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B1 NOTE B1.99.3
May 18, 1999
Load Tests for Selection of the Rod Insert
Material
Kari Tammi
Helsinki Institute of Physics
Abstract
The purpose of the tests was to verify equations used to calculate the displacements and the
stresses in the ball-support insert contact of the MSGC rod. The equations show that the yield
strengths of materials are easily exceeded in a small area. The purpose of the test was also to
study what exceeding the yield strengths, and even the ultimate strengths, affects on the materials.
Aluminium and polyetherimide (PEI) were used as test materials. The measured results correlate
with the calculated values, but the equations give smaller displacements than was measured. The
tests and calculations show that the area of plastic deformation is very small.
2
Table of contents
1 MEASURING ARRANGEMENT............................................................................................................3
2 RESULTS ...................................................................................................................................................4
2.1 MEASURED DISPLACEMENTS .................................................................................................................4
2.2 LONGER PERIOD TEST............................................................................................................................5
2.3 SQUEEZE TEST.......................................................................................................................................5
2.4 REMARKS DURING TESTS .......................................................................................................................6
3 DISCUSSION.............................................................................................................................................6
3.1 CALCULATIONS .....................................................................................................................................6
3.2 COMPARISON TO THE MEASUREMENTS..................................................................................................8
4 CONCLUSIONS ........................................................................................................................................9
5 REFERENCES.........................................................................................................................................10
3
1 Measuring arrangement
The test pieces were machined of bars (diameter 20 mm) of aluminium and polyetherimide (PEI).
Two test pieces were piled up with Dixi precision polished sapphire balls between them. To get a
stable pile three balls were applied between the test pieces and supported by a tube around (Fig.
1). Weights were applied onto the pile and the displacement was measured by measurement
gauges.
Figure 1. Two test pieces and three balls between the pieces supported by a tube and a
foundation.
The displacement between the pieces was measured with three measurement gauges. Calculating
an average value of three gauges showed to be the only way to perform the measurements
accurately. The pile was unsteady; it inclined easily because the balls were very close to each
other. Figure 2 shows the pieces needed for the measurements (left) and the set-up (right). On the
pile, there was used a collar; the probes of the measurement gauges touched underneath of the
collar and its weight was enough to compensate the spring forces, that were lifting the collar, of
the measurement gauges. Weights were placed onto the collar.
4
Figure 2. The collar (on left), the test pieces made of aluminium and PEI, the Dixi balls placed in
the locator plate and the tube connected to the foundation. The complete measurement set-up is
showed on right.
First, one test piece was put in the bottom of the tube. Then the balls with their locator plate were
applied onto the piece and the other test piece was placed on them. The collar was put onto the
second test piece and the measurement gauges were positioned in such a way that their probes
were in the horizontal position and touching underneath to the collar. The measurement gauges
were set to zero displacement after the collar was applied.
After resetting the measurement gauges, the weights were piled up. Piling the weights required
attention due to the pile inclined very easily. Inclination of the pile was noticed from the
measurement gauges; a gauge showed a large displacement while another indicated a negative
displacement. Calculating the average value of three measures compensates this error, because
three gauges were spread by a spacing of 120o around the pile.
2 Results
2.1 Measured displacements
The displacement was first set to zero and then it was measured with weights of 3.9 kg and 7.7
kg. Table 1 shows the corresponding displacements. From Table 2 can be seen that the standard
deviations are almost as high as the measured values. The error due to the measurement gauge
resolution is 5 m. It is marked in the next column to the standard deviation in Table 2.
5
Table 1. Four sets of measurements with PEI and aluminium (values are in micrometres).
Measurement 1 Measurement 2
PEI Gauge 1 Gauge 2 Gauge 3 Average Gauge 1 Gauge 2 Gauge 3 Average
3851.8 g 60 70 20 50.0 50 20 50 40.0
7703.6 g 120 150 90 120.0 140 -30 70 60.0
Aluminium
3851.8 g 20 0 20 13.3 10 10 0 6.7
7703.6 g 30 0 20 16.7 20 20 10 16.7
Measurement 3 Measurement 4
PEI Gauge 1 Gauge 2 Gauge 3 Average Gauge 1 Gauge 2 Gauge 3 Average
3851.8 g 10 10 40 20.0 30 0 80 36.7
7703.6 g 50 0 90 46.7 10 60 100 56.7
Aluminium
3851.8 g 0 10 20 10.0 10 0 20 10.0
7703.6 g 10 0 30 13.3 0 10 40 16.7
Table 2. The average values and the standard deviations of the measurements. Values are in
micrometres percentage error in the rightmost column (percentage part of the standard deviation
plus the gauge resolution from the average value).
PEI Overall average Standard deviation Gauge resolution Error %
3851.8 g 37 26 5 84
7703.6 g 71 56 5 86
Aluminium
3851.8 g 10 9 5 135
7703.6 g 16 13 5 114
2.2 Longer period test
A weight of 7.7 kg was also left onto the pile for a longer time. The purpose was to test a possible
drift of PEI material. The measurement gauges were reset after applying the load in order to see if
the balls start to penetrate into the PEI pieces. The system displaced 10 m during first two days,
but after that it did not deform more. The pieces were under the load for five days.
2.3 Squeeze test
Finally, test pieces were compressed towards to each other in a bench vise. The bench vise was
tightened until the displacement was about one millimetre. This required very much force with
the aluminium test pieces and the balls left easily noticeable holes on the aluminium pieces. With
6
the PEI test pieces, much less force was needed to compress them, but only a very small plastic
deformation remained. The balls did not deform at all according to a visual inspection
2.4 Remarks during tests
Applying a load of 7.7 kg leaves slightly noticeable traces on test pieces. However,
examination with a microscope showed that they are smaller than grooves due to machining.
The traces were bigger (and easier to notice) in aluminium test pieces. The surface quality of
the pieces corresponds a roughness of 3.2 or better.
Difference between modules of elasticity was influenced in testing; weights were more stable
on aluminium test pieces.
PEI showed to be a very elastic material.
3 Discussion
3.1 Calculations
Displacements and stresses caused by a force can be derived from equations in Figure 3.
Calculations are performed according to Reference 1.
Figure 3. A ball on a plane, loaded by a force. [1].
7
The dimensions ( ba,) of the contact area (radii of contact ellipse) can be obtained from:
)3/1(
)(721.0 JFKba (1)
where Fis the force in Figure 3, K equals the diameter of the ball and coefficient Jcan be
calculated from equation:
2
2
2
1
2
111 EE
QQ
J
(2)
where 21,QQ are the Poisson’s ratios of the materials and 21 ,EE the Modules of Elasticity of the
materials. [1].
The maximum stress in the contact, c
V, is got by [1]:
)3/1(
2
)(
918.0 ¸
¸
¹
·
¨
¨
©
§
J
VKF
c(3)
and finally, maximum displacement dby:
)3/1(
2
)(
040.1 ¸
¸
¹
·
¨
¨
©
§
K
F
dJ(4)
For Dixi polished balls, the Modulus of Elasticity is between 350 GPa and 640 GPa [2]. Poisson’s
ratios were difficult to find, there is used 0.2, which is common value for ceramics, carbides and
diamonds [3]. The equations above are not sensitive for the material properties of the balls
because the other material is more elastic and deforms mostly. For aluminium and PEI, were used
their common material properties (Table 3) [3].
Table 3. The material properties used for aluminium and PEI.
Ball Aluminium PEI
Modulus of elasticity [GPa] 350 70 3
Poisson's ratio 0.2 0.25 0.38
Ultimate strength [MPa] 280 140
The weight of the rod is about 500 g. Thus, a rod loads one of four connections roughly with a
force of 1.2 N (500 g 9.81 m/s2/4). However, the force used in the tests was much bigger due to
the connection is loaded by springs, or it is tight, in order to have a proper connection. In the
tests, three balls were loaded with weights of 3.9 kg and 7.7 kg. That corresponds the forces of
12.6 N and 25.2 N per ball. The corresponding displacements are obtained by substituting the
8
material properties and the force in Equations 2 and 4. For aluminium with the forces of 12.6 N
and 25.2 N the displacements equal:
0.2)6.12( NFdalu m(5)
1.3)2.25( NFdalu m(6)
and for PEI, the displacements are:
5.13)6.12( NFdPEI m(7)
5.21)2.25( NFdPEI m(8)
The maximum stresses in contacts can be calculated form Equation 3. The stresses in aluminium
are:
1013)6.12( NF
alu
VMPa (9)
1276)2.25( NF
alu
VMPa (10)
and in PEI, respectively:
148)6.12( NF
PEI
VMPa (11)
187)2.25( NF
PEI
VMPa (12)
Although the stresses are high and the ultimate strengths are remarkably exceeded, especially in
the case of aluminium, the contact areas are very small. The radius of the contact area can be
calculated by using Equation 1. By calculating the radii, there was noticed that the contact areas
were in every case less than 0.20 mm2 (the areas are the biggest for PEI).
3.2 Comparison to the measurements
The equations give a displacement between one ball and one flat surface. The measured
displacements were between two test pieces i.e. two ball-surface contacts. Thus, Equations 5, 6, 7
and 8 have to be multiplied by two to get results that are comparable to the measurements (Table
4).
9
Table 4. Measured and calculated displacement (in microns).
PEI Measured Calculated
3851.8 g 37 27.0
7703.6 g 71 43.0
Aluminium
3851.8 g 10 4.0
7703.6 g 16 6.2
The measured and the calculated displacements differ from each even by factor 2.5 in the case of
aluminium. Some of the error can be explained by the uncertainty of the measurements. Another
factor could be approximate equations that can be exact only for certain sizes of objects and
certain material properties.
As the calculations show, the contact areas are very small. This was verified during tests.
Although calculations indicate high maximum stresses, they are concentrated in a very small area.
4 Conclusions
The displacements derived from the equations differ from the measured displacements. This can
be cause of approximate equations, variations of material properties and errors during the
measurements.
However, the gained information is valuable. It shows that exceeding the ultimate strength very
locally is not critical. The traces due to the loads are hardly noticeable even the stresses indicate
plastic deformation.
According the calculations and the tests, balls leave smaller traces on PEI material. The ultimate
strength was exceeded less in that case. Furthermore, PEI did not have a drift under a local stress,
slightly over its ultimate strength. According the gained information, PEI is a suitable material
with a Dixi polished ball to support the MSGC rod.
10
5 References
1. Airila M, Ekman K, et al. Koneenosien suunnittelu. WSOY. Juva, Finland. 1995.796 p.
2. DIXI S.A. Precision polished balls. DIXI Product bulletin. DIXI LTD. Switzerland. 6 p.
3. MatWeb, The Online Materials Information Resource. http:/ /www.matls.com/ search.htm.
[Word Wide Web document]. Accessed: 30 March 1999.