Stepper motors and vertically lifting a platform

Question

I am trying to select what stepper motor size (nema17,23,34...) to use for my project and quantity of motors needed. But am not sure how to apply the motors "torque" to real scenarios. The scenario I am interested in is moving a table, with some weight, a precise distance in the z direction using an 8mm lead screw (2mm pitch and 8 starts).

This may be a tall order but I have 3 scenarios below that I could really benefit in understanding how to apply stepper torque rating to calculate the max vertical lifting abilities for a typical Nema17. Basically what I am looking for is what is the maximum mass I can vertically lift at a reasonable velocity/acceleration (whichever is limiting) without taking the motor beyond its torque rating. I am not sure what assumptions are needed here.

Also I'd like to ask if I ensure that the stepper's acceleration and velocity is infinitely slow will my vertical lifting abilities be much higher?

Scenario1

A single stepper with a circular pedestal. Assuming the weights added to the pedestal were doughnut shaped and the pedestal itself is weightless, what is the max mass one could lift at reasonable speeds without experiencing missed steps or taking the motor beyond its torque rating? Scenario2

Same question, assuming a weightless platform 600mmx50mm with 2 steppers on each end what is the maximum mass we can lift? Assuming the weight is precisely in the center may be necessary.

Scenario3

And finally with a weightless platform approx. 600mmx800mm what is the maximum weight we can lift with 4 steppers.

Answer 1

There are many parameters that you need to consider here, so I will just focus on the first scenario (i.e. A single stepper with a circular pedestal.

Assuming the weights added to the pedestal were doughnut shaped and the pedestal itself is weightless, what is the max mass one could lift at reasonable speeds without experiencing missed steps or taking the motor beyond its torque rating?

Torque calculation as a function of rpm and supply voltage

First of all, the rpm and the supply voltage are two critical factors. In the following image you can see that depending on the rpm and the Voltage you get significantly different torque.

Figure 1: Nema 17 torque vs rpm curves (source: moons motoros)

What is important to note here is the significant drop in Torque after 100rpm (for this particular model).

Calculating the maximum weight

In order to calculate the maximum weight the next thing that's required is the thread pitch (e.g. p = 1 mm/revolution). Then the most convenient thing is to use the following equations:

$$P = M\cdot \omega = F\cdot v \tag{eq.1}$$

where:

• $P$: power
• $M$: torque in [Nm]
• $\omega$: angular velocity [rad/s] ($=\frac{2\pi n}{60}$)
• $F$: weight on [N]
• $v$: velocity [m/s] (the velocity $v=\frac{n}{60}\cdot p$)

In the above equations I am assumming.

• $n$: revolutions per minute of the shaft units:[rpm]
• $p$: travel per revolution of the shaft (preferred unit [m/rev])

As a result you can rewrite Eq.1 as $$ M\cdot \frac{2\pi n}{60}= F\cdot \left(\frac{n}{60}\cdot p\right)$$

$$ F = \frac{2\pi }{p} \cdot M$$

This is the theoretical maximum weight if there is no acceleration. However, in reality it is lower for a number of reason, eg:

• during the acceleration stage some of the torque is expended in the rotational energy of the rotational masses. usually this can be neglected in most application. (if you want to include that its easy assuming you know the acceleration profile, but IMHO its not worth the effort, because low accel will have almost no effect, high accels will only last a few seconds).
• friction on the setup
• cogging torque
• ...

In general, the implementation parameters (e.g. alignment) are the most difficult to estimate.