4 Experiments 19
4.2 Experimental setup
4.2.1 The force transducers
One of the sixteen force transducers that are used during the experiments is shown in Fig- ure 4.2. The force transducer consists of a bronze cantilever beam, which is fixed in a frame at one tip and has one degree of freedom at the other tip, where the force is applied on the membrane via a metal hook. When a force is applied on the hook, the cantilever beam un- dergoes a small deformation in the plane of symmetry of the transducer (the plane of drawing in Figure 4.2), which is almost uniquely related to the applied force. The displacement of the beam can then be measured with a Hall-effect sensor.
'Before this becomes reality, first the size and shape of the force transducers has to be adapted to create this possibility
Exveriments 21
A
m
l
actuator outer p d i l
// 1
recess
I
I
B
Figure 4.1: Top view of a part of the mechanical subsystem; A: picture; B: schematic drawing, where the outer edge of the specimen (the membrane) i s depicted b y a dashed line
Two roughly identical magnets (the shaded objects in Figure 4.2) are glued on the frame of the transducer with the N-poles directed towards each other, they will cause a static position- dependent magnetic field in the space between the magnets. This magnetic field strength can then be measured as a function of position by means of a Hall effect sensor (Honeywell, type SS495A), The sensor produces an output voltage VOut which is related to
11?
(Figure 4.3).When the Hall-effect sensor is mounted on the cantilever beam close to the hook, the po- sition of that part of the beam near the sensor can be accurately determined. Advantages of the sensor is that it is relatively cheap and insensitive for environment influences such as light or temperature. As the cantilever has only one degree of freedom, only normal forces of the membrane can be measured. The sixteen force transducers are calibrated (see Appendix A) and after calibration, an inaccuracy in the measurement of the forces of about 3-4% was apparent.
4.2.2
The entire experiment is controlled in real time by a workstation (IBM RISC System/6000) and a UNIMA (UNiversal Interface Modules and Adapters) box. A flow diagram for control and data acquisition is shown in Figure 4.4. The computer interfaces to external devices via the UNIMA 1/0 system, which is a real time analog and digital 1/0 interface system.
A
graphic user (biaxial control) interface provides the user an easy way of adjusting system parameters, moving the actuators and running the experiments. The biaxial control interface sends commands to the UNIMA 1/0 card which sends digital signals via a 24 bit custom bus to four ”Quad Controller” printed circuit boards (PCBs).Data acquisition and control hardware subsystem
22 C h a p t e r
4
A
Intersection A
beam
33
34
J
B
Figure 4.2: T h e force transducer; A : picture; B: drawing, where the connector is left out of consid- eration; dimensions in [mm]
Each quad controller PCB contains four HCTL-1100 chips, which individually control a single actuator. Signals from the PCBs are passed through small actuator control cards connected to the actuators. These consist of a micrometer with a non-rotating spindle coupled without play to a DC-motor. As they are high precision drives they allow displacement steps of less than 0.1 [ p m ] and have a travel range of 50 [mm].
The analog output voltages from the force transducers are sent to voltage dividers, which are positioned on the same board as the actuator control cards. These transform the original output voltage span, which was [-10;10]
[u,
to a span of [-350;350] [ m u ; These analog volt- age outputs from the board are acquired by EMAP (Electro physiological MAPping system [ S I ) , converted to digital signals and sent via UNIMA to the workstation and the controlling interface where they were timed and recorded to disk.A black and white camera (640 x 480 pixels, Pulnix TM-9701 Progressive Scanning) was mounted above the test rig. The camera signal is monitored and send to a Silicon Graphics
0 2 workstation. The 0 2 contains a frame-grabber which communicates with the biaxial con- trol interface on the R6000 via the Internet. The biaxial control diagram sends a message to the 0 2 which would save the incoming video image (the frame) to disk with a reference number
Experiments 23
_ -
Magnetic field strength Output voltage of sensor along 21-axis along 21-axis
Figure 4.3: Relationships of the magnetic field strength
G(ë‘1)
and the output voltage of the sensor VOut(&) to its position along the ë‘l-axis (approximated). Also, the magnetic field lines are drawn(left); The characters N and S illustrate the North and South pole of the magnets respectively
attached. The IBM/6000 workstation is controlled by a custom application program called X V G [3], running under the UNIX operating system on the Silicon Graphics 0 2 workstation.
4.2.3
In case of the rubber and the pericardium, a circular shaped specimen with a radius of approximately 30 [mm] is made up. For the pericardium, this is the largest possible size. In case of the rubber, a random square black and white dot pattern is generated and directly printed on the specimen by a inkjet printer. With the pericardium, one has to be more careful and the random pattern was hand-painted with Indian ink. The reason for putting on this dot pattern will be explained in section 4.3. Also, pieces of paper with a black and white dot pattern are glued on top of the actuators (see Figure 4.5A). The dot size is chosen approximately three times as large as the pixel size of the camera. Also, the magnetic parts of the force transducers are covered with a black paper to prevent reflections of the magnets.
It is decided not to attach the specimen directly on the hooks of the force transducers but in an indirect way by means of strong surgical wires. Two important reasons for this are:
The mounting of the specimen on the
rigo The size of the specimens are too small; the minimum radius described by the hooks of the force transducers is about 40 [mrn]; when they move further inwards they will hit each other.
24 Chapter
4
Silicon Grôphics 0 2 Low rout
Analog voltage +arnes
Quad Cards Controller
(x4)
I I
Actuator Control Cards and Volta e Devifers
Force transducer
Membrane
Figure 4.4: Flow diagram for control and data acquisition
o It will be possible to determine both radial and tangential force components via the radial component and the direction of the total force, the latter is identical to the direction of the wire. In this way, the measured forces are corrected (see Appendix B).
E x p e r i m e n t s 25
A B
Figure 4.5: A : Top view photo of the rubber specimen at maximum extension; B: schematic illustra- tion, where only four out of sixteen wires are drawn
At sixteen positions on the specimen, at approximately 5 [mm] from the edge, white painted wires are attached by stabbing them directly through the specimen by means of a iron nee- dle. The positions of the points where the wire is stabbed into the specimen will be further referred to as the aflection points. Sixteen nooses are created from the wires by tying their tips together and the nooses are put around the hooks of the force transducer. When the specimen is pre-stretched, all sixteen affection points will be located in one single plane.
The camera (640 x 480 square pixels) is placed above the specimen. The distance is cho- sen in a way that the maximal extended state of the specimen covers an area on the camera which is as large as possible. The indices of all pixels on the camera @,q) can be expressed in [mm] with respect to a reference point C on the rig by introducing a orthogonal coordinate system ( I C , ~ ) with its origin positioned in this reference point (see Figure 4.5B). The reference point with pixei indices @c,qc) is placed in the center of the rig, which is the intersection point of imaginary lines between the hooks of pairs of two opposite force transducers and set to (0,O) [mm]. Now, the pixel indices of a random point A ( p ~ , q ~ ) can be transformed into
( I C A , ~ A ) in [mm], via Equation 4.1 and Equation 4.2:
where s is the p i x e l spacing, obtained by a precision ruler lying flat on the rig. In this study, s = 0.2024 [mm/pixel] and (pc,qc)=(322,244) [pized. When everything is setup, an initial s t a t e or reference state of the specimen is defined; this is the state of the specimen after the pre-stretching. In this state, reaction forces and strain quantities are s e t to zero. Further on in this thesis, every quantity (e.g. reaction forces, displacements and strains of the deformed sample) will be defined with respect to this reference state.