§ 18
How much does my measuring tool show wrong because the item and tool are not the same material?
Answer: A dimension on the drawing applies at 20 °C. If the piece and measuring tool are the same temperature but not 20 °C, they both expand. It's the difference in their coefficient of expansion that gives the error. An aluminium piece measured with a steel micrometre in a workshop at 26 °C therefore reads too large. The calculator works out the error and the dimension the piece has at 20 °C.
Fejl ≈ L × (α_emne − α_måler) × (t − 20 °C)
Mål ved 20 °C = aflæst mål − fejl
If α is the same (steel measured with steel), the error cancels out regardless of temperature
ISO 3650 kræver α = (11,5 ± 1) · 10⁻⁶/K for endemål af stål
| Symbol | Meaning | Unit |
|---|---|---|
| maalt | Measured dimension | mm |
| alfa_emne | Item's material (α) | ×10⁻⁶/K |
| alfa_maaler | Measuring tool's material (α) | ×10⁻⁶/K |
| temp | Shared temperature for piece and tool | °C |
| = | The reading is too large by | µm |
| = | Item's dimension at 20°C | mm |
| = | For comparison: error if only the workpiece was warm | µm |
Does not apply when
The calculator's own default values inserted. The figures are calculated with exactly the formula the tool uses.
Substituted
Giver
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Måler du en aluminiums- eller messingdel med stålmikrometer i et værksted, der ikke er 20 °C, viser du forkert, selv om emne og mikrometer har samme temperatur. Beregneren regner fejlen og emnets mål ved 20 °C.
Du måler en 100 mm aluminiumsdel med en stålmikrometer. Værkstedet er 26 °C.
It means: Aflæsningen er for stor med 6.9 µm. Ved 20 °C er emnet 99.9931 mm. Var mikrometeret koldt, ville fejlen være 13.8 µm.
En 50 mm messingbøsning måles med stålværktøj i et køligt værksted på 16 °C.
It means: Fejlen er -1.5 µm. Et negativt tal betyder, at aflæsningen er for lille, fordi værkstedet er under 20 °C. Ved 20 °C er målet 50.0015 mm.
Aluminium målt med stål: ca. 1 µm pr. 100 mm pr. 1 °C fra 20 °C.
Stål målt med stål giver 0 fejl ved alle temperaturer.