[MichaelMack]

Hi There,
Sorry for the basic questions,
I've been trying to undertake some calculations for a CNC router utilising rack and pinion.
Hoping for some feedback on my calcs.
Also, for Module 2 straight cut rack and pinion what is a realistic number for positioning accuracy at any point as well as over a length of 3 meters?
Currently in my calculation i have 0.053mm of max positional error which is made up of the gearbox alone.
Furthermore, Are the cutting force and jogging speed realistic? For cutting full aluminium sheets of 2400x1200mm.

Thanks for your help.

[peteeng]

Hi MM - Your numbers check out BUT:
1) To answer about the rack tolerance - they are made to a tolerance so you have to ask the supplier what tolerance it is
2) To calculate the full operational tolerance you have to add the stepper motor tolerance (usually +/-5% of 1.8deg if you have std motors. Can be less if you have high grade motors eg some motors are 2%) then the gearbox tolerance it will have an arc radius tolerance or backlash tolerance then add the rack tolerance. Also there's the microsteps to consider and there is no tolerance on those, they are fuzzy steps that get corrected every mechanical step of 1.8deg to within the 5% tolerance. There is always the question does the controller cut the steps off or add one in when close to the target spot
3) Its unlikely you will get any torque at 1200rpm. The 9Nm is the stall torque or very close to 0rpm. I usually assume its linear from 0-1200rpm say so you have 4.5Nm at 600rpm. Do you have an actual torque curve for the motor driver combo?
4) So assuming you have 4.5Nm at 600rpm then you are moving at 8m/min rapid and have 140kgf available. Some of this torque is consumed by the motor inertia and the gears inertia plus various frictions. For instance seals on cars can be 2kgf each so 4 cars can be 8kgf drag. You can calculate that as well, the motor reflected torque can be considerable if accelerating. Since you only need 10-20kgf to cut the aluminium in a full slot I expect you will be OK depends on what feed speeds you actually want. Maybe 5m/min? at 5m/min the motor is at 312rpm so has good torque
5) if the machine is going to be used for aluminium exclusively I suggest you consider AC servos. They are more expensive but offer a flat torque curve 0-3000rpm and can be over driven. This means if the motor is loaded up the available torque increases overcoming the issue. Steppers if overloaded die immediately. Then the games over lost steps/lost position screwed job. To cut aluminium fast and effectively (commercially) you need high feed speeds to get good chip loads at high rpm spindle speeds. This means servos are the answer. Aluminium if not cut dry correctly or with mist or flood will gall on the tool and effectively weld the tool to the job stopping everything fast. Tools have to be uber sharp and changed regularly etc etc.

What tolerance do you need? and do you know the difference between tolerance, accuracy and repeatability? If you have high repeatability but a poor tolerance sometimes it does not matter. So depends on what work you are doing. If you are trying to compete with a commercial mill I don't think you will get there with a router... So what parts are you making? Peter

[servtech]

Hi MM - Your numbers check out BUT:
1) To answer about the rack tolerance - they are made to a tolerance so you have to ask the supplier what tolerance it is
2) To calculate the full operational tolerance you have to add the stepper motor tolerance (usually +/-5% of 1.8deg if you have std motors. Can be less if you have high grade motors eg some motors are 2%) then the gearbox tolerance it will have an arc radius tolerance or backlash tolerance then add the rack tolerance. Also there's the microsteps to consider and there is no tolerance on those, they are fuzzy steps that get corrected every mechanical step of 1.8deg to within the 5% tolerance. There is always the question does the controller cut the steps off or add one in when close to the target spot
3) Its unlikely you will get any torque at 1200rpm. The 9Nm is the stall torque or very close to 0rpm. I usually assume its linear from 0-1200rpm say so you have 4.5Nm at 600rpm. Do you have an actual torque curve for the motor driver combo?
4) So assuming you have 4.5Nm at 600rpm then you are moving at 8m/min rapid and have 140kgf available. Some of this torque is consumed by the motor inertia and the gears inertia plus various frictions. For instance seals on cars can be 2kgf each so 4 cars can be 8kgf drag. You can calculate that as well, the motor reflected torque can be considerable if accelerating. Since you only need 10-20kgf to cut the aluminium in a full slot I expect you will be OK depends on what feed speeds you actually want. Maybe 5m/min? at 5m/min the motor is at 312rpm so has good torque
5) if the machine is going to be used for aluminium exclusively I suggest you consider AC servos. They are more expensive but offer a flat torque curve 0-3000rpm and can be over driven. This means if the motor is loaded up the available torque increases overcoming the issue. Steppers if overloaded die immediately. Then the games over lost steps/lost position screwed job. To cut aluminium fast and effectively (commercially) you need high feed speeds to get good chip loads at high rpm spindle speeds. This means servos are the answer. Aluminium if not cut dry correctly or with mist or flood will gall on the tool and effectively weld the tool to the job stopping everything fast. Tools have to be uber sharp and changed regularly etc etc.

What tolerance do you need? and do you know the difference between tolerance, accuracy and repeatability? If you have high repeatability but a poor tolerance sometimes it does not matter. So depends on what work you are doing. If you are trying to compete with a commercial mill I don't think you will get there with a router... So what parts are you making? Peter

By convention, a straight cut rack and pinion drive needs 0.05mm (0.002") play between the teeth for a smooth operation, too tight will vibrate due to teeth binding, too loose you'd have vibration due to excessive backlash.

Helical cut and ground rack and pinion reduce both of these outcomes.

It is also possible to fit a backlash elimination gear (teflon etc) to the pinion, if space available. Also, if parameters exist, set backlash elimination up to 0.05mm / 0.002" would help positional accuracy.

Rack and pinions can give a mechanical accuracy of 0.02mm / 0.0005" if correctly set up.

[MichaelMack]

Hi There,
Thanks for your comprehensive reply. And for checking my math. !
I'm not really sure how to respond at this point, but its been a week and I've re-read your reply a few times now. I don't want to leave this open ended.
1) Will have to wait and see what turns up, if it all. Big gamble on my part I know. (see my other thread on this subject).
2) 5% on the stepper for 'normal' steps. can't understand the error for micro steps but technical data is within: https://www.omc-stepperonline.com/do...L86T(V3.0).pdf The gearbox is 20 arc/minute at no load backlash.
3) Torque curve here: https://www.omc-stepperonline.com/do...rque_Curve.pdf
4) This is not by any means a production machine so speed is not a factor in relation to productivity. Looking after cutting bits and reducing noise would be my main value drivers.
5) I understand AC servos are the best option but I'm severely limited by funds on this build. it is not going to 'make money' so must adhere to strict budget. I'm going the closed loop stepper route to try and reduce the margin for error in lost steps. Interesting remarks on the galling, I have experienced similar on my knee mill.

By tolerance I think I mean repeatability. Not so much the absolute size of a cube for example. if it were 0.1mm out of design that wouldn't worry me. If I made 10,000 of them from a sheet I'd want 10,000 okay versions rather than half at .0001mm and half at 1mm. For critical shafts and other items i have the lathe and mill, so this would be mainly profile cutting, chamfering of edges, tab & slot style designs. I wouldn't class it as a high accuracy requirements.

I hope that helps paint a clearer picture on my intentions.

Thanks again for your engagement.

[MichaelMack]

Hi servtech, thanks very much for your input.
I'm picturing some ideas on twin spur gears preloaded laterally to reduce backlash.
I'll have to do some more research to see if what I'm picturing is at all feasible.
Thanks !

[peteeng]

Hi MM - Look at helical gears they solve all of those issues. By the time you cost out a complex backlash compensation device the helicals could look good. Speed is relative and most people once they settle into a "slow" machine want more speed. So may as well try to get it as fast as possible in the beginning. I'm designing an 8x4 machine at the moment and will use 30mm belts on the long axis and ballscrew across the gantry and on the Z. It is possible to use 20mm ballscrews (2010 or 2020 with a mid support and preload it) on the long axis but 2.6m screws can't be sent fedex to my area.. So have a look at long screws from your supplier. They can be speed limited due to vibration but a centre support / preload can fix that. I'd go 2020 or 2525 if you go screws....Peter

quick calc shows 20mm screw vibrates at 500rpm if 2600mm long. If 1300mm long its 2886rpm so centre support is good. 25mm screw vibs at 635rpm so 20mm with support is the go...