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Frequency converter: frequency to a belt speed

Which frequency must frequency converter run to give belt that speed?

Answer: A conveyor belt often needs to run at a certain speed in m/min. The calculator works backwards from speed through the drum and gearbox to the motor's rpm and the frequency the frequency converter must be set to, with the motor's slip accounted for. It also shows the belt speed at 50 Hz and how much torque is available if the frequency goes above the base frequency.

Formula

Tromlens omdrejningstal = båndhastighed / (π · D)

Motorens omdrejningstal = tromlens omdrejningstal × gearudveksling

Frekvens = motorens omdrejningstal × poltal / 120 / (1 − slip)

Above base frequency the voltage is fully supplied and the motor works in field weakening: moment falls approx. with base frequency / frequency.

Symbols and units in the formula
SymbolMeaningUnit
vDesired belt speedm/min
tromle_dDrive drum diameter (incl. covering)mm
gear_iGear ratio—
poltalMotor's pole number—
slipSlip at rated load (from nameplate)%
f_basisMotor's base frequency (nameplate)Hz
=Frequency to be setHz
=Motor's RPMo/min
=Drum speedo/min
=Band speed at base frequencym/min
=Moment available (fraction of rated moment)%

Validity and source

Source
Motorteori ns = 120·f/p (IEC 60034) · fagbilag: frekvensomformere i automatiserede anlæg

Does not apply when

  • Slip depends on load. If the frequency converter runs with slip compensation, slip is nearly 0 and power follows load linearly.

Worked example

The calculator's own default values inserted. The figures are calculated with exactly the formula the tool uses.

Substituted

  • Desired belt speed25 m/min
  • Drive drum diameter (incl. covering)200 mm
  • Gear ratio20
  • Motor's pole number4
  • Slip at rated load (from nameplate)4 %
  • Motor's base frequency (nameplate)50 Hz

Giver

  • Frequency to be set27.6 Hz
  • Motor's RPM796 o/min
  • Drum speed39.8 o/min
  • Band speed at base frequency45.2 m/min
  • Moment available (fraction of rated moment)100 %

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Sådan bruger du den

Når en kunde vil have et transportbånd til at køre en bestemt hastighed, eller når I skifter tromle eller gear, skal du finde den frekvens, frekvensomformeren skal køre. Beregneren regner fra båndhastigheden tilbage gennem tromle og gear til motor og frekvens.

Step by step

  1. Mål drivtromlens diameter med belægning, og find gearets udveksling på typeskiltet.
  2. Aflæs poltal og slip på motorens typeskilt: slippet er forskellen mellem synkron og mærkeomdrejningstal.
  3. Indtast den ønskede båndhastighed.
  4. Sæt den beregnede frekvens i frekvensomformeren, og mål båndhastigheden.
  5. Er frekvensen over basisfrekvensen, så tjek at momentet stadig rækker.

Typical errors

  • At måle tromlen uden belægning. Belægningen gør diameteren større og båndet hurtigere.
  • At glemme slippet. Uden slip bliver båndet ca. 3-5 % for langsomt.
  • At køre langt over basisfrekvensen uden at tjekke momentet.
  • At glemme, at slipkompensering i frekvensomformeren fjerner det meste af slippet.

Examples from everyday life

Pakkebånd på 25 m/min

Et pakkebånd har 200 mm drivtromle og et 1:20-gear med en 4-polet motor, der har 4 % slip. Båndet skal køre 25 m/min.

Desired belt speed
25 m/min
Drive drum diameter (incl. covering)
200 mm
Gear ratio
20
Motor's pole number
4-pole (~1,500 rpm)
Slip at rated load (from nameplate)
4 %
Motor's base frequency (nameplate)
50 Hz

It means: Sæt frekvensomformeren til 27.6 Hz. Motoren drejer 796 rpm, og ved 50 Hz ville båndet køre 45.2 m/min.

Samme bånd hurtigere end 50 Hz

Produktionen vil have båndet op på 55 m/min uden at skifte gear.

Desired belt speed
55 m/min
Drive drum diameter (incl. covering)
200 mm
Gear ratio
20
Motor's pole number
4-pole (~1,500 rpm)
Slip at rated load (from nameplate)
4 %
Motor's base frequency (nameplate)
50 Hz

It means: Det kræver 60.8 Hz, altså over basisfrekvensen. Motoren har kun ca. 82 % af sit mærkemoment. Tjek motorens strøm ved fuld last, eller skift gear.

Langsomt doseringsbånd

Et doseringsbånd med 320 mm tromle, et 1:10-gear og en 6-polet motor med 4 % slip skal køre 40 m/min.

Desired belt speed
40 m/min
Drive drum diameter (incl. covering)
320 mm
Gear ratio
10
Motor's pole number
6-pole (~1,000 rpm)
Slip at rated load (from nameplate)
4 %
Motor's base frequency (nameplate)
50 Hz

It means: Frekvensen skal være 20.7 Hz, og tromlen drejer 39.8 rpm. Ved så lav frekvens skal du tjekke, om den selvkølende motor kan klare lasten i lang tid.

Rule of thumb

Båndhastigheden følger frekvensen lineært: halv frekvens, halv hastighed.

How to check the answer

Mål båndet med en hastighedsmåler eller tag tid på et mærke over en kendt længde. Afviger det, så tjek tromlediameter og slip.