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Motor Sizing Calculations
This section describes certain items that must be calculated to find the optimum motor for a particular application.
Selection procedures and examples are given.
Selection Procedure
Determine the drive
mechanism component
●
First, determine certain features of the design, such as drive mechanism, rough dimensions,
distances moved, and positioning period.
Confirm the required specifications
●
Confirm the required specifications for the drive system and equipment (stop accuracy,
position holding, speed range, operating voltage, resolution, durability, etc.).
●
Calculate the value for load torque, load inertia, speed, etc. at the motor drive shaft of the
mechanism. Refer to page 3 for calculating the speed, load torque and load inertia for various
mechanisms.
Calculate the speed and load
Select motor type
●
Select a motor type from AC Motors, Brushless DC Motors or Stepping Motors based on the
required specifications.
●
Make a final determination of the motor after confirming that the specifications of the selected
motor/gearhead satisfy all of the requirements (mechanical strength, acceleration time,
acceleration torque etc.).
Check the selected motor
F-2
ORIENTAL MOTOR GENERAL CATALOG 2003/2004
Formulas for Calculating Load Torque
Formulas for Calculating Moment of
Inertia
Ball Screw
m
Direct Coupling
Inertia of a Cylinder
F
A
D
1
x
m
y
L
T
L
(
FP
B
0
F
0
P
B
)
1
[oz-in]
......................................
2
π
2
π
i
F
F
A
m
(sin
cos
)[oz.]
.......................................
J
x
1
π
mD
1
2
LD
1
4
[oz-in
2
]
.....................................
8
32
Pulley
1
D
1
2
L
2
J
y
m
(
)
[oz-in
2
]
............................................
4
4
3
D
Inertia of a Hollow Cylinder
D
1
x
D
2
F
A
m
y
L
T
L
F
A
·
2
π
i
D
1
π
J
x
m
(
D
1
2
D
2
2
)
L
(
D
1
4
D
2
4
)
[oz-in
2
]
............
8
32
F
A
m
)
D
[oz-in]
....................................................
1
D
1
2
D
2
2
L
2
2
i
J
y
m
(
)
[oz-in
2
]
.................................
4
4
3
Wire Belt Mechanism, Rack and Pinion Mechanism
Inertia for Off-center Axis of Rotation
l
x
0
F
A
F
F
A
m
F
x
m
D
C
F
π
DD
B
l
Distance between
x
and
x
0
axes [in.]
A
T
L
[oz-in]
..............................................
2
π
i
2
i
1
12
l
2
)[oz-in
2
]
...............
m
(sin cos )[oz.]
.......................................
J
x
J
x
0
m
l
2
m
(
A
2
B
2
F
F
A
12
By Actual Measurement
Inertia of a Rectangular Pillar
Spring Balance
A
x
B
F
B
C
y
Machine
D
Pulley
J
x
1
m
(
A
2
B
2
)
ABC
(
A
2
1
B
2
)[oz-in
2
]
...........
12
12
F
B
D
T
L
[oz-in]
...............................................................
2
1
1
J
y
m
(
B
2
C
2
)
ABC
(
B
2
C
2
)[oz-in
2
]
...........
12
12
Inertia of an Object in Linear Motion
F
Force of moving direction [oz.]
J
m
( )
2
m
(
A
)
2
[oz-in
2
]
.........................................
F
0
Pilot pressure weight [oz.] (
1/3 F)
2
π
Internal friction coefficient of pilot pressure nut (0.1 to 0.3)
0
Efficiency (0.85 to 0.95)
A
Unit of movement [inch/rev]
i
Gear ratio
J
x
Inertia on
x
axis [oz-in
2
]
P
B
Ball screw pitch [inch/rev]
J
y
Inertia on
y
axis [oz-in
2
]
F
A
External force [oz.]
J
x
0
Inertia on
x
0
axis [oz-in
2
]
Density
Iron
F
B
Force when main shaft begins to rotate [oz.]
m
Weight [oz.]
Total weight of work and table [oz.]
D
1
External diameter [inch]
4.64 [oz/in
3
]
Frictional coefficient of sliding surfaces (0.05)
Internal diameter [inch]
Aluminum
1.65 [oz/in
3
]
Angle of inclination [°]
Density [oz/in
3
]
Bronze
5 [oz/in
3
]
D
Final pulley diameter [inch]
L
Length [inch]
Nylon
0.65 [oz/in
3
]
ORIENTAL MOTOR GENERAL CATALOG 2003/2004
F-3
m
(
m
D
2
Stepping Motors
This section describes in detail the key concerns in the
selection procedure, such as the determination of the motion
profile, the calculation of the required torque and the
confirmation of the selected motor.
For Start-Stop Operation
Start-stop is a method of operation in which the operating
pulse speed of a motor being used in a low-speed region
is suddenly increased without an acceleration period. It is
found by the following equation. Since rapid changes in
speed are required, the acceleration torque is very large.
Operating Patterns
There are 2 basic motion profiles.
One is a start/stop operation and the other is an acceleration/
deceleration operation.
Acceleration/deceleration operation is the most common.
When load inertia is small, start/stop operation can be used.
Operating Pulse
Speed
(
f
2
)
[Hz]
Number of Operating Pulses [Pulses]
Positioning Period [s]
A
t
0
Calculate the Acceleration/Deceleration Rate
T
R
Calculate the acceleration/deceleration rate from the
following equation.
Operating Pulse
Speed
Operating Pulse
Speed
(
f
2
)
(
f
2
)
Number of
Operating Pulses
(A)
Number of Operating Pulses
(A)
Acceleration/deceleration
rate
T
R
[ms/kHz]
Acceleration (Deceleration) Period [ms]
Starting Pulse
Speed
Operating Pulse
Speed [Hz]
Starting Pulse
Speed [Hz]
(
f
1
)
Start/Stop Operation
(
t
0
)
Acceleration Period
(
t
1
)
Positioning Period
(
t
0
)
Acceleration/Deceleration Operation
Deceleration Period
(
t
1
)
f
2
t
1
f
1
✽
Calculate the pulse speed in full-step equivalents.
Find the Number of Operating Pulses A [pulses]
The number of operating pulses is expressed as the number
of pulse signals that adds up to the angle that the motor must
move to get the work from point A to point B.
T
R
Operating Pulse (A)
[Pulses]
Distance per Movement
Distance per Motor Rotation
No. of Pulses
Required for
1 Motor Rotation
t
1
l
l
rev
360
°
s
s
: Step Angle
Calculate the Operating Speed from Operating
Pulse speed
Determine the Operating Pulse Speed
f
2
[Hz]
The operating pulse speed can be found from the number of
operating pulses, the positioning period and the
acceleration/deceleration period.
Operating
Speed [r/min]
Operating Pulse
Speed [Hz]
Step Angle
360°
60
For Acceleration/Deceleration Operation
Acceleration/deceleration is a method of operation in
which the operating pulses of a motor being used in a
medium- or high-speed region are gradually changed. It is
found by the equation below. Usually, the acceleration
(deceleration) period (
t
1
) is set at roughly 25% of the
positioning periods. For gentle speed changes, the
acceleration torque can be kept lower than in start-stop
operations.
When a motor is operated under an operating pattern like
this, the acceleration/deceleration period needs to be
calculated using the positioning period.
Calculate the Load Torque
T
L
(See basic equations on pages F-3)
Calculate the Acceleration Torque
Ta
For Acceleration/Deceleration Operation
Acceleration Torque (
T
a
) [oz-in]
Inertia of Rotor
[oz-in
2
]
Total Inertia
[oz-in
2
]
π
Step Angle [
°
]
180°
Acceleration (Deceleration) Period [s]
Starting Pulse
Speed [Hz]
(
J
0
J
L
)
•
s
180
f
2
f
1
t
1
Acceleration/Deceleration
Period [s]
For Start-Stop Operation
Positioning Period [s]
0.25
Acceleration Torque
(
T
a
) [oz-in]
Inertia of Rotor
[oz-in
2
]
Total Inertia
[oz-in
2
]
Number of
Operating Pulses
[Pulses]
Acceleration
(Deceleration)
Period [s]
Starting Pulse
Speed [Hz]
π
Step Angle [
°
]
(Operating Pulse Speed)
2
[Hz]
180°
Operating Pulse
Speed
f
2
[Hz]
Coefficient
Positioning
Period [s]
Acceleration (Deceleration)
Period [s]
π
•
s
•
f
2
2
(
J
0
J
L
)
180°
•
n
n: 3.6°/
s
A
f
1
•
t
1
Calculate the Required Torque
T
M
t
0
t
1
Required Torque
T
M
[oz-in]
(Load Torque
[oz-in]
Acceleration Torque)
[oz-in]
Safety Factor
(
T
L
T
a
)
S
f
F-4
ORIENTAL MOTOR GENERAL CATALOG 2003/2004
Operating Pulse
Speed [Hz]
π
Choosing Between Standard AC
Motors and Stepping Motors
Check the Acceleration/Deceleration Rate
Most controllers, when set for acceleration or
deceleration, adjust the pulse speed in steps. For that
reason, operation may sometimes not be possible, even
though it can be calculated.
Calculate the acceleration/deceleration rate from the
following equation and check that the value is at or above
the acceleration/deceleration rate in the table.
Selection Considerations
There are differences in characteristics between standard AC
motors and stepping motors. Shown below are some of the
points you should know when sizing a motor.
Standard AC Motors
The speed of Induction Motors and Reversible Motors
vary with the size of the load torque. So, the selection
should be made between the rated speed and the
synchronous speed.
Acceleration/Deceleration
Rate
T
R
[ms/kHz]
Acceleration (Deceleration) Period [ms]
Operating Pulse
Speed [Hz]
Starting Pulse
Speed [Hz]
t
1
There can be a difference of continuous and short-term
ratings, due to the difference in motor specifications,
despite the fact that two motors have the same output
power. Motor selection should be based on the operating
time (operating pattern).
f
2
f
1
Calculate the pulse speed in full-step equivalents.
Each gearhead has maximum permissible load inertia.
When using a dynamic brake, changing direction quickly,
or quick starts and stops, the total load inertia must be
less than the maximum permissible load inertia.
T
R
Stepping Motors
t
1
Checking the Running Duty Cycle
A stepping motor is not intended to be run continuously
with rated current. Lower than 50% running duty cycle is
recommended.
Acceleration Rate (Reference Values with
EMP
Series)
Model
Motor Frame Size
inch (mm)
Acceleration/
Deceleration Rate
T
R
[ms/kHz]
If below the minimum
value, change the
operating pattern’s
acceleration
(deceleration)
period.
Running Duty Cycle
Running Time
Running Time
Stopping Time
100
A
1.10(28), 1.65(42),
2.36(60), 3.35(85)
0.5 Min.
Checking the Inertia Ratio
Large inertia ratios cause large overshooting and
undershooting during starting and stopping, which can
affect start-up times and settling times. Depending on the
conditions of usage, operation may be impossible.
Calculate the inertia ratio with the following equation and
check that the values found are at or below the inertia
ratios shown in the table.
RK
Series
1.65(42), 2.36(60)
3.35(85), 3.54(90)
20 Min.
30 Min.
Checking the Required Torque
Check that the required torque falls within the pull-out
torque of the speed-torque characteristics.
Safety Factor: Sf (Reference Value)
Product Series
A
RK
Series
Safety Factor
1.5
2
Total Inertia of the Machine [oz-in
2
]
Rotor Inertia of the Motor [oz-in
2
]
2
Inertia Ratio
J
L
J
0
Required Torque
Inertia Ratio (Reference Values)
When these values are exceeded,
we recommend a geared motor.
Using a geared motor can
increase the drivable inertia load.
Product Series Inertia Ratio
A
30
RK
Series
Speed [r/min]
(Pulse Speed [kHz])
10 Maximum
✽
Except geared motor types
Inertia Ratio
Total Inertia of the Machine
[oz-in
2
]
Rotor Inertia of the Motor
[oz-in
2
]
(Gear Ratio)
2
J
L
J
0
•
i
2
ORIENTAL MOTOR GENERAL CATALOG 2003/2004
F-5
✽
Sizing Example
(3) Determine the Operating Pulse Speed ƒ
2
[Hz]
Ball Screw
Number of
Operating
Pulses [A]
Starting
Pulses
Acceleration
(Deceleration)
Period [t
1
]
Speed [f
1
]
Using Stepping Motors (
A
)
Operating pulse
speed f
2
m
Positioning
Period [t
0
]
Acceleration (Deceleration)
Period [t
1
]
Stepping
Motor
6000
0.2
0
10000 Hz
0.8
Coupling
Direct
Connection
10000
Pulse
Generator
Driver
6000 Pulses
P
B
0.2
t
1
t
1
0.2
Period [sec]
Programmable
Controller
t
0
=0.8
(4) Calculate the Operating Speed N [r/min]
Determine the Drive Mechanism
Total mass of the table and work:
Operating Speed
f
2
360
S
60
m
90 lb. (40 kg)
Frictional coefficient of sliding surfaces:
0.05
10000
0.72
60
1200 [r/min]
360
Ball screw efficiency:
0.9
Internal frictional coefficient of pilot pressure nut:
0
0.3
Calculate the Required Torque
T
M
[oz-in]
(see page F-4)
(1) Calculate the Load Torque
T
L
[oz-in]
Ball screw shaft diameter:
D
B
0.6 inch (1.5 cm)
Total length of ball screw:
L
B
23.6 inch (60 cm)
Material of ball screw:
Iron [density
4.64 oz/in
3
Load in Shaft Direction F
F
A
m (sin
cos
)
(7.9
10
-3
kg /cm
3
)]
0
90 (sin 0
0.05 cos 0)
Pitch of ball screw:
P
B
0.6 inch (1.5 cm)
4.5 lb.
Desired Resolution (feed per pulse):
l
0.001 inch (0.03 mm)/step
F
4.5
Feed:
l
7.01 inch (180 mm)
Pilot Pressure Load F
0
3
3
1.5 lb.
Positioning period:
t
0
0.8 sec.
F
P
2
π
•
•
F
0
•
P
B
Load Torque T
L
B
0
2
π
Calculate the Required Resolution
4.5 0.6
2
π
0.3 1.5 0.6
2
π
0.9
Required Resolution
360
°
Desired Resolution (
l
)
S
Ball Screw Pitch (
P
B
)
0.52 lb-in
8.3 oz-in
0.001
15
0.72
°
(2) Calculate the Acceleration Torque
T
a
[oz-in]
A
can be connected directly to the application.
Calculate the total moment of inertia
J
L
[oz-in
2
]
(See page F-3 for basic equations)
Determine the Operating Pattern
(see page F-4, see basic equations on pages F-3)
(1) Finding the Number of Operating Pulses (A)
[pulses]
Inertia of Ball Screw J
B
π
32
• • L
B
• D
4
B
π
32
4.64
23.6
0.6
4
1.39 oz-i n
2
Operating pulses (A)
Feed per Unit (
l
)
Ball Screw Pitch (P
B
)
360
°
Step Angle (
P
B
2
π
2
0.6
2
π
2
S
)
Inertia of Table and Work J
T
m
90
7.01
360
°
0.72
°
0.6
6000 pulses
0.82 lb- in
2
13.1 oz-in
2
(2) Determine the Acceleration (Deceleration)
Period
t
1
[sec]
An acceleration (deceleration) period of 25% of the
positioning period is appropriate.
Acceleration (deceleration) period (
t
1
)
Total Inertia J
L
J
B
J
T
1.39
13.1
14.5 oz- in
2
Calculate the acceleration torque
T
a
[oz-in]
Acceleration
torque T
a
J
0
J
L
π
S
180
°
•
f
2
f
1
g
t
1
0.8 0.25
0.2 sec
J
0
14.5
386
π
0.72
180
10000
0
0.2
1.63 J
0
23.6 oz-in
(3) Calculate the Required Torque
T
M
[oz-in]
Required torque
T
M
[oz-in]
(T
L
T
a
)
2
{8.3
(1.63 J
0
23.6) }
2
3.26 J
0
63.8 oz-in
F-6
ORIENTAL MOTOR GENERAL CATALOG 2003/2004
360
°
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