Motor Sizing Calculations

1 F-2 Technical ReferenceMotor Sizing CalculationsThis section describes certain items that must be calculated to find the optimum Motor for a particular procedures and examples are given. Selection Procedure First, determine certain features of the design, such as drive mechanism, rough dimensions, distances moved, and positioning period. Confirm the required specifications for the drive system and equipment (stop accuracy, position holding, speed range, operating voltage, resolution, durability, etc.). Calculate the value for load torque, load inertia, speed, etc. at the Motor drive shaft of the mechanism. Refer to page 3 for calculating the speed, load torque and load inertia for various mechanisms. Select a Motor type from AC Motors, Brushless DC Motors or Stepping Motors based on the required specifications.

2 Make a final determination of the Motor after confirming that the specifications of the selected Motor /gearhead satisfy all of the requirements (mechanical strength, acceleration time, acceleration torque etc.).Determine the drivemechanism componentCalculate the speed and loadConfirm the required specificationsCheck the selected motorSelect Motor type Wire Belt Mechanism, Rack and Pinion Mechanism By Actual MeasurementFBDTL [oz-in].. 2 DPulleyMachineFBSpring BalanceF FA m (sin cos )[oz.].. F DFDTL [oz-in].. 2 i2 iFmFAmFAFD Formulas for Calculating Load Torque Ball Screw Pulley FA m DTL 2 i( FA m)D [oz-in].. 2i DmFAF FA m (sin cos )[oz.].. FPB 0F0PB1TL ( ) [oz-in].. 2 2 iFAF mmDirect CouplingFAF-3 Technical ReferenceStandardAC MotorsSpeed ControlSystemsSteppingMotorsGearheadsLin earMotionCoolingFansMotor andFan Sizing Formulas for Calculating Moment ofInertia Inertia of a Cylinder Inertia of a Hollow Cylinder1D12 D22L2Jy m( )[oz-in2].

3 4431 Jx m (D12 D22) L (D14 D24) [oz-in2].. 832 LyxD1D21D12L2Jy m( )[oz-in2].. 4431 Jx mD12 LD14 [oz-in2].. 832D1xLy Inertia for Off-center Axis of Rotation Inertia of a Rectangular Pillar Inertia of an Object in Linear MotionA Unit of movement [inch/rev] AJ m()2 m()2[oz-in2].. 2 11Jy m( B2 C2) ABC ( B2 C2)[oz-in2].. 121211Jx m( A2 B2) ABC ( A2 B2)[oz-in2].. 1212 BCxAy1Jx Jx0 ml2 m( A2 B2 12l2)[oz-in2].. 12lxx0 CABl Distance between x and x0 axes [in.]F Force of moving direction [oz.]F0 Pilot pressure weight [oz.] ( 1/3 F) 0 Internal friction coefficient of pilot pressure nut ( to ) Efficiency ( to )i Gear ratioPB Ball screw pitch [inch/rev]FA External force [oz.]FB Force when main shaft begins to rotate [oz.]m Total weight of work and table [oz.] Frictional coefficient of sliding surfaces ( ) Angle of inclination [ ]D Final pulley diameter [inch]Jx Inertia on xaxis [oz-in2]Jy Inertia on yaxis [oz-in2]Jx0 Inertia on x0axis [oz-in2]m Weight [oz.]

4 ]D1 External diameter [inch]D2 Internal diameter [inch] Density [oz/in3]L Length [inch]DensityIron [oz/in3]Aluminum [oz/in3]Bronze 5 [oz/in3]Nylon [oz/in3]F-4 Technical Reference Stepping Motors This section describes in detail the key concerns in theselection procedure, such as the determination of the motionprofile, the calculation of the required torque and theconfirmation of the selected Motor . Operating PatternsThere are 2 basic motion is a start/stop operation and the other is an acceleration/deceleration operation is the most load inertia is small, start/stop operation can be used. Find the Number of Operating Pulses A [pulses]The number of operating pulses is expressed as the numberof pulse signals that adds up to the angle that the Motor mustmove to get the work from point A to point B.

5 Determine the Operating Pulse Speed f2[Hz]The operating pulse speed can be found from the number ofoperating pulses, the positioning period and theacceleration/deceleration period. For Acceleration/Deceleration OperationAcceleration/deceleration is a method of operation inwhich the operating pulses of a Motor being used in amedium- or high-speed region are gradually changed. It isfound by the equation below. Usually, the acceleration(deceleration) period (t1) is set at roughly 25% of thepositioning periods. For gentle speed changes, theacceleration torque can be kept lower than in a Motor is operated under an operating pattern likethis, the acceleration/deceleration period needs to becalculated using the positioning [s] Positioning Period [s] Operating PulseSpeed f2 [Hz]Number ofOperating Pulses[Pulses]Starting PulseSpeed [Hz]Acceleration(Deceleration)Period [s]PositioningPeriod [s] Acceleration (Deceleration)Period [s] A f1 t1t0 t1 No.

6 Of PulsesRequired for1 Motor RotationOperating Pulse (A)[Pulses]Distance per MovementDistance per Motor Rotation s: Step Anglellrev360 sPositioning Period(t0)Acceleration/Deceleration OperationAcceleration Period(t1)Deceleration Period(t1)Operating PulseSpeedNumber of Operating Pulses(A)Starting PulseSpeed(f2)(f1) For Start-Stop OperationStart-stop is a method of operation in which the operatingpulse speed of a Motor being used in a low-speed regionis suddenly increased without an acceleration period. It isfound by the following equation. Since rapid changes inspeed are required, the acceleration torque is very large. Calculate the Acceleration/Deceleration Rate TRCalculate the acceleration/deceleration rate from thefollowing equation. Calculate the Operating Speed from OperatingPulse speed Calculate the Load Torque TL(See basic equations on pages F-3) Calculate the Acceleration Torque Ta For Acceleration/Deceleration Operation For Start-Stop Operation Calculate the Required Torque TM (Load Torque [oz-in]Acceleration Torque)[oz-in] Safety FactorRequired TorqueTM [oz-in](TL Ta) Sf Acceleration Torque (Ta) [oz-in]Inertia of Rotor[oz-in2]Total Inertia[oz-in2] Step Angle [ ] (Operating Pulse Speed)2 [Hz]180 Coefficient (J0 JL) s f22180 nn.

7 / s 112 Gravitational Acceleration [ft/s2] 1g Acceleration Torque (Ta) [oz-in]Inertia of Rotor[oz-in2]Total Inertia[oz-in2] Operating PulseSpeed [Hz]Starting PulseSpeed [Hz] Acceleration (Deceleration) Period [s] Step Angle [ ]180 112 Gravitational Acceleration [ft/s2] (J0 JL) f2 f1t1 s180 1g 60 Operating PulseSpeed [Hz]OperatingSpeed [r/min]Step Angle360 t1 TRPulse Speed [kHz] Calculate the pulse speed in full-step Pulse Speed [kHz]Starting PulseSpeed [kHz] Acceleration (Deceleration) Period [ms] f2 f1t1 Acceleration/decelerationrate TR [ms/kHz] Operating PulseSpeed ( f2) [Hz]Number of Operating Pulses [Pulses]Positioning Period [s] At0 Start/Stop Operation (t0)Operating PulseSpeedNumber of Operating Pulses(A)(f2)F-5 Technical ReferenceStandardAC MotorsSpeed ControlSystemsSteppingMotorsGearheadsLin earMotionCoolingFansMotor andFan Sizing Choosing Between Standard ACMotors and Stepping Motors Selection ConsiderationsThere are differences in characteristics between standard ACmotors and stepping motors.

8 Shown below are some of thepoints you should know when Sizing a Motor . Standard AC Motors The speed of Induction Motors and Reversible Motorsvary with the size of the load torque. So, the selectionshould be made between the rated speed and thesynchronous speed. There can be a difference of continuous and short-termratings, due to the difference in Motor specifications,despite the fact that two motors have the same outputpower. Motor selection should be based on the operatingtime (operating pattern). Each gearhead has maximum permissible load using a dynamic brake, changing direction quickly,or quick starts and stops, the total load inertia must beless than the maximum permissible load inertia. Stepping Motors Checking the Running Duty CycleA stepping Motor is not intended to be run continuouslywith rated current.

9 Lower than 50% running duty cycle isrecommended. Checking the Inertia RatioLarge inertia ratios cause large overshooting andundershooting during starting and stopping, which canaffect start-up times and settling times. Depending on theconditions of usage, operation may be the inertia ratio with the following equation andcheck that the values found are at or below the inertiaratios shown in the Ratio (Reference Values)When these values are exceeded,we recommend a geared a geared Motor canincrease the drivable inertia load. Inertia RatioTotal Inertia of the Machine [oz-in2]Rotor Inertia of the Motor [oz-in2] (Gear Ratio)2 JLJ0 i2 Inertia RatioTotal Inertia of the Machine [oz-in2]Rotor Inertia of the Motor [oz-in2] JLJ0 Running Duty Cycle100 Running TimeRunning Time Stopping Time Check the Acceleration/Deceleration RateMost controllers, when set for acceleration ordeceleration, adjust the pulse speed in steps.

10 For thatreason, operation may sometimes not be possible, eventhough it can be the acceleration/deceleration rate from thefollowing equation and check that the value is at or abovethe acceleration/deceleration rate in the Rate (Reference Values with EMPS eries)If below the minimumvalue, change theoperating pattern sacceleration(deceleration)period. Checking the Required TorqueCheck that the required torque falls within the pull-outtorque of the speed-torque Factor: Sf (Reference Value)Speed [r/min](Pulse Speed [kHz])Torque [oz-in]Required Torque Acceleration/Deceleration Rate TR [ms/kHz] Calculate the pulse speed in full-step PulseSpeed [Hz]Starting PulseSpeed [Hz] Acceleration (Deceleration) Period [ms] f2 f1t1t1 TRPulse Speed [kHz]Product SeriesInertia RatioA30 RKSeries Except geared Motor types10 MaximumModelMotor Frame Sizeinch (mm)Acceleration/Deceleration RateTR[ms/kHz] (28), (42), (60), (85) (42), (60) (85), (90) SeriesARKS eriesSafety 22F-6 Technical Reference Sizing Example Ball Screw Determine the Drive MechanismTotal mass of the table and work:m 90 lb.