Plasma Attempt #2

[Jonathan]

I can simply add the tube weight to the gantry weight.

Wait what... I thought this tube was spinning? Either way yes you do need to add its weight to the gantry, but if it's spinning the moment of inertia of the tube is far more significant than that.

Moment of inertia of 16 gauge is 3.35 times less than 10 gauge, so 0.135Nm as opposed to 0.45Nm - still a lot.

P.S. By my definition I've not used any maths yet, let alone made it slightly complicated!

[Robin Hewitt]

Wait what... I thought this tube was spinning?

This is the difference between maths and arithmetic. I happily put all the mass on the outside diameter, assume 10g is twice the weight of 16g and overestimate the inertia somewhat.

You work to three decimal places and we disagree

Incidentally, what thickness are you using for gauge? Once you get past tiny the OD goes up in multiples of 1/8". People like tubing to fit snug one inside another so the wall thickness is usually 1/16" for 16g and 1/8" for 10g.

My 4 x 4 * 10g box section has a 1/8" wall, I just measured it.

[Jonathan]

You work to three decimal places and we disagree

Not quite - we disagreed because we're talking about fundamentally different things. I should have explained myself more clearly. It's three significant figures anyway :whistling:
To accelerate the gantry the motor needs to impart translational kinetic energy into the whole gantry and rotational kinetic energy into the rotating parts. Therefore we must consider the sum of the torque contribution from each. So far you've only considered the translational kinetic energy, so I worked out the torque contribution from rotation. For that instead of calculating the inertia, you find the moment of inertia (I), which is a measure of an objects resistance to changes in its angular velocity and use the formula torque=angular acceleration * moment of inertia, where acceleration is in rad/s^2.

In post #4 I calculated the moment of inertia of your 10g (well not quite, see below) tube using the formula, courtesy of Wikipedia:


In post #5 I calculated the acceleration of the tube and stuck that in the above formula for torque to get 0.45Nm and subsequently 0.135Nm. With the mass of the tube included your estimate for the torque due linear motion is now 0.55Nm, so just add that to the figures I get to find the overall system, i.e. 1.0Nm or 0.68Nm. Or if you used 12mm steel bar it's <0.01Nm added... I should also calculate the moment of inertia of each pulley and add that to the system, but it's not going to change the conclusion. Either way the 3Nm motors even on 50V drivers (although clearly 70V preferable) will be a good match and surely the best option since they are the best price/Nm!

Incidentally, what thickness are you using for gauge? Once you get past tiny the OD goes up in multiples of 1/8". People like tubing to fit snug one inside another so the wall thickness is usually 1/16" for 16g and 1/8" for 10g.

I used:
http://www.engineeringtoolbox.com/ga...eet-d_915.html

Is this some silly American/English difference in the gauge system (like with wire gauges)?

I got some 15mm wide, steel reinforced belting which is probably massive overkill but I'd rather it stretched as little as possible.

It would be interesting to know how much it actually stretches - i.e. find out the spring constant. You could hang up a length of it and attach something heavy, put DTI underneath and zero it, then add known mass and see by how much it stretches. I've spent ages trying to find the spring constant of different types of timing belts, but just can't find anything.

[Robin Hewitt]

use the formula torque=angular acceleration * moment of inertia, where acceleration is in rad/s^2.

In post #4 I calculated the moment of inertia of your 10g (well not quite, see below) tube using the formula, courtesy of Wikipedia:

I'm sorry to do this to you, good try and all that, know you only want to help, but you can't bamboozle me with your arithmetic and Wiki-whatsit

force = mass * acceleration

If you want torque you add a distance component

Torque = mass * acceleration * radius

Of course the acceleration here is peripheral acceleration, not radians/s/s

If you insist on radians/s/s and moments of inertia... One turn is 2 pi radians and moves you by 2 pi radius so they simply cancel out after you have gone all the way round the houses.

The 1/8" wall tube weighs 2.35 kg, the peripheral acceleration is the same 2.94 m/s/s as the gantry, the worst case radius is 0.019 m

2.35 * 2.94 * 0.019 = 0.131 Nm

But geared 3:1 down the motor only needs to find an extra 0.044 Nm

[Jonathan]

Fair enough, that's a nice intuitive way to work it out for a thin-wall tube since you can assume the mass is concentrated at the radius. This clearly is an approximation, since the tube does have thickness, so to work it out accurately you have to consider the integral of mass*radius^2 and you end up with the formula I quoted after touching upon real maths! In this context the approximation is of course valid (error is <10%), however this method wont get you very far if the tube was substituted for a simple shaft.

The 1/8" wall tube weighs 2.35 kg

Now your numbers make sense, it must be 2700kg/m^3 and therefore aluminium tube...I thought it was steel! Hmm to be fair you did say it was aluminium originally. Whoops...