In this chapter you will learn about:
- The reluctance principle
- Reluctance-start induction motors
- Hysteresis motors
- Reluctance torque and hysteresis torque
- Stepper motors for precise positioning of mechanical systems
- Types of stepper motors and their applications
- Step angle per input pulse
- Permanent magnet stepper motors
- Variable-reluctance stepper motors
- Hybrid stepper motors
- Linear induction motors
- Unrolling conventional squirrel-cage induction motor to produce a linear induction motor
- Universal motors
- Simple problems on the above
Permanent magnet stepper motor
A.c. and D.c. machines and combinations of these machines are used, in general, for the conversion of mechanical energy to electrical energy and vice versa. There are, however, other kinds of dynamos and combinations of dynamos that perform similar energy conversion and are more specialized in nature and in application.
Machines, such as reluctance motors and hysteresis motors, are used for timing devices, tape recorders, tachometers, and other such devices with constant speed requirements. They are used extensively in process industries, such as the man-made fibre industry, where many components of the process line must operate in sync.
Stepper motors are used in conjunction with pulse-driving circuits for precise positioning of mechanical systems. They are essential components of disk drives, printers, plotters, and other applications that require step-by-step positioning.
Linear induction motors (LIMs) are used to apply mechanical forces and to cause movement in a straight or curved line. They are used in conveyer systems, door openers, aircraft launchers, electromagnetic guns, liquid metal pumps for nuclear reactors, high-speed rail transportation, etc.
Universal motors have applications in low-power apparatus, such as vacuum cleaners, small-power tools, and kitchen appliances.
42.2 RELUCTANCE-START INDUCTION MOTOR
The reluctance motor is an induction motor with a modified squirrel-cage rotor such as that shown in Figure 42.1. The notches, flats, or barrier slots provide equally spaced areas of high reluctance. The sections of rotor periphery between the high-reluctance areas are called salient poles; the number of salient poles must match the number of slots. The stator winding may be three phase or single phase.
Figure 42.1 Types of Rotor Laminations Used in Reluctance Motors
According to the reluctance principle, mechanical force is exerted on a sample of magnetic material located in a magnetic field. The force tends to act on the material in such a way as to bring the material into the portion of the magnetic field that has the greatest density. If the sample is irregularly shaped, it will tend to be aligned in such a way as to produce minimum magnetic reluctance, and, consequently, maximum flux density. Thus, particles of iron filings are aligned in the presence of a magnetic field parallel to the field direction.
The reluctance-start induction motor whose starting is initiated by the reluctance principle is not the same as a non-excited synchronous motor. The reluctance principle states that where the air gap is small, the self-inductance of the field winding is high, causing the current in the field winding to lag the flux that produced it; conversely, where the air gap is high, the self-inductance is reduced and the current is more exactly in phase with the flux. The mutual air gap flux is delayed, therefore, in the vicinity of air gap, producing a sweeping effect similar to that produced in the shaded-pole motor. Since the fluxes are displaced somewhat in time and also in space, a rotating magnetic field is produced at all field poles at instants t1 t2 and t3 successively, as shown in Figure 42.2.
Figure 42.2 Reluctance-start Induction Motor and Development of Rotating Field
The running torque characteristics of the salient-pole reluctance-start induction motors are not as good as those of the non-salient-pole shaded-pole motor. This is evident because, in order for the speed e.m.f. to develop a rotating magnetic field once rotation has been initiated, the air gap must be fairly uniform. Furthermore, similar to the shaded-pole motor, the starting torque of the reluctance-start motor is also poor. Other than reversing the poles on the stator, there is no way of changing the direction of rotation of the reluctance-start induction motor. Operation is always in the direction from high to low air gap, i.e. to maximize the field.
The shaded-pole motor is generally preferred over the reluctance-start induction motor since it is less expensive to manufacture, has higher efficiency and better running torque characteristics and it is reversible. Speed control is the same for both the motors.
Single-phase cylindrical (non-salient-pole) synchronous induction or shaded-pole motors are classified as hysteresis motors. The difference between this motor and the reluctance motor is in (1) the shape of the rotor and (2) the nature of torque produced.
The reluctance motor is pulled into synchronism and runs on reluctance torque, whereas the hysteresis motor pulls into synchronism and runs on hysteresis torque. Hysteresis-type laminations are made of hardened high-retentivity steel rather than commercial low retentivity dynamo steel.
The stator of the hysteresis motor is the same as that for an induction motor. The rotor, however, consists of a smooth cylinder made of very hard permanent-magnet alloy material and a nonmagnetic support as shown in Figure 42.3(a).
Rotating magnetic field produced by phase splitting or a shaded-pole stator induces eddy currents in the steel of the rotor and travel across the two bar paths (Figure 42.3(b)). A high-retentivity steel produces a high hysteresis loss, and an appreciable amount of energy is consumed from the rotating field in reversing the direction of the rotor.
At the same time, the rotor magnetic field set up by eddy currents causes the rotor to rotate. A high starting torque is produced as a result of the high rotor resistance (proportional to the hysteresis loss). As the rotor approaches synchronous speed, the frequency of current reversal in the crossbars decreases and the rotor becomes permanently magnetized in one direction as a result of the high retentiveness of the steel rotor. With two field poles, the rotor shown in Figure 42.3 (b) develops a speed of 3600 r.p.m. at 60 Hz. The motor runs as a hysteresis motor on hysteresis torque because the rotor is permanently magnetized.
Figure 42.3 (a) Rotator for Hysteresis Motor (b) Hysteresis-type Laminations of Hardened High-retentivity Steel
The principle of hysteresis motor action is further explained using the elementary hysteresis motor shown in Figure 42.4. The magnets represent the stator flux, which serves to induce opposite magnetic polarity in the hardened alloy rotor. With the magnets stationary, as shown in Figure 42.4(a), the magnetic axis of the rotor poles is coincident with the magnetic axis of the stator. Spinning the stator magnets, with the rotor blocked as shown in Figures 42.4(b, c), provides a rotating magnetic field that exerts a torque on the induced magnetic poles of the rotor. As the stator poles rotate, the induced magnetic poles in the rotor constantly reform in new positions, following the rotating flux. Because of hysteresis, the rotor poles always lag the stator poles by angle δh. The constant lag angle results in a constant force of attraction, and hence a constant accelerating torque. Releasing the rotor, and assuming no overload, the constant torque will accelerate the rotor to synchronous speed.
Figure 42.4 Hysteresis Motor Behaviour: (a) Magnets and Rotor Stationary (b) and (c) Rotor Blocked and Magnets Rotating
The amount of torque produced as a result of this magnetization is not as high as that of a reluctance torque. However, hysteresis torque is extremely steady in both amplitude and phase despite fluctuations in supply voltage; hence, it is widely used in high- quality cassette players, compact disk players, record players, and tape recorders. As reluctance torque can be produced more cheaply than hysteresis torque for the same fractional horse power, high-torque hysteresis motors are more expensive than reluctance synchronous motor of the same rating.
Because of their low inertia, smaller single-phase hysteresis motors accelerate to their synchronous speed in a few cycles of input. These motors find great application in timing and clock mechanisms (Figure 42.5), where the synchronous speed (for two poles) is 3600 r.p.m. This speed lends itself quite well to high-torque gear reductions, i.e., 1 r.p.m. for the second hand and/or 1 r.p.m. for the minute hand. Yet another important application of the polyphase hysteresis motor is found in inertial guidance and gyroscope rotors, which require absolutely constant speed as a function of line frequency.
Figure 42.5 Timing Clock
The following are some unique features of the hysteresis motor:
- The constant-hysteresis torque (Figure 42.6) from locked rotor to synchronous speed permits the hysteresis motor to synchronize any load that it can accelerate; no other motor can perform in this manner.
- The smooth rotor provides quiet operation. It does not suffer from magnetic pulsations caused by slots and/or salient poles that are present in the rotors of other motors.
- The relatively high resistance and high reactance of the hysteresis rotor limit the starting current to approximately 150 per cent rated current. This contrasts significantly with the reluctance rotor, whose low reactance and low resistance result in a locked-rotor current of approximately 600 per cent rated current.
Figure 42.6 Torque–speed Characteristic of the Hysteresis Motor
42.4 STEPPER MOTORS
Stepper motors, also called stepping motors are highly accurate pulse-driven motors that change their angular position in steps, in response to input pulses from digitally controlled systems. Stepper motors are used for precise positioning of mechanical systems and may be used without feedback. Examples of their applications include head positioning in computer disk drives, positioning of carriage, ribbon, point head and paper feed in typewriters, as well as printers, robots, etc.
The step angle per input pulse depends on the construction of the stepper motor and the control system used. Stepper motors with a 45° step angle provide a resolution of 360/45 equal to eight steps per revolution; stepper motors with a 1.8 step angle provide a resolution of 360/1.8 equal to 200 steps revolution etc. The total angle travelled by the rotor is equal to the step angle times the number of steps. It can be expressed mathematically as follows:
where, β = step angle (deg/pulse)
θ = total angle travelled by rotor (degree)
The speed of a stepper motor is a function of the step angle and stepping frequency (called the pulse rate). Thus,
where, n = shaft speed (rps)
ƒp = stepping frequency (pulses/s)
A stepper motor has a 2.0° step angle. Determine (1) resolution, (2) number of steps required for the rotor to make 20.6 revolutions, (3) shaft speed if the stepping frequency is 1800 pulses/s.
Resolution = steps/rev= 360/2.0 = 180
θ = β × step= 20.6 × 360 = 2.0 × steps
42.4.1 Types of Stepper Motors
In all types of stepper motors, rotation is produced by switching suitably connected windings in some predetermined sequence to produce angular discrete rotation steps that are essentially uniform in magnitude. The three most popular types of stepper motors are as follows:
- Variable-reluctance (VR) type, also known as reactive-rotor type.
- Permanent magnet (PM) type, sometimes called active-rotor type.
- Hybrid type, a combination of PM and VR.
42.4.2 Variable-reluctance Stepper Motors
The toothed stator and toothed rotor of a variable-reluctance stepper motor, as shown in Figure 42.7, are constructed from soft steel that retains very little residual magnetism. Coils wound around the stator teeth provide the magnetic attraction that establishes the rotor position. The reluctance of the magnetic circuit formed by the rotor and stator teeth varies with the angular position of the rotor. Energizing one or more stator coils causes the rotor to step forward, or to step backward, to a position that forms a path of least reluctance with the magnetized stator’s teeth.
Figure 42.7 Variable-reluctance Stepper Motor Showing Different Step Positions Corresponding to the Switching Sequence in (f)
A simple circuit arrangement for sequencing current to the stator coils is shown in Figure 42.7(f). The eight stator coils are connected in two-coil groups to form four separate circuits called phases. Each phase has its own independent switch. Although shown as mechanical switches in Figure 42.7, in actual practice, switching of phases is accomplished with solid-state control.
Figure 42.7(a) illustrates the position of the rotor with SW1 closed, energizing phase A; the rotor is in a position of minimum reluctance with rotor teeth 1 and 4 aligning with stator teeth 1 and 5, respectively. Closing switch SW2 and opening switch SW1 energize phase B, causing rotor teeth 3 and 6 to align with stator teeth 4 and 8, respectively, as shown in Figure 42.7(b), for an angular step of 15°. Closing switch SW3 and opening switch SW2 energize phase C, causing rotor teeth 2 and 5 to align with stator teeth 3 and 7, respectively, as shown in Figure 42.7(c). As each switch is closed and the preceding one opened, the rotor moves an additional step angle of 15°. The stepping sequence, as shown in Figure 42.7(a, c), follows the sequence of switches repeating 1 through 4, over and over, until the desired number of revolutions or a fraction of a revolution is achieved.
The direction of rotation for 1 – 4 switching sequence (shown in Figure 42.7) results in clockwise (CW) stepping of the rotor. Reversing the sequence of pulses by closing the switches in the order 188.8.131.52 will cause counter-clockwise stepping.
The relationship between step angle and the number of teeth in the rotor and the number of teeth in the stator is
where, β = step angle in space degrees
Ns = number of teeth in stator core
Nr = number of teeth in rotor core
42.4.3 Permanent-magnet Stepper Motors
A simplified diagram of a permanent-magnet stepper motor is shown in Figure 42.8. The rotor shown in Figure 42.8(b) has two toothed sections separated by a permanent magnet. The two sections are offset from each other by one-half of a tooth pitch. The magnet provides opposite polarity to each section, developing north poles in one section and south poles in the other section. Figures 42.8(a, c) show the two end views of the combined rotor and stator. All north poles are on one end and all south poles are on the other end. The stator coils shown in Figures 42.8(a, c) span both rotor sections. An axial view of the assembled stepper motor is shown in Figure 42.8(d).
Figure 42.8 Permanent Magnet Stepper Motor: (a) Stator and South Section of Rotor (b) Rotor (c) Stator and North Section of Rotor (d) Axial View of Assembled Motor
Each rotor section contributes to the development of torque. In effect, the sections are in parallel. The net effect is that of a five-tooth rotor with a four-tooth stator (in this illustration). The step angle for the stepper in Figure 42.8 is
The principle of operation of a permanent magnet stepper motor is developed using the circuit diagram, switching table, and the corresponding rotor positions in Figure 42.9. For simplicity, only the south section of the rotor is shown. The rotor positions are keyed to the switching sequence for clockwise rotation; phase A is energized by SWI and phase B is energized by SW2.
Figure 42.9 Circuit Diagram of a Permanent Magnet Stepper Motor with Rotor Positions Keyed to Switching Sequence for Clockwise Rotation
The hybrid stepper motor is a combination of the PM and the VR types. Typically, most hybrid stators have eight poles and each pole has between two and four teeth.
Two phases are wound on the eight poles, i.e., there are four poles per phase. The rotor always has a permanent magnet along with soft-iron pole structure containing an even number of teeth (typically 18). The PM or stepper motors, along with the stepping angle, is independent of the number of phases and is purely a function of the number of rotor teeth. For each change of stator excitation, the stepping angle is
where, P is the number of rotor teeth.
A hybrid stepper motor has fifty variable-reluctance teeth. Calculate the stepping angle in degrees.
42.4.5 Comparison of Stepper Motor Types
The major advantage of hybrid motors is their small stepping angle. This is important whenever high-resolution angular positioning is required. The torque produced by hybrids is greater than that for VR and/or PM types for a given motor volume. Consequently, whenever high torque and small stepping angles are required and space is limited, the hybrid stepping motor is used.
VR stepping motors are chosen for the following two major applications:
- The VR motor is used whenever the load must be moved by a considerable distance requiring several revolutions of the motor. As the stepping angle is greater, fewer steps and correspondingly fewer excitation changes are needed to reach the required distance. This results in less time to produce the change.
- The inertia of the V/R motor is lower because it does not carry a permanent magnet. This reduced inertia enables the VR motors to accelerate the load faster and reduces the possibility of overshoot or oscillation at the end of a step.
PM stepper motors exhibit the highest inertia and the highest rotational speed because they usually rotate at higher stepping angles. Because of their inherently higher speed, the torque for a given hp rating is lower. Production of PM stepper motors is, therefore, limited to the smallest power ratings.
The major difference between conventional induction motor (producing rotary motion) and a linear induction motor (producing linear motion) is the difference in their respective air gaps. The rotating induction motor has a closed air gap, whereas the linear induction motor has an open air gap with an entry end and exit end.
Figure 42.10(a) shows the cross-section of a conventional squirrel-cage induction motor. Primary conductors are embedded in the stator core and secondary conductors are embedded in the rotor core. The air gap is closed upon itself. If we imagine that the conventional squirrel-cage induction motor in Figure 42.10(a) is unrolled to the left and right, as shown in Figure 42.10(b), we obtain the LIM. In effect, the magnetic rotor core may now be considered as a magnetic strip and the secondary rotor conductors as a conductive strip. The primary conductors embedded in a magnetic flat-slotted bed still continue to produce a moving (gliding) flux as a result of their polyphase currents.
If we assume that the primary winding in Figure 42.10(b) is stationary and produces a gliding flux continuously from left to right, the secondary conductive and magnetic strip will also move from left to right, but not at the same speed as the flux. There must be some slip theoretically in order to develop force on the secondary.
Figure 42.10 Unrolling Conventional Squirrel-cage Induction Motor to Produce a Linear Induction Motor
Figure 42.11(a) shows one common form of LIM with a short primary and relatively long secondary magnetic sheet and conductive sheet. In this short primary single-sided linear induction motor (SLIM), the secondary is stationary and the primary is capable of motion. In this mode, SLIM is used for long operating distances, because it would be too expensive to design a full-length primary winding. As the secondary is stationary and fixed, the induced secondary currents produce flux to propel the primary along the conductive strip. This design is typically used in cranes, where the three-phase power is available in the crane cab, and the secondary is a steel I-beam.
Figure 42.11(b) shows the short-secondary single-sided SLIM, in which the secondary conductors are embedded in a flat-slotted core.
This type of LIM is suitable for limited distances but develops relatively high thrust forces.
Figure 42.11(c) shows the double-sided primary LIM with a coreless secondary. The double-primary construction provides a more definite magnetic circuit. It is essentially the design used with a railway car LIM. The secondary sheet shown in Figure 42.11(c) may be either a magnetic or a non-magnetic material.
Figure 42.11 Flat Three-phase Linear Induction Motors
42.6 UNIVERSAL MOTORS
Universal motor is a name given to a type of motor that can operate either on a.c. or d.c. with about the same speed characteristics. This is a series-connected motor, in which the armature and the field coils are connected in series.
An elementary universal motor (Figure 42.12(b, c)) has its rotating part, called the armature, connected in series with the series-field winding. The rotating commutator and stationary brushes constitute a rotary switch that reverses the direction of the current in the armature coil as the coil rotates. The equivalent circuit diagram is shown in Figure 42.12(d).
Figure 42.12 Universal Motor and its Equivalent Circuit
The direction of developed torque, and hence the direction of armature rotation, is independent of polarity of the a.c. source. This is shown in Figure 42.12(b, c) for the respective alternations of the a.c. source. The direction of the mechanical force exerted on each conductor is determined by the flux bushing rule.
The torque developed by the universal motor is proportional to the flux density of the series field and the current in the armature conductors. That is,
where, TD = developed torque
Bp = flux density due to current in series-field winding
Ia = armature current
As indicated in Figure 42.12(d), however, the current in the series-field is the armature current. Hence, neglecting magnetic saturation effects,
Substituting into Equation (42.7)
Hence, the torque developed by a universal motor is approximately proportional to the square of the armature current.
Universal motors can develop higher torques, can accelerate to higher speeds, and have a higher power-to-weight ratio than induction motors of the same power rating.
Reversing the direction of rotation of a universal motor is achieved by reversing the direction of current in series field or in the armature, but not in both. Speed adjustment is accomplished by using an auto transformer or solid-state control to reduce the voltage applied to the motor; reducing the applied voltage reduces the armature current, which reduces the developed torque, and hence reduces the speed.
The torque and speed characteristics of the universal motor are essentially the same, whether operating on a.c. or d.c. Furthermore, because of its relatively small dimensions, no load speeds in excess of 12,000 r.p.m. are achieved without damage.
Universal motors have applications in vacuum cleaners, portable power tools, and kitchen appliances. Series motors, operating from a 25 Hz single-phase system, are used for traction purposes on some electrified railroads.
- The reluctance motor is an induction motor with a modified squirrel cage.
- Where the air gap is small, the self-inductance of the field winding is high.
- Where the air gap is high, the self-inductance is reduced.
- The mutual air gap flux is delayed in the vicinity of the air gap.
- Operation is always in the direction from high to low air gap.
- The reluctance motor runs on reluctance torque.
- The hysteresis motor runs on hysteresis torque.
- With the magnets stationary, the magnetic axis of the rotor poles is coincident with the magnetic axis of the stator.
- Spinning the stator magnets with the rotor blocked provides a rotating magnetic field.
- Hysteresis torque is steady in both amplitude and phase.
- Stepper motors change their angular position in steps.
- The total angle travelled by a stepper motor is equal to the step angle multiplied by the number of steps.
- Hybrid stepper motors have a small stepping angle.
- VR stepper motors have a greater stepping angle.
- PM stepper motors have the highest inertia and the highest rotational speed.
- LIMs produce linear motion.
- Universal motors can operate either on a.c. or on d.c.
- The torque developed by a universal motor is approximately proportional to the square of the armature current.
MULTIPLE CHOICE QUESTIONS (MCQ)
- The synchronous speed of a linear induction motor does not depend on
- Supply frequency
- Width of pole pitch
- Number of poles
- Any of the above
- The secondary of a linear motor normally consists of
- Distributed single-phase winding
- Solid conducting plate
- Distributed three-phase winding
- Concentrated single-phase winding
- Which of the following motors can be run on both a.c. and d.c. supply?
- Repulsion motor
- Reluctance motor
- Universal motor
- Synchronous motor
- Which motor has a rotor with no teeth or winding?
- Hysteresis motor
- Universal motor
- Split-phase motor
- Reluctance winding
- Which of the following applications use a universal motor?
- Oil expellers
- Portable tools
- Lathe machines
- Floor-polishing machines
- Which of the following motors do not have a winding on it?
- Repulsion motor
- Reluctance motor
- Hysteresis motor
- Universal motor
- Which motor will make least noise?
- Shaded-pole motor
- Hysteresis motor
- Universal motor
- Reluctance motor
- Which of the following motors is used in mixies?
- Hysteresis motor
- Reluctance motor
- Universal motor
- Repulsion motor
- The direction of rotation of a universal motor can be reversed by reversing the flow of current in
- Armature winding
- Field winding
- Either (a) or (b)
- Neither (a) nor (b)
- For which of these applications is reluctance motor preferred?
- Electronic shavers
- Lifts and hoists
- Signalling and timing devices
- Which stepper motor has the least stepping angle?
- Which stepping motor has the greatest stepping angle?
- Explain the principle of reluctance-motor operation: how does it start, accelerate, and synchronize?
- Explain the principle of hysteresis motor operation: how does it start, accelerate, and synchronize?
- Will the overall accuracy of a stepper motor be greater at 100 steps than at 10 steps? Explain.
- Name and briefly explain the three types of stepper motors.
- Explain why any rotary motor principle may have a linear counterpart?
- Explain the principle of linear-induction-motor operation, and state how a LIM may be reversed?
- Explain why the torque developed by a universal motor varies as the square of the armature current.
- How may the speed of a universal motor be adjusted?