How to calculate the linear speed of my roller conveyor?

You are looking to use the Vention HD Roller Conveyor and you would like to verify if the motor and reducer are adapted to the linear speeds your application requires. Well, don’t look further, I’m going to show you how!

First of all, let me introduce you to the formula that will give you a linear speed (or tangential speed) for a given rotational speed and the radius of a circle:

V = R x Ω

  • V is the tangential speed in meters/seconds of the circle.

  • R is the radius of the circle in meters (could be a pulley, wheel, bearing, etc…).

  • Ω is the angular velocity in radians per second.

To use this formula, we need to know the rotational speed of the roller with the chosen motor and gearbox. Our standard electric AC motor gives us a nominal rotational speed of 1750rpm at 60Hz (North America standard grid frequency).

With that motor, we offer 4 reducer options:

Since this topic is specific to the HD Roller Conveyor we’re going to use the 3:1 ratio gearbox to do our calculations. But what does a 3:1 ratio gearbox mean?

This means that the motor needs to do 3 rotations for the output shaft of the reducer to do 1 rotation.

Let’s do the math:

Gearbox output rotational speed = Input rotational speed / 3

Gearbox output rotational speed = 1750 / 3

Gearbox output rotational speed = 583rpm

To transmit the movement from the reducer to the roller, we use a belt and pinion transmission. You can see the details and the drawings on this page: HD Roller Conveyor.

To calculate the reducing ratio of a belted transmission, we divide the diameter of the driving pinon (the one mounted on the reducer) by the diameter of the driven pinon (the one mounted on the roller).

In our case, it would give the following equation:

Belted transmission ratio = driving pulley diameter / driven pulley diameter

Belted transmission ratio = 45.5 / 35

Belted transmission ratio = 0.77

To obtain the rotational speed of the roller, let’s multiply this ratio by the output rotational speed of the reducer:

Roller rotational speed = Gearbox output rotational speed x belted transmission ratio

Roller rotational speed = 583 x 0.77

Roller rotational speed = 449rpm

The main formula needs the rotational speed in radians per second, so let’s start by converting rotations per minute into rotations per second.

Rotations per second = Rotations per minute / 60

Rotations per second = 449 / 60

Rotations per second = 7.5 rps

Now we need to convert the rotational speed (rps) into rotational velocity (rad/s):

Rotational velocity (Ω) = Rotations per second x 2 x pi

Rotational velocity (Ω) = 7.5 x 2 x 3.14

Rotational velocity (Ω) = 47 rad/s

The time has come to use our main formula:

V (m/s)= R (radius of the roller in meters) x Ω (rotational velocity of the roller in rad/s):

V (m/s)= 0.025 x 47

V (m/s)= 1.18m/s

Let’s multiply this value by 1000 to obtain the linear speed in millimeters per second:

V(mm/s)= V (m/s) x 1000

V(mm/s)= 1.18 x 1000

V(mm/s)= 1180 mm/s

We now know that the nominal linear speed of our conveyor is 1180mm/s. I suggest you do all this math in an Excel sheet so you will be able to adjust the motor speed to check if it fits your needs.

Keep in mind that to adjust the rotational speed of a motor we use what’s called a VFD, a Variable Frequency Drive. To avoid damage to an electric AC motor, we strongly suggest that the frequency stays in a range between 40Hz and 70Hz.

If you’re close to these limits or completely out of range, feel free to contact our engineers and we will be happy to review your solution and help you find alternatives if needed.

I hope this topic helped you in the process of defining and de-risking your application. If you have any remarks or observations feel free to reply.