Well,
Here is my problem I am trying to figure out torque loss or gain in a belt drive system so correct me if I am wrong but all the math is the same as with a rack and pinion system correct so what is the formula for cut torque here are the numbers direct drive 269ozin motors driven with lots of voltage directlly connected pully of 1.75"pitch diameter motor spinning say 800 rpm how do I figure out the torque(not concened with friction losses etc at this time) now what if I put in a 2:1 reduction now what and how do I figure the resolution as I am sure it is really small I have 200 steps motors with Gecko 203 for 1/10 microstep

I will attempt answer, even though I am still new to cnc machine building. Everyone, feel free to correct the answer.

1) Torque from the motor
My understanding is that
- servo motors are approx the same torque over most of their normal speed range.
- stepper motors are approx the same power over their speed range, so they have the most torque at low speeds.

In order to actually know the torque of a stepper motor at a given speed, you need to look at its torque curve. Here is a link to some example motors from kelinginc.net. http://www.kelinginc.net/SMotorstock.html Notice how the torque drops off with rotation speed. This is more or less true with normal stepper motors AFAIK.

My understanding is that micro stepping a motor will result in approx. 30 % loss of torque compared to its "full step" torque rating.

As far as down wind of the motor, every thing is pretty much just ratios after that. If the (pitch) diameter of the pulley on the motor is 1/2 the diameter of the one you are estimating, then the torque will double, and the speed will drop by 1/2. Each 1/10th micro step will now be equivalent to a 1/20th micro step.

If you are driving a screw, then you just keep multiplying the ratios out until you have the motion per revolution of the motor.

In general, I think it is easier to just calculate what happens to the linear motion when the motor makes one full rotation, and then just divide by 200 to see what happens for one full step, and then again by whatever microstep you are using.

BTW - I think 800 rpm is a bit fast for a small, low torque stepper motor to be very useful - the torque will be so low that it might be prone to loosing steps. I am not sure if this is better or not, but I am hoping to run more like 5 - 50 rpm in my build, although that is on the very slow end for most users. Maybe consider a slower motor speed and more microsteps ?

harryn,
yes I am sure you are correct I am sure the numbers are not do able I dont plan to use those numbers I was just throwing stuff out there my main concern is how to figure the torque with belt drives if I have a pitch of the belt and the pitch diameter or number of teeth for the pulley and I know the torque of the motor what are the formulas to figure out the torque available to apply to moving the gantry and pushing the router throught the material wood, foam, etc..? Now remember the gantry is connected to the belt and ther are no screws think of a rack and pinion system with belts but the belt spins around the pulleys instead of the pinion riding down the rack and the gantry is connected to the belt unlike rack and pinion where the motor in connected to the gantry.

Yes, I think I understand - this is called a trolley setup. It also applies to rack and pinion designs. I am getting a lot of useful info from www.brecoflex.com

Example

Motor torque = 100 (oz) (inches)
Pulley pitch radius = 2 inches (diameter = 4 inches)

Belt force or movement force = (100 oz inches) divided by (2 inches) = 50 oz.

In other words, if the world is perfect, this setup could pick up a 50 oz weight (about 3 lbs) If you need more force than this, you either need a stronger motor or smaller pulley - or counteract the weight with a constant force spring. ( I need to do this on mine)

I am doing something similar to you, but decided to risk it all and use 50mm wide, 10mm pitch belt as the rack, along with 50mm wide timing pulleys as the pinion. Drive with NEMA 34 size motors, as this needs hefty torque to work.

If I remember right, you are thinking about a fairly large (4 x 8 ft) project. Large projects like that tend to have at least 500 oz inch motors and some are over 1000. I am still trying to really understand the impact of cutting forces on the required motor torque, but this actually might be more than the movement force needed.

BTW, steel tension members stretch less than Kevlar, but are a lot less flexible.

The random walk decision making process to this point is outlined in my build thread. (so far, more like a shopping list ) It might be dangerous to base your design on my very unproven approach.

Good luck

If someone could check my figures ...be most appreciated.

I've already ordered and paid for the parts so there's no turning back now .

Building a steel machine 2.8 meter X 1.6 meter , got a 4 axis controller /micro stepping 1600 steps (which i'm pirating from my old machine) & 4 X 269 0z steppers.

2 motors on x axis = 538 oz .....got 3 pulleys (Heavy duty 15mm wide , 4 mm thick belt---glass fibre tension ) on each motor ( 15 teeth to a 45 teeth ---- 45 teeth to the belt) , in my book that increases my torque 3 fold equaling 1614 oz in total or close onto 45kgs

----
! 15 ! Teeth -------motor
! !
! !
! !
! 45 ! Teeth ------------- ! 45 ! Teeth
----- ^ -----
shaft/axle BBBBBB Belt

reducing my rpm 3 to 1 ....considering most steppers are at optimum rmp around 300 ..... reduced in my case -- say 100 rpm . which means my 50 mm diameter pulley has a circumfrence of 157mm or will travel 157mm per revolution. 100 rpm X 157mm = 15.7 meters per minute or 628 IPM ( inches per minute). accuracy 157/1600 = 0.098 per step

are these calculations correct??? :?

Sorry ... a bit late, but this is a good site for all things belt and pulley. http://www.mulco.net/eng/index.php Need to reg but worth it. Inch and metric sets


Paul