Welcome Back.
In part one we saw it was pretty easy to calculate the number of pulses needed, the step resolution
and the motor speed.
In this video we’ll learn how to calculate the torque required and then use that and
the speed to select a motor.
We’ll also take a look at how to use that information to so the same thing for other
types of mechanisms.
Here we go.
Step 4: How much Torque do we need to move the carriage on the linear slide?
The total torque we need to worry about is how much Torque it takes to keep things moving
and how much torque it takes to accelerate the load.
And acceleration torque is inertia times the change in speed over the change in time.
What exactly is inertia?
It’s just a measure of how much an object resists being moved.
And it’s solely dependent on the mass of the object.
For example, which is harder to get moving – a clay brick or a Styrofoam brick?
The clay brick of course.
Why?
Because it has more mass.
And because it has more mass it takes more force to get it moving.
That force has to be large enough to overcome what?
The inertia of the object.
So inertia is just a measure of how much an object doesn’t want to be moved.
And since we are rotating stuff here, we need torque to get it moving.
Get what moving?
Well, for a linear slide: The motor has to rotate, the gearbox has to rotate, the coupler
has to rotate, the screw has to rotate, and the carriage has to move.
And all of those things have mass so they all have inertia – which means they are
all going to work against us when we try to get things moving.
So we need to sum all of those inertia’s to get the total inertia.
The gearbox impacts the inertia of everything behind it by the square of the gear ratio.
In our example we don’t have a gear box so there is no inertia and the gear ratio
is 1 to 1 so that gets rid of this term.
If you look in the SureStep user manual, Appendix C there’s a whole bunch of scary looking
equations that show you how to calculate all of this stuff.
And while you CAN do all that math that if you want to, there is a MUCH easier way to
do it.
For the motor inertia, we just go to the spec sheet and see the inertia of the rotor is
0.56 oz.-inches squared.
If you don’t know what motor you are using yet, just leave it blank.
You can add it in later once you have selected one to make sure it doesn’t affect anything.
And if we go to the lead screw spec sheet – look at this!
It’s already calculated the inertia of everything associated with the linear slide AND it gives
us a factor we multiply the payload mass by to give us that inertia.
Be careful here – is this the weight in pounds?
No, it’s the mass.
And since force is mass times acceleration, we just divide the payload weight by the acceleration
– which is gravity in this case, 32.2 feet per second per second, or since we need inches
in this example that would be 386.4 inches per second per second.
This slide can handle 110 pounds, so let’s divide that by the acceleration to get our
mass number, multiply that by the handy inertia factor and we now have the inertia for this
payload and the system inertia of the carriage and coupler.
Let’s add those to our chart.
If we had a gear box, same thing – just get the inertia from that datasheet.
We don’t have a gear box but if we did, we would put it’s here and divide the downstream
inertias by the square of the gear ratio.
This is really important: We need for all of our inertia values to be in the same units.
For this demo we want ounce inch seconds squared so when we’re done we can just read the
answer right off the motor curves which are in ounce inches of torque.
The only problem is all of these units are different and how in the world do you convert
these units with inches squared to these units with seconds squared – that doesn’t seem
right does it?
Here’s the trick.
Go out on the web and search for an inertia units converter.
Put the units you have here, the units you want here and there’s the answer.
Easy.
Here’s all of our inertia’s converted to the correct units.
The bottom line is we didn’t have to do any math did we?
AutomationDirect provides all the inertias we need in the data sheets and we used an
on line calculator to do the units conversions.
So to get the acceleration torque, we just sum those, multiply by the change in speed
in revolutions per second - which we found back in step one of this video series – and
divide that by the change in speed in seconds – which is our ramp time.
To get rid of this revolutions term we just multiply by 2 pi radians per revolution.
We now know the Torque needed to overcome acceleration inertia.
The other Torque term is just the torque needed to overcome friction, gravity and any other
external influences.
Gravity is important if you are lifting something – we aren’t so we’ll set that to zero.
Friction is if there is any additional drag on the system – that was built into the
numbers we got from the datasheet, so we can set that to zero.
The External Toruqe is to account for any other additional drag that might be placed
on the system.
Maybe you’re pulling something out from a stack and the weight of the stuff above
it is adding drag for example - we don’t have any of that so we’ll set that one to
zero.
So we just looked up the inertia numbers in the datasheets, summed them, and then multiplied
by the change in speed and divided by the change in time.
That’s it.
We now have the torque required by the motor and the max speed, so we can flip over to
the motor curves and see how we stack up.
Our max level is at 720 RPM and .35 oz-in of torque.
As you can see, we are not even coming close to stressing this motor – even with the
full 110 lbs of load on the slide!
And that’s not really a surprise because all of the weight is being supported by the
slide – not the motor – and the 0.2 pitch screw has a lot of mechanical advantage.
Which also explains why we didn’t need a gear box for this application.
For applications where more torque IS required, we recommend that you leave yourself 50% head
room on these charts – treat these curves as the absolute maximum that you do not want
to exceed.
What if you wanted to use belts and pulleys instead of a lead screw.
Well, it’s the same thing right?
You just gather up the inertias calculate the torque and lookup which motor you need
to do the job.
The only difference is you’re not going to find a lot of the inertia values for pulleys
and indexing tables, so you will have to fall back to the equations in the user manual to
calculate those.
The good news is there are step by step examples in the user manual showing you exactly how
to do it for all three – linear slides, belts and pulleys and indexing tables.
By the way, did you know that AutomationDirect has a free tool that helps you with all of
this?
It’s the Visual Sizer and it’s a free download from here.
It’s intended for servo systems, but it works perfectly for Steppers too.
You just build your system, enter each devices specs, setup your velocity profile, specify
your motor and you instantly see how much torque you will need.
And it even handles S-Curves and triangular and trapezoidal profiles.
You can then view your system performance.
Here’s what the motor is capable of peak and rated and what your system requires, peak
and RMS.
If you do a lot of this kind of stuff it’s worth spending the time to learn how to use
this really cool tool.
Regardless of how you calculate the inertia, please remember that these calculated numbers
are just a good starting point.
You still need to apply some experience and common sense.
So, how close are these calculated numbers to the actual measured numbers?
Well, check out the next video where we compare these calculated numbers with real live results
… If you need any help with selecting an AutomationDirect
Stepper Motor please contact AutomationDirect’s free, award winning support team during regular
business hours – they will be happy to help.
And don’t forget the forums.
There are lots of folks there that love to share their years of experience.
Just don’t post and questions directed at AutomationDirect’s support staff there,
they don’t monitor the forums on a regular basis.