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Acta Polytechnica Vol. 52 No. 4/2012

Checking the Geometric Accuracy of a Machine Tool for

Selected Geometric Parameters

Adam Janásek1, Robert Čep1, Josef Brychta1

1
VŠB — Technical University of Ostrava, Department of Machining and Assembly,
17. listopadu 15/2172, 708 33 Ostrava-Poruba, Czech Republic

Correspondence to: adam.janasek@vsb.cz

Abstract

This paper deals with the control parameters for selected geometric accuracy measurements for a machine tool. The

parameters were needed after a refurbished milling machine was purchased. After setting up the machine, it was necessary

to check the geometric accuracy that can be used for precise milling. The whole check was performed in accordance

with ISO 10791. Only selected parameters of geometric accuracy were inspected, and they were later compared with the

prescribed values. On the basis of a comparison of these values we were able to determine whether the machine tool can

be used for accurate machining.

Keywords: geometric accuracy, testing, milling machine.

Selected geometric parameters

The measurements were performed on a vertical spin-
dle milling machine, see Figure 1. For this milling
machine, we selected eight geometrical accuracy tests
from the ISO 10791-2 standard for a machine with a
vertical spindle, and two accuracy tests for horizontal
milling machines. For each geometric accuracy test,
we performed at least as many measurements as were
stipulated in the standard. Before each measurement
was performed, the gauge adjustment required for
the specific test was made, and surface cleaning was
done (on the measured surfaces). The tests were per-
formed at a constant temperature of 20 ◦C. The test
scheme is shown for each test of geometric accuracy
from the ISO 10791-2 standard. Further tests were
supplemented by an individual value, as allowed by
the ISO 10791-2 standard.

Tests performed on the milling machine: [1]
a) Measurement of periodic axial spindle movement

on the lateral surface, test G10b.
b) Measurement of periodic axial spindle move-

ment, test G10a.
c) Measurement of peripheral whipping — inter-

nal taper spindle at the end of the spindle, test
G11a.

d) Measurement of peripheral whipping — internal
taper spindle at a distance of 110 mm from the
end of the spindle, test G11b.

e) Measurement of axial parallelism with spindle
movement on the Z axis, test G12.

f) Measurement of the angular deviation movement
on the Y axis, test G5a.

g) Measurement of the angular deviation movement
on the X axis, test G4a.

h) Measurement of the middle guide groove — par-
allel to the table feed at a distance of 500 mm,
test 8a and measured opposite side of the guide
groove, test 8b.

i) Measurement of the movement parallelism on
the Y axis with the table surface, distance Y =
170 mm, test G17.

Figure 1: Tested milling machine with a vertical spin-
dle — side view [3]

Test G10B

This test was conducted on a radius of A = 40 mm.
The measurement was based on the fact that the dial
indicator was attached to the lateral surface of the

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Acta Polytechnica Vol. 52 No. 4/2012

spindle, and deviation can be controlled thanks to the
rotation of the spindle. Before making the measure-
ments we had to remove the drag-stones, which are
hindered by the measurements. Ten measurements
were performed, and the values were processed.

Figure 2: Measurement scheme [1]

uA =

√∑n
i=1(Xi − X)2
n · (n − 1) = 8.33 · 10

−4 mm

X = X ± uA
X = (0.007 50 ± 0.000 83) mm

Measured value: (0.007 50 ± 0.000 83) mm
Value according to the standard: 0.01 mm
The milling machine is satisfactory in terms of this
test.

Test G10A

This test was conducted inside the spindle at a height
of 10 mm above the drag-stones. The measurement
was based on the fact that the dial indicator was at-
tached to the internal surface of the spindle, and the
deviation can be controlled thanks to the rotation
of the spindle. Again, ten measurements were per-
formed and the values were processed [3]. Finally,
the drag-stones were remounted on the spindle.

uA =

√∑n
i=1(Xi − X)2
n · (n − 1) = 7.65 · 10

−4 mm

X = X ± uA
X = (0.003 50 ± 0.000 77) mm

Measured value: (0.003 50 ± 0.000 77) mm
Value according to the standard: 0.005 mm
The milling machine is satisfactory in terms of this
test.

Figure 3: Measurement scheme [1]

Test G11A

This test was conducted at the end of the spindle.
The mandrel is clamped to the spindle and the pe-
ripheral whipping was evaluated. The perpendicular
axis of the mandrel (or the spindle on the axis of the
longitudinal feed table) was checked before starting
the measurements [3]. Thus control was important
for precise testing of the peripheral spindle whipping.
The measurement was based on the fact that dial in-
dicator was attached to the mandrel.

Figure 4: Measurement scheme [1]

uA =

√∑n
i=1(Xi − X)2
n · (n − 1) = 8.16 · 10

−4 mm

X = X ± uA
X = (0.013 00 ± 0.000 82) mm

Measured value: (0.013 00 ± 0.000 82) mm
Value according to the standard: 0.01 mm
The milling machine is unsatisfactory in terms of
this test.

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Acta Polytechnica Vol. 52 No. 4/2012

Test G11B

This test was conducted at a distance of 110 mm
from the end of the milling spindle. The mandrel
was clamped into the milling spindle, and periph-
eral whipping was carried out. It was not neces-
sary to check the perpendicularity of the axis of
the mandrel because this had been done in previ-
ous measurements. The measurements were taken
after measuring at a distance of 110 mm from the
end of the spindle and after establishing a mag-
netic pedestal with a dial indicator on the milling
table. The measurements were based on the fact
that the mandrel was attached to the dial indica-
tor and the deviation was controlled during rota-
tion. For this test, it was necessary to convert the
allowed values according to [1], because the toler-
ance on a measured length of 300 mm is given by
the standard [3]. Our measurement was performed
on a length of 110 mm.

Figure 5: Measurement scheme [1]

uA =

√∑n
i=1(Xi − X)2
n · (n − 1) = 8.5 · 10

−4 mm

X = X ± uA
X = (0, 023 00 ± 0.000 85) mm

Conversion of standard values for length 110 mm:
length 300 mm allows 0.01 mm according to
[1] ⇒ allowed 1 mm on: 0.01/300 = 3.33·10−5 mm ⇒
110 mm = 0.014 mm
Measured value: (0.023 00 ± 0.000 85) mm
Value according to the standard: 0.014 mm
The milling machine is unsatisfactory in terms of
this test.

Test G12

This test was conducted at a distance of 110 mm.
The mandrel was clamped to the milling spindle and
axial parallelism was carried out with spindle move-

ment on the Z axis. Measurements were taken after
measuring a distance of 110 mm and after establish-
ing a magnetic pedestal with a dial indicator on the
milling table. Ten measurements were performed at
position 0◦, and the next ten measurements were per-
formed at mandrel rotation 180◦, in order to elimi-
nate errors resulting from inaccuracies of the man-
drel itself. For this test, it was necessary to convert
the allowed values according to [1], because the toler-
ance given by the standard is for a measured length
of 300 mm. Our measurement was performed on a
length of 110 mm.

Figure 6: Measurement scheme [1]

uA =

√∑n
i=1(Xi − X)2
n · (n − 1) = 8.16 · 10

−4 mm

X = X ± uA
X = (0.003 00 ± 0.000 82) mm

Conversion of standard values for length 110 mm:
length 300 mm allows 0.015 mm according to
[1] ⇒ allowed 1 mm on: 0.015/300 = 5 · 10−5 mm ⇒
on 110 mm = 0.005 5 mm
Measured value: (0.003 ± 0.000 82) mm
Value according to the standard: 0.005 5 mm
The milling machine is satisfactory in terms of this
test.

Test G5A

This test was conducted at a distance of 1 000 mm
and was performed in the transverse direction. A co-
incidence spirit level was set up on the milling table,
and was gradually placed at three locations. First,
on the right side of the table, then in the middle,
and finally on the left side. In each of these posi-
tions we gradually made ten measurements. After
these measurements, the coincidence spirit level was
rotated 180◦, and the measurements were again per-

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Acta Polytechnica Vol. 52 No. 4/2012

formed ten times in the same places [4]. The mea-
surements were based on the fact that the examined
deviation of each of the halves inside the coincidence
spirit level and the deflection were recorded at the
time when the two halves for the spirit level were es-
tablished [2]. The resultant values were obtained by
differential measurements of the maximum and min-
imum values.

Figure 7: Measurement scheme [1]

uA = (uAP + uAL)/2

X = Xmax − Xmin
X = XP − XL = (0.190 0 ± 0.0047) mm

uAP =

√∑n
i=1(XiP − XP )2
n · (n − 1) = 4.43 · 10

−3 mm

XP = XP ± uAP = (2.120 0 ± 0.004 4) mm

uAS =

√∑n
i=1(XiS − XS)2
n · (n − 1) = 0.010 089 mm

XS = XS ± uAS = (2.076 000 ± 0.010 089) mm

uAL =

√∑n
i=1(XiL − XL)2
n · (n − 1) = 5 · 10

−3 mm

XL = XL ± uAL = (1.930 ± 0.005) mm

Measured value: (0.190 0 ± 0.004 7) mm
Value according to the standard: 0.04 mm
The milling machine is unsatisfactory in terms of
this test.

Test G4A

This test was conducted at a distance of 1 000 mm,
and was performed in the longitudinal direction. A
coincidence spirit level was set up on the milling ta-
ble and was gradually placed at three locations. The
order of the placements was as for the previous mea-
surement. In each of these positions we gradually
made ten measurements [3]. In essence, the prin-

ciple of measurement was the same as in test G5a
(above).

Figure 8: Measurement scheme [1]

uA = (uAS + uAP )/2

X = XP − XL = Xmax − Xmin
X = XS − XP = (0.200 0 ± 0.009 5) mm

uAP =

√∑n
i=1(XiP − XP )2
n · (n − 1) = 0.011 mm

XP = XP ± uAP = (2.630 ± 0.011) mm

uAS =

√∑n
i=1(XiS − XS)2
n · (n − 1) = 0.007 9 mm

XS = XS ± uAS = (2.830 0 ± 0.007 9) mm

uAL =

√∑n
i=1(XiL − XL)2
n · (n − 1) = 0.008 9 mm

XL = XL ± uAL = (2.710 0 ± 0.008 9) mm

Measured value: (0.2000 ± 0.009 5) mm
Value according to the standard: 0.06 mm
The milling machine is unsatisfactory in terms of
this test.

Test 8A and test 8B

This test was conducted at a distance of 500 mm. In-
dividual measurements were performed after 50 mm.
The measurements were based on the fact that the
magnetic pedestal was attached to the structure of
the mill. The point of the dial indicator was attached
to the surface side of the guide groove. The measured
deflection was noted every 50 mm with the passing
of the groove [5]. Then we measured the opposite
side of the guide groove. The principle is exactly the
same as in test 8a (above).

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Acta Polytechnica Vol. 52 No. 4/2012

Figure 9: Measurement scheme [1]

uA =

√∑n
i=1(Xi − X)2
n · (n − 1) = 4.69 · 10

−3 mm

X = X ± uA = (0.023 0 ± 0.004 7) mm

uA =

√∑n
i=1(Xi − X)2
n · (n − 1) = 1.95 · 10

−3 mm

X = X ± uA = (0.007 3 ± 0.002 0) mm

Measured value: (0.023 0 ± 0.004 7) mm
Value according to the standard: 0.02 mm
The milling machine is unsatisfactory in terms of
this test. (8a test)
Measured value: (0.007 3 ± 0.002 0) mm
Value according to the standard: 0.02 mm
The milling machine is satisfactory in terms of this
test. (8b test)

Test G17

This test was conducted on the right and left side of
the milling table. First, a ruler had to be assembled
at a distance of 250 mm from the centre of the ta-
ble to the right side and then on the left side of the
milling table. Ten measurements were performed for
the right side, and then ten measurements for the left
side.

Figure 10: Measurement scheme [1]

uAP =

√∑n
i=1(XiP − XP )2
n · (n − 1) = 1.25 · 10

−3 mm

uAL =

√∑n
i=1(XiL − XL)2
n · (n − 1) = 8.16 · 10

−4 mm

XP = XP ± uAP = (0.0140 ± 0.001 3) mm
XL = XL ± uAL = (0.008 00 ± 0.000 82) mm

Measured value: (0.014 0 ± 0.001 3) mm
Value according to the standard: 0.02 mm
Measured value: (0.008 00 ± 0.000 82) mm
Value according to the standard: 0.02 mm
The milling machine is satisfactory in terms of these
tests.

Conclusions

This paper has reported on tests of selected geomet-
rical precision parameters for a milling machine in
the laboratories of the Department of Machining and
Assembly, Faculty of Mechanical Engineering, VŠB –
Technical University of Ostrava. The measurements
were performed after selecting suitable tests and pro-
viding the necessary gauges and equipment for the
tests.

On the basis of the results of the geomet-
ric precision tests for a milling machine with a
vertical spindle, the following conclusions can
be drawn:
• The milling machine failed 5 out of the 10 tests
that were performed.

• Measurement of the middle guide groove, paral-
lel to table feed at a distance of 500 mm (test 8a):
the main reason for the unsatisfactory test re-
sults was the groove that ran through the whole
side. The same measurement was therefore per-
formed on the opposite side of the groove, and
in this case c ompliance was achieved.

• Measurement of the angular deviation movement
on the Y axis (test G5a), and measurement of
the angular deviation movement on the X axis
(test G4a): the main reason for the unsatisfac-
tory test result was bad setting up in the lab-
oratory. It was not possible to establish into
the correct position, because the milling machine
was not equipped with establishing screws.

• The peripheral whipping measurement — the in-
ternal taper spindle at the end of the spindle
(test G11a) and the peripheral whipping mea-
surement – the internal taper spindle at a dis-
tance of 110 mm from the end of the spindle
(test G11b): the main reason for the unsatis-
factory test result was perhaps gear-wear with
a constant gear ratio inside the milling head, or
bearing-wear. In order to eliminate this inac-

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Acta Polytechnica Vol. 52 No. 4/2012

curacy, it would be necessary to overhaul the
milling head.

Acknowledgement

This paper is an outcome of project no.
CZ.1.07/2.4.00/17.0082: Increasing of Professional
Skills by Practical Acquirements and Knowledge,
supported by the Education for Competitiveness Op-
erational Programme, funded from European Union
Structural Funds and from the state budget of the
Czech Republic.

References

[1] ISO 10791-2 – Test conditions for machine cen-
tres — Part 2: Geometric tests for machines with
vertical spindle or universal heads with vertical
primary rotary axis (vertical Z-axis).

[2] Tichá, Š.: Stroj́ırenská metrologie – část 1. Os-
trava : VŠB – TU Ostrava, 2006, p. 112.
ISBN 80-248-0671-1.

[3] Brázda, F.: Kontrola vybraných parametr̊u ge-
ometrické přesnosti obráběćıho stroje. Ostrava :
Katedra obráběńı a montáže, 2006. Bakalářská
práce. VŠB – Technical University of Ostrava.
Bachelor project supervisor: Robert Čep.

[4] Čep, R., Janásek, A., Vaĺıček, J., Čepová, L.:
Testing of Greenleaf Ceramic Cutting Tools
with and Interrupted Cutting. Tehnički Vjest-
nik – Technical Gazette. Vol. 18, no. 3, 2011,
p. 327–332. ISSN 1330-3651.

[5] ISO 10791-1 – Test conditions for machine cen-
tres — Part 1: Geometric tests for machines with
horizontal spindle and with accessory heads (hor-
izontal Z-axis).

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