Considerations to design of metrological confirmation processes in mechanical manufacturing systems.

Villeta, Maria ; Lobera, Alfredo Sanz ; Rubio, Eva Maria 等

1. INTRODUCTION

Metrological confirmation process represents a fundamental element in the assurance of the quality of the mechanical manufacturing systems. It must be designed and implemented to ensure that metrological characteristics of the measurement system meet metrological requirements of the measurement process (ISO 10012:2003, 2003). The confirmation process includes the calibration, the verification and also the measurement uncertainty. Measurement uncertainty (ISO/IEC Guide 98-3:2008(E), 2008), internationally recognized parameter and widely used in metrological studies such as (Casalino & Ludovico, 2003) and (Seferovic et al., 2003), is the mainstay of this process. Direct comparison of the measurement uncertainty with the metrological requirements will determine whether the measurement system is confirmed or not for a particular measurement process. In this sense, whether or not the tolerance/uncertainty ratio falls within a predetermined range of values, such as that established by (Sanz et al., 1985) or (Sanchez, 1999) to cite only the most relevant, has been a routinely procedure used at the time of carrying out the metrological verification process.

This paper presents a possible alternative way to the design of confirmation processes. It is based on a new criterion for the evaluation of metrological systems (Villeta et al., 2009). Next, both are going to be exposed briefly. Finally a practical case in the field of mechanical manufacturing shows the application of such new way of design.

2. EVALUATING MEASUREMENT SYSTEMS

In mechanical manufacturing field, measurement systems are often used for evaluating and improving manufacturing processes. The variability of the measurement system affects on the data obtained from the measurement process, so these data can show a distorted image of the variation of the manufacturing process.

In order to guarantee capable measurement systems for controlling manufacturing process, Villeta (Villeta, 2008) has proposed the ICC index (Index of Contamination of the Capability). The model of equation (1) has been considered for obtain this index.

Y=X+[epsilon] (1)

Where Y is the observed result after a measuring operation, X is the true value of the characteristic of a product and [epsilon] is the random error due to the measurement inaccuracy. It was assumed that X is normally distributed with average [mu] and variance [[sigma].sub.P.sup.2] and [epsilon] is independent of X normally distributed with average zero and variance [[sigma].sub.M.sup.2]. Thus in agreement with equation (1) instead of observing the characteristic X, the empirical variable Y normally distributed with average [mu] and total variance [[sigma].sup.2] is observed:

[sigma].sup.2] = [[sigma].sup.2.sub.P] + [[sigma].sup.2.sub.M] (2)

From this model and with the idea of controlling the manufacturing process by mean of the capability index [C.sub.p] ([C.sub.p]=T/6[[sigma].sub.P], where T represents the manufacture tolerance) evaluated throughout the measurement system, equations (3) and (4) have been developed:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

where [z.sub.[alpha]/2] represents the value of a standard normal distribution which leaves on its right a probability of [alpha]/2 and [gamma]=U/T, where U is the expanded uncertainty of measurement (ISO/IEC Guide 98-3:2008(E), 2008). [[??].sub.p,obs] represents the observed process capability and [[??].sub.p,real] is an approach to the capability that the manufacturing process really has.

Due to the uncertainty of measurement, a capability lower than the manufacturing process really has is observed. With the aim of quantifying the adequacy of measurement systems in this context, the mentioned ICC index has been proposed by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

3. WAY TO METROLOGICAL CONFIRMATION

As it was mentioned before, the relationship between tolerance and uncertainty has a great interest in metrological confirmation process. A very usual requisite for verification in mechanical manufacturing systems, but not unique (Aguilar et al., 2006), consist on the requirement of the following rank of values (Sanz et al., 1985):

3 [less than or equal to] T/2U [less than or equal to] 10 (6)

On the other hand, fixing a minimum value for ICC index so that in case of observing a 1.33 capability and taking [alpha]=0.05 the minimum index agrees with the lower limit of the rank of values for the ratio tolerance/uncertainty in equation (6), it can be obtained next criterion (Villeta et al., 2009):

T/2U [greater than or equal to] (4.42)[[??].sub.p,obs]/[z.sub.a/2] (7)

Considering this result and with the idea of establishing a two-side limits rank of values useful in the process of metrological verification, equation (8) can be obtained now proceeding with the upper limit of equation (6) in a similar way as in the lower one:

T/2U [less than or equal to] (14.74)[[??].sub.p,obs]/[z.sub.[alpha]/2] (8)

Therefore, equations (7) and (8) offer a rank of values for the ratio tolerance/uncertainty that can help in concluding or not if a measurement system is according to metrological confirmation for a defined measurement process in a mechanical manufacturing process. It can be noticed that the rank of values is bigger for processes more capable, but more demanding with the uncertainty too.

4. A PRACTICAL CASE

In order to illustrate the above considerations to the design of the confirmation process, a practical case is going to be exposed.

Assume the experimental study of Saenz de Pipaon (Saenz de Pipaon et al., 2008) where cylindrical bars of magnesium alloy UNS M11311 were dry turned. To measure the roughness of the workpieces, a surface roughness tester Mitutoyo Surftest SJ401 was used. Suppose that this measurement system owns a ratio T/2U=3.5. Suppose also that a capability of 1.2 is observed in the machining process with the roughness tester. Then, by the equations (7) and (8) (with [alpha]=0.05): 2.71<3.50<9.02; this suggests that the roughness tester is in adequate state of confirmation to measure the machining process.

Nevertheless, the same roughness tester would not be in adequate state of confirmation for a turning process with an observed capability of 1.8, because 4.42[[??].sub.p,obs] / [z.sub.[alpha]/2] = 4.07 >3.5. Figure 1 shows this situation.

[FIGURE 1 OMITTED]

5. CONCLUSION

This paper offers an alternative way to the traditional requirements about the relationship between tolerance and measurement uncertainty, considered in metrological verification processes applied to mechanical manufacturing systems. In such way, the capability of the manufacturing process has been considered for fixing the limits of tolerance/uncertainty ratio. More capable processes will be more demanding with the tolerance/uncertainty ratio. Depending on such capability, among other parameters, the measurement system will be or will not be in adequate state of metrological confirmation for the measurement process.

6. REFERENCES

Aguilar, J. J.; Sanz, M.; Guillomia, D.; Lope, M. & Bueno, I. (2006). Analysis, characterization and accuracy improvement of optical coordinate measurement systems for car body assembly quality control. International Journal of Advanced Manufacturing Technology, Vol. 30, No. 11-12, (October 2006) 1174-1190, ISSN: 0268-3768

Casalino, G. & Ludovico, A. D. (2003). Estimation of target uncertainty in GPS measurement, Proceedings of the 14th International DAAAM Symposium, Katalinic, B. (Ed.), pp. 85-86, ISBN: 978-3-901509-34-6, Sarajevo, October 2003, DAAAM INT VIENNA, Vienna

ISO 10012:2003, (2003). Measurement management systems. Requirements for measurement processes and measuring equipment, ISO, Geneva

ISO/IEC Guide 98-3:2008(E) (2008). Uncertainty of measurement--Part 3: Guide to the expression of uncertainty in measurement (GUM:1995), ISO/IEC, Geneva

Saenz de Pipaon, J. M.; Rubio, E. M.; Villeta, M. & Sebastian, M. A. (2008). Influence of cutting conditions and tool coatings on the surface finish of workpieces of magnesium obtained by dry turning, Proceedings of the 19th International DAAAM Symposium, Katalinic, B. (Ed.), pp. 609-610, ISBN: 978-3-901509-68-1, Vienna, October 2008, DAAAM INT VIENNA, Vienna

Sanchez, A. M. (1999). Fundamentals of metrology, Publication Section of the ETSII-UPM, ISBN: 84-7484138-0, Madrid

Sanz, A.; Perez, J. M. & Sebastian, M. A. (1985). Considerations to the determination of the ratio manufacturing tolerance/measurement uncertainty, Proceedings of 2nd International Congress of Industrial Metrology, Torres, F. (Ed.), pp. 106-118, Zaragoza, November 1985, Zaragoza University, Zaragoza

Seferovic, E.; Begic, D. & Halilagic, M. (2003). Measurement uncertainty of the perthometer concept in roughness measurement, Proceedings of the 14th International DAAAM Symposium, Katalinic, B. (Ed.), pp. 405-406, ISBN: 978-3-901509-34-6, Sarajevo, October 2003, DAAAM INT VIENNA, Vienna

Villeta, M. (2008). Integrated analysis of statistical quality assurance into measurement systems, PhD Thesis, Department of Manufacturing Engineering, Industrial Engineering School, National University of Distance Education, Madrid

Villeta, M.; Sanz, A.; Gonzalez, C. & Sebastian, M. A. (2009). Evaluation of dimensional measurement systems applied to statistical control of the manufacturing process, Proceedings of 3rd Manufacturing Engineering Society International Conference, Segui, V. J. and Reig, M. J. (Ed.), pp. 559-566, ISBN: 978-84-613-3166-6, Alcoy, June 2009, UPV, Alicante