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Measurement of the Apparent Density of Green Ceramic Tiles by a Non-contact Ultrasonic Method

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Abstract

This paper discusses the problem of the measurement of the apparent density of green ceramic tiles during production. This is a fundamental parameter for the quality of the final product. In fact, the apparent density determines the entity of the dimensional shrinkage of the ceramic body during the firing of tiles, and it is proportional to the final mechanical resistance. Currently, non-destructive systems for the on-line measurement of this parameter are not available. The work presents an innovative method for non-intrusive measurement of the apparent density of green ceramic tiles during the production stage. This method uses non-contact ultrasonic probes. The time of flight of ultrasonic waves is measured during the transmission through the tile. From the time of flight, with the distance between probes known, the propagation velocity can be achieved, which is proportional to the apparent density. The conversion factor between velocity and apparent density is determined by a calibration procedure with a reference method of known uncertainty, e.g. based on a hydrostatic weighing in a mercury bath. This experimental procedure is extensively validated in the work and supported by a theoretical model. The paper presents the theory on which this measurement method lays and the instrumental apparatus, and discusses in detail the analysis of uncertainty. In the end, the paper presents the results of an on-line application.

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Abbreviations

ρ :

Apparent density

ρ s :

Average actual density

m :

Mass

V a :

Apparent volume (pores included)

V s :

Skeleton volume

p :

Porosity (%)

v :

Longitudinal wave velocity

v t :

Transversal wave velocity

v a :

Sound velocity in air

t c :

Total time of flight through tile and air

T :

Air temperature (°C)

u(x):

Standard uncertainty of quantity x

u s :

Type A standard uncertainty

u a :

Standard uncertainty evaluated as half-width of a rectangular distribution (Type B)

S ρ :

Standard deviation of ρ achieved by least-squares linear interpolation of the experimental data over the whole considered range

SNR:

Signal-to-noise ratio

E :

Young’s modulus of the porous body

G :

Elasticity tangential modulus of the porous body

μ :

Poisson coefficient

E 0 :

Young’s modulus at null porosity

G 0 :

Elasticity tangential modulus at null porosity

b :

Empiric parameter proposed by Spriggs [11]

D :

Distance between the probes

d m :

Tile thickness

t a :

Time of flight in air without the tile

t m :

Time of flight through the tile thickness

θ :

Air relative humidity (%)

r(t m , t c ):

Correlation coefficient between t m and t c

c j :

Sensitivity coefficients for quantity x j

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Acknowledgments

This research has been carried out within the SENSOCER project, funded by the European Commission in the 5° Frame Programme (Standard, Measurement & Testing, G6RD-CT2001-00637). The author would like to thank all the project’s partners. Finally, the author also thanks Dr. Paolo Pietroni for the useful discussions during the analysis of the results.

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  1. Dipartimento di Meccanica, Università Politecnica delle Marche, Via Brecce Bianche, 60131, Ancona, Italy

    G. M. Revel

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  1. G. M. Revel
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Correspondence to G. M. Revel.

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Revel, G.M. Measurement of the Apparent Density of Green Ceramic Tiles by a Non-contact Ultrasonic Method. Exp Mech 47, 637–648 (2007). https://doi.org/10.1007/s11340-006-9032-6

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  • DOI: https://doi.org/10.1007/s11340-006-9032-6

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