Table of Contents
Setting The Gap
Height gauge = 5.96mm +/- 0.02mm
What limits precision?
- Slight amount of play in measurement based on how tight you adjust the mic.
Initial mic settings
A = 8.18mm +/- 0.03mm
B = 9.50mm +/- 0.03mm
C = 9.37mm +/- 0.03mm
What limits precision?
- Adjusting one mic changes the height of the plate at the other two positions.
- Judging exactly when contact is made.
Force Measurement
HV = 1450V at start HV = 1448V at end
| Force | A | B | C | d |
|---|---|---|---|---|
| -0.35 | 8.17 | 9.50 | 9.38 | 5.96 |
| -40.62 | 2.81 | 4.14 | 4.02 | 0.6 |
| -32.48 | 4.19 | 0.65 | ||
| -27.03 | 4.24 | 0.70 | ||
| -22.87 | 4.29 | 0.75 | ||
| -19.8 | 4.34 | 0.8 | ||
| -15.31 | 4.44 | 0.9 | ||
| -10.07 | 4.64 | 1.1 | ||
| -8.43 | 4.74 | 1.2 | ||
| -6.02 | 4.94 | 1.4 | ||
| -4.76 | 5.14 | 1.6 | ||
| -2.82 | 5.64 | 2.1 | ||
| -1.86 | 6.14 | 2.6 | ||
| -1.02 | 7.14 | 3.6 | ||
| -0.67 | 8.14 | 4.6 | ||
| -0.40 | 7.81 | 9.14 | 9.03 | 5.6 |
| -0.45 | 8.17 | 9.50 | 9.38 | 5.96 |
Micrometer adjustments need to be made with careful attention paid to ensure that each one is adjusted by the same amount in the same direction. The net displacement of each micrometer should be checked multiple times through the data collection process.
Linear fit to the data yields $F=12.31 \pm 0.07 d - 0.15 \pm 0.10$
For comparison green line shows fit to dsiplacements 1mm and less.
Calibration
Mass measurements +/- 0.01. Precision of the apparatus. Height measurements +/- 0.01.
| Mass (g) | D (mm) | H1 (mm) |
|---|---|---|
| 0 | 0 | 13.54 |
| 59.91 | 0.08 | 13.46 |
| 49.91 | 0.06 | 13.48 |
| 39.95 | 0.07 | 13.47 |
| 29.92 | 0.04 | 13.50 |
| 19.94 | 0.04 | 13.50 |
| 0 | 0.02 | 13.52 |
Concerns about the repeatability of the measurements. Deflections are so small that great care needs to be taken to ensure accuracy of the data.
| Mass (g) | D (mm) | H1 (mm) | ||
|---|---|---|---|---|
| 59.90 | 13.55 | 13.54 | 13.58 | 13.54 |
| 49.94 | 13.41 | 13.42 | 13.41 | 13.41 |
| 39.96 | 13.42 | 13.43 | 13.42 | 13.42 |
| 29.92 | 13.43 | 13.43 | 13.42 | 13.43 |
| 19.89 | 13.45 | 13.44 | 13.45 | 13.45 |
| 0 | 13.47 | 13.47 | 13.47 | 13.47 |
| 59.84 | 13.4 | 13.40 | 13.40 | 13.40 |
| 0 | 13.47 | 13.47 | 13.47 | 13.47 |
| 39.93 | 13.42 | 13.42 | 13.42 | 13.42 |
| 0 | 13.47 | 13.47 | 13.47 | 13.47 |
| 19.87 | 13.44 | 13.45 | 13.44 | 13.44 |
| 0 | 13.47 | 13.47 | 13.47 | 13.47 |
| 9.91 | 13.46 | 13.46 | 13.46 | 13.46 |
Started rechecking zero mass reading to establish if there is drift.
There is some subtlety in determining the initial contact of the micrometer head with the mass pan. Many things, including hand pressure on the micrometer, can cause the scale reading to fluctuate and appear as if contact has been made.
Finally settled on a procedure where I would establish at least 1g of pressure with the mic head, then carefully back off and reinitiate contact to obtain about 0.05g force.
| Mass (g) | D (mm) | H1 (mm) | ||
|---|---|---|---|---|
| 19.89 | 0.02 | 13.44 | 13.45 | 13.45 |
| 59.84 | 0.07 | 13.40 | 13.40 | 13.40 |
| 39.93 | 0.05 | 13.42 | 13.42 | 13.42 |
| 19.87 | 0.03 | 13.45 | 13.44 | 13.44 |
| 9.91 | 0.01 | 13.46 | 13.46 | 13.46 |
Final correction formula
$D = 0.0012mm \pm 0.0001 * F + 0.0003mm \pm 0.002$
Corrected Data
Apply correction to displacement values
| Force | d | Corrected d |
|---|---|---|
| -0.35 | 5.96 | 5.95928 |
| -40.62 | 0.6 | 0.55 |
| -32.48 | 0.65 | 0.611 |
| -27.03 | 0.70 | 0.667 |
| -22.87 | 0.75 | 0.722 |
| -19.8 | 0.8 | 0.800 |
| -15.31 | 0.9 | 0.881 |
| -10.07 | 1.1 | 1.087 |
| -8.43 | 1.2 | 1.190 |
| -6.02 | 1.4 | 1.392 |
| -4.76 | 1.6 | 1.594 |
| -2.82 | 2.1 | 2.096 |
| -1.86 | 2.6 | 2.600 |
| -1.02 | 3.6 | 3.6 |
| -0.67 | 4.6 | 4.6 |
| -0.40 | 5.6 | 5.6 |
| -0.45 | 5.96 | 5.96 |
$d = D - (.0012 D - 0.0003)$
Best fit to corrected data.
$F = 12.06 \pm 0.06 D - 0.11 \pm 0.09$
For comparison the best fit to displacements 1mm and less gives.
$F = 12.05 \pm 0.29 D + 0.003 \pm 0.37 $