4. STEPS OF NEEDLE GRIPPER DESIGN FOR DEMOULDING FLEXIBLE
4.3 Determining the pull-out force for one needle by experiments, measuring the needle force
It is necessary in the design process to know the amount of force needed for a needle to penetrate the foam at full length and the force needed to pull it out from this position. The forces exerted by the needle have to be verified by measurements. To obtain data about, what happens at the insertion and at the pulling out of the needle, an experiment was designed to measure the forces according to the displacement of the needle. The other task is to check the results of the theories presented in the previous Chapters. The diameter of the initial hole that is used in the initial value problem for solving the differential equations (97), or (99), (100) also has to be checked from this test by observing the remaining permanent hole after the needle has been pulled out. The active length of penetration of the needle is also an important parameter for the calculation, because the foam has an area where it compresses under the needle, so its active (inserted) length will not be equal to its full length. This parameter can also be measured from this test. From the calculated pressure, the friction coefficient and from the measured force, the active area of contact between the needle and the foam may be deter-mined. The work and the consumed energy of the process may also be determined from the test. From a range of needles used in the test a comparison can be made to choose the needle geometry best suited for the task. The conditions to be satisfied would be the largest applied force per unit surface and the smallest caused damage by a needle.
4.3.1 The test
The idea of the test is to penetrate foams of given material parameters with needles of defi-nite geometry and measure the force needed to push in such a needle all the way in the foam and pull it out again. All the needles have the same material properties and are manufactured the same way. The range of needle geometry can be seen in Table 5. When the needle has penetrated the foam at full length the process is reversed. The two maximum force values (one just before the reverse of the process and one immediately after the reversion) are taken as the two required forces. The first one is the maximum insertion force and the latter is the maximum pull out force. The two forces are collinear but have different signs and value.
For the test a versatile Zwick-WS4 tensile test machine was chosen (Fig. 45). The test foam was fixed to the moving part of the machine. To its upper part, where the force sensor is situ-ated, a fixture was attached with a specially designed connecting part to which a hypodermic needle can be easily attached (Fig. 44 and Fig. 46). The force is measured on the needles and is collinear to the axis of the needles.
The test foams were of dimensions of 100x100x90 mms for every part. This is large enough so the sides of the foam do not have an effect on the stress field. The bottom side of the foam was glued to a fixture that was fixed to the moving part of the tensile machine. The velocity of the insertion and pull out was set to 100 mm/min. This value was used in every other experi-ment. For every needle the height of the start was set. It was 10 mms plus the length of the needle. The bottom level was set, so at the end of the process the whole needle is fully in-serted into the foam. When the insertion was stopped, the pull out started instantly, by revers-ing the process with the same speed. The pull out process was carried on until the needle re-turned to it original position. The insertion path was set collinear to the axis of the needle and it was perpendicular to the top surface of the test foam. (The hypodermic needle and the fix-ture can be seen on Fig. 43 and Fig. 44). Five of this test processes were repeated for every
3 The test was carried out at the Department of Polymer Engineering in 2001.06.26 with the kind help of the de-partment’s staff.
needle and every foam, changing the needle after every insertion. It was necessary, because the needle may lose its sharpness and this could affect the measured values.
After every insertion the test foam was moved to a different location of more than 30 mms from the previous insertion point to make sure that the foam is always tested at an intact area.
During the tests no bending of the needles was noticed. In some cases after the needle was pulled out it was noticed that the point of the needle became blunt. It was no surprise because these needles were designed for one use only. The register paper motion was proportional to that of the needle. The insertion was set to the normal feed direction and the pull out to the backward direction.
Fig. 43: hypodermic needle Fig. 44:Fixture for needle
Fig. 45: Arrangement for testing the needle force base on a universal Zwick-WS4test machine
Fig. 46 The needle above the test foam Fig. 47 The needle fully inserted in the test foam
The needles given in Table 5 were applied in the experiment. These dimension of needles were commercially available at the time. They are carefully tested according to ISO 9626. For the measurements 10 types of needle were used with 5 different diameter and 9 different length categories (Not all diameter-length combination is manufactured.). These needles were made and provided by courtesy of Dispomedicor Rt. (Hungary). From the 15 different test foams five significantly different were chosen for the test. Testing the entire range of foams Adapter
Fixture for needle
Needle Test foam
Force sensor
was too expensive and time-consuming. Only foams 1,6,7,12 and 15 were used in the test (Appendix A.6 and all the foam that were used in this test are marked by “D”). Penetration force and pulling out force were measured on a Zwick-WS4 tensile test machine. After the test some foams were cut to pieces perpendicular to the axis of the needle for further analysis.
Table 5: Dimensions of the hypodermic needles used in the tests, (X available, √ used)
Diameter [mm]
0.5 0.6 0.7 0.8 0.9 1.1 1.2 1.5 1.6
40 √
42 √
50 X √ X X √
60 √
Length []
70 √
4.3.2 Results
The results were registered on a plotting paper by the test machine. Let us analyse the re-sults on these diagrams according to Fig. 48 and Fig. 49. From their shape we shall call them
‘Butterfly Diagrams’. The plot illustrates the force (F[N]) vs. the insertion length (L[mm]).The direction of the insertion is from left to right. The insertion part is on the upper part of the diagram that is upward sloping. The feed is reversed instantly when the pull-out begins. A quick direction change can be seen on the paper. When the needle returns to its original position the indicator plot touches the start point. This means that there is no loss or remanence of force in the process or at least very little. So the whole process can be consid-ered ideal. The area surrounded by the plotted curve is of work dimension [Nm], which is the energy of the whole process. If the diagram is divided by an imaginary line through the origin at the null displacement, the diagram can be split into two parts. The upper part is a triangle of the work of the insertion and the lower triangle is the work for the pull-out process. The two areas are not equal. The maximum force of the insertion is much larger than the maximum force of the pull-out. Also the displacement is different, due to the compression and re-stretching of the foam under the needle point. The foam does not tear all the way, so there is always a bit where the foam suffers only a reversible compression. When the process is re-versed this foam part springs back and thus reduces the actual penetration length. This length of penetration loss may be determined from the diagram by the distance of the two imaginary line between the two maximum force points (Lneedle-Leffective). The work of the springing back can be determined from the diagram. The area difference between the two processes is equal to the energy that is required to form the permanent hole in the foam. This can also be easily obtained from the diagram. Data that were acquired from the test can be seen on Table 6 for Foam7. These serve as inputs for further calculations and were determined from the diagram of Fig. 49.
Table 6: All the data acquired that were from the test (for foam 7D).
Foam 7 D Active length
Needle
diameter[mm] Needle
length Lin
[mm] Lout [mm] Ldiff in
[mm] Ldiffout
[mm] Fin[N] Fout[N] σfrict
[kPa]
0.5 42 37.2 39,5 4 4.2 1.816 0.992 15.988
0.6 60 55 51 4 7 3.832 2.328 24.216
0.8 50 44.2 41 4 8 3.920 2.040 19.797
0.9 70 70 63 3 9.7 6.608 3.920 22.006
1.5 50 45 42 3 8 4.488 2.920 14.753
1.6 40 34.5 29.5 3.5 8.5 3.880 2.288 15.429
Fig. 48: The whole process of a 9x70 needle,
for foam 7 Fig. 49: The data obtained from the experiment
The data of maximum pull out force were measured from the point of the lowest point of the bottom triangle to the middle line of the diagram of Fig. 48 and Fig. 49. (Fmaxout on the dia-grams.) From these values the real pull out forces was determined.
To compare the needle to one another the real force per unit area of needle has to be deter-mined. The pull out force (Fmaxout) has to be divided by the active surface of the needle (µ0) to get σfrict.
] [ 1000
max kPa
L D
F
effective needle
frict π out
σ = (141)
Where: Dneedle is the diameter of the used needle, σFrict is the maximal stress. The division by the frictional coefficient is not really necessary, because it is a constant for the given material, so it will not affect the comparison.
The summary of these data can be seen in Table 7.
Table 7: Measured data of pulling out force for the tested foams
Maximum frictional stress caused by the fully in-serted needle in the foam [kPa]
Diameter
of needles Foam 1 Foam 6 Foam 7 Foam 12 Foam 15
0.5 15.99711 22.63537 15.98802 23.14981 22.56374 0.6 19.29151 24.59217 24.21652 27.22651 27.43528 0.8 15.17051 20.99329 19.79732 23.33067 23.18126 0.9 17.81144 24.64335 22.00661 25.86268 26.03952 1.5 13.1366 15.94137 14.75341 16.10841 16.26917 1.6 12.68266 17.40757 15.42994 17.59081 18.25601
These data are shown on a diagram when the maximal frictional stress versus the needle di-ameter is drawn (Fig. 50). On the diagram the trend lines for the values are also illustrated. It can be seen that the trend lines have a maximum in the examined region. The maximum is at the point where a needle diameter produces the maximal friction stress for a given foam. This result was unawaited, because from the used theory of continuums the stress was independent of the needle diameter. From the diagram it can be seen that needle diameter from 0.6 to 1 mm has the best performance.
10 12 14 16 18 20 22 24 26 28
0,5 0,6 0,8 0,9 1,5 1,6
ne e dle diame te rs [mm]
σ frict [kPa]
Foam 1D Foam 6D Foam 7D
Foam 12D Foam 15D Polinom . (Foam 12D)
Polinom . (Foam 6D) Polinom . (Foam 7D) Polinom . (Foam 1D)
Polinom . (Foam 15D)
Fig. 50. Stress caused by pulling needles out from a given foam material vs. needle diameter
4.3.3 Explanation of the results
From the range of needles an optimal needle diameter had to be determined. The conditions have to be that the damage caused by a needle has to be as small as possible, that means the needle diameter has to be the smallest possible. The needle has to have proper stability against buckling this means that the diameter has to be large. Also the surface of the needle where the friction force acts has to be as large as possible, that means that the diameter and the length have to be as large as possible. These conditions are in contradiction. That means that there should be a compromise in the diameter. From the results it can be seen that there has to be no compromise, because there is always an optimum in this range of needle diameters with foams of examined parameters. The explanation is in the structure of the foam. The larger the diameter of the inserted needle is the larger the permanent hole will be cut out. This means that the radial stress will not grow beyond a certain point determined by the unified stress (σtangential-σradial) (See previous Chapter). This results in the down sloping curve of diameters larger than 1 mm. On the other side of the diagram with needle diameters less than 0.6 mm (Fig. 50) the curve is also down sloping. It is caused by the open celled structure of the foam.
In these dimensions the needle diameter can be compared to the size of the GSE (See: Chapter 2.3.3). This means that the needle has little contact with the polymer structure of the foam and has a very small surface where the friction force can take effect. Its diameter is so small that it does not produce a significant displacement it rather just cuts the foam and leaves a hole al-most as large as the needle. From these results the optimum of needle diameter can be easily determined. This optimum satisfies all the conditions that were made: minimal damage, maximal friction stress and has good strength for mechanical load.
The other important result is that the largest stresses do not belong to foam 6, that has the largest initial modulus and the largest tearing stress. From the diagram it can be seen that the two highest stresses belong to foam 12 and 15 (which are the second and third hardest foams) then to foam 6 and then foam 7 and foam 1. The only one out of the sequence is foam 6 which is also the most rigid of them all.
4.3.4 Conclusion
With the tests the pull out forces and insertion forces were determined and the whole course of the process were analysed with the idea of active needle surfaces. A diagram for the
deter-mination of the energy involved in the process was proposed. The optimal needle diameters for the maximal pullout forces were determined. By cutting some foam to pieces that were perpendicular to the insertion axis the geometry of the permanent hole could be investigated.
The diameters of these holes do not change along their axis. This means that for the developed theory they can be taken as the initial hole for the calculations. The other important fact was that the pull-out forces per unit area increase in the function of the initial shear modulus up to a point and then decrease. This means that the correlations between these stresses and the ma-terial properties are not linear.