PMAC Whitepaper PDF
PMAC Whitepaper PDF
PMAC Whitepaper PDF
Contents
Chapter One: AC
Induction Motors. . . . . . . . 2
Operation and
technology overview. . . . . . 2
Understanding
Capabilities for force,
torque, speed and
other factors. . . . . . . . . . . . . 3
technologies:
Operation and
technology overview. . . . . . 6
Caveats: Limitations,
performance challenges
and potential concerns . . . 8
Jim Murphy, Senior Application Engineer
PM & Large Motors Commercial Leader
LEESON Electric Corp., Grafton, Wis.
Chapter Three:
Servomotors. . . . . . . . . . . . 9
C
suitable for a given set of applications.
ur
re
nt
Magnetic flux
Illustrated here are magnet-induced flux and current-induced N N N
-
flux, upon which all electric motor operation is based.
Magnetic flux
Chapter One: AC induced current and magnetism cause it to follow the field gen-
Induction Motors erated by the stator, rotary motion is output.
Because an AC induction motor increases the flux enclosed
In all its iterations, the induction motor induces magnetism by its stationary coils, it is a transformer with a rotating sec-
that is leveraged to output rotary motion. The stationary outer ondary (rotor). The rotor currents effect on the air gap flux
stator is connected to an external electrical power source; this causes torque.
is fed to the rotors poles in a rotating progression that causes AC induction motors are built by manufacturers according
revolutions of the magnetic field within the motor. Conducting to established National Electrical Manufacturers Association
bars in the rotor interact with the stators magnetic fields; cur- (NEMA) standards in myriad fractional and integral horse-
rent is induced in those bars, which in turn generate magnetic power ratings and associated frame sizes. These AC induction
fields that are attracted to those of the stator. As the rotors motors are quite common the workhorse of industry.
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Understanding AC induction, permanent magnet and servo motor technologies:
OPERATION, CAPABILITIES AND CAVEATS
when the moving magnetic field induces current in the Theyre also classified by how they are started, as these motors
shorted conductors, and the rate at which it rotates is the alone develop no starting torque, but require external means
motors synchronous speed determined by power-supply for initial actuation.
frequency and the number of stator poles. The simple split-phase (induction-start-induction-run)
motor has a small-gage-start winding with fewer turns than
the main winding to create more resistance and put the start
windings field at a different electrical angle than that of the
main causing the motor to rotate until it reaches 75% of
rated speed. Then the main winding of heavier wire keeps the
motor running. This inexpensive design develops high start-
ing current (700% to 1,000% of rated), so prolonged starts
cause overheating. Suitable applications include small grind-
ers, blowers and low-starting-torque applications requiring
up to 1/3 hp.
Synchronous speed is the fastest theoretical speed a motor
can spin when the rotor spins at the same speed as the
motors internal rotating magnetic field. In practice, an AC
induction motor is an asynchronous motor (in which the
rotor lags field speed), so its rotor must spin more slowly than
the field, or slip. This allows the induction of rotor current to
flow, and production of torque to drive attached load while
overcoming internal losses.
N +
This single-phase, capacitor-start, induction-run motor from
+
Courtesy Motion System Design
Current is induced in the rotors conducting bars and Split-capacitor motors are common but slowly being
associated magnetic fields interact with those of the stator. replaced with more efficient motors and variable-frequency
This causes the rotor to follow the field generated by the drives (VFDs), which well explore later. Split-capacitor
stator, to rotate the output shaft. motors have a run-type capacitor permanently connected in
series with the start winding, making the latter an auxiliary
AC induction motor capabilities for winding once the motor reaches running speed. Starting
force, torque, speed and other factors torques are 30% to 150% of rated load, unsuitable for hard-to-
AC induction motors are either single-phase or poly-phase. start applications. However, starting current is less than 200%
Single-phase AC motors power myriad low-horsepower com- of rated load current, making them suitable for cycling or
mercial and industrial applications where three-phase power frequent reversals in fans, blowers, intermittent adjusting
is impractical; theyre not efficient, but can last a lifetime. mechanisms and quick-reversing garage door openers.
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Understanding AC induction, permanent magnet and servo motor technologies:
OPERATION, CAPABILITIES AND CAVEATS
all three-phase AC induction motors are used in industrial constant V/Hz vector vector
Closed loop
applications. Why? The standard utility has three-phase brushless
Torque
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Understanding AC induction, permanent magnet and servo motor technologies:
OPERATION, CAPABILITIES AND CAVEATS
which a motors rotor cannot be magnetized further, caus- AC induction motor limitations, performance
ing high currents); voltage to be applied is calculated from challenges and potential concerns
the applied frequency required to maintain air-gap flux a Even under sophisticated VFD control, AC induction motors
method that provides passable speed control, though no exhibit inherent efficiency limitations and can require an
direct control of motor torque. encoder for feedback if low-speed accuracy is required. In
Sensorless vector control also modulates frequency addition, retrofitting an existing design with a new VFD
but measures (and compensates for) slip by determining the can be troublesome, particularly when equipped with older
amount of current in phase with the voltage for approximated motors. Why? Its inverters synthesized AC waveform accel-
torque current for both magnitude and angle between erates heating (although advances continue to improve the
current and voltage. This helps to keep the motor running at waveform to more closely approximate an AC sine wave).
target speed even under varied load. Extended operation of a VFD-powered motor at less than
50% of base speed also is unacceptable; modern inverter-
With its power range up to 25 hp, duty motors have higher insulation ratings but extreme cases
LEESON Electric SM2 Flux Vector require a separately powered cooling fan.
Series inverters excel in applications
where inverter technology once was
considered too costly. They carry four
modes of operation V/Hz, enhanced
V/Hz, vector speed and Torque.
Applications include packaging,
material handling and HVAC.
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Understanding AC induction, permanent magnet and servo motor technologies:
OPERATION, CAPABILITIES AND CAVEATS
based on 104F maximum ambient plus the temperature rise which accelerates heating. NEMA limits three-phase, contin-
generated by motor operation. 5 hp and greater, premium uous-duty induction motors to two starts in succession before
efficiency and inverter-duty motors typically have Class F allowing the motor to stabilize to its maximum continuous
insulation. Beyond that, many manufacturers design their operating temperature.
motors to operate more coolly than their thermal class defi- Finally, the VFDs commonly used to drive three-phase AC
nitions. Class H insulation is reserved for heavy-duty, hot or induction motors are sensitive to inertia, horsepower, motor
high-altitude conditions. lead length and power quality, so they must be programmed
Another consideration is cycling: Motors built for frequent with full-load and no-load amps, base speed and frequency,
reversals can withstand it but start-stop cycles in others can and motor voltage when initially connected to a new motor.
cause overheating. This is because a typical motor under these Typically, VFDs also require tuning, during which motor
conditions draws five to six times the rated running current, response and electrical characteristics are logged.
mous terms. Until recently, PMAC motors were available but V3-2 V1-2 V1-3 ... +
V1-2 0
Phase to phase
+
V V1-3 0
All PMAC motors require a matched PM-drive and must be 1-2 0-
Phase to phase
+ 1 On
Off
Drive excitation
V2-3 0 2 On
Off
0 180 0 0 180 0
2 On
modern applications. Magnets made of rare-earth metals are 3 On Off Rotor position (Degrees electrical)
Off
particularly powerful alloys with crystalline structures that 1 OnOff
Back EMF is the voltage generated by a rotating permanent
have high magnetic anistropy which means they read- 2 On Off
3 On magnet machine. As the rotor spins (either with or without
ily align in one direction, and resist it in others. Discovered Off power applied
0 180to the stator
0 windings) the 0 mechanical 180 rotation0
in the 1940s and identified in 1966, rare-earth magnets are generates a voltage Rotor
in other words,
position (Degreesbecomes
electrical) a generator.
one-third to two times more powerful than traditional ferrite The resultant voltage waveform from back EMF is either
magnets generating fields up to 1.4 Teslas, in some cases. shaped like a sine wave (AC) or a trapezoid (DC), depending
Their magnets are used in MRI machines, portable electronic on the power supply from the drive. In fact, as well explore, the
devices, hysteresis clutches, accelerometers and last but not major difference between PMAC and permanent magnet DC
motors is that the faster a PMACs rotor spins, the higher back-
least permanent-magnet rotary and linear motors.
EMF voltage is generated.
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Understanding AC induction, permanent magnet and servo motor technologies:
OPERATION, CAPABILITIES AND CAVEATS
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Understanding AC induction, permanent magnet and servo motor technologies:
OPERATION, CAPABILITIES AND CAVEATS
Most manufacturers of synchronous motors hold pole POT or any external device that can create and communi-
count constant so input frequency dictates the motors speed. cate a value to the drive. This normally is a velocity signal,
For example, for a 48-frame motor with six poles, the motors sometimes further processed in the drive before it is used as
input frequency from the drive must be 90 Hz to obtain 1,800 a command.
rpm. To extract the same speed from a 10-pole 180-frame
motor, input frequency must be 150 Hz. To calculate required Permanent-magnet motor
input frequency (Hz) when the number of poles and speed limitations, performance challenges
are known: and potential concerns
PMAC motor speed is limited by back EMF because the
latter increases directly with motor speed. The motor is con-
nected to the electronic drive and its electronic components
are designed for a maximum voltage above the rated drive
voltage. Normally, the motor and controls are designed to
PMAC motors are suitable for variable or constant-torque operate well below the maximum voltage of the components.
applications: The drive and application parameters dictate to However, if motor speed exceeds the design speed range
the motor how much torque to produce at any given speed. (either being powered from the control or being driven by
This flexibility makes PMACs suitable for variable-speed the load), it is possible to exceed the maximum voltage of
operation requiring ultra-high motor efficiency. the drive components and cause failures. Note that VFD
Now a word on a common misconception: Cogging the drives are capable of limiting motor back EMF when operat-
unwanted jerking during motor spinning from repeatedly ing properly. However, if the drive faults and loses control
overcoming the attraction of permanent magnets and sta- during overspeed, it cannot protect itself.
tors steel structure is often associated with PM motors. In addition, PMAC motor control requires some technical
Particularly at startup, cogging arises from the interaction knowledge for implementation: All commercially available
of the rotor magnets and stator winding when it is energized, PMAC motors require a PM-compatible drive to operate,
due to harmonics. Cogging, in turn, causes noise, vibration although there is ongoing research in the development of a
and non-uniform rotation. line-start PMAC motor.
Many methods for reducing PMAC motors also require careful servicing: Rare earth
Saliency cogging can be leveraged to permanent magnets, such as Neodymium or Samarium
eliminate torque and speed Cobalt found in PMAC motors, have very strong magnetic
In reference to PMAC ripple. Some PMAC motors properties. This makes them indispensable for producing
motors, saliency refers to the are designed with more poles high flux levels but also means they must be handled with
difference in motor inductance than equivalent AC induction care. Catching ones finger between two of these magnets
at the motor terminals as the motors, which helps reduce (during servicing, for example) poses a serious pinching
motor rotor is rotated. This these issues. Case in point: hazard, so the motor supplier or an authorized shop should
difference corresponds to LEESON Platinum e PMAC generally execute any magnet-related maintenance tasks on
alignment and misalignment fractional-horsepower motors PM motors. Those with pacemak-
of the stators rotor a (48-56/140 frames) have a ers or other medically implanted
characteristic that a motors
six-pole design; Platinum e devices (including hearing aids) Warning
drive tracks to monitor rotor
integral-horsepower PMAC should exercise extra caution Terminal voltage rises
position during operation.
motors (180 frame and larger) when working around the strong with shaft speed during
utilize a 10-pole rotor design. magnetic fields of these devices; windmilling. Therefore,
cell phones and credit cards also even with power off, never
Closed loop functionality may be at risk. That said, when touch a PMACs terminals
In specialty cases, PMAC motors are used in closed-loop con- a PM motors rotor is secured if its shaft is rotating,
figurations using speed feedback. Feedback allows the drive within the enclosure, radiated as they present a shock
to track the exact rotor position to provide true infinite magnetic energy is no higher than hazard. At high shaft
speed, voltage can rise
speed range, including full torque at zero speed. The speed that of an induction motor.
to levels that can cause
reference required from an external source can be an analog Not all AC drives are suitable
serious injury or death.
signal and encoder feedback, or a serial command from a for operation of PMAC motors;
feedback device on an axis one wishes to follow or a PLS, only drives specifically designed
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Understanding AC induction, permanent magnet and servo motor technologies:
OPERATION, CAPABILITIES AND CAVEATS
for permanent magnet motor compatibility are suitable. ties. Permanent magnets, once demagnetized, cannot recover,
Often, a parameter in the drive programming allows an even if the current or temperatures return to normal levels.
operator to set the drive for a PM motor. Some drives not PM drives reduce the risk of high-current demagnetization,
specifically designed for it can run and control PM motors, as these are equipped with over-current protection. Some
though performance is degraded and one can damage the motor designs further minimize the possibility of exces-
motor or drive if they are mismatched. sive-temperatures magnet failure with high-temperature
Finally, high current or operating temperatures can cause magnets, integrated thermostats and restricted motor operat-
the magnets in PMAC motors to lose their magnetic proper- ing temperature.
A designs form factor determines which orientation is most suitable: Does the machinery require a longer, skinnier
radial motor or is a pancake axial design more appropriate? The final determining factor may be cost as the axial
design, once tooled for production, provides equivalent torque but uses less active material for better power density.
Though not yet suitable for elevator applications, engineers are developing PMAC radial motors to incorporate axial
air-gap PMAC designs into elevators sans machine rooms.
Chapter Three: Servomotors Wound-field DC motors (in various iterations, with copper
segments in the rotor connected by magnetic-wire wind-
Servomotors are motors that use feedback for closed-loop ings and stator windings) are another option. More often,
control of systems in which work is the variable.
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Understanding AC induction, permanent magnet and servo motor technologies:
OPERATION, CAPABILITIES AND CAVEATS
however, compact brush DC motors (which employ perma- fitted with a trio of Hall sensors at one stator end. These Hall
nent magnets affixed to the inside of the motor frame, plus sensors output low and high signals when the rotors south
a rotating wound armature and commutating brushes) are and north magnet poles pass to allow the following of
used as servomotors because speed control is easy: The only energizing sequence and rotor position.
variable is voltage applied to the rotating armature. There are In its most basic form, the drive for a servomotor receives
no field windings to excite, so these motors use less energy a voltage command that represents a desired motor current.
than wound DC designs, and have better power density than The servomotor is modeled in terms of inertia (including
wound-field motors. Servo-built brushed DC motors also servomotor and load inertia) damping, and a torque constant.
include more wire wound onto the laminations, to boost The load is considered rigidly coupled so that the natural
torque.
Three-phase PMDC motors (brushless motors) also are
commonly used for servo applications. Most brushless DC Permanent-magnet
windings are interconnected in an array and most units are DC motors in servo
applications
DC servocontrol: Today, many PM motors are DC and used
Sophisticated in servo applications requiring adjustable
speed. For quick stops, these can minimize
Reliable speed controls for DC motors abound. mechanical brake size (or eliminate the
Many use solid-state devices; silicon controlled brake) by leveraging dynamic braking (motor-
rectifiers (SCRs or thyristors) are common, con- generated energy fed to a resistor grid)
verting AC line voltage to controlled DC voltage or regenerative braking (motor-generated
that is applied to the DC motors armature. energy returned to the ac supply). In addi-
Increasing voltage increases speed so this tion, PMDC motor speed can be controlled
is sometimes called armature-voltage control. smoothly down to zero, followed immediately
Its highly effective for motors up to approxi- by acceleration in the opposite direction
mately 3 hp, allowing 60:1 speed regulation without power circuit switching.
and constant torque even at reduced speeds.
Servocontrol, on the other hand, takes control In typical three-phase brushless DC motors,
to the next level with feedback and is suit- energization is controlled electronically.
able for larger designs. In some designs, permanent magnets are
installed on the stator. More common designs
High-voltage DC motors are typically used include stators with stacked steel lamina-
with an SCR or PWM controller in applica- tions and windings through axial slots;
tions requiring adjustable speed and constant permanent magnets are installed on the
torque throughout the speed range. The rotor. Here, the stator winding is trapezoidally
LEESON Electric SCR Rated/General Purpose wound to generate a trapezoidal back EMF
motor (shown here) is widely used in applica- waveform with six-step commutation.
tions requiring dynamic braking or adjustable
speed and reversing. The brush holder design Brushless DC switches energize changing
provides easy access, while the brushes them- pairs of motor phases in a predefined com-
selves are large for extended life. mutation sequence. Most units are fitted with
a trio of Hall sensors at one stator end, to
allow the following of energizing sequence
and rotor position. Output torque has con-
siderable torque ripple, which occurs at
each step of the trapezoidal commutation.
However, due to a high torque-to-inertia ratio,
brushless DC motors respond quickly to con-
trol-signal changes making them useful in
servo applications.
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Understanding AC induction, permanent magnet and servo motor technologies:
OPERATION, CAPABILITIES AND CAVEATS
mechanical resonance is safely beyond the servocontrollers A digital servocontroller sends velocity command signals to
bandwidth. Motor position is usually measured by an encoder an amplifier, which drives the servomotor. With the help of
or resolver coupled to the motor shaft. resolvers, encoders or tachometers for feedback (mounted
A basic servocontrol generally contains both a trajectory in the motor or on the load), the controller then compares
generator and a PID controller: The former provides position actual position and speed to the target motion profile, and
setpoint commands; the latter uses position error to output differences are corrected.
a corrective torque command that sometimes is scaled to
the motors torque generation for a specific current (torque Servomotor limitations, performance
constant.) challenges and potential concerns
Most importantly, the increased performance of servomotor
Servomotor capabilities for force, designs comes at dramatically increased cost.
torque, speed and other factors In addition, there are two situations in which servomo-
Servocontrol exhibits less steady state error, transient tor efficiency declines low voltage and high torque. In
responses and sensitivity to load parameters than open-loop short, servomotors are most often employed because of their
systems. Improving transient response increases system ability to produce high peak torque, thus providing rapid
bandwidth, for shorter settling times and higher through- acceleration but high torque often requires that servo-
put. Minimizing steady-state errors boosts accuracy. Finally, motors run two to three times their normal torque range,
reducing load sensitivity allows a motion system to tolerate which degrades efficiency.
fluctuations in voltage, torque and load inertia. Finally, servos are designed to operate over a wide range
Typically, a profile is programmed for instructions that of voltages (as this is how their speed is varied) but efficiency
define the operation in terms of time, position and velocity: drops with voltage.
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Understanding AC induction, permanent magnet and servo motor technologies:
OPERATION, CAPABILITIES AND CAVEATS
ezoidal and sinusoidal current waveforms, respectively. One magnet wire (with a machine or by hand) is problematic,
cannot differentiate the two by visual inspection. as manufacturers in this case must redesign the stator and
A controller that produces trapezoidal waveforms is rotor fairly extensively to ensure that the setup is physically
less costly than those that produce sinusoidal waveforms. possible.
However, sinusoidal controllers and motors produce more
consistent shaft rotation than trapezoidal and rotor inertia, AC induction motors versus PMAC motors
motor rating and specific controller characteristics magnify For an apples-to-apples comparison of AC induction motors
the difference in performance. to PMAC motors, we must consider both with a drive as
One caveat: In low-voltage applications (anything below the latter requires a drive for operation, and cannot connect
110 V), traditional brushless DC or AC induction motors are directly to supply power as typical AC motors can.
still better choices than PMAC motors although theres System efficiency is higher for a PMAC motor/drive setup
work being done to address the issues that arise in these situ- from 40% to beyond 120% load. In addition, a PMAC motor
ations. In short, brushless DC motors are commonly built for exhibits higher power density than an equivalent induc-
voltages down to 12 or 24 V. However, to wind a PMAC for tion motor: Rare-earth permanent magnets produce more
this voltage is (in effect) taking a 200 or 300 hp and winding flux for their physical size than the magnetic energy (and
it for 200 V. Here, lead sizes can grow to the size of an aver- resultant torque) produced by an induction motors squir-
age coffee cup (an inane result) and winding such a motors rel cage rotor. In the latter, the effect of back EMF also is
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Understanding AC induction, permanent magnet and servo motor technologies:
OPERATION, CAPABILITIES AND CAVEATS
Power factor
Efciency
0.85 0.85
for variable or constant torque to 20:1 without 0.80 0.80
feedback (open loop) or 2,000:1 for closed loop 0.75 0.75
(with an encoder). 0.70 0.70
Power (hp)
speed-control precision a major benefit in 150 Torque 2.50
high-inertia positioning applications. Although 135
120
in some cases the system power factor with a 105
2.00
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Understanding AC induction, permanent magnet and servo motor technologies:
OPERATION, CAPABILITIES AND CAVEATS
On one specific integral-horsepower line (of LEESONs the gearbox by a size or two which then allows downsizing
Platinum e PMAC motors), the winding design has shorter of other equipment as well. For example, a 48-frame PMAC
end turns and a concentrated bobbin-type winding. Unlike a can carry 72 in.-lb of torque, which equates to roughly 4 hp at
distributed winding, used in induction machines, there are 3,600 rpm. One caveat: PMACs are not particularly suitable
no shared slots so the potential for phase-to-phase shorts in fixed-speed applications, as PMAC motors require PM
is eliminated. Shorter end turns reduce waste and make more drives.
room in the housing for more active material, enhancing If an average AC induction motor is replaced or retrofit-
power density (as end turns do nothing to generate torque). ted with a PMAC system, typically the drive also must be
PMAC sound and vibration is often comparable to that of replaced. The drive topologies and logarithms are different;
an induction motor, though the sound and vibration of PM divergent, too, are the software and ladder logic, particularly
motors varies widely from manufacturer to manufacturer with regards to how the two drive types handle back EMF. In
and models designed for quiet operation exist. This tends (as addition, the motor must be able to communicate with the
with most other motor types) to depend on the type of appli- drive and vice versa. Stated another way, PMAC motors are
cation for which a specific motor is designed. controlled by a PWM AC drive similar to those used with
Although the term service factor (SF) often is misunderstood induction motors, but with software to control a PM machine.
and not recognized by the International Electrotechnical In most situations, replacing existing induction motors
Commission (IEC), its still commonly applied to describe the with PMACs requires no mechanical changes to the equip-
maximum output of NEMA motors. LEESONs Platinum e ment. In addition, proprietary tools abound to simplify
PMAC motors have a Service Factor (SF) of 1.0 on inverter conversion.
power, which is comparable to that of inverter-duty induction A Performance Matched Solution for LEESONs PMACs
motors. Operating any motor beyond its rated power results in ensures that the latter are tested and qualified with RBC PM
additional (possibly detrimental) heating. Intermittent opera- drives plus a variety of commercially available PM drives
tion above rated power is most normally acceptable, as long as to ensure superior performance. A list of qualified drives is
its components can withstand the additional thermal stress. available upon request, while testing is ongoing with others.
On a similar note, reserve torque capability is an expres- Platinum e PMAC motors incorporate patented IRIS
sion of a motors ability to safely deliver increased torque, due Insulation to provide long, reliable service life under the
to higher peak torque capability, and is subject to the drives stresses of todays fast switching IGBT-based PM drives
ability to deliver increased current. LEESONs Platinum e and protection from voltage stresses imposed by PM-type
PMAC motor has a reserve torque capability of 150% for 60 operation.
seconds. Due to the incorporation of a terminal block (IHP only)
for electrical connections, Platinum e PMAC motor installa-
Making the change to PMAC motors tion is quicker and safer compared to flying leads.
Most applications compatible with induction motors can
utilize PMAC motors. In centrifugally loaded variable speed
applications (pumps, fans and blowers), PMACs boost effi-
ciency and, in many instances, can direct-drive these
designs. Fans are unique in that theyre typically sized by
torque; yet here, direct-driving PMAC motors can eliminate
the need for belts, pulleys and sheaves. This in turn simplifies
maintenance, which is particularly helpful where fans are
installed on roofs.
In applications that incorporate belts, chains or gearboxes,
PMACs boost power density and its these applications in
which reducing or eliminating power transmission devices
makes the most improvement in efficiency and reduced
maintenance cost.
There are situations for which direct driving isnt possible Platinum e IHP integral-horsepower PMAC motors are
equipped with a full Class H insulation; however, the
or desirable. Consider conveyors driven by gearbox-fitted
design intentionally limits operating temperature to no more
motors: Here, a PMAC motor may not be able to eliminate than Class B rise, for extra thermal protection and longer
the need for a gearbox, but can typically help designers reduce insulation life.
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Understanding AC induction, permanent magnet and servo motor technologies:
OPERATION, CAPABILITIES AND CAVEATS
Useful formulas
Converting hp to kw: hp 0.746 (kw/hp)
Hand calculate full load amps (fla) = (hp 746) / (volts efficiency power factor)
Efficiency and power factor (pf) is at full load, and entry is a decimal
suggested reading
Electrical Machinery & Transformers 2nd Ed. Guru and Hiziroglu.
Electric Machines Steady State Theory and Dynamic Performance. Mulukutla S. Sarma
DC Motors Speed Controls Servo Systems 4th Ed. Electro-Craft Corp. Handbook
Switched Reluctance Motor Drives A Reference Book of Collected Papers. T.J.E. Miller, Ed. University of
Glasgow, Intertec Communications Inc.
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