Micrometer Screw Gauge

What is modelled

A precision screw of 0.5 mm pitch advances the spindle by half a millimetre per thimble turn. The thimble has 50 divisions, so one division is 0.01 mm. The sleeve counts whole turns in half-millimetre marks.

Equations

• Spindle advance x = p · turns, p = 0.50 mm.
• Least count LC = p / N = 0.50 / 50 = 0.01 mm.
• Reading R = nsleeve (0.5 mm) + kthimble (0.01 mm), corrected length L = R - z for zero error z.
• Thermal growth ΔL = α L ΔT, α = 11.5e-6 /K for steel.

Checks run in the page

• Quantisation never exceeds half a least count.
• The screw transmission arithmetic for 12.36 mm.
• The zero-error correction recovers the true length.
• Thermal growth against the linear formula.

Honest simplifications

A perfect screw with no backlash, no frame bending and no anvil parallelism error; the ratchet force is not modelled. Real micrometers are calibrated with gauge blocks.

• Press Close on the block and read the sleeve and thimble yourself before reading the answer.
• Choose Worn anvils: the reading is 0.03 mm too large until you subtract the zero error.
• Heat the part to 40 C and compare its growth with the least count.