Requesting Guidance on Designing a CNC Machine for Machining Wood and Polystyrene

[joeavaerage]

Hi,
the frequency of oscillation is:

w (angular frequency in rad/sec) = (k/m)^1/2

Where k is the stiffness of the spring and m is the accelerated mass. If k is very high (relative to the mass) then the oscillatory frequency is likewise very high.
It is low frequency vibrations that cause chatter which is extremely harmful to CNC machining operations.

Has been that way since Newton first wrote the differential equation of oscillatory motion.

You can bang on all you like about input shaping and jerk control ........you cannot change the basic physics, you're trying to 'put lipstick on a pig'.
The bottom line is increase the rigidity of the structure to the extent that the lowest natural frequency is no longer troublesome. Its not hard....just demanding!.

Craig

[peteeng]

Hi Craig - I'm not changing the physics just improving the machine performance. Anyways I have been asked a couple of times about comparing R&P to ballscrews. So here's a sample calculation. R&P's require gearboxes to reduce the potentially very high feed velocities. This also means you get more torque so you can use a small motor. Depending on what feeds your machine requires (lasers need very high speeds, mills require much slower feeds etc ) sets the gearbox ratio. In this case I have compared a 400W servo with 10:1 gearbox to my large NEMA23 motors with 10mm pitch ballscrew. They provide about the same force depending on the speed needed. So the servo being a constant torque machine can push with 97kgf no matter the speed and the 10mm ballscrew is 173kgf at stall reduced to 86kgf at 500rpm... 400W is a small servo. Since R&P has no vibration issues you can run them very fast. I suggest using helical racks vs straight cut, they are readily available these days and by my costings they are not any dearer then a ballscrew set up. Peter

using a 10:1 gearbox results in a top feed of 25m/min this maybe a bit fast for some people so if you used a 20:1 giving 12m/min that would give the rack a force of 194kgf across its speed range. Thats quite a healthy force at 12m/min feed. The 10mm ballscrew at 500rpm is 5m/min. A 16mm ballscrew 1400mm long will whirl at 1228rpm.. so maybe you could rapid at 1000rpm or 10m/min.

[POORIAPK]

Hi PRPK - Whichever machine material you choose is fine. You need to understand its pros and cons and what you are trying to do. Your first entry says wood and plastic. An MDF machine will be fine for those and be lower cost. If you want to mill aluminium and steel then MDF won't work. If you choose metal you can bolt the machine together or you can weld it together. Both approaches work and use a different philosophy & resources. Make the machine the size required and make the Z a bit taller then you think you need. The Z height is the one that gets me into trouble with long tooling. To solve the Z height issue consider an apron on the machine or a bed well. This allows larger objects to sit lower so you can work on them. I don't know what you intend machining so the "best" machine configuration I can't help with at the moment. There is a company in Germany that make very large routers for cabinet makers and their machines are plywood. Gantries are 3m long and machines can be 16m long or longer. So ply as a machine material is fine if you take the time to understand it.

What Craig is trying to say is make every component as big as possible. Take up every available space for that component. Geometry is your friend and a big object is significantly stiffer then a small object even considering the material modulus. With construction extrusions there is a lot of material on the inside of the section that does not contribute to the global stiffness of the section. They also have a lot of thin free edges which vibrate, Speaking of which the dynamic stiffness of a machine is a very big topic but if its static stiffness (initial rigidity) is sufficient you have sorted most of the issues. Keep at it - Peter

Thank you very much for the information you provided; it will be very useful for me. I completely agree with you on the use of different materials and selecting the material based on need and budget. Every material used yields a result, and we should choose according to our requirements. In designing the machine shown in the above picture, I tried to do almost what others have done and succeeded with, mostly by imitation rather than design. This approach can be both good and bad! I overlooked some calculations, but as I mentioned, I am currently designing another version. This time, the design will include analysis, and I will definitely share the results in this forum.

[POORIAPK]

If you're adding a 4th axis, consider installing it so that the center of the rotary axis is at or around table height. This will minimize the length of the Z axis, compared to simply perching the assembly on top of the table. Since cutting is almost never done any lower than the center point, you don't lose any useful area that way. It will require either cutting out a section of the table, or mounting the 4th axis and tailstock assembly outboard, but neither are too difficult to implement.

I have something like this picture in mind for the fourth axis, but with some modifications.

[POORIAPK]

Hi,
an aluminum SHS of 80x80x6 has a moment of inertia of 3,413,225 mm⁴
An aluminum SHS of 100x100x4. has a moment of 8,333,289 mm⁴


If you had two sections, both 1000mm long, the 80mm section will deflect 2.44 times as much as the 100mm section. Both of these section weigh the same, that is to say they have the same amount of material
in each, but the bigger 'geometry' is nearly 2.5 times stiffer.

The idea is to use the biggest geometrical section you can to maximize the stiffness.

Aluminum has a modulus of 70GPa , while steel has a modulus of 207GPa. If you had two sections 100x100x4.8, both 1000mm long, then the aluminum section will deflect 2.95 times as much as the steel section.

The idea is to use the material of the highest possible modulus. For practical CNC purposes that is steel.

If you have two sections of 100 x100x4.8, one 1m long and the other 2m long the long one deflects 8 times as much!!!! That is huge.

I suggest you avail yourself of one of the online beam deflection calculators, they are very instructive. As an example:

https://skyciv.com/free-beam-calculator/

Just to put some real numbers on these assertions. From the calculator a 1m long cantilevered 80 x 80 x 6 aluminum SHS loaded with a 1kg (10N) force at the very end deflects by 14mm.
A 1m long cantilevered 100x100x4.8 SHS loaded with the same 1kg (10N) force deflects by only 6mm. The same weight of material in the two sections but the larger geometric section deflects by less than
one half.

A 1m long cantilevered 100x100x4.8 SHS but of steel, loaded with the same 1 kg at the very end deflects by only 2mm, about one third of the same section in aluminum.

A 2m long cantilevered 100x100x4.8 SHS steel loaded again with 1kg at the very end deflects by 16mm....so fully eight times the 1m steel section.

The takeaway is that if you made your machine half the size (1.25m x 0.65m) you would in general expect it to be eight times stiffer than the full size (2.5m x 1.3m) machine made from the same
materials.

Big geometric sections are your friend for stiffness, as is steel by comparison to aluminum, and a smaller machine tends to be a LOT stiffer than a large machine.

Craig

Your information is complete, accurate, and sufficient, and I enjoy reading it. Thank you. We must also consider whether the force needed to deform an aluminum profile or any other material is actually applied to it. This depends not only on the material but also on the design. I completely agree with you that using profiles with larger diameters results in a more rigid structure. However, we should also consider that the forces applied to each profile might be such that even smaller and lighter profiles, less than 80mm, could still work well! Or perhaps the deformations in a material might occur in areas that are not critical to us and thus do not significantly affect the final outcome. (This needs to be investigated.) I need to choose between switching to larger diameter aluminum profiles and using steel profiles or other materials. But first, I need to accurately determine what forces of what magnitude are applied to which parts of my CNC machine

[peteeng]

Hi Pooria - The design shown is good but it can be better. The issue with a rotary on the bed of the machine means that the Z height will need to be much higher then the bed requires. This means for normal use (using the bed) the Z axis will be extended downwards a long way and therefore will not be rigid. If the rotary is something that will be used alot then it is better to place it at the apron (the front) of the machine in a well or to the side of the machine again in a well. This makes the Z axis more compact and stiffer. It also means the bed is available for the normal work without upsetting the rotary set up. If the rotary is something that will be used alot then definitely don't make one that sits on the bed. In the case of the Maverick it has a bed cover so in "normal" use the rotary is covered and the space is available for flat sheet work. My first machine had an apron and I miss it. Was great for doing edge work.

Usually with a gantry machine it has a lot of forward envelope due to the Z axis and spindle fwd offset. It therefore has lost space at the rear. Using the fwd space for the apron does not take much effort as the spindle will reach it easily... You can put the rotary on the apron if it is not often used. If you have to reach over it for normal use it would become an irritation.

Here is such a machine. It has the rotary to the side and an apron for edge work. I suggest you look at this style of machine.
Maverick 4×8 | Legacy Woodworking Machinery, LLC

Peter

edit - the machine you imaged with the steel bed and rotary will be difficult to access due to the walls on the long axis. If you do a high rail design with walls make the gantry in the long direction so you have easier access to the machine bed. I expect that machine will use a bolster for its work. A bolster is a sub table that gets assembled off the machine then gets craned onto the machine and it gets bolted down. Thats great for production work if you have cranes and forklifts and require rapid setup / changeover times... I expect something like the maverick works better as it will allow side access. If your machine is big side access will be needed.

[POORIAPK]

They work very well in foam but in harder materials they will increase the load on the spindle bearings quite a lot.They are also quite expensive and hard to find once you look for diameter/length ratios above six.

The dimensions of raw materials and cutting tools are always designed and manufactured according to our needs and the available conditions. For example, foam material can easily be obtained in large foam blocks from the market, and the machines that perform foam machining usually have a longer Z-axis. As a result, the cutting tools used in these machines can be longer if needed, without limitations. However, the harder the material to be machined, the more limited the conditions become.

[POORIAPK]

Morning Pooria and others - In prior posts you have said that vibrations "transmit" through the machine. Other people also think that stress "flows" through structures. These are incorrect ways to think about the process (I appreciate its the conventional way to think about it but there are better ways to conceptualise it) . Everything vibrates even people. Structures and their parts have a "natural vibration frequency" and if there is a freq or a harmonic near that the structure or part it will vibrate at its natural freq. You can also get things to vibrate at non natural freqs (forced vibration). A vibration implies a deflection which can be tiny or large. The issue with machines is that if the driving freq is persistent (like the teeth of a tool impacting the cut surface at constant timing) then the deflection (vibration) will reinforce itself and become bigger (resonance). If you wipe your finger around a champagne glass the sound starts small but if you continue exciting it the sound becomes louder as the deflection becomes bigger (moving more air). Now materials have internal friction. Materials are not continuous but consist of "grains" or chains that are kept together with friction. When the material deflects these grains rub together and convert the movement to heat. Just like when you rub your hands together and they get warm. Some materials have large slippery grains like cast iron some have tiny grains that are locked together quite tight like steel. That's one reason steel is strong as its grains are highly locked up. This is called material hysterisis. So every part in the machine is vibrating and at any point in time its also damping itself. We need to avoid resonance or a forced vibration ie the vibration input gets bigger then the internal damping can slow it down. So to get back to the point.

An operating machine is vibrating everywhere. When cutting material the main issue is to not get chatter. This is when the teeth of the tool excite the machine at a freq that is detrimental to the cut and particularly if the machine head has a resonant freq near the cutting speed. Look up tap testing, input shaping, active damping. These are advanced methods of vibration control. Material damping is not enough to produce an overall "damp" machine. Currently we more or less operate machines in zones that avoid resonance. The 3D printing market has had to address light machines with low rigidity so implement input shaping for instance and jerk control... These produce much smoother paths then maker lever cnc machines. Peter

see page 10 - materials are not damp enough

Two good controllers that have jerk control are Dynomotion and Buildbotics...

The discussion of natural frequency and solving vibration issues becomes more important when we are talking about rotating components. For example, when a turbine is supposed to transfer power through a clutch and coupling to a gearbox and generator, and these components are mounted on a chassis. When a cutting tool is rotating and comes into contact with a material, the natural frequency isn't as critical as in the previous example. To avoid chatter, we can reduce the spindle speed or adjust the feed rate of the tool into the material.

The discussion of natural frequency and vibrations is indeed important and serious, and I appreciate the valuable information you provide to me and others. This issue definitely needs to be examined in large and professional CNC machines. However, keep in mind that I am building a relatively inexpensive machine, and the hardest material it will be machining is wood

[POORIAPK]

Hi,
the frequency of oscillation is:

w (angular frequency in rad/sec) = (k/m)^1/2

Where k is the stiffness of the spring and m is the accelerated mass. If k is very high (relative to the mass) then the oscillatory frequency is likewise very high.
It is low frequency vibrations that cause chatter which is extremely harmful to CNC machining operations.

Has been that way since Newton first wrote the differential equation of oscillatory motion.

You can bang on all you like about input shaping and jerk control ........you cannot change the basic physics, you're trying to 'put lipstick on a pig'.
The bottom line is increase the rigidity of the structure to the extent that the lowest natural frequency is no longer troublesome. Its not hard....just demanding!.

Craig

In the new design, I will try to consider all the conditions that I have the knowledge to calculate. Thank you.

[peteeng]

Hi Pooria - Chatter is something that every machinist will experience at some point. I was making timber spoons yesterday and got some chatter that resulted in the timber splitting. Mainly due to its fixturing but chatter all the same...
The strategy of reducing rpm or adjusting feed rate is a compromise that these days does not have to happen. My experience with some Makers is that once they settle into the machine they want to machine faster. Why take 30mins to do a job when you can do it in 15? Why take 3hrs to do a job when you can do it in an hour? Modern CAM systems provide high speed machining options that allow this if the machine can do it. So even though you may build an in-expensive machine these issues can be addressed at the design stage. They can't be fixed once built... Once you design it, the machines DNA is baked in and it takes drastic action to fix or improve it. So I'm saying its worth a think and a conversation to take your machine to its best possible development on paper, costs nothing and may give you an advantage over the next few years of the machines life... This forum and other forums are filled with inexpensive machines attempting to be upgraded. Plastic parts to metal parts, bigger gantries, bigger z axes etc etc. By the time they get through all of those "upgrades" the machine has doubled in cost and its performance has been improved slightly. Better to sort it out at the beginning... as I'm sure your aiming at doing... Peter

[POORIAPK]

Hi Pooria - The design shown is good but it can be better. The issue with a rotary on the bed of the machine means that the Z height will need to be much higher then the bed requires. This means for normal use (using the bed) the Z axis will be extended downwards a long way and therefore will not be rigid. If the rotary is something that will be used alot then it is better to place it at the apron (the front) of the machine in a well or to the side of the machine again in a well. This makes the Z axis more compact and stiffer. It also means the bed is available for the normal work without upsetting the rotary set up. If the rotary is something that will be used alot then definitely don't make one that sits on the bed. In the case of the Maverick it has a bed cover so in "normal" use the rotary is covered and the space is available for flat sheet work. My first machine had an apron and I miss it. Was great for doing edge work.

Usually with a gantry machine it has a lot of forward envelope due to the Z axis and spindle fwd offset. It therefore has lost space at the rear. Using the fwd space for the apron does not take much effort as the spindle will reach it easily... You can put the rotary on the apron if it is not often used. If you have to reach over it for normal use it would become an irritation.

Here is such a machine. It has the rotary to the side and an apron for edge work. I suggest you look at this style of machine.
Maverick 4×8 | Legacy Woodworking Machinery, LLC

Peter

edit - the machine you imaged with the steel bed and rotary will be difficult to access due to the walls on the long axis. If you do a high rail design with walls make the gantry in the long direction so you have easier access to the machine bed. I expect that machine will use a bolster for its work. A bolster is a sub table that gets assembled off the machine then gets craned onto the machine and it gets bolted down. Thats great for production work if you have cranes and forklifts and require rapid setup / changeover times... I expect something like the maverick works better as it will allow side access. If your machine is big side access will be needed.

I've seen the operation of a machine from the company you linked to, and I must say, they make high-quality machines, even though they are a bit pricey . Initially, I was planning to use the space behind the spindle and the rear of the machine to house electrical components, like building the electrical box into the structure itself. As we know, most machines that place the fourth axis on the side or front typically have a shorter Z-axis compared to my machine, and I decided to take full advantage of the taller Z-axis. While placing the fourth axis on the structure, as you mentioned, would indeed provide better machining conditions—thanks for pointing that out—I'm not planning to use the fourth axis frequently, and the material I'll be machining on this axis won't be very large. I'll have to see how things evolve in the next version.