Accuracy Issues and Calibration Overview

Wiki
21

A catenary is the result of an equilibrium of forces among the chain links. A few important property of the uniform density catenary are:

  • vertical tension is null at the apex.
  • horizontal tension is constant through the catenary
  • tension accross a chain link in only determined by the horizontal tension, and by the vertical tension due to the catenary segment that lies below that link down to the catenary apex.

Now the Maslow sled and ring kit rollers are lumps of mass. At a first degree, we could say it is not a uniform density catenary. But it can be simplified by:

  1. first considering the whole sled, including rollers, as a mass lump.
  2. Divide the lump in two parts reflecting the part of the weight held by each chain (this depends on the sled horizontal position).
  3. Replace the mass lump at the tip of each chain by an equivalent chain length of same weight.
  4. Combine each real chain length with the equivalent chain length it holds, and from that point on, stop assuming these two long chain connect together: Consider those as two separate catenaries having the same horizontal tension.
  5. Calculate a horizontal tension on the sprockets based on the sled weight and position. It is a valid approximation.
  6. Use the simple catenary calculations to find its shape, knowing that one part hangs from the sprocket, end the other is flat horizontal where vertical tension is null (the apex).
  7. Now you want to compute the relative coordinates of two points on each of these catenaries:
  • the position of the highest point (where the sprocket tengeant contact occurs
  • the position of the chain tip that hangs at the length of the real chain minus the part the wraps around the sprocket.
  1. Also compute the angle of each to figure out the tangeant points on sprocket and the connection point on the ring,
  2. Now you might get something that does not exactly fit between the sprockets. That is not an error. Remember your horizontal tension estimation was assuming a sled position, but the catenary equilibrium is moving away from that. So use this first catenary calculation to better estimate the position and horizontal tension, and iterate until you get a stable result that fit between the sprockets for the given chain lenghts.

And there you get a catenary calculation of the sled position.

Is that the optimal way to compute the solution? I don’t know. But you can play with it :slight_smile:
I did implement that catenary calculation here to analyse the MaslowCNC errors and document the list of sources of errors.

22

Do you get different horizontal tension for the two different chains?

23

Good point @Joshua. I edited my post to make it clear to keep the same horizontal tension.

24

Let me just ask really quick. Regarding the above discussion about the catenary equation; is there a different forum topic where we should move it?

25

This wiki thread is initially the introductory topic, and it covers explanation of what is chain sag.
We should clean this up to leave the simple yet accurate introductory topic.

Then we could move the catenary /approximation/more advanced diagrams to a thread about “Sag compensation accuracy” and attach that new thread to section 7 of the Wiki table of content “technical details”. I can’t clean-up with my current forum user status. Maybe we should ask @Gero or @dlang or @madgrizzle or…

26

What specifically are you trying to do? You should have the ability to edit any of the initial posts or placeholders. if you are referring to deleting posts after those, I don’t know who has that ability (I don’t either), but I wouldn’t necessarily worry about it too much.

1 Like
27

Let me know if I can do something. Have received admin rights to create a category and they forgot to take them back :slight_smile:

28

Considering you keep bumping zombie threads, I don’t think you should have any sort of privileged access to the boards. :wink:

29

Warning :smiley: I plan to bump several wiki “zombie threads” to refresh first line information about the basic Maslow mechanical behavior, parameters settings, then add advanced technical details topics.

Would you have some recommendations? :open_book:

2 Likes