# Selection Procedure B-24 ORIENTAL MOTOR GENERAL CATALOGUE

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1 STEPPING MOTORS to This section describes certain items that must be calculated to find the optimum stepping motor for a particular application. This section shows the selection procedure and gives examples. Selection Procedure 1. Determining the drive mechanism component Determine the mechanism and required specifications. First, determine certain features of the design, such as mechanism, rough dimensions, distances moved, and positioning period.. Calculate the required resolution Find the resolution the motor requires. From the required resolution, determine whether a motor only or a geared motor is to be used. 3. Determine the operating pattern Determine the operating pattern that fulfills the required specifications. Find the acceleration (deceleration) period and operating pulse speed in order to calculate the acceleration torque. 4. Calculate the required torque Calculate load torque. Calculate acceleration torque. Calculate required torque. Calculate the load torque and acceleration torque and find the required torque demanded by the motor. Q & A Glossary Before Using a 5. Select the motor Make a provisional selection of a motor based on required torque. Determine the motor to be used from the speed-torque characteristics. 6. Check the selected motor Confirm the acceleration/deceleration rate and inertia ratio. Selection complete For technical questions about selection calculations, contact your nearest Oriental Motor office. Select a motor whose speed-torque characteristics satisfy the requirement. Check the acceleration/deceleration rate and inertia ratio in order to determine the suitability of the selection. B-4 ORIENTAL MOTOR GENERAL CATALOGUE

2 Approaches to Selection Calculations This section describes in detail the key concerns in the selection procedure: the determination of the operating pattern, the calculation of the required torque and the confirmation of the selected motor. 1. Determining the Operating Pattern The required changes in the movement of the drive mechanism are translated into motor movement, creating an operating pattern as shown in the figure below. Motor selection is based on the operating pattern. Operating speed Acceleration period Movement Positioning period Operating Pattern Deceleration period (1) Finding 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. No. of pulses Operating pulses (A) Distance per movement required for [Pulses] Distance per motor rotation 1 motor rotation l 36 lrev s s : Step angle () Determining the operating pulse speed ƒ [Hz] The operating pulse speed is the pulse speed required to rotate the motor the required number of operating pulses during the positioning period. The operating pulse speed can be found from the number of operating pulses, the positioning period and the acceleration (deceleration) period. 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 pulse speed Operating pulse speed (ƒ) [Hz] Number of operating pulses Positioning period 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 following equation below. Usually, the acceleration (deceleration) period (t1) is set as a proportion of acceleration torque at roughly 5% of the respective positioning periods. For gentle speed changes, the acceleration torque can be kept lower than in start-stop operations. Operating pulse speed Starting pulse speed Acceleration period A t Number of operating pulses [pulses] Positioning period [s] Number of operating pulses t 1 Positioning period t 1 t Deceleration period Number of Acceleration Starting pulse operating pulses (Deceleration) speed [Hz] Operating pulse [pulses] period [s] speed (ƒ) [Hz] Acceleration (deceleration) Positioning period [s] period [s] A ƒ1 t 1 t t 1 STEPPING MOTORS to Q & A Glossary Before Using a ORIENTAL MOTOR GENERAL CATALOGUE B-5

3 STEPPING MOTORS to. Calculating the Required Torque TM [Nm] Calculate the required torque from the operating pattern by the following procedure. (1) Calculate the load torque TL [Nm] Load torque is the frictional resistance produced by the parts of the drive mechanism that come into contact with each other. It is the torque constantly required when the motor is operating. Load torque varies greatly with the type of drive mechanism and the mass of the work. See page B-36 for methods of finding the load torque for different drive mechanisms. () Calculate the acceleration torque Ta [Nm] Acceleration torque is the torque only required in acceleration and deceleration operation of the motor. Find the acceleration torque using the equations below depending on what slope is used for acceleration (deceleration) of the drive mechanism s total inertia. See page B-37 for formulas that can be used to calculate the total inertia of the drive mechanism section. For start-stop operation Acceleration torque (Ta) [Nm] ( ) Inertia of rotor Total inertia [kgm ] [kgm ] Step angle [ ](Operating pulse speed) [Hz] 18 Coefficient s ƒ ( J J L ) 18 n For acceleration/deceleration operation n:3.6 /s Q & A Glossary Before Using a Acceleration torque (Ta) [Nm] ( ) (3) Calculate the required torque TM [Nm] The required torque is the sum of the load torque required by the stepping motor and the acceleration torque. The motor requires the most torque during the acceleration portion of the operating pattern. During acceleration, load torque from the frictional resistance and acceleration torque from the inertia are both required. To avoid problems when incorporating a stepping motor into a device, an additional safety factor needs to be estimated. The required torque can be found from the following equation. Required torque Load torque Acceleration torque ( ) Safety factor (TM) [Nm] [Nm] [Nm] (TL Ta) Inertia of rotor Total inertia [kgm ] [kgm ] ( J J L ) s 18 Step angle [ ] 18 Select a motor for which this required torque falls within the pull-out torque of the speed-torque characteristics. ƒ ƒ1 t 1 Operating pulse speed [Hz] Starting pulse speed [Hz] Acceleration (deceleration) period [s] Torque [Nm] Required torque Speed [r/min] B-6 ORIENTAL MOTOR GENERAL CATALOGUE

4 3. Checking the Motor Selection Check the following two items for the selected motor in order to ensure an optimal selection. (No need for AS Series) (1) 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. The table below shows reference data for a stepping motor combined with our controller. 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. Acceleration/deceleration Acceleration (deceleration) period [s] rate (TR) [ms/khz] Operating pulse Starting pulse speed [khz] speed [khz] t 1 ƒ ƒ1 * Calculate the pulse speed in full-step equivalents. Speed [khz] ƒ ƒ1 TR Acceleration Rate (Reference Values) Motor Frame Size [mm] t1 Acceleration/deceleration rate TR [ms/khz] minimum 3 minimum If below the minimum value, change the operating pattern s acceleration (deceleration) period. () Check the inertia ratio Large inertia ratios (inertial loads) cause large overshooting and undershooting during starts and stops, which can affect startup 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. Total inertia of the machine [kgm ] Inertia ratio Rotor inertia of the motor [kgm ] J L J Inertia Ratio (Reference values) RK Series 5-Phase CSK Series RFK -Phase CSK Series PMC Series Package Except geared motor types. Total inertia of the machine [kgm ] Inertia ratio Rotor inertia of the motor [kgm ] (Gear ratio) J L J i Inertia ratio 1 maximum 5 maximum When these values are exceeded, we recommend a geared motor. Using a geared motor can increase the drivable inertial load. STEPPING MOTORS to Q & A Glossary Note: These values are estimates of common conditions. Your application conditions may vary. If in doubt, contact your local Oriental Motor office for assistance. Before Using a ORIENTAL MOTOR GENERAL CATALOGUE B-7

5 STEPPING MOTORS to Selecting Example Example 1 Belt Drive In this example, the AS series is selected for a belt drive system. 1. Determine the Drive Mechanism () Determining the operating pulse speed ƒ [Hz] Operating pulse speed f Num ber of operating pulses [A] Positioning period[t ] 1.7. [Hz] Starting Acceleration pulses (deceleration) speed [f1] period[t 1] Acceleration(deceleration) period[t 1] Q & A Glossary Before Using a Total mass of the table and work: m 3kg External force: FA kg Frictional coefficient of sliding surfaces:.5 Table tilt: Belt and pulley efficiency:.8 Pulley diameter: DP 31.8mm Length of pulley: LP mm Material of belt drive: Aluminum [density.81-3 kg/m 3 ] Resolution (feed per pulse): l.1 Feed: l 1mm Positioning period: to.7 s Acceleration and deceleration period: to. s. Calculating the Required Resolution (Refer to basic equations on page B-34) Required resolutions 36 Demanded resolution(l) Pulley diameter (DP) [ ] 3. Determine the Operating Pulse (Refer to basic equations on pages B-5, 34 and 35) (1) Finding the number of operating pulses (A) [pulses] Operating pulses (A) Feed per unit (l) Pulley diameter (DP) 36 Step angle (s) [pulses].36 Operatingz PulsezSpeed Hz t1 1 Pulse t = t1 Periods (3) Determining the operating speed N [r/min] Operating Speed f s r/min Calculating the Required Torque TM (Refer to page B-6) (1) Calculate the load torque TL [N.m] (Refer to page B-36 for basic equations) Load in shaft direction F FA mg (sin α cos α) 39.8(sin.5 cos ) 1.47[N] D P Load torque T L F [N m] () Calculate the acceleration torque Ta [N.m] 1 Calculate the total inertial moment J L [kg m ] (See page B-37 for basic equations) Inertia of belt drive J p 3 L p D p [kg m ] B-8 ORIENTAL MOTOR GENERAL CATALOGUE

6 Inertia of table and work J T m Total inertia J L J p J T D p [kg. m ] STEPPING MOTORS to Calculate the acceleration torque Ta [N.m] Acceleration torque T a (J J L) s 18 (J J.48 [N m]. f f 1 t 1.36 ) 18. (3) Calculate the required Torque TM [N.m] Required torque T M (T L T a) 1.5 {.3 ( 68J.48. )} J.765 [N. m] 5. Motor (1) Provisional motor selection Package Model () Determine the motor from the speed-torque characteristics AS66AC AS66AC Torque [Nm] Rotor Inertia (kg m ) Speed [r/min] Pulse Speed[kHz] Resolution Setting: 1P/R Required torque N m.8 Q & A Glossary Select a motor for which the required torque falls within the pull-out torque of the speed-torque characteristics. Before Using a ORIENTAL MOTOR GENERAL CATALOGUE B-9

7 STEPPING MOTORS to Q & A Glossary Before Using a Example : Ball Screw In these examples, 5-phase stepping motors and drivers in the RK series are selected for a ball screw system, an index table system and a belt drive. 1. Determine the Drive Mechanism Programmable controller Driver Stepping motor Coupling Direct connection Total mass of the table and work: m 4kg Frictional coefficient of sliding surfaces:.5 Ball screw efficiency:.9 Internal frictional coefficient of pilot pressure nut:.3 Ball screw shaft diameter: DB 15mm Total length of ball screw: LB 6mm Material of ball screw: Iron (density kg/cm 3 ) Pitch of ball screw: PB 15mm Resolution (feed per pulse): l.3mm/step Feed: l 18mm Positioning period: to.8s or shorter. Calculating the Required Resolution (Refer to basic equation on page B-34) 36 Demanded resolution ( l) Required resolution (s) Ball screw pitch (P B) [ ] 15 A 5-phase stepping motor and driver in the RK series can be connected directly to the application. 3. Determine the Operating Pulse (Refer to basic equations on pages B-5, 34 and 35) (1) Finding the number of operating pulses (A) [pulses] Feed per unit (l) 36 Operating pulses (A) Ball screw pitch (P B) Step angle (s) [pulses] 15.7 () Determining the acceleration (deceleration) period t1 [sec] An acceleration (deceleration) period of 5% of the positioning period is appropriate. Acceleration (deceleration) period (t 1).8.5. [s] DB W PB (3) Determining the operating pulse speed ƒ [Hz] Number of Starting Acceleration operating pulses (deceleration) Operating pulse pulses (A) speed (ƒ1) period (t 1) speed (ƒ) Positioning Acceleration (deceleration) period (t ) period (t 1) 6 1 [Hz].8. Operating pulse speed [Hz] 1 6 pulses. t1 t1. t=.8 4. Calculating the Required Torque TM [Nm] (Refer to page B-6) (1) Calculate the load torque TL [Nm] (Refer to page B-36 for basic equations) Load in shaft direction (F) F A W. g (sin cos ) (sin.5 cos ) 19.6 [N] F 19.6 Pilot pressure load (F ) 6.53 [N] 3 3 F P B F PB Load torque (T L) [Nm] () Calculate the acceleration torque Ta [Nm] Calculate the total inertial moment J L [kg.m ] (Refer to page B-37 for basic equations) Inertia of ball screw (J B) L B D B 4 3 P B Inertia of table and work (J T) m ( ) [kgm ].15 4 ( ) [kgm ] Period [s] Total inertia (J L) J B J T [kgm ] B-3 ORIENTAL MOTOR GENERAL CATALOGUE

8 Calculate the acceleration torque Ta [N.m] Acceleration S ƒ ƒ1 ( J J L) torque (T a) 18 t 1 (3) Calculate the required torque TM [Nm] Required torque (T M) (T L Ta) {.57 (68 J.158)} 156 J.43 [Nm] 5. Motor (1) Provisional motor selection Package Model RK566BC RK569BC () Determine the motor from the speed-torque characteristics Driver Input Current [A] RK566BC 8 4 Torque [Nm] () 1 (1) Rotor Inertia [kgm ] Current: 1.4A/phase JL=kgm Step Angle:.7/step (J ) J.158 [Nm] fs CURRENT Required torque [Nm] PULLOUT TORQUE Speed [r/min] () Pulse Speed [khz] 3 (3) Resolution 1 Resolution 1 Select a motor for which the required torque falls within the pull-out torque of the speed-torque characteristics. 6. Checking the Motor Selection (See Page B-7) (1) Check the acceleration/deceleration rate Acceleration/deceleration Acceleration (deceleration) period (t 1) rate (TR) Operating pulse Starting pulse speed (ƒ) speed (ƒ). [s] [ms/khz] 1 [khz] T R = 48 [ms/khz], so the motor can be used. () Check the inertia ratio Total inertia (J L) Inertia ratio Rotor inertia of the motor (J ) Therefore, the motor can be used Based on the above, the selection for this application is the Standard RK series motor RK566BC. STEPPING MOTORS to Q & A Glossary Before Using a ORIENTAL MOTOR GENERAL CATALOGUE B-31

9 STEPPING MOTORS to Example 3: Index Table Geared stepping motors are suitable for systems with high inertia, such as index tables. 1. Determine the Drive Mechanism DT=3mm. r=15mm. () Determining the acceleration (deceleration) period t1 [sec] An acceleration (deceleration) period of 5% of the positioning period is appropriate. Acceleration (deceleration) period (t 1) [sec] (3) Determining the operating pulse speed ƒ [Hz] Number of Starting Acceleration operating pulses (deceleration) Operating pulse pulses (A) speed (ƒ1) period (t 1) speed (ƒ) Positioning Acceleration (deceleration) period (t ) period (t 1) 15 5 [Hz].4.1 Programmable controller Driver Operating pulse speed [Hz] 5 Q & A Glossary Before Using a Diameter of index table: DT 3mm Index table thickness: LT 1mm Diameter of load: DW 3mm Thickness of load: LW 4mm Material of table and load: Iron (density kg/m 3 ) Number of load: 1 (one every 3 ) Distance from center of index table to center of load: l 15mm Positioning angle: 3 Resolution:.4 Positioning period: t.4 s. Calculating the Required Resolution Required resolution ( S).4. [pulses] The RK Series PN geared type (gear ratio 1:36,. /step) can be used. 3. Determine the Operating Pulse (see basic equations on pages B-5, 34 and 35) (1) Finding the number of operating pulses (A) [pulses] Angle rotated per movement () Operating pulses (A) Gear output shaft step angle ( S) 3 15 [pulses]..1 t1 t1.1 t=.4 4. Calculating the Required Torque TM [Nm] (Refer to page B-6) (1) Calculate the load torque TL [Nm] Period [sec] Frictional load is omitted because it is negligible. Load torque is considered. () Calculate the acceleration torque Ta [Nm] Calculate the total inertia J L [kg.m ] (Refer to page B-37 for basic equations) Inertia of table (J T) L T D T [kgm ] Inertia of work (Jw') L W D W [kgm ] B-3 ORIENTAL MOTOR GENERAL CATALOGUE

10 The center of the load is not on the center of rotation, so: J w" J w' ml { ( ) } [kgm ] Since there are 1 pieces of work: J W [kgm ] Total inertia (J L) J T J W [kgm ] Calculate the acceleration torque Ta [Nm] Acceleration S ƒ ƒ1 ( J i J L) torque (T a) 18 t 1. 5 (J ) J 1.9 [Nm] (3) Culculate the required Torque TM [Nm] Required torque (T M) (T L Ta) { ( J 1.9)} J 3.84 [Nm] 5. Motor (1) Provisional motor selection Package Model RK564BC-N36 RK596BC-N36 Rotor Inertia [kgm ] Required torque [Nm] () Determine the motor from the speed-torque characteristics RK564BC-N36 Current: 1.4A/phase JL=kgm Step Angle:./step 1 6. Checking the Motor Selection (See Page B-7) (1) Check the acceleration/deceleration rate Acceleration/deceleration Acceleration (deceleration) period (t 1) rate (TR) Operating pulse Starting pulse speed (ƒ) speed (ƒ).1 [s] [ms/khz] 5 [khz] TR = [ms/khz], so the motor can be used. () Check the inertia ratio Total inertia (J L) Inertia ratio Rotor inertia of the motor (J ) i Therefore, the motor can be used Based on the above, the selection for this application is the RK series PN geared motor RK564BC-N36. STEPPING MOTORS to Q & A Glossary 8 PERMISSIBLE TORQUE Driver Input Current [A] 4 Torque [Nm] 6 4 fs CURRENT 4 6 Speed [r/min] Before Using a () 5 (5) 1 (1) Pulse Speed [khz] 15 (15) Resolution 1 Resolution 1 Select a motor for which the required torque falls within the pull-out torque of the speed-torque characteristics. ORIENTAL MOTOR GENERAL CATALOGUE B-33

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