Cutler Hammer, Div of Eaton Corp S752 Application Note
10
10
18
Solid-State Soft Start Motor Controller and Starter
Application Note
February 2005
Supersedes January 2001
Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
About This Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Basic Motor and Soft Start Theory
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
AC Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
AC Motor Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Induction Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Enclosures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Ventilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Control of AC Motors . . . . . . . . . . . . . . . . . . . . . . . . . 3
Soft Start Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Soft Start Applications . . . . . . . . . . . . . . . . . . . . . . . . 5
Other Reduced Voltage Starting Methods . . . . . . . . 5
Basic Mechanics
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Calculating Torque . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Calculating Horsepower . . . . . . . . . . . . . . . . . . . . . . . 7
Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Cylinders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Pulley/Gear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2
WK
Reflected to the Motor Shaft . . . . . . . . . . . . . . . 8
Speed Reducer Selection . . . . . . . . . . . . . . . . . . . . . . 9
Gear Reducer Selection . . . . . . . . . . . . . . . . . . . . . . . 9
Gear Reducer — Overhung Load . . . . . . . . . . . . . . . . 9
Other Gear Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Controllers and Starters, Theory and Application
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Benefits of Using Soft Start Controllers and
Starters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Basic Principles of Soft Start Controllers and
Starters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Load Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Typical Soft Start Adjustments . . . . . . . . . . . . . . . . . 11
Motor Application Considerations . . . . . . . . . . . . . . 12
Installation Compatibility . . . . . . . . . . . . . . . . . . . . . . 12
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
. . . . . . . . . . . . . . . . 2
. . . . 10
Load Types and Characteristics
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Load Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Other Functional Considerations . . . . . . . . . . . . . . . 13
Typical Load Torque . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Controller and Starter Selection
Selection Considerations . . . . . . . . . . . . . . . . . . . . . . 15
Selecting a Soft Start for a Machine . . . . . . . . . . . . . 15
Measuring Machine Torque . . . . . . . . . . . . . . . . . . . . 16
Soft Start Application Questions . . . . . . . . . . . . . . . . 16
Soft Starter Application Data Worksheet . . . . . . . . . 17
Formulae, Conversions and Tables
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
How to Calculate Torque . . . . . . . . . . . . . . . . . . . . . . 18
How to Calculate Horsepower . . . . . . . . . . . . . . . . . . 18
How to Calculate Surface Speed . . . . . . . . . . . . . . . . 18
How to Calculate Horsepower for Pumps . . . . . . . . 18
How to Calculate Horsepower for Fans and
Blowers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
How to Calculate Horsepower for Conveyors . . . . . 18
How to Calculate Accelerating Torque . . . . . . . . . . . 18
How to Calculate Maximum Motor Torque . . . . . . . 19
How to Calculate WK
How to Calculate Equivalent WK
Electrical Formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Induction Motor Formulae . . . . . . . . . . . . . . . . . . . . . 20
Tables of Conversions and Abbreviations . . . . . . . . 20
Glossary
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
. . . . . . . . . . . . . . . . . . . 12
. . . . . . . . . . . . . . . . . . 15
. . . . . . . . . . . . . . . . 18
2
. . . . . . . . . . . . . . . . . . . . . . . . 19
2
at Motor Shaft . . 19
AP03902001E For more information visit: www.EatonElectrical.com
Application Note
Page 2
Introduction
About This Guide
The following material is intended to
acquaint the user with the theory and
operation of solid-state soft start
motor controllers and starters. This
material will enable the user to better
select the controller or starter and take
into consideration the parameters necessary for proper application to a
given load.
The reference material provided is for
the convenience of the user. It is taken
from current handbooks and standards such as NEC, NEMA, IEEE and
others. It is intended as reference
material for standard applications and
may not cover all actual and special
applications. Experienced factory
application engineers are available to
assist users in the application of motor
controllers and starters for most motor
loads. Specific ratings and external
signals used for control and logic are
the user’s responsibility.
The user must determine the final
suitability and acceptability for controllers and starters used on specific
equipment.
Basic Motor and Soft Start
Theory
Introduction
A solid-state soft start controller or
starter controls the starting torque and
current of an AC motor electronically.
They can be used in almost any
application such as:
■
commercial – HVAC fans and pumps
■
general industrial – fans, pumps,
conveyors, material handling and
processing equipment
■
others – forest products, mining,
metals and printing
The guide provides the basics required
to evaluate motor controller and
starter application needs.
Effective: February 2005
Solid-State Soft Start
Motor Controller and
Starter
AC Motor Types
AC motors can be divided into two
main types: Induction and Synchronous. In this guide we will only cover
the use of a three-phase induction
motor and soft starter device, although
in some cases a soft starter device
may be used with a single-phase
motor.
Induction Motors
The induction motor is the simplest
and most rugged of all electric motors.
The typical varieties are the standard
induction motor and the wound rotor
motor.
Three-Phase
The three-phase induction motor is
divided into four classifications
according to NEMA. (Note that there
are IEC design standards which differ
somewhat from the NEMA versions.)
The classification or design, is determined by the locked rotor torque and
current, breakdown torque, pull-up
torque and the percent slip. The
speed-torque curve and characteristics
of each design are given below. These
characteristics apply for operation
from fixed frequency and voltage as
normally supplied from commercial
utility power sources at 60 Hz.
■
Design A motors have a slightly
higher breakdown, and lower starting torque than Design B motors.
The slip is usually 3 to 5% or less.
The major difference between the
Design A and Design B motor is that
the starting current is limited on the
Design B, but not on the Design A.
Design A motors are applied to the
same applications as Design B
motors. Design A motors may be
used with solid-state soft start
devices.
%
Rated
Tor qu e
300
200
Breakdown
(Maximum)
To rq ue
■
Design B motors are general pur-
pose type motors and account for
the largest share of the induction
motors sold. The slip of a Design B
motor is approximately 3 to 5% or
less. Design B motors are used on
applications where starting torque
requirements are low such as general industry, fans, blowers and centrifugal pumps and compressors.
Design B motors are often used with
solid-state soft start devices.
%
Rated
Tor qu e
300
200
100
0
020406080100
% Rated Speed
Figure 2. Design B Polyphase Motor
Design C motors have a high start-
■
ing torque with a normal starting
current and low slip. The Design C
motor is usually used where breakaway loads are high at starting, but
are normally run at rated full load,
and are not subject to high overload
demands after running speed has
been reached. The slip of the Design
C motor is 5% or less. Design C
motors are often used where high
starting torques under loaded conditions are required including crushers, agitators, reciprocating pumps
and high friction conveyors. Care
must be exercised when using a
Design C motor with a soft start controller or starter to assure that the
application starting torque and time
to start requirements can be met.
%
Rated
Tor qu e
300
AC Motors
Cutler-Hammer
and starters operate with standard
motors. In most cases, an existing
motor sized for another method of soft
start, can be directly applied. For new
installations the user must understand
the nature of the application in terms
of the load characteristic requirements
and the motor capability when used
with a soft start controller or starter.
®
soft start controllers
100
0
02040
% Rated Speed
Figure 1. Design A Polyphase Motor
For more information visit: www.EatonElectrical.com
60 80
100
200
100
0
020406080100
% Rated Speed
Figure 3. Design C Polyphase Motor
AP03902001E
■
Design D motors have high slip,
high starting torque, low starting
current and low full load speed.
Because of the high amount of slip,
the speed will vary if fluctuating
loads are encountered. The slip of
this type of motor is approximately
5 to 13%. Design D motors are used
on applications with high peak loads
with flywheels like punch presses,
shears, hoists, oil well pumps and
extractors. Care must be exercised
when using a Design D motor with a
soft start controller or starter, since
the limitation of the starting torque
or increase of the starting time may
cause thermal concerns for the
motor and soft start.
%
Rated
Tor que
300
200
100
0
020406080
% Rated Speed
Figure 4. Design D Polyphase Motor
100
Wound Rotor Motors
The wound rotor motor allows controllable speed and torque compared to
the conventional induction motor.
Wound rotor motors are generally
started with a secondary resistance in
the rotor. As the resistance is reduced,
the motor will come up to speed. Thus
the motor can develop substantial
torque while limiting the locked rotor
current. The secondary resistance can
be designed for continuous service to
dissipate the heat produced by continuous operation at reduced speed and
frequent start/stops or acceleration of
a large inertia load. This external resistance gives the motor a characteristic
that results in a large drop in rpm for a
small change in load. Reduced speed
typically can be provided down to
approximately 50% of rated speed,
although at a very low efficiency.
These motors are sometimes used (in
large horsepower ratings) in slip
recovery systems. In these systems
the external (secondary) resistance
element is replaced with a solid-state
circuit to convert the rotor slip energy
to useful AC power. These motors can
be used with a soft starter in some
applications. The use is dependent
Solid-State Soft Start
Motor Controller and
Starter
upon why the motor’s secondary resistance was selected and how the use of
the soft starter will impact the load
requirements. If the rotor resistance
was selected to be stepped through
various sizes to provide a gentle start,
a soft starter can likely be used. If the
resistor is just a single value and was
selected to give high starting torque,
the use of a soft starter might not
allow the same level of torque to be
generated. The application requirements must be determined.
Enclosures
The basic protective enclosures for AC
motors are: open dripproof (ODP),
totally enclosed fan cooled (TEFC),
totally enclosed non-ventilated (TENV)
and totally enclosed air over (TEAO).
Other special enclosures available
include: pipe-ventilated, weather protected, water cooled and explosion
proof.
Ventilation
The system for ventilating motors
depends on the type of motor enclosure as mentioned previously and
described below:
ODP (Open Dripproof) – The ODP
■
motor is ventilated (cooled) by
means of a shaft mounted internal
fan which drives air through the
open ends of the motor and discharges it out the sides. These
motors are often supplied as
protected, fully-guarded or
splash-proof.
TEFC (Totally Enclosed Fan Cooled)
■
– This type of motor is cooled by air
passing over the outer frame of the
motor. The air is supplied by a shaft
mounted fan opposite the shaft end
of motor.
TENV (Totally Enclosed Non-
■
Ventilated)
a shaft mounted internal fan used to
circulate air within the motor to prevent hot spots. No external fan or air
is supplied. These are suitable for
very dirty and contaminant laden
environments that would clog most
exposed cooling fans. These motors
dissipate their heat through their
frames and are thus oversized compared to other enclosure types.
They are generally available only in
smaller hp ratings (up to 7-1/2 hp).
– This type of motor has
Application Note
Effective: February 2005 Page 3
■
TEAO (Totally Enclosed Air Over) –
This type of motor is cooled by
externally provided air blowing over
the frame. The air may be supplied
by an integrally mounted blower
and motor or from a separate
source. This type of ventilation
provides constant cooling under
all operating conditions.
■
Special Enclosures – The Pipe-
Ventilated motor is available for
either an open or totally enclosed
type of enclosure and is used in very
dirty environments. Ventilating air
(supplied by the User) enters and
exits the motor through inlet and
outlet ducts or pipes. The air is circulated by means either integral or
external to the motor.
The Weather-Protected motor uses
an open type enclosure for ventilation. The motor is constructed to
minimize the entrance of rain, snow
and airborne particles to the electrical parts of the motor. External air
can be circulated through the motor
for cooling.
Totally Enclosed Air-to-Air and
Totally Enclosed Water-to-Air cooled
enclosures are normally used on
high horsepower motors that generate large amounts of heat. A heat
exchanger is used for both types to
remove the heat generated by the
motor. An AC motor driven blower
circulates air through the windings
and heat exchanger tubes. The heat
in the heat exchanger is removed by
either an external air system (air-toair) or water provided by the user
(water-to-air cooled).
Explosion Proof motors are
designed to operate in hazardous
environments such as explosive
vapors, coal or grain dust and other
classified areas. These are selected
on the basis of the appropriate
Class, Group, and Division of hazard, as defined by the National Electrical Code (NEC).
Control of AC Motors
The most common control of an AC
motor is by using a motor starter. This
device connects the motor to the commercial AC power line. It is rated to
operate with the typical high starting
(inrush) current that occurs when a
motor is directly connected to the utility line. A motor starter also contains a
protective device known as a motor
overload. This device is designed to
protect the motor from continued
overloads and stalling due to excessive machine loads on starting or jamming when operating.
AP03902001E For more information visit: www.EatonElectrical.com
Application Note
Page 4
With the above method of control, AC
motors will operate as described by
their NEMA (or IEC) characteristics for
their design type on industrial AC
power. This includes a prescribed
overload capability, regulation due to
slip, starting inrush current and starting (locked rotor) torque. The load on
the driven machine determines the
acceleration time and motor load (or
overload).
Special control hardware is available
to modify some of the above characteristics. Part winding, autotransformer and wye-delta motor starters
will reduce the inrush current when
starting an AC motor. But using these
devices does not provide for a soft
controlled stepless start.
Solid-state soft start motor controllers
and starters have the ability to control
the starting characteristics to match
the application requirements, such as
acceleration and deceleration time,
starting and overload current and
motor torque. In addition, motor
protection may be provided for a
number of potential damaging circumstances by the soft starter (a soft start
controller does not provide any motor
protection).
Soft Start Basics
Why do we want to use a reduced voltage soft starter?
The first reason is to limit the inrush
current that a motor draws from the
utility when it is first started. This is a
concern because the large starting current may cause the line voltage to dip,
impacting other loads which are sensitive to low voltages. There may also be
a concern if the utility limits the peak
current which can be drawn or charges
for exceeding the limit.
The second is reduced mechanical
system stress. When the large inrush
current occurs, there are significant
magnetic forces created in the motor
windings. These cause some parts of
the winding to be attracted to each
other and other parts repulsed. This
mechanical shock can damage the
winding insulation leading to early failure. The mechanical shock of the high
torques produced with the large starting current can cause failure of system
elements such as the motor shaft, belting, gear box, drive train and damage
to fragile product.
Effective: February 2005
Solid-State Soft Start
Motor Controller and
Starter
Current
600
Figure 5. Motor Current vs. Speed
This graph shows the impact of using
a soft start. For this motor, the initial
current when it is started is 600 percent, or six times the motor’s full load
current rating. The soft starter can be
set to reduce this current, for example
in this case to 300 percent. This limits
the inrush current on the utility line.
Tor qu e
300
200
100
Figure 6. Motor Torque vs. Speed
As a result of the reduction in current,
the motor’s ability to generate torque
is also reduced. The upper curve
shows the same motor started across
the line. The initial torque is about 180
percent with a peak torque of over 300
percent. With the soft start limiting the
current, the torque speed curve is
reduced, reducing mechanical stress.
The torque available from the motor at
reduced current is equal to the locked
rotor or starting torque, times the
square of the reduced current divided
by the locked rotor current. Thus if we
reduce the current from 600 percent to
300 percent, the torque varies as the
square of this reduction. The torque is
thus reduced to 25 percent of the
across the line starting torque.
How Does Torque Vary?
Where:
T
T
I
1
I
2
V
V
Full Voltage Starter
%
Solid-State Starter
0
Speed RPM
%
Full Voltage
%
%
0
T2T
= Torque at recued current/voltage
2
= torque at locked rotor current
1
= Locked rotor current
Starter
Solid-State Starter
Speed RPM
2
I
2
T
≈=
----
1
I
1
V
2
------
1
V
1
2
= Reduced current
= Full voltage
1
= Reduced voltage
2
100
100
%
%
Some soft starters control voltage
instead of current. The torque available varies proportionately with the
square of the ratio of the reduced
voltage to the normal line voltage.
When the operator depresses the
START button, the soft starter logic
issues an ON command to the power
module, causing the SCRs to turn on
and gently increase the voltage across
the motor terminals, or the current
into the motor based on the adjustments made to the soft start logic.
When the SCRs are fully on, the motor
reaches full voltage.
A block diagram of a typical soft start
starter would look like
L1
3-Phase
Power
Supply
Control
Power
Stop
L2
L3
Reset
Start
Figure 7 .
Control Logic
• Current limit
• Running
overload
protection
• Phase loss
protection
• Undervoltage
protection
• Energy saver
control
Motor
Figure 7. Typical Block Diagram
This solid-state starter utilizes six full
current rated SCRs as its power
devices. The logic circuit monitors
three-phase input voltage, three-phase
output voltage, and the three output
currents. From these inputs it can provide starting current limitation, running overcurrent protection, phase
loss and undervoltage protection.
This starter interfaces with standard
control circuits.
In some products a bypass contactor
may be closed to provide higher operating efficiency after the SCRs are fully
Figure 8 is a single-phase leg of the
on.
soft starter with the SCRs turning on
and becoming the current path for
power to flow from the utility to the
motor.
A
Motor
Figure 8. SCRs as Current Path
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AP03902001E
Solid-State Soft Start
Motor Controller and
Starter
Application Note
Effective: February 2005 Page 5
After the motor has come up to speed,
the bypass contactor closes and it
becomes the current path for the
motor.
A
Motor
Figure 9. Bypass Contactor as Path
At this time the SCRs no longer conduct any current.
Bypass operation eliminates the SCR
losses once the motor is up to speed,
resulting in significantly lower heat
generation. Soft starters with internal
run bypass mode are typically much
smaller and lighter than devices without run bypass.
Soft Start Applications
We would like to identify problems
that can be solved by the use of a soft
starter. One challenge is that it can be
difficult for the user to recognize a
problem as a problem. Frequently the
problem is mistaken for a normal
operational or maintenance issue.
It is the intent of this section to help
to determine solutions, using soft
starters for both new and retrofit
installations.
Typical problems can be categorized
as mechanical, motor, starting equipment, inrush current, or fragile product
related.
Typical mechanical problems are:
stretching, squealing or breaking of
drive belts; breakage of gear boxes; couplings wearing out prematurely; shaft
breakage within the drive train; and,
water hammer in hydraulic systems.
To get an idea of the effect of starting
torque on the mechanical system, lets
consider an automobile. If you were to
put the transmission in neutral and
quickly press the accelerator to the
floor, you would feel the car reacting
to the sudden increase in motor torque
as it rotates slightly in response to the
torque being developed by the engine.
This same type of effect is what causes
these mechanical problems, except
that the torque levels may be considerably greater than those experienced
with an automobile.
Motor problems include: motor insulation deterioration or premature winding failure due to the mechanical
stresses put on the winding during
starting, or the high temperatures
imposed by high starting currents;
mechanical stresses on the system
such as foundation bolts or mounting
failures, bearing lock-up and failure,
and motor shaft cracking and breakage; coupling failures; and, excessive
energy losses due to duty cycle or frequent start/stop operation.
Benefits of Using Soft Start Starters:
■ Controlled starting – Limited start-
ing current, reduction of power line
disturbance on starting, lower
power demand on starting.
■ Controlled acceleration – Soft start,
adjustable acceleration based on
time or load, reduced motor size for
pure inertial load acceleration.
■ Adjustable torque limiting – Protects
machinery from damage, protects
process or product.
■ Controlled stopping – Soft slow
down, timed stopping, fast reversal
with much less stress on AC motor
than plug reverse.
Typical Fixed Speed Applications:
■ Conveyors, belts, chains, screws,
bulk material, packaged material
■ Fans, blowers, compressors, pumps
■ Machine tools, grinders, lathes,
stamping presses
■ Custom machinery, labelers, pack-
aging machines, bottle washers,
wire drawing, textiles, etc.
■ Extruders
■ Process machinery, kilns, grinders,
blenders, agitators. See the section
on load types for particular evaluation of specific loads.
Other Reduced Voltage Starting
Methods
There are several reduced voltage
starting methods that predate solidstate soft start motor controllers and
starters. Table 1 illustrates these meth-
ods and their typical applications.
AP03902001E For more information visit: www.EatonElectrical.com
Application Note
Page 6 Effective: February 2005
Solid-State Soft Start
Motor Controller and
Starter
Table 1. Comparison of Electromechanical Soft Starters
Type of
Starter
Autotransformer8065
Primary
Resistor
Part
Winding
Wye Delta 100 33 33 Open
Starting Characteristics in Percent of Full
Transition Extra
Voltage Values
% Line
Voltage at
Motor
50
% Motor
Locked Rotor
Amps
64
42
25
% of Motor
Locked
Rotor Torque
64
42
25
Closed No
65 65 42 Closed Yes
100 65 48 Closed Yes (but very
(Closed
available
for about
30% price
adder)
Acceleration
Steps
Available
uncommon)
No
Advantages Disadvantages Applications
■ Provides highest
torque per ampere of
line current
■ 3 different starting
torques available
through
■ In lower horsepower
ratings is most
expensive design
■ Low power factor
■ Large physical size
Blowers
Pumps
Compressors
Conveyors
autotransformer taps
■ Suitable for relatively
long starting periods
■ Motor current is
greater than line
current during starting
■ Smooth acceleration –
motor voltage
increases with speed
■ High power factor
during start
■ Less expensive than
autotransformer
starter in lower
horsepower ratings
■ Available with as
■ Low torque efficiency
■ Resistors give off heat
■ Starting time in excess
of 5 seconds requires
expensive resistors
■ Difficult to change
starting torques under
varying conditions
Belt and gear
drives
Conveyors
Textile
machines
many as 5 accelerating
points
■ Least expensive
reduced voltage
starter
■ Most dual voltage
motors can be started
part winding on lower
voltage
■ Small physical size
■ Unsuited for high
inertia, long starting
time loads
■ Requires special motor
design for voltage
higher than 230 volts
■ Motor will not start if
the torque demanded
Reciprocating
compressors
Pumps
Blowers
Fans
by the load exceeds
that developed by the
motor when the first
half of the motor is
energized
■ First step of
acceleration must not
exceed 5 seconds or
else motor will
overheat
■ Suitable for high
inertia, long
acceleration loads
■ High torque efficiency
■ Ideal for especially
stringent inrush
restrictions
■ Ideal for frequent
■ Requires special motor
■ Low starting torque
■ During open transition
there is a high
momentary inrush
when the delta
contactor is closed
Centrifugal
compressors
Centrifuges
starts
For more information visit: www.EatonElectrical.com AP03902001E
Solid-State Soft Start
Motor Controller and
Starter
Application Note
Effective: February 2005 Page 7
Basic Mechanics
Introduction
In order to apply a soft start properly,
certain mechanical parameters must
be taken into consideration. This section explains what these parameters
are and how to calculate or measure
them.
Torque
Torque is the action of a force producing or tending to produce rotation.
Unlike work (which only occurs during
movement) torque may exist even
though no movement or rotation
occurs.
Torque consists of a force (Lb.) acting
upon a length of a lever arm (Ft.). The
product of these two factors produces
the term lb-ft, which is the unit of measurement for torque (see Figure 10).
Mathematically, it is expressed as:
Torque (lb-ft) = Force (Lbs.) x
Distance (Ft.)
Example:
Torque = Force x Distance
Torque = 50 Lbs. x 1 Ft.
Torque = 50 lb-ft
Because most power transmission is
based upon rotating elements, torque
is important as a measurement of the
effort required to produce work.
Force
Lever Arm – 1 Ft.
Figure 10. Calculating Torque
Calculating Torque
Acceleration Torque Required for Rotating
Motion
Some machines must be accelerated
to a given speed in a certain period of
time. The torque rating of the motor
may have to be increased to accomplish this objective. The following
equation may be used to calculate the
average torque required to accelerate
a known inertia (WK
must be added to all the other torque
requirements of the machine when
determining the motor’s required peak
torque output.
2
). This torque
50 Lbs.
2
WK
xdN
-------------------------
T
=
308t
Where:
T = Acceleration Torque (lb-ft)
2
= Total system inertia (lb-ft2) that
WK
the motor must accelerate. This value
includes motor rotor, speed reducer
and load.
dN = Change in speed required (rpm)
t = Time to accelerate total system load
(seconds)
Note: The number substituted for (WK2) in
this equation must be in units of lb-ft
The same formula can also be rearranged to determine the minimum
acceleration time of a given system, or
if a motor can accomplish the desired
change in speed within the required
time period.
Rearranged Equation:
2
xdN
WK
-------------------------=
t
308T
2
.
Calculating Horsepower
Note: The following equations for calculating horsepower are to be used for estimating purposes only. These equations do not
include any allowance for machine friction,
windage or other factors. These factors
must be considered when selecting a motor
for an application. Once the machine torque
is determined, the required horsepower is
calculated using the formula:
TxN
hp
-------------=
5250
Where:
hp = Horsepower
T = Torque (lb-ft)
N = Speed of motor at rated load (rpm)
If the calculated horsepower falls
between standard available motor
ratings, select the higher available
horsepower rating. It is good practice
to allow some margin when selecting
the motor horsepower. Also note that
the motor’s torque output is reduced
during a soft start. The load requirements must be related to the soft
starter settings.
For many applications, it is possible
to calculate the horsepower required
without actually measuring the torque.
The following equations will be
helpful:
Conveyors
hp =
(Vertical)
hp =
(Horizontal
Where:
F/W = force/weight in Lbs.
V = Velocity in feet per minute
Coef. = Coefficient of friction
F / W (lbs) x V (fpm)
33,000 x Efficiency
F / W (lbs) x V (fpm) x Coef
)
33,000 x Efficiency
Fans and Blowers
hp =
cfm x Pressure (psi)
33,000 x Efficiency of Fan
hp =
cfm x Pressure (lb-ft
2
)
229 x Efficiency of Fan
cfm x (Inches of Water Gauge)
hp =
6356 x (Efficiency of Fan)
Pumps
gpm x Head (ft.) x (Specific Gravity)
hp =
Where:
psi = pounds per square inch
cfm = cubic feet per minute
gpm = gallons per minute
Specific gravity of water = 1.0
1 cubic foot per second = 448 gpm
1 psi = a head of 2.309 ft. for water
weighing 62.36 lbs. per cu. ft. at 62°F.
Efficiency of fan or pump = %/100
Displacement pump efficiency:
Displacement pumps vary between 85
and 90% efficiency depending on size
of pumps.
Centrifugal pump efficiency (at design
point):
500 to 1000 gal. per min. = 70 to 75%
1000 to 1500 gal. per min. = 75 to 80%
Larger than 1500 gal. per min. =
80 to 85%
3960 x (Efficiency of Pump)
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Application Note
Page 8 Effective: February 2005
Solid-State Soft Start
Motor Controller and
Starter
Inertia
Inertia is a measure of a body’s resistance to changes in velocity, whether
the body is at rest or moving at a constant velocity. The velocity can be
either linear or rotational.
2
The moment of Inertia (WK
) is the
product of the weight (W) of an object
and the square of the radius of gyra-
2
tion (K
). The radius of gyration is a
measure of how the mass of the object
is distributed about the axis or rotation. Because of the distribution of
mass, a small diameter cylindrical part
has a much lower inertia than a large
diameter part.
The inertia calculations for typical
shapes follow.
WK2 or WR
2
WR2 refers to the inertia of a rotating
member that was calculated by
assuming the weight of the object
was concentrated around its rim at a
distance R (radius) from the center.
2
refers to the inertia of a rotating
WK
member that was calculated by
assuming the weight of the object was
concentrated at some smaller radius,
K (termed the radius of gyration). To
determine the WK
2
of a part, the
weight is normally required.
Calculations
When performing calculations, be consistent with the formulae and units
used. Common mistakes are substituting inches for feet, etc.
Cylinders
D
L
Figure 11. Solid Cylinder
Equations:
2
WK
= .000681 x p x L x (D)
4
D1D
2
L
Figure 12. Hollow Cylinder
Equations:
2
WK
= .000681 x p x L (D
4
- D1 4)
2
Where:
2
= inertia of a cylinder (lb-ft2)
WK
p = density of cylinder material in lb-in
(see density chart below)
= inside diameter of cylinder
D
1
(inches)
= outside diameter of cylinder
D
2
(inches)
L = Length of cylinder (inches)
Table 2. Common Material Densities (p)
Aluminum
Brass
Cast Iron
Steel
Rubber
Paper
0.0977
0.3110
0.2816
0.2816
0.0341
0.0250 to 0.0420
Pulley/Gear
To calculate the inertia of a pulley or
gear, divide up the piece (shown in
Figure 13) as shown in Figure 14.
Using the same equation for calculating hollow cylinders, perform the calculations of each separate part and
add them together for a total inertia.
End View
2
and WK
1
Note: WK
inertia calculations.
Figure 13. Complete Pulley/Gear
2
are the separate
2
3"
2.5"
Side View
3"
2"
1.375"
Motor
Shaft
In this example the pulley is made of
steel. We will divide it up to calculate
as shown.
3"
2.5"
3"
Figure 14. Pulley/Gear Components
3
WK
2
1
Equations:
2
= .000681 x p x L (D
WK
4
2
Calculations:
2
= .000681 x 0.2816 x 3 x
WK
1
4
– 2.54)
(3
= .0241 lb-ft
2
WK
= .000681 x 0.2816 x 2 x
2
(2.5
= .0136 lb-ft
Total Inertia = WK
2
4
– 1.3754)
2
2
+ WK
1
.0136
= .0377 lb-ft
2
WK2 Reflected to the Motor Shaft
In most mechanical systems not all the
moving parts operate at the same
speed. If speeds of the various parts
have a continuous fixed relationship
to the motor speed, the equation can
be used to convert all of the various
inertia values to an equivalent WK
applied to the motor shaft.
WK2 of Rotating Parts
2
WK
---------------DR()
2
N
--------N
Equivalent WK2 = WK2
Where:
2
= inertia of the moving part
WK
N = speed of the moving part (rpm)
= speed of the driving motor (rpm)
N
M
When using speed reducers, and the
machine inertia is reflected back to the
motor shaft, the equivalent inertia is
equal to the machine inertia divided by
the square of the drive reduction ratio.
2
Equivalent WK
=
2"
1.375"
2
WK
2
- D1 4)
2
= .0241 +
2
2
M
2
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Solid-State Soft Start
Motor Controller and
Starter
Application Note
Effective: February 2005 Page 9
Where:
DR = drive reduction ratio =
Input
1 hp
3 lb-ft
1750 RPM
Reducer
N
---------
Output
(Less Efficiency)
76.5 lb-ft
57.5 Rpm
Gear
(30:1)
M
N
1 hp
Figure 15. Gear Reducer Characteristics
WK2 of Linear Motion
Not all driven systems involve rotating
motion. The equivalent WK
2
of linearly
moving parts can also be reduced to
the motor shaft speed as follows:
2
WV()
2
=
Equivalent WK
-----------------------------
39.5 NM()
2
Where:
W = weight of load (Lbs.)
V = linear velocity of rack and load or
conveyor and load (fpm)
= speed of the driving motor (rpm)
N
M
This equation can only be used where
the linear speed bears a continuous
fixed relationship to the motor speed,
such as a conveyor.
Speed Reducer Selection
The motor should always be coupled
to the driven machine by a power
transmission that will permit maximum motor rpm at maximum
machine speed. The power transmission may be a simple belt-sheave or
sprocket-chain arrangement or a
compact gear reducer. In most applications requiring speed reductions
greater than 5:1, the gear reducer
may be the most economical choice.
Gear Reducer Selection
A gear reducer transmits power by an
arrangement of various forms of
gears. It provides an efficient, positive
method to change speed, direction,
and torque. This may mean a change
of speed with a corresponding change
in torque, or a change in output direction or position. A common result is a
combination of the above.
The gear reducer serves as a torque
amplifier, increasing the torque by a
factor proportional to the reducer
ratio, less an efficiency factor. See
Figure 13.
A 1 hp, 1750 rpm motor has an output
torque of 3 lb-ft. If a 30:1 ratio reducer
with 85% efficiency is used, the
reducer output torque will be
3x30x0.85 = 76.5 lb-ft.
A typical application involves selecting
a gear reducer that permits the drive
motor to operate at nameplate speed
when the driven machine is at maximum speed. The gear reducer should
also provide adequate torque to drive
the machine.
Application Example
A 1750 rpm motor is selected for a
machine which is to operate at 57.5
rpm maximum speed and requires
70 lb-ft of torque.
To find the answer, the following two
steps must be accomplished.
1. Determine the required ratio:
Reducer =
Ratio
Maximum Motor rpm
Maximum Driven
Machine rpm
1750
Reducer Ratio = = 30.4 or a 30:1
Note: When the calculated reducer ratio is
not close to a standard speed reducer ratio,
a chain, belt or additional gears with further
reduction are necessary (located on the
input or output side).
-------------
57.5
ratio
2. Determine the motor torque &
horsepower
A 30:1 gear reducer is selected which
is capable of supplying 70 lb-ft of output torque. Since the machine torque
requirement is known, this value is
divided by the reduction ratio and an
efficiency factor, to arrive at the
required motor torque (TM).
TM =
Required torque (lb-ft)
Reducer Ratio x
Efficiency Factory
70
------------------------
TM = = 2.75 lb-ft
30 0.85×
Since a 1 hp, 1750 rpm motor delivers
3 lb-ft of torque, it is chosen for this
application along with a 30:1 gear
reducer with a minimum of 70 lb-ft
output torque.
Where the reduction ratio permits the
use of a chain or belt, the same formulae are used as with the reducers.
Gear Reducer — Overhung Load
An overhung load (OHL) is defined as
dead weight the gear reducer bearings
can support on an output shaft at a
distance equal to the shaft diameter.
This distance is measured from the
outside end of the bearing housing
along the shaft (see Figure 16). If the
acting load is at a point different from
the OHL point, it must be converted to
the reference point and compared to
the manufacturer’s catalog value.
Overhung Load
Reference Points
Side
Thrust
Side
Thrust
Output
Side
Gear
Reducer
Figure 16. Overhung Load
When a gear reducer is driven by a
belt, chain or gear drive, or when the
gear reducer drives a driven unit
through a belt, chain or gear drive,
an overhung load (side thrust) is
produced. The overhung load must
not exceed the rating of the gear
reducer as listed by the manufacturer.
The magnitude of the overhung load
should always be kept to a minimum.
Excessive loads could lead to fatigue
failure of either the bearing or shaft.
The sprocket or pulley should always
be located as close to the gear housing
as possible.
Increasing the sprocket or pulley diameter results in a reduced overhung
load. Use the following equation to
determine the overhung load:
=2 x Shaft Torque (lb-in) x K
OHL
(lb. )
Diameter (in)
Where:
Diameter is of the sprocket, sheave,
pulley or gear.
Note: K is a constant which is:
1.00 for chain drives
1.25 for gears or gear-belt drives
1.50 for V belt drives
2.50 for flat belt drives
Input
Side
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