Stepper Motor

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Stepper Motor [1/Ch. 39] Introduction [1/39.1/p.1536]

The examples of special machines, whose stator coils are energized by electronically switched currents and whose have special applications, are: various types of stepper motors, brushless dc motor, and switch reluctance motor etc.

Stepper Motor [1/39.2/p.1536]

A motor whose rotation is produced by switching signals to suitably connected windings in some predetermined sequence to produce uniform angular steps of rotation is called stepper motor.

These motor are also called stepping motors or step motors. The name is used because this motor rotates through a fixed angular step in response to each input current pulse received by its controller.

In recent years, there has been wide-spread demand of stepping motors because of the explosive growth of computer industry. Their popularity is due to the fact that they can be controlled directly by computers, microprocessor and programmable controller.

The unique feature of a stepping motor is that its output shaft rotates in a series of

discrete angular intervals or steps, one step being taken each time a command pulse is received. The stepping motor therefore allows control of the loads velocity, distance and direction.

In a stepper motor, when a definite number of pulses are supplied, the shaft turns through a definite known angle. This fact makes the motor well-suited for open-loop position control because no feedback need be taken from the output shaft.

A significant advantage of the stepping motor is its compatibility with digital electronic systems. These systems are becoming increasingly common in a wide variety application and at the same time are becoming both more powerful and less expensive.

Such motors develop torques ranging from 1 µN-m upto 40 N-m. Their power output ranges from about 1W to a maximum 2500W. Step Angle (Step Length)

The angle through which the motor rotates for each command pulse is called step angle β. Smaller the step angle, greater the number of steps per revolution and higher the resolution or accuracy of positioning obtained. The step size can be as small as 0.72o or as large as 90o. But the most common step sizes are: 1.8o, 2.5o, 7.5o, and 15o.

The value of step angle can be expressed either in terms of the rotor and stator poles (teeth) Nr and Ns, respectively or in terms of the number of stator phases, m, and the number of rotor teeth.

°×= 360~

rs

rs

NNNN

β

poles)rotor (orteethrotorofNo.stacks)(or phasesstatorofNo.360360×

°=

°=

rmNβ

Resolution is given by the number of steps needed to complete one revolution of the rotor shaft. Higher the resolution, greater accuracy of positioning of objects by the motor.

β°

==360

revolutionstepsofNo.resolution

Stepper Motor

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A stepper motor has the extraordinary ability to operate at very high stepping rates and yet to remain fully in synchronism with the command pulses.

When the pulse rate is high, the shaft rotation seems continuous. Operation at high speeds is called ‘slewing’.

If f is the stepping frequency (or pulse rate) in pulses per second (pps) and β is the step angle, then motor shaft speed is given by

resolutionfrequencypulserps360

=°

×=

fn β

If the stepping rate is increased too quickly, the motor losses synchronism and stops. Same happens if when the motor is slewing, command pulses are suddenly stopped instead of being progressively slowed.

Stepping motors are designed to operate for long periods with the rotor held in a fixed position and with rated current flowing in the stator windings. It means that stalling is no problem for such motors whereas for most of the other motors, stalling results in the collapse of back emf and a very high current which can lead to a quick burn out. Example 11-2 [5] calculate the stepping angle for (a) a 3-stacks, 16 tooth rotor VR stepper motor, and (b) a 3-phase, 24-pole PM stepper motor. Solution: We know that

poles)rotor (orteethrotorofNo.stacks)(or phasesstatorofNo.360360×

°=

°=

rmNβ

(a) step/5.7163

360°=

×°

=β (b) step/5243

360°=

×°

=β

Example 39.1. A hybrid VR stepping has motor 8 main poles which have been castleated to have 5 teeth each. If rotor has 50 teeth, calculate the stepping angle.

Solution: Ns=8×5=40; Nr=50; °=°××−

= 8.136040504050β

Example 39.2. A stepper motor has a step angle of 2.5o. Determine (a) resolution, (b) number of steps required for the shaft to make 25 revolutions and (c) shaft speed, if the stepping frequency is 3600 pps.

Solution: (a) revolutionsteps /1445.2

360360resolution =°°

=°

=β

(b) Now, steps/revolution= 144. Hence, steps required for making 25 revolutions=144×25=36000.

(c) rps25rps360

36005.2rps360

=°

×°=

°×

=fn β

Problem: What is the required resolution of a stepper motor that is to operate at a pulse frequency of 6000 pps and travel 180o in 0.025s. Solution: Given stepper motor travels 180o in 0.025 sec. So to complete one revolution, stepper motor needs 0.025×2=0.05 sec. Since 6000 pulses sent to the motor terminal per second, the resolution is the number of pulses to complete one revolution. So, resolution= 6000×0.05=300 steps/revolution.

Stepper Motor

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Applications Such motors are used for operation control in computer peripherals, textile industry,

IC fabrications and robotics etc. Applications requiring incremental motion are typewrites, line printers, tape drivers,

floppy disk drivers, numerically-controlled machine tools, process control systems and X-Y plotters.

Usually, position information can be obtained simply by keeping count of the pulses sent to the motor thereby eliminating the need for expensive position sensors and feedback controls.

Stepper motors also perform countless tasks outside the computer industry. It includes commercial, military and medical applications where these motors perform such function as mixing, cutting, striking, metering, and blending.

Difference between conventional motor and stepper motor

1. Conventional ac and dc motors have a free turning shaft. But, the stepper motor shaft rotation is incremental.

2. Conventional motors are used to convert electrical energy to mechanical energy but they cannot be used for precision positioning of an object or precision control of speed without using closed-loop feedback. But, stepping motors are ideally suitable for situation where either precise positioning or precise speed control or both are required in automation system without any feedback system.

3. In the case of conventional motor, the repeatability (ability to position through the same pattern of movements a number of times) is very poor. But, in the case of stepper motor, the repeatability is very good.

4. The moving part in a conventional motor is less robust and reliable as compared with that in a stepper motor.

5. Stalling is no problem for stepper motors whereas for conventional motors, stalling results in the collapse of back emf and a very high current which can lead to a quick burn out.

Stepper Motor Advantages and Disadvantages

Advantages: 1. The rotation angle of the motor is proportional to the input pulse. 2. The motor has full torque at standstill (if the windings are energized). 3. Precise positioning and repeatability of movement since good stepper motors have an

accuracy of 3 – 5% of a step and this error is non cumulative from one step to the next.

4. Excellent response to starting/stopping/reversing. 5. Very reliable since there are no contact brushes in the motor. Therefore the life of the

motor is simply dependant on the life of the bearing. 6. The motors response to digital input pulses provides open-loop control, making the

motor simpler and less costly to control. 7. It is possible to achieve very low speed synchronous rotation with a load that is

directly coupled to the shaft. 8. A wide range of rotational speeds can be realized as the speed is proportional to the

frequency of the input pulses.

Stepper Motor

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Disadvantages: 1. Resonances can occur if not properly controlled. 2. Not easy to operate at extremely high speeds.

Types of Stepper Motor [1/39.3/p.1538]

There is a large variety of stepper motors which ca be divided into the following three basic categories:

(i) Variable Reluctance (VR) (or Reactive-Rotor) Stepper Motor

It has wound stator poles but the rotor poles are made of a ferromagnetic material as shown in Fig. 39.1(a). It has a rectangular rotor.

It can be of the single stack type (Fig. 39.2) or multi stack type (Fig. 39.5) which gives smaller step angles.

Direction of the motor rotation is independent of the polarity of the stator current. It is called variable reluctance motor because the reluctance of the magnetic circuit formed by the rotor and stator teeth varies with the angular position of the rotor.

As a variable speed machine, VR motor is sometime designed as a switched-reluctance motor.

VR stepper motor produces the reluctance torque which is varied at twice the sine of the displacement angle of rotor as shown in Fig. 39.1-1(a).

(a) Variable reluctance

stepper motor (b) Permanent magnet

stepper motor (c) Hybrid stepper motor

Fig. 39.1

(ii) Permanent Magnet (PM) (or Active-Rotor) Stepper Motor It also has wound stator poles but its rotor poles are permanently magnetized. It has a

cylindrical rotor as shown in Fig. 39.1(b). Its direction depends on the polarity of the stator current.

As a variable speed machine, PM stepper motor is also called variable speed brushless dc motor.

PM stepper motor produces the excitation torque which is varied as the sine of the displacement angle of rotor as shown in Fig. 39.1-1(b).

(iii) Hybrid Stepper Motor It has wound stator poles and permanently-magnetized rotor poles as shown in Fig.

39.1(c). It is best suited when small step angles of 1.8o, 2.5o etc. are required. It has a rectangular rotor.

The hybrid motor combines the features of VR stepper motor and PM stepper motor. Its construction is similar to the single stack VR motor but the rotor is composed of radially

Stepper Motor

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magnetized permanent magnets. A recent type uses a disc rotor which is magnetized axially to give a small stepping angle and low inertia.

Unlike the VR or PM stepping motors, the step angle (step length) is independent of the number of phases or stacks and is purely a function of the number of rotor teeth or pole. So the step angle for hybrid stepping motor is given by:

poles)rotor (orteethrotorofNo.360360 °

=°

=rN

β

Hybrid stepper motor produces both excitation torque (varying as the sine of the displacement angle of rotor) and reluctance torque (varying at twice the sine of the displacement angle of rotor) as shown in Fig. 39.1-1(c).

(a) Variable reluctance stepper motor

(b) Permanent magnet stepper motor (c) Hybrid stepper motor

Fig. 39.1-1 Example 11-3[5] A hybrid stepping motor has 50 variable reluctance rotor teeth. Calculate the stepping angle (stepping length) in degrees. Solution: We know for hybrid stepper motor that

poles)rotor (orteethrotorofNo.360360 °

=°

=rN

β

stepNr

/8.150

360360°=

°=

°=∴β

Variable Reluctance Stepper Motors [1/39.4/p.1539]

Construction: A variable reluctance motor is constructed from ferromagnetic material with salient poles as shown in Fig. 39.2.

The stator is made from a stack of steel lamination and has six equally-spaced projecting poles (or teeth) each wound with an exciting coil.

The rotor which may be solid or laminated has four poles (or teeth) of the same width as the stator teeth.

As seen, there are three independent stator circuits or phases A, B, and C and each one can be energized by a direct current pulse from the drive circuit (not shown in figure).

A simple circuit arrangement for applying current to the stator coils in proper sequence is shown in Fig. 39.2(e). The six stator coils are connected in 2-coil group to form three separate circuit called phases. Each phase has its own independent switch.

Stepper Motor

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Diametrically opposite pairs of stator coils are connected in series such that when one tooth becomes a N-pole, the other one becomes a S-pole. Although shown as mechanical switches in Fig. 39.2(e), in actual practice, switching of the phase current is done with the help of solid-state control.

(a) (b) (c)

Truth Table No.1 A B C θ + 0 0 0o 0 + 0 30o 0 0 + 60o + 0 0 90o

(d) (e) (f) Fig. 39.2

When there is no current in the stator coils, the rotor is completely free to rotate. Energizing one or more stator coils causes the rotor to step forward (or backward) to a position that forms a path of least reluctance with the magnetized stator teeth. The step angle of this three-phase, four rotor teeth motor is β=360o/(4×3)= 30o.

Working: The motor has following modes of operation: (a) 1-phase-ON or Full-Step Operation (b) 2-Phase ON Mode (c) Half-Step Operation (d) Microstepping (a) 1-phase-ON or Full-Step Operation Initially, if switch S1 is closed and S2 and S3 are kept open, the phase A is energized to

make magnetic flux with its axis along the stator poles of phase A. The rotor is, therefore, attracted into a position of minimum reluctance of rotor teeth 1’ and 3’ lining up with stator teeth 1 and 4, respectively, as shown in Fig. 29. 2(b).

If switch S2 is closed and S1 and S3 are kept open, the phase B is energized to make magnetic flux with its axis along the stator poles of phase B. The rotor is, therefore, attracted

Stepper Motor

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into a position of minimum reluctance of rotor teeth 2’ and 4’ lining up with stator teeth 3 and 6, respectively, as shown in Fig. 29. 2(c). The rotor rotates through full-step of 30o in the clockwise (CW) direction.

If switch S3 is closed and S1 and S2 are kept open, the phase C is energized to make magnetic flux with its axis along the stator poles of phase C. The rotor is, therefore, attracted into a position of minimum reluctance of rotor teeth 1’ and 3’ lining up with stator teeth 2 and 5, respectively, as shown in Fig. 29. 2(d). The rotor rotates through an additional angle of 30o in the CW direction.

If switch S1 is closed and S2 and S3 are kept open, the phase A is energized to make magnetic flux with its axis along the stator poles of phase A. The rotor is, therefore, attracted into a position of minimum reluctance of rotor teeth 2’ and 4’ lining up with stator teeth 4 and 1, respectively. The rotor rotates through a further angle of 30o in the CW direction.

By now the total angle turned is 90o. As each switch is closed and the preceding one opened, the rotor each time rotates through an angle of 30o.

By repetitively closing the switches in the sequence 1-2-3-1 and thus energizing stator phases in sequence ABCA etc., the rotor will rotate CW in 30o steps.

If the switch sequence is made 3-2-1-3 which makes phase sequence CBAC (or ACB), the rotor will rotate counter-clockwise (CCW).

(b) 2-Phase ON Mode In this mode of operation, two stator phases are excited simultaneously. When phases A and B are energized together, the rotor experiences torque from both

phases and come to rest at a point mid-way between the two adjacent full-step positions. If the stator phases are switched in the sequence AB, BC, CA, AB etc. the motor will

take full steps of 30o each (as in the 1-phase ON mode) but its equilibrium positions will be interleaved between the full-step positions. The phase switching truth table for this mode is shown in Fig. 39.3(a).

Truth Table No. 2 A B C θ + + 0 15o 0 + + 45o + 0 + 75o + + 0 105o

Truth Table No. 2 A B C θ

+ 0 0 0o A + + 0 15o 0 + 0 30o B 0 + + 45o 0 0 + 60o C + 0 + 75o

A + 0 0 90o (a) (b)

Fig. 39.3

The 2-phase-ON mode provides greater holding torque and a much better damped single-stack response than the 1-phase-ON mode of operation.

Stepper Motor

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(c) Half-Step Operation Half-step operation or ‘half-stepping’ can be obtained by exciting the three phases in

the sequence A, AB, B, BC, C, CA etc. i.e. alternately in the 1-phase-ON and 2-phase-ON modes. It is sometime known as ‘wave’excitation and it causes the rotor to advance in steps of 15o i.e. half the full-step angle. The truth table for the phase pulsating sequence in half-stepping is shown in Fig. 39.3(b).

Half-stepping can be illustrated with the help of Fig. 39.4 where only three successive pulses have been considered. Energizing only phase A causes the rotor position shown in Fig. 39.4(a). Energizing phases A and B simultaneously moves the rotor to the position shown in Fig. 39.4(b) where the rotor has moved through half a step only. Energizing only phase B moves the rotor through another half-step as shown in Fig. 39.4(c). With each pulse, the rotor moves 30o/2=15o in the CCW direction.

(a) (b) (c)

Fig. 39.4 It will be seen that in half-stepping mode, the step angle is halved thereby doubling

the resolution. Moreover, continuous half-stepping produces a smoother shaft rotation.

(d) Microstepping It is also known as mini-stepping. It utilizes two phases simultaneously as in 2-phase-ON mode but with the two

currents deliberately made unequal (unlike in half-stepping where the two phase currents have to be kept equal).

The current in phase A is held constant while that in phase B is increased in very small increments until maximum current is reached. The current in phase A is then reduced to zero using the same very small increments. In this way, the resultant step becomes very small and is called microstep.

For example, a VR stepper motor with a resolution of 200 steps/rev (β=1.8o) can with microstepping have a resolution of 20,000 steps/rev (β=0.018o).

Stepper motors employing microstepping technique are used in printing and phototypesetting where very fine resolution is called for. As seen, microstepping provides smooth low-speed operation and high resolution. Possible Questions: 1. What are differences between a stepper motor and a conventional motor? Or, compare a stepper motor with a conventional motor. 2. Write some applications of stepper motors?

Stepper Motor

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3. What are the advantages and disadvantages of stepper motor? 4. Write detailed classifications of stepper motors. 5. What are the different methods of operation of variable reluctance stepper motors? 6. Briefly described with proper diagram, 2-phase ON mode of operation of a stepper motor having 6 stator and 4 rotor poles. 7. Briefly described with proper diagram, the one phase ON mode of operation of a stepper motor having 6 stator and 4 rotor poles. 8. Briefly described with proper diagram, the half-step operation of a stepper motor having 6 stator and 4 rotor poles. 9. Briefly described with proper diagram, the microstepping operation of a stepper motor having 6 stator and 4 rotor poles. 10. Briefly describe the different types of stepper motors. Example 11-2 [5] calculate the stepping angle for (a) a 3-stacks, 16 tooth rotor VR stepper motor, and (b) a 3-phase, 24-pole PM stepper motor. Example 39.1. A hybrid VR stepping has motor 8 main poles which have been castleated to have 5 teeth each. If rotor has 50 teeth, calculate the stepping angle. Example 39.2. A stepper motor has a step angle of 2.5o. Determine (a) resolution, (b) number of steps required for the shaft to make 25 revolutions and (c) shaft speed, if the stepping frequency is 3600 pps. Example 11-3[5] A hybrid stepping motor has 50 variable reluctance rotor teeth. Calculate the stepping angle (stepping length) in degrees. Problem: What is the required resolution of a stepper motor that is to operate at a pulse frequency of 6000 pps and travel 1800 in 0.025s.

References

[1] B. L. Theraja, A. K. Theraja, “A Textbook of ELECTRICAL TECHNOLOGY in SI Units Volume II, AC & DC Machines”, S. Chand & Company Ltd., (Multicolour illustrative Edition). [2] A. F. Puchstein, T. C. Lloyd, A.G. Conrad, “Alternating Current Machines”, © 1942, Asia Publishing House, Third Edition (Fully revised and corrected Edition 2006-07). [3] Jack Rosenblatt, M. Harold Friedman, “Direct and Alternating Current Machinery”, Indian Edition (2nd Edition), CBS Publishers & Distributors. [4] A. E. Fitzgerald, Charles Kingsley, Jr. Stephen D. Umans, Electric Machinery, 5th Edition in SI units, ©1992 Metric Edition, McGraw Hill Book Company. [5] Irving L. Kosow, Electrical Machinery and Transformers, Second Edition, Prentice –Hall India Pvt. Limited.