A major objective was to design a fiber Bragg grating-based force torque sensor fitting into the volume of 10 x 10 x 10mm3. With this, the above mentioned difficulties, arising from the bending limitation of the fiber, come along. It also would be favorable to use the serial or Wavelength Division Multiplexing capabilities of FBGs. An important parameter is the length of each fiber Bragg grating sensor of approximately 3mm. Along its length, the FBG should encounter no bending, since this would lead to Birefringence, causing the reflection spectrum to become polarization dependent (Huard 1996; Lawrence et al. 1999).
As all FBG measurement systems have a more or less strong sensitivity towards polarization, this is something to be avoided. In turn, this leads to the constraint that the 3 mm long FBGs have to be placed within the sensor volume following a straight line. Also, due to the bending condition, the FBGs have to be connected by a piece of fiber with a bending diameter of more than 5mm. Additionally, the FBG sensors should not be bonded to the mechanical transducer structure in order to avoid generation of strain gradients along the length of the FBG. This leads to the necessity of freely spanned FBGs. The strain within thefiber is then determined by the relative change in distance of the two fixation points. At last, having a through hole at the center of the transducer structure would allow feeding through cables for control tools placed on top of the force/torque sensor.
The design procedure thus starts by choosing a simple mechanical transducer structure with a hole in the middle in order to allow the feed through of communication cables in an application. A thick walled pipe like structure was chosen as it allows the analytical calculation or at least approximation of parts of the stiffness matrix. Then the FBG sensors were positioned as three millimeter long rods in the remaining volume following the Stewart platform design, where the legs of the Steward platform were taken as the positions of the FBG sensors.
By choosing the separation of the sensors carefully, the radius of the connecting fiber pieces can fulfill the minimum requirement of 5 mm bending diameter. The fiber is supported along the lengths of the bent parts by a structure following the desired bending line. The result of this design process is shown in Figure 3. We used the commercial CAD Software package CoCreate Onespace Modeling 2007 for designing the structure.
The fiber contains six fiber Bragg gratings with a length of 3mm each and a spacing of 12mm (see Figure 4). The gratings are written during fiber drawing consecutively into the same fiber (Hagemann et al. I998). The sensors interfere negligibly, since they possess different Bragg-wavelengths.
The full width halt maximum (FWHM) width of each sensor is approximately 200 pm, the reflectivity is approximately 15%. The I25 µm diameter fiber is coated with an Ormocere coating yielding a total diameter of 250 µm. The fiber is wrapped around the mechanical transducer structure, supported only along the lengths of the bent connection pieces. At the position of the supports, the fiber has to be glued to the transducer structure, to avoid slipping under load. The sensor region of the fiber follows a straight line in the CAD model, but will show some bending in the actual implementation since no bending torque can be applied by the bending supports.
Each FBG sensor is required to measure negative as well as positive strains, to be able to reconstruct f in the equation ( f = C x ?) . As the FBGs are not glued to the structure this is realized by pre-stressing the fiber. This will also aid in straightening the FBG sensors. An optical fiber allows strain of a few percent before braking, corresponding to a pre-stress force in the range of several ten Newton. This high value is even obtained with Bragg gratings inscribed in the fiber, if the gratings are written during the drawing process, before application of the coating (Hagemann et al. I998).
The complexity of the mechanical transducer structure makes a machining fabrication approach difficult and costly. Therefore a direct writing rapid prototyping approach was chosen. The spatial resolution is good enough and the surface finish is of minor importance for this functional demonstrator.
One drawback with this kind of fabrication is the restriction in terms of available materials. Compared to metals like steels, aluminium or brass they show an increased nonlinear behavior, which will lead to nonlinearities of the force/torque sensor’s response. To that point, thermal stability is lower. On the other side, the lower Young’s modulus suggests, that a higher sensitivity of the mechanical transducer structure may be obtained. Since the goal of this work is the realization of a functional demonstrator, and design optimization is considered as a second step, the drawbacks of rapid prototyping seem acceptable.
Fixing the fiber to the structure starts with gluing the fiber to the first bending support structure. Pre-stress of the fiber is then applied by means of a weight which is attached to the free end of the fiber (compare to Figure 5). Then the fiber is wrapped around the mechanical transducer structure. The distance of the FBGs is 9.5mm, matching the distance of the free spanned parts. The weight was chosen to be well below the breaking limit at 140g, corresponding to a force of 1.37 N. This ensured that an unintentional spot of low bending radius did not lead to fiber breakage.
The fiber was then sequentially glued to every bending structure, while monitoring the applied pre-stress with the measurement setup, pictured in Figure 6. It could be observed, that the initial load of some FBG sensors decreased during gluing, which might be attributed to a creep behavior of the glue.