Stepper Motors

Stepper Motors  Au : May-03, 05, 07, 10, Dec.-04, 05, 06, 07,17

Stepper motor is known by its important property to convert a train of input pulses i.e. a square wave pulses into a precisely defined increment in the shaft position. Each pulse moves the shaft through a fixed angle. So the stepper motor is an electromechanical device which actuates a train of step movements of shaft in response to train of input pulses. The step movement may be angular or linear. There is one-one relationship between an input pulse and step movement of the shaft. Each pulse input actuates one step movement of the shaft. When a given number of drive pulses are supplied to the motor, the shaft gets turned through a known angle. The angle through which the motor turns or shaft moves for each pulse is known as the step angle, expressed in degrees.

As such angle is dependent on the number of input pulses, the motor is suitable for controlling position by controlling the number of input pulses. Such system, used to control the position is called position control system. The average motor speed is proportional to the rate at which the input pulse command is delivered. When the rate is low, the motor rotates in steps but for high rate of pulses, due to inertia, it rotates smoothly like d.c. motors. Due to this property it is also used in speed control systems. These motors are available in sub-fractional horse power ratings. As the input command is in pulses, the stepper motor is compatible with modem digital equipments.

Due to its compatibility with digital equipments, its market is greatly increased in recent times. The stepper motors are widely used in X-Y plotters, floppy disk drives, machine tools, process control systems, robotics, printers, tape drives and variety of other industrial applications.

 

1. Types of Stepper Motors

The stepper motors can be divided into three categories :

1) Variable reluctance stepper motors

2) Permanent magnet stepper motors

3) Hybrid stepper motors.

Let us see the details of each. 

Variable Reluctance Motors

 

2. Variable Reluctance Motors

It is the most basic type of stepper motor. This helps to explain the principle of operation of the stepper motors.

The motor has a stator which is usually wound for three phases. The stator has six salient poles with concentrated exciting windings around each one of them. The stator construction is laminated and assembled in a single stack. The number of poles on the stator and rotor are different. This gives the motor ability of

1) Bidirection rotation and

2) Self starting capability.

The rotor is made out of slotted steel laminations. If the number of stator poles are N_s and the number of rotor poles are N_r then for a three phase motor, the rotor poles in terms of N _s and q are given by,

N_r = N_s ± (N_s / q)  q = Number of phases

For example for N_r = 6 and q = 3, the rotor poles are,

N_r = 6  ± (6 / 3)  = 8,4

For our discussion, 4 pole rotor construction is selected. So rotor has 4 salient poles without any exciting winding as shown in the Fig. 9.11.1.

The coils wound around diametrically opposite poles are connected in series and the three phases are energised from a d.c. source with the help of switches.

The basic driving circuit is shown in the Fig. 9.11.2.

 

a. operation

The operation is based on various reluctance positions of rotor with respect to stator. When any one phase of the stator is excited, it produces its magnetic field whose axis lies along the poles, the phase around which is excited. Then rotor moves in such a direction so as to achieve minimum reluctance position. Such a position means a position where axis of magnetic field of stator matches with the axis passing through any two poles of the rotor. Let us see the operation when phases A, B and C are energised in sequence one after the other, with the help of switches SW1, SW2 and SW3.

1) When the phase AA' is excited with the switch SW1 closed, then stator magnetic axis exists along the poles formed due to AA' i.e. vertical. Then rotor adjusts itself in a minimum reluctance position i.e. matching its own axis passing through the two poles exactly with stator magnetic axis. This position is shown in the Fig. 9.11.3 (a).

2) When the phase BB' is excited with the switch SW2 closed and phase AA' de-energised with the switch SW1 open, then stator magnetic axis shifts along the poles formed due to BB', shown dotted in the Fig. 9.11.3 (b). Then rotor tries to align in the minimum reluctance position and turns through 30° in anticlockwise direction. So axis passing through two diagonally opposite poles of rotor matches with the stator magnetic axis. This is the new minimum reluctance position. The point P shown on the rotor has rotated through 30° in anticlockwise direction as shown in the Fig. 9.11.3 (b). 

3) When the phase CC' is excited with the switch SW3 closed and the phases AA' and BB' are de-energised, then the stator magnetic axis shifts along the poles formed due to CC', shown dotted in the Fig. 9.11.3 (c).

Then to achieve minimum reluctance position, rotor gets subjected to further anticlockwise torque. So it turns through further 30° in anticlockwise direction.

Hence point P is now at 60° from its starting position, in anticlockwise direction as shown in the Fig. 9.11.3 (c). By successively exciting the three phases in the specific sequence, the motor takes twelve steps to complete one revolution.

Now if i is the current passing through the phase which is excited then the torque developed by the motor, which acts on the rotor is expressed as,

where L is the inductance of the relevant phase at an angle θ

Since the torque is proportional to the aquare current (T ∝ i²), it is independent of the direction of i. The direction of rotation is totally decided from the sequence in which the phases are excited.

b. Impotant Observations

From the above discussion, the following important observations can be made :

i)  The rotor can be moved in a specific direction, by exciting the stator phases in a specific sequence.

ii) When the phases are excited in the sequence A-B-C-A ..., the rotor moves in the anticlockwise direction, as explained earlier.

iii) When the phases are excited in the sequence C-B-A-C ..., the rotor moves in the clockwise direction, which can be easily verified. 

iv) The distance through which the rotor moves when all three phases are excited once is called one rotor tooth pitch.

Rotor tooth pitch = 360° / N_r

v) The step angle is denoted as ɑ_s and given by,

ɑ_s 360° / qN_r

So for three phases and four rotor poles the step angle is,

ɑ_s = 360° / 3 × 4 = 30°

This is shown in the previous section. If the number of phases are increased to eight and the number of rotor poles to six then the step angle becomes,

ɑ_s = 360° / 8 × 6 = 7.5°

c. Microstepping

In the above discussion we have assumed that the windings are excited one at a time. If the two phases are excited simultaneously i.e. keeping AA' excited, the BB' is also excited with switch SW1 and SW2 closed, then the stator magnetic axis shifts to a mid position rather than along BB'. Hence rotor gets aligned along this moves through a half step i.e. 15°.

A logical extension of this technique is to control the currents in the phase windings so that several stable equilibrium positions are created. Normally the step angle is reduced by factor of 1/2,1/5,       1/10, 1/16 or 1/32. This technique is called microstepping.

A further reduction in step angle can be achieved by increasing the number of poles of the stator and rotor or by adopting different constructions such as,

i) Using reduction gear mechanism

ii) Using multistack arrangement

d. Reduction Gear Stepper Motor

Fig. 9.11.4 shows a reduction gear stepper motor. The stator has 8 salient poles and four phases for use as exciting winding. The rotor has 18 teeth and 18 slots uniformly distributed around. Each salient pole of the stator consists of two teeth, forming an interleaving slot of the same angular periphery as the rotor teeth or slots. When the coil A-A' is excited, the resulting electromechanical torque brings the rotor to the position as shown in the Fig. 9.11.4.

With this arrangement, the step angle reduces to 5°. By successive excitation of coils A-A', B-B', C-C' and D-D', the rotor makes 72 steps to complete one revolution. The general relationship between step angle ɑ_s , number of stator phases q and rotor poles or teeth Nr remains same as,

ɑ_s = 360° / qN_r

Key Point By choosing different combinations of number of rotor teeth and stator phases, any desired step angle can be achieved.

e. Multistack Stepper Motor

As mentioned earlier, these are used to obtain small step size, typically ranging between 2 to 15°.

In a m stack motor, the motor is divided into a m number of magnetically isolated sections called stacks, along its axial length. The m stacks of stator have a common frame while the rotors are mounted on a common shaft. The stators and rotors have the same number of poles (teeth). The stator poles in all m stacks are aligned while the rotor poles are shifted by (1/m ) of the pole pitch from one another. All the stator windings in a stator stack are excited simultaneously hence each stator stack forms a phase. So number of stator phases is equal to number of stator stacks. Generally three stack stepper motors are used. The Fig. 9.11.5 shows the arrangement in three stack stepper motor alongwith shifting of the rotor poles by ( 1/3 ) of the pole pitch from one another.

The Fig. 9.11.6 shows the cross-sectional view of a three stack, three phase variable reluctance motor. In each stack, the stator and rotor laminations have 12 poles. The poles of the stator are in one line while the rotor poles are offset from each other by one third of the pole pitch.

The various windings in one stack are energised simultaneously. When phase A of stator is excited then rotor poles of stack A get aligned with the stator poles. But due to offset, rotor poles of stack B and C do not align. Now if phase A is de-energised and phase B is energised, rotor poles of stack B get aligned with the stator poles. Thus, rotor moves by one third of pole pitch. When B is de-energised and C is excited, rotor further moves by one third of pole pitch so that rotor poles of stack C get aligned with the stator poles.

If m is the number of stacks i.e. phases and Nr be the rotor poles then the step angle is given by,

ɑ_s = 360° / m N_r

In the case discussed above, m = 3 and N_r = 12 hence the step angle is,

ɑ_s = 360° / 3 × 12 = 10°

An alternative design where the rotor stacks are aligned and stator stacks are offset also is used in practice.

f. Advantages of Variable Reluctance Motor

The variable reluctance stepper motor has following advantages :

1) High torque to inertia ratio.

2) High rates of acceleration.

3) Fast dynamic response.

4) Simple and low cost machine.

5) Efficient cooling arrangement as all the windings are on stator and there is no winding on rotor.

6) Rotor construction is robust due to absence of brushes.

 

3. Permanent Magnet Stepper Motor

The stator of this type is multipolar. As shown in the Fig. 9.11.7, the stator has four poles. Around the poles the exciting coils are wound. The number of slots per pole per phase is usually chosen as one in such multipolar machines.

The rotor may be salient or smooth cylindrical. But generally it is smooth cylindrical type as shown in the Fig. 9.11.7.

It is made out of ferrite material which permanently magnetised. Due to this the motor is called permanent magnet stepper motor. 

The voltage pulses to the stator winding can be obtained by using a driving circuit. The basic driving circuit for four phase permanent magnet stepper motor is shown in the Fig. 9.11.8.

a. Operation

As soon as the voltage pulses are applied to various phases with the help of driving circuit, a rotor starts rotating through a step for each input voltage pulse.

1) At first, switch SW1 is closed exciting the phase A. Due to its excitation we have N pole in phase A as shown in the Fig. 9.11.9 (a). Due to the electromechanical torque developed, rotor rotates such that magnetic axis of permanent magnet rotor adjusts with the magnetic axis of the stator, as shown in the Fig. 9.11.9 (a).

2) Next phase B is excited with switch SW2, disconnecting phase A. Due to this, rotor further adjusts its own magnetic axis with N pole of phase B. Hence it rotates through 90° further in clockwise direction as shown in the Fig. 9.11.9 (b).

Similarly when phase C and phase D are sequentially excited, the rotor tends to rotate through 90° in clockwise direction, every time when phase is excited. When such sequence is repeated, it results into a step motion of a permanent magnet stepper motor. 

The stepper motors with permanent magnet rotors with large number of poles can not be manufactured in small size. Hence small steps are not possible. This is the biggest disadvantage of permanent magnet stepper motor. This is overcome by the use of variable reluctance type stepper motor.

 

4. Comparison between Variable Reluctance and Permanent Magnet Stepper Motor

Variable reluctance steppr motor   

1. The rotor is not magnetised.        

2. High torque to inertia ratio.

3. Acceleration is slow.

4. The dynamic response is fast.      

5. Maximum stepping rate can be as high as 1200 pulses per second.      

6. It can be manufactured for large number of poles     

7. Very small step angle is possible.

8. It does not have a detent torque.  

9. The rotor has salient pole construction.

Permanent magnet stepper motor

1. The rotor is magnetised.

2. Low torque to inertia ratio.

3. High rates of acceleration.  

4. Very slow dynamic response.

5. Maximum stepping rate can be around 300 pulses per second.

6. It can not be manufactured for large number of poles due to difficulties in construction.

7. The step angles are high in the range of 30° to 90°.

8. Its main advantage is the presence of a detent torque.

9. The rotor has mostly smooth cylindrical type of construction.

However, now a days a disk type of permanent magnet stepper motors are designed which have the low inertia and smaller step angles.

 

5. Hybrid Stepper Motor

The hybrid stepper motor uses the principles of the permanent magnet and variable reluctance stepper motors. In the hybrid motors, the rotor flux is produced by the permanent magnet and is directed by the rotor teeth to the appropriate parts of the airgap. The permanent magnet is placed in the middle of the rotor. It is magnetized in the axial direction. Each pole of the magnet is surrounded with soft-toothed laminations.

The construction of the hybrid stepper motor is shown in the Fig. 9.11.10.

The main flux path is from the north pole of the magnet, into the end stack, across the airgap through the stator pole, axially along the stator, through the stator pole, across the air gap and back to the magnet south pole via the other end stack. 

There are usually 8 poles on the stator. Each pole has between 2 to 6 teeth. There is two phase winding. The coils on poles 1, 3, 5 and 7 are connected in series to form phase A while the coils on poles 2, 4, 6 and 8 are connected in series to form phase B. The windings A and B are energised alternately.

When phase A carries positive current, stator poles 1 and 5 become south and 3 and 7 become north. The rotor teeth with north and south polarity align with the teeth of stator poles 1 and 5 and 3 and 7 respectively. When phase A is de-energised and phase B is excited, rotor will move by one quarter of tooth pitch.

The torque in a hybrid motor is produced by the interaction of the rotor and the stator produced fluxes. The rotor field remains constant as it is produced by the permanent magnet. The motor torque Tm is proportional to the phase current.

Following are the main advantages of the hybrid stepper motor :

1) Very small step angles upto 1.8°.

2) Higher torque per unit volume which is more than in case of variable reluctance motor.

3) Due to permanent magnet, the motor has some detent torque which is absent in variable reluctance motor.

These are the various types of the stepper motors. After discussing the various types and the operating principle, let us discuss the important parameters related to a stepper motor. The stepper motor characteristics are mainly the indication of its important parameters.

 

6. Important Definitions

1) Holding torque :

It is defined as the maximum static torque that can be applied to the shaft of an excited motor without causing a continuous rotation. 

2) Detent torque :

It is defined as the maximum static torque that can be applied to the shaft of an unexcited motor without causing a continuous rotation.

Under this torque the rotor comes back to the normal rest position even if excitation ceases. Such positions of the rotor are referred as the detent positions.

3) Step angle :

It is defined as the angular displacement of the rotor in response to each input pulse.

4) Critical torque :

It is defined as the maximum load torque at which rotor does not move when an exciting winding is energised. This is also called pullout torque.

5) Limiting torque :

It is defined for a given pulsing rate or stepping rate measured in pulses per second, as the maximum load torque at which motor follows the control pulses without missing any step. This is also called pull in torque.

6) Synchronous stepping rate :

It is defined as the maximum rate at which the motor can step without missing steps. The motor can start, stop or reverse at this rate.

7) Slewing rate :

It is defined as the maximum rate at which the motor can step unidirectionally. The slewing rate is much higher than the synchronous stepping rate. Motor will not be able to stop or reverse without missing steps at this rate.

 

7. Stepper Motor Characteristics

The Stepper motor characteristics are classified as 1) Static characteristics and 2) Dynamic characteristics

The static are at the stationary position of the motor while the dynamic are under running conditions of the motor.

a. Static Characteristics

These characteristics include 1) Torque-displacement characteristics

Torque-Displacement characteristics :

This gives the relationship between electromagnetic torque developed and displacement angle 0 from steady state position. These characteristics are shown in the Fig. 9.11.11.

Torque-Current characteristics : The holding torque of the stepper motor increases with the exciting current. The relationship between the holding torque and the current is called          as torque-current characteristics. These characteristics are shown in the Fig. 9.11.12.

b. Dynamic Characteristics

The stepping rate selection is very important in proper controlling of the stepper motor. The dynamic characteristics gives the information regarding torque stepping rate. These are also called torque stepping rate curves of the stepper motor. These curves are shown in the Fig. 9.11.13.

When stepping rate increases, rotor gets less time to drive the load from one position to other. If stepping rate is increased beyond certain limit, rotor can not follow the command and starts missing the pulses.

Now if the values of load torque and stepping rate are such that point of operation lies to the left of curve I, then motor can start and synchronise without missing a pulse.

For example, for a load torque of T_L, the stepping rate selection should be less than f₁ so that motor can start and synchronize, without missing a step.

But the interesting thing is that once motor has started and synchronized, then stepping rate can be increased e.g. upto f₂ for the above example. Such an increase in stepping rate from f₁ to f₂ is without missing a step and without missing the synchronism. But beyond f₂, if stepping rate is increased, motor will loose its synchronism.

So point A as shown in the Fig. 9.11.13 indicates the maximum starting stepping rate or maximum starting frequency. It is defined as the maximum stepping rate with which unloaded motor can start or stop without loosing a single step.

While point B as shown in the Fig. 9.11.13 indicates the maximum slewing frequency. It is defined as the maximum stepping rate which unloaded motor continues to run without missing a step.

Thus area between the curves I and II shown hatched indicates, for various torque values, the range of stepping rate which the motor can follow without missing a step, provided that the motor is started and synchronized. This area of operation of the stepper motor is called slew range. The motor is said to be operating in slewing mode.

Key Point It is important to remember that in a slew range the stepper motor can not be started, stopped or reversed without losing steps.

Thus slew range is important for speed control applications. In position control, to get the exact position the motor may be required to be stopped or reversed. But it is not possible in a slew range. Hence slew range is not useful for position control applications.

To achieve the operation of the motor in the slew range motor must be accelerated carefully using lower pulse rate. Similarly to stop or reverse the motor without loosing acceleration and deceleration of the stepper motor, without losing any step is called ramping.

 

8. Applications of Stepper Motors

Due to the digital circuit compatibility of the stepper motors, they are widely used in computer peripherals such as serial printers, linear stepper motors to printers, tape drives, floppy disc drives, memory access mechanisms etc. The stepper motors are also used in serial printers in typewriters or word processor systems, numerical control of machine tools, robotic control systems, number of process control systems, actuators, spacecrafts, watches etc. X-Y recorders and plotters is another field in which stepper motors are preferred. 

Review Questions

1. Explain the operation of the types of stepper motor. Compare them. State applications of stepper Au : May-03, Dec.-04, Marks 16

2. i) What are stepping motors ? ii) Discuss the types of stepper motors with an application for each, iii) Explain the few important definitions associated with stepper motor, iv) Explain the operation cf any one type of stepper motor with neat sketches and applications. AU : May-05, 07, 10, Dec.-05, 06, 07, Marks 16

3. Describe the working principle of any one type of stepper motor.