Basic theory of Stepping Motors
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Table of Contents Chapter 1 Construction Variable reluctance Permanent Magnet Hybrid Chapter 2 Stepping motor resolution and step angle Flux vectors Chapter 3 Operation Phase switching sequences Chapter 4 Stepping motor characteristics Static or holding torque - displacement characteristic Static load angle Friction torque Systematic angle tolerance Resonance Torque ripple Defining the start / stop frequency Read more : Stepper Motor Basics

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Construction

Stepping motors are electromagnetic, rotary, incremental devices which convert digital pulses into mechanical rotation. The amount of rotation is directly proportional to the number of pulses and the speed of rotation is relative to the frequency of those pulses.

Stepping motors are simple to drive in an open loop configuration and for their size provide excellent torque at low speed.

The benefits offered by stepping motors include:

• a simple and cost effective design
• high reliability

• maintenance free (no brushes)
• open loop (no feed back device required)
• known limit to the 'dynamic position error'

 

Although various types of stepping motor have been developed, they all fall into three basic categories.

1. variable reluctance (V.R)
2. permanent magnet (tin can)
3. hybrid
   
   

The variable reluctance or V.R. (fig 1) motor consist of a rotor and stator each with a different number of teeth. As the rotor does not have a permanent magnet it spins freely i.e. it has no detent torque. Although the torque to inertia ratio is good, the rated torque for a given frame size is restricted. Therefore small frame sizes are generally used and then very seldom for industrial applications.


Figure 1. cross section through a variable reluctance stepping motor

The permanent magnet (PM) or tin can (fig. 2) motor is perhaps the most widely used stepping motor in non-industrial applications. In it's simplest form the motor consists of a radially magnetized permanent magnet rotor and a stator similar to the V.R. motor. Due to the manufacturing techniques used in constructing the stator they are also sometimes known as 'claw pole' motors.

Figure 2. cross section through a permanent magnet



The Hybrid is probably the most widely used of all stepping motors. Originally developed as a slow speed synchronous PM motor it's construction is a combination of the V.R. and tin can designs. The Hybrid consists of a multi-phased toothed stator and a three part rotor (single stack). The single stack rotor contains two toothed pole pieces separated by an axially magnetized permanent magnet, with the opposing teeth off-set by half of one tooth pitch (fig. 3) to enable a high resolution of steps.

Figure 3. exploded drawing illustrating the tooth pitch off-set

The increasing demands on the modern stepping motor system of reducing acoustic noise, improving drive performance while at the same time reducing costs were satisfied in the past with two main types of Hybrid stepping motor. The 2(4) phase which has generally been implemented in simple applications and the 5 phase which has proven to be ideal for more the demanding of tasks. The advantages offered by the 5 phase included:

• higher resolution
• lower acoustic noise
• lower operational resonance
• lower detent torque

 

Although the characteristics of the 5 phase offered many benefits; especially when micro stepping, the increased number of power switches and the additional wiring required could have an adverse affect on a system's cost. With advances in electronics allowing circuits with ever higher degrees of integration and ever more features to be realized, SIG Positec saw an opportunity and took the initiative in their ground breaking development in stepping motor technology.



The 3 phase Hybrid stepping motor
Although similar in construction to other Hybrid stepping motors (see fig. 4), implementing 3-phase sine drive technology made it possible for the number of motor phases to be reduced leaving the number of rotor pole pairs and the drive electronics to determine the resolution (steps per revolution).

Figure 4. Sections illustrating laminations and rotors for 2-, 3- and 5-phase stepping motors


Figure 5. Cross section through a Hybrid stepping motor (3 phase)

As 3-phase technology has been used for decades as a cost effective method of generating rotating fields, the advantages of this system are self evident. The 3-phase stepping motor was therefore a natural progression incorporating all the best features from the 5-phase system at a significant cost reduction.

Stepping motor resolution and step angle

As already mentioned, the resolution (number of steps) and step angle of a stepping motor is dependent on:

• the number of rotor pole pairs

• the number of motor phases

• the drive mode (full or half step)

The resolution can be calculated using the formula:

The step angle can then be calculated by dividing one rotation (360) by the number of steps.

Exercise

Calculate the following:

A two phase stepping motor driven in half step mode completes an angle of 63.75 after moving 17 steps. How many pole pairs does the motor have?

Flux vectors

Flux vectors are used to illustrate the natural step angles of stepping motors




Figure 6. Flux vector diagrams for 2-, 3- and 5 phase stepping motors

If the phase currents are switched in small increments, these field vectors can point in virtually any direction.

Operation

Phase switching sequences

To enable rotation the magnetic field generated by the stator windings needs to move. This is achieved by switching the direction of current flow through each winding.
Full step: Using a simple two phase stepping motor with one pole pair as an example the phase switching sequence when driven in full step mode is as follows:

(fig. 7a) Start = Step angle 0 - Windings W1 and W2 are energized producing a north and south pole which attracts the rotor's respective poles and holds the rotor in position.

Figure 7a

(fig. 7b) Step 1 = Step angle 90 - Winding W1 remains the same but the current flow in winding W2 is switched (reversed). This results in a movement of the stator's magnetic field which the rotor follows until it is held at the new position.


Figure 7b



(fig. 7c) Step 2 = Step angle 180 - This time the current flow in Winding W1 is switched (reversed) and W2 stays the same. Again, the stator's magnetic field moves, the rotor follows and is held in the new position.

Figure 7c

(fig. 7d) Step 3 = Step angle 270 - Winding W1 stays as before, the current flow in W2 is switched (reversed) and the rotor follows the stator field to it's new position.


Figure 7d

Switching phases further can then either return the rotor to the starting position or the switching sequence can be reversed. Current traces can also be used to illustrate switching sequences as follows:



Figure 8 Current trace for a 2 phase stepping motor driven in full step mode

Fig. 3-1 :Current trace for a 2 phase stepping motor driven in full step mode

Half step: Using the same stepping motor driven in half step mode doubles the resolution (steps per rotation). Although the switching sequence is similar, instead of just reversing the flow of current through a phase, a phase is switched off, allowing the rotor to follow and take up even more positions. The sequence for one rotation is as follows:

Figure 9 Rotation sequence for a 2 phase stepping motor driven in half step

Fig. 3-2 : Current trace for a 2 phase stepping motor driven in half step

Figure 10 Current trace for a 2 phase stepping motor driven in half step

By using these simplified models, we have demonstrated the operational principle of the 2 phase stepping motor. This step by step switching of current results in a 'virtual' rotating field which the permanent magnet rotor then follows.


Figure 11 illustrates this step by step switching of current for a 3 phase motor in half step mode and it's corresponding current trace. Full step operation occurs when only the even (t) numbers are used in the step sequence.

Figure 11 Step sequence and current trace of a 3 phase stepping motor

Stepping motor characteristics

Static or holding torque - displacement characteristic

The characteristic of static (holding) torque - displacement is best explained using an electro-magnet and a single pole rotor (fig. 12). In the example the electro-magnet represents the motor stator and is energized with it's north pole facing the rotor


Figure 12 Curve illustrating static torque verses rotor position

Assuming there are no frictional or static loads on the rotor, fig. 11 illustrates how the restoring torque varies with rotor position as it is deflected from it's stable point. As the rotor moves away from it's stable position, the torque steadily increases until it reaches a maximum. This maximum value is called the holding torque and represents the maximum load that can be applied to the shaft without causing continuous rotation. If, the shaft is deflected beyond this point, the torque will fall until it is again at zero. However, this zero point is unstable and the torque reverses immediately beyond it back to the stable point. A pendulum (fig. 13) can also be used to demonstrate the effects we observe.




Figure 13 Pendulum effect of static torque verses rotor position

Depending on the number of phases, the cycle in figures 11 and 12 would be equivalent to the following number of full steps:

• 2 phase 4 steps
• 3 phase 6 steps
• 5 phase 10 steps
  

The torque required to deflect the shaft by a given angle can be calculated using the formula:

Although this static torque characteristic is not a great deal of use on it's own, it does explain some of the effects we observe. For example, it dictates the static stiffness of the system, in other words; how the shaft position changes when a load is applied to a stationary motor. The shaft must deflect until the torque generated matches the applied load. Therefore, the static position varies with the load.

Static load angle

The static load angle is defined as, the angle between the actual rotor position and the stable end position for a given load. Figure 14 illustrates (whether for full or half step) that as the torque increases so does the shaft deflection from the stable position.



Figure 14

The static load angle can be calculated using the formula:

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Friction torque Systematic angle tolerance Resonance Torque ripple Defining the start / stop frequency

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