The cross-sectional view of the 2 pole PMDC motor is  shown in the figure below.

The Permanent Magnet DC motor generally operates on 6 V, 12 V or 24 Volts DC supply obtained from the batteries or rectifiers. The interaction between the axial current carrying rotor conductors and the magnetic flux produced by the permanent magnet results in the generation of the torque.

The circuit diagram of the PMDC is shown below.

In conventional DC motor, the generated or back EMF is given by the equation shown below.

The electromagnetic torque is given as

In Permanent Magnet DC motor, the value of flux ϕ is constant. Therefore, the above equation (1) and (2) becomes

Considering the above circuit diagram the following equations are expressed.

Putting the value of E from the equation (3) in equation (5) we get

Where k₁ = k ϕ and is known as speed-voltage constant or torque constant. Its value depends upon the number of field poles and armature conductors.

The speed control of the PMDC motor cannot be controlled by using flux control method as the flux remains constant in this type of motor. Both speed and torque can be controlled by armature voltage control, armature rheostat control, and chopper control methods. These motors are used where the motor speed below the base speed is required as they cannot be operated above the base speed.

Types of Permanent Magnet Materials

There are three types of Permanent Magnet Materials used in PMDC Motor. The detailed information is given below.

Alnicos

Alnicos has a low coercive magnetizing intensity and high residual flux density. Hence, it is used where low current and high voltage is required.

Ferrites

They are used in cost sensitive applications such as Air conditioners, compressors, and refrigerators.

Rare earths

Rare earth magnets are made of Samarium cobalt, neodymium-iron-boron. They have a high residual flux and high coercive magnetizing intensity. The rare earth magnets are exempted from demagnetizing problems due to armature reaction. It is an expensive material.

The Neodymium iron boron is cheaper as compared to Samarium cobalt. But it can withstand higher temperature. Rare earth magnets are used for size-sensitive applications. They are used in automobiles, servo industrial drives and in large industrial motors.

Applications of the Permanent Magnet DC Motor

The PMDC motors are used in various applications ranging from fractions to several horsepower.  They are developed up to about 200 kW for use in various industries. The following applications are given below.

• PMDC motors are mainly used in automobiles to operate windshield wipers and washers, to raise the lower windows, to drive blowers for heaters and air conditioners etc.
• They are also used in computer drives.
• These types of motors are also used in toy industries.
• PMDC motors are used in electric toothbrushes, portable vacuum cleaners, food mixers.
• Used in a portable electric tool such as drilling machines, hedge trimmers etc.

Advantages of the Permanent Magnet DC Motor

Following are the advantages of the PMDC Motor.

• They are smaller in size.
• For smaller rating Permanent Magnet reduces the manufacturing cost and thus PMDC motor are cheaper.
• As these motors do not require field windings, they do not have field circuit copper losses. This increases their efficiency.

Disadvantages of the Permanent Magnet DC Motor

The disadvantages of the PMDC motor are given below.

• Permanent magnets cannot produce a high flux density as that as an externally supplied shunt field does. Therefore, a PMDC motor has a lower induced torque per ampere turns of armature current then a shunt motor of the same rating.
• There is a risk of demagnetization of the poles which may be caused by large armature currents. Demagnetization can also occur due to excessive heating and also when the motor is overloaded for a long period of time.
• The magnetic field of PMDC motor is present at all time, even when the motor is not being used.
• Extra ampere turns cannot be added to reduce the armature reaction.

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The torque is generated between the two fields twisting the object around the line with the magnetic field. Thus, torque is exerted on the object so that it tries to position itself to give minimum reluctance for the magnetic flux. It is also known as Saliency torque because it causes due to the saliency of the machine. Reluctance Motor depends on the reluctance torque for its operation. it is calculated by the formula Where, T_rel – average value of reluctant torque.
V – applied voltage
f – line frequency
δ_rel – torque angle (electrical degree)
K – motor constant

Reluctance torque is mainly developed in the reluctance motor. It is produced in the motor due to the varying reluctance. Their stability limit can occur between +δ/4 to -δ/4. The stator of the reluctance motor is similar to single phase induction motor and their rotor is generally a squirrel cage.

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The schematic diagram of the Amplidyne is shown below.

The compensating winding is located in the direct (d axis) on the stator. This compensating winding carries the load current i_d. The winding produces a flux which opposes the flux produced by the direct axis armature current. The effect of the negative feedback of the load current is minimized. The d axis flux now depends on the field winding current.

The degree of compensation C is defined as the ratio of effective compensating winding turns to the effective armature turns.

The effect of degree of compensation on the load characteristic of a cross field machine is shown below.

In case of the Metadyne, there is no compensating winging thus, the value of C = 0. In Amplidyne full compensation exists and hence, C = 1. The terminal voltage of an Amplidyne is considered almost constant. The power amplification (e_adi_d/e_fi_f) is of the order of 10⁵ as compared to 100 for a direct current generator.

A series connected quadrature axis (q axis) winding is placed on the stator of the amplidyne to improve its performance and, as a result, quadrature (q axis) commutation also improves. They were used before the origin of high power, high speed of response of solid state power amplifier and control equipment.

They were used to supply DC power to process control motors, excitation systems of large AC generators and Ward Leonard speed control systems. They are now replaced by the solid state power amplifiers.

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The stator and rotor are made of high-quality magnetic materials having very high permeability. Thus, a very small exciting current is required. When a DC source is applied to the stator phase with the help of a semiconductor switch, a magnetic field is produced. The axis of the rotor aligns with the axis of the stator

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The schematic diagram of a Metadyne is shown below.

A stator of the machine has a control field winding. A current i_f flows through the control field winding. The generator is rotating at a constant speed; an EMF e_aq is induced between the quadrature axis brushes qq’ because of the control field winding MMF.

This EMF is given by the equation shown below.

Where, K_af is a constant and i_f is the field current.

The brushes qq’ are short-circuited, a quadrature axis armature current i_q flows and establish an MMF F_q if the quadrature axis. Since the impedance of the short-circuited path is low, a small change in control field current produces a greater armature current in the q axis.

The magnetic field is stationary in space because of the commutator action. Rotation in the q axis flux produces an EMF in the armature. This EMF appears across the direct axis brushes dd’ and is given by the equation shown below.

Where, K_dq is a constant and i_q is the quadrature axis armature current.

If the load resistance R_L is connected across the direct axis brushes, the direct axis armature current i_d will flow through the load. A direct axis flux F_d is produced by this current and according to Lenz’s law, it opposes its main cause, i.e., the control field MMF F_f.

The magnetic field of the current produced is 90 degrees ahead of the flux wave producing the voltage. Since, there are two stages of voltage generation, the MMF of the direct axis output current is shifted twice by 90 degrees. As a result, it opposes the control field MMF.

The voltage generated in the quadrature axis is given as

Where K_qd is a constant if the magnetic saturation is neglected and speed is assumed to be constant.

An increase in i_d decreases e_aq and as a result, i_q is reduced. Hence, e_ad and i_d are reduced. Thus, over a wide range of load variation the value of field excitation current i_f and the output current i_d remains constant. A Metadyne acts as a constant current generator.

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All the stator poles are aligned in a Multi-Stack motor. But the rotor poles are displaced by 1/m of the pole pitch angle from each other. The stator windings of each stack form one phase as the stator pole windings are excited simultaneously. Thus, the number of phases and the number of stacks are the same.

Consider the cross-sectional view of the three stack motor parallel to the shaft is shown below:

There are 12 stator and rotor poles in each stack. The pole pitch for the 12 pole rotor is 30, and the step angle or the rotor pole teeth are displaced by 10 degrees from each other. The calculation is shown below:

Let N_r be the number of rotor teeth and m be the number of stacks or phases.

Hence, tooth pitch is represented by the equation shown below:

As there are 12 poles in the stator and rotor, thus the value of N_r = 12. Now, putting the value of N_r in the equation (1) we get,

The value of m = 3. Therefore, the step angle will be calculated by putting the value of m in equation (2)

When the phase winding A is excited the rotor teeth of stack A is aligned with the stator teeth as shown in the figure below:

When phase A is de-energized, and phase B is excited, rotor teeth of stack B are aligned with the stator teeth. The rotor movement is about 10 degrees in the anticlockwise direction. The motor moves one step which is equal to ½ of the pole pitch due to a change of excitation from stack A to stack B. The figure below shows the position of the stator and rotor teeth when phase B is excited.

Similarly, now phase B is de-energized, and phase C is excited. The rotor moves another step of 1/3 of the pole pitch in the anticlockwise direction. Again, another change in the excitation of the rotor takes place, and the stator and rotor teeth align it with stack A. However, during this whole process (A – B – C – A ) the rotor has moved one rotor tooth pitch.

Multi Stack Variable Reluctance Stepper Motors are widely used to obtain smaller step angles in the range of 2 to 15 degrees. Both the Variable reluctance motor Single Stack and Multi Stack types have a high torque to inertia ratio.

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The word Hybrid means combination or mixture. The Hybrid Stepper Motor is a combination of the features of the Variable Reluctance Stepper Motor and Permanent Magnet Stepper Motor. In the center of the rotor, an axial permanent magnet is provided. It is magnetized to produce a pair of poles as North (N) and South (S) as shown in the figure below:

At both the end of the axial magnet the end caps are provided, which contains an equal number of teeth that are magnetized by the magnet. The figure of the cross-section of the two end caps of the rotor is shown below:

The stator has 8 poles, each of which has one coil and S number of teeth. There are 40 poles on the stator, and each end cap has 50 teeth. As the stator and rotor teeth are 40 and 50 respectively, the step angle is expressed as shown below:

The rotor teeth are perfectly aligned with the stator teeth. The teeth of the two end caps are displaced from each other by half of the pole pitch. As the magnet is axially magnetized, all the teeth on the left and right end cap acquire polarity as south and north pole respectively.

The coils on poles 1, 3, 5, and 7 are connected in series to form phase A. Similarly, the coils on poles 2, 4, 6, and 8 are connected in series to form phase B.

When the phase is excited by supplying a positive current, the stator poles 1 and 5 become south poles and stator pole 3 and 7 becomes north poles.

Now, when phase A is de-energized, and phase B is excited, the rotor will turn by a full step angle of 1.8⁰ in the anticlockwise direction. Phase A is now energized negatively; the rotor moves further by 1.8⁰ in the same anti-clockwise direction. Further rotation of the rotor requires phase B to be excited negatively. Thus, to produce anticlockwise motion of the rotor the phases are energized in the following sequence +A, +B, -A, -B, +B, +A…….. For the clockwise rotation, the sequence is +A, -B, +B, +A……..

One of the main advantages of the Hybrid stepper motor is that, if the excitation of the motor is removed the rotor continues to remain locked in the same position as before the removal of the excitation. This is because of the Detent Torque produced by the permanent magnet.

Advantages of Hybrid Stepper Motor

The advantages of the Hybrid Stepper Motor are as follows:

• The length of the step is smaller.
• It has greater torque.
• It provides Detent Torque with the de-energized windings.
• Higher efficiency at a lower speed.
• Lower stepping rate.

Disadvantages of Hybrid Stepper Motor

The Hybrid Stepper Motor has the following drawbacks:

• Higher inertia.
• The weight of the motor is more because of the presence of the rotor magnet.
• If the magnetic strength is varied, the performance of the motor is affected.
• The cost of the Hybrid motor is more as compared to the Variable Reluctance Motor.

This is all about Hybrid Stepper Motor.

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• Single Stack Variable Reluctance Motor
• Multi Stack Variable Reluctance Motor

Working of a Variable Reluctance Stepper Motor

A four-phase or (4/2 pole), single stack variable reluctance stepper motor is shown below. Here, (4/2 pole) means that the stator has four poles and the rotor has two poles.

The four phases A, B, C, and D are connected to the DC source with the help of a semiconductor, switches S_A, S_B, S_C, and S_D respectively, as shown in the above figure. The phase windings of the stator are energized in the sequence A, B, C, D, A. The rotor aligns itself with the axis of phase A as winding A is energized. The rotor is stable in this position and cannot move until phase A is de-energized.

Now, phase B is excited and phase A is disconnected. The rotor moves 90 degrees in the clockwise direction to align with the resultant air-gap field which lies along the axis of phase B. Similarly phase C is energized, and phase B is disconnected, and the rotor moves again in 90 degrees to align itself with the axis of the phase.

Thus, as the Phases are excited in the order as A, B, C, D, A, the rotor moves 90 degrees at each transition step in the clockwise direction. The rotor completes one revolution in 4 steps. The direction of the rotation depends on the sequence of switching the phase and does not depend on the direction of the current flowing through the phase. Thus, the direction can be reversed by changing the phase sequence like A, D, C, B, A.

The magnitude of the step angle of the variable reluctance motor is given as:

Where,

• α is the step angle
• m_s is the number of stator phases
• N_r is the number of rotor teeth

The step angle is expressed as shown below:

Where, N_S is the stator poles

The step angle can be reduced from 90 degrees to 45 degrees in a clockwise direction by exciting the phase in the sequence A, A+B, B, B+C, C, C+ D, D, D+A, A.

Similarly, if the sequence is reversed as A, A+D, D, D+C, C, C+B, B, B+A, A, the rotor rotates at a step angle of 45 degrees in the anticlockwise direction.

Here, (A+B) means that the phase windings A and B both are energized together. The resultant field is midway between the two poles. i.e. it makes an angle of 45 degrees with the axis of the pole in the clockwise direction. This method of shifting excitation from one phase to another is known as Microstepping. By using Stepper Motor, lower values of the step angle can be obtained with a number of poles on the stator.

Consider a 4 phase, (8/6 pole) single stack variable reluctance motor shown in the figure below:

The opposite poles are connected in series forming 4 phases. The rotor has 6 poles. Here we have considered only phase A to make the connection simple. When the coil AA’ is excited, the rotor teeth 1 and 4 are aligned along the axis of the winding of phase A. Thus, the rotor occupies the position as shown in the above figure (a).

Now, phase A is de-energized, and phase winding B is energized. The rotor teeth 3 and 6 get aligned along the axis of phase B. The rotor moves a step of the phase angle of 15 degrees in the clockwise direction. Further, phase B is de-energized, and winding C is excited. The rotor moves again 15⁰ phase angle.

The sequence A, B, C, D, A is followed, and the four steps of rotation are completed, and the rotor moves 60 degrees in a clockwise direction. For one complete revolution of the rotor 24 steps are required. Thus, any desired step angle can be obtained by choosing different combinations of the number of rotor teeth and stator exciting coils.

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Similarly, curve 2 represented by Red color line is known as pullout torque characteristics. It shows the maximum stepping rate of the motor where it can run for the various values of load torque. But it cannot start, stop or reverse at this rate.

Let us understand this with the help of an example, considering the above curve.

The motor can start, synchronize and stop or reverse for the load torque Ʈ_L if the pulse rate is less than S₁. The stepping rate can be increased for the same load as the rotor started the rotation and synchronized. Now, for the load Ʈ_L1, after starting and synchronizing, the stepping rate can be increased up to S₂ without losing the synchronism.

If the stepping rate is increased beyond S₂, the motor will lose synchronism. Thus, the area between curves 1 and 2 represents the various torque values, the range of stepping rate, which the motors follow without losing the synchronism when it has already been started and synchronized. This is known as Slew Range. The motor is said to operate in slewing mode.

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The rotor poles align with the stator teeth depending on the excitation of the winding. The two coils AA’ connected in series to form a winding of Phase A. Similarly the two coil BB’ is connected in series forming a phase B windings.The figure below shows 4/2 Pole Permanent Magnet Stepper Motor.

In figure (a) the current flows start to the end of phase A. The phase winding is denoted by A⁺ and the current by i⁺_A. The figure shows the condition when the phase winding is excited with the current i⁺_A. The south pole of the rotor is attracted by the stator phase A. Thus, the magnetic axis of the stator and rotor coincide and α = 0⁰

Similarly, in the figure (b) the current flows from the start to the end at phase B. The current is denoted by i⁺_B  and the winding by B⁺. Considering the figure (b), the windings of phase A does not carry any current and the phase B is excited by the i⁺_B   current. The stator pole attracts the rotor pole and the rotor moves by 90⁰ in the clockwise direction. Here α = 90⁰

The figure (c) below shows that the current flows from the end to the start of the phase A. This current is denoted by i^–_A and the winding is denoted by A^–. The current i^–_A is opposite to the current i⁺_A. Here, phase B winding is de-energized and phase A winding is excited by the current i^–_A. The rotor moves further 90⁰ in clockwise direction and the α = 180⁰

In the above figure (d), the current flows from end to starting point of phase B. The current is represented by i^–_B and the winding by B^–. Phase A carries no current and the phase B is excited. The rotor again moves further 90⁰ and the value of α = 270⁰

Completing the one revolution of the rotor for making α = 360⁰ the rotor moves further 90 degrees by de-energizing the winding of phase B and exciting the phase A. In the permanent magnet stepper motor the direction of the rotation depends on the polarity of the phase current.The sequence A⁺, B⁺, A^–, B^–, A⁺ is followed by the clockwise movement of the rotor and for the anticlockwise movement, the sequence becomes A⁺ B^–, A^–, B⁺, A⁺.

The permanent magnet rotor with large number of poles is difficult to make, therefore, stepper motors of this type are restricted to large step size in the range of 30 to 90⁰. They have higher inertia and therefore, lower acceleration than variable stepper motors. The Permanent Magnet stepper motor produces more torque than the Variable Reluctance Stepper Motor.

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