Stepper Motor Calculations Sanity Check Needed

I'm in the beginning stages of designing a CNC router and just need a sanity check.

I'm thinking of using a belt drive for the Z axis with no reducer. If I use a pulley with a 1" diameter, a 0.9 degree step is... uh.... (brain hurts)... 0.00785 inches.

I plan on doing 2D cutting almost exclusively on my machine. Z axis resolution is not a priority for me. This is plenty of resolution for my Z axis, and if I want more I can always microstep, right?

Let's say my router and the Z carriage weigh a total of 10 pounds. Now, if I want to move the Z axis at a rate of, say, 1 inch per second, I need a motor that will do 128 steps/sec with a torque of 5 pound-inches (10 pound load with a 0.5" radius), or 80 oz-in. Uh... right?

It seems that many NEMA 17 sized motors would be able to direct-drive a Z axis in this manner.

Is there any reason not to use such a simple setup? Am I missing something terribly obvious?

Most steppers use 1.8 degree steps, not .9, so there are 200 steps per revolution. Are you using a halfstepping drive? Microstepping smooths out the motion, but it doesn't make the router more accurate.

80 oz-in is not a lot of torque, and stepper motor torque falls off rapidly with increasing speed. So even if your motor is rated at 80 oz-in holding torque, that doesn't mean it will be able to reliably lift that load at the speed you want.

NEMA 17 motors are too weak for anything but the smallest and slowest cutting machines, although they can be used for light machines which don't have to deal with cutting forces, like 3D printers. If you want something suitable for a reasonable-sized router that's useful for cutting wood, I'd say go with NEMA 23 or bigger.

Andrew Werby
www.computersculpture.com

Thanks, Andrew.

Even if I go with 1.8 degrees per step, I'll have enough accuracy in the Z axis for my needs. (Most of my needs will be either 'entirely through the workpiece' or 'not touching the workpiece at all.')

Attached is a torque curve of a NEMA 17 motor with 0.9 degree steps that seems to have plenty of torque for my needs.

Unless I'm missing something. Which is what I fear. Any comments after looking at the graph?

Edit: Oops. This motor is indeed 1.8 deg/step. But I'm still wondering if there's any reason it wouldn't meet my needs. It just seems that I'm missing something by doing something simple when I compare my design to others' designs.

Eidt 2: Yeah, actually, 80 oz. in. is cutting it pretty close with this motor. Probably a step up to something bigger would be appropriate.

You don't say what kind of screws you're using with this setup, but even high-quality ball screws have some friction that isn't accounted for in your calculations. Acme screws have a lot more, and regular hardware-store all-thread has much more than that. Any sliding parts will also take some torque to move, both due to friction and inertia, which increases significantly when the axes have to change direction at speed. The screws do give you some mechanical advantage, but the more you get from them, the faster they have to spin, placing them further down that torque curve. That curve, as you may have noticed, looks best when you're giving the motors a lot of juice. But if you're as cheap when you're buying drivers as you are with your motor purchasing, then you'll find the cheap drivers won't take that much - some are limited to 24 volts. Sure, you can try doing this with the absolute minimum expenditure on everything and see how it works, but a machine that is constantly losing steps due to insufficient torque isn't a lot of fun to use, unless you're a real masochist...

Andrew Werby
www.computersculpture.com

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Let's say my router and the Z carriage weigh a total of 10 pounds. Now, if I want to move the Z axis at a rate of, say, 1 inch per second, I need a motor that will do 128 steps/sec with a torque of 5 pound-inches (10 pound load with a 0.5" radius), or 80 oz-in. Uh... right?

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No, not really. It's more complicated than that. Your calculations are in a perfect world", but you're leaving out a few things.

First, a stepper motor's rated torque is it's holding torque, when it's NOT spinning. As soon as it starts to spin, it will have less torque, which will no longer be enough to lift your load.

You also need to account for frictional losses and other inefficiencies in the drive system, which will increase your toque requirements.

And when you start movement from a rest position, you need to accelerate to get up to a certain speed. Acceleration requires even more force.

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This is plenty of resolution for my Z axis, and if I want more I can always microstep, right?

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Depends on who you ask, but the general consensus is no, you can't. Well, maybe a little. The main reason that most people use microstepping drives is because they run the motors much smoother, and decrease resonance. Resonance can cause your motors to lose torque and stall. Also, as the microstepping amount increases, the available torque for each microstep becomes less and less.

What you really need to do, is calculate the force required to accelerate at a given rate (maybe 0.1G). This determines the maximum torque you'll need. Add 10-15% for friction and inefficiency. Then add at least 25% for headroom. I'd probably go 50%. Then determine how fast you want to go. Calculate the rpm at this speed, and look at the curve and see how much torque the motor has at that particular rpm.


You also might want to make sure you can build an entire Z axis including router that weighs 10lbs.

Steppers have a holding torque rating which is the max torque they'll ever deliver. This falls off with speed and also rotor position & heat.

You need to design very conservatively as although most folks are aware that hitting the max means catastrophic position loss, many are not aware that as torque is gradually applied up to the max the rotor will gradually shift position like a spring. When the max is exceeded, it will suddenly "jump" to the next magnetically identical position, usually 4 steps away (1/50 rev). Stiffness matters as well as being able to handle the load entire.

Don't overlook some simple engineering principles:

- a counterweight or spring can reduce the total load on the actuator
- a simple test with the belt drive and a "brick" can give you an idea of the performance before you build something elaborate
- don't forget that the router wlll deliver forces of its own
- design some space in to put in a bigger/different motor if you upgrade later.

Hope this helps!

All the little things Andrew mentions below are real factors to contend with in a machine design. Further these sources of friction can and will change over time. Obviously doing the engineering up front can eliminate gross mistakes but I'd suggest that you look at figures derived as minimal and leave yourself lots of margin in stepper selection. This is especially the case on home built machines that aren't as rigged or stable as would be ideal, simple twisting of the frame can impact the ability of the stepper to drive the axis. Also with ball screws and ball slide you have the reality of lubrication changing the axis behavior as the lube works out or gets contaminated with dust and filth.

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Originally Posted by awerby

You don't say what kind of screws you're using with this setup, but even high-quality ball screws have some friction that isn't accounted for in your calculations. Acme screws have a lot more, and regular hardware-store all-thread has much more than that. Any sliding parts will also take some torque to move, both due to friction and inertia, which increases significantly when the axes have to change direction at speed. The screws do give you some mechanical advantage, but the more you get from them, the faster they have to spin, placing them further down that torque curve. That curve, as you may have noticed, looks best when you're giving the motors a lot of juice. But if you're as cheap when you're buying drivers as you are with your motor purchasing, then you'll find the cheap drivers won't take that much - some are limited to 24 volts. Sure, you can try doing this with the absolute minimum expenditure on everything and see how it works, but a machine that is constantly losing steps due to insufficient torque isn't a lot of fun to use, unless you're a real masochist...

Andrew Werby
ComputerSculpture.com ? Home Page for Discount Hardware & Software

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an useful calculator, helped me a lot
File:Motorcalc.xls - TAMI

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Let's say my router and the Z carriage weigh a total of 10 pounds. Now, if I want to move the Z axis at a rate of, say, 1 inch per second, I need a motor that will do 128 steps/sec with a torque of 5 pound-inches (10 pound load with a 0.5" radius), or 80 oz-in. Uh... right?

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To move 1"/sec or 60ipm the motor would have to spin 60ipm/3.14 or about 19rpm. So if there was absolutely no friction on your linear ways, you'd need 80in-oz at 19rpm. But you have to consider that the linear ways will have some friction. and that you must also have enough torque to plunge or ramp the tool into the workpiece, and keep it there. Then I would figure another 10% overhead.

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Is there any reason not to use such a simple setup? Am I missing something terribly obvious?

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The minute you power off your drive, the Z axis will drop toward the table. You would require a brake of some sort, which can be very expensive. This is usually the reaon most belt drive tables still use a leadscrew for the Z.

The thing with microsteps is that they are not 100% linear. I guess that's not too much a concern if you are only doing through-cuts. I think it's a bit of a misnomer that you lose torque with microsteps. You'll have (close to) full available torque when the motor is at a full step. When it stops at a microstep is when there is less torque. Once the force against the stepper exceeds that torque the stepper will "jump" to the next full step.