[joeavaerage]

Hi,
depends on size.

A BK15,FK15 or EK15 are the standard size for 20mm diameter ballscrews. They use a DF pair of 7002 bearings for a stiffness of 100N/um
A FK20 or EK20 are standard size for 32mm diameter ballscrews and use a DF pair of 7204 bearings for 190N/um. The BK20, also used for 32mm diameter ballscrews
but uses a lesser bearing pair of bearings DF 7004 for 140N/um.

I'm not sure what the standard size for 25mm or 28mm ballscrews, but I rather suspect BK20,FK20 and EK20. The EK20 and FK20 use beefier 72xx bearing and are preferred over BK20 types.

The bottom line is that the screw is many times stiffer than the fixed mount and therefore to secure a given stiffness you must choose the correct fixed end mounts largely irrespective of the ballscrew size.

The ballscrews I got and used are 32mm diameter but machined for fixed mounts at both ends and uses two FK20 (DF paired 7204) fixed end mounts. I did not really consider at the time, what that
might mean. If your construction were perfect then both mounts would share the load. My construction, as good as I tried to make it will no doubt have favoured one mount over another, so I don't
think I can reasonably claim 2 x 190=380N/um, but I might guess that I'd get 200N/um.

Craig

[joeavaerage]

Hi,
found it, BK17 are the standard size for 25mm screws, a DF pair of 7003 bearings at 125N/um.

Craig

PS: Have seen a typo in the previous post, I claimed 190N/um for FK20's, they are in fact 170N/um, I misquoted the FK25 number.

[CallumRD]

Hi,
consider also that a 400w servo (1.27Nm@3000rpm) or a 750W servo (2.4Nm@3000rpm) will exhibit a great deal more thrust than the acceleration alone.

A 5mm pitch ballscrew exerts 125kg (1250N) thrust per 1Nm applied torque. Thus a 750W servo will easily exert a thrust of 2500N. Acting on a 32mm screw results
in 2.25um flex whereas the same servo operating on a 20mm screw results in 3.3um flex.....and that's the screw alone, not counting the fixed end bearing mount.

Craig

Thanks for all the info. Just one point, the servos can't exhibit more thrust than the force required for acceleration plus the force necessary to sustain the cut plus the force to overcome friction. Force is a conserved quantity in this context.

[joeavaerage]

Hi,
my training is in Physics and Engineering, and I would agree that the max thrust is acceleration plus cutting thrust plus friction.......and that's fine until you are standing in front of the
machine. The transient forces are many times your calculation.

My estimate, from personal experience having built and operated a machine of similar size and capacity to yours, is that 20mm is marginally to small, 25mm is about the best balance and that 32mm
is marginally larger than need be. That's not a theoretical calculation but an observation of reality.

Your money, your choice.

Craig

[CallumRD]

Hi,
my training is in Physics and Engineering, and I would agree that the max thrust is acceleration plus cutting thrust plus friction.......and that's fine until you are standing in front of the
machine. The transient forces are many times your calculation.

My estimate, from personal experience having built and operated a machine of similar size and capacity to yours, is that 20mm is marginally to small, 25mm is about the best balance and that 32mm
is marginally larger than need be. That's not a theoretical calculation but an observation of reality.

Your money, your choice.

Craig

I appreciate the insight. My background is in physics myself. The fundamentals are all simple enough, it's figuring out the realities of imperfect parts coming together that's hard.

[peteeng]

Hi - There are two main modes of motion in a machine. Feeding and rapids. Rapids require large accelerations for commercial machines to reduce air time. Feeding speeds require constant velocity for best cutting performance. When cutting, the cutting forces and friction dominate, when doing rapids inertial forces dominate. We generally calculate for rapids and let the cutting forces look after themselves as they are smaller then the rapids forces.. The issue is that with "normal" motion controllers using trapizoidal velocity curves we do not know what the accels are at the knee of the curve. We dimension motors and forces based on constant state accels & velocities from near zero to somewhere up the curve. Say 0.1g or 0.2g or even 2g or more if you need. That's great but what happens at the knee of the curve? Depending on the controller strategy you may get twice or 3x the "design" accel at the knee. If the look ahead is set well then changes are identified well in advance and the machine slows down and smoothly changes direction, but often this is a slow way to go. But if the velocity strategy and accel strategy is to clip at settings then accels can get out of hand. Some commercial systems use engineering jerk control to smooth the motion... all good physics to play with. So its the unknown motion control elements that create "extra" accels over the design accels that are the issue... This is especially true if your work involves lots of small fast moves then this "jerk' control becomes very important for smooth motion... Peter

Engineering jerk is the change of accel over time and has no physical consequences other than rough accels which lead to rough inertial forces.. Lay term "jerky action" is rough motion and could be a quite different thing to engineering jerk.

[joeavaerage]

Hi peteeng,

trapizoidal velocity curves we do not know what the accels are at the knee of the curve.

You've obviously forgotten your calculus over the years.

Trapezoidal velocity means just that. A machine travelling at speed V₀. It is then commanded to accelerate at max acceleration, a_max to speed V₁.

The time to accelerate is t=(V₁-V₀)/a_max. That is a trapazoidal velocity trajectory....the acceleration is know at all times, it is 0 prior to the command
and zero again after the commanded speed increase and a_max it between.

Acceleration=dV/dt. Provided there is no instantaneous velocity increase/decrease the acceleration is known, defined and finite at all times. The acceleration may be zero at one instant
and a_max in the next instant...but that contravenes no laws of physics.

Craig

[peteeng]

Hi Craig - just because we have a trapezoidal velocity plan does not mean it is held to in reality. The path can overshoot, it can undershoot it can do several things depending on the motion planner strategy implemented in the controller. It cannot physically change velocity in an instant at the knee so the physical conditions of friction. inertia, damping and body loads all combine to some sort of averaging... which is actually an uncontrolled motion. Peter

[joeavaerage]

Hi peteeng,

It cannot physically change velocity in an instant at the knee so the physical conditions of friction

You are correct, any instantaneous change in velocity would imply an infinite acceleration.....but that is NOT what a trapozoidal planner, also called a second order planner does.
It NEVER calls for an instantaneous velocity change.

What you are talking about is where the acceleration changes from zero at one instant to some non zero value at the next instant, most people call that jerk.. Mathematically the acceleration curve is not smooth,
but the velocity is......ie the velocity differential exists and is well defined and at no time goes infinite.

You can eliminate jerk with a S curve planner or that is the same as saying that the time differential of acceleration is fixed at some maximum....ie a third order planner.

This can also be achieved just by reducing a_max and is vastly simpler.

Craig

[peteeng]

Hi Craig - All of this is covered in the jerk thread I started elsewhere, very big subject. All I can say is that hobby level and lots of commercial level velocity planners are very crude in the motion control department. Thats because we are happy with relatively slow speeds and low accels. Commercial level controllers do various things much better than hobby level (as expected) and 3D printers do much better as well for less cost. Up to the machine builder to pick the performance they need and can afford. Peter

by the way I researched S curve planners and they do not control acceleration only velocity... and hobby level s curve planners do not control jerk as far as I can tell... Tiny G is an exception...

[CallumRD]

As interesting as this talk about velocity, acceleration, and jerk is, let’s try to refocus on the hardware decisions that must be made long before I think about what kind of motion control algorithms I choose.

[joeavaerage]

Hi,
I've made my suggestions.

1) Genuine ground C5 or C3 screws, second hand or new old stock if budget precludes buying new.

2) 25mm diameter, adequate stiffness without undue rotational inertia, allowing use of 400W servos. 20mm diameter is too small. 32mm diameter is fine but will require 750W servos

3) 5mm pitch preferred. With 3000rpm servos that allows 15m/min when direct coupled.....which is entirely fast enough. 10mm pitch results in 30m/min rapids with the same servo
but will likely never be used. 10mm pitch halves the thrust (625N/Nm) which will probably mean you are forced to adopt a counterweight or gas springs on the Z axis. With 5mm pitch (1250N/Nm)
you can avoid the counter weight/gas springs as such a small proportion of the torque is required to hold the Z axis aloft. 10mm pitch is fine IF you use a gear or belt reduction, where 5mm allows
direct coupling which is simpler and cheaper.

4) FK or EK fixed end mounts using DF paired 72xx bearings as opposed to paired DF 70xx bearings, the 72xx bearings being marked stiffer axially.

Craig

[CallumRD]

Does anyone have any opinions about HGH20 versus HGH25 rails for the X and Y axes? I've already settled on HGH25 for the Z axis.

[joeavaerage]

Hi,
I used THK HSR20 rails/cars on all three axes. They were new old stock. I would have preferred 25mm but that was what I could get at the time, and they are OK.

I would suggest HGH20's would be OK, but HGH25's would be better.

Craig

[peteeng]

Hi Callum - bigger is always better in machine parts. Peter

[CallumRD]

Are there any good reliable sources for reasonably priced THK or HYWIN HGH rails? I'm finding lots of stuff on eBay and Ali but not so much from proper storefronts.

[joeavaerage]

Hi Callum,
'reasonably priced' and 'reliable sources' do not usually occur in the same sentence.

There seems to be 'cheap but questionable' or 'good supplier but pricey'.

With respect to Hiwin rail you are very wise to be cautious. There are a boatload of Hiwin knock-offs. They have the some coloring, even the same part numbers as Hiwin, but they are
Chinese made copies. Very hard to tell the difference, except genuine might be $200 whereas knock-off might be $100.

I have had repeat purchases from this company, and they have my confidence:

https://www.fasttobuy.com/

They list Hiwin rail/cars and I believe are genuine.

Plenty of hobbyists use:

https://www.bstautomation.com/

I have not had any dealings with this company, but many others have and report reliable and genuine service.

Craig

[jackjr-123]

Hi,
consider also that a 400w servo (1.27Nm@3000rpm) or a 750W servo (2.4Nm@3000rpm) will exhibit a great deal more thrust than the acceleration alone.

A 5mm pitch ballscrew exerts 125kg (1250N) thrust per 1Nm applied torque. Thus a 750W servo will easily exert a thrust of 2500N. Acting on a 32mm screw results
in 2.25um flex whereas the same servo operating on a 20mm screw results in 3.3um flex.....and that's the screw alone, not counting the fixed end bearing mount.

Craig

The stiffness values from the THK catalog are for ballscrew nuts!
The stiffness of the screw itself is calculated from its root diameter, length, and how it's supported at both ends.

A fixed-fixed ballscrew is 4x stiffer than a fixed-supported one. In a fixed-supported configuration, the screw itself is often the weakest part.

[joeavaerage]

Hi Jackjr,
why don't you post the pics of the mill you have built showing the materials and techniques and parts you have used.

I am always interested to see what other people have made, and the decisions they took to get there.

Craig

[jackjr-123]

Hi Jackjr,
why don't you post the pics of the mill you have built showing the materials and techniques and parts you have used.

I'm not sure it's very relevant to the actual topic, but here's some old pictures of the build.

It was my first build and certainly far from perfect. But it was designed for milling aluminium and it works well in that regard.
The fixed gantry structure is very good when all is needed is a HF motorized spindle.