Inspection and GD&T
How do you calculate true position?
Technical review pending. Formulas and values are cited. This notice comes down after a machinist review.
Take the X and Y deviations from the basic location, square them, add them, take the square root and multiply by 2: position deviation = 2 x sqrt(dX^2 + dY^2). A hole 0.004 in off in X and 0.003 in off in Y has a position deviation of 0.010 in, which you compare to the tolerance in the feature control frame plus any MMC bonus.
Source: ASME Y14.5-2018 (dimensioning and tolerancing), position tolerance with a diameter tolerance zone
True position calculator
Position deviation (diametral)
in
Position = 2 x sqrt(dX^2 + dY^2) = 2 x sqrt(0.004^2 + (-0.003)^2) = 0.0100 in
Radial offset 0.0050 in. Deviation 0.0100 in (0.254 mm).
Allowed position tolerance
in
Allowed = T + (Actual - MMC) = 0.0100 + (0.2530 - 0.2500) = 0.0130 in
Bonus 0.0030 in. PASS: 0.0100 in is within 0.0130 in.
Metric results are shown to 0.001 mm because position tolerances are that fine.
Position = 2 x sqrt(dX^2 + dY^2); Allowed = T + (Actual - MMC)
| Symbol | Meaning | Unit |
|---|---|---|
| dX, dY | Measured location minus basic (drawing) location, from the datum reference frame | in or mm |
| Position | Diametral position deviation, compared to a Ø tolerance zone | in or mm |
| T | Stated position tolerance in the feature control frame | in or mm |
| MMC | Maximum material size: smallest hole or largest pin | in or mm |
| Actual | Measured size of the feature (for a pin, bonus = MMC - Actual) | in or mm |
| Allowed | Total position tolerance available at the actual size | in or mm |
Step by step
Drawing location X 1.000 in, Y 2.000 in from datums B and C. The CMM reads X 1.004 in, Y 1.997 in.
- Find the X and Y deviations: measured location minus the basic location from the drawing. dX = 1.004 - 1.000 = 0.004 in; dY = 1.997 - 2.000 = -0.003 in.
- Square each deviation and add them: 0.004^2 + (-0.003)^2 = 0.000016 + 0.000009 = 0.000025 sq in.
- Take the square root to get the radial offset: sqrt(0.000025) = 0.005 in.
- Multiply by 2 to get the diametral position deviation: 2 x 0.005 = 0.010 in.
- Compare it to the position tolerance in the feature control frame, plus any MMC bonus.
Result: position deviation 0.010 in (diametral). The radial offset is 0.005 in.
Bonus tolerance at MMC
When the frame shows the circled M after the tolerance, the hole gets extra position tolerance as it grows away from its smallest size. Bonus = actual size - MMC size for a hole, and MMC size - actual size for a pin.
MMC bonus example
Hole 0.250 +0.005/-0.000 in, position Ø 0.010 in at MMC. Measured size 0.253 in, measured position deviation 0.010 in.
- Find the MMC size. For a hole it is the smallest size allowed: 0.250 + 0.000 = 0.250 in.
- Measure the actual hole size: 0.253 in. Check it is within size first: 0.250 to 0.255 in, so it is good.
- Bonus = actual - MMC = 0.253 - 0.250 = 0.003 in.
- Allowed position = stated tolerance + bonus = 0.010 + 0.003 = 0.013 in.
- Compare: the measured position deviation of 0.010 in is less than 0.013 in, so the hole passes.
Result: bonus 0.003 in, allowed 0.013 in, measured 0.010 in. The hole passes.
Check size before position. A hole outside its size limits is rejected on size, and a bonus figured from an out-of-size hole means nothing.
Common mistakes
- Comparing the radial offset to the diametral tolerance. 0.005 in radial is 0.010 in of position.
- Figuring bonus from the LMC size instead of the MMC size.
- Taking bonus on a callout without the circled M. With no modifier the tolerance applies regardless of feature size, and there is no bonus.
- Measuring from the wrong zero. dX and dY come from the datum reference frame in the order the frame lists it, not from whichever edge was easiest to pick up.
- Rounding dX and dY before squaring. Keep every digit the CMM or DRO gives until the final result.
FAQ
Why does the CMM say position is out when X and Y both look fine?
Position is diametral: it is 2 x the radial offset. A hole off by 0.004 in in X and 0.003 in in Y sits 0.005 in from true position, a position deviation of 0.010 in. Held against a 0.010 in tolerance, each axis looks like it has room to spare, but the hole is at the limit with no bonus.
What is the formula for true position?
Position deviation = 2 x sqrt(dX^2 + dY^2), where dX and dY are the measured location minus the basic location. For dX = 0.004 in and dY = -0.003 in, the deviation is 2 x 0.005 = 0.010 in.
How do you calculate bonus tolerance at MMC?
Bonus = actual size - MMC size for a hole (MMC is the smallest hole), or MMC size - actual size for a pin (MMC is the largest pin). A 0.250 +0.005/-0.000 in hole measured at 0.253 in gets 0.003 in of bonus, so a 0.010 in position tolerance at MMC allows 0.013 in.
What does zero position tolerance at MMC mean?
The hole must be at true position when it is at its MMC size, and all of its position tolerance comes from bonus. A hole with 0 in position at MMC, measured 0.003 in over its MMC size, is allowed 0.003 in of position deviation.
Can you use the LMC size to figure bonus?
No. Bonus on an MMC callout is measured from the MMC size: the smallest hole or the largest pin. Using the LMC size gives the wrong sign or the wrong amount.
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