Bench Dogs - How to Calculate Maximum Squareness over 12"?

[Bugsysiegals]

Wood Peckers squares are spec'd to have an accuracy of within 0.001" over 12".  It would be nice to know the maximum "theoretical" accuracy a given set a bench dogs (19.90mm vs 19.98mm) "could" produce assuming perfect 20.00mm dog holes, dogs seated perfectly, etc. 

I assume accuracy would be measured using 2 dogs positioned 12" apart horizontally and 2 dogs positioned 12" apart vertically but am not sure it's as simple as doubling the amount of "play" they have to account for horizontal/vertical movement since there's 4 end points involved.

So, for those of you who are more technical savvy in this area, how do you calculate this?

 

[AstroKeith]

I think this is much more complicated. Contributions to 'out of squareness' are at least

Variations in dog diameter
Variations in hole diameter
variations in hole position from 'perfect'
variations in tilt of dog due to sideways pressure from workpiece.

I reckon if you work out the accuracy over 12" in one axis, you can simply double it for 'squareness', assuming the accuracy in the other axis should be the same. So worse case is its double, best case its zero because the errors just happen to cancel each other out.

Even with perfect holes and perfect hole positioning. tight dogs (19.98) could produce an accuracy that could be as bad as .04mm which is worse than the Wood Peckers tolerance (0.001" = 0.025mm). If the dogs were 19.9 it would mean 0.2mm accuracy, ie about x10 worse than the Wood Peckers square.

The advantage of an MFT is that the dogs could be much further apart than 12", thereby improving the accuracy in proportion.

By way of experiment I just placed two UJK fences at right angles on my 'MFT' with UJK dogs about 500mm apart. The dogs seemed tight and I couldn't move the fences under reasonable pressure. My framing square showed an error in the fences of about 0.2mm over 300mm (12").I strongly suspect the holes are not in the perfect positions.

 

[afish]

What Astrokieth said:

"variations in tilt of dog due to sideways pressure from workpiece."  This is assuming the dog is perfectly square with no pressure.

This is one of if not the biggest problem with dogs. I just went over this in the ther post actually.  Even if and that's a big "even" since most of the holes will not be drilled perfectly square to the top. Any slop or wear or variance in in the hole will allow more tilt of the dog.  I mentioned in the other post to check the squareness and deflection of the dog holes. insert your tallest dog and check from both X and Y directions how square they stick up.  Then apply some lateral pressure to see how easy they deflect. Even with tight fitting dogs today the problem will only get worse over time as the holes get looser.  Add to that each hole has the potential to be out varying amounts and in different direction wear and tear from repeated use etc.  All these small variances make it impossible to get accurate repeatable cuts.  As I said in other post sure its close enough for one off cuts but when you start adding up all the cuts on a set of cabinets the problem tends to compound.  When you make a cut out of square on a panel and flip the opposing panel now the error just doubled.  I think the parf MKii does a good job of locating the holes at the table top level but the dog projection and tilt is a big problem. 

 

[AlexThePalex]

It would be nice to know the maximum "theoretical" accuracy a given set a bench dogs (19.90mm vs 19.98mm) "could" produce assuming perfect 20.00mm dog holes, dogs seated perfectly, etc. 

That's easy. The maximum theoretical squareness is always 100%.

Because it could always happen that out of millions of possibilities you're the lucky guy where the dogs line up perfectly.

Theoretically.

In practice of course, you can only hope to get as close as possible, but there simply is no way to calculate that in a reliable fashion. For instance, wood moves, even MDF, and what is true today might not be true tomorrow.

When Woodpeckers gives a tolerance spec, that tolerance is derived from what the engineers calculated for the machines that make those Woodpecker items.

 

[Stone Message]

I hope that I have got this right....

Take a look at the possible worst case:

[attachimg=1]

On the left we have the perfect case of a (grey) guide rail against a pair of dogs (A and B) and perfectly square. However, it is possible that a smaller dog in a larger hole can move the guide rail to the left or right (the two examples on the right).

If the distance between the dogs is D and we take both dogs being out (one to the left and one to the right) then the combined error of the dogs is 2X.

The angular eroor for a small displacement over a large distance is therefore:

2X divided by D  radians.

If the distance is 300 mm (close to 12") and X is 0.08 mm then the angular error is = 0.0005333

To change radians to degree divide by 2 x Pi and multiply by 360.

This give the angular error in degrees as 0.03054 degrees.

That is not a huge amount to worry about in woodworking terms.

In reality the true error would be somewhere in between. It does become significant if one is fabricating multiple pieces that need to be joined together which means a compound error can occur.

It might be worth looking at my 5 cut test (some call it 4 cut test) video to put this error into perspective:


Peter

 

[Bugsysiegals]

Thanks for all the information and clarification!  [big grin] 

It seems the consensus is that while one can get pretty good cuts on a table using the bench dogs as alignment points that cutting on this style of table in this way should be avoided for panels where compounded errors really matter such as cabinets, desks, and other large furniture? 

It also seems from the comments that even if the fence/guide rail is square that pressure can easily move things out of position by enough to matter for these larger projects where compounded errors really matter? 

I was really looking forward to not having to break panels down and final dimension with the table saw but it seems you would recommend to final dimension with table saw?

What sort of panels would you cut on this style top which would be acceptable? 

 

[Packard]

I just started breaking down to final sizes with the track saw.  I added TSO parallel edge guide square rail (two), and then later the parallel guide system. 

I was working slow the first time but the accuracy seemed sufficient for cabinets (I made two uppers). 

I got the saw just for the reason that I (at 72) was having a hard time carrying full sheets down to the basement.  Now I bring up two roller stands and roll the sheet from the mini-van directly onto the sawhorses and cut the pieces to size. 

Initially, I was just measuring and leaving a little extra and making the final cuts on the table saw.  With the squaring arm and the parallel guide, I am going directly to finished sizes.

Is it as repeatable as the table saw?  I think if I made all the saw cuts at the same time on the table saw it would have an edge.  But if I was moving the fence for some of the cuts then returning to the original position, then I would say that there was no difference. 

By working carefully with the TSO equipment I feel it is accurate enough that there would be no discernable difference in quality on the finished product. 

I start with a cut list.  I come home from the lumber yard.  I cut it and carry the pieces to the basement and start right in on assembly. 

It also means I can build cabinets in "the field" (meaning my niece wants new cabinets), and then make the doors at home after the fact.  That is something I could not do before. Now I can show up with a chop saw, a track saw, and a few jigs and assemble boxes.  I'm looking forward to it.

 

[Stone Message]

Thanks for all the information and clarification!  [big grin] 

It seems the consensus is that while one can get pretty good cuts on a table using the bench dogs as alignment points that cutting on this style of table in this way should be avoided for panels where compounded errors really matter such as cabinets, desks, and other large furniture? 

It also seems from the comments that even if the fence/guide rail is square that pressure can easily move things out of position by enough to matter for these larger projects where compounded errors really matter? 

I was really looking forward to not having to break panels down and final dimension with the table saw but it seems you would recommend to final dimension with table saw?

What sort of panels would you cut on this style top which would be acceptable?

Wow - don't get too worried about my remark on compound error - that was just me giving a complete answer.

In general terms, if you can be within the accuracy of my tracksaw cutting station then you can cut cabinet parts to perfection.

Cheers.

Peter

 

[afish]

Bugs, my workflow went something like this (of course it depends on what you are cutting and the sizes of the pieces) I would typically layout my sheet for the best yield and trying to spit the sheet somewhere close to the middle (just to make it more manageable on the table saw). So for example I would use a track saw just to rip the sheet long ways rough cut . Then I will rip the two halves to final dimension and remove any factory edges along the 2 sides. This helps insure you have all your pieces exactly the same dimension and parallel. Try to group all your rips to minimize fence moves.  Then I set up for cross cuts on the MFT bench.  Unless you have a sliding table saw there isnt a better way to square up your panels. If you send a out of square panel through a table saw you still have a out of square panel. Unless you have a very wide cross cut sled but thats going to be cumbersome especially trying to crosscut something 24" x 8'. The MFT is the easiest and best option for anything over 12" wide. smaller than that you can use a crosscut sled or miter saw if you like or the MFT at that point its pretty much your choice.  Make a trim cut and then I would rough cut my panels plus 1/8 or so since I didnt have enough room to the right of the saw for a good stop system I would cut my panels a touch long and then set a stop to the left and trim everything to length.  I screwed a flat plate to the top of my 8020 fence so I could have stops for common sizes or repeat cuts.  I have also used similar stops to TSO's TDS stops but mine where just made from BB and anchor dogs but they work good since you can pop them on and off without effecting the length (you just need to keep track of which holes you are using.  The stop on top of the 8020 works best and is cheap.  My favorite combo.  After I cut my first two panelas I would stack them on top of eachother and match up all edges then spin the top panel 180° if you did your job right they should match up along all edges and you know your cutting square.  Thats the best quickest way to verify square on big panels since any error will be doubled.