Question about the small arc method

When using the fixed rad method, you really need to take an iterative approach. Think of how you would check a small, partial radius manually, using radius gauges. You would offer up a gauge and look for gaps, before trying progressively larger/smaller gauges until you were satisfied that the gauge fitted snugly into the radius with no visible gap anywhere. It's the same with the fixed rad method - when you fix the radius, this is like saying "I have a radius gauge of this size". PC-DMIS will give you the co-ordinates for the centre of that known diameter when it is in contact with the hits. You then origin on those co-ordinates and take additional polar radial points along the radius. Depending on the deviation you see for each hit, you would then need to adjust your fixed rad size and repeat.

For example, suppose you had a partial radius going from 0° to 45° of arc whose theoretical size was Ø20. You would start by measuring a fixed rad circle (Ø20) with a reasonable spread of hits, covering as much of the arc as possible. You would then origin on that circle and take three polar radial hits, one at 0°, one at 22.5° (the middle of the arc) and one at 45°. Next, you would check the polar value of the hits. If the "middle" (22.5°) hit was larger than 10, it would indicate that the original fixed rad size was too large - think of what you would see if you were to offer up a radius gauge that was larger than the actual radius, you would see a gap near the middle of the arc. Similarly, if the polar value of your middle point was ~10 but the polar radial value for the other two hits (the ones at each end of the arc) were larger, it would indicate that your original fixed rad size was too small. Again, think of a radius gauge. A gauge that is smaller than the actual radius would contact in the middle but have a gap at each end of the arc. Based on this, you would measure another fixed rad circle, this time with the fixed rad size adjusted by some amount, origin on it and take another three polar radial hits. You would repeat this process until the polar radial values of all three hits were as close to each other as possible (you may need to increase the decimal precision) allowing for the accuracy of your CMM. You would then have both an accurate size and set of centre co-ordinates for the radius.

Obviously, the smaller the degree of arc and the bigger the uncertainty statement for your CMM, the harder it will be to make this assessment, but the principle is sound. It can, however, be extremely time consuming and difficult to code up, relying on logical expressions and looping or many "trial and error" attempts. This is why most people feel it is generally better to report profile of a line / surface to determine whether the radius is acceptable.

When using the fixed rad method, you really need to take an iterative approach. Think of how you would check a small, partial radius manually, using radius gauges. You would offer up a gauge and look for gaps, before trying progressively larger/smaller gauges until you were satisfied that the gauge fitted snugly into the radius with no visible gap anywhere. It's the same with the fixed rad method - when you fix the radius, this is like saying "I have a radius gauge of this size". PC-DMIS will give you the co-ordinates for the centre of that known diameter when it is in contact with the hits. You then origin on those co-ordinates and take additional polar radial points along the radius. Depending on the deviation you see for each hit, you would then need to adjust your fixed rad size and repeat.

For example, suppose you had a partial radius going from 0° to 45° of arc whose theoretical size was Ø20. You would start by measuring a fixed rad circle (Ø20) with a reasonable spread of hits, covering as much of the arc as possible. You would then origin on that circle and take three polar radial hits, one at 0°, one at 22.5° (the middle of the arc) and one at 45°. Next, you would check the polar value of the hits. If the "middle" (22.5°) hit was larger than 10, it would indicate that the original fixed rad size was too large - think of what you would see if you were to offer up a radius gauge that was larger than the actual radius, you would see a gap near the middle of the arc. Similarly, if the polar value of your middle point was ~10 but the polar radial value for the other two hits (the ones at each end of the arc) were larger, it would indicate that your original fixed rad size was too small. Again, think of a radius gauge. A gauge that is smaller than the actual radius would contact in the middle but have a gap at each end of the arc. Based on this, you would measure another fixed rad circle, this time with the fixed rad size adjusted by some amount, origin on it and take another three polar radial hits. You would repeat this process until the polar radial values of all three hits were as close to each other as possible (you may need to increase the decimal precision) allowing for the accuracy of your CMM. You would then have both an accurate size and set of centre co-ordinates for the radius.

Obviously, the smaller the degree of arc and the bigger the uncertainty statement for your CMM, the harder it will be to make this assessment, but the principle is sound. It can, however, be extremely time consuming and difficult to code up, relying on logical expressions and looping or many "trial and error" attempts. This is why most people feel it is generally better to report profile of a line / surface to determine whether the radius is acceptable.