# No.32** When measuring the line speed with Roller encoder, why is the number of pulses per rotation relevant?
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Our Roller encoder RP-7400 enables line speed and distance measurement by contacting the roller with the measured object. We explain why output pulses such as 120 and 1200 P/R is necessary for speed measurement in terms of measurement mechanism.

Since the speed is the distance traveled per unit time, it is calculated as **Speed = Travelling distance / Time taken**.

When measuring Line speed by Roller encoder RP-7400,

Travelling distance = Rotation of roller

**Speed = Distance per 1 pulse x Number of output pulses/ Time taken**

**•**** Speed per second (mm)?**

**Number of output pulses/ Time taken** is equivalent to Frequency (output pulses per second).

Thus, Speed (mm/s) = Distance per 1 pulse x Number of output pulses/ Time taken is equivalent to **(Circumferential length of roller (mm)/ Number of pulse per rotation) x Frequency**.

If **Circumferential**** length (mm)/ Number of pulses** is “1”, Output frequency of Encoder equals to Circumferential speed.

Since Circumferential length of RP-7400 is 200 mm, circumferential speed (mm/s) can be represented by frequency counter if selecting 200 P/R.

If number of pulses per second is measured by pulse counter, number of counts will be represented as frequency. Thus, if pulse counter has 1 second gate function, circumferential speed can be obtained from frequency.

* Since the unit of measurement resolution is 1 Hz, the unit of speed resolution is 1 mm/s.

**•**** ****Speed per minute (m)?**** **

It is also calculated by** Speed (m/min) = Distance per 1 pulse x Number of output pulses/ Time taken**, however, the unit of length and time is different from the above mentioned.

The first half of equation is **Distance per 1 pulse = (200/ Number of pulses per rotation) / 1000**, the latter half of equation is **Number of output pulses/ Time = Number of pulses per minute = Frequency x 60**.

Then, **Speed (m/min) = (200/ Number of pulses per rotation) / 1000) x Frequency x 60**.

Further, if numerical values are lumped together,

Speed (m/min) = (200 x 60/ 1000/ Number of pulses per rotation) x Frequency

= **(12/ Number of pulses per rotation) x Frequency**

If the number of pulses per rotation of the roller is 1, 10, 100, etc. times of 12, the speed can be expressed as 1, 1/10, 1/100 times of frequency.

Using RP-7400 (120 P/R),

Speed (m/min) = **Frequency x 0.1**

Using RP-7400 (1200 P/R),

Speed (m/min) = **Output frequency x 0.01**

And using frequency counter or pulse counter with 1 second gate, Circumferential speed (m/min) can be measured.

Since the unit of measurement resolution of pulse counter with 1 second gate is 1 Hz, the speed resolution is as follow:

- 0.1 m/min (120 P/R)
- 0.01 m/min (1200 P/R)

Please select the appropriate pulse of Roller Encoder such as 120/1200 or 200 according to the unit of speed.

**■**** ****Supplement**

On circumferential speed measurement, circumferential ring size for HT-3200 and HT-5500 is fixed based on the above calculation method.

The basic calculation is Speed (m/min) = Distance per 1 pulse x Number of output pulses/ Time taken.

As for HT, number of pulse per rotation is fixed as 1,

Distance per pulse is **Circumferential length of circumferential ring**.

Number of output pulses/ Time taken is **Rotation speed (r/min)**.

If circumferential length of circumferential ring is 1m, rotation speed value equals to circumferential speed.

As for HT-3200, circumferential speed can be taken by using circumferential ring KS-200 (circumferential length 100 mm) and changing value to 1/10.

If you would like to measure mm/s,

Number of output pulses/ Time taken is equal to Rotation speed (r/min) ÷ 60.

Circumferential speed (mm/s) can be taken by using circumferential ring KS-100 (circumferential length 60 mm).

(HO)