Inspection and GD&T
Inspection calculators for QC and GD&T
Position = 2 x sqrt(dX^2 + dY^2); a hole 0.004 in off in X and 0.003 in off in Y sits at 0.010 in position. The tools below cover the rest of the inspection bench math.
Technical review pending. Formulas and values are cited. This notice comes down after a machinist review.
Inspection formulas
Position = 2 x sqrt(dX^2 + dY^2); allowed at MMC = T + |actual - MMC|; sine bar H = L x sin(A); dovetail c = D x (1 + cot(alpha / 2)); V-groove pin center = r / sin(A / 2) above the vertex
| Symbol | Meaning | Unit |
|---|---|---|
| dX, dY | Measured minus nominal location | in or mm |
| T | Stated position tolerance | in or mm |
| MMC | Maximum material condition size | in or mm |
| actual | Measured hole size | in or mm |
| H | Gage block stack height | in or mm |
| L | Sine bar length, center to center of the rolls | in or mm |
| A | Angle (sine bar) or included groove angle (V-groove) | ° |
| D | Pin diameter (dovetail) | in or mm |
| alpha | Dovetail flank angle | ° |
| r | Pin radius (V-groove) | in or mm |
Source: ASME Y14.5 (dimensioning and tolerancing); Machinery's Handbook (sine bars, gage blocks, measuring dovetails and V-grooves with pins).
Inspection tools
- Position deviation, MMC bonus and pass or fail come from the true position calculator.
- The same math, step by step with a CMM reading, is in the guide on how to calculate true position.
- The 14 geometric characteristic symbols, modifiers and dimensioning symbols are on the blueprint and GD&T symbols chart.
- Any size from an 81-piece set with the fewest blocks comes from the gage block stack calculator.
- The stack for an angle on a 5 in, 10 in, 100 mm or 200 mm bar comes from the sine bar calculator.
- Width over or between pins for male and female dovetails comes from measuring dovetails with pins.
- Pin height, depth and groove angle for V-grooves come from the V-groove measuring calculator.
Thread and setup checks from other categories
- Pitch diameter over wires for 60° threads comes from the 3-wire thread measuring calculator.
- Acme threads are checked over wires with the Acme 3-wire measuring calculator.
- Metric trapezoidal threads are checked over wires with the trapezoidal 3-wire measuring calculator.
- Sides and angles for setups come from right triangle solutions.
How to choose
- Position: RFS (regardless of feature size) is a fixed zone. MMC (maximum material condition) adds bonus as the hole departs from its MMC size, so a hole cut toward the top of its size limit can sit farther off location and still pass.
- Gage block stacks: clear the rightmost digit first; it keeps the block count low.
- Sine bar length: a 10 in bar gives finer angle resolution; a 5 in bar suits small parts and small setups.
- Pins for angles and forms: dovetails take two equal pins in the corners, measured over (male) or between (female). A V-groove takes one pin and a depth reading for depth, or two pin sizes for the angle. On both, pick a pin that touches the flanks below the top edge.
- Threads: three wires and a micrometer give pitch diameter; ring and plug gauges give go or no-go only.
FAQ
What is the formula for true position?
2 x sqrt(dX^2 + dY^2). A dX of 0.004 in and a dY of 0.003 in give 2 x 0.005 = 0.010 in, not 0.014 in.
How much bonus tolerance does MMC add?
Actual hole size minus MMC size. A 0.5020 in hole with a 0.5000 in MMC size gets 0.0020 in, so a 0.010 in tolerance allows 0.0120 in.
What stack sets 12° on a 5 in sine bar?
5 x sin(12°) = 1.0396 in, built from an 81-piece set as 0.1006 + 0.139 + 0.800 in, three blocks.
5 in or 10 in sine bar?
The 10 in bar gives finer resolution; the same 30° takes a 5.0000 in stack on a 10 in bar and a 2.5000 in stack on a 5 in bar.
What is the pin constant for a 60° dovetail with 0.250 in pins?
c = 0.250 x (1 + cot 30°) = 0.6830 in; add it for a male dovetail, subtract it for a female slot.
How do you check a V-groove with a pin?
Measure from the surface to the pin top. A 0.250 in pin in a 90° groove 0.500 in wide tops out 0.0518 in above the surface.
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