I was explaining the issues we are fighting with for accuracy to someone and started enumerating all the potential sources of error. I thought it would be good to go through them all and list how they are (or are not) being addressed as of the beginning of Nov 2018.

This assumes that the chains, sprockets, chain slack are all kept in the same plane so that there is no error from the chain attempting to skip or the efforts to prevent it from skipping.

This is assuming triangular kinematics (using some triangulation kit on the sled so that the chains are always pointing directly at the bit)

Error | description | error result | type of error | handled? |
---|---|---|---|---|

motor spacing | distance between the center of the motors | primarily affects vertical travel | constant base lenth | careful manual measurement (best accuracy 0.5mm). we know that the current process of measuring with the chain is not accurate due to chain sag and stretch, it is consistantly off by 10+ mm |

y offset | distance from the motor shaft to the top of the workpiece | offsets the coordinates in the Y direction | constant Y offset | if this is wrong, the current calibration may change other variables to incorrect values trying to make things work |

rotation radius | âextraâ distance to add to the actual chain length to reach the bit | affects effective chain length | constant chain length | known values for common triangulation kits |

chain sag | flexible chain/line will sag under itâs own weight in a catenary curve | makes the chains shorter than the machine thinks they are | up to -3% of chain length | |

chain stretch/tolerance | gap between chain links to allow them to move | makes the chain longer than the machines thinks they are. This may be different for each chain, and we have not yet tested to see if this is consistent through the length of the chain | up to +1.5% of chain length (for new chains) | |

sprocket â12 oâclockâ error | the chain is positioned on the sprocket with one pin at 12 oâclock | makes the chain length larger or smaller than expected | constant chain length .5mm/degree | |

incorrect âmanual calibrationâ value | if the chain length used when resetting the chains to the same length is not the actual length (with the sprockets at the 12 oâclock position) this introduces a chain length error | constant chain length | current settings introduce 1-2mm of error | |

chordal action | the amount of chain fed out for a given amount of rotation is not a constant as the effective radius of the sprocket changes | http://chain-guide.com/basics/2-2-1-chordal-action.html | for a 10 tooth sprocket, Â± 2.5%, a 25 tooth sprocket would be Â±0.4% | could be calculated |

sprocket-chain departure angle | since the chain leaves the sprocket at a different angle depending on where the sled is, the top corner of the triangle moves | compensated for in software as if the sprocket was a circle (ignores chordal action) | ||

top beam flex (front/rear) | since the chains are not pulling perfectly aligned with the center of the top beam, there is the potential for the top beam to flex forward slightly | changes the effective motor spacing | we believe this to be very small with the current design, but was substantial with the original âwingedâ frame | |

top beam flex (up/down) | the weight of the sled moves from side to side, changing the downward force on the ends of the beam | measured to be severall mm on a unistrut top beam | introduces tilt (both types) | |

top beam tilt (compared to workpiece) | if the top beam is tilted compared to the workpiece, coordinates are wrong | cut supports parallel to the top beam with the router | ||

top beam tilt (compared to gravity) | if the top beam is tilted compared to gravity, tensions on the chains will not be whatâs expected, which will throw off the position | |||

triangulation kit flex | if the triangulation kit doesnât keep the end of the chain the exact same distance from the bit, (due to flexing under tension, shifting of joints, or other reasons) this will affect the effective chain length | small effect on chain length | varies by tension/angle | |

sled rotation | if the sled rotates to the point that the triangulation kit hits a limit, the line of the chain effectivly bends | the effective length of the chain is shorter than expected | tiny effect on chain length | varies by tension and the force driving the sled against the stop |

triangulation kit sag | the triangulation kit is heavier than the same effective length of chain | this causes the point where the chain connects to the kit to be slightly lower than a perfect line from the sprocket to the bit. This is the same effect as the sled rotation error. varies by tension | tiny effect on chain length | |

encoder error | the encoder measures steps of the sprocket, movement less than that amount cannot be measured | <0.008mm on chain length with the current 8k steps/rotation and a 10 tooth sprocket. | ||

backlash | as tension moves from mostly being on the sled side to mostly being on the âslackâ side the motor moves without moving the chain | makes the chain shorter than the machine thinks in the bottom corners | constant amount when chain length is âtoo longâ | tiny effect on chain length |

weight of cords/vacuum hose | depending on where the sled is, there is a different amount of weight added to the sled by the cords/vacuum hosts | makes the sled heavier than expected, adding additional tension | believed to be small effect on tension | changes chain sag |

some of these errors are very small, some are accounted for in the model, some we havenât tried to address yet.

Are there any other sources of errors that anyone can think of? are there any comments on the amount of error introduced by each type?