theory of Stepping Motors
This information is intended to provide basic information to technicians about a kind of motor ( known as step motor , stepping motor or
stepper motor ) widely applied in precision machines, the industry, in minilabs to develop photography, printers, in sewing machines, etc. that differs from the concept of simple
rotary motors , and giving a help in the service of those mechanisms .
- Table of
- ------- Chapter 1
- Chapter 2
motor resolution and step angle
- Chapter 3
- Chapter 4
- 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.
- variable reluctance (V.R)
- permanent magnet (tin can)
- 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
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
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
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
- The step angle can then be calculated by
dividing one rotation (360) by the number of steps.
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 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.
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
(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.
(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.
(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.
(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.
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
- 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.
The static load angle can be calculated using the formula: