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A new way to think about frame size and angle

#1

Hey all,

I took my time to think about the optimum frame size and angle. I think that the optimum can be found, when looking at the cutting force that the maslow can provide at every position of the working area. So I made an analysis of how to calculate this value. See the attachments.

I uploaded an overview of the procedure I am using:
analysis.pdf (539.9 KB)

And the matlab code to calculate the values:
analysis_maslowcnc.m (4.4 KB)

Before I want to do a more thorough analysis, I just wanted to know what you are thinking. If I’m on the right track, or if I missed something?

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#2

there is this spreadsheet that lets you try various dimensions, it doesn’t account for the frame angle (changes would be welcome)

the force available to the motors is always higher than the force of gravity, unless the force to move exceeds the force available from the motors (depends on real-world variables that you don’t know).

so you have two limits

  1. the top center where the limit is how close the force needed comes to the force the motors can apply - friction

  2. the bottom corner where the limit is the force of gravity to swing the sled, which matches the tension on the chain from the far corner - friction

The friction (both static and dynamic) is constant across the work area as long as the chains are parallel to the workpiece (and this ‘constant’ varies based on the surface it’s riding on, including the amount of tear-out from the current cut). Static friction matters because most CAM programs have the sled stop moving when you plunge into the workpiece.

All of the above varies by the frame angle, the closer to vertical, the better the numbers are (lower friction, more gravity available)

but the closer you get to vertical, the less force there is to let you drive the bit into the workpiece (but we don’t know how much force is needed, and that will vary on the bit and wood in use)

In the spreadsheet I don’t try to figure out the friction and plunge force needed, I just take the ‘make these numbers better than stock and your machine will perform better’ approach.

I believe that you come to similar conclusions, with pretty graphs, with a lot more effort, because you map out the entire space and the spreadsheet is just calculating the trouble spots.

There is an earlier tool ( http://lang.hm/maslow/v-plotter.py ) that does a more primitive version of the full map, which helped identify the spots to test.

The real problem is the unknowns that are needed to tie any of these numbers to the real-world

  1. how much friction is there?

    Of the (3.2 pounds-force modified by frame angle) available to move the sled into the bottom corner, how much is lost due to friction?

    The closer to vertical you are, the less friction there will be.

    If friction is 2 pounds of force, then going to a 12’ top beam which gives you 6.4 pounds of force takes you from 1.2 pounds net to 4.4 pounds net, even more dramatic than the doubled number looks.

  2. how much force is needed to plunge into the workpiece?

    As you approach vertical, the available force approaches zero.

without these two values, I don’t see how to modify either the spreadsheet you your mathlab work to do anything better than guidance as we can’t predict the actual results.

We could find the friction number by having someone with a high-speed camera measuring the acceleration of the sled from gravity (get a well-chewed workpiece, hold the sled with only one chain near the bottom corner, let go and measure it’s acceleration)

we can have people try tipping the machine forward while drilling holes and see how close to vertical they can get before the sled starts to rise (try with a fairly dull bit and hard wood)

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#3

FWW - If all Maslow CNCs were the same this could be true.

<> All Maslows are created equal

Thank you

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#4

I really like the work. What I like most is that it is an attempt to explicitly state the performance attributes (minimum available force) which drive a decision for frame geometry. In order to really get this right, all the potential constraints would have to be considered.

I think @dlang did a good job discussing a number of other potential limiting factors.

It is not clear to me that minimum available force is what constrains the Maslow. Here a few other performance attributes which may be constraining:

  • Stiffness:
    • Stiffness in the bottom corners is limited by chain-sag. If a cutting force is in the same direction of the chain’s tension, the chain’s tension is reduced; the chain sags more. This leads to a positional error.
    • Stiffness in the top center is limited by the chain’s elasticity. If a cutting force is downward, the chains will stretch, which leads to a positional error.

What I like is: if you create a script/model/function which can take the frame geometry as inputs, and calculate these you can quickly analyze a frame design.

My recommendation is to just be as meticulous as is reasonable, to include all the performance attributes and parameters. That way you will be more likely to create something that is broadly applicable.

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#5

We have work in place to account for chain sag and stretch (it was developed as
part of the holey calibration work and has been at least partly ported and
merged into the main tree, but there hasn’t been a release yet that includes it)

David Lang

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