11. Calculation of profile error obtained by the fuzzy logic method

Concluding that the proposed method presents the maximum error in curve peaks, among its values are 0.15, 0.14, 0.1, and 0.1 mm. These peaks have been found to represent intersections between two curves. The weakness of this method is in the intersections of the curves. But in the journey with himself, he does not have any difference.

Indeed, it has been deduced that the result of fuzzy logic is the closest to the ideal curve because of some points that appeared to define the involute curve; at this moment; we could not calculate them by the normal vector method. The graph was constructed by the following formula:

$$\begin{cases} Err\_i = \sqrt{\left(\mathbf{x}\_f - \mathbf{x}\_v\right)^2 - \left(y\_f - y\_v\right)^2} \\ Err\_i \le \varepsilon\_i \end{cases} \tag{14}$$

12. Conclusion and perspectives

mance according to the designer.

contradictory inference rules.

Author details

Bloul Benattia

References

47-54

In this respect, we can conclude that by the principle of fuzzy logic, there is not really the right or the wrong answer as has already been pointed out several times. While the choice of calculation method the profile taken is conditioned between the installation and the perfor-

Fuzzy Logic Applications in Metrology Processes http://dx.doi.org/10.5772/intechopen.79381 59

Some researchers even suggest averaging the different methods, but this is not a generalization, and the calculations become even more complicated. Finally, we mention that this problem of probing is solved, thanks to the development of the fuzzy logic, which relies on the linguistic knowledge, nonlinearity, and not the needs of the model; the solution was obtained by means of a computer. Nevertheless, it lacks precise guidelines for the design, because of

Reliability Laboratory of Petroleum Equipment and Materials-Boumerdes, M'hamed Bougara

[1] Wozniak A, Mayer JRR, Balazinski M. Stylus tip envelop method: corrected measured point determination in high definition coordinate metrology. International Journal of

[2] Bloul B, Bourdim A. Control inspection involute curve of gear tooth of pinion type cutter using the fuzzy logic. International Journal of Metrology and Quality Engineering. 2012;3:

[3] Achiche S, Fan Z, Baron L, Wozniak A, Balazinski M, Sorensen T. 3D CMM strain-gauge

[4] Wozniak A, Dobosz. Methods of testing of static in-accuracy of the CMM scanning probe.

[5] Ginnity SM, Irwin GW. Fuzzy logic approach to manoeuvring target tracking. IEE Pro-

[6] Wozniak A, Mayer R, Balazinski M. Application of Fuzzy Knowledge Base for Corrected

triggering probe error characteristics modeling using fuzzy logic. IEEE; 2008

Address all correspondence to: bloul.benattia@univ-boumerdes.dz

Advanced Manufacturing Technology. 2009;42:505-514

Metrology and Measurement Systems. 2003;10(2):191-203

ceedings - Radar, Sonar and Navigation. 1998;145(6):337-341

Measured Point Determination in Coordinate Metrology. IEEE; 2007

University of Boumerdès, Boumerdes, Algeria

The fuzzy logic algorithm is used to estimate the actual tooth area of the gears. The performance results given by our approach were compared to the performance of these data using the ideal model.

It is clear that the use of the fuzzy logic estimator is appropriate and estimates the actual area of the tooth which consists of a very complicated path when detecting teeth by CMMs in the sense that the application of the logic technique with estimation of dynamic non-linear systems, special cases, and the surface of the gear which contains several parameters is the best (see Figure 13).

Anyway, this problem is solved by this approach. Thus, the role of this work is the determination of the tooth curve to estimate the shape defect of the gears. In our future work, we will try to implement other learning algorithms such as the Kalman estimator or fuzzy neuron.

Figure 13. Calculation of the error of the result of the fuzzy logic and the normal vector.
