# Specification calculation for choosing a proper stepper motor for Ball Lead / Screw system

I'm trying to build a motorized stage which moves in one direction as below picture based on this article.

Desired characteristic properties are: 1. screw length = 150 mm 2. screw diameter = 14mm 3. screw pitch = 2mm 4. linear velocity = 0.15 mm/seconds 5. load weight = 10Kg

What should I consider to choose a proper stepper motor?

• You link to an article characterising the dynamics as 'high acceleration' without specifying the acceleration you want to achieve. Jul 1, 2019 at 14:27
• @PeteKirkham Acceleration is not important for my application. Jul 2, 2019 at 12:38
• There are two ways the motor power is used - overcoming friction, and accelerating the load. Linear bearings have friction coefficients of around 0.001, so if you want more than 0.001g acceleration on a horizontal stage then the acceleration is what will determine the power requirement. Jul 2, 2019 at 15:41

When looking for motors, you usually are trying to figure out specific things with specific requirements.

1. Holding Torque
2. Torque at Speed
3. Resolution (for steppers)
4. NEMA size
5. Positional Accuracy vs speed vs torque
6. Movement Profile
7. Budget

You're dealing with a 10kg load and your linear vel. is very slow at 0.15mm/sec...which is 9 millimetres / minute.

A good way to start is to look at what power you need to move the load in general...

$$P\text{:=}\frac{F s}{t}$$

Where F is your force, S your movement distance, and t the time you want to move such a load.

$$P=\frac{10kg*9.81m/s^2*0.15m}{1000s}=0.0147 \text{W}$$

So like, basically nothing. You could sit there and calculate more to be more accurate...including frictional torques and inertia torques or worry about step vibration...as each time you 'step' a small vibration comes into the motor rotor, which can translate to your positional accuracy, if thats something important to you, visible here:

There are other things of course, bearing frictions...'stick and slip' problems.

But we'll ignore that for now....back to your system.

So you need less than a watt and you have an rpm of 9/2...

At this point we can go to a company like nanotec and look for a motor.

As an example:

This Nema17 can give out 0.2Nm at very slow speeds at 48V (the red line)...we didn't really calculate what torques you really need and in praxis these motors always seem to achieve a lot less, especially when you start using microsteps to get higher linear resolution. So barring we don't want to do actual math, we just over size everything, and go to a nema23 motor.

So up to a RPM of 100 (you're only doing 4.5...), you're doing 0.8Nm at 48V...Which is simply way oversized, however guaranteed to match your requirements.

What usually seems to happen at the companies I've worked at, is a methodology such as this. Approximate what is needed, and oversize 2x or more whats required and forget about the rest.

Since acceleration and velocity arn't high requirements on your list. I wouldn't bother doing much as far as proper design goes and just buy the largest motor I can afford and be done with it.

However a proper method would go as follows:

1. How much power is needed to move the load in the required time?
2. What motor technology is best for this application?
3. What’s the velocity, reflected inertia, and reflected load at the (gear) motor output shaft 4.Determine the total reflected inertia, JT, back from the load to the leadscrew shaft
4. Determine the shaft torque needed to accelerate the load inertia
5. What are the first-approximation power requirements to drive the leadscrew shaft?
6. What are the final load parameters at the leadscrew input shaft (acting as the gearmotor output shaft)?
7. Can the drive and power supply meet the requirements of the load?
8. What is the motor's (estimated) worst-case temperature under load at an ambient temperature of 30°C?

Courtesy of MachineDesign

• 10kg∗9.81m/s2∗0.15m/16.6s seems to be off. You seem to be using an acceleration of 1g but the stage is horizontal, the velocity is 0.15mm/s not 0.15m/16.6s. If acceleration of the stage is negligible, then we have force = weight * friction coefficient, which is typically in the 0.001 range, and a velocity of 0.00015m/s so power = 10*9.81*0.00015*0.001W = 14.7μW. Most of the power will instead by related to accelerating the load, and the OP refuses to give a value of required acceleration. Jul 2, 2019 at 15:39
• ah, yes I calculated in feedrates of 9mm/minute instead of mm/s for some reason? Not sure where that came from.....thanks for catching that! Jul 2, 2019 at 15:46