Technical Reference F-1. Technical Reference. Selection Calculations F-2. Service Life F-30. Standard AC Motors F-34. Speed Control Systems F-40

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1 F Calculations F- Service Life F-3 F-3 F- Motors F- Gearheads F-57 F-5 and Actuators F-7 Cooling Fans F- and F-1

2 Calculations For Motors Selecting a motor that satisfies the specifications required by the equipment is an important key to ensuring the desired reliability and economy of the equipment. This section describes the procedure to select the optimum motor for a particular application, as well as the selection calculations, selection points and examples. Procedure An overview of selection procedure is explained below. First, determine the drive mechanism. Representative drive mechanisms include simple body of Determine the drive mechanism rotation, ball screw, belt and pulley, and rack and pinion. Along with the type of drive mechanism, you must also determine the mass of load, dimensions of each part, friction coefficient of the sliding surface, and so on. Check the required specifications (Equipment specifications) Confirm the drive conditions such as the speed of movement, drive time, and also positioning distance and positioning time if positioning operation will be performed. Also confirm the stopping accuracy, resolution, position holding, operating voltage, operating environment, and so on. Calculate the load Calculate the values for load torque and load inertia at the motor drive shaft. Refer to the left column on page F-3 for the calculation of load torque for representative mechanisms. Refer to the right column on page F-3 for the calculation of inertia for representative shapes. Select motor type Select a motor type from standard AC motors, brushless motors or stepping motors based on the required specifications. calculation Make a final determination of the motor after confirming that the specifications of the selected motor and gearhead satisfy all of the requirements, such as mechanical strength, acceleration time and acceleration torque. Since the specific items that must be checked will vary depending on the motor model, refer to the selection calculations and selection points explained on page F- and subsequent pages. F- ORIENTAL MOTOR GENERAL CATALOG 9/

3 Calculate the Load Torque of Each Drive Mechanism TL [N m] Calculate the Load Torque Ball Screw Drive TL FPB μfpb 1 ( + ) [N m] 1 πη π i F FA + mg (sin α + μ cos α) [N] FA m Direct Connection Pulley Drive μfa + mg TL π πd i ϕd α m FA F (μfa + mg) D [N m] 3 i Calculate the Moment of Inertia J [kg m ] Calculate the Moment of Inertia Inertia of a Cylinder 1 π Jx md1 ρld1 [kg m ] D1 Jy m ( + ) [kg m ] 3 y L D1 x Inertia of a Hollow Cylinder 1 π Jx m (D1 + D ) ρl (D1 [kg m ] 9 D ) 3 D1 L Jy 1 D1 + D L m ( + ) [kg m ] 3 x D FA m Wire or Belt Drive, Rack and Pinion Drive TL F πd FD [N m] πη i ηi F FA + mg (sin α + μ cos α) [N] 5 y L Inertia on Off-Center Axis 1 Jx Jx + ml m (A + B + l ) [kg m ] 11 x x FA m F ϕd FA m F ϕd l : Distance between x and x axes [m] C A B By Actual Measurement TL FBD [N m] Spring Balance FB Inertia of a Rectangular Pillar 1 1 Jx m (A + B ) ρabc (A [kg m ] + B ) 1 Jy m (B + C ) A 1 ρabc (B + C ) x B [kg m ] 13 and Machinery ϕd y C Pulley F : Force of moving direction [N] F : Preload [N] ( 1/3F) μ : Internal friction coefficient of preload nut (.1.3) η : Efficiency (.5.95) i : Gear ratio (This is the gear ratio of the mechanism and not the gear ratio of the Oriental Motor's gearhead you are selecting.) PB : Ball screw lead [m/rev] FA : External force [N] FB : Force when main shaft begins to rotate [N] (FB value for spring balance [kg] g [m/s ]) m : Total mass of the table and load [kg] μ : Friction coefficient of sliding surface (.5) α : Tilt angle [deg] D : Final pulley diameter [m] g : Gravitational acceleration [m/s ] (9.7) Inertia of an Object in Motion A J m ( π ) [kg m ] 1 A : Unit of movement [m/rev] Density Iron ρ7.9 3 [kg/m 3 ] Aluminum ρ. 3 [kg/m 3 ] Brass ρ.5 3 [kg/m 3 ] Nylon ρ1.1 3 [kg/m 3 ] Jx : Inertia on x axis [kg m ] Jy : Inertia on y axis [kg m ] J : Inertia on x axis (passing through center of gravity) [kg m ] m : Mass [kg] D1 : Outer diameter [m] D : Inner diameter [m] ρ : Density [kg/m 3 ] L : Length [m] F-3

4 Motor Calculations The following explains the calculation for selecting a stepping motor based on pulse control: Operating Pattern There are two basic motion profiles. Acceleration/deceleration operation is the most common. When operating speed is low and load inertia is small, start/stop operation can be used. TR [ms/khz] t1 f f1 Pulse [khz] TR t1 Time [ms] Calculate the pulse speed in full-step equivalents. In this example, acceleration (deceleration) time is calculated in [khz], while time is calculated in [ms]. f f1 Pulse f f1 A Pulse f A Calculate the Operating NM [r/min] from Operating Pulse f [Hz] θs NM [r/min] f [Hz] 3 t1 t1 t Acceleration/Deceleration Operation t Start/Stop Operation f1 : Starting pulse speed [Hz] f : Operating pulse speed [Hz] A : Number of operating pulses t : Positioning time [s] t1 : Acceleration (deceleration) time [s] Calculate the Number of Operating Pulses A [Pulse] 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 load from point A to B. A [Pulse] l lrev 3 θs l : Movement distance from point A to B [m] lrev : Movement distance per motor rotation [m/rev] θs : Step angle [deg] Calculate the Operating Pulse f [Hz] The operating pulse speed can be found from the number of operating pulses, the positioning time and the acceleration (deceleration) time. 1 For acceleration/deceleration operation The level of acceleration (deceleration) time is an important point in the selection. The acceleration (deceleration) time cannot be set hastily, because it correlates with the acceleration torque and acceleration/deceleration rate. Initially, set the acceleration (deceleration) time at roughly 5% of the positioning time. (The setting must be fine-tuned before the final decision can be made.) t1 [s] t [s].5 f [Hz] A f1 t1 t t1 For start/stop operation A f [Hz] t Calculate the Acceleration/Deceleration Rate TR [ms/khz] The values represent the specifications of Oriental Motor's controllers. The acceleration/deceleration rate indicates the degree of acceleration of pulse speed and is calculated using the following formula: Calculate the Load Torque Refer to basic formulas on page F-3. Calculate the Acceleration Torque Ta [N m] Regardless of the motor type, the acceleration/deceleration torque must always be set if the speed is to be varied. The basic formula is the same for all motors. However, different formula applies to stepping motors, as shown below, because the specifications of stepping motors are often calculated on the basis of pulse speed. Brushless Motors, (J + JL) NM Ta [N m] 9.55 t1 Operating NM [r/min] Motors 1 For acceleration/deceleration operation Ta [N m] π θs (J + JL) For start/stop operation t1 t Using Brushless Motors J : Rotor inertia [kg m ] JL : Total load inertia [kg m ] NM : Operating speed of motor [r/min] t1 : Acceleration (deceleration) time [s] f f1 π θs Ta [N m] (J + JL) f n n: 3. /θs Calculate the Required Torque TM [N m] The required torque is calculated by multiplying the sum of load torque and acceleration torque by the safety factor. TM (TL + Ta) Sf TM : Required torque [N m] TL : Load torque [N m] Ta : Acceleration torque [N m] Sf : Safety factor t1 t1 F- ORIENTAL MOTOR GENERAL CATALOG 9/

5 Points There are differences in characteristics between standard AC motors and stepping motors. Shown below are some of the points you should know when selecting a motor. 1 variation by load The speed of induction motors and reversible motors varies by several percent with the load torque. Therefore, when selecting an induction motor or reversible motor, the selection should take into account this possible speed variation by load. Time rating There can be a difference of continuous and short time ratings, due to the difference in motor specifications, even if motors have the same output power. Motor selection should be based on the operating time (operating pattern). 3 Permissible load inertia of gearhead If instantaneous stop (using a brake pack etc.), frequent intermittent operations or instantaneous bi-directional operations will be performed using a gearhead, an excessive load inertia may damage the gearhead. In these applications, therefore, the selection must be made so the load inertia does not exceed the permissible load inertia of gearhead. (Refer to page A-17) Motors 1 Check the duty cycle A stepping motor is not intended to be run continuously. It is suitable for an application that the duty cycle, which represents rate of running time and stopping time, is 5% or less. Duty cycle Running time Running time + Stopping time Check the inertia ratio Large inertia ratios cause large overshooting and undershooting during starting and stopping, which can affect starting time and settling time. Depending on the conditions of usage, operation may be impossible. Calculate the inertia ratio with the following formula and check that the value found is at or below the inertia ratios shown in the table. 3 Check the acceleration/deceleration rate Most controllers, when set for acceleration or deceleration, adjust the pulse speed in steps. For that reason, operation may sometimes not be possible, even though it can be calculated. Calculate the acceleration/deceleration rate from the previous formula and check that the value is at or above the acceleration/ deceleration rate shown in the table. Acceleration/Deceleration Rate (Reference values with EMP Series) Product Motor Frame Size Acceleration/Deceleration Rate TR [ms/khz],,, 5.5 Min. Motor and Driver Package This item need not be checked for of setting for the EMP Series.,,, Min. 5, 9 3 Min.. The value in the table represents the lower limit Check the required torque Check that the operation range indicated by operating speed NM ( f) and required torque TM falls within the pullout torque of the speed torque characteristics. Safety Factor: Sf (Reference value) Product Motor and Driver Package Safety Factor (Reference value) 1.5 Torque TM Operation Range Pullout Torque NM f Pulse and Inertia ratio JL J Inertia Ratio (Reference values) Product Motor Frame Size Inertia Ratio,,, 5 3 Max. Motor and Driver Package Except for geared types, 5 Max.,, 5 Max. When the inertia ratio exceeds the values in the table, we recommend a geared type. Using a geared type can increase the drivable load inertia. Inertia ratio JL J i i: Gear ratio F-5

6 Ball Screw Mechanism Using Motors ( ) (1) Specifications and Operating Conditions of the Drive Mechanism ler Driver Motor Coupling Direct Connection m Calculate the operating speed NM [r/min] NM θs f 3 [r/min].7 3 () Calculate the Required Torque TM [N m] (Refer to page F-) 1 Calculate the load torque TL [N m] Force of moving direction F FA + mg (sin α + μ cos α) (sin +.5 cos ) 19. [N] Preload F F [N] DB PB Load torque TL F PB πη + μ F PB π Programmable ler π.9.57 [N m] π Total mass of the table and load... m [kg] Friction coefficient of sliding surface... μ.5 Ball screw efficiency... η.9 Internal friction coefficient of preload nut...μ.3 Ball screw shaft diameter...db 15 [mm] Total length of ball screw...lb [mm] Ball screw material... Iron (density ρ [kg/m 3 ]) Ball screw lead... PB 15 [mm] Desired resolution... Δl.3 [mm/step] (feed per pulse) Feed... l [mm] Positioning time...t within. sec. Tilt angle...α [deg] () Calculate the Required Resolution θs 3 Δl 3.3 θs.7 PB 15 can be connected directly to the application. (3) Determine the Operating Pattern (Refer to page F- for formula) 1 Calculate the number of operating pulses A [Pulse] l A PB 15 3 θs 3.7 [Pulse] Determine the acceleration (deceleration) time t1 [s] An acceleration (deceleration) time of 5% of the positioning time is appropriate. t1..5. [s] Calculate the acceleration torque Ta [N m] -1 Calculate the moment of load inertia JL [kg m ] (Refer to page F-3 for formula) Inertia of ball screw JB Inertia of table and load JT m ( Load inertia JL JB + JT π ρ LB DB 3 π (15 3 ).3 [kg m ] PB π ( ) 15 3 π. [kg m ] [kg m ] - Calculate the acceleration torque Ta [N m] π θs Ta (J + JL) t1 π.7 (J +.5 ) J +.15 [N m] f f1 3 Calculate the required torque TM [N m] TM (TL + Ta) {.57 + (J +.15) } 5J +.9 [N m] (5) Select a Motor 1 Tentative motor selection Model Rotor Inertia [kg m ] ). Required Torque [N m] ASAAE Calculate the operating pulse speed f [Hz] f Pulse [Hz] A f1 t1 t t1.. Pulses [Hz] t1. Determine the motor from the speed torque characteristics ASAAE. Select a motor for which the operating 1.5 area indicated by 1..5 Operating Area operating speed and required torque falls within the pullout torque of the speed torque characteristics. Torque [N m] t1. t1 Time [s] 3 [r/min] 3 5 Pulse [khz] (Resolution setting: P/R) F- ORIENTAL MOTOR GENERAL CATALOG 9/

7 Using (1) Specifications and Operating Conditions of the Drive Mechanism This selection example demonstrates an electromagnetic brake motor for use on a table moving vertically on a ball screw. In this case, a motor must be selected that meets the following required specifications. Ball Screw v FA m Motor Gearhead Coupling Guide Total mass of the table and load... m 5 [kg] Table speed...v 15± [mm/s] External force... FA [N] Ball screw tilt angle... α 9 [deg] Total length of ball screw...lb [mm] Ball screw shaft diameter...db [mm] Ball screw lead...pb 5 [mm] Distance moved for one rotation of ball screw... A 5 [mm] Ball screw efficiency... η.9 Ball screw material... Iron (density ρ [kg/m 3 ]) Internal friction coefficient of preload nut...μ.3 Friction coefficient of sliding surface... μ.5 Motor power supply...single-phase 115 VAC Hz Operating time... Intermittent operation, 5 hours/day Load with repeated starts and stops Required load holding () Determine the Gear Ratio V (15 ± ) at the gearhead output shaft NG A 5 ± [r/min] Because the rated speed for a -pole motor at Hz is 15 to 155 r/min, the gear ratio is calculated as follows: Gear ratio i NG ± This gives us a gear ratio of i 9. Select an electromagnetic brake motor and gearhead satisfying the permissible torque of gearhead based on the calculation results (gear ratio i 9, load torque TL. [N m]) obtained so far. Here, RK5GN-AWMU and GN9SA are tentatively selected as the motor and gearhead, respectively, by referring to the "gearmotor torque table" on page A-5. Next, convert this load torque to a value on the motor output shaft to obtain the required torque TM, as follows: TM TL i ηg..11 [N m] 11 [mn m] 9.1 (Gearhead efficiency ηg.1) The starting torque of the RK5GN-AWMU motor selected earlier is mn m. Since this is greater than the required torque of 11 mn m, this motor can start the mechanism in question. Next, check if the gravitational load acting upon the mechanism in standstill state can be held with the electromagnetic brake. Here, the load equivalent to the load torque obtained earlier is assumed to act. Torque T'M required for load holding on the motor output shaft: T'M TL i..95 [N m] 95. [mn m] 9 The static friction torque generated by the electromagnetic brake of the RK5GN-AWMU motor selected earlier is mn m, which is greater than 95. mn m required for the load holding. () Check the Moment of Load Inertia J [kg m ] Inertia of ball screw JB π ρ LB DB 3 A Inertia of table and load Jm m ( ) π π ( 3 ).993 [kg m ] ( ) π. [kg m ] Load inertia at the gearhead shaft J is calculated as follows: J JB + Jm [kg m ] Here, permissible load inertia of gearhead GN9SA (gear ratio i 9) JG is (Refer to page A-17): JG [kg m ] and (3) Calculate the Required Torque TM [N m] Force of moving direction F FA + m g (sin θ + μ cos θ) (sin cos 9 ) 1 [N] Ball screw preload F Load torque T'L F PB πη F 3 17 [N] π.9. [N m] Allow for a safety factor of times. μ F PB π π Therefore, J<JG, the load inertia is less than the permissible value, so there is no problem. There is margin for the torque, so the traveling speed is checked with the speed under no load (approximately 175 r/min). V NM PB i [mm/s] NM: Motor speed This confirms that the motor meets the specifications. Based on the above, RK5GN-AWMU and GN9SA are selected as the motor and gearhead, respectively. TL T'L.. [N m] F-7

8 Belt and Pulley Mechanism Using (1) Specifications and Operating Conditions of the Drive Mechanism Here is an example of how to select an induction motor to drive a belt conveyor. In this case, a motor must be selected that meets the following required specifications. V load () Check the Moment of Load Inertia J [kg m ] Inertia of belt and load Jm1 Inertia of roller Jm 1 m D π D π m1 ( ) π 9 3 π 5 ( ) 57 [kg m ] 1 1 (9 3 ) D Gearhead Belt Conveyor Motor Total mass of belt and load...m1 5 [kg] External force... FA [N] Friction coefficient of sliding surface...μ.3 Roller diameter... D 9 [mm] Roller mass...m 1 [kg] Belt and roller efficiency...η.9 Belt speed...v 15 [mm/s]±% Motor power supply...single-phase 115 VAC Hz Operating time... hours/day () Determine the Gear Ratio at the gearhead output shaft NG V π D 31. ± 3. [r/min] (15 ± 15) π 9 Because the rated speed for a -pole motor at Hz is 15 to 155 r/min, the gear ratio is calculated as follows: Gear ratio i NG 31. ± 3. This gives us a gear ratio of i 5. (3) Calculate the Required Torque TM [N m] Friction coefficient of sliding surface F is calculated as follows: F FA + m g (sin θ + μ cos θ ) (sin +.3 cos ) 73. [N] F D Load torque T'L 3. [N m] η.9 Allow for a safety factor of times.. [kg m ] Load inertia at the gearhead shaft J is calculated as follows: J Jm1 + Jm [kg m ] Here, permissible load inertia of gearhead 5GE5SA (gear ratio i 5) JG is (Refer to page A-17): JG [kg m ] Therefore, J<JG, the load inertia is less than the permissible inertia, so there is no problem. Since the motor selected has a rated torque of 5 mn m, which is greater than the actual load torque, the motor will operate at a higher speed than the rated speed. Therefore, the belt speed is calculated from the speed under no load (approximately 17 r/min), and thus determine whether the selected product meets the required specifications. V NM π D i 175 π [mm/s] NM: Motor speed This confirms that the motor meets the specifications. Based on the above, 5IKGE-AWU and 5GE5SA are selected as the motor and gearhead, respectively. TL T'L [N m] Select an induction motor and gearhead satisfying the permissible torque of gearhead based on the calculation results (gear ratio i 5, load torque TL 7.3 [N m]) obtained so far. Here, 5IKGE-AWU and 5GE5SA are tentatively selected as the motor and gearhead, respectively, by referring to the "gearmotor torque table" on page A-9. Next, convert this load torque to a value on the motor output shaft to obtain the required torque TM, as follows: TM TL i ηg 7.3. [N m] [mn m] 5. (Gearhead efficiency ηg.) Since the starting torque of the 5IKGE-AWU motor is 3 mn m, this is greater than the required torque of mn m. F- ORIENTAL MOTOR GENERAL CATALOG 9/

9 Using Brushless Motors (1) Specifications and Operating Conditions of the Drive Mechanism Here is an example of how to select a brushless motor to drive a belt conveyor. Load V Roller Motor Belt speed... VL.5 1 [m/s] Motor power supply...single-phase 115 VAC Belt conveyor drive Roller diameter...d.1 [m] Roller mass...m 1 [kg] Total mass of belt and load...m1 7 [kg] External force... FA [N] Friction coefficient of sliding surface...μ.3 Belt and roller efficiency... η.9 () Find the Required Range For the gear ratio, select 15:1 (speed range: 5.3 ) from the "Gearmotor torque table of combination type" on page B- so that the minimum/maximum speed falls within the speed range. VL NG NG: at the gearhead shaft π D Belt speed.15 [m/s] [r/min] (Minimum speed) π.1 1 [m/s]... 1 π.1 D 191 [r/min] (Maximum speed) (3) Calculate the Moment of Load Inertia JG [kg m ] π D Inertia of belt and load Jm1 m1 ( π ) π.1 7 ( ) π Inertia of roller Jm [kg m ] m D [kg m ] The load inertia JG is calculated as follows: JG Jm1 + Jm [kg m ] Using Low- Synchronous Motors (SMK Series) (1) Specifications and Operating Conditions of the Drive Mechanism The mass of load is selected that can be driven with SMK5A-AA when the belt-drive table shown in Fig. 1 is driven in the operation pattern shown in Fig.. V F m Roller 1 Load Motor Fig. 1 Example of Belt Drive Roller Total mass of belt and load m1 1.5 [kg] Roller diameter D 3 [mm] Mass of roller m.1 [kg] Frictional coefficient of sliding surfaces μ. Belt and pulley efficiency η.9 Frequency of power supply Hz (Motor speed: 7 r/min) Motor speed [r/min] 5 Fig. Operating Pattern 15sec [sec] Low-speed synchronous motors share the same basic operating principle with -phase stepping motors. Accordingly, the torque for a low-speed synchronous motor is calculated in the same manner as for a -phase stepping motor. () Belt speed V [mm/s] Check the belt (load) speed V π D N π [mm/s] (3) Calculate the Required Torque TL [N m] Frictional coefficient of sliding surfaces F μ m1 g [N] Load Torque TL F D η [N m].9 () Calculate the Moment of Load Inertia JG [kg m ] Load inertia of belt and load Jm1 m1 ( πd π ) and From the specifications on page B-7, the permissible load inertia of BLF5A-15 is 5 [kg m ]. () Calculate the Load Torque TL [N m] Friction coefficient of sliding surface Load torque TL F FA + m g (sin θ + μ cos θ) (sin +.3 cos ). [N] F D [N m] η.9 Select BLF5A-15 from the "gearmotor torque table of combination type" on page B-. Since the permissible torque is 5. N m, the safety factor is TM / TL 5. / Usually, a motor can operate at the safety factor of 1.5 or more. 1.5 ( π 3 3 ) π 3.3 [kg m ] Load Inertia of Roller Jm 1 m D 1.1 (3 3 ).113 [kg m ] The load inertia JL is calculated as follows: JL Jm1 + Jm [kg m ] F-9

10 (5) Calculate the Acceleration Torque Ta [N m] Ta (J + JL) π θs (J ) π 7. f n.5 95 J +.3 [N m] Here, θ s 7., f Hz, n 3. /θ s.5 J: Rotor Inertia () Calculate the Required Torque TM [N m] (Look for a margin of safety of times) Index Mechanism (1) Specifications and Operating Conditions of the Drive Mechanism Geared stepping motors are suitable for systems with high inertia, such as index tables. DT 3 mm 5 mm Required Torque TM (TL + Ta) ( J +.3) 1 J +. [N m] (7) Select a Motor Select a motor that satisfies both the required torque and the permissible load inertia. Motor Rotor Inertia [kg m ] Permissible Load Inertia [kg m ] Output Torque [N m] SMK5A-AA When the required torque is calculated by substituting the rotor inertia, T M is obtained as.91 N m, which is below the output torque. Next, check the permissible load inertia. Since the load inertia calculated in () is also below the permissible load inertia, SMK5A-AA can be used in this application. ler Programmable ler Driver Geared Motor Index table diameter... DT 3 [mm] Index table thickness...lt [mm] Load diameter... DW [mm] Load thickness...lw 3 [mm] Material of table... Iron (density ρ [kg/m 3 ]) Number of loads... (one every 3 ) Distance from center of index table to center of load... l 5 [mm] Positioning angle... θ 3 Positioning time... t.5 sec. The PN geared type (gear ratio :1, resolution per pulse.3 ) can be used. The PN geared type can be used at the maximum starting/stopping torque in the inertial drive mode. Gear ratio... i Resolution...θs.3 () Determine the Operating Pattern (Refer to page F- for formula) 1 Calculate the number of operating pulses A [Pulse] θ A θs 3.3 [Pulse] Determine the acceleration (deceleration) time t1 [s] An acceleration (deceleration) time of 5% of the positioning time is appropriate. Here we shall let t1.1 [s]. 3 Calculate the operating speed NM [r/min] θ 3 NM 3 t t [r/min] The permissible speed range for the PN geared motor with a gear ratio of is to 3 r/min. F- ORIENTAL MOTOR GENERAL CATALOG 9/

11 Calculate the operating pulse speed f [Hz] f A t t1.5.1 Pulse speed [Hz] 7 [Hz] t1.1 - Calculate the acceleration torque Ta [N m] π θs (J i f f1 Ta + JL) t1 (J + 11 ).19 3 J +.1 [N m] π t1 t.5 t1 Time [s] (3) Calculate the Required Torque TM [N m] (Refer to page F-) 1 Calculate the load torque TL [N m] Friction load is negligible and therefore omitted. The load torque is assumed as. TL [N m] Calculate the acceleration torque Ta [N m] -1 Calculate the moment of load inertia JL [kg m ] (Refer to page F-3 for formula) Inertia of table JT π ρ LT DT 3 π ( 3 ) (3 3 ). [kg m ] Inertia of load π JW1 ρ LW DW 3 (Center shaft of load) π (3 3 ) ( 3 ).59 [kg m ] π Mass of load mw ρ LW DW π (3 3 ) ( 3 ).3 [kg] 3 Calculate the required torque TM [N m] Safety factor Sf. TM (TL + Ta) Sf { + (.19 3 J +.1) }..3 3 J + 9. [N m] () Select a Motor 1 Tentative motor selection Model Rotor Inertia [kg m ] Required Torque [N m] ASAAE-N Determine the motor from the speed torque characteristics ASAAE-N Torque [N m] Operating Area Permissible Torque [r/min] Pulse [khz] (Resolution setting: P/R) PN geared type can operate inertia load up at starting/stopping to acceleration torque less than maximum torque. Select a motor for which the operating area indicated by operating speed and required torque falls within the speed torque characteristics. If the load torque is applied, the selection must be made so the value of the safety factor multiplied by the load torque does not exceed the permissible torque. 5 5 and Inertia of load JW [kg m ] relative to the center of rotation can be obtained from distance L [mm] between the center of load and center of rotation, mass of load mw [kg], and inertia of load (center shaft of load) JW1 [kg m ]. Since the number of loads, n [pcs], Inertia of load JW n (JW1 + mw L ) (Center shaft of load) {(.59 ) +.3 (5 3 ) }.71 [kg m ] Load inertia JL JT + JW (. +.71) 11 [kg m ] F-11

12 Calculations For and Actuators Motorized Slides After you have determined which to use, select an appropriate model. Select a linear slide of the size that satisfies your desired condition. Select an appropriate model by following the steps below. Refer to page F- for selection calculations using a dual axes mounting bracket. (1) Select a Slide Satisfying the Transportable Mass By referring to " specifications of linear slide," select a linear slide satisfying the transportable mass. Condition: Drive a load of over a horizontal distance of mm within 1.5 seconds. EZS: Specifications of Width 7 mm Height 5 mm, VDC Slide Specifications of Slide Drive Method Ball Screw Repetitive Positioning Accuracy [mm] ±. Resolution [mm].1 Traveling Parallelism [mm].3 Maximum Load Moment [N m] MP: MY: MR: 7. Model Lead Transportable Mass [kg] Thrust Electromagnetic Brake Maximum (Stroke) [mm/s] [mm] Horizontal Vertical [N] Holding Force [N] 5 55 mm mm 5 mm 7 mm EZSD -K 15 7 EZSD M-K EZSE -K 3 EZSE M-K Enter the stroke length in the box ( ) within the model name. This applies when a parallelism is. mm or less along the mounting plate, per mm of guide length. Based on the "condition" and "specifications of linear slide," select EZSD-K. () Check the Positioning Time From the graph " positioning distance positioning time" below, check if the selected linear slide satisfies the desired positioning time. As a rough guideline, the positioning time required by the selected linear slide corresponds to the positioning time identified from the graph, multiplied by the "positioning time coefficient" applicable to the linear slide. From the graph, find the "positioning time of 1. s" for the "positioning distance of mm." You obtain the "positioning time of 1. s." Since the stroke is below 55 mm, multiply "positioning time of 1. s" by the "positioning time coefficient of 1." to obtain an approximate positioning time. Notes: The calculated positioning time does not include the settling time. Use a settling time of.15 s as a reference. The duty cycle, which represents the relationship of running time and stopping time, should be kept to 5% or less (reference). Duty cycle [%] running time [s] / (running time [s] + stopping time [s]) Positioning Distance Positioning Time EZSD (Lead: mm) Horizontal Installation 1. s Positioning Time [s] kg Positioning Time Coefficient Stroke Horizontal Installation Vertical Installation [mm] kg kg 3.5 kg 7 kg F- ORIENTAL MOTOR GENERAL CATALOG 9/

13 (3) Check the Operating and Acceleration of the Slides The time calculated from " positioning distance positioning time" assumes the operating speed and acceleration that achieve the shortest positioning time. Check the specific operating speed and acceleration at which to drive the linear slides based on the time calculated in step (). Operating and Acceleration of the Slides Check the operating speed and acceleration by referring to " positioning distance operating speed" and " positioning distance acceleration." If the identified speed exceeds the maximum speed specified in specifications of linear slide, use the maximum speed specified in specifications of linear slide as the operating speed of the linear slide. Example) For a positioning distance of mm on the graph, the operating speed is mm/s, and the acceleration is 1.5 m/s. EZSD-K [ Positioning Distance Operating ] 7 mm/s Operating [mm/s] 5 3 kg EZSD-K [ Positioning Distance Acceleration] Acceleration [m/s ] m/s () Check the Load Moment kg Maximum by Stroke Stroke [mm] Max. [mm/s] Calculate the load that will generate under the applicable condition, and confirm that the calculated result is smaller than the "maximum load moment specified in specifications of linear slide." If the maximum load moment is exceeded, select another model. The maximum load has been calculated by considering the estimated traveling life of each model. If a given model is operated at load exceeding the designed limit, the life of the linear slide will decrease. The life is also affected by the operating environment and conditions. and MP MY MR F-13

14 How to Calculate the for Sensorless Return to Home Operation The EZS Series can perform the high-speed, sensorless return to home operation. The maximum return to home speed is mm/s when the lead is mm, and the maximum speed becomes 5 mm/s when the lead is mm. Select an applicable calculating formula by referring to the linear slide installation conditions and calculate the maximum settable speed for return to home operation from the specific overhung length and load mass. Note that the load will receive impact if the sensorless return to home operation is performed at high speed. If there are overhangs along both the Z-axis and Y-axis, compare VZ and VY. The smaller of the two provides the maximum settable speed for return to home operation. Slide Installation Conditions (Horizontal, wall-mounted or ceiling-mounted) Overhang in Z-Axis Direction k VZ [mm/s] 3 mlz [Overhang in Z direction] Load Overhang in Y-Axis Direction k VY [mm/s] 3 mly [Overhang in Y direction] LZ Center of Gravity Center of Gravity LY Load LY : Center of gravity of load [mm] m : Mass of load [kg] Slide Size Strength Coefficient k Lead mm Lead mm EZS3.7. EZS EZS 1..1 LZ : Center of gravity of load [mm] m : Mass of load [kg] Slide Size Strength Coefficient k Lead mm Lead mm EZS3..5 EZS EZS 7.5. Slide Installation Conditions (Vertical) If the linear slide is installed vertically, the applicable coefficient varies depending on the return to home direction (upward or downward). Use the correct coefficient according to the specific direction. Overhang in Z-Axis Direction k VZ [mm/s] ( 3 + i ) mlz [Overhang in Z direction] Overhang in Y-Axis Direction k VY [mm/s] ( 3 + i mly ) [Overhang in Y direction] Center of Gravity Center of Gravity Load Upward: LZ LZ : Center of gravity of load [mm] m : Mass of load [kg] Slide Strength Coefficient k Upward Coefficient i Size Lead mm Lead mm Lead mm Lead mm EZS EZS EZS Downward: Slide Strength Coefficient k Downward Coefficient i Size Lead mm Lead mm Lead mm Lead mm EZS EZS EZS Upward: LY Load LY : Center of gravity of load [mm] m : Mass of load [kg] Slide Strength Coefficient k Upward Coefficient i Size Lead mm Lead mm Lead mm Lead mm EZS EZS EZS Downward: Slide Strength Coefficient k Downward Coefficient i Size Lead mm Lead mm Lead mm Lead mm EZS EZS EZS F-1 ORIENTAL MOTOR GENERAL CATALOG 9/

15 Positioning Distance Operating, Positioning Distance Acceleration EZS3D -K (Lead mm, VDC) Horizontal Installation Positioning Distance Operating Operating [mm/s] kg kg Vertical Installation Positioning Distance Operating Operating [mm/s] kg kg 3.5 kg EZS3E -K (Lead mm, VDC) Horizontal Installation Positioning Distance Operating Operating [mm/s] kg Vertical Installation Positioning Distance Operating Operating [mm/s] kg 3.5 kg 7 kg Maximum by Stroke Stroke [mm] Max. [mm/s] Maximum by Stroke Stroke [mm] Max. [mm/s] Maximum by Stroke Stroke [mm] Max. [mm/s] Maximum by Stroke Stroke [mm] Max. [mm/s] Acceleration [m/s ] 1 1 kg kg Acceleration [m/s ] 1 1 kg kg 3.5 kg Acceleration [m/s ] 1 1 kg Acceleration [m/s ] 1 1 kg 3.5 kg 7 kg and EZS3D -A/EZS3D -C (Lead mm, Single-Phase -115 VAC/Single-Phase -3 VAC) Horizontal Installation Positioning Distance Operating Maximum by Stroke Operating [mm/s] kg kg Stroke [mm] Max. [mm/s] Acceleration [m/s ] 1 1 kg kg F-15

16 Vertical Installation Positioning Distance Operating Operating [mm/s] kg kg 3.5 kg Maximum by Stroke Stroke [mm] Max. [mm/s] Acceleration [m/s ] 1 1 kg kg 3.5 kg EZS3E -A/EZS3E -C (Lead mm, Single-Phase -115 VAC/Single-Phase -3 VAC) Horizontal Installation Positioning Distance Operating Maximum by Stroke Operating [mm/s] kg Stroke [mm] Max. [mm/s] Acceleration [m/s ] 1 1 kg Vertical Installation Positioning Distance Operating Operating [mm/s] kg 3.5 kg 7 kg EZSD -K (Lead mm, VDC) Horizontal Installation Positioning Distance Operating Operating [mm/s] Vertical Installation Positioning Distance Operating Operating [mm/s] kg kg 3.5 kg 7 kg Maximum by Stroke Stroke [mm] Max. [mm/s] Maximum by Stroke Stroke [mm] Max. [mm/s] Maximum by Stroke Stroke [mm] Max. [mm/s] Acceleration [m/s ] 1 1 kg 3.5 kg Acceleration [m/s ] Acceleration [m/s ] kg kg 3.5 kg 7 kg F- ORIENTAL MOTOR GENERAL CATALOG 9/

17 EZSE -K (Lead mm, VDC) Horizontal Installation Positioning Distance Operating Operating [mm/s] Vertical Installation Positioning Distance Operating Operating [mm/s] kg 7 kg 1 kg kg 3 kg Maximum by Stroke Stroke [mm] Max. [mm/s] Maximum by Stroke Stroke [mm] Max. [mm/s] Acceleration [m/s ] Acceleration [m/s ] kg 3 kg kg 7 kg 1 kg EZSD -A/EZSD -C (Lead mm, Single-Phase -115 VAC/Single-Phase -3 VAC) Horizontal Installation Positioning Distance Operating Maximum by Stroke Operating [mm/s] kg Vertical Installation Positioning Distance Operating Operating [mm/s] kg 3.5 kg 7 kg Stroke [mm] Max. [mm/s] Maximum by Stroke Stroke [mm] Max. [mm/s] Acceleration [m/s ] 1 1 kg Acceleration [m/s ] 1 1 kg 3.5 kg 7 kg and EZSE -A/EZSE -C (Lead mm, Single-Phase -115 VAC/Single-Phase -3 VAC) Horizontal Installation Positioning Distance Operating Maximum by Stroke Operating [mm/s] kg 3 kg Stroke [mm] Max. [mm/s] Acceleration [m/s ] 1 1 kg 3 kg F-17

18 Vertical Installation Positioning Distance Operating Operating [mm/s] kg 7 kg 1 kg Maximum by Stroke Stroke [mm] Max. [mm/s] Acceleration [m/s ] 1 1 kg 7 kg 1 kg EZSD -K (Lead mm, VDC) Horizontal Installation Positioning Distance Operating Operating [mm/s] kg 3 kg Maximum by Stroke Stroke [mm] Max. [mm/s] Acceleration [m/s ] 1 1 kg 3 kg Vertical Installation Positioning Distance Operating Operating [mm/s] kg Maximum by Stroke Stroke [mm] Max. [mm/s] Acceleration [m/s ] 1 1 kg EZSE -K (Lead mm, VDC) Horizontal Installation Positioning Distance Operating Operating [mm/s] kg 3 kg kg Maximum by Stroke Stroke [mm] Max. [mm/s] Acceleration [m/s ] kg 3 kg kg Vertical Installation Positioning Distance Operating Operating [mm/s] kg 3 kg Maximum by Stroke Stroke [mm] Max. [mm/s] Acceleration [m/s ] kg 3 kg F-1 ORIENTAL MOTOR GENERAL CATALOG 9/

19 EZSD -A/EZSD -C (Lead mm, Single-Phase -115 VAC/Single-Phase -3 VAC) Horizontal Installation Positioning Distance Operating Maximum by Stroke 9 Stroke [mm] Max. [mm/s] kg kg kg kg 5 3 Operating [mm/s] Vertical Installation Positioning Distance Operating Operating [mm/s] kg Maximum by Stroke Stroke [mm] Max. [mm/s] Acceleration [m/s ] Acceleration [m/s ] kg EZSE -A/EZSE -C (Lead mm, Single-Phase -115 VAC/Single-Phase -3 VAC) Horizontal Installation Positioning Distance Operating Maximum by Stroke 7 Stroke [mm] Max. [mm/s] kg 5 55 kg 5 3 kg 3 kg kg 35 kg Operating [mm/s] Vertical Installation Positioning Distance Operating Operating [mm/s] kg 3 kg Maximum by Stroke Stroke [mm] Max. [mm/s] Acceleration [m/s ] Acceleration [m/s ] kg 3 kg and F-19

20 For Motorized Slides Using Dual Axes Mounting Brackets The following explains the calculation when using a dual axes mounting bracket dedicated to the Required dual axes mounting bracket is determined by selecting any biaxial combination of the on your conditions. You can select an optimum combination by following the procedure. Series. Series based Procedure Check your conditions Select the combination of motorized linear slides Select the combination of motorized linear slides using the table of transportable mass per acceleration. Once the combination is determined, you can figure out required dual axes mounting bracket. Check the acceleration Check the operating speed Find an acceleration from the table of transportable mass per acceleration, and check a speed of each axis in the speed transportable mass characteristics graph. Check the positioning time Calculate a positioning time. Check if your preferred positioning time can be met. Example of Follow the procedure for selection based on the following conditions. Z [Conditions] Load 3 kg mass in X-Y mounting with mm in.5 s. Moveable range is 5 mm in X-axis and 5 mm in Y-axis. The center of gravity for load in Y-axis: (G1, G, G3) (5,, 5) Power supply voltage: VDC input 5 Y G G3 G1 X 5 (1) Select the Combination of Motorized Slides and Dual Axes Mounting Bracket Check the combination of motorized linear slides using the "transportable mass per acceleration" table (Refer to page F-). Find the maximum absolute value within G1, G, G3. As the conditions state G1 5 is the maximum value, check the table for center of gravity conditions of 3 < Gn 5. The following combination of linear slides can bear a mass of 3 kg with a 5 mm stroke. [Combination 1] X-axis: EZSD Y-axis: EZS3D or [Combination ] X-axis: EZSD Y-axis: EZSD Select [Combination 1] as the smaller product size. The following products are tentatively selected. X-axis: EZSD5-K Y-axis: EZS3D5-K EZSD is tentatively selected for the first axis, and EZS3D for the second. As the second axis stroke is 5 mm, and the combination pattern (Refer to page D-55) is R-type, the required dual axes mounting bracket can be determined as PAB-SS3R5. F- ORIENTAL MOTOR GENERAL CATALOG 9/

21 Transportable Mass per Acceleration X-Y Mounting Y-axis transportable mass [kg] X-Axis: EZSD Y-Axis: EZS3D X-Axis: EZSD Y-Axis: EZS3D X-Axis: EZSD Y-Axis: EZSD 3< Gn 5 Acceleration Stroke [mm] m/s m/s m/s.3 Acceleration Stroke [mm] m/s m/s m/s Acceleration Stroke [mm] m/s m/s m/s () Check the Acceleration of Slides Check an acceleration value from the "transportable mass per acceleration" table. The maximum acceleration is.5 m/s when a transportable mass is 3 kg. (3) Check the of Slides X-Y Mounting Y-axis transportable mass [kg] X-Axis: EZSD Y-Axis: EZS3D 3< Gn 5 Acceleration Stroke [mm] m/s m/s m/s Check the "speed transportable mass characteristics" graph (Refer to page F-3). Draw a horizontal line for 3 kg mass in Y-axis. The speed at which the acceleration.5 m/s line intersects with the above-mentioned line is the maximum speed (upper limit) for dual axes combined configuration. X-axis speed: mm/s or less Y-axis speed: 5 mm/s or less and acceleration can be increased for the same mass, by replacing the power supply with single-phase -115 VAC/single-phase -3 VAC and/or by using linear slides with greater size. Transportable Mass Characteristics X-Axis VDC EZSD (M)-K Y/Z-Axis Transportable Mass [kg] mm/s 3 5 [mm/s] Acceleration 1. m/s.5 m/s 5. m/s Y-Axis VDC EZS3D (M)-K Y-Axis Transportable Mass [kg] [mm/s] 5 mm/s Acceleration 1. m/s.5 m/s 5. m/s and () Check the Positioning Time Make a simple calculation of the positioning time to verify if your preferred positioning time can be met. The simple formulas are as follows: 1 Check the operating pattern VRmax L a 3 L : Positioning distance [mm] a : Acceleration [m/s ] VRmax VR Triangular drive VR : Operating speed [mm/s] VRmax > VR Trapezoidal drive Calculate the positioning time Triangular drive VRmax : Maximum speed for triangular drive [mm/s] T : Positioning time [s] Trapezoidal drive VRmax L T or T a 3 a 3 VR T L + VR a 3 F-1

22 Example of Calculation Check if the combination on page F- can move mm in.5 s. X-Axis: EZSD5-K Conditions VR : mm/s Acceleration a :.5 mm/s Positioning distance L : mm Y-Axis: EZS3D5-K Conditions VR : 5 mm/s Acceleration a :.5 mm/s Positioning distance L : mm Check the operating pattern VRmax > VR Trapezoidal drive Calculate the positioning time T s Calculation revealed that the preferred positioning time can be met. Check the operating pattern VRmax Calculate the positioning time T VR Triangular drive. s Transportable Mass per Acceleration X-Y Mounting Y-axis transportable mass [kg] X-Axis: EZSD Y-Axis: EZS3D X-Axis: EZSD Y-Axis: EZS3D X-Axis: EZSD Y-Axis: EZSD Gn 3 [mm] 3< Gn 5 [mm] 5< Gn [mm] Acceleration Stroke [mm] Stroke [mm] Stroke [mm] m/s m/s m/s.3.3. Acceleration Stroke [mm] Stroke [mm] Stroke [mm] m/s m/s m/s Acceleration Stroke [mm] Stroke [mm] Stroke [mm] m/s m/s m/s X-Z Mounting Z-axis transportable mass [kg] X-Axis: EZSD Y-Axis: EZS3D X-Axis: EZSD Y-Axis: EZS3D X-Axis: EZSD Y-Axis: EZSD Gn 3 [mm] 3< Gn 5 [mm] 5< Gn [mm] Acceleration Stroke [mm] Stroke [mm] Stroke [mm] m/s m/s m/s Acceleration Stroke [mm] Stroke [mm] Stroke [mm] m/s m/s m/s Acceleration Stroke [mm] Stroke [mm] Stroke [mm] m/s m/s m/s Gn represents the distance from table to center of gravity of the load (unit: mm). F- ORIENTAL MOTOR GENERAL CATALOG 9/

23 Transportable Mass Characteristics X-Axis (Common to electromagnetic brake type) Acceleration VDC 1. m/s.5 m/s 5. m/s EZSD (M)-K EZSD (M)-K Y/Z-Axis Transportable Mass [kg] [mm/s] Single-Phase -115 VAC/Single-Phase -3 VAC EZSD (M)-A/EZSD (M)-C Y/Z-Axis Transportable Mass [kg] [mm/s] Y/Z-Axis Transportable Mass [kg] [mm/s] EZSD (M)-A/EZSD (M)-C Y/Z-Axis Transportable Mass [kg] [mm/s] For X-axis, the maximum speed read from the graph is limited by the stroke. Check the maximum speed for each stroke in Series products. Y-Axis (Common to electromagnetic brake type) VDC 1. m/s Acceleration.5 m/s 5. m/s EZS3D (M)-K EZSD (M)-K Y-Axis Transportable Mass [kg] [mm/s] Single-Phase -115 VAC/Single-Phase -3 VAC EZS3D (M)-A/EZS3D (M)-C Y-Axis Transportable Mass [kg] [mm/s] Y-Axis Transportable Mass [kg] [mm/s] EZSD (M)-A/EZSD (M)-C Y-Axis Transportable Mass [kg] [mm/s] and Enter the stroke in the box ( ) within the model name. F-3

24 Z-Axis (Common to electromagnetic brake type) VDC 1. m/s Acceleration.5 m/s 5. m/s EZS3D (M)-K EZSD (M)-K Z-Axis Transportable Mass [kg] Z-Axis Transportable Mass [kg] [mm/s] 3 5 [mm/s] Single-Phase -115 VAC/Single-Phase -3 VAC EZS3D (M)-A/EZS3D (M)-C Z-Axis Transportable Mass [kg] [mm/s] EZSD (M)-A/EZSD (M)-C Z-Axis Transportable Mass [kg] [mm/s] Enter the stroke in the box ( ) within the model name. Motorized Cylinders The parameters listed below are required when selecting motorized cylinders for transferring a load from A to B, as shown below. B Load A Guide The required parameters are as follows: Mass of load (m) or thrust force (F) Positioning distance (L) Positioning time (T ) Repetitive positioning accuracy Maximum stroke Among the above parameters, the thrust force and positioning time can be calculated using the formula shown below. Calculate the Thrust Force The specified maximum thrust force indicates the value when no load is added to the rod, which is operating at a constant speed. In an application where an external force is pushed or pulled, it is general that the load mounted to the rod receives an external force. The method to check the thrust force in this application is explained below: Calculate the thrust force that allows for pushing or pulling F Fmax Fa If the external force applied to the load is smaller than F, then pushpull motion is enabled. Fmax : Maximum thrust force of the motorized cylinder [N] Fa : Required thrust force during acceleration/deceleration operation [N] F : Thrust force that allows for pushing or pulling of external force [N] m : Mass of load mounted to the rod [kg] a : Acceleration [m/s ] g : Gravitational acceleration 9.7 [m/s ] μ : Friction coefficient of the guide supporting the load.1 α : Angle formed by the traveling direction and the horizontal plane [deg] External Force α 1 Calculate the required thrust force when accelerating the load mounted to the rod. Fa m {a + g ( μ cos α + sin α)} F- ORIENTAL MOTOR GENERAL CATALOG 9/

25 Calculate the Positioning Time Check to see if the motorized cylinders can perform the specified positioning within the specified time. This can be checked by determining a rough positioning time from a graph or by obtaining a fairly accurate positioning time by calculation. The respective check procedures are explained below. The obtained positioning time should be used only as a reference, since there is always a small margin of error with respect to the actual operation time. Obtaining from a Graph In this section, the EZHC series will be used as an example. For the EZHC, EZC, and EZHP Series, the speed will change depending on the mass of the load being transferred. The target load mass and speed must be confirmed using the graph shown in the catalog. [kg] 15 5 EZHC EZHC [mm/s] If the load mass is kg and the speed is mm/s, it will be EZHC. Example) Position a kg load over a distance of mm at the speed of mm/s within 1.5 second via vertical drive, using EZHCA-3MA (tentative selection). Check line 1 on the EZHCA-3MA graph. Positioning Time [s] mm/s mm/s mm/s 3 1 Obtaining by Calculations 1 Check the operating conditions Check the following conditions: Mounting direction, load mass, positioning distance, starting speed, acceleration, operating speed From the above operating conditions, check to see if the drive pattern constitutes a triangular drive or trapezoidal drive. Calculate the maximum speed of triangular drive from the positioning distance, starting speed, acceleration and operating speed. If the calculated maximum speed is equal to or below the operating speed, the operation is considered a triangular drive. If the maximum speed exceeds the operating speed, the operation is considered a trapezoidal drive. VRmax VRmax VRmax a1 a L a1 + a VR Triangular drive > VR Trapezoidal drive 3 + Vs 3 Calculate the positioning time Trapezoidal drive T T1 + T + T3 VR VS VR VS L + + a1 3 a 3 VR Triangular drive T T1 + T VR VS VRmax VS VRmax VS + a1 3 a 3 a1 VRmax (a1 + a) (VR VS ) a1 a VR 3 Pattern 1 Pattern Trapezoidal Drive T1 T3 T T1 T T a Time VS a1 Triangular Drive VRmax : Calculated maximum speed of triangular drive [mm/s] VR : Operating speed [mm/s] Vs : Starting speed [mm/s] L : Positioning distance [mm] a1 : Acceleration [m/s ] a : Deceleration [m/s ] T : Positioning time [s] T1 : Acceleration time [s] T : Deceleration time [s] T3 : Constant speed time [s] Other conversion formula is explained below. The pulse speed and operating speed can be converted to each other using the formula shown below. Keep the operating speed below the specified maximum speed: Operating speed [mm/s] Pulse speed [Hz] Resolution [mm] T a Time and The above graph shows that the load can be positioned over mm within 1.5 second. If the load mass is less than kg, the positioning time can be shortened. Calculate the positioning time using the following formula. However, for the motorized cylinder(s), the load generated by the guide mechanism will become unknown when used in combination with the customer's guide mechanism. Therefore, the load of the guide mechanism will be assumed to be in this section. The number of operating pulses and movement can be converted to each other using the formula shown below: Movement [mm] Number of operating pulses [pulses] Resolution [mm] The acceleration/deceleration rate and acceleration can be converted to each other using the formula shown below: Resolution [mm] 3 Acceleration/deceleration rate [ms/khz] Acceleration [m/s ] F-5