[joeavaerage]

Hi,
OK.

The first moment of inertia of the ballscrew is:
J_screw= pi x r² x l x rho x 1/2 x r² where r=radius of the screw, l is the length and rho is the density of steel
=0.51 x 10^-4kg.m²

The first moment of inertia of a 23/24 size stepper is approx:
J_stepper=0.7 x 10^-4kg.m²

The first moment of inertia of the load, assuming 20kg:
J_load= (m x p²)/4.pi² where m is the axis mass and p is the pitch
=0.13 x 10^-4 kg.m²

So the momentum balance is:
38% is the ballscrew
52% is the armature of the stepper
10% is the linear axis mass

The important thing here is that the mass of the axis is a small proportion (10%) of the momentum thus making it a bit heavier or lighter has a very small effect
overall. Given that is the case then making a plate, while being somewhat heavier is not a disadvantage or least enough to outweigh the advantage of simplicity in terms
of manufacture and cost of materials.

Craig

[Thunza]

Hi,
OK.

The first moment of inertia of the ballscrew is:
J_screw= pi x r² x l x rho x 1/2 x r² where r=radius of the screw, l is the length and rho is the density of steel
=0.51 x 10^-4kg.m²

The first moment of inertia of a 23/24 size stepper is approx:
J_stepper=0.7 x 10^-4kg.m²

The first moment of inertia of the load, assuming 20kg:
J_load= (m x p²)/4.pi² where m is the axis mass and p is the pitch
=0.13 x 10^-4 kg.m²

So the momentum balance is:
38% is the ballscrew
52% is the armature of the stepper
10% is the linear axis mass

The important thing here is that the mass of the axis is a small proportion (10%) of the momentum thus making it a bit heavier or lighter has a very small effect
overall. Given that is the case then making a plate, while being somewhat heavier is not a disadvantage or least enough to outweigh the advantage of simplicity in terms
of manufacture and cost of materials.

Craig

Thanks that's interesting to see. I don't think I have enough knowledge to understand confidently but I think I can see your paint point about weight being a rather small element.

[joeavaerage]

Hi,

but I think I can see your paint point about weight being a rather small element.

Yes, that is the most important take away.

As recently as a couple of years ago I'd never bothered to do the detailed calculation and like you imagined that the axis mass would
dominate the momentum and acceleration equations. Only once I started to do the calculations myself did I realise how wrong I was.
Hiwin and Yaskawa publish the same equations albeit in differing and confusing units, but my calculations agree exactly with the principles published.

Again the important point it to be aware of those elements that affect machine performance the most and recognize that other elements, in this case the Z axis mass,
make a small contribution. Thus while you can't be cavalier about the axis mass neither is it a critical parameter.

Craig

[Thunza]

Hi,



Yes, that is the most important take away.

As recently as a couple of years ago I'd never bothered to do the detailed calculation and like you imagined that the axis mass would
dominate the momentum and acceleration equations. Only once I started to do the calculations myself did I realise how wrong I was.
Hiwin and Yaskawa publish the same equations albeit in differing and confusing units, but my calculations agree exactly with the principles published.

Again the important point it to be aware of those elements that affect machine performance the most and recognize that other elements, in this case the Z axis mass,
make a small contribution. Thus while you can't be cavalier about the axis mass neither is it a critical parameter.

Craig

Very helpful, thanks you! I guess even if the stepper can handle it I would still need to make the Y axis robust enough not to sag.

[joeavaerage]

Hi,

I would still need to make the Y axis robust enough not to sag.

If the Y axis, or any axis, sags under its own weight then its grossly too flexible to be considered anything like rigid enough for CNC purposes.

Craig