3 ms·

It absolutely matters. The type of fit you get between a shaft and a hole differs on the order of 5 - 10 microns [1]. A micron is 0.01% of a cm so 0.03% can con

It absolutely matters. The type of fit you get between a shaft and a hole differs on the order of 5 - 10 microns [1]. A micron is 0.01% of a cm so 0.03% can consume a large portion of your tolerance budget. For example, you can make a shaft that fits in a hole like a spring because it can slide freely but air can't get out and you can shave a few microns off and it will sink into the hole at a controlled rate. This is all easily achievable in a home machine shop on a manual lathe. With Wire EDM, you can achieve even tighter tolerances and it would be perfectly possible to generate a part that could fit but could not spin because of the PDF error. [1] https://en.wikipedia.org/wiki/Interference_fit https://en.wikipedia.org/wiki/Interference_fit

mrb 3y ago
It doesn't matter. The error is 0.03% only with one of the most simplistic approximations of 1 Bézier curve per quarter circle. Bump this to 2 or 4 curves, and the error drops to 4.0e-6 or 6.2e-8 (https://pomax.github.io/bezierinfo/#circles_cubic https://pomax.github.io/bezierinfo/#circles_cubic) You are going to have a really hard time finding an industrial application where a 6.2e-8 error matters. In fact, check this out: the Epilog Fusion M2 40 laser machine that the author chooses to picture as the problem instance can engrave a circle of at most 28-inch diameter, and has a resolution of 1200 dpi. Therefore two (gasp!) Bézier curves per quarter circle offers far more precision (4.0e-6) than this machine's error (1/1200/28 = 3.0e-5). Edit: or take the world's roundest object: a sphere made out of a single crystal of silicon-28 atoms, with a roundness delta of less than 50 nanometres over a 93.6 mm diameter (https://www.heason.com/news-media/technical-blog-archive/world-s-roundest-object https://www.heason.com/news-media/technical-blog-archive/wor...) This is an error of 5.3e-7. Four puny Bézier curves per quarter circle (6.2e-8) are more perfect than this sphere.
- shalmanese 3y ago
  That's the answer to a different question. I was just pointing out that, in most industrial applications, 0.03% tolerances are rarely seen but in the specific question of circular dimensions, it's a pretty common requirement. And while it's possible to approximate with higher bezier curves, PDFs are auto generated with software libraries and it's going to be non-trivial to dive into the guts of a library of a library of a library and tweak the logic for generating circles for this one specific type of application.
  - mlyle 3y ago
    When we're talking about a CO2 laser, the errors from taper, variations in laser power, rigidity, trueness of optical path, etc, etc, far exceed 0.03%. If you want a circle that's better than a 0.03% tolerance, odds are you're not making it by tracing a circular path in g-code, but instead using something like a lathe. > And while it's possible to approximate with higher bezier curves, PDFs are auto generated with software libraries and it's going to be non-trivial to dive into the guts of a library of a library of a library and tweak the logic for generating circles for this one specific type of application. A lot of work on CO2 lasers you do with something like Coreldraw or Inkscape. You absolutely can pick the number of vertices with some slight work. Lasers are a bit weird in that most of their work is for signmaking. Most end-user use cases are closer to a printer than that of a typical CNC machine. Indeed, it can be annoying to take something from CAD to lasers that want PDF, because you can end up with things like the resultant PDF not joining lines together properly into one shape and the laser "stopping" on each vertex. You end up pretty carefully picking tools and processes for this flow. Ideally you figure out how to give the laser a dxf...
firebat45 3y ago
>For example, you can make a shaft that fits in a hole like a spring because it can slide freely but air can't get out and you can shave a few microns off and it will sink into the hole at a controlled rate. This is all easily achievable in a home machine shop on a manual lathe. I can tell from this statement that you do not have a home machine shop with a manual lathe. Home machine shops most certainly do ~not~ typically (or easily) achieve micron accuracy.
TheRealPomax 3y ago
In the category "using your hammer to screw in a rivet", you don't machine a shaft with a laser-cutter. As you point out: you use a lathe. For "circular" work that you do use a laser cutter for, 0.03% tolerances are below the variance you get from the cutter itself. Expecting higher precision from the cutter that is somehow "messed up" by the deviation from the standard Bezier approximation of a circle, when the machine you're using can't give you that precision is using that proverbial hammer. Of course, if that's really all you have access to (first of all: what are you even doing? look into buying a second hand lathe, or have everyone pitch in so your hobby space can buy one, they'll set you back less than a thousand bucks) the laser cutting is step one, you're not done after cutting, and you know you're not done after cutting because you know laser cutters are not high-precision machining tools like lathes or mills. You cut slightly oversized, and then you clean up the part and machine it down to final dimensions until your micrometer says you're within tolerance.

mrb 3y ago

It doesn't matter. The error is 0.03% only with one of the most simplistic approximations of 1 Bézier curve per quarter circle. Bump this to 2 or 4 curves, and the error drops to 4.0e-6 or 6.2e-8 (https://pomax.github.io/bezierinfo/#circles_cubic https://pomax.github.io/bezierinfo/#circles_cubic) You are going to have a really hard time finding an industrial application where a 6.2e-8 error matters. In fact, check this out: the Epilog Fusion M2 40 laser machine that the author chooses to picture as the problem instance can engrave a circle of at most 28-inch diameter, and has a resolution of 1200 dpi. Therefore two (gasp!) Bézier curves per quarter circle offers far more precision (4.0e-6) than this machine's error (1/1200/28 = 3.0e-5). Edit: or take the world's roundest object: a sphere made out of a single crystal of silicon-28 atoms, with a roundness delta of less than 50 nanometres over a 93.6 mm diameter (https://www.heason.com/news-media/technical-blog-archive/world-s-roundest-object https://www.heason.com/news-media/technical-blog-archive/wor...) This is an error of 5.3e-7. Four puny Bézier curves per quarter circle (6.2e-8) are more perfect than this sphere.

shalmanese 3y ago
That's the answer to a different question. I was just pointing out that, in most industrial applications, 0.03% tolerances are rarely seen but in the specific question of circular dimensions, it's a pretty common requirement. And while it's possible to approximate with higher bezier curves, PDFs are auto generated with software libraries and it's going to be non-trivial to dive into the guts of a library of a library of a library and tweak the logic for generating circles for this one specific type of application.
- mlyle 3y ago
  When we're talking about a CO2 laser, the errors from taper, variations in laser power, rigidity, trueness of optical path, etc, etc, far exceed 0.03%. If you want a circle that's better than a 0.03% tolerance, odds are you're not making it by tracing a circular path in g-code, but instead using something like a lathe. > And while it's possible to approximate with higher bezier curves, PDFs are auto generated with software libraries and it's going to be non-trivial to dive into the guts of a library of a library of a library and tweak the logic for generating circles for this one specific type of application. A lot of work on CO2 lasers you do with something like Coreldraw or Inkscape. You absolutely can pick the number of vertices with some slight work. Lasers are a bit weird in that most of their work is for signmaking. Most end-user use cases are closer to a printer than that of a typical CNC machine. Indeed, it can be annoying to take something from CAD to lasers that want PDF, because you can end up with things like the resultant PDF not joining lines together properly into one shape and the laser "stopping" on each vertex. You end up pretty carefully picking tools and processes for this flow. Ideally you figure out how to give the laser a dxf...

firebat45 3y ago

>For example, you can make a shaft that fits in a hole like a spring because it can slide freely but air can't get out and you can shave a few microns off and it will sink into the hole at a controlled rate. This is all easily achievable in a home machine shop on a manual lathe. I can tell from this statement that you do not have a home machine shop with a manual lathe. Home machine shops most certainly do ~not~ typically (or easily) achieve micron accuracy.

TheRealPomax 3y ago

In the category "using your hammer to screw in a rivet", you don't machine a shaft with a laser-cutter. As you point out: you use a lathe. For "circular" work that you do use a laser cutter for, 0.03% tolerances are below the variance you get from the cutter itself. Expecting higher precision from the cutter that is somehow "messed up" by the deviation from the standard Bezier approximation of a circle, when the machine you're using can't give you that precision is using that proverbial hammer. Of course, if that's really all you have access to (first of all: what are you even doing? look into buying a second hand lathe, or have everyone pitch in so your hobby space can buy one, they'll set you back less than a thousand bucks) the laser cutting is step one, you're not done after cutting, and you know you're not done after cutting because you know laser cutters are not high-precision machining tools like lathes or mills. You cut slightly oversized, and then you clean up the part and machine it down to final dimensions until your micrometer says you're within tolerance.