ISO 1101 angularity tolerance and the sine bar
The drawing of the angled face of a tooling setting block gives a theoretically exact angle of 30° and an angularity tolerance frame of 0.02 A. The metrologist has to check the position of the angled face relative to datum plane A, using a sine bar and gauge blocks.
Principle and measurement of an ISO 1101 angularity tolerance
| Theoretical angle (TED) | Measuring instrument | Sine bar set-up formula | Tolerance zone |
|---|---|---|---|
| 30° 00’ 00“ | Sine bar L=100 mm + gauge blocks | Height H = L * sin(30°) = 50.000 mm | Two parallel planes 0.02 mm apart |
| 45° 00’ 00“ | Sine bar L=200 mm + gauge blocks | Height H = L * sin(45°) = 141.421 mm | Two parallel planes 0.015 mm apart |
All values are given for the reference environmental conditions of 20 °C.
Setting up the sine bar and calculating the gauge block height
To measure a face angled at alpha, the part is placed on a sine bar of length L (e.g. 100 mm). The height of gauge blocks to stack under the roller is H = L * sin(alpha). Once the bar is tilted, the inspected face becomes, in theory, horizontal on the surface plate. Sweeping it with a dial indicator gives the angularity error directly. To go over other geometric tolerances, read our guide to ISO 1101 geometric symbols.
The angularity tolerance zone
The tolerance zone is bounded by two parallel planes set apart by the specified value (0.02 mm) and inclined at the theoretically exact angle (TED) to datum A. The angle itself carries no angular tolerance in degrees.
Worked example: a block angled at 30 degrees
Block angled at 30°, toleranced 0.02 A. Sine bar L=100 mm, H=50.000 mm. Dial indicator sweep over 80 mm: low point = 0.000 mm, high point = +0.025 mm. Verdict: the variation (0.025 mm) exceeds the allowed limit of 0.020 mm. The part is declared non-conforming.
Shop-floor pitfalls when inspecting angularity
The first pitfall is a mistake in calculating the gauge block height H. The second is using the wrong face as datum A. The third comes from forgetting the temperature of the sine bar. To record your geometric measurements, discover the CoteCote inspection and report modules.