P r e c i s i o n G e a r i n g & M o t i o n C o n t r o l
SAFETY GUIDE
CAUTIO
CAUTIO
G
CAUTIO
CAUTIO
G
CAUTIO
CAUTIO
G
G
G
For actuators, motors, control units and drivers
Read this manual thoroughly before designing the application, installation, maintenance or inspection of the actuator.
Indicates a potentially hazardous situation,
which, if not avoided, could result in death
or serious personal injury.
LIMITATION OF APPLICATIONS:
The equipment listed in this document may not be used for the applications listed below:
Space equipmentAutomobile, automotive parts
Aircraft, aeronautic equipmentAmusement equipment, sport equipment, game machines
Nuclear equipmentMachine or devices acting directly on the human body
Household apparatusInstruments or devices to transport or carry people
Vacuum equipmentApparatus or devices used in special environments
If the above list includes your intending application for our products, please consult us.
Safety measures are essential to prevent accidents resulting in death, injury or damage of the equipment due to
malfunction or faulty operation.
CAUTIONS FOR ACTUATORS AT APPLICATION DESIGNING
Always use under followings conditions:
-Ambient temperature: 0˚C to 40˚C
-Ambient humidity: 20% to 80%RH (Non-condensation)
-Vibration: Max 24.5 m/S
-No contamination by water, oil
N
-No corrosive or explosive gas
CAUTION FOR ACTUATORS IN OPERATIONS
Keep limited torques of the actuator.
-Keep limited torques of the actuator.
-Be aware, that if arms attached to output element hits
by accident an solid, the output element may be
uncontrollable.
Do not apply impacts and shocks
-Do not use a hammer during installation
WARNIN
-Failure to observe this caution could damage the
encoder and may cause uncontrollable operation.
manufactured by Harmonic Drive LLC
2
Indicates a potentially hazardous situation, which, if
not avoided, may result in minor or moderate personal
injury and/or damage to the equipment.
NWARNIN
Follow exactly the instructions in the relating
manuals to install the actuator in the equipment.
-Ensure exact alignment of actuator shaft center and
corresponding center in the application.
Failure to observe this caution may lead to vibration,
resulting in damage of output elements.
Never connect cables directly to a power supply
socket.
-Each actuator must be operated with a proper driver.
WARNIN
-Failure to observe this caution may lead to injury, fire or
damage of the actuator.
Avoid handling of actuators by cables.
-Failure to observe this caution may damage the wiring,
WARNIN
causing uncontrollable or faulty operation.
CAUTIONS FOR DRIVERS AT APPLICATION DESIGNING
Always use drivers under followings conditions:
-Mount in a vertical position keeping sufficient distance
to other devices to let heat generated by the driver
radiate freely.
-Ambient temperature: 0˚C to 50˚C
N
-Ambient humidity: less than 95% RH (Non
condensation)
-No contamination by water, oil or foreign matters
-No corrosive, inflammable or explosive gas
Pay attention to negative torque by inverse load.
–Inverse load may cause damages of drivers.
-Please consult our sales office, if you intent to apply
products for inverse load.
Use sufficient noise suppressing means and safe
grounding.
-Keep signal and power leads separated.
-Keep leads as short as possible.
-Ground actuator and driver at one single point, minimum
ground resistance class: D (less than 100 ohms)
-Do not use a power line filter in the motor circuit.
Use a fast-response type ground-fault detector
designed for PWM inverters.
-Do not use a time-delay-type ground-fault detector.
N
CAUTION FOR DRIVERS IN OPERATIONS
WARNIN
Never change wiring while power is active.
-Make sure of power non-active before servicing the
products.
-Failure to observe this caution may result in electric
shock or personal injury.
Do not make a voltage resistance test.
-Failure to observe this caution may result in damage of
the control unit.
-Please consult our sales office, if you intent to make a
N
voltage resistance test.
Do not touch terminals or inspect products at least
5 minutes after turning OFF power.
-Otherwise residual electric charges may result in
electric shock.
-Make installation of products not easy to touch their
inner electric components.
Do not operate control units by means of power
ON/OFF switching.
-Start/stop operation should be performed via input
signals.
N
Failure to observe this caution may result in deterioration
of electronic parts.
DISPOSAL OF AN ACTUATOR, A MOTOR, A CONTROL UNIT AND/OR THEIR PARTS
All products or parts have to be disposed of as industrial waste.
-Since the case or the box of drivers have a material indication, classify parts and dispose them separately.
1
RSF supermini series AC servo actuator manual
Contents
Chapter 1 Overview of the RSF supermini series ................................................................................... 1
1-1 Major characteristics................................................................................................................... 1
1-2 Ordering information ................................................................................................................... 2
1-3 Combinations with drivers .......................................................................................................... 2
1-4 Specifications of RSF supermini actuators................................................................................. 3
1-5 External dimensions of actuators ............................................................................................... 4
Appendix 1 Conversion of Unit ...................................................................................................App. 1-1
Appendix 2 Moment of inertia .....................................................................................................App. 2-1
1. Calculation of mass and moment of inertia .................................................................App. 2-1
2. Moment of inertia of circular cylinder...........................................................................App. 2-3
RSF-super_V1_01 - contents 2 -
Chapter 1 Overview of the RSF supermini series
Chapter 1 Overview of the RSF supermini series
The RSF supermini series are ultra-small AC servo actuators combining ultra-precision control
deceleration device Harmonic Drive® that provides precision rotation operation at a high torque with
ultra-small AC servo motor developed to make use of the performance of the decelerator.
Actuators with an electromagnetic brake are also included in the lineup. They can meet fail-safe
requirements of equipment to prevent accidents upon power supply failure.
The dedicated servo driver HA-680 is an AC servo driver for 24VDC power supply. The small and
multi-functional HA-680 driver is equipped with position control, speed control, and torque control as
standard to control operation of the RSF supermini series correctly and precisely.
The RSF supermini series can contribute to downsizing of driving of robot joints, semiconductor/LCD
panel manufacturing equipment, machine tools, and other FA equipment. By utilizing its small and
high-torque characteristics, it can also be used for small equipment and for research.
1-1 Major characteristics
◆Small, lightweight, and high-torque
The RSF supermini series with the precision-control deceleration device Harmonic Drive® realizes a
high torque and has a very high output torque for the outer dimensions compared to the direct driving
method with a high-capacity motor alone.
Also, combination with the dedicated AC servo motor realizes size and weight reduction that are never
possible before.
◆ Standard lineup of actuators with a brake (only RSF-5A)
The standard lineup of AC servo actuators includes the deenergisation operation type actuators with
an electromagnetic brake for the first time for this size of actuators.
Fail-safe requirements of equipment can be met to prevent accidents upon power failure without
providing any external brake or changing the equipment structure to install a brake.
◆ Superior positioning precision
The characteristics of the control deceleration device Harmonic Drive® such as non-backlash and
superior positioning precision realize high-precision mechanisms.
◆ Stable controllability
The high deceleration gear ratio of the control deceleration device Harmonic Drive® provides stable
controllability for large variations of load moment of inertia.
RSF-Super_V1_02 - 1 -
Chapter 1 Overview of the RSF supermini series
1-2 Ordering information
Model codes for the RSF supermini series actuators are as follows:
Insulation resistance: DC500V 100MΩor more Lubricant: Grease (Harmonic Grease) Structure:Totallyenclosedselfcooling
type
Note 1: The table shows typical output values of actuators.
Note 2: The values in the table above are obtained when it is combined with the combined driver (HA-680-4B-24).
Note 3: All values are typical.
Note 4: The moment of inertia is the total value of the motor shaft and Harmonic Drive moment of inertia values
converted to the output side. The values in parentheses are for equipment with a brake.
Note 5: The encoder resolution is (motor shaft encoder resolution when multiplied by 4) x (gear ratio).
Allowable Radial Load
(output shaft central value)
Allowable Thrust Load
Encoder Pulses (motor shaft)Pulse200500
Encoder Resolution
(Output shaft: when multiplied by 4)
Note 5
Motor Shaft Brake
Mass
Combined DriverHA-680-4B-24HA-680-4B-24
GD2/4kg•m
Jkgf•cm•s21.07x10
Input
Power
Supply
Voltage
Retention
Torque
w/o brakeg
w/ brakeg86.0 (except clamp filter)
Model
30501003050100
N•m0.030.060.080.180.290.44
Kgf•cm0.310.610.821.832.954.48
r/min15090451509045
N•m0.040.080.120.280.440.65
kgf•cm0.410.821.222.854.486.62
N•m0.090.150.210.50.91.4
kgf•cm0.921.532.145.109.1714.3
N•m/A0.110.180.400.300.541.1
kgf•cm/A1.121.844.083.065.5111.22
Ω
2
0.11x10
N4090
kgf4.09.1
N130270
kgf13.227.5
Pulse/
Rotation
V———DC24
N•m———0.180.290.44
kgf•cm———1.832.954.48
24,00040,00080,00060,000100,000200,000
RSF-3ARSF-5A
1.340.82
-4
-4
31.0 (except clamp filter)
0.29x10
2.98x10
-4
-4
1.17x10
11.90x10
0.66x10
-4
(0.11x10-3)
0.67x10
-4
(1.13x10-3)
-4
-3
66.0 (except clamp filter)
1.83x10
(0.31x10-3)
1.87x10
(3.15x10-3)
-4
-4
7.31x10
(1.23x10-3)
7.45x10
(12.6x10-3)
-4
-3
-3-
Chapter 1 Overview of the RSF supermini series
1-5 External dimensions of actuators
The external drawings are shown as follows:
■ RSF-3
B-XXX-E020-C
4-M1.6 tap 3.2
evenly spaced
Maximum diameter
of rotation part
0
-0.018
φ12 h7
0
-0.008
φ3.5 h6
Motor lead wire
Encoder lead wire
Line locating range of Encoder cable wire
Clamp filter(2) ZCAT1518-0730(TDK)
Note) For detailed outside dimensions, check the delivery specification drawing issued by us.
RSF-Super_V1_02 - 4 -
■ RSF-5A-XXX-E050-C
Chapter 1 Overview of the RSF supermini series
3-M2x3 evenly spaced
2-φ2.3 evenly spaced
3-φ2x2.5 evenly spaced
■ RSF-5A-XXX-E050-BC
■ RSF-5A-XXX-E050-BC(with brake)
3-M2x3 evenly spaced
3-φ2x2.5 evenly spaced
2-φ2.3 evenly spaced
Maximum diameter
of rotation part
Maximum diameter
of rotation part
Motor lead wire
Encoder lead wire
Clamp filter
ZCAT1518-0730(TDK)
FG line
Motor lead wire
FG line
Brake lead wire
Motor and
Brake lead wire
Encoder lead wire
Note) For detailed outside dimensions, check the delivery specification drawing issued by us.
Clamp filter
ZCAT1518-0730(TDK)
RSF-Super_V1_02 - 5 -
Chapter 1 Overview of the RSF supermini series
1-6 One-way positioning accuracy
The following table shows the “one-way positioning accuracy” and “repeated positioning accuracy.”
The following table contains representing values. (JIS B 6201:1987)
The one-way positioning accuracy of RSF supermini actuators is almost equal to the angular
positioning accuracy of the Harmonic® drive gearing, because the effect on the positioning error of the
built-in motor is reducted to its 1/30 or 1/50 or 1/100 by the gearing.
The accuracy for each gear ratio is shown below.
Mode RSF-3B RSF-5A
Gear ratio
Item
30 50 100 30 50 100
One-way positioning accuracy
arc min 10 4 3 3
-3
rad 2.9×10
1.20×10
■ Reference
(Accuracy display and measurement method according to JIS B 6201: 1987)
● One-way positioning of rotation shaft motion
First, perform positioning at any one position in a fixed
direction. This position is the reference position. Next,
One-way positioning
accuracy
perform positioning in succession in the same direction,
and measure the difference between the angle actually
rotated from the reference position and the desired angle
at each position. The maximum difference in one
rotation among these values is taken as the
measurement value. Measurement of equipment with
the continuous positioning function for rotational motion
shall be done once per 30 degrees or 12 positions
throughout the entire rotation range as a rule.
Start position
-3
0.87×10-3 0.87×10
Positional difference
-3
Actual position
RSF-Super_V1_02 - 6 -
Chapter 1 Overview of the RSF supermini series
1-7 Torsional stiffness
When a torque is applied to the output flange of the actuator with the motor locked, the resulting
torsional wind up is near proportional to the torque.
The upper right figure shows the torsional stiffness
characteristics of the output flange applying torque starting
from zero to plus side [+T
trajectory is called torque-torsion characteristics which
typically follows a loop 0→A→B→A’→B’→A as illustrated.
The torsional stiffness of the RSF supermini actuator is
expressed by the slope of the curve that is a spring rate
(wind-up) (unit:N・m/rad).
The torsional stiffness may be evaluated by dividing
torque-torsion characteristics curve into three major regions.
The spring rate of each region is expressed K
respectively.
K
1: spring rate for torque region 0-T1
2: spring rate for torque region T1-T2
K
3: spring rate for torque region over T2
K
0]and minus side [–T0]. This
1, K2, and K3
The wind-up for each region is expressed as follows:
◆ wind-up for torque region 0-T
◆ wind-up for torque region T
◆ wind-up for torque region over T
1:
1-T2:
2:
The following table shows average values of T
different gear ratios.
Kgf m/arc min 0.0015 0.0017 0.0020 0.004 0.005 0.006
Gear ratio
30 50 100 30 50 100
T
=ϕ
1K
1
TT −
1
+θ=ϕ
2
K
2
2
TT −
+θ=ϕ
3
K
1 through T3, K1 through K3, and θ1 through θ2 for
RSF-Super_V1_02 - 7 -
Chapter 1 Overview of the RSF supermini series
1-8 Detector resolution
An encoder with 500 pulses per rotation is incorporated in the motor unit of the RSF supermini series
actuators, and the motor output is decelerated by 1/30, 1/50, or 1/100 by the precision control
decelerator Harmonic Drive®. Therefore, the resolution per one rotation of the actuator output shaft
is 30, 50, or 100 times of the actual encoder resolution. In addition, the encoder signal is electrically
multiplied by 4.
The following table shows the resolution at the output shaft for different gear ratios.
The machining accuracy of the output flange and the mounting flange of RSF supermini actuators are
indicated in the table below.
RSF-3B RSF-5A
Machined accuracy of the output flange * T.I.R. unit: mm
Symbol Accuracy value
Model
a Runout of the tip of the output shaft
b Concentricity of installed spigot joint
c Squareness of installation surface
d Output flange surface contact
Parallelism of installation surface
e
and output flange
*) T.I.R(Total Indicator Reading): Indicates the total amount of dial gage reading when the measurement unit is
rotated once.
Machined parts
RSF-3BRSF-5A
0.03 0.03
0.02 0.04
0.02 0.02
0.005 0.005
0.015 0.015
RSF-Super_V1_02 - 8 -
Chapter 1 Overview of the RSF supermini series
1-10 Allowable load
1-10-1 Allowable radial load and allowable thrust load
The gear head used in the RSF supermini series incorporates the high-precision 4-point contact ball
bearing for direct support of external load (output part).
The allowable radial load and thrust load of the
output shaft are shown below.
L
R
L
a
The allowable radial load F
is obtained with
r
respect to the center (L/2) 0 point of the output
shaft.
The values in the following table are designed
by considering the life of the bearing.
F
S
0 point
The allowable values must not be exceeded.
F
R
L/2
F
r
Model Unit RSF-3B RSF-5A
Allowable radial load (Fr)
Allowable thrust load (FS)
N
kgf
N
kgf
36 90
3.6 9.1
130 270
13 27
L
1-10-2 Radial load when the operating point is different
If the operating point of radial load is different, the allowable radial load value is also different.
The relation between radial load position L
following formula.
The allowable values must not be exceeded.
L
a
F+=
R
F
: Allowable radial load at distance L
R
F
: Allowable radial load at the 0 point [N]
r
L
: Distance from the bearing starting point to the 0 point [mm]
a
L
: Distance from the position where radial load is exerted to the 0 point [mm]
R
F
r
LL
Ra
L : Shaft length [mm]
Model RSF-3B RSF-5A
Allowable radial load (Fr)
La mm 8.6 9.85
L mm 7 10
N 36 90
kgf 3.6 9.1
and allowable radial value FR is obtained from the
R
from the 0 point [N]
R
RSF-Super_V1_02 - 9 -
Chapter 1 Overview of the RSF supermini series
1-11 Rotary direction
The rotary direction of the RSF supermini series actuators when a forward rotation command is given
from the HA-680 driver is forward rotation seen from the output shaft side (i.e. counterclockwise: CW).
The rotary direction of the HA-680 can be switched by using the Parameter → “20: Rotary direction
command” setting.
1 White (WHT) A A phase output
2 Green (GRN) B B phase output
3 Yellow (YEL) Z Z phase output
4 Brown (BRW) U U phase output
5 Blue (BLU) V V phase output
6 Orange (ORG) W W phase output
7 Red (RED) +5V Power supply input
8 Black (BLK) GND Power supply input
9
Connector used Housing: 51021
Terminal: 50058
Manufactured by J.S.T. Mfg Co., Ltd
Manufactured by Molex
RSF-Super_V1_02 - 13 -
(
)
(
)
+
Chapter 2 Selection of the RSF supermini Series
Chapter 2 Selection of the RSF supermini Series
2-1 Allowable load moment of inertia
To make full use of high precision and high performance of the RSF supermini series actuator, perform
temporary selection by considering the load moment of inertia and rotation speed.
As a guideline, the load moment of inertia should be 3 to 5 times the moment of inertia of the actuator.
For the moment of inertia of the actuator, refer to “1-4 Specifications of RSF supermini actuators.”
Refer to appendix 1 for the calculation of moment inertia.
The rotation speed cannot exceed the maximum rotation speed of the actuator. For the maximum
rotation speed, refer to “1-4 Specifications of RSF supermini actuators.”
2-2 Variable load moment of inertia
RSF supermini series actuators include Harmonic Drive® gearing that has a high reduction ratio.
Because of this there are minimal effects of variable load moment of inertias to the servo drive system.
In comparison to direct servo systems this benefit will drive the load with a better servo response.
For example, assume that the load moment of inertia increases to N-times during its motion (for
example, robot arms). The effect of the variable load moment of inertia to the [total inertia converted
into motor shaft] is as follows:
The symbols in the formulas are:
: total moment of inertia converted into
J
S
L: Ratio of load moment of inertia to motor inertia
motor shaft
J
: moment inertia of motor N: variation ratio of load moment of inertia
M
R: reduction ratio of RSF supermini series
◆ Direct drive
NL1
Before:
L1JJM +=S
After:
=S
Ratio:
NL1J'JM
+
/JsJs'
=
L1
+
◆ RSF supermini actuator drive
⎛
⎜
Before:
M=S
⎜
⎜
⎝
In the case of the RSF supermini actuator drive, as the reduction ratio is [R=30], [R=50], or [R=100] and
the square of the reduction ratio [R
⎞
L
⎟
+
1JJ
After:
⎟
2
⎟
R
⎠
2
=900], [R2=2500], or [R2=10000] the denominator and the
⎛
⎜
M=S
⎜
⎜
⎝
⎞
NL
⎟
+
1J'J
Ratio:
⎟
2
⎟
R
⎠
+
/JsJs'
=
11R/L
2
R/NL
2
+
numerator of the ratio are almost [1]. Then the ratio is [F≒1]. This means that drive systems are hardly
affected by the load moment of inertia variation. Therefore, it is not necessary to take the load moment
of inertia variation in consideration for selecting an RSF supermini actuator or for setting up the HA-680
driver.
2-3 Verifying loads
The RSF supermini series incorporates a precision 4-point contact ball bearing for direct support of
external load. To make full use of the performance of the RSF supermini series, check the maximum
load moment, life of the 4-point contact ball bearing, and static safety factor.
For detailed calculation methods for the maximum load moment, life of the 4-point contact ball bearing,
and static safety factor, refer to the “Harmonic Drive® CSF Mini series” catalogue.
RSF-super_V1_02 - 14 -
Chapter 2 Selection of the RSF supermini Series
2-4 Duty cycles
When a duty cycle includes many frequent start and stop operations, the actuator generates heat by big
starting and braking current. Therefore, it is necessary to study the duty cycle profile.
The study is as follows:
2-4-1 Actuator speed
Calculate the required RSF supermini
actuator speed (r/min) to drive the load.
Rotary speed (r/min) =
For linear motion, convert with the formula
below:
Select a reduction ratio from [30], [50] and
[100] of an RSF supermini actuator of which
the maximum speed is more than the
required speed.
Liner speed (mm/min)
Pitch of screw(mm)
Screw pitch (mm)
Speed (r/min)
45r/min
90r/min
100r/min
150r/min
200r/min
333r/min
Linear speed (mm/min)
2-4-2 Load moment of inertia
Calculate the load moment of inertia driven by the RSF supermini series actuator.
Refer to appendix 1 for the calculation.
Tentatively select an RSF supermini actuator referring to section [2-1 allowable load moment of inertia]
with the calculated value.
2-4-3 Load torque
Calculate the load torque as follows:
◆ Rotary motion
The torque for the rotating mass [W] on the friction
ring of radius [r] as shown in the figure to the right.
rW8.9T××μ×=
T: torque (N・m) μ: coefficient of friction
W: mass (kg)
r: radius of friction face (m)
The load torque is restricted by the allowable load of the actuator (refer to “1-10 Allowable load”) and
load moment of inertia as well as by the load driven by the actuator.
Examine them carefully before using the actuator.
Friction:μ
Mass: W
Radius: r
RSF-super_V1_02 - 15 -
Chapter 2 Selection of the RSF supermini Series
◆ Horizontal linear motion
The following formula calculates the torque for horizontal linear motion of mass [W] fed by the screw of
pitch [P].
P
××μ×=
W8.9T
π×
2
Pitch: P
T: torque (N・m) μ: coefficient of friction
W: mass (kg)
P: screw pitch (m)
◆ Vertical linear motion
The following formula calculates the torque for vertical linear
motion of mass [W] fed by the screw of pitch [P].
P
W8.9T
××=
π×
2
2-4-4 Acceleration time and deceleration time
Calculate acceleration and deceleration times for the selected actuator.
Acceleration:
()
JJt
LAa
2
×+=
60
N
π×
×
(1)
−
LM
TT
Mass: W
Friction: μ
Mass: W
Pitch: P
Deceleration:
()
JJt
LAd
2
π×
60
×
×+=
N
−×+
T
a: acceleration time (sec)
d: deceleration time (sec)
T
J
A: actuator inertia (kg・m
J
L: load moment of inertia (kg・m
2
)
2
)
N: actuator speed (r/min)
T
M: maximum torque of actuator (N・m)
T
L: load torque (N・m)
note that the polarity of the load torque is plus (+) for counter direction of revolution , and
minus (-) for same direction.
The friction torque of the actuator T
T
F=KT×IM-TM (3)
K
T : Torque constant [N・m/A]
M: Maximum current [A]
I
(N・m) can also be obtained from the following formula:
F
(2)
LFM
TT2T
Speed
N
Time
tatd
RSF-super_V1_02 - 16 -
r
p
● Example: 1
The load conditions are:
Chapter 2 Selection of the RSF supermini Series
• Rotary speed: 140r/min
• Load moment of inertia: 0.9×10
-3
kg・m2
• Load torque is so small as to be negrected.
• Acceleration/deceleration time is 0.03sec (30msec) or less.
(1) Compare these conditions with the “1-4 Specifications of RSF supermini actuators” and
temporarily select RSF-5A-50.
(2) Obtain J
A=1.83×10
-4
kg・m2, TM =0.9 N・m, KT=0.54 N・m/A, and IM =2.2A from “1-4 Specifications of
RSF supermini actuators.”
(3) The friction torque of the actuator is T
F = 0.54×2.2-0.9 = 0.29 N・m from Formula (3) on the
previous page.
(4) Therefore, the shortest acceleration time and deceleration time can be obtained from Formula (1)
and Formula (2), as follows:
t
a = (0.183×10
t
d = (0.183×10
-3
+0.9×10-3)×2×π/60×140/0.9 = 0.018 sec (18msec)
-3
+0.9×10-3)×2×π/60×140/(0.9+2×0.29) = 0.011 s (11msec)
(5) Because the assumed acceleration/deceleration time is 0.03sec (30msec) or less, the temporarily
selected actuator can be used for acceleration/deceleration, based on the result of (4).
(6) If the calculation results of the acceleration/deceleration time do not fall within the desired time
range, examine them again as follows.
• Try to reduce the load moment of inertia.
• Re-examine the gear ratio and gear head model.
2-4-5 Calculating equivalent duty
The load conditions, which are torque, speed,
moment of inertia, acceleration/deceleration time,
loading time, are limited by the actuator to drive the
load. To select the proper actuator, the equivalent
duty of the load should be calculated.
S
eed
N
ts: stop time
The %ED (percent equivalent duty) is:
tKtKtK
dLdrLraLa
ED%
=
t
×+×+×
100
×
(4)
where, ta: acceleration time in second
td: deceleration time in second
tr: driving time in second
t: single cycle time in second
K
La: duty factor for acceleration time
Lr: duty factor for driving time
K
Ld: duty factor for deceleration time
K
RSF-super_V1_02 - 17 -
ta
To rq u e
Ta, Tr, Td: output torque
t
t: duty cycle
td
Td
Time
ts
Time
Chapter 2 Selection of the RSF supermini Series
◆ Example 2: getting duty factors of KLa, KLr and KLd
As a result of Calculation Example 1 shown below, the selected actuator RSF-5A-50 works fine, so
RSF-5A-50 can be used for duty factor graphs.
Operation conditions:
• The inertial load is accelecated at the maximum torque of the actuator, and decelerated at the
maximum torque after operation at a fixed speed.
• The movement angle θ of one cycle is 120°.
• The duration of one cycle is 0.4 (s).
• The other conditions are the same as Calculation Example 1.
(1) KLa and KLd: The average speed during the rotation speed change from 0 to 140r/min is 70r/min.
From the duty factor graphs, K
Lr: Tr≒0 for the inertial load. Similarly, from the duty factor graphs, KLr≒0.29 can be read.
(2) K
La=KLd≒1.5 can be obtained.
(3) The movement angle can be obtained from the area in the “Rotation speed-Time” diagram above.
In other words, the movement angle θ can be expressed as follows:
θ = (N / 60) x {tr + (ta + td) / 2} x 360
Solving the formula above for tr (operation time at a fixed speed of N), the following can be
obtained.
tr = θ/ (6 x N) – (ta + td) / 2
Substituting θ= 120° and ta= 0.03(s), td= 0.03(s), and N= 140r/min from Example 1, tr=0.113(s).
(4) Because the cycle time is 0.4(s), the %ED is obtained as follows:
%ED = (1.5x 0.03 + 0.29 x 0.113 + 1.5 x 0.03) / 0.4 x 100 = 30.7%
Because the value of %ED obtained is below 100, continuous repeated operation of this cycle can
be done.
If the %ED is exceeded 100%, correct the situation by:
• Changing the speed-time profile
• Reducing load moment of inertia
RSF-5A-50-E050-C
1.0
0.8
0.6
0.4
トルク[Nm]
Torque [Nm]
0.2
Estimation line for
KL=0.29
KL=0.33
0.67
Radiation plate: 150×150×3[mm]
(1) KLa, KLd
1.5
1
Allowed range
(2) KLr
0.0
050100150200250
RSF-super_V1_02 - 18 -
70
140
回転速度[r/min]
Speed [r/min]
Graphs of duty factor
RSF-3
B-30-E020-C
Chapter 2 Selection of the RSF supermini Series
0.1
0.09
0.08
0.07
0.06
0.05
0.04
トルク[Nm]
Torque [Nm]
0.03
0.02
0.01
1.5
1.0
0.67
KL=0.33
0
050100150200250300350
回転速度 [r/min]
Radiation plate: 85×85×3[mm]
Speed [r/min]
Allowed range
運転可能領域
RSF-3B-50-E020-C
RSF-3B-100-E020-C
0.16
0.14
0.12
0.1
0.08
0.06
トルク[Nm]
Torque [Nm]
0.04
0.02
0.25
0.15
トルク[Nm]
Torque [Nm]
Radiation plate: 85×85×3[mm]
運転可能領域
Allowed range
1.5
1.0
0.67
KL=0.33
0
050100150200250
Speed [r/min]
回転速度 [r/min]
Radiation plate: 85×85×3[mm]
Allowed range
0.2
0.1
0.67
KL=0.33
運転可能領域
0.05
0
RSF-super_V1_02 - 19 -
020406080100120
Speed [r/min]
回転速度 [r/min]
Torque [Nm]
Torque [Nm]
Torque [Nm]
Chapter 2 Selection of the RSF supermini Series
RSF-5A-30-E050-C
0.6
0.5
0.4
0.3
トルク「Nm]
0.2
0.1
0.0
050100150200250300350
0.67
KL=0.33
Radiation plate: 150×150×3[mm]
Allowed range
1.5
1
Speed [r/min]
回転速度[r/min]
RSF-5A-50-E050-C
1.0
0.9
0.8
0.7
0.6
0.5
トルク[Nm]
0.4
0.3
0.2
0.1
0.0
KL=0.33
050100150200250
Radiation plate: 150×150×3[mm]
1.5
1
0.67
Allowed range
回転速度[r/min]
Speed [r/min]
RSF-5A-100-E050-C
1.6
1.4
1.2
1.0
0.8
トルク「Nm]
0.6
0.4
0.2
KL=0.33
Radiation plate: 150×150×3[mm]
Allowed range
0.67
RSF-5A-30-E050-BC
0.6
0.5
0.4
0.3
トルク[Nm]
Torque [Nm]
0.2
0.1
0.0
KL=0.33
050100150200250300350
Radiation plate: 150×150×3[mm]
2
1.5
1
0.67
Speed [r/min]
回転速度[r/min]
Allowed range
RSF-5A-50-E050-BC
1.0
0.9
0.8
0.7
0.6
0.5
トルク[Nm]
0.4
Torque [Nm]
0.3
KL=0.33
0.2
0.1
0.0
050100150200250
Radiation plate: 150×150×3[mm]
2
Allowed range
1.5
1
0.67
Speed [r/min]
回転速度[r/min]
RSF-5A-100-E050-BC
1.6
1.4
1.2
1.0
0.8
トルク[Nm]
0.6
Torque [Nm]
0.4
0.2
KL=0.33
Radiation plate: 150×150×3[mm]
1
0.67
Allowed range
0.0
020406080100120
RSF-super_V1_02 - 20 -
Speed [r/min]
回転速度[r/min]
0.0
020406080100120
Speed [r/min]
回転速度[r/min]
Chapter 2 Selection of the RSF supermini Series
2-4-6 Effective torque and average speed
Addionally to the former studies, the effective torque and the average speed should be studied.
(1) The effective torque should be less than allowable continuous torque specified by the driver.
(2) The average speed should be less than allowable continuous speed of the actuator.
Calculate the effective torque and the average speed of an operating cycle as shown in “2-4-5
Calculating equivalent duty”.
m: effective torque (N・m)
m
T
=
()
22
tTttT
rrdaa
×++×
t
N
tNt
t
dra
×+×+×
2
N
av
N
2
=
t
If the calculation results for the effective torque and average rotation speed are not within the range of
continuous usage in the graph shown in “1-14 Usable range,” take measures to reduce the duty.
T
T
a: maximum torque (N・m )
T
r: load torque (N・m)
a: acceleration time (s)
t
d: deceleration time (s)
t
r: running time at constant speed (s)
t
t: time for one duty cycle (s)
av: average speed (r/min)
N
N: driving speed (r/min)
◆ Example 3: getting effective torque and average speed
Effective torque and average speed are studied by using the operation conditions of Example 1 and 2.
1) Effective torque
From the parameters of T
2
T
m⋅=
=
()
a = 8.3 N・m, Tr = 0 N・m, ta = 0.113 s, tr = td = 0.03 s, t=0.4 s,
03.003.09.0
+×
mN349.0
4.0
The value exceeds the allowable continuous torque (0.29 N・m) of RSF-5A-50 temporarily selected in
Example 1, so continuous operation cannot be done using the cycle set in Example 2. The following
formula is the formula for effective torque solved for t. By substituting the value of allowable
continuous torque in T
t
=
Substituting 0.9 N・m for T
d :
t
t
=
()
2
()
0.29
Namely, when the time for one duty cycle is set more than 0.578 s, the effective torque [T
less than 2.9 N・m, and the actuator can drive the load with lower torque than the continuous torque
continuously.
of this formula, the allowable value for one cycle time can be obtained.
m
22
rrdaa
tTttT
×++×
2
m
T
a, 0 N・m for Tr , 0.349 N・m for T
0.030.030.9
+×
2
=
]s[578.0
, 0.03 s for ta ,0.113 s for tr, and 0.03 s for
m
m] becomes
2) Average speed
From the parameters of N = 140 r/min, ta = 0.03 s, tr = 0.113 s, td = 0.03 s, t = 0.4 s
140
N
av=
=
2
0.1131400.03
140
0.03
×+×+×
2
][r/min64.34
0.578
As the speed is less than the continuous speed (90 r/min) of RSF-5A-50, it is possible to drive it
continuously on new duty cycle.
RSF-super_V1_02 - 21 -
Chapter 2 Selection of the RSF supermini Series
2-4-7 Permissible overloaded time
In case RSF supermini series is intermittently operated in allowable continuous torque or more, the
overloaded time is limited by the protective function in the driver even if the duty cycle is allowed. The
limits are shown in the figure below.
RSF-3B-50
RSF-3B-100
Loaded time [s]
Loaded time [s]
RSF-3B-30
Torque [Nm]
RSF-5A-50
RSF-5A-100
RSF-5A-30
Torque [Nm]
RSF-super_V1_02- 22 -
Chapter 3 Installing the actuator
Chapter 3 Installing the actuator
3-1 Receiving Inspection
Check the following when products are received.
● Inspection procedure
(1) Check the shipping container and item for any damage that may have been caused during
transportation. If the item is damaged, immediately report the damage to the dealer it was
purchased from.
(2) A label is attached on the right side of the RSF supermini series actuator. Confirm the products you
ordered by comparing with the model on the [TYPE] line of the label. If it is different, immediately
contact the dealer it was purchased from.
The model code is interpreted as follows:
RSF-5 A-50-E 050-C
For details of model symbols, refer to “1-2 Models” on page 2.
RSF series actuator
Frame size
Design version
Reduction ratio of Harmonic drive® gearing
Encoder specifications
Number of pulses of the encoder
Specification
(3) On the label of the HA-680 driver, the model code of the actuator to be driven is indicated on the
[ADJUSTED FOR USE WITH] line. Match the actuator with its driver so as not to confuse the item
with the other actuators.
WARNING
(4) The HA-680 driver is for 24VDC supply voltage only. Any power supply voltage other than
24VDC cannot be used.
WARNING
Only connect the actuator specified on the driver label.
The drivers have been tuned for the actuator specified on the driver label. Wrong
combination of drivers and actuators may cause low torque problems or over current
that may cause physical injury and fire.
Do not connect a supply voltage other than the voltage specified
on the label.
The wrong power supply voltage (other than 24VDC) may damage the driver resulting
physical injury and fire.
RSF-super_V1_02 - 23 -
Chapter 3 Installing the actuator
3-2 Notice on handling
Handle RSF supermini series actuators with care, specifically:
WARNING
CAUTION
Do not plug the actuators directly into a commercial line power
source.
This could burn out the actuator, potentially resulting in a fire and/or electrical hazard.
(1) Do not apply impact or unnecessary excessive force to output
flange of actuators.
(2) Do not put actuators on in a location where the driver could
easily fall.
(3) The allowable temperature for storage is from -20°C to +60°C.
Do not expose it to the sunlight for a long time and do not
store it in areas with widely fluctuating temperatures.
(4) The allowable relative humidity for storage is less than 80%.
Do not storage it in highly humid place or in a place where
temperature changes excessively during the course of a day.
(5) Do not store units in locations with corrosive gas or particles.
RSF-super_V1_02 - 24 -
Chapter 3 Installing the actuator
3-3 Location and installation
3-3-1 Environment of location
The environmental conditions of the location for RSF supermini series actuators must be as follows.
Service temperature: 0°C to 40°C
When the actuator is installed in a closed space, the temperature in the
space may be higher than the atmosphere because of heat emission by the
actuator. Design the closed space size, ventilation system, and device
locations so the ambient temperature near the actuator is always less than
40°C.
Service humidity: 20 to 80% relative humidity, without condensation
Make sure no water condensation occurs at the place where there is a large
temperature change in a day or due to frequent heat-and-cool cycles due to
the operation of the actuator.
2
Vibration: less than 49m/sec
Impact: less than 300 m/sec
Make sure the actuator is in an area free from: dust, water condensation, metal powder, corrosive
gas, water, water drops, and oil mist.
(10Hz~400Hz)
2
Locate the driver indoors. Do not expose it to the sunlight.
3-3-2 Considerations into External Noise
Pay sufficient attention when installing the actuator: The actuator may malfunction by external noise
depending on the conditions of installation.
Make sure that the FG line of RSF-5A is securely grounded.
Because RSF-3B does not have any FG line from the motor enclosure. Thus, when using it,
make sure that that enclosure is securely grounded to the body of the equipment through the gear
head house. In addition, make sure that the body of the equipment is securely grounded.
Do not bind the motor line and encoder signal line together.
Do not draw any external power line (i.e., driver power supply line, 100/200 VAC line.), actuator
signal line, and motor line through the same pipe or duct or bind them together.
The noise tolerance values of RSF supermini equipment are listed below.
They are guide values from a measurement that were performed using a standard relay cable in a
noise test environment while the clamp filter included with the product was installed to the equipment.
Note that the noise tolerance values in your actual environment of use may differ from them.
Model
Noise tolerance (encoder signal line)
RSF-3B RSF-5A
Vk0.2 Vk5.1
RSF-super_V1_02- 25 -
Chapter 3 Installing the actuator
3-3-3 Installation
Since the RSF supermini series actuator is a high precision servo mechanism, great care is required for
proper installation.
Install the actuator taking care not to damage accurately machined surfaces. Do not hit the actuator
with a hammer. Take note that actuators provide a glass encoder, which may be damaged by impact.
● Procedure
(1) Align the axis of rotation of the actuator and the load mechanism precisely.
Note 1: Very careful alignment is required especially when a rigid coupling is applied. Slight
differences between centerlines will cause failure of the output shaft of the actuator.
Note 2: When installing the actuator to a coupling, use a plastic hammer to avoid excessive
physical shocks.
(2) Fasten the flange of the actuator with flat washers and high strength bolts. Use a torque wrench
when tightening the fasteners.
The recommended tightening torque is shown in the table below:
Model RSF-3B RSF-5A
Number of bolts 4 2
Bolt size M1.6
Installation PCD mm
Wrenching torque
Transfer torque
Recommended bolt: JIS B 1176 bolt with hexagonal hole; Strength category: JIS B 1051 12.9 or greater
N・m
kgf・cm
N・m
kgf・cm
15
0.26
0.03
3.0
0.2
(3) For wiring operation, refer to “AC Servo Driver for 24VDC Power Supply HA-680 Series Technical
Data.”
M2
25
0.25
0.03
2.0
0.2
(4) Motor cable and encoder cable
Do not pull the cable. Do not hang the actuator with the cable. If you do, the connection part
may be damaged. Install the cable with slack not to apply tension to the actuator. Especially, do
not use the actuator under any condition where the cable is bent repeatedly.
CAUTION
Do not disassemble and re-assemble the actuator.
The Harmonic Drive Systems, Inc. does not guarantee the actuator that has been
reassembled by others than the authorized persons by the Harmonic Drive Systems,
Inc.
RSF-super_V1_02 - 26 -
Chapter 4 Motor shaft retention brake
Chapter 4 Motor shaft retention brake(RSF-5A)
The RSF supermini series provides an actuator with a motor shaft retention brake as standard (Option
symbol: B), which can meet the fail-safe requirement without any additional brake.
The brake has 2 coils; one for releasing brake, and another for retaining the released state. By
controlling the currents through the coils, power consumption during retention of brake release can be
reduced.
4-1 Motor shaft retention brake specifications
Gear ratio
Item
Method
Brake operating voltage V 24VDC±10%
Current consumption during release
(at 20°C)
Current consumption during retention
of release (at 20°C)
Retention torque Note 1
Moment of inertia Note 1
Weight Note 2 g 86.0
Number of allowable brake
operations
Note 1: This is a value at the output shaft of the actuator.
Note 2: This is a value for the entire actuator.
Note 3: The motor shaft rotation speed is controlled as shown in the following table.
Gear ratio
Note 3 100,000 times
1:30 5.0
1:50 3.0
1:100 1.5
A 0.8
A 0.05
N・m 0.18 0.29 0.44
kgf・cm 1.84 2.96 4.49
(GD2/4)
kg・cm2
(J)
kgf・cm・s
Output shaft rotation speed
2
[r/min]
30 50 100
Single disc dry type deenergisation operation type
(Separate attraction coil and retention coil)
0.111 10-3 0.309 10-3 1.234 10-3
1.132 10-3 3.151 10-3 12.58 10-3
Motor shaft rotation speed
[r/min]
150
4-2 Controlling the brake power supply
4-2-1 Using a relay cable (Recommended method)
The optional relay cables for brakes (EWA-B -JST 03-TMC) incorporate a circuit that controls the
brake current.
You don’t have to control the brake current, so it is recommended to use the actuator with a brake in
combination with a relay cable for brakes.
If the relay cable for brakes is used, brake can be operated by turning on/off the brake power supply.
The power supply for the brake (that can output 24VDC±10%) shall be provided by the customer. Use
a power supply unit that can output the current during release as described in “4-1 Motor shaft retention
brake specifications.”
The supply duration of the current consumption during release is 0.5sec or less at 24VDC±10%.
RSF-super_V1_02 - 27 -
Chapter 4 Motor shaft retention brake
4-2-2 Not using a relay cable
If the optional relay cable for brakes (EWA-B -JST 03-TMC) is not used, the customer must control the
brake power supply to the brake release coil and release retention coil.
Supply the power upon brake release and during brake release retention, as shown below.
Lead wire color Applied voltage
Upon brake
release
During release
retention
During brake use
Supply the power to the coils according to the following time chart.
Control the power supply so that the duration in which the power is supplied to the brake release coil
(gray/yellow) is 100ms or less. The brake will not be released only by the power supply to the brake
release retention coil. To release the brake, also supply the power to the brake release coil.
Warning
The power supply to the brake must be controlled.
Control the power supply to the brake as described in “4-2 Controlling the brake power
supply.” If the current flows continuously to the attraction coil, the actuator burns due
to temperature rise, causing fire or electric shock.
Warning
Be careful not to exceed the number of allowable brake operations
(Refer to “4-1 Motor shaft retention brake specifications”).
If the number is exceeded, the retention torque drops and it cannot be
used as a brake.
RSF-super_V1_02 - 28 -
Chapter 5 Options
Chapter 5 Options
5-1 Relay cables
There are relay cables that connect the RSF supermini series actuator and driver.
There are 3 types of relay cables for encoders, motors, and brakes. Select an appropriate type
according to the model of the actuator you ordered.
● Relay cable model (XX indicates the cable length 3m, 5m, or 10m.)
(1) For encoders
EWA-E××
-M09-3M14
(2) For motors
EWA-M××
-JST04-TN2
Round crimp-style
terminal
1.25-4
Mfg by Omron
XW4B-06B1-H1
(3) For brakes
Wafer right angle type
53048-0910
Mfg by Molex
Cable length (03=3m, 05=5m, 10=10m)
Shield
E Green/Yellow
Cable length (03=3m, 05=5m, 10=10m)
Clamp filter
ZCAT2032-0930 (TDK)
W Black
V White
U Red
Clamp filter
ZCAT2032-0930 (TDK)
Connector: 10114-3000VE
Cover: 10314-52F0-008
Mfg by 3M
Mfg by J.S.T. Mfg. Co., Ltd.
PARP-04V
EWA-B××
-JST03-TMC
Cable length (03=3m, 05=5m, 10=10m)
Round crimp-style
terminal
1.25-4
RSF-super_V1_02 - 29 -
Application of 24VDC (non polar)
Mfg by J.S.T. Mfg. Co., Ltd.
PARP-03V
Chapter 5 Options
5-2 Relay cable wire bound specifications
The following tables show the wire bound specifications of the relay cables.
(1) For encoders (EWA-E -M09-3M14 )
Actuator side
Pin NO.
1 A phase 6 W phase 1 +5V 8 GND
2 B phase 7 +5V 2 B+ phase9 U+ phase
3 Z phase 8 GND 3 Z+ phase10 U- phase
4 U phase 9 N.C. 4 B- phase 11 V+ phase
5 V phase 5 A+ phase12 V- phase
Driver side
Signal
name
Pin NO.
Connector: 53048-0910
(2) For motors (EWA-M -JST04-TN2)
Actuator side
Pin NO. Signal name Signal nameConnector
1 U phase U phase
2 V phase V phase
3 W phase W phase
4 FG FG
Connector Housing: PARP-04V
Driver side
Retainer: PMS-04V-S
Contact: S(B)PA-001T-P0.5
Signal
name
Molex
Pin NO.
Shield
J.S.T. Mfg Co.,Ltd
Signal
name
6 Z- phase 13 W+ phase
7 A- phase 14 W- phase
Connector: 10114-3000VE
Cover: 10314-52F0-008
Round crimp-style terminal 1.25-4
Pin NO. Signal name
XW4B-06B1-H1
Omron
With insulating coating
3M
(3) For brakes (EWA-B -JST03-TMC)
Actuator side
Pin NO. Wire color Wire color Connector
1 Red
2 White
3 Black
Power supply side for brake
Housing: PARP-03V
Contact: S(B)PA-001T-P0.5
Connector Retainer: PMS-03V-S
J.S.T. Mfg Co.,Ltd
Red, black
(nonpolar)
Round crimp-style terminal 1.25-4
With insulating coating
RSF-super_V1_02 - 30 -
Chapter 5 Options
5-3 Connectors
There are 2 types of connectors for the driver for different set types:
● Connector model: CNK-HA68-S1
For CN1, CN2, actuator line connection, power supply connection ......................... 4 types
● Connector model: CNK-HA68-S2
For CN2, power supply connection...........................................................................2 types
Connector for CN1
Mfg by Sumitomo 3M
Connector type: 10114-3000VE
Case type: 10314-52F0-008
Connector for actuator connection
Mfg by Phoenix Contact
Model: MC1.5/6 – ST – 3.81
Or
Mfg by Omron
Model: XW4B – 06B1 – H1
Connector for CN2
Mfg by Sumitomo 3M
Connector type: 10150-3000VE
Case type: 10350-52F0-008
Connector for power supply
Mfg by Phoenix Contact
Model: MC1.5/5 – ST – 3.81
Or
Mfg by Omron
Model: XW4B – 05B1 – H1
RSF-super_V1_02 - 31 -
Appendix 1 Conversion of unit
Appendix 1 Conversion of unit
This technical manual basically uses the SI unit system. The conversion coefficients between the SI unit
system and other unit systems are shown below.
(1) Length
SI unit m Unit ft. in.
Coefficient0.3048 0.0254
Unit ft. in.
Coefficient 3.281 39.37 SI unit m
(2) Linear speed
SI unit m/s Unit m/minft./min ft./s in/s
Coefficient0.0167 5.08x10-3 0.3048 0.0254
Unit m/min ft./min ft./s in/s
Coefficient 60 196.9 3.281 39.37SI unit m/s
(3) Linear acceleration
SI unit m/s2 Unit m/min2ft./min2 ft./s2 in/s2
Coefficient 2.78 x10-48.47x10-5 0.3048 0.0254
Unit m/min2 ft./min2 ft./s2 in/s2
Coefficient 3600 1.18x104 3.281 39.37 SI unit m/s2
(4) Force
SI unit N Unit kgf lb (force) oz (force)
Coefficient9.81 4.45 0.278
Unit kgf lb (force) oz (force)
Coefficient 0.102 0.225 4.386 SI unit N
(5) Mass
SI unit kg Unit lb. oz.
Coefficient0.4535 0.02835
Unit lb. oz.
Coefficient 2.205 35.27 SI unit kg
RSF-super_V1_02
-Appendix 1-1 –
(6) Angle
Appendix 1 Conversion of unit
SI unit rad Unit Deg. Min. Sec.
Coefficient0.01755 2.93x10-4 4.88x10
Unit Deg. Min. Sec.
Coefficient 57.3 3.44x103 2.06x105 SI unit rad
(7) Angular speed
SI unit rad/s Unit Deg./sDeg./min r/s r/min
Coefficient0.017552.93x10-4 6.28 0.1047
Unit
Coefficient 57.3 3.44x103 0.1592 9.55 SI unit rad/s
Deg./s Deg./min
r/s r/min
(8) Angular acceleration
SI unit rad/s2 Unit Deg./s2 Deg./min2
Coefficient0.01755 2.93x10-4
Unit Deg./s2 Deg./min2
Coefficient 57.3 3.44x103 SI unit rad/s2
(9) Torque
SI unit Nm Unit kgfm lbft lbin ozin
Coefficient9.81 1.356 0.1130 7.06x10
Unit kgfm lbft lbin ozin
Coefficient 0.102 0.738 8.85 141.6 SI unit Nm
-6
-3
(10) Moment of inertia
SI unit kgm2
Unit kgfms
Coefficient 0.102 10.2 23.73 0.7376 3.42x10
2
kgfcms
2
lbft2 lbfts2 lbin2 lbins2 ozin2 ozins2
3
8.85 5.47x104 141.6
Unit kgfms
Coefficient 9.81 0.0981 0.04211.356 2.93x10
SI unit kgm2
2
kgfcms
2
lbft2 lbfts2 lbin2 lbins2 ozin2 ozins2
-4
0.113 1.829x10-5 7.06x10
(11) Torsional spring constant, moment of rigidity
SI unit Nm/rad
Unit kgfm/rad
Coefficient 0.102 2.97 x10-5 1.78x10
Unit kgfm/rad Kgfm/arc min kgfm/Deg.lbft/Deg.lbin/Deg.
Coefficient 9.81 3.37 x104 562 77.6 6.47
SI unit Nm/rad
kgfm/arc min
kgfm/Deg.lbft/Deg.lbin/Deg.
-3
0.0129 0.1546
-3
RSF-super_V1_02
-Appendix 1-2 –
A
A
Appendix 2 Calculations of moment of inertia
Appendix 2 Calculations of moment of inertia
1. Calculation formulas for mass and moment of inertia
(1) When center of revolution and line of center of gravity match
Calculation formulas for mass and moment of inertia are shown below.
m: Mass (kg)
Ix, Iy, Iz: moment of inertia (kgm
2
) making Axes x, y and z as centers of revolution
G: Distance from edge surface of center of gravity
ρ: Specific gravity
Units - Length: m, mass: kg, moment of inertia: kgm
Shape of object
Circular cylinder Round pipe
z
R
x
y
L
Tilted circular cylinder Sphere
R
θ
Mass, inertia,
position of center of gravity
ρLRm2π=
1
Ix =
Iy
Iz
2
Rm
2
⎛
1
⎜
⎜
4
⎝
⎛
1
⎜
⎜
4
⎝
2
⎞
L
2
⎟
+=
Rm
Rm
⎟
3
⎠
2
⎞
L
2
⎟
+=
⎟
3
⎠
ρLRm2π=
Shape of object
z
R1
x
R2
L
R1: Outside diameter
R2: Inside diameter
y
R
1
m
I
=
θ
12
(
{}
)
2222
θθ
sinLcos13R
++×
L
Mass, inertia,
position of center of gravity
2
R
+= π
2
2
)
RRm
2
L
2
)
++=
RRm
2
L
2
)
++=
RRm
2
3
Ix+=
Iy
Iz
mπ=
I =
2
⎛
Rm
⎜
1
⎝
1
2
(
1
2
⎧
1
⎪
2
(
⎨
1
4
⎪
⎩
⎧
1
⎪
2
(
⎨
1
4
⎪
⎩
4
ρ3R
3
2
2
Rm
5
2
⎞
ρL
⎟
⎠
2
⎫
⎪
⎬
3
⎪
⎭
2
⎫
⎪
⎬
⎪
⎭
Elliptic circular cylinder Cone
z
B
x
L
Prism Regular square pipe
B
z
x
RSF-super_V1_02
y
C
y
C
Ix+=
Iy
Iz
Ix+=
Iy+=
Iz+=
16
1
4
12
12
1
4
12
1
1
ρLBCm π=
1
⎛
⎜
m
⎜
⎝
⎛
⎜
m
⎜
⎝
1
22
(
C
B
(
(
(
)
CBm
22
⎞
L
⎟
+=
⎟
3
4
4
ρA BCm =
⎠
22
⎞
L
⎟
+=
⎟
3
⎠
22
)
CBm
22
)
ACm
22
)
BAm
x
D
x
z
R
G
y
L
B
z
y
- Appendix 2-1 -
mππ=
Ix =
Iy+=
Iz+=
G =
Ix+=
Iy++=
Iz++=
ρL2R
3
3
2
Rm
10
3
(
80
3
(
80
L
4
()
1
()
{}
3
1
2
{}
6
1
2
{}
6
22
)
L4Rm
22
)
L4Rm
ρD-B4AD=m
2
2
DD-Bm
2
()
()
2
DD-BAm
2
2
DD-BAm
A
r
A
A
A
Shape of object
z
B
x
Equilateral triangular
prism
z
G
x
B
Appendix 2 Calculations of moment of inertia
Mass, inertia,
position of center of gravity
1
ρ
ABC
m =
2
1
Ix+=
C
Iy+=
y
Iz+=
m =
Ix
C
Iy
y
Iz
G =
24
24
24
(
1
(
1
1
ρABC
2
B
1
m
(
2
12
1
Am
(
12
1
Am
(
12
C
3
Shape of object
msirp nogaxeh ralugeR msirp cibmohR
22
CBm
)
22
)
2ACm
22
2ABm
2
2
2
+=
C
)
3
2
22
+=
C
)
3
2
B
2
+=
)
2
B√ 3
x
Right-angled triangular
prism
G
x
z
Ix =
Iy
B
y
Iz
z
1
C
G2
y
A
B
Mass, inertia,
position of center of gravity
33
2
ρ
AB
=m
2
5
2
Bm
12
5
22
+=
B
Am
(
Am
(
(
Am
(
Am
(
)
2
5
22
+=
B
)
2
22
CBm
)
2
22
+=
C
)
3
2
22
+=
B
)
3
B
=
G
2
3
m =
Ix+=
Iy
Iz
G
1
12
12
1
1
=
1
2
1
36
1
12
1
12
C
3
ABC ρ
Example of specific gravity
The following table shows informative values of specific gravity. Please check actual specific gravities of
materials individually.
Material Specific gravity Material Specific gravityMaterial Specific gravity
(2) When center of revolution and line of center of gravity do not match
Moment of inertia when axis of center of gravity and axis of revolution of an inertia field do not match is
calculated by the following formula.
2
mFIgI+=
I: Moment of inertia when axis of center of gravity and axis of
revolution do not match (kgm
Ig: Moment of inertia when axis of center of gravity and axis of
revolution match (kgm
2
)
2
)
Calculated by formula shown in (1) in accordance with shape.
Axis of
revolution
F
xis of cente
of gravity
m: Mass (kg)
F: Distance between axis of revolution and axis of center of gravity (m)
(3) Moment of inertia of linear motion object
The moment of inertia converted into an RSF-supermini actuator axis of a linear motion object driven
by a screw is calculated by the following formula.
mIπ=
P
()
2
2
2
)
I: Moment of inertia converted into actuator axis of a linear motion object (kgm
m: Mass (kg)
P: Amount of linear movement per revolution of actuator (m/rev)
RSF-super_V1_02
- Appendix 2-2 -
4
5
6
4
5
6
Appendix 2 Calculations of moment of inertia
2. Moment of inertia of circular cylinder
Approximate values of moment of
inertia of circular cylinder can be
calculated from the graph on the
right.
Length
Radius
The top graph is applied to
aluminum (specific gravity 2.7) and
the bottom graph, to steel (specific
gravity 7.85).
Since the outside diameter is
100mm, the radius is 50mm.
Based on the top graph, moment of
inertia is about 1.9 x 10-4 kgm
(Calculated value: 0.000186kgm
2
.
2
)
RSF-super_V1_02
1
0.1
0.01
0.001
-
10
-
10
-
10
10100100020305070200 300 500 700
Radius R (mm)
- Appendix 2-3 -
1
Warranty Period and Terms
The RSF supermini series actuators are warranted as follows:
Warranty period
•
Under the condition that the actuator are handled, used and maintained properly
followed each item of the documents and the manuals, all the RSF supermini series
actuators are warranted against defects in workmanship and materials for the shorter
period of either one year after delivery or 2,000 hours of operation time.
Warranty terms
•
All the RSF supermini series actuators are warranted against defects in workmanship
and materials for the warranted period. This limited warranty does not apply to any
product that has been subject to:
(1) user's misapplication, improper installation, inadequate maintenance, or misuse.
(2) disassembling, modification or repair by others than Harmonic Drive LLC.
(3) imperfection caused by the other than the RSF supermini series actuator and the
HA-655/675/680 servo driver.
(4) disaster or others that does not belong to the responsibility of Harmonic Drive LLC.
Our liability shall be limited exclusively to repairing or replacing the product only found
by Harmonic Drive LLC to be defective. Harmonic Drive LLC shall not be liable for
consequential damages of other equipment caused by the defective products,
and shall not be liable for the incidental and consequential expenses and the labor
Harmonic Drive LLC
Boston
247 Lynnfield Street
Peabody, MA 01960
800-921-3332
F: 978-532-9406
www.HarmonicDrive.net
Worldwide Locations:
Harmonic Drive Systems, Inc.
Minamiohi 6-25-3, Shinagawa-ku
Tokyo 140, Japan
Harmonic Drive AG
Hoenbergstr, 14
Limburg/Lahn, D-65555 Germany
RSF manual rev_01-08
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