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Micrometer Expansion due to Holding Frame with Effect of Changing Support Method and
the Bare Hand Orientation (Unit: µm)
14 Changing the support method and/or orientation of a micrometer after zero
13 setting affects subsequent measuring results. The tables below highlight the
12 measurement errors to be expected in three other cases after micrometers are zero-
11 300 set in the ‘Supported at the bottom and centre' case. These actual results show
10
9 that it is best to set and measure using the same orientation and support method.
B8 Expansion (µm) Supporting method Supported at the bottom and centre Supported only at the centre
7 200
Attitude
6
5 100 Maximum
4 measuring
length (mm)
3 50 325 0 -5.5
2
1 425 0 -2.5
0 2 4 6 8 10 15 20 30 525 0 -5.5
625 0 -11.0
Time (minutes) 725 0 -9.5
825 0 -18.0
The above graph shows micrometer frame expansion due to heat transfer
from hand to frame when the frame is held in the bare hand which, as can
be seen, may result in a significant measurement error due to temperature- 925 0 -22.5
1025 0 -26.0
induced expansion. If the micrometer must be held by hand during Supporting method Supported at the centre in a lateral Supported by hand downward.
measurement then try to minimize contact time. A heat insulator will reduce orientation.
this effect considerably if fitted, or gloves may be worn. (Note that the above Attitude
graph shows typical effects, and is not guaranteed).
Setting Standard Expansion with Maximum
Change of Temperature (for 200 mm bar initially at 20C) measuring
length (mm)
20
31°CThermal expansion (µm) 325 +1.5 -4.5
425 +2.0 -10.5
15 525 -4.5 -10.0
10 625 0 -5.5
725 -9.5 -19.0
27°C 825 -5.0 -35.0
5 21°C 925 -14.0 -27.0
0 0 1 2 3 4 5 6 7 8 9 10 1025 -5.0 -40.0
Lapse of time (minutes) Abbe’s Principle
The above experimental graph shows how a particular micrometer standard Abbe’s principle states that “maximum accuracy
expanded with time as people whose hand temperatures were different R L is obtained when the scale and the measurement
(as shown) held the end of it at a room temperature of 20°C. This graph
shows that it is important not to set a micrometer while directly holding the axes are common”.
micrometer setting standard but to make adjustments only while wearing This is because any variation in the relative
gloves or lightly supporting the standard by its heat insulators. angle ( ) of the moving measuring jaw on an
When performing a measurement, note also that it takes time until the instrument, such as a caliper jaw micrometer,
expanded standard returns to the original length. causes displacement that is not measured
(Note that the graph values are not guaranteed values but experimental values.)
on the instrument’s scale and this is an Abbe error ( = - L in the
Difference in Thermal Expansion between
Micrometer and Setting Standard diagram). Spindle straightness error, play in the spindle guide or
variation of measuring force can all cause to vary and the error
increases with R.
Difference in expansion (µm) +3 0°C Hooke's Law
+2
Hooke’s law states that strain in an elastic material is proportional to
+1 20°C the stress causing that strain, providing the strain remains within the
0 elastic limit for that material.
-1 Hertz's Formulae
-2 Hertz’s formulae give the apparent reduction in diameter of spheres
-3 10°C
and cylinders due to elastic compression when measured between
plane surfaces. These formulae are useful for determining the
125 225 325 425 525 deformation of a workpiece caused by the measuring force in point
and line contact situations.
Nominal length (mm) PP
In the above experiment, after the micrometer and its standard were left at a room
temperature of 20C for about 24 hours for temperature stabilization, the start Assuming that the material is steel and units are as follows:
point was adjusted using the micrometer standard. Then, the micrometer with L Modulus of elasticity: E =205 GPa
its standard were left at the temperatures of 0C and 10C for about the same Amount of deformation: (µm)
period of time, and the start point was tested for shift. The above graph shows 2 D 2 Diameter of sphere or cylinder: D (mm)
the results for each of the sizes from 125 through 525 mm at each temperature. SD
This graph shows that both the micrometer and its standard must be left at the Length of cylinder: L (mm)
same location for at least several hours before adjusting the start point. (Note that 2 2 Measuring force: P (N)
the graph values are not guaranteed values but experimental values.)
a) Apparent reduction in diameter of sphere
B-77 1=0.82 3 P2/D
(a) (b) b) Apparent reduction in diameter of cylinder
Sphere between Cylinder between 2 =0.094·P/L 3 1/D
two planes two planes
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