In order to calibrate the sensor well defined loads have to be generated. Such a setup does not necessarily need to generate individual components of the load vector for calibration, but it facilitates the process. Therefore, the setup illustrated in Figure 7 was used. With it each entry of the load vector fi from the equation (f = C x ?) can be applied to the force/torque sensor individually.
As described in section 2, the inverse of the compliance matrix in the equation (CN = NE-1 x C x Nf) may be obtained in that way. The required forces in the various directions are generated by weights tied to strings and directed by rolls. The holding torque of the rolls needs to be low enough not to influence the measurement. This is ensured by using roller bearings. The holding torque was found to be 0.002 Ncm at 10 N radial bearing load and thus negligible.
The results of the calibration measurements are shown in Figures 8—13. The individual entries of the load vector are applied and the respective values are increased. The Bragg wavelengths are recorded by the measurement setup, shown in Figure 6. The light of a broadband light source is split up by an optical fiber coupler and directed to the sensor fiber. The reflected light from the Bragg-gratings passes the fiber coupler again and is coupled into the optical spectrum analyzer (OSA), where it is recorded on a personal computer.
Figure 8 depicts the shift in Bragg wavelengths upon loading of the transducer with a force along the x-axis. The response of the FBGs is fairly, but not perfectly linear. Comparing Figures 8 and 9, it can be observed that the graphs look similar. However, the FBG number that shows for example the steepest increase is different in both measurements. This property of the transducer ensures that different states of loading, in the mentioned case Fx and Fy may be distinguished. For all six load cases the respond of the transducer shows some deviation from perfect linearity. This might be attributed to the polymer used for manufacturing the transducer structure.
When we load the sensor with a torque around the z-axis, the FBG have a positive sensitivity for and odd sensor number and a negative sensitivity for en even sensor number. This is to be expected from the FBGs distribution within the force/torque sensor as they are ordered at alternating angles along the fiber. The force/torque sensor possesses a symmetry with respect to the z-axis which should yeld a Bragg wavelength sensitivity with comparable absolute values.
It can be seen that despite the symmetry of the sensor not all Bragg peaks share the same absolute value of sensitivity. For all measurements shown, the loads represent the maximum possible loading of the polymer structure. The standard deviation of the optical measurement system is 4-pm. With a maximum wavelength shift of approximately 500 pm at 12 N load this gives a maximum force resolution ?F2 of ~100mN, neglecting a negative effect of the conditioning of the sensor.