Supported rail or other?

[irving2008]

Hi All,
Been doing further research into cutting forces etc to get an idea on what size rails apply for different situations. To do this I investigated drilling and side and end milling operations.

Example 1: Drilling 5mm hole, 10mm deep into Aluminium. Based on a cutting speed of 100m/min this requires a drill speed of 6500rpm. Assuming a feed rate of .018mm/rev = 120mm/min (2mm/sec) this will take 5seconds (although you'd probably peck it so might take twice this in reality). At that feedrate the axial force is approximately 25N (i.e. equivalent to a point weight of 2.5kg). The equivalent for for steel is 2500rpm and .75mm/sec giving a cutting load of 60N. This shows that machine for steel has to be at least 3 times as rigid for the same accuracy as one for drilling aluminium.

Example 2: Drilling 2mm hole, 10mm deep into aluminium using a high spindle speed of 25000rpm. Assuming the same feedrate of .018mm/rev gives a minimum cutting time of 1.3sec and an axial force of 10N

Example 3: Endmilling a 5mm wide cut in aluminium using a 10mm, 2 flute cutter and 0.5mm deep cuts. Normally you'd work out the spindle speed here, but actually for a hobby machine its feed rate thats the issue as we ned to try and get the feed rate per tooth high enough. For a 10mm cutter we are ideally looking for 0.05-0.1mm/tooth so for a 5000rpm spindle speed with a 2 flute cutter we need 500mm/min which is quite high for a hobby machine, single flute cutters would be better but hard to find. Assuming for the moment a feed rate of 500mm/min (thats 100rpm on a 5mm pitch leadscrew) and a spindle speed of 5000rpm, giving a cutting surface speed of 157m/min which is in the range for aluminium (100 - 1000 approx, but the higher you go the more critical coolant/lubricant becomes - at the lower speeds a squirt of WD40 is OK, higher needs more sophistication) and a feed per tooth of .05mm/dent (2 flute). The material removal rate is 1.25cc/min and the input power (over the no load power) needed at the spindle is about 45W with a radial cutting force of 4.5N. Assuming no Z movement there will be little axial forces. This sounds low, but remember we are only removing 1cc/min which is a tiny cut. To put this in perspective, to create a stepper motor mount 80 x 80mm x 8mm from 100mm square, 10mm stock would take 30min or more just in cutting time to rough out and up to 10min for the finishing cut.

Example 4: To remove 1mm from the edge of a 10mm thick piece of stock using an endmill in one pass using a 10mm cutter. At 500mm/min and a 2 flute cutter the spindle speed needs to be reduced to 2500rpm and the power input will be approx 170W above no load power. Cutting forces will be around 40 - 50N primarily in the feed direction with a proportion (20%) perpendicular to the feed.

From these examples we can see a machine to mill/drill aluminium needs to be fairly rigid against forces of around 70 - 100N to give a reasonable safety margin.

For drilling the forces act vertically on both the X-rails and the Y-rails and can be considered to be 50% on each. The worst case situation for deflection is where the spindle is in the middle of both X and Y. The Z-axis has to remain stationary under the vertical load which will be determined by the backdrive on the leadscrew and the motor holding torque and any gearing. For a 5mm lead on a 16mm screw that represents a holding torque of 0.11Nm in addition to anything required to hold the Z assembly in place (about the same again for a 9 - 10kg Z assy). The tricky bit is that the deflection of the Y axis is driven by the weight of the Z assy initially until the drill hits the work at which point the cutting force transfers 50/50 to the X and Y rails. If 50% of the cutting force is < the Z assy weight this has the effect of reducing the deflection in Y until that 50% of the cutting force exceeds the ZAssy weight then the Y deflection goes negative (up).

Assume that the X and Y rails are the same diameter for a bed of 1m x 1m with an active work area of 800 x 800mm.

For 30mm end supported rails the deflection in the centre of the Y rails for a 10kg Z assy is .04mm, reducing to .01mm when the zAssy is 100mm from the end of the Y axis. Drilling as per example 1 would reduce the Y deflection to .03mm but introduce deflection of .015mm in the X rails. At the extremity of Y and X the total deflection is around 0.005mm. Therefore 30mm unsupported rails provide within a .05mm accuracy for Z across the entire work area. A similar displacement error in X/Y would be true of example 4. Anything smaller than 30mm is likely to introduce too much error.

With 12mm fully supported rails the deflection is reduced to .001mm assuming that the forces are vertical with regard to the upright of the support. This of course isn't directly true for Y-rails where the rail support is acting as a cantilever. In that respect the 12mm rail would show much a higher deflection as it is only partly constrained by the support. It is much harder to analyse this but even so the deflection of the support alone is less than .005mm

SO.... the outcome of all of that is what we already knew... a 12mm supported rail is infinitely better than 30mm unsupported rails...

[Lee Roberts]

and now we know ;-)

[irving2008]

I wait with baited breath for you to try 100m/min....Nice theory work....Have you used the milling machine you bought yet?

Nope because I've been in India the last 10 days and its still sitting on the garage floor waiting for me to make a stand for it...

So, Keith, I'm not sure what you're implying about the theory... as regards your video.. I very much doubt a Dremel can deliver enough power to achieve any of my examples, it certainly needs something more beefy in the order of 300W+...

[Lee Roberts]

Sigh...no lube !

[Lee Roberts]

Do you mean coolant? If you did you would notice no build up of chips...coolant finely atomised with a flow of compressed air removing the chips and depositing them everywhere.

Yes i did, how do you atomise the coolant? all the other setups i'v seen they seem to be flooding the cutter with coolant?

[irving2008]

Hey guys - coolant mist is OT, take it to another thread.. btw theres a thread on CNCZone about how to do this using a cheap airbrush spray unit and shop compressed air (for those of us with a compressor)...

[irving2008]

Regarding theory work Irving I'm implying that it's just that, Not fact just an idea thrown out for appraisal.

A good memory and "suck it and see" is a better teacher imho.

True, but the calculations are based on real-world laws of physics. I'm not saying certain things are impossible, you can always empirically achieve theoretically diffcult things - like milling Aluminum with a Dremel - but how long will those bearings last, how does the accuracy drop off as the runout increases, how hot does it get before the poor thing melts, etc... There's no harm in understanding the limitations and designing around them...

All I was trying to show was that the fact that 30mm end-supported rail isnt as good as 12mm supported rail under a range of common tasks that a router/mill might be designed for - which we already knew empirically. I agree "suck it and see" is a good teacher, but equally if I don't have the personal experience I don't take someone else's word for it verbatim without some level of research into the issue. :D