Hey guys I'm still fairly new here but I've spent quite a bit of time doing all sorts of research. One of these areas is choosing the stepper motors and even though it is not the most efficient or effective way to settle on a motor I would like to understand how to actually calculate what kind of torque I would need. For now I'm trying to get a basic understanding of what is needed without factoring every little detail and instead making some estimations to compesate for some of the smaller details.
Most places you can buy motors from give you the resistance, inductance, current rating, step angle or steps per revolution and the holding torque. Some of the math I have already done may seem somewhat involved but here is what I have so far.
I'm estimating a moving mass of around 1kg, pulses per second for Smoothieboard is up to 200khz I think, desired max speed of around 150mm/s, not sure on max acceleration I'm assuming more capability is better. On one website selling motors I saw they had the holding torque rating as 25% more than the 'rated torque.' Not sure if I should derate holding torque for motors with non-specified 'rated torque' down to match.
First I take the inductance and divide it by the resistance to find the motor's time constant. Then I can plug that into the equation 1-(1/e^(t/tao)) where tao is the time constant and 't' is how long electricity is allowed to flow into the motor (pulse time). Next I take the supply voltage and divide it by the motors resistance to find the current that would flow through the motor if left on long enough. This current is multiplied by the percentage found from the current equation to make sure it's not exceeding the current rating of the motor. The percentage from the current equation is also multiplied against the holding torque rating of the motor to find it's maximum torque produced based on the pulse time and input voltage.
Next I would need to convert that torque based on how large of a pulley I have on the motor since I probably won't have a 1cm radius pulley which tells me how much torque is being produced at the perimeter of the pulley. Then I need to figure out the distance moved on the pulley for one step. If I know the torque produced by the motor at the pulley then divide by the step distance and by the mass of the load I can solve for the acceleration.
Also the way I understand it, speed is based only on pulses per second, steps per revolution and pulley diameter. Anyway please let me know if I'm missing something.
Most places you can buy motors from give you the resistance, inductance, current rating, step angle or steps per revolution and the holding torque. Some of the math I have already done may seem somewhat involved but here is what I have so far.
I'm estimating a moving mass of around 1kg, pulses per second for Smoothieboard is up to 200khz I think, desired max speed of around 150mm/s, not sure on max acceleration I'm assuming more capability is better. On one website selling motors I saw they had the holding torque rating as 25% more than the 'rated torque.' Not sure if I should derate holding torque for motors with non-specified 'rated torque' down to match.
First I take the inductance and divide it by the resistance to find the motor's time constant. Then I can plug that into the equation 1-(1/e^(t/tao)) where tao is the time constant and 't' is how long electricity is allowed to flow into the motor (pulse time). Next I take the supply voltage and divide it by the motors resistance to find the current that would flow through the motor if left on long enough. This current is multiplied by the percentage found from the current equation to make sure it's not exceeding the current rating of the motor. The percentage from the current equation is also multiplied against the holding torque rating of the motor to find it's maximum torque produced based on the pulse time and input voltage.
Next I would need to convert that torque based on how large of a pulley I have on the motor since I probably won't have a 1cm radius pulley which tells me how much torque is being produced at the perimeter of the pulley. Then I need to figure out the distance moved on the pulley for one step. If I know the torque produced by the motor at the pulley then divide by the step distance and by the mass of the load I can solve for the acceleration.
Also the way I understand it, speed is based only on pulses per second, steps per revolution and pulley diameter. Anyway please let me know if I'm missing something.