OPTIMIZATION OF THE COMPOSITION OF HIGH-TEMPERATURE
COATINGS USING A B-SPLINE APPROXIMATION METHOD
V. E. Ved’,
N. I. Guseva,
and A. G. Verba
Translated from Novye Ogneupory, No. 2, pp. 50 – 54, February, 2005.
Original article submitted September 20, 2004.
The operational characteristics (fracture energy, apparent density, and open porosity) of multicomponent
phosphate-hardened coatings are studied as a function of the component concentration using a B-spline ap
proximation method and optimum compositions for the coating material are obtained.
Phosphate-hardened coatings find wide application in
technology owing to their low shaping temperature and good
fabricability. Establishing a balanced combination of supe-
rior operational properties even within a particular coating
material requires a significant amount of experimental re-
Our goal in this study was, first, establishing the rational
compositions for high-temperature coatings with the re-
quired set of properties using a minimum amount of experi-
mental data and, second, establishing relationships between
properties and processing parameters.
To that effect, the following properties (parametrized as
independent variables x
) were considered: x
ratio in an alumophosphate binder (APB); x
tration of APB in a mixture with a filler, wt.%; x
tration of Al
in a mixture of Al
tained in the filler (on condition that Al
) concentration of S-13 finely ground synthetic
glass in the filler, wt.%.
Expressing one independent variable by another variable
and using intrinsic relations for one of the variables makes it
possible to analyze in what manner various factors — such
as the conditional acidity of the binder (determined by the
ratio), concentration of the binder (correspond
ingly, concentration of the filler, considering that the sum
thereof is 100%), and concentrations of Al
glass — may control properties of the coating.
The properties of coatings were studied using an array
built on a full factorial design 2
(Tables 1 and 2) .
A paste-like mixture of the precursor components pre
pared on the basis of the array in Table 2 was cast into spe
cial fluoroplastic molds or applied onto 100 ´ 50 ´ 12 mm
plates made up from ZhS-6K aircraft blade alloy; the green
performs were initially dried in air and then in a drying cabi-
net at 300°C for 2 h.
The response function was modeled by experimental pa-
rameters: open porosity P, %; apparent density g,kg/m
specimens sintered at 1100°C for 0.5 h, and fracture energy
, J) of coatings supported on a metal substrate and heat-
treated at 300 and 1100°C. Relevant data are given in Ta-
The experimental parameters as a function of the compo-
sition were approximated using B-splines .
The order (k )ofB-splines in the general case is chosen
on condition of continuity of the (k – 1)th derivative of the
approximated function. In the composition range of interest,
all properties under study vary continuously, which implies
that the second derivative is continuous, that is, k =3.
B-spline of order 3 in a single variable is a finite (that is,
different from zero on the finite interval) piecewise polyno
21 05 1
Refractories and Industrial Ceramics Vol. 46, No. 2, 2005
1083-4877/05/4602-0143 © 2005 Springer Science+Business Media, Inc.
Kharkov Polytechnical University (National Technical Univer
sity), Kharkov, Ukraine.
TABLE 1. Natural Value of Independent Variables
Basic level 3.5 15 50 40
Variation interval 1.0 7 20 20
Upper level 4.5 22 70 60
Lower level 2.5 8 30 20