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9.6 Dynamic Braking of a DC Micromotor
Many times customers not only
ask for the acceleration characteristics but also need to know the dynamics of
stopping. This addresses the case of dynamic braking of a motor with both
friction and inertial load. Gearhead parameters are included for completeness;
however, a ratio and efficiency of unity may be used for cases involving direct
motor output.
If we assume a switch closure
across the motor terminals at time zero, the time to stop, ts, is calculated by
the following expression:
where:
tm is the unloaded motor time
constant (catalog value) |
Note that the units of ts are the same as tm.
Example as follows:
A 22C11-210-5/B24.0-128 drives
a 10 oz-in load at 55 rpm.
Load inertia is 2 x 10-4 Kgm2.
The time to stop is:
ts = 0.50 second
Due to the high deceleration
torque developed by dynamic braking, care must be exercised when using a gearbox
that the resulting reverse torque does not exceed the torque rating of the
gearbox (both first stage and last stage ratings). Please refer to Section Two
paragraph 5.0 of this handbook dealing with Minimization of Gear Train Inertia
and the effects of "back driving" through a speed reducer.
9.7 Example of Graphing Motor
Characteristics
The graph of motor characteristics is based upon the following given information:
Motor: 26P11-216-35 |
9.71 MOTOR CHARACTERISTICS 26P11-216-35 |
|
9.8 ConsideratIons for Tachometer Applications
The most significant considerations of a tachometer application are:| 1. | Voltage Constant (kv)
expressed as volts per 1,000 RPM (V/K RPM). This defines the signal output of
the tach In terms of Its mechanical input in RPM. |
|
| 2. | Linearity expressed as a
percent. This defines the stability of the voltage constant over a given speed
range and load condition. Between 500 and 5000 RPM Escap tachs have an unloaded
linearity of ± 0.2% and with a 10 K W load ± 0.7%. Because Escap uses precious
metals in the brushes and commutator there is no requirement for a minimum
current flow to keep the brushes "clean". Therefore, Escap tachs may
be used with high load impedances to take advantage of the ± 0.2% unloaded
linearity. |
|
| 3. | Ripple is a result of the
frequency of the induced emf. The ripple frequency is equal to twice the number
of commutator segments (coils) multiplied by the Revolutions per Second (RPS). |
|
| 4. | A.C. Variation is a
fluctuation in the base generator output signal. It is caused by non-symmetry in
the coils. Escap® tachs are characterized by their precise coil winding and thus
have an absolute minimum of a.c. variation. The frequency of a.c. variation is
equal to twice the RPS. |
|
| 5. | Thermal Stability. The
temperature coefficient of Escap® tachometers is - 0.02%/Cº due to the use of
Al cc magnets which are very stable and therefore will require little if any
temperature compensation. |
|
| 6. | Inertia. The Escap® tachometer is a low inertia device and is therefore well suited for certain applications which cannot tolerate non-active load inertias, i.e.: sensing velocity characteristics of a very low mass load such as a print wheel. Since the tachometer is primarily used as an analog sensor for measuring system speed (RPM) the designer usually begins by selecting a tachometer having an output signal (over entire system speed range) which is compatible with other system requirements and limitations such as: amplifier gain and saturation level; electrical noise; etc. There is no single "cook book" approach to tachometer selection. The designer must, as always, match his skills against the advantages and disadvantages of all of the elements involved. |
9.9 Light Chopper Drive Motor
This application is for a motor
to drive a slotted wheel which in turn interrupts (chops) a light beam at a
frequency of 200 Hz. The chopper wheel has only a single slot and an
inertia of 0.2 gcm. Supply voltage available is 4 Vdc.
Given: Vo = 4 Vdc Max
ML = 0.2 gcm (2 x 10-4 NM)
Chopper freq. = 200 Hz
Solution:
Pin = MLw = 2 x
10-4 x 1.257 x 103 = 0.25 Watts
Propose to use 16 C11-210 Motor
From catalog: K = 23 x 10-4
Nm/A
R =7.5W
lo = 0.015A
Now: 
Vo = Rl + Kw
Vo = (7.5 x
0.102) + 23 x 10-4 x 1257 = 3.66 volts
4Volt supply is acceptable
and motor choice checks out.
10.0 REVIEW OF ESCAP® STEP MOTORS
10.1 Description
The Escap® family of permanent
magnet step motors are the result of a unique patented technology.
The motors can be built with
one phase per stack, with two or more phases per stack (each phase-covers a given angular sector) or with two or more phases imbricated in one single stack.
Patents are protecting these different designs. The-following described motor has two phases arranged in one single stack. This new step motor design is based upon a homoheteropolar structure.
Figure 25 illustrates the motor's design in a simplified mechanical schematic.
The motor is in the form of a
thin axially magnetized disc made from somarium -- cobalt magnetic alloy. A special magnetization process allows for a high number
of magnetic poles and small step angles. The magnetic path is closed by the use
of "C" shaped silicon iron lamination cores. These cores are
symmetrically arranged in the two stator halves. These lamination cores act as
the stator "teeth" and are surrounded with a "bean" shaped
coil for each electrical phase.
The magnet is fixed to a shaft by virtue of two end-bells thus,
forming the rotor assembly. It should be obvious that the inertia of such a
rotor assembly is very low -- an advantage of this motor. Figure 26 shows the construction of the Escap® step motor.
The two stator halves forming the housing are precision molded of Ryton. This material has a very good modulus of elasticity, low shrinkage, and excellent thermal stability. The four bean shaped coils are identical and are manufactured by standard winding methods.
10.2 Advantages and Unique
Features
The advantages and unique features of the Escap® P series
motors can be summarized as follows:
10.3 Detent Torque
The P series step motor does provide some holding torque with the windings
do-energized. This torque is the result of an interaction between the rotor
poles and the stator poles. For this motor design the detent torque is a fourth
harmonic of the fundamental sinusoid torque curve and is defined as
Tq = 2T4 Sin (4Nα - Φ4)
During manufacture
of the motor it is possible to increase or decrease the detent torque over a
range of almost zero to about 10% of the one-phase-on holding torque.
10.4 Holding Torque
The P series motor is a two phase step motor. With one phase energized with a dc current, the rotor poles will align themselves with the corresponding stator poles of the energized phase.
A motor so aligned is in a position of stable equilibrium. If an external torque is applied to the motor shaft causing the rotor and stator poles to misalign, a counteracting torque is developed which tends to restore the original condition of equilibrium.
This restoring torque is called the static holding torque and its value varies with rotor position. This torque is zero when the rotor and stator poles are aligned and increases with the angle of misalignment up to some maximum value for the particular motor (static torque characteristics).
With two phases energized the static holding torque is obtained by adding the torques of the two phases energized separately.
Theoretically the two-phase-on scheme produces √2 times the torque developed with one-phase-on. In practice the actual static torque is less because the individual torque curves are not sinusoidal.
Under conditions of negligible detent torque the mathematical expression for Static holding torque (one-phase-on) is given by:
T = γ ni sin Nα
where
N = number of pole pairs (25 for 100 steps per revolution)
γ = torque per ampere-turn (a motor constant)
ni = number of ampere-turns
α = total mechanical displacement (0 to 360º)
The torque curves of Figures 27
and 28 present a graphic explanation of the various torques under one and
two-phase-on operation. A review of these curves yields the following helpful
observations:
(A) One-phase-on
· The stable equilibrium positions of the detent torque and the holding torque are
the same.
· The stiffness of the stable equilibrium positions is increased by the detent
torque.
(B) Two-phases-on
· The stable equilibrium
positions of the holding torque (phase 1 + 2 and 1 - 2) are unstable positions
of the detent torque.
· The stiffness of the stable
equilibrium positions is decreased by the detent torque.
| T1 | DETENT TORQUE AMPLITUDE | |
| T2 | THEORETICAL MAXIMAL DYNAMIC TORQUE WITH ONE PHASE ENERGIZED | |
| T3 | THEORETICAL MAXIMAL DYNAMIC TORQUE WITH TWO PHASE ENERGIZED | |
| T4 | HOLDING TORQUE AMPLITUDE WITH ONE PHASE ENERGIZED | |
| T5 | HOLDING TORQUE AMPLITUDE WITH TWO PHASES ENERGIZED | |
| A, B | STABLE EQUILIBRIUM WITH ONE PHASE ENERGIZED | |
| C, D | STABLE EQUILIBRIUM WITH TWO PHASES ENERGIZED | |
| A, C, B, D | SUCCESSIVE ROTOR POSITIONS WHEN HALF-STEPPING (8 STEP SWITCHING SEQUENCE) |
| T2 | THEORETICAL MAXIMAL DYNAMIC TORQUE WITH ONE PHASE ENERGIZED | |
| T4 | HOLDING TORQUE AMPLITUDE WITH ONE PHASE ENERGIZED | |
| L TL A, B A', B' |
AMOUNT OF APPLIED LOAD COUNTERACTING TORQUE WHEN LOAD L IS APPLIED STABLE EQUILIBRIUM WITH ONE PHASE ENERGIZED STABLE EQUILIBRIUM WHEN LOAD L IS APPLIED |
Figure 28 Descriptive Torque Curves
10.5 Dynamic Characteristics
The performance curves of the P312 and P532 step motors are shown in Figure 29. It should be noted that the start-stop torque versus speed will be affected by both the load inertia and friction.
However, the pull-out torque is usually affected by friction alone. It should be realized however, that in some cases static friction and running friction are often different values.
A good dynamic behavior can be claimed when this motor is compared to equivalent hybrid type 3.6º motors with a rare-earth cobalt magnet, or even to traditional hybrid type 1.8º motors.
For the same number of steps per second, the P532 is rotating twice as fast as a 1.8º motor; the mechanical work is therefore equivalent, as long as torque is
at least half the torque of the competition motor.
It is effectively the case, even though the volume and the mass
are respectively 27% and 42%
lower. The rotor inertia is 5 times lower but, as a matter of fact, should be
multiplied by 4 in order to compare the inertia of both motors on a shaft which
runs at the same speed. As far as mechanical power is concerned, the P532 motor
is equivalent to a size 22 motor, 2" long, with 1.8 times more volume, 2.4
times more mass and 2.5 times more equivalent inertia.
The reason why the P532 has good performances with regard to its
volume and its mass is essentially because of its low inertia and low magnetic
losses (due to a total silicon-iron magnetic circuit which weighs only 50g). At
1000 steps per second, the P532 needs 0.4W and conventional 1.8º motors need
0.7W to 1.1W. At 2000 steps per second, this becomes 1.1W against 1.9 and 2.9W.
At 5000 steps per second, the P532 needs 4W, of which 1W is due to friction in
the ball bearings viscous friction of the magnet in the air gap. Referred to a
chopper drive, the Joule power in the coils represents about 6W. A total of 10W
power losses can so be figured out. This rough calculation gives an idea of the
motor efficiency, since the available mechanical power is more than 20W.
10.6 Damping Considerations
At low speed, the P532 and P312
have less losses than other step motors. Thus, the damping of the settling
oscillations will need longer time. However, the damping effect created by the
short-circuit of the coils or simply by connecting the coils across a low source
impedance is better, up to 3000 steps/s. At 1600 steps/s for example, an 80%
power loss increase can be achieved by short-circuit of only one coil or by
connecting one phase across an adapted low resistance. Similar measurements with
size 22 by 2" long hybrid typemotors, shows that no damping effect occurs
after 800 to 1500 steps/s under the same circumstances.
The effect on damping by increasing the load inertia is to increase
the settling time and overshoot amplitude. Likewise the effect on damping by
increasing the load friction is to decrease the settling time and overshoot
amplitude. Friction sometimes improves system performance.
10.7 Resonance
The mechanical resonance of a
P532 motor with no load inertia is about 190 Hz. It is calculated by the
following expression:
where: T is the holding torque,
N is number of pole
pairs
J is total inertia
From this formula it can be observed that load inertia will reduce the primary resonant frequency. In applications where the motor must be operated near its primary resonance the addition of load inertia may provide a safer operating speed range. However, higher order harmonics may appear at higher speeds as inertia is increased. The addition of friction can sometimes be used to reduce the severity of resonance.
10.8 Accuracy
Step accuracy is defined as a non-cumulative error which represents the step to step error in one full revolution. Inertia and viscous friction do not affect step accuracy. Friction does however, create a dead band around the normal resting position of the motor. This is due to the fact that the rotor comes to rest in a position where the static torque matches the friction torque of the system. Thus, the rotor is offset from its ideal rest position by an angle where the static torque curve equals the friction. This is called position accuracy and is not to be confused with step accuracy which is really a mechanical property of the motor. It should be obvious that the steeper the static torque curve the better will be the position accuracy. This is very important in selecting the proper step motor.
10.9 Motor Drive Techniques
The performance of a step motor
is greatly influenced by the type of drive circuitry utilized.
An obvious advantage of any step motor is its compatibility with
digital electronics. The motor making a fixed incremental displacement (step)
for each single pulse of energy supplied to it.
Although step motors can be run closed loop, they have the cost
saving advantage of being able to operate quite satisfactorily in open loop
mode. Provided, of course, that the response characteristics (torque, speed,
etc.) of the motor are not exceeded.
The three types of driver configuration recommended for the Escap® steppers are: resistance limited, 
(unipolar or bipolar), or a bipolar chopper type.
The unipolar 
drive system is low cost and most commonly used in
lower performance applications. Its disadvantage is due to the fact that only
one winding per phase is in use at any particular time.
The bipolar drive developes higher motor performance since both
windings per phase are utilized. This requires either series or parallel
connected windings. Also the bipolar requires a dual polarity power supply or a
transistor bridge for each motor phase. Bipolar driving yields a √2 increase in low
speed torque for the same electrical input power as delivered by a unipolar
drive.
The bipolar chopper drive is
known for its high performance and improved efficiency (due to the absence of
external resistance). This type of drive is best used at higher speeds.
A chopper drive may cause
audible noise due to the motor laminations vibrating at the chopper frequency.
Single step motion is with a high acceleration due to the short current rise
time of a chopper drive. The response therefore can be more oscillatory
especially at speeds near the natural resonance of the motor.
Half step techniques usually
reduces resonant effects, and microstepping schemes will completely eliminate
resonance and speed instability problems.
10.10 Application Example
10.10.1 Description
The application is a matrix dot
printer carriage drive. The carriage is moving along a metallic bar; its weight
is 5 oz. and the friction is 4 oz. in. The motor has a 3.6º step angle and has
to be able to drive the carriage at 1200 steps per second. The motion is
transferred from the motor shaft to the carriage through a pulley and a cable.
An acceleration time of 100 ms is allowed from standstill to 1200 steps per
second. The supply voltage is specified below or equal to 24V.
10.10.2 Mechanical Requirements
When the P532 has to replace a 1.8º motor without any change in the electronics, especially the number of
pulses per second, or in the carriage travel speed, one has to provide the
system with a half diameter pulley. This sometimes creates a problem as far as
the cable is concerned. In the present application, no pulley diameter is
specified but we don't want the reflected inertia to be higher than 4 times the
motor inertia. This will lead to the same kind of cable problems.
The motor inertia
is JM = 1.2 x 10-6 kg•m2
The load inertia should be less than 4 x 1.2 x 10-6 kg•m2
JL ≤ 4.8 x 10-6 kg•m2
If the pulley diameter is D = 0.45", then
x 5 x 28 x 10-3 = 4.6 x 10-6 kg•m2
The stress on each cable strand
due to this radius of curvature is
d is the diameter of a single
cable strand
E = 2 x 1011 N/m2 (Young's
modulus of elasticity)
A good steel will tolerate h =
1500 N/mm2; let's use h = 700 N/mm2 for a more conservative calculation. Then
In addition, there will be a
stress on the cable during the acceleration phase. It will be negligible,
because there is no drastic acceleration requirement. Nevertheless if the P532
is used with a high acceleration rate like 105 steps/S2, there will be an
additional force on the cable:
F = m•Γ = (5 x 28 x
10-3)
Using a 0.5 mm cable diameter,
the steel section will be approximately 0.12 mm2. This means an additional
stress of
Then
Finally, each strand diameter
must be as low as 0.0015". In addition, the cable should be teflon coated.
It may be easier to find a steel band in that thickness, instead of a cable. The
following design may be used in that case
10.10.3 Electrical
Requirements
Each motor coil has 320 turns and R = 12Ω resistance. One should decide now if the coils will be connected in series, or
in parallel. If a series connection is chosen, then the back emf will be (peak
value)
γ = Torque per ampere-turns = 4.6 x 10-4 Nm
n = Number of turns per coil = 320
Eemf = 22V
If a parallel connection is chosen, then the back emf will only be
The requirement made about the supply voltage assigns the coil connection to be
parallel.
Suggested driving technique: drive the P532 with constant voltage
applied to an IC (SGS L 293), using a 2-phases-on scheme. This supply voltage
calculation can be done as the following.
a) Required torque
= 0.032 Nm (4.56 oz. in.)
Let's use a 1.5 factor to get a
more conservative system. It becomes:
Ts = 1.5 x 0.032 = 0.048 Nm
(6.76 oz. in.)
b) The required number of
ampere-turns; torque is related to the number of ampere-turns in the coils. With
the influence of the detent torque subtracted out, the running torque, which is 
times lower than the holding torque, is 0.048 Nm.
A running torque of 0.048 Nm
consequently needs the holding torque to be
0.048 x √2 = 0.068 Nm (9.57 oz.
in.)
This torque can be reached if
the number of ampere-turns in the 2 phases is 100 A-T.
C) Required supply voltage
The voltage calculation is
referred to
It is difficult to use this
differential equation as it is. Our purpose is to get an idea of the supply
voltage and the following approximation will give it close enough
E = Rl + Eemf
Normally 
is not negligible above 1000 steps/s. but it is hard to figure out.
With 100 A-T input power, the
temperature raise is approximately 10ºC, the phase resistance the becomes
R = 6 (1 + 0.004 x 10) 6.25 ohms
then
The voltage drop in the
transistor is about 1V; finally E = 14V
The experiment shows that the
actual value must be E = 15V
If a 10W series resistor is
used to improve dynamic performances, then
An analog experiment indicates
E = 19V
A further experiment result is
the maximum running torque 0.042 Nm (5.92 oz.in.) slight less then expected. The
difference represents the losses inside the motor which we did not take cared
of.*
The above calculation is only a
guide and cannot replace experiment. An undesirable resonace frequency cannot
especially be predicted by the above formulas.
*If the motor is running at 400
steps/s with 15V supply voltage (400 steps/s is the frequency when the
acceleration ramp starts), then the back emf is only 3.6V. It means that the
current will raise to 1.6A. The chip cannot tolerate this current very long;
consequently one should not leave this frequency for more than one step. If the
motor is suddenly stopped, the current becomes very high and must be switched
off by using the inhibit function of the IC. When the series resistor is
connected this situation is not as critical.
REFRENCES
Physical Properties of Small DC Motors Using an Ironless Rotor: Dr. Erich Jucker-Portescap
Reliability and Life of DC Motors: The New REE System-Dr. Marc Heyraud-Portescap
Selecting Low Inertia d-c Servomotors for Incremental Motion: Dr. Marc Heyraud-Portescap
Damping of D.C. Motors with Ironless Rotors: Dr. Erich Jucker-Portescap
Inductance of Micromotors with lronless Rotors: Jean-Bernard Kureth-Portescap
DC Motors, Speed Controls, Servo Systems: An Engineering Handbook by Electro-Craft Corp.
Regulate motor-shaft speed better with an inactive bridge: James M. Pihl, Electronic Design, Feb. 15, 1978
Control the speed and phase of a dc motor by comparison against a control frequency: Mike Yakymyshyn, Electronic Design, 16 Aug. 1977
Incremental Motion Control, DC Motors and Control Systems: Dr. Benjamin Kuo and Dr. Jacob Tol, SRL Publishing Co., 1978
Individual collections of application engineering data and instruction material by the following persons:
F. Prautzsch |
Portescap Portescap Portescap Portescap Portescap |
A New Family of Multipolar P.M. Stepper Motors: Dr. Claude Oudet-Portescap
Various Step motor application and training notes prepared by: R. Welterlin and A. Ugnat-Portescap
Ironless Rotor D.C. Motors, A Consideration For Magnetic Tape Transport Design: A. Ugnat-Portescap
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