Determining required torque for a chain and sprocket conveyor belt

Question

I am working on a project for an electronics class, but need some help with one of the mechanical details. My job is to program a stepper motor to move a conveyor belt back and forth as specified. The "belt" will have a chain and the shaft of the motor will have the sprocket. But before I choose my stepper, I need to know what the required torque for my stepper motor is. Unfortunately my physics knowledge isn't great, so I googled to find the equation I should use. This is what I came up with.

I also found this equation which comes out to be similar to the above equation except this one doesn't have the efficiency and gear ratio involved.

So I have 3 questions:

1. what kind of force would I calculate for F? If the object is laying flat horizontally, what kind of force would be pushing against it east to west?

2. the two equations give me very different results due to the efficiency and gear ratio. when would I use one equation over the other?

3. where would the required speed come into the picture? if I want to move my object quickly vs slowly, would this affect the torque needed?

If you are still reading this, I thank you for your time, and hope you could help me with any or all of my questions...

Thanks :)

Answer 1

1. F is an external force which is simply any forces outside of your conveyor setup that may need to be accounted for. For example, if your load was very tall you may need to consider wind resistance. Under normal circumstances F is negligible and can be set to 0.

2. If you plan on using some sort of gear mechanism between your motor shaft and your drive pulley on your conveyor, gear ratio and gear efficiency needs to be considered as well. If you plan on driving your conveyor pulley directly by your motor shaft you do not need to consider it.

   The conveyor belt will always have some belt efficiency so this must be considered and it can be easily looked up.

3. The above equations are mainly used to calculate the torque required by the motor due to "frictional forces". Generally speaking, conveyors are designed to not require fast acceleration since they usually just run continuously so they are given a long startup time. If you do need to consider acceleration there is a separate equation that you will need to use to calculate acceleration torque. Acceleration torque will very much depend on your operating speed. Refer to the following site for more information about calculating acceleration torque.

https://www.mechatronicscenter.com/uploads/7/5/6/2/75629763/introduction_to_motor_sizing.pdf

Once you determined acceleration torque, to calculate the total torque for your motor add your frictional torque + acceleration torque. Usually, you want to add a safety factor of around 1.5-2 depending on what's available on the market. For example, if the sum of your friction torque and acceleration torque is 10Nm you would want a motor that could handle at least 15Nm-20Nm.