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How to Read the Scale Airy and Bessel Points
Graduation 0.005mm When a length standard bar or internal micrometer lies horizontally, supported
as simply as possible at two points, it bends under its own weight into a shape
(1) Outer sleeve 35 mm Thimble (2) that depends on the spacing of those points. There are two distances between
(2) Thimble 0.015 mm the points that control this deformation in useful ways, as shown below.
(1) 45
Reading 35.015 mm 9 40
0 45
8
57
06 35
5
Sleeve
10
Set and Measure in the Same Way 45 a Airy points (a 0.577 ) C
0 The ends of a bar (or micrometer) can be made exactly horizontal by spacing
The measured value provided by a Holtest 51DIV. 0.005mmthe two supports symmetrically as shown above. These points are known as the
differs slightly according to which section ‘Airy Points’ and are commonly used to ensure that the ends of a length bar are
of the anvils is used. This is a characteristic 45 parallel to one another, so that the length is well defined.
of the product mechanism. Therefore 4
maximum accuracy is obtained when the
instrument is set using the same section of 1DIV. 0.005mm
the anvils as for the measurement.
45
4
Example: if the measurement will be made Workpiece Set at mouth a Bessel points (a 0.559 )
using only the tips of the anvils, set the of ring
instrument using the mouth of the setting The change in length of a bar (or micrometer) due to bending can be minimized
ring as shown. by spacing the two supports symmetrically as shown above. These points
are known as the ‘Bessel Points’ and may be useful when using a long inside
Measurement Error Due to Temperature micrometer.
Variation of Micrometer
Bore Gauges
Heat transfer from the operator to the micrometer should be minimized to
avoid any significant measuring error due to temperature difference between Mitutoyo bore gauges for small holes feature contact elements with a large
the workpiece and micrometer. If the micrometer is held directly by hand curvature so they can be easily positioned for measuring the true diameter (in
when measuring, use gloves or hold the heat shield (if fitted). the direction a-a’) of a hole. The true diameter is the minimum value seen on
the dial gauge while rocking the bore gauge as indicated by the arrow.
Misalignment Errors
a Workpiece
X X
Figure 1 Figure 2
L a'
L Guide plate
: Inside diameter to be measured : Inside diameter to be measured The spring-loaded guide plate on a Mitutoyo two-point bore gauge
automatically ensures radial alignment so that only an axial rocking
L: Length measured with axial offset X movement is needed to find the minimum reading (true diameter).
X: Offset in axial direction L: Length measured with radial offset X
: Error in measurement
: L- = 2+X2 - X: Offset in radial direction Anvil
: Error in measurement a Workpiece
: L- = 2–X2 -
If an inside micrometer is misaligned in the axial or radial direction by an offset
distance X when a measurement is taken, as in Figures 1 and 2, then that
measurement will be in error as shown in the graph below (constructed from
the formulae given above). The error is positive for axial misalignment and
negative for radial misalignment.
a'
Guide plate Contact point
C-44
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