5 ... 120, which consequently results in a small starting torque. The motors shown in FIG. 2 can theoretically achieve θ0 close to 90 deg.
With zero current in the stator winding, the rest angle θ0 > 0 as the at tractive forces between PM poles and the stator stack align the rotor center axis with the minimum air gap (minimum reluctance). After switching on the stator voltage the stator magnetic flux will push the PM rotor towards the center axis of the stator poles. The rotor oscillates with its eigen-frequency.
If this eigen-frequency is close enough to the stator winding supply frequency, the amplitude of mechanical oscillations will increase and the motor will begin to rotate continuously. The eigenfrequency depends on the moment of inertia of the rotor and mechanical parameters. Larger motors with lower eigenfrequency thus require lower supply frequencies. It is important to know the dynamic behavior of these motors at the design stage to ensure the desired speed characteristics.
The advantages of these motors are their simple mechanical construction and relatively high efficiency at small dimensions and rated power. Owing to a simple manufacturing process, it is easier to fabricate the asymmetrical stator than the symmetrical stator. The symmetrical design can achieve almost the maximum possible starting torque (θ0 close to 90 deg.), while the asymmetrical design has a relatively small starting torque. It should be noted that the direction of rotation in both designs cannot be predetermined.
The disadvantage is the limited size of the motor if it is to be utilized in its self-starting mode. FIG. 3 shows the oscillations of speed and current during start-up of a lightly loaded small motor. If the load increases, the oscillations of speed decrease more quickly than those in FIG. 3.
The electromagnetic torque developed by the motor can be found by taking the derivative of the magnetic co-energy with respect of the rotor angular position θ . If the magnetic saturation is neglected, the torque developed by the motor with p = 1 is […]
1.2 Single-phase multi-pole motors with oscillatory starting
Single-phase PM motors rated up to a few watts can also have a cylindrical magnetic circuit, multi-pole stator and rotor and the self-starting ability as a result of mechanical oscillations. The magnetic circuit of such a motor is schematically sketched in FIG. 4a. The PM rotor is shaped as a six-point star . Each pole is divided into two parts. Distances between two parts of poles are not equal: the distance between every second pole is equal to 2t; for the remaining poles the distance is 1.5t. The stator toroidal winding is fed from a single-phase source and creates 36 poles. The number of poles is equal to the number of teeth. Under the action of a.c. current the stator poles change their polarity periodically and attract the points of rotor star alternately in one or the other direction. The rotor starts to oscillate. The amplitude of mechanical oscillations increases until the rotor is pulled into synchronism.
The direction of rotation is not determined. To obtain the requested direction, the motor must be equipped with a mechanical blocking system to oppose the undesirable direction of rotation, e.g., spiral spring, locking pawl.
Owing to constant speed, these motors have been used in automatic control systems, electric clocks, sound and video equipment, movie projectors, impulse counters, etc.
The PM single-phase motor with oscillatory starting for impulse counters manufactured by AEG has a disk rotor magnetized axially as shown in Fig. 5. Mild steel claw poles are placed at both sides of the disk-shaped PM (Fig. 6). To obtain the requested direction of rotation each pole is asymmetrical.
The stator consists of a toroidal single-phase winding with inner salient poles, the number of which is equal to the number of rotor poles. The stator poles are distributed asymmetrically pair by pair. One pole of each pair is shorted by a ring. Polarity of each pole pair is the same and changes according to the stator a.c. current. The oscillatory starting is similar to that of the motor shown in FIG. 4. Specification data of SSLK-375 AEG motor is:
Pout ˜ 0.15 W, Pin ˜ 2W, V1 = 110/220 V, 2p = 16, f = 50 Hz, ns = 375 rpm, ? =7.5%, starting torque Tst =0.785 Nm with regard to 1 rpm, shaft torque at synchronous speed Tsh =1.47 Nm. This motor can be used for measurement of d.c. pulses. The stator winding fed with a d.c. pulse can produce a magnetic field in the air gap which turns the rotor by one pole pitch, i.e. each pulse turns the rotor by 22.50 since the motor has 16 poles and 360 deg./16=22.50. Thus, one full revolution corresponds to 16 pulses. Such motors are sometimes equipped with a mechanical reducer. In this case the angle of rotation is determined by the gear ratio.
PM multi-pole synchronous motors with oscillatory starting are characterized by high reliability, small dimensions, relatively good power factor and poor efficiency as compared with their low rated power and price.
1.3 Single-phase cost-effective PM brushless motors
Single-phase and two-phase PM brushless motors are used in many applications including computer fans, bar code scanners (Table 1), bathroom equipment, vision and sound equipment, radio-controlled toys, mobile phones (vibration motors), automobiles, etc.
A single-phase PM brushless motor behaves as a self-starting motor if the input voltage is controlled with regard to the rotor position. The motor is self-starting independently of the North or South rotor pole facing Hall sensor which is placed in the q-axis of the stator. The desired direction of rotation can be achieved with the aid of the electronic circuitry which produces the stator field with a proper phase shift related to the rotor position, etc.
The simplest electronics circuitry with a triac is shown in FIG. 7a. The triac is switched on only when the supply voltage and the motor EMF are both positive or negative. The task of the electronics circuitry is to feed the motor at starting and at transient operation, e.g., sudden overload.
The motor is also equipped with a synchronization circuit which bypasses the power electronics converter and connects the motor directly to the mains at rated speed.
In the line-frequency variable-voltage converter shown in FIG. 7b the switches 1 and 3 are in on-state when the supply voltage and the motor EMF are both positive or negative. The switches 2 and 4 conduct the current when the supply voltage and motor EMF have opposite signs and the voltage across the motor terminals is zero. Converters according to Figs 7a and 7b produce pulse voltage waveforms, low frequency harmonics (torque ripple) and transient state at starting is relatively long.
The d.c. link power electronics converter according to FIG. 7c provides the starting transient independent of the supply frequency and reduces the harmonic distortion of the inverter input current. The motor is supplied with a square voltage waveform at variable frequency.
The cost effective single-phase brushless motor has a salient pole stator and ring-shaped PM. FIG. 7d shows a four pole motor with external rotor designed for cooling fans of computers and instruments.
The cost-effective single phase PM brushless motor can also be designed as a TFM with star-shaped stator core embracing the single-coil winding.
In the single phase motor shown in FIG. 8 the stator has six teeth, i.e., half of the rotor PM poles. The stator left and right star-shaped steel disks are shifted by 30 mechanical degrees, i.e., one pole pitch to face rotor poles of opposite polarity. In this way closed transverse magnetic flux paths are created. The cogging torque can be reduced by proper shaping of the stator salient poles.
2. Actuators for automotive applications
PM brushless actuators can provide high torque density and conversion of electric energy into mechanical energy at high efficiency. Most rotary electromechanical actuators for motor vehicles must meet the following requirements:
• working stroke less than one full revolution (less than 360 deg.)
• high torque
• symmetrical performance both in left and right directions of rotation
• the same stable equilibrium position for the PM cogging torque and electromagnetic torque.
Basic topologies of PM brushless actuators are shown in FIG. 9. The stator consists of an external magnetic circuit and excitation coil.
The rotor is comprised of two mechanically coupled toothed ferromagnetic structures and a multipole PM ring or disk inserted between them (cylindrical and disk actuators) or below them (claw pole actuator). The number of salient teeth of the magnetic parts is equal to half of the PM poles and depends on the required angle of limited angular motion. The limited angular motion of the PM with respect of the toothed ferromagnetic parts is performed in addition to the full rotary motion of the rotor. This feature requires an additional air gap between the stator and rotor which deteriorates the performance. Since the torque is proportional to the number of independent magnetic circuit sections equal to the number of PM pole pairs, multipole rotary actuators provide the so-called "gearing effect".
With the increase of the PM energy and applied magnetic field strength the magnetic flux density distribution in the air gap changes from sinusoidal to trapezoidal when the saturation level is approached. The actuators shown in FIG. 9 have been successfully implemented in General Motor's Magnasteer power steering assist system. Both sintered and die quench NdFeB magnets have been used.
3. Integrated starter-generator
The integrated starter-generator (ISG) replaces the conventional starter, generator and flywheel of the engine, integrates starting and generating in a single electromechanical device and provides the following auxiliary functions:
• automatic vehicle start-stop system which switches off the combustion engine at zero load (at traffic lights) and automatically restarts engine in less than 0.3 s when the gas pedal is pressed;
• pulse-start acceleration of the combustion engine to the required cranking idle speed and only then the combustion process is initiated;
• boost mode operation, i.e., the ISG operates as electric auxiliary motor to shortly drive or accelerate the vehicle at low speeds;
• regenerative mode operation, i.e., when the vehicle brakes, the ISG operates as an electric generator, converts mechanical energy into electrical energy and helps to recharge the battery;
• active damping of torsional vibration which improves driveability.
Automatic vehicle start-stop system and pulse-start acceleration improves the fuel economy up to 20% and reduces emissions up to 15%. The rotor of the ISG, like a flywheel, is axially fastened on the crankshaft between the combustion engine and clutch (transmission) as shown in FIG. 10. Because the application of ISG eliminates the traditional generator (alternator), starter, flywheel, pulley and generator belt, the number of components of the vehicle propulsion system is reduced.
The ISG rated between 8 and 20 kW and operates on a 42 V electrical system. Both induction and PM brushless machines can be used. To reduce the cost of ISGs, ferrite PMs are economically justified. The ISG is a flat machine with the outer stator diameter approximately 0.3 m and number of poles 2p = 10. Buried magnet rotor topology is recommended. For example, for a three-phase 12 pole machine the number of the stator slots is 72. The ISG is interfaced with the vehicle electrical system with the aid of 42 V d.c. six switch inverter.
4. Large diameter motors
A thin annular ring with a large diameter-to-length ratio, allows the motor to be wrapped around a driven shaft. The direct connection of the motor to the load effectively eliminates problems of torsional resonances due to couplings.
The absence of gears removes errors caused by friction and backlash, creating a high performance positioning system. Direct integration with the shaft also results in minimal volume of the motor. A large-diameter PM brushless motor with inner stator is shown in FIG. 11.
The outer diameters are up to 850 mm, the outer diameter-to-axial stack width ratio is 20 to 80 and number of poles 2p is from 16 to 64. Comparison of large diameter 20 Nm, 800 rpm PM brushless, induction and switched reluctance motors is given in Table 2. The PM brushless motor has the highest efficiency, lowest stator winding current density, lowest mass and highest torque density.
The direct-drive large-diameter PM brushless motor is ideally suited to high acceleration applications requiring improved response for rapid start-stop action. Applications include semiconductor manufacturing, laser scanning and printing, machine tool axis drives, robot bases and joints, coordinate measuring systems, stabilized gun platforms and other defense force equipment.
5. Three-axis torque motor
The three-axis torque motor can be designed as a PM or reluctance spherical motor . It can be used, e.g., in airborne telescopes. This motor has double-sided stator coils, similar to disk motors. There are usually slotless stator coils to reduce torque pulsations. The rotor can rotate 360 degrees around the x-axis, and by only a few degrees in the y- and z-axis.
FIG. 12 shows an example of a three-axis torque motor, designed and tested at the Technical University of Darmstadt. The rotor segments cover a larger angle than the stator segments. The overhang ensures a constant torque production for the range of y- and z-axis movement - 100 for this motor ( FIG. 12).
In designs with a complete spherical rotor three stator windings shaped as spherical sections have to envelop the rotor. The three windings correspond to the three spatial axes and are thus aligned perpendicularly to each other.
These three stator windings can be replaced with just one winding when the spherical rotor and stator have a diameter smaller than the diameter of the sphere, as shown in FIG. 12 The stator winding can then be divided into four sections with each section being controlled separately. Depending on the number of the winding sections activated and on the direction of the MMF wave, each of the three torques may be produced. The four inverters supplying the winding sections are shown in FIG. 13.
Owing to the 3D spherical structure, the performance calculation of this type of motor is usually done using the FEM.
6. Slotless motors
Cogging effect can be eliminated if PM brushless motors are designed with out stator slots, i.e., the winding is fixed to the inner surface of the laminated stator yoke. Sometimes, a toroidal winding, e.g., coils wound around the cylindrical stator core, are more convenient for small motors. In addition to zero cogging torque, slotless PM brushless motors have the following advantages over slotted motors:
• higher efficiency in the higher speed range which makes them excellent small power high speed motors;
• lower winding cost in small sizes;
• higher winding-to-frame thermal conductivity;
• smaller eddy current losses in rotor retaining ring and/or PMs due to larger air gap and less higher harmonic contents in the air gap magnetic flux density distribution;
• lower acoustic noise
The drawbacks include lower torque density, more PM material, lower efficiency in the lower speed range and higher armature current. With the increase in the total air gap (mechanical clearance plus winding radial thickness) the air gap magnetic flux density decreases and consequently so does the electromagnetic torque. The volume (radial height) of PMs must significantly increase to keep the torque close to that of an equivalent slotted motor.
A high speed slotless PM brushless motor is shown in FIG. 14. PMs are protected against centrifugal forces with the aid of a composite retaining sleeve. Two rings made of GFRP can be inserted into the stator core, one ring at each end of the stator. The outer diameter of the GFRP ring is equal to the stator core inner diameter and the inner diameter of the GFRP ring is determined by the mechanical clearance between the stator and rotor. Then, holes are drilled in GFRP rings at the conductor positions and conductors are threaded through these holes.
The armature reaction reactances Xad and Xaq of slotless motors with surface configuration of PMs can be calculated with the aid of equations, in which g_ = g + hM/µrrec and q_ q = gq, provided that both g and gq comprise the radial thickness of the armature winding. Owing to large nonferromagnetic gap, the magnetic saturation both in the d and q axis can be neglected.
Applications of slotless motors include medical equipment (handpieces, drills and saws), robotic systems, test and measurement equipment, pumps, scanners, data storage, semiconductor handling. Specifications of small two pole high speed motors with slotless armature winding are given in Table 2.
7. Tip driven fan motors
In the tip driven fan (TDF) the outer stator of PM brushless motor consists of four portions, one at each corner ( FIG. 15a). A cylindrical PM embraces the tips of fan blades. In comparison with traditional fans, the motor hub area is reduced by 75%, the air flow is increased by 30% and the efficiency of heat dissipation is increased by 15%. Typical specifications of a TDF for CPU coolers ( FIG. 15b) are: dimensions 75 mm × 75 mm × 75 mm, number of poles 2p = 12, power consumption 2 W, rated current 0.17 A, rated speed 4500 rpm, rated voltage 12 C d.c. maximum air flow 0.014 m3/s, noise level 34 dB(A). Corner-located PM brushless motors rated at 120 to 600 W and speed 2700 rpm are used in cooling TDFs with volume flow 0.335 to 0.8 m3/s (ABB, Flakt Oy, Sweden).
Numerical example 1
Find the performance characteristics of the single-phase two-pole PM synchronous motor with oscillatory starting shown in FIG. 16a. The input voltage is V1 = 220 V, input frequency is f = 50 Hz, conductor diameter is da =0.28 mm, number of turns per coil is N1 = 3000, number of coils is Nc = 2 and NdFeB PM diameter is dM = 23 mm.
For the class F enamel insulation of the 0.28-mm conductor, its diameter with insulation is 0.315 mm. If the conductors are distributed in 20 layers (20 × 0.315=6.3 mm), 150 turns in each layer (150 × 0.315=47.25 mm), they require a space of 6.3 × 47.25 = 297.7mm2. Assuming a spool thickness of 1 mm, 9 layers of insulating paper of thickness 0.1 mm (every second layer) and an external protective insulation layer of 0.6 mm, the dimensions of the coil are: length 47.25+2×1.0 ˜ 50 mm and thickness 6.3+9×0.1+0.6=7.8 mm plus the necessary spacing, in total, the radial thickness will be about 8.6 mm.
The average length of the stator turn on the basis of FIG. 16a is:
l1av = 2(9+8.6+20+8.6) = 92.4 mm.
The resistance of the stator winding is calculated at a temperature of 750C.
The conductivity of copper at 750 Cis s1 =47 × 106 S/m. The cross section area of a conductor sa = pd2 a/4= p ×(0.28×10-3)2)/4=0.0616×10-6 m2.
The total winding resistance of the two coils is R1 = 2l1avN1 s1sa = 2 × 0.0924 × 3 000 47 × 10^6 × 0.0616 × 10^-6 = 191.5 Ohm
The calculation of the winding inductance and reluctance torque is done using a two-dimensional finite element model and the energy/current perturbation method. FIG. 16b shows a flux plot of the motor in its rest position at an angle of 50. The reluctance torque and total torque as functions of rotor angle are shown in FIG. 17a. The stator current at V1 = 220 V is about 0.26 A which corresponds to the current density Ja = 0.26/0.0616 = 4.22 A/mm^2. The self-inductance as a function of the rotor angle is plotted in FIG. 17b.
Numerical example 2
A 1.5 kW, 1500 rpm, 50 Hz PM brushless motor has the stator inner diameter D1in =82.5 mm and air gap (mechanical clearance) in the d-axis g =0.5 mm. The height of surface NdFeB PMs is hM = 5 mm, remanence Br =1.25 T and coercivity Hc = 965 kA/m. The standard slotted stator has been re placed by a slotless stator with inner diameter D_ in = 94 mm (inner diameter of winding) and winding thickness tw =6.5 mm. The rotor yoke diameter has proportionally been increased to keep the same mechanical clearance g =0.5 mm between magnets and stator winding.
Neglecting the saturation of magnetic circuit and armature reaction find the torque of the slotless motor. How should the rotor be redesigned to obtain 80% of the torque of the standard slotted motor?
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