Motor Sizing Calculations

Transcription

1 Motor Sizing Calculations This section describes certain ites that ust be calculated to find the optiu otor for a particular application. Selection procedures and exaples are given. Selection Procedure Deterine the drive echanis coponent Confir the required specifications Calculate the speed and load First, deterine certain features of the design, such as drive echanis, rough diensions, distances oved, and positioning period. Confir the required specifications for the drive syste and equipent (stop accuracy, position holding, speed range, operating voltage, resolution, durability, etc.). Calculate the value for load torque, load inertia, speed, etc. at the otor drive shaft of the echanis. Refer to page 3 for calculating the speed, load torque and load inertia for various echaniss. Select otor type Select a otor type fro C Motors, Brushless DC Motors or Stepping Motors based on the required specifications. Check the selected otor Make a final deterination of the otor after confiring that the specifications of the selected otor/gearhead satisfy all of the requireents (echanical strength, acceleration tie, acceleration torque etc.). F- ORIENTL MOTOR GENERL CTLOG 003/004

2 Forulas for Calculating Load Torque Ball Screw FP B 0F 0P B 1 TL ( ) [oz-in]... π π i F (sin cos ) [oz.]... Pulley D TL π i ( ) D [oz-in]... i Wire Belt Mechanis, Rack and Pinion Mechanis Direct Coupling F D D F F Forulas for Calculating Moent of Inertia Inertia of a Cylinder 1 π Jx D 1 LD1 4 [oz-in ] D 1 L Jy ( ) [oz-in ] Inertia of a Hollow Cylinder y y D1 D1 x x 1 π Jx (D 1 D ) L (D 1 4 D 4 ) [oz-in ] D 1 D L Jy ( ) [oz-in ] Inertia for Off-center xis of Rotation C x l D x0 L L Technical Reference Motor and Standard Speed Control Stepping Linear Fan Sizing C Motors Systes Motors Gearheads Motion Cooling Fans F πd FD TL [oz-in]... π i i F (sin cos ) [oz.]... By ctual Measureent Spring Balance B l Distance between x and x0 axes [in.] 1 Jx Jx0 l ( B 1 l )[oz-in ]... 1 Inertia of a Rectangular Pillar x B Machine D FB y C TL FBD Pulley [oz-in]... F Force of oving direction [oz.] F0 Pilot pressure weight [oz.] (1/3 F) 0 Internal friction coefficient of pilot pressure nut (0.1 to 0.3) Efficiency (0.85 to 0.95) i Gear ratio PB Ball screw pitch [inch/rev] External force [oz.] FB Force when ain shaft begins to rotate [oz.] Total weight of work and table [oz.] Frictional coefficient of sliding surfaces (0.05) ngle of inclination [ ] D Final pulley diaeter [inch] 1 1 Jx ( B ) BC ( B )[oz-in ] Jy ( B C ) BC ( B C )[oz-in ] Inertia of an Object in Linear Motion J ( ) ( ) [oz-in ]... π Jx Inertia on x axis [oz-in ] Jy Inertia on y axis [oz-in ] Jx0 Inertia on x0 axis [oz-in ] Weight [oz.] D1 External diaeter [inch] D Internal diaeter [inch] Density [oz/in 3 ] L Length [inch] Unit of oveent [inch/rev] Density Iron 4.64 [oz/in 3 ] luinu 1.65 [oz/in 3 ] Bronze 5 [oz/in 3 ] Nylon 0.65 [oz/in 3 ] ORIENTL MOTOR GENERL CTLOG 003/004 F-3

3 Stepping Motors This section describes in detail the key concerns in the selection procedure, such as the deterination of the otion profile, the calculation of the required torque and the confiration of the selected otor. Operating Patterns There are basic otion profiles. One is a start/stop operation and the other is an acceleration/ deceleration operation. cceleration/deceleration operation is the ost coon. When load inertia is sall, start/stop operation can be used. Speed ( f) Starting Pulse Speed ( f1) cceleration Period (t1) Nuber of s () Positioning Period (t0) cceleration/deceleration Operation Speed ( f) Deceleration Period (t1) Nuber of s () Start/Stop Operation (t0) For Start-Stop Operation Start-stop is a ethod of operation in which the operating pulse speed of a otor 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. Speed ( f) [Hz] Nuber of s [Pulses] Positioning Period [s] ff1 Calculate the pulse speed in full-step equivalents. t0 Calculate the cceleration/deceleration Rate TR Calculate the acceleration/deceleration rate fro the following equation. cceleration/deceleration cceleration (Deceleration) Period [s] rate TR [s/khz] Starting Pulse t1 Find the Nuber of s [pulses] The nuber of operating pulses is expressed as the nuber of pulse signals that adds up to the angle that the otor ust ove to get the work fro point to point B. No. of Pulses () Distance per Moveent Required for [Pulses] Distance per Motor Rotation 1 Motor Rotation l 360 lrev s s: Step ngle Deterine the Speed f [Hz] The operating pulse speed can be found fro the nuber of operating pulses, the positioning period and the acceleration/deceleration period. For cceleration/deceleration Operation cceleration/deceleration is a ethod of operation in which the operating pulses of a otor being used in a ediu- or high-speed region are gradually changed. It is found by the equation below. Usually, the acceleration (deceleration) period (t1) is set at roughly 5% of the positioning periods. For gentle speed changes, the acceleration torque can be kept lower than in start-stop operations. When a otor is operated under an operating pattern like this, the acceleration/deceleration period needs to be calculated using the positioning period. cceleration/deceleration Period [s]positioning Period [s]0.5 Speed f [Hz] Nuber of s [Pulses] Positioning Period [s] Starting Pulse cceleration (Deceleration) Period [s] cceleration (Deceleration) Period [s] Pulse Speed [khz] Calculate the Operating Speed fro Operating Pulse speed Calculate the Load Torque TL (See basic equations on pages F-3) Calculate the cceleration Torque Ta For cceleration/deceleration Operation π s (J0JL) ff1 180 t1 For Start-Stop Operation cceleration Torque (Ta) [oz-in] cceleration Torque (Ta) [oz-in] Inertia of Rotor [oz-in ] πstep ngle [ ]( Speed) [Hz] (J0JL) Inertia of Rotor [oz-in ] T R t 1 Operating Speed [r/in] Total Inertia [oz-in ] 180 Coefficient πstep ngle [ ] 180 Starting Pulse cceleration (Deceleration) Period [s] Step ngle 360 π s f 180 n n: 3.6 /s 60 Total Inertia [oz-in ] f1 t1 t0t1 Calculate the Required Torque TM Required Torque (Load Torquecceleration Torque) Safety Factor TM [oz-in] [oz-in] [oz-in] (TLTa)Sf F-4 ORIENTL MOTOR GENERL CTLOG 003/004

4 Choosing Between Standard C Motors and Stepping Motors Selection Considerations There are differences in characteristics between standard C otors and stepping otors. Shown below are soe of the points you should know when sizing a otor. Standard C Motors The speed of Induction Motors and Reversible Motors vary with the size of the load torque. So, the selection should be ade between the rated speed and the synchronous speed. There can be a difference of continuous and short-ter ratings, due to the difference in otor specifications, despite the fact that two otors have the sae output power. Motor selection should be based on the operating tie (operating pattern). Each gearhead has axiu perissible load inertia. When using a dynaic brake, changing direction quickly, or quick starts and stops, the total load inertia ust be less than the axiu perissible load inertia. Stepping Motors Checking the Running Duty Cycle stepping otor is not intended to be run continuously with rated current. Lower than 50% running duty cycle is recoended. Running Tie Running Duty Cycle 100 Running Tie Stopping Tie Checking the Inertia Ratio Large inertia ratios cause large overshooting and undershooting during starting and stopping, which can affect start-up ties and settling ties. Depending on the conditions of usage, operation ay be ipossible. 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. Inertia Ratio Inertia Ratio (Reference Values) Product Series RK Series Inertia Ratio Maxiu When these values are exceeded, we recoend a geared otor. Using a geared otor can Except geared otor types increase the drivable inertia load. Inertia Ratio Total Inertia of the Machine [oz-in ] Rotor Inertia of the Motor [oz-in ] JL J0 Total Inertia of the Machine [oz-in ] Rotor Inertia of the Motor [oz-in ](Gear Ratio) Check the cceleration/deceleration Rate Most controllers, when set for acceleration or deceleration, adjust the pulse speed in steps. For that reason, operation ay soeties not be possible, even though it can be calculated. Calculate the acceleration/deceleration rate fro the following equation and check that the value is at or above the acceleration/deceleration rate in the table. cceleration/deceleration Rate TR [s/khz] cceleration Rate (Reference Values with EMP Series) If below the iniu value, change the operating pattern s acceleration (deceleration) period. 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 Safety Factor 1.5 RK Series Torque [oz-in] cceleration (Deceleration) Period [s] ff1 Calculate the pulse speed in full-step equivalents. Pulse Speed [khz] Model RK Series T R t 1 Motor Frae Size inch () 1.10(8), 1.65(4),.36(60), 3.35(85) 1.65(4),.36(60) 3.35(85), 3.54(90) t1 cceleration/ Deceleration Rate TR [s/khz] 0.5 Min. 0 Min. 30 Min. Required Torque Starting Pulse Speed [r/in] (Pulse Speed [khz]) Technical Reference Motor and Standard Speed Control Stepping Linear Fan Sizing C Motors Systes Motors Gearheads Motion Cooling Fans JL J0 i ORIENTL MOTOR GENERL CTLOG 003/004 F-5

5 Sizing Exaple Ball Screw Using Stepping Motors () Stepping Motor Coupling (3) Deterine the Speed ƒ [Hz] Operating pulse speed f Nuber of Operating Pulses [] Positioning Period [t0] Starting Pulses Speed [f1] cceleration (Deceleration) Period [t1] cceleration (Deceleration) Period [t1] Hz Pulse Generator Prograable Controller Driver Deterine the Drive Mechanis Total ass of the table and work: 90 lb. (40 kg) Frictional coefficient of sliding surfaces: 0.05 Ball screw efficiency: 0.9 Internal frictional coefficient of pilot pressure nut: Ball screw shaft diaeter: DB 0.6 inch (1.5 c) Total length of ball screw: LB 3.6 inch (60 c) Material of ball screw: Iron [density 4.64 oz/in 3 ( kg /c 3 )] Pitch of ball screw: PB 0.6 inch (1.5 c) Desired Resolution (feed per pulse): l inch (0.03 )/step Feed: l 7.01 inch (180 ) Positioning period: t0 0.8 sec. Calculate the Required Resolution Required Resolution S Direct Connection 360 Desired Resolution (l) Ball Screw Pitch (P B ) can be connected directly to the application. Deterine the Operating Pattern (see page F-4, see basic equations on pages F-3) (1) Finding the Nuber of s () [pulses] Feed per Unit (l) Operating pulses () Ball Screw Pitch (PB) 360 Step ngle(s) pulses () Deterine the cceleration (Deceleration) Period t1 [sec] n acceleration (deceleration) period of 5% of the positioning period is appropriate. cceleration (deceleration) period (t 1) sec DB PB (4) Calculate the Operating Speed N [r/in] Operating Speed f Calculate the Required Torque TM [oz-in] (see page F-4) (1) Calculate the Load Torque TL [oz-in] Load in Shaft Direction F F (sin cos ) 0 90 (sin cos 0) 4.5 lb. Pilot Pressure Load F 0 F 3 Load Torque T L F P B 0 F 0 PB π π π 0.9 π 0.5 lb-in 8.3 oz-in () Calculate the cceleration Torque Ta [oz-in] Calculate the total oent of inertia JL [oz-in ] (See page F-3 for basic equations) Inertia of Ball Screw J B π B B 3 L D 4 Inertia of Table and Work J T P B π Total Inertia J L J B J T oz- in Calculate the acceleration torque Ta [oz-in] cceleration J 0 J L torque Ta g 6000 Pulses 0. t1 t1 0. Period [sec] t0=0.8 S π oz-in π S 180 J π J0 3.6 oz-in (3) Calculate the Required Torque TM [oz-in] Required torque (T L Ta ) TM [oz-in] {8.3 (1.63 J0 3.6) } 3.6 J oz-in 1.5 lb π 0.8 lb-in 13.1 oz-in f f 1 t [r/in] F-6 ORIENTL MOTOR GENERL CTLOG 003/004

6 Select a Motor (1) Provisional Motor Selection () Deterine the Motor fro the Speed-Torque Characteristics S66 Torque [N ] Model S Torque [oz-in] Select a otor for which the required torque falls within the pull-out torque of the speed-torque characteristics. Ball Screw 0 Rotor Inertia [oz-in ] Speed [r/in] Pulse Speed [khz] (Resolution Setting: 1000 P/R) Using Standard C Motors This exaple deonstrates how to select an C otor with an electroagnetic brake for use on a tabletop oving vertically on a ball screw. In this case, a otor ust be selected that eets the following basic specifications. Required and Structural Specifications Ball Screw 1 v Required Torque oz-in N Motor Gearhead Coupling Slide Guide Total weight of table and work lb. Table speed... V 0.6 in./s10% Ball screw pitch... P B in. Ball screw efficiency Ball screw friction coefficient Friction coefficient of sliding surface (Slide guide) Motor power supply... Single-Phase 115 VC 60 Hz Ball screw total length... L B 31.5 in. Ball screw shaft diaeter... D B in. Ball screw aterial... Iron (density 4.64 oz/in. 3 ) Distance oved for one rotation of ball screw in. External force... 0 lb. Ball screw tilt angle Moveent tie...5 hours/day Brake ust provide holding torque Deterine the Gear Ratio Speed at the gearhead output shaft: NG NG V 60 ( ) r/in PB Because the rated speed for a 4-pole otor at 60 Hz is r/in, the gear ratio (i ) is calculated as follows: i NG 1818 Fro within this range a gear ratio of i = 9 is selected. Calculate the Required Torque F, the load weight in the direction of the ball screw shaft, is obtained as follows: F (sin cos ) 0100 (sin cos 90 ) 100 lb. Preload weight F0: F0 F 33.3 lb. 3 Load torque TL: TL FPB 0F0PB π π π0.9 π 3.8 lb-in This value is the load torque at the gearhead drive shaft, and ust be converted into load torque at the otor output shaft. The required torque at the otor output shaft (TM) is given by: TM TL [lb-in] 8.3 oz-in i G (Gearhead transission efficiency G 0.81) Look for a argin of safety of ties. 8.3 = oz-in To find a otor with a start-up torque of oz-in or ore, select otor 5RK40GN-WMU. This otor is equipped with an electroagnetic brake to hold a load. gearhead with a gear ratio of 9:1 that can be connected to the otor 5RK40GN-WMU is 5GN9K. The rated otor torque is greater than the required torque, so the speed under no-load conditions (1740 r/in) is used to confir that the otor produces the required speed. Load Inertia Check Ball Screw π LBDB 4 π (0.787) 4 Moent of Inertia J oz-in Table and Work Moent of Inertia J π π 1.57 oz-in Gearhead shaft total load inertia J [oz-in ] Here, the 5GN9K peritted load inertia is (see page -1): JG JM i oz-in Therefore, J < JG, the load inertia is less than the peritted inertia, so there is no proble. There is argin for the torque, so the rotation rate is checked with the no-load rotation rate (about 1750 r/in). NM P V 0.64 in./s (where NM is the otor speed) 60 i This confirs that the otor eets the specifications. Technical Reference Motor and Standard Speed Control Stepping Linear Fan Sizing C Motors Systes Motors Gearheads Motion Cooling Fans ORIENTL MOTOR GENERL CTLOG 003/004 F-7

7 Belt and Pully Using Standard C Motors Here is an exaple of how to select an induction otor to drive a belt conveyor. In this case, a otor ust be selected that eets the following basic specifications. Required Specifications and Structural Specifications V D Gearhead Total weight of belt and work lb. Friction coefficient of sliding surface Dru radius... D 4 inch Weight of dru oz. Belt roller efficiency Belt speed... V 7 inch/s10% Motor power supply... Single-Phase 115 VC 60 Hz Deterine the Gear Ratio Speed at the gearhead output shaft: Belt Conveyor Motor NG V 60 (70.7) r/in π D π4 Because the rated speed for a 4-pole otor at 60 Hz is r/in, the gear ratio (i ) is calculated as follows: i NG Fro within this range a gear ratio of i 50 is selected. Calculate the Required Torque On a belt conveyor, the greatest torque is needed when starting the belt. To calculate the torque needed for start-up, the friction coefficient (F) of the sliding surface is first deterined: F lb. 144 oz. Load torque (TL) is then calculated by: TL F D oz-in 0.9 The load torque obtained is actually the load torque at the gearhead drive shaft, so this value ust be converted into load torque at the otor output shaft. If the required torque at the otor output shaft is TM, then: TM TL oz-in i G (Gearhead transission efficiency G 0.66) Look for a argin of safety of ties, taking into consideration coercial power voltage fluctuation oz-in The suitable otor is one with a starting torque of 19.4 oz-in or ore. Therefore, otor 5IK40GN-WU is the best choice. Since a gear ratio of 50:1 is required, select the gearhead 5GN50K which ay be connected to the 5IK40GN-WU otor. Load Inertia Roller Moent of Inertia J1 1 D oz-in 8 8 Belt and Work Moent of Inertia πd J π4 190 oz-in π π Gearhead Shaft Load Inertia JJ1J oz-in Here, the 5GN50K peritted load inertia is: J G oz-in (See page -1) Therefore, J < JG, the load inertia is less than the peritted inertia, so there is no proble. Since the otor selected has a rated torque of 36.1 oz-in, which is soewhat larger than the actual load torque, the otor will run at a higher speed than the rated speed. Therefore the speed is used under no-load conditions (approxiately 1740 r/in) to calculate belt speed, and thus deterine whether the selected product eets the required specifications. V NM π D 1740π4 7.3 in/s 60 i 6050 (Where NM is the otor speed) The otor eets the specifications. F-8 ORIENTL MOTOR GENERL CTLOG 003/004

8 Conveyor Using Brushless DC Motors Here is an exaple of how to select a speed control otor to drive a belt conveyor. Perforance Belt speed VL is 0.6 in./s40 in./s Specifications for belt and work Condition: Motor power supply... Single-Phase 115 VC Belt conveyor drive Roller diaeter... D 4 inch Mass of roller lb. Total ass of belt and work lb. Friction coefficient of sliding surface Belt roller efficiency Find the Required Speed Range For the gear ratio, select 15:1 (speed range: 00) fro the perissible torque table for cobination type on page B-14 so that the iniu/axiu speeds fall within the speed range. 60VL NG NG: Speed at the gearhead output shaft πd Belt Speed 0.6 inch/s π4 40 inch/s π4 Work.87 r/in (Miniu Speed) 191 r/in (Miniu Speed) Index Table Using Stepping Motors Geared stepping otors are suitable for systes with high inertia, such as index tables. Deterine the Drive Mechanis Pulse Generator Prograable Controller DT11.8 inch (300 ) l4.9 inch (15 ) Diaeter of index table: D T 11.8 inch (300 ) Index table thickness: LT 0.39 inch (10 ) Thickness of work: LW 1.18 inch (30 ) Diaeter of work: D W 1.57 inch (40 ) Material of table and load: Iron [density 4.64 oz/in 3 ( kg /c 3 )] Nuber of loads: 1 (one every 30 ) Distance fro center of index table to center of load: l 4.9 inch (15 ) Positioning angle: 30 Positioning period: t0 0.3 [sec] Technical Reference Motor and Standard Speed Control Stepping Linear Fan Sizing C Motors Systes Motors Gearheads Motion Cooling Fans Calculate the Load Inertia JG Load Inertia of Roller : J1 1 J1 8 1D oz-in Load inertia of belt and work : J πd π4 J ( ) 33( ) 13 oz-in π π The load inertia JG is calculated as follows: JGJ1J oz-in Fro the specifications on page B-15, the perissible load inertia for BX is 300 oz-in (4.10 kg ) Calculate the Load Torque TL Friction Coefficient of the Sliding Surface: F lb. F D 9.94 Load Torque TL lb-in 0.9 Select BX fro the perissible torque table on page B-14. Since the perissible torque is 47 lb-in (5.4 N ), the safety argin is TM/TL50/.3 Usually, a otor can operate at the safety argin of 1.5 or ore. The PN geared (gear ratio 7.:1) can be used. Gear Ratio: i 7. Resolution: s0.05 Speed Range (Gear Ratio 7.:1) is 0416 r/in Deterine the Operating Pattern (see page F-4, see basic equations on page F-3) (1) Find the Nuber of s () [pulses] Operating pulses() () Deterine the cceleration (Deceleration) Period t1 [sec] n acceleration (deceleration) period of 5% of the positioning period is appropriate. cceleration (deceleration) period (t 1) t sec (3) Calculate the Operation Speed Operating N 360 t0t [r/in] ngle rotated per oveent () Gear output shaft step angle (s) Pulses 0.05 ORIENTL MOTOR GENERL CTLOG 003/004 F-9

9 (4) Deterine the Speed ƒ [Hz] Nu ber of Starting cceleration Operating Pulses (Deceleration) Pulses [] Speed [f1] Period [t1] Speedf 5000 Positioning Period [t 0] [Hz] t1 t t0=0.3 cceleration (deceleration) Period [t 1] Period [sec] Calculating the cceleration Torque Ta [oz-in] (J0 i JL) π s cceleration Torque Ta ff1 g 180 t1 (3) Calculate the Required Torque TM [oz-in] Safety Factor Sf Required Torque (T L T a ) T M [oz-in] {0 (4.16J0 57) } Select a Motor (1) Provisional Motor Selection Model S66-N7. (J ) π J057 [oz-in] 8.3J [oz-in] Rotor Inertia oz-in J0. Required Torque lb-in 67 [N ] 7.6 Calculate the Required Torque TM [oz-in] (See page F-4) (1) Calculate the Load Torque TL [oz-in] (See page F-3 for basic equations) Frictional load is oitted because it is negligible. Load torque is considered 0. () Calculate the cceleration Torque Ta [oz-in] Calculate the Total Inertia JL [oz-in ] (See page F-4 for basic equations) Inertia of TableJ T π L D T 3 T 4 Inertia of WorkJ C π W W 4 3 L D (Center of gravity) π Weight of Work π( π oz-in 3.3 oz-in DW ) LW 1.57 π( ) oz. The center of the load is not on the center of rotation, so since there are 1 pieces of work: Inertia of Work JW 1 (JCl ) (Center of rotation) 1( ) 3118 [oz-in ] Total Inertia JL JTJW oz-in () Deterine the Motor fro the Speed-Torque Characteristics S66-N7. Torque [N in] Torque [lb-in] Perissible Torque Speed [r/in] Pulse Speed [khz] (Resolution Setting: 1000P/R) Select a otor for which the required torque falls within the pull-out torque of the speed-torque characteristics. PN geared type can operate inertia load up to acceleration torque less than Maxiu torque. F-10 ORIENTL MOTOR GENERL CTLOG 003/004