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Appendix 2 Moment of inertia

m = ABC

:outer, R

:inner

Appendix 2 Moment of inertia

1.Calculation of mass and moment of inertia

(1) Both centerlines of rotation and gravity are the same:

The following table includes formulas to calculate mass and moment of inertia.

m: mass (kg); Ix, Iy, Iz: moment of inertia for rotation center of x-, y-, z-axis respectively (kg•m2);
G: distance from gravity center to the surface;

: specific gravity

Unit Length: m; Mass: kg; Inertia: kg•m2

Object form

Mass, inertia, gravity center

Object form

Mass, inertia, gravity center

Cylinder

Circular

pipe

Slanted

cylinder

Ball

Ellipsoidal

cylinder

Cone

Rectangular

pillar

Square

pipe

Содержание FHA Series

Страница 1: ...H O L L O W S H A F T A C T U A T O R S 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 Total Motion Control FHA Series...

Страница 2: ...FHA C series...

Страница 3: ...es 24 2 4 1 Actuator speed 24 2 4 2 Load inertia 24 2 4 3 Load torque 24 2 4 4 Acceleration time and deceleration time 25 2 4 5 Calculating equivalent duty 26 2 4 6 Effective torque and average speed...

Страница 4: ...in this document may not be used for the following applications Space equipment Automobile automotive parts Aircraft aeronautic equipment Amusement equipment sport equipment game machines Nuclear equi...

Страница 5: ...r at one single point minimum ground resistance class D less than 100 ohms Do not use a power line filter in the motor circuit Pay attention to negative torque by inverse load Inverse load may cause d...

Страница 6: ...s 30 flatter than our previous models The compact size allows smaller machines to be designed Through hole shaft The center through hole shaft allows for the insertion of electric cables air pipes or...

Страница 7: ...lic mechanism with position sensors D 5 meter cables 5m for each motor cable and encoder cable F5 24V available for FHA 17C only E Note 1 For more details refer to chapter 4 Note 2 For requirement of...

Страница 8: ...llowable Radial Load kN 2 9 4 9 9 5 14 7 Allowable Axial Load kN 9 8 14 7 24 5 39 2 Allowable Torsional Moment N m 188 370 530 690 Moment stiffness N m rad 220x103 490x103 790x103 1400x103 One way Pos...

Страница 9: ...50 1 100 1 60 1 50 1 100 1 60 Allowable Radial Load kN 2 9 4 9 9 5 14 7 Allowable Axial Load kN 9 8 14 7 24 5 39 2 Allowable Torsional Moment N m 188 370 530 690 Moment stiffness N m rad 220x103 490x...

Страница 10: ...5 1 Incremental Systems INC The external drawings are shown as follows FHA 17C xx US250 INC FHA 25C xx US250 INC Note 1 The parenthesized dimensions are applied for the actuators with a brake option...

Страница 11: ...he FHA C series Unit mm third angle projection FHA 32C xx US250 INC FHA 40C xx US250 INC Note 1 The parenthesized dimensions are applied for the actuators with a brake option Note 2 For detail dimensi...

Страница 12: ...ems ABS The external drawings are shown as follows FHA 17C xx S248 ABS FHA 25C xx S248 ABS Note 1 The parenthesized dimensions are applied for the actuators with a brake option Note 2 For detail dimen...

Страница 13: ...the FHA C series Unit mm third angle projection FHA 32C xx S248 ABS FHA 40C xx S248 ABS Note 1 The parenthesized dimensions are applied for the actuators with a brake option Note 2 For detail dimensio...

Страница 14: ...ll values are T I R Total Indicator Reading The measuring for the values are as follows Axial run out of output flange The indicator 1 on a fixed portion measures the axial run out T I R of perimeter...

Страница 15: ...or 1 160 by the Harmonic drive component the resolution of the output flange is 50 or 100 or 160 times the encoder revolution Additionally the incremental encoder signal is used in signal is used in...

Страница 16: ...rque region over T2 2 K3 Wind up The table below shows T1 T3 K1 K3 and 1 2 values of each actuator Model FHA 17C FHA 25C FHA 32C FHA 40C Reduction Ratio 1 50 1 100 1 160 1 50 1 100 1 160 1 50 1 100 1...

Страница 17: ...nce The allowable vibration from all directions is as follows Vibration acceleration 24 5 m s2 Frequency 10 400Hz 1 13 Torque speed characteristics The following are actuator speed torque characterist...

Страница 18: ...18 mm Torque Nm Speed r min 50 duty range Continuous range Radiation plate 300x300x15 mm Torque Nm Speed r min 50 duty range Continuous range Radiation plate 350x350x18 mm Torque Nm Speed r min 50 dut...

Страница 19: ...d r min Acc dec range 50 duty range Continuous range Radiation plate 400x400x20 mm Torque Nm Speed r min Acc dec range 50 duty range Continuous range Radiation plate 500x500x25 mm Torque Nm Speed r mi...

Страница 20: ...r phase W Motor phase W Green yellow PE PE Blue No connection Brake Yellow No connection Brake Shield FG FG Encoder Lead for 14 Wire Incremental Encoder INC Color Signal Color Signal Red Vcc Black GND...

Страница 21: ...the actuator output shaft Figure 1 a b c d 1 4T 1 10T a b b c 1 2T 1 8T Tz 1 2T 3 2T The Z phase includes a HIGH state in case of both of A and B phase is HIGH state T 360 2500 a 10 Mechanical angle F...

Страница 22: ...iable load inertia FHA C series actuators include Harmonic Drive gearing that has a high reduction ratio Because of this there are minimal effects of variable load inertias to the servo drive system I...

Страница 23: ...the static equivalent radial load Po Verify the static safety coefficient Specifications of the cross roller bearing The following table shows the specifications of the cross roller bearings built in...

Страница 24: ...3 range Average output speed Nav 10 3 n1 t1 n2t2 nntn 4 Nav t1 t2 tn Calculating radial load factor and axial load factor Both load factors are different with average loads as follows When the right f...

Страница 25: ...bearing in hour Nav Average output speed in r min obtained by formula 4 C Basic dynamic load rating in N kgf See Table 1 Pc Average dynamic radial load in N kgf obtained by formula 6 below fw Load fa...

Страница 26: ...dp Circular pitch of roller See Fig 1 and Table 1 Static safety factor Generally the static safety factor is limited by the basic static load rating Co However for the heavy duty the factor is limited...

Страница 27: ...e load For linear motion convert with the formula below Linear speed mm min Rotary speed r min 9 Pitch of screw mm Select a reduction ratio from 50 100 and 160 of an actuator of which the maximum spee...

Страница 28: ...x IM TM where KT torque constant N m A IM maximum current A TL load torque N m note that the polarity of the load torque is plus for counter direction of revolution and minus for same direction Examp...

Страница 29: ...are the same as the example described in example 1 the inertia load is accelerated by the maximum torque and is driven with a constant speed and decelerated by the maximum torque The displacement ang...

Страница 30: ...hs of duty factor 27 Torque Nm Speed r min Allowed range Allowed range Allowed range Allowed range Allowed range Allowed range Torque Nm Speed r min Torque Nm Speed r min Torque Nm Speed r min Torque...

Страница 31: ...r 2 Guidelines for sizing Torque Nm Speed r min Allowed range Allowed range Torque Nm Speed r min Torque Nm Speed r min Torque Nm Speed r min Torque Nm Speed r min Torque Nm Speed r min Allowed range...

Страница 32: ...16 Example 3 getting effective torque and average speed The parameters are the same as the example 1 and 2 for an FHA 25C 50 1 Effective torque From the parameters of Ta Td 150 N m Tr 0 N m ta 0 097...

Страница 33: ...Wr JA JL x x 40 W 2 60 t Wr capacity of external resistor W JA actuator inertia kg m2 JL load inertia kg m2 N actuator speed at deceleration r min T time for one duty cycle s Additional resistors are...

Страница 34: ...with its driver so as not to confuse the item with the other actuators Only connect the actuator specified on the driver label The drivers have been tuned for the actuator specified on the driver lab...

Страница 35: ...C When the actuator is installed in a closed space the temperature in the space may be higher than the atmosphere because of heat generation by the actuator Design the closed space size ventilation s...

Страница 36: ...HA 40C Item Output Flange Output Flange Output Flange Output Flange Flange Flange Flange Flange Screw 6 M5 6 M5 8 M6 8 M6 16 M6 12 M6 8 M10 8 M10 hole depth depth 8 depth 10 depth 12 depth 15 Wrenchin...

Страница 37: ...2x103 50x103 80x103 One way positioning arc 60 40 40 40 30 30 40 30 30 accuracy second Motor encoder 2500 pulse rev 2500 pulse rev 2500 pulse rev Quad encoder Pulse rev 500 000 1 000 000 1 600 000 500...

Страница 38: ...ote 4 kg 2 9 4 8 7 4 14 Service time for normal 100 000 times holding note 5 Service time for emergency stop note 6 200 times Note 1 Power supply is user s responsibility Use a DC power supply having...

Страница 39: ...nector for incremental encoder cable 09 0009 02 04 manufactured by Franz Binder recommended connector for extension encoder cable 09 0010 02 04 Connector for absolute encoder cable 09 0471 02 08 manuf...

Страница 40: ...5 Each cable for the motor and the encoder is possible to make 5 meters long 4 6 Cable outlets on back face option code K It is possible to set both outlets for motor cable and the encoder cable on th...

Страница 41: ...rrent consumption 35mA or less Control output DC5 to 24V load current Ic 100mA residual voltage Vce 0 8V maximum For TTL load load current Ic 40mA residual voltage Vce 0 4V maximum Timing chart Light...

Страница 42: ...find the best position for the origin monitoring the output of the origin sensor After finding the origin position fix the disk with the two loosened screws Note 1 The screws for the disk and the dog...

Страница 43: ...veable range for limit switch 2 Moveable range Actuating position Actuating position Movable range for limit switch 1 Moveable range for limit switch 2 Moveable range Actuating position Actuating posi...

Страница 44: ...cremental or absolute encoder Note RS 232C communication cable is user s responsibility Recommended cable is RS 232C cross cable with a DSUB female 9 pin connector for HA 655 or HA 675 driver KRS L09...

Страница 45: ...s Factor 60 196 9 3 281 39 37 SI system m s 3 Linear acceleration SI system m s2 Unit m min2 ft min2 ft s2 in s2 Factor 2 78 x10 4 8 47x10 5 0 3048 0 0254 Unit m min2 ft min2 ft s2 in s2 Factor 3600...

Страница 46: ...n oz in Factor 0 102 0 738 8 85 141 6 SI system N m 10 Moment of inertia SI system kg m2 Unit kgf m s2 kgf cm s2 lb ft2 lb ft s2 lb in2 lb in s2 oz in2 oz in s2 Factor 0 102 10 2 23 73 0 7376 3 42x103...

Страница 47: ...includes formulas to calculate mass and moment of inertia m mass kg Ix Iy Iz moment of inertia for rotation center of x y z axis respectively kg m2 G distance from gravity center to the surface p spec...

Страница 48: ...carbon resin 2 2 Chloroprene rubber 1 15 2 Both center lines of rotation and gravity are not the same The following formula calculates the moment of inertia when the rotary center is different from th...

Страница 49: ...ied for aluminum specific gravity 2 7 and the lower for steel specific gravity 7 85 The double dot chain lines indicate the allowable inertia for each actuator Example Material Aluminum Diameter 100mm...

Страница 50: ...Drive LLC 3 imperfection caused by the other than the FHA C series actuator and the HA 650 670 servo driver 4 disaster or others that does not belong to the responsibility of Harmonic Drive LLC All pr...

Страница 51: ...Shinagawa ku Tokyo 140 Japan Harmonic Drive AG Hoenbergstr 14 Limburg Lahn D 65555 Germany FHA rev 03 06 Harmonic Drive LLC Boston 247 Lynnfield Street Peabody MA 01960 New York 89 Cabot Court Hauppa...

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