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Application Note 828 Increasing the High Speed Torque of Bipolar Stepper Motors
Increasing the High Speed
Torque of Bipolar Stepper
Motors
Introduction
To successfully follow a velocity profile, a motor and drive
combination must generate enough torque to: accelerate the
load inertia at the desired rates, and drive the load torque at
the desired speeds. While the size of a bipolar stepper motor
generally dictates the low speed torque, the ability of the
drive electronics to force current through the windings of the
motor dictates the high speed torque. This application note
shows that increasing the slew rates of the winding currents
in a bipolar stepper motor pushes the motor to deliver more
torque at high speeds. Simple voltage drives, L/R drives, and
chopper drives are explained. L/R drives and chopper drives
achieve slew rates higher than those achieved by simple
voltage drives. Finally, an example chopper drive is pre-
sented.
Background
In standard full-step operation, quadrature (out of phase by
90) bipolar currents (Figure 1) energize the windings of a
bipolar stepper motor. One step occurs at each change of
direction of either winding current, and the motor steps at
four times the frequency of the currents. The ideal winding
currents of Figure 1 exhibit infinite slew rates.
Ideally, each phase contributes a sinusoidal torque;
T
1
= i
1
Tsin(N
) and
(1)
T
2
= i
2
Tcos(N
),
(2)
with the winding currents, i(t), in amps and the torque con-
stants, -Tsin(N ) and Tcos(N ), in newton centimeters per
amp.
represents the angular displacement of the rotor
relative to a stable detent (zero torque) position. N repre-
sents the number of motor poles; that is, the number of
electrical cycles per mechanical cycle or revolution. N ,
therefore, represents the electrical equivalent of the me-
chanical rotor position. The torque contributions add directly
to yield a total torque of
T
t
= T
1
+ T
2
= T (i
2
cos (N
) i
1
sin (N
)).
(3)
Integrating (3) over a full period of one of the torque con-
stants and multiplying the result by the reciprocal of that
period gives the average torque generated by the motor.
Assuming ideal square wave winding currents and sinusoi-
dal torque constants (Figure 2), the motor generates an
average torque of
(4)
(5)
In open loop applications,
adjusts automatically to match
the average torque generated by the motor with that required
to execute a motion task. When the winding currents and
their respective torque constants are in phase (
is zero), the
motor generates the maximum average torque or pull-out
torque;
(6)
Square waves make good approximations for the winding
currents at low speeds only, and (6), therefore, makes a
good approximation of the pull-out torque at low speeds only.
Real winding currents have an exponential shape dictated
by the L/R-time constants of the windings, the voltage ap-
plied across the windings, and, to a lesser extent, the back
emf generated by the motor as the rotor spins. For either
winding,
(7)
01145301
FIGURE 1. Ideal Quadrature Currents Drive the Windings of a Bipolar Stepper Motor
National Semiconductor
Application Note 828
Steven Hunt
May 1993
Increasing
the
High
Speed
T
orque
of
Bipolar
Stepper
Motors
AN-828
© 2002 National Semiconductor Corporation
AN011453
www.national.com Background
(Continued)
describes the winding current at a change in the direction of
that current, where I
o
is the initial winding current, V
CC
is the
voltage applied across the winding, V
emf
is the back emf,
and R and L are the winding resistance and inductance. At
low step rates, assuming V
CC
= V
rated
>>
V
emf
, the current
easily slews to the peak value of V
rated
/R before a subse-
quent direction change (Figure 3a). At higher step rates,
because the time between direction changes is shorter, the
current cannot reach the peak value (Figure 3a). V
rated
is the
rated voltage of the windings.
Clearly from (4) and Figure 3, as the speed increases,
decreases in the winding currents result in decreases in
T
pull-out
. The torque vs. speed characteristic of a typical
bipolar stepper motor (Figure 4) reflects this phenomenon.
Each pull-out torque curve bounds (on the right) a region of
torque-speed combinations inside which the stepper motor
runs and outside which the stepper motor stalls.
It follows then, that the goal of increasing the high speed
torque is achieved by increasing the winding currents at high
speeds. This, in turn, is achieved by increasing the slew
rates of the winding currents; for example, with the increased
slew rates realized by raising V
CC
well above V
rated
, the
winding current easily slews to the peak value of V
rated
/R at
01145314
FIGURE 2. Ideal Square Wave Winding Currents and Sinusoidal Torque Constants for Average Torque Calculation
01145319
(a)
01145320
(b)
FIGURE 3. Real Winding Current and Sinusoidal Torque Constant
vs Step Rate at Low Step Rates (a) and at High Step Rates (b)
AN-828
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2 Background
(Continued)
both low and high step rates (Figure 5). Winding currents
realized with V
CC
= V
rated
are represented with dashed lines,
and, assuming a means for limiting at V
rated
/R, winding
currents realized with V
CC
>>
V
rated
are represented with
solid lines.
Both decreasing the L/R-time constants of the windings and
increasing the voltage applied across the windings increases
the slew rates of the winding currents. L/R drives and chop-
per drives take these tactics to raise the slew rates of the
winding currents well above those realized by simply apply-
ing the rated voltage to the windings. The torque vs. speed
characteristic of a typical bipolar stepper motor (Figure 4
again) reflects the resulting high speed torque gains.
It is important to note, however, that applying V
CC
>>
V
rated
also results in excessive winding currents at low speeds.
The winding currents must be held at or below the rated limit
(usually V
rated
/R per winding) to hold power dissipated inside
the motor at or below the rated limit (usually 2 x V
rated
x
I
rated
).
Simple Voltage Drives
Simple drives employ two H-bridge power amplifiers to drive
bipolar currents through the phase windings (Figure 6). For
either amplifier, closing switches S1 and S4 forces the rated
voltage (less two switch drops) across the winding, and
current flows from supply to ground via S1, the winding, and
S4. After opening S1 and S4, closing S2 and S3 reverses the
direction of current in the winding. This drive scheme is
commonly referred to as simple voltage drive. Because only
the winding resistances limit the winding currents, V
CC
can-
not exceed V
rated
.
L/R Drives
L/R drives employ two series power resistors to decrease
the L/R-time constants of the windings; for example, a 45 power resistor in series with each of two 15
winding resis-
tances divdes the L/R-time constants by four and allows the
rated supply voltage to be increased by a factor of four. Both
the crispness of the response and the high speed torque are
increased. While the rotor holds position or moves at low
step rates, the series power resistors protect the motor by
holding the winding currents to the rated limit. Since both the
L/R-time constants of the phase windings and the rated
01145303
FIGURE 4. A Typical Torque vs Speed Characteristic of
a Bipolar Stepper Motor
01145321
(a)
01145322
(b)
FIGURE 5. Real Winding Current vs Step Rate with V
CC
>>
V
rated
at Low Step Rates (a) and at High Step Rates (b)
AN-828
www.national.com
3 L/R Drives
(Continued)
supply voltage were increased by a factor of four, the ex-
ample drive would commonly be referred to as an L/4R drive.
The maximum operating supply voltage of the power ampli-
fiers can limit the factor by which the supply voltage is
increased above the rated voltage of the windings, but power
losses in the series resistors more likely limit this factor. If, for
example, 60V is applied across two 0.5A, 15
phase wind-
ings, two 105
series resistors are required to hold the
winding currents to the 0.5A/phase limit. This is an L/8R
drive. Power dissipated in the series resistors while the rotor
holds position is 105 x 0.5 x 0.5 x 2 = 52.5W, while power
dissipated in the entire drive is 60 x 0.5 x 2 = 60W. The drive
efficiency approaches 12.5%. After looking at these num-
bers, the drive designer may opt to cut losses by using the
30V power supply/45
series resistor combination of an
L/4R drive. Unfortunately, while the rotor holds position, total
power dissipated in the series