Stepper Motors

What is a Step Motor?

A step motor is defined as a device whose normal shaft motion consists of discrete angular movements of essentially uniform magnitude when driven from a sequentially switched DC power supply.

A step motor is a digital input-output device. It is particularly well suited to the type of application where control signals appear as digital pulses rather than analog voltages. One digital pulse to a step motor drive or translator causes the motor to increment one precise angle of motion. As the digital pulses increase in frequency, the step movement changes into continuous rotation.

Types of Step Motors

There are three basic types of step motors in use, though in industrial automation the most common type is the hybrid type:

• Active rotor: permanent magnet (PM)
• Reactive rotor: variable reluctance (VR)
• Combination of PM and VR: hybrid (HY) 

Applied Motion Products offer primarily hybrid type step motors with a 1.8° step angle.

Permanent Magnet Type

This type of step motor has a permanent magnet rotor. The stator can be similar to that of a conventional 2- or 3-phase induction motor or constructed similar to a stamped motor. The latter is the most popular type.

A) Conventional permanent magnet type. Figure 1 shows a diagram of a conventional permanent magnet rotor step motor. A 2-phase winding is illustrated. Figure 1a shows Phase A energized with the "A" terminal positive. The field is at 0°. With the coil wound as shown, the north seeking pole of the rotor is also at 0°. The motor steps as shown in Table I.

TABLE I

Step	Position Rotor & Shaft	(Mechanical Degrees) Electromagnetic Field	Energization				Figure
			phase		phase
			A	A'	B	B'
0	0	0	+	-	off	off	1a
1	90	90	off	off	+	-	1b
2	180	180	-	+	off	off	1c
3	270	270	off	off	-	+	1d

The shaft completes one revolution for each complete revolution of the electromagnetic field in this motor.

Figure 2 shows the same motor with both windings energized. The important difference here is that the resultant electromagnetic field is between two poles. In figure 2, the field has moved 45° from the field in figure 1. Table II shows the energization sequence and rotor positions.

TABLE II

Step	Position Rotor & Shaft	(Mechanical Degrees) Electromagnetic Field	Energization				Figure
			phase		phase
			A	A'	B	B'
0	45	45	+	-	+	-	2a
1	135	135	-	+	+	-	2b
2	225	225	-	+	-	+	2c
3	315	315	+	-	-	+	2d

As in the one-phase-on energizing scheme, the shaft completes one revolution for each complete revolution of the electromagnetic field.

It should be evident that this motor can half step; i.e., step in small step increments. This is possible by combining the energization shown in Figure 1 with that shown in Figure 2. Figure 3 shows the diagrams of a motor with half-step rotor motion. The energizing sequence and rotor positions are shown in table III.

TABLE III

Step	Position Rotor & Shaft	(Mechanical Degrees) Electromagnetic Field	Energization				Figure
			phase		phase
			A	A'	B	B'
0	0	0	+	-	off	off	3a
1	45	45	+	-	+	-	3b
2	90	90	off	off	+	-	3c
3	135	135	-	+	+	-	3d

As in the previous diagrams, the rotor and shaft move through the same angle as the field. Note that each step resulted in a 45° rotation instead of 90° in the previous diagram.

A permanent magnet step motor may be wound with a bifilar winding to avoid the necessity of reversing the polarity of the winding. Figure 4 shows the bifilar winding while Table IV shows the energization sequence.

TABLE IV

Step	Position Rotor & Shaft	(Mechanical Degrees) Electromagnetic Field	Energization				Figure
			phase		phase
			A	B	C	D
0	0	0	on	off	off	off	4a
1	90	90	off	off	on	off	4b
2	180	180	off	on	off	off	4c
3	270	270	off	off	off	on	4d

Bifilar windings are easier to switch using a transistor controller. Fewer switching transistors are required.

B) Stamped or can stack permanent magnet step motor. The most popular type of permanent magnet step motor is the so called stamped type, claw tooth, sheet metal, tin can or simply low cost step motor. This motor is difficult to illustrate clearly because of the way it is constructed. The cutaway in Figure 5 is an attempt to show how this type of PM step motor looks. The motor is shown with both phases energized. The rotor is shown with 12 poles resulting in 24 steps per revolution with a 15° step angle. A schematic diagram of a PM step motor of the type illustrated in Figure 5 is shown in Figure 6. This motor has a pair of coils surrounding a permanent magnet rotor. The coils are enclosed in a soft iron housing with teeth on the inside reacting with the rotor. Each coil housing has the same number of teeth as the number of rotor poles. The housings are radially offset from each other by one-half the tooth pitch.

PM step motors are available with the following step angles:

Step Angle Degrees	Steps Per Revolution
1.8	200
3.6	100
3.75	96
7.5	48
9	40
10	36
11.25	32
15	24
18	20
22.5	16
30	12
45	8
90	4

Variable Reluctance Type

This type of step motor has an electromagnetic stator with a magnetically soft iron rotor having teeth and slots similar to the rotor of an inductor alternator. Whereas PM motors are basically 2-phase machines, VR motors require at least 3 phases. Most VR step motors have 3 or 4 phases although 5-phase VR motors are available.

A 3-phase VR motor diagram is shown in Figure 7. The motor shown has 12 stator teeth, 8 rotor teeth, and step angle of 15°. The energization sequence is shown in Table V.

TABLE V

Step	Position Rotor & Shaft	(Mechanical Degrees) Electromagnetic Field	Energization Phase
			A	B	C
0	15	60	on	off	off
1	30	120	off	on	off
2	45	180	off	off	on
3	60	240	on	off	off

In a VR step motor, the field moves at a different rate than the rotor.

Figure 8 shows a diagram of a 4-phase 15° step angle motor with one phase energized. The energization diagram is shown in Table VI.

TABLE VI

Step	Position Rotor & Shaft	(Mechanical Degrees) Electromagnetic Field	Phases
			A	B	C	D
0	15	-45	on	off	off	off
1	30	-90	off	on	off	off
2	45	-135	off	off	on	off
3	60	135	off	off	off	on

Note the rotation of the electromagnetic field. The field takes a big jump in rotation between steps 2 and 3. This is characteristic of a motor connected this way. Figure 9 shows this motor with two phases energized at a time. The rotation of the field remains the same. A way to correct this is shown by the diagram in Figure 10. The diagrams in figures 8 and 9 illustrate windings connected 4N and 4S. This indicates the magnetic poles as they are energized. The coil hookup shown in Figure 10 shows a symmetrical hookup called N-S-N-S because of the coil polarity. Note that Phase A coil has two south poles and no north poles for a flux return path. You may rest assured that there will be one. The flux will return through the path of least reluctance, namely through the pole pairs which are nearest to two rotor teeth. This varies with rotor position. The flux induces a voltage in the coils wound on the pole. This induces a current in the winding slowing the rotor. The amount of current is determined by the voltage across the coil. A diode-clamped coil will have more current than a resistor diode or zener diode-clamped winding. Figure 11 illustrates the diagram of a 4-phase VR step motor with N-S-N-S hookup and two phases energized. Note the short flux path between poles.

It is frequently necessary to make the step angle smaller without using gearing. One method is to double the number of rotor and stator teeth. If the motor was constructed as shown in Figure 7, the teeth would be slender and difficult to wind. A better method of doing this is shown in Figure 12. The number of rotor and stator poles is reduced.

Figure 13 shows a diagram of a 5° per step variable reluctance step motor. A 1.8° per step VR motor diagram is shown in Figure 14.

Variable reluctance step motors are available with the following step angles:

Step Angle Degrees	Steps Per Revolution
1.8	200
5	72
7.5	48
15	24

Hybrid Type

This type of motor is frequently referred to as a permanent magnet motor. It uses a combination of permanent magnet and variable reluctance structure. Its construction is similar to that of an induction motor. Figure 15 shows a simplified type of hybrid motor to illustrate its construction. The rotor has two end pieces (yokes) with salient poles equally spaced but radially offset from each other by one-half tooth pitch. A circular permanent magnet separates them. The yokes have essentially uniform flux of opposite polarity. The stator is formed from laminated steel. The motor shown in Figure 15 has 4 coils arranged in two groups of 2 coils in series. One coil pair is called Phase A and the other Phase B. For the motor illustrated, each pole has one tooth.

The number of full steps per revolution may be determined from the following formula:

SPR = NR x Ø
Where:	SPR = number of steps per revolution
	NR = total number of rotor teeth (total for both yokes)
	Ø = number of motor phases
	or: NR = SPR/Ø

Example: The motor shown in Figure 15 has a 2 Ø winding and a rotor with 5 teeth per yoke for a total of 10 teeth. Calculate the number of steps/rev.

SPR = 10 x 2 = 20 steps/rev

The step angle may be found from the following formula:

SA = 360/SPR
Where:	SA = step angle in degrees
	SPR = steps per revolution

Example: Calculate the step angle for the above motor.

SA = 360/20 = 18°

The step angle may be calculated directly without knowing the number of phases if the number of stator teeth and teeth per pole are known. Figure 15 shows one tooth per pole and a total of 4 teeth on the stator.

Formula:	SA = (1/NST - 1/NRP) x 360 x NSTP
Where:	SA = step angle in degrees
	NST = number of stator teeth
	NRP = number of rotor teeth per pole or yoke
	NSTP = number of stator teeth per pole

Note that motors are frequently built with one or two teeth between each pole left out to facilitate winding the motor and reduce flux leakage between poles. This formula requires that the theoretical number of teeth be used.

Note that here, too, the theoretical number of teeth must be used. It is usually easy to visually determine if a tooth or two has been left out between poles.

Example: The motor in Figure 15 has 5 teeth on each rotor yoke and one tooth per pole with 4 teeth total.

SA	= (1/4 - 1/5) x 360 x 1
	= (.25 - .20) x 360
	= 18°

Figure 16 shows the shaft rotation with 2-phase-on. The switching sequence, field rotation and output shaft rotation are shown in Table VII.

TABLE VII

Step	Position Rotor & Shaft	(Mechanical Degrees) Electromagnetic Field	Phases		Figure
			A	B
0	9°	45°	+	+	16a
1	27°	135°	-	+	16b
2	45°	215°	-	-	16c
3	63°	305°	+	-	16d

Figure 17 shows a 5° hybrid step motor. Note that the rotor has 18 teeth on each yoke for a total of 36 teeth. The commonly available 1.8° hybrid diagram is shown in Figure 18.

Hybrid step motors are available in the following step angles:

Step Angle Degrees	Steps Per Revolution
0.45	800
0.72	500
0.9	400
1.8	200
1.875	192
2	180
2.5	144
3.6	100
5	72

This article originally appeared in the Applied Motion Products "Motor-Drives-Controls" catalog in 1997.

Design Tips

• Parallel connect the lead wires for best torque over the widest speed range.
• If not enough current is available from the drive, series connect the lead wires for full torque at low speeds.
• Keep motor case temperature below 100 °C. This can be achieved by lowering the motor current or limiting the duty cycle.
• Allow sufficient time to accelerate load.
• Use a microstepping drive for smoothest motor performance over a wide speed range.
• For open loop operation, size the motor with a 30-50% torque margin at speed. Including an encoder in the system and using Applied Motion’s Stall Prevention feature may allow operation all the way down to a 0% torque margin.
• Do not disassemble motors. A significant reduction in motor performance will result.
• Do not machine shafts without consulting Applied Motion Products.
• Do not disconnect motor from drive while power is applied. Remove power from the drive before disconnecting the motor.
• Do not use holding torque/detent torque of motor as fail-safe brake.
• Use an Applied Motion stepper drive with your step motor to ensure best performance. Recommended motor-drive pairings are displayed on each product page (in the Related & Recommended Products section), as well as in the hardware manuals of the stepper drives.

Motion Installation Tips

• Mount the motor securely against a surface with good thermal conductivity such as steel or aluminum.
• Properly align the motor with the load using a flexible coupling.
• Protect the motor shaft from excessive thrust, overhung and shock loads.

Accuracy (step)
The correctness of the distance a step motor moves during each step. Does not include errors due to hysteresis.

Axial play
The axial shaft displacement due to a reversal of an axial force on the shaft. (End play).

Bifilar (winding)
Two windings wound (in parallel) on the same pole. This permits magnet polarity reversal with simple switching means.

Bi-level drive (dual voltage drive)
A drive where two levels of voltage are used to drive a step motor. A high (over drive) voltage is applied to the winding each time it is switched on. The high voltage stays on until the current reaches a predetermined level. The high voltage is turned off after a time period determined experimentally or by sensing winding current. The low voltage maintains the rated or desired current.

Bipolar drive
A drive which reverses the magnetic polarity of a pole by electronically switching the polarity of the current to the winding (+ or -). Bipolar drives can be used with 4, 6 or 8 lead motors. With 4 and 8 lead motors bipolar drives are usually more efficient than unipolar drives.

Chopper drive
A step motor drive that uses switching amplifiers to control motor current. Chopper drives are more efficient than L/R or voltage drives.

Controller (step motor)
A system consisting of a DC power supply and power switches plus associated circuits to control the switches in the proper sequence.

Detent torque
The maximum torque required to slowly rotate a step motor shaft with no power applied to the windings. This applies only to permanent magnet or hybrid motors. The leads are separated from each other.

Driver or drive
An electronic package to convert digital step and direction inputs to currents to drive a step motor.

Duty cycle
The percentage of ON time vs. OFF time. A device that is always on has a 100% duty cycle. Half on and half off is a 50% duty cycle.

End play
The axial shaft motion, due to the reversal of an axial force acting on a shaft with axial clearance or low axial preload.

Friction (coulomb)
A resistance to motion between non-lubricated surfaces. This force remains constant with velocity.

Friction (viscous)
A resistance to motion between lubricated surfaces. This force is proportional to the relative velocity between the surfaces.

Holding torque (static torque)
The maximum restoring torque that is developed by the energized motor when the shaft is slowly rotated by external means. The windings are on but not being switched.

Hybrid step motor (HY)
A type of step motor comprising a permanent magnet and variable reluctance stator and rotor structures. It uses a double salient pole construction.

Hysteresis (positional)
The difference between the step positions when moving CW and the step position when moving CCW. A step motor may stop slightly short of the true position thus producing a slight difference in position CW to CCW.

Indexer
An electronic control which converts motion commands from a computer terminal into pulse and direction signals for use by a step motor driver.

Inductance (mutual)
The property that exists between two current-carrying conductors or coils when magnetic lines of flux from one link with those of the other.

Inductance (self)
The constant by which the time rate of change of the coil current must be multiplied to give the self-induced counter emf.

Instantaneous start-stop rate
The maximum switching rate that an unloaded step motor will follow without missing steps when starting from rest.

L/R drive
A drive that uses external resistance to allow a higher voltage than that of a voltage drive. L/R drives have better performance than voltage drives, but have less performance and efficiency than a chopper drive.

Maximum reversing rate
The maximum switching rate at which an unloaded motor will reverse direction of rotation without missing steps.

Maximum slew rate
The maximum pulse rate at which a step motor with no load will run and remain in synchronism.

Microstepping
A technique in which motor steps are electronically divided by the drive into smaller steps. The most common microstep resolutions are 10, 25 and 50 steps per full step, but many resolutions, ranging from 2 to 256 microsteps per full step are available.

Oscillator
A device that is used to produce pulses for driving a step motor at a preset speed. Many Applied Motion drives are available with built in oscillators.

Overshoot
The amount the step motor shaft rotates beyond the commanded stopping position. Usually applies to a single step.

Permanent magnet step motor (PM)
A step motor having a permanent magnet rotor and wound stator.

Positional accuracy
The maximum error in one revolution of a full step in 360°. Expressed as a percentage of a full step.

Pull-in rate (response rate)
The maximum switching rate at which an unloaded motor can start without losing step positions.

Pull-in torque
The maximum torque load at which a step motor will start and run in synchronism with a fixed frequency pulse train without losing step positions.

Pull-out torque
The maximum torque load that can be applied to a motor running at a fixed stepping rate while maintaining synchronism. Any additional load torque will cause the motor to stall or miss steps.

Pulse rate
The rate at which successive steps are initiated or the windings switched.

Radial play
The side to side movement of the shaft due to clearances between the shaft and bearing, bearing to housing, and bearing internal clearance for ball and roller bearings. (Side play).

Response rate (pull-in rate)
The switching rate an unloaded motor can follow from a standing start without missing steps.

Settling time
The elapsed time starting the instant the rotor reaches the commanded step position and the oscillations settle to within a specified displacement band about the final position, usually ±3 to ±5 percent.

Stall torque (holding or static torque)
The maximum restoring torque that is developed by the energized motor when the shaft is slowly rotated by external means. The windings are not switched.

Step angle
The nominal angle through which the step motor shaft rotates between adjacent step positions.

Step rate (speed)
The number of steps a shaft rotates during a specified time interval.

Step-to-step accuracy
The maximum error that occurs between any adjacent step, expressed as a percentage of one full step.

Switching amplifier
A device that switches a high voltage on and off to control current. Some amplifiers (PWM types) switch at a constant frequency and adjust duty cycle to control current. Other types have a fixed off time and adjust the frequency.

Switching sequence (energizing sequence)
The sequence and polarity of voltages applied to the coils of a step motor that result in a specified direction of rotation.

Thermal resistance
The resistance to the flow of heat between two surfaces of the same body or different bodies. Thermal resistance as it pertains to step motors equals the rise in winding temperature above ambient divided by the Watts dissipated in the winding. (Winding temp rise above ambient) / (Watts dissipated in winding) = °C/Watt.

Thermal time constant
The time required for the motor winding to reach 63.2% of its final temperature.

Torque displacement curve
The holding (restoring) torque plotted as a function of rotor angular displacement with the motor energized.

Torque gradient (stiffness)
The ratio of the change in holding torque for a particular change in shaft position when the motor is energized.

Unipolar drive
The motor phase winding current is switched in one direction only. The polarity of the applied voltage to each winding is always the same. Unipolar drives require 6 or 8 lead motors.

Variable reluctance step motor (VR)
A step motor having a wound stator or stators with salient poles working with a soft iron rotor having salient poles on the periphery. There are no permanent magnets in a variable reluctance step motor.

Viscous damping
A damper which provides a drag or friction torque proportional to speed. At zero speed the drag torque is reduced to zero.

Viscous inertia damper
A damper with an inertia coupled to the motor shaft, through a film of viscous fluid, usually silicone oil to minimize viscosity variations due to temperature changes. This damper only responds when the velocity between the damper inertia and motor shaft changes. At steady state speed there is no effect from the damper.

Voltage drive
A drive operated at the minimum voltage required to safely limit motor current. Motors used with voltage drives produce less torque at higher speeds than when used with L/R or chopper drives.

Wave drive
Energizing the motor phases on at a time. Driving the motor one phase or winding on at a time.