How much does a stepper motor have to be geared down for X and Y axis ?

[Danno]

I'm thinking of using belts instead of a rack and pinion for my plasma table, but would like to know how much gearing down I'm going to have to do.
I'm planning on using the motors from CandCNC, and I believe they are rated around 800 in/lb.
Basically what I need to know is how far should an axis move per revolution of the stepper motor.
Thanks, Dan

[plain ol Bill]

I geared mine down to 4:1 ratio. I believe Tom reccomends 5:1 but I could not find the correct gears for that. Mine is working fine. My system is working with 2547 steps per inch.

[Danno]

5:1 makes sense, but what diameter is your pinion gear ??
Judging by the pictures I've seen, they seem to be about 1" in diameter.
Dan

[plain ol Bill]

Danny I believe my pinion is 1" dia. I'll look at it tomorrow and check diameter and # of teeth.

[Torchhead]

Here is how we arrived at the 5:1. You take the 800 RPM (average loaded RPM you can get from the motors). The pinion is a Gear increase based on the DP of the pinion gear. It's PI times the diameter (good old geometry and is the circumference of the gear). Think about a smooth wheel sitting on a flat surface. When you spin the axle one revolution, the distance traveled is the surface (circumference) of the wheel. Thus a 1" pinion travels 3.1416 inches per rev. If you connect a stepper directly to the pinion you can get some really impressive speeds (>2400 IPM) because of the step up ratio. Nothing is for free. For that extra speed capability you give up equal amounts of torque (acceleration) and resolution (accuracy). Even if you don't use it (the speed) you still "Paid" for it with the losses in Torque.

Like anything else in engineering there are trade offs you have to decide on.

To gain back your lost torque and increase the resolution you put belt reduction to trade speed for the balance of torque and resolution. Plasma cutting is more like a road race with lots of sharp turns rather than a long sprint. It needs to be fast but agile with good acceleration to make sharp turns. Poor acceleration means your corners get rounded and smaller features are harder to cut.

If you use 5:1 reduction with a 1" pinion you get the following:

Max torque is 5 times the motor torque at a given RPM. (You don't get 100% return because now you have to spin the motor faster to get the same speeds which may cost you 1/2 your 5X gain). Max resolution (smallest distance you can move in one step from the PC) is 5 times the direct coupled number. Max speed drops from 2400 IPM to about 480 IPM.

It's somewhat more complex because of inertia; having 5 times the torque at low PRM helps lower end of the acceleration curve more than the upper part

The number of teeth on a pinion divided by PI will give you the Teeth per inch. Divide that into 1 and you get the pitch.

If you want more speed you make the belt reduction ratio lower. Just remember you will always be trading speed for the other two factors. If you have a light gantry and dual drive motor setup then a 3:1 ratio will give you a good compromise. If you plan on doing any contact cutting and need more force than the higher belt ratio is a better compromise.

Acceleration is the ability to more a mass to a given speed over time. Typically measured in seconds. Lower the mass and/or frictional forces and the load accelerates faster. Increase the torque (force) and the load accelerates faster.

[Danno]

Thanks Torchhead for that excellent explanation !!
Since I'm not too familliar with steppers, I was not aware of their rated RPM under load.
Being a tool maker, I'm always trying different ways of improving things, and right now I'm trying to figure out a way of moving the gantry as well as the torch slide using timming belts intead of a rack and pinion.
Obviously if I use 2 1/2" dia timming pulleys, the 5:1 ratio gets thrown out the window.
My concern is to slow the stepper motor down enough to be able to use that large 2 1/2 pulley, but I don't want to get into gear reducers ( $$$ ), and I also don't want to use multiple stepdown puleys and jackshafts because all these things will use up precious energy from the motors.
If I use that 2 1/2 timming gear, I now have to reduce the motor down
12.5 :1 .
Maybe I shouldn't over engineer this things and use a rack and pinion like everyone else !!

[Torchhead]

You are right. The same math holds true for belt drive (basically a wheel running on a surface but the wheel is fixed and the surface moves) I played with some belt drive concepts. The one I liked best was where the motors were on the gantry and the belts went over sprockets and idlers like an old 16mm film projector. Using that method you can use smaller pulleys (reduce the step up ratio) and easily do a 3:1 reduction between the motor and the drive pulley.

I never got one built but I have seen it done on commercial machines used in automation. The belt is fixed on either end and the drive runs alone the belt. By wrapping the belt around the smaller pulley and engaging more teeth you get the same effect and having a bigger pulley.

I think the thing that stopped the project was that a cost analysis showed that a R&P was less expensive to build and at the end of the day the performance was the same. The major advantage if the belt drive was it was a lot more quiet but in a shop with plasma's, router, mills, and air compressors, grinders and local C&W radio stations blaring the noise reduction seemed less of a reason to switch topology!

The machines I have seen with belt drives were used in the semiconductor fabrication business (often in clean rooms) where it was QUIET!

Steppers are easier to gear down than servos. You only have to get them in the 3 to 5 range (one set of pulleys) whereas you really need about 10:1 for servos. You get a much better payback from running servos at high RPM because they don't lose torque with RPM like steppers so every bit of reduction goes to increased torque and resolution.

Gearheads have to have a low backlash coefficient (rated in arc-minutes). On an R&P or belt you have to multiply the arc-minutes by the step up ratio of the final drive pulley. An error of 10 arc minutes is a 2.7% error. If your diameter of the pinion or belt pulley is 2" then you have a possible error of 2.7% of 6" of travel or about .162"

TOM Caudle
www.CandCNC.com

[Danno]

Hmmmm !! Having the belt fixed is also a thought..
My thinking was to keep the carriage that the the plasma torch rides on as light as possible, therefore there would be less mass for the gantry motor to have to move back and forth.
In order to keep a R&P with zero backlash, you have to bottom the pinion into the rack with spring pressure, and that just doesn't sit well with me. Gears are designed to run along their diametrical pitch, and in order for them to do so, one must allow for clearance between the teeth.
At the end of the day, I will probably go the R&P route, because it will be less costly.

BTW;
If I had C&W music playing in the backgroud, I would add a playing card beside the pinion, so that it would run into the rail. Hopefully the noise that would be created would drown out the radio !! LOL

www.dantechfabricating.com

[acmeng]

I recently built my first table, it has a cutting area of about 24 x 48" (it would be bigger if I had the space!) - it is a fixed belt design on X and the two side of the Y axis. I designed it to be light and easy to move (no legs or frame other than for the linear rail), and it is, the whole thing probably weighs 120-150#. The gantry beam is a 2"x4" aluminum extrusion. I'm using actual THK-style linear rail (actually Hiwin), two 15mm rails on the gantry (X axis) and a single 20mm on each side of the Y axis.

I am using Keling 270 oz steppers geared 3:1 with XL timing belt. They are plenty strong even for routing, and that's only running at about 60% of their rated current! The "Drive" belts are 1" wide "L" pitch timing belt. The pinion pulleys are 10 teeth, so about 1" diameter.

[Danno]

acmeng;
I would love to see pictures of your setup !!
I'm actually in the process of building 2 tables. Mine will be able to hold a 4X4 sheet, while my buddy's table will be 2X4 because he is limited for room also.
We'll both be using Hypertherm45's, and the same electronics.

[acmeng]

I will try to get some pictures soon. Right now I am working on a frame to put the machine on top of, then moving it into the garage at my new house (at my parents now).

The plasma cutter is a Riland CUT40. I think the cutting works differently than with a "real" machine and a machine torch - I touch off with a floating head, but pierce is at 0 (actually -0.01 to allow the torch to float up on the slide) to allow the tip to be grounded and cut height is at 0.01 or so.

I would love to have a Powermax45, maybe if I can figure out how to make money with it (working on paying for college and my upcoming wedding now). The first real cutting I did was about a week ago, cutting the support slats out of a sheet. The next phase after the frame is a water table... I've done manual cutting, but I didn't realize how much it would contaminate the air and ground, and any surface the grit can settle on.

Andy

[Bigtoy302]

I am running a 3.75 reduction on mine but I am only using a .75PD pinion on the rack. Works great no problems. I do have mine spring loaded to the rack.