We are often asked for recommended speed settings for our conveyors and accumulation tables. Here are some handy formulas to use for converting product rates to chain speeds and the frequencies of the variable frequency drives (VFDs) that power them.

This formula converts products per minute (ppm) to feet per minute (fpm) for a simple conveyor:

d * r * 1.1 = c

d = Product diameter (ft)
r = Desired product rate (products per minute)
c = Conveyor speed (fpm)

The 1.1 modifier is to overcome a shallow angle in a side transfer from one conveyor to the next. This may be more or less depending on the angle and the type of the transfer.

This formula converts products per minute (ppm) to feet per minute (fpm) for Bi Flo Accumulation tables and Infinity Accumulation tables:

d * r * 1.5 = Bc
d * r * 1.25 = Ic

Bc = Bi Flo conveyor speed (fpm)
Ic = Infinity conveyor speed (fpm)

The modifiers (1.5 and 1.25) may vary depending on how steep the outfeed guides are, but these are the most common starting points.

Shaft mounted gear reducers. That's me on the right.

There are a lot more variables to consider when converting the speed of a conveyor to the Hertz on a VFD. You need to calculate the revolutions per minute of the drive shaft. Sometimes this is given on the faceplate of the gearmotor as “Out RPMs” or “Shaft RPMs.” If not, the gearbox will have a ratio on it (10:1, 20:1, 60:1, etc.) and the motor will list how many RPMs it makes at its standard voltage (typically 60Hz). The conveyor pitch is the length of each link in the modular belt that engages one tooth of the drive sprocket. If the gearbox is mounted right on the drive shaft, it is called a shaft mounted motor and there is only one point of reduction. If there is a drive chain between the gearbox and the conveyor drive shaft (base mounted motor), there is an additional point of gear reduction in the ratio of the drive and driven sprockets on the drive chain:

60 * ( s / ( (p * t * v) )) = h
m / g / b = v


s = Conveyor speed (fpm)
p = Conveyor chain pitch
t = Teeth of the conveyor drive sprocket
v = Conveyor drift shaft RPMs at 60Hz
h = Frequency of VFD at desired conveyor speed (Hz)
m = Motor RPMs at 60Hz
g = Gearbox ratio
b = Ratio of drive to driven sprockets on base mounted systems

Basemounted drive system. The motor is mounted underneath and the drive chain is covered by the rounded guard on the left.

For example:
Desired conveyor speed: 84fpm
Chain pitch: 1.5″
# of teeth on conveyor drive sprocket: 16
Motor RPMs at 60Hz: 1700
Gearbox ratio: 30:1
Drive sprocket for base mount: 20 teeth
Driven sprocket for base mount: 24 teeth

(84 / ( (1.5" / 12") * 16 * (1700 / 30 / (24/20) ) ) * 60 = 53.3 Hz

Variable Frequency Drives (VFDs) control the frequency of the power being sent to the motor. This allows a control system to change the conveyor speeds based on line conditions.

So to get REALLY crazy and go all the way from product rate to the frequency coming out of the VFD, we use this for an Infinity Accumulation table:
60 * ((d * 1.25) / ( (p * t * (m / g / b) ) )) = h

Bi Flo Accumulation table:
60 * ((d * 1.5) / ( (p * t * (m / g / b) ) )) = h

Tags: controls, conveyor, hz, math, speeds, vfd

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