Lubrication impact on the value of friction coefficient of coffee beans

ECONTECHMOD. AN INTERNATIONAL QUARTERLY JOURNAL – 2014. Vol. 3. No. 4. 91-95
91
Lubrication impact on the value of friction coefficient of coffee beans sliding
ever the steel surfaces of various roughness
R. Kuzminskyi, O. Sokolovskyi, R. Lozovyi, R. Sheremeta, V. Zholobko
Lviv National Agrarian University; e-mail: romansheremeta@mail.ru
Received September 09.2014: accepted September 11.2014
Abstract. The article analyzes the influence of steel
surfaces processing quality on the value of sliding friction coefficient of Robusta and Arabica coffee beans at
dry and lubricated fricbica. The research obtained coffee
dry and lubrication functions and parameters of sliding
friction coefficients distributions and mathematical
models for determining the index which depends on the
roughness of steel surfaces.
Key words: coffee beans, steel surfaces, roughness,
dry friction, sliding friction coefficient, lubrication.
INTRODUCTION
Advanced technologies of procession, transportation and storage of agricultural production as well as
planning of new production operations and designing of
new machines and tools are impossible without studies
of physical and mechanical properties of agricultural
materials serving the functions of structural and technological parameters of machines and equipment.
The research of friction coefficient is especially
important [28]. In fact the working surfaces of machines
are made mainly of steel or cast-iron of different grades
with the use of various technological methods, and that
is why their surfaces are characterized by the different
processing quality. Inaccuracies in friction coefficient
determination result in the increasing of energy and material consumption of equipment, and also result in machines breakage.
A lot of articles are devoted to the method of physical properties investigation of agricultural materials [6,
9, 14, 25, 26]. It is established [3, 12, 16, 19] that relative humidity of seeds and beans has a significant impact on their physical and mechanical properties. Varieties in differences are also essential.
Researches pay a particular attention to the study of
friction coefficients of different agricultural materials
[10; 11; 15; 16; 19] and to the development of the special means of index measuring [2; 27]. As to coeffi-
cients of static friction and sliding it is known that the
values of these indexes depend on the sizes of seeds or
beans, and value on the relative humidity, and on the
friction surfaces material [4; 10; 11; 15; 16; 19]. However, the conducted researches concerned the values of
friction coefficients of seeds of different crops in pairs
with various materials (steel, aluminum, concrete, glass,
etc.) not taking into account the roughness of friction
surfaces. At the same time the first researches of friction
coefficient concerning the seed of oil-bearing flax [13]
showed the necessity to take into account this important
index of surfaces processing quality.
As to the coffee beans, the size of seeds [21, 22],
coefficients of external and internal friction [20, 23, 24],
aerodynamic [1] and thermal properties [7, 17] are determined. At the same time, the published results contain mainly average values and also values range of
physical and mechanical properties for different varieties of coffee beans without specifying the nature of the
distribution of these random values.
Thus, there is a need for clarification of values of
sliding friction coefficients of coffee beans taking into
accounts not only their relative humidity and varietal
differences, but also surface roughness of sliding and
lubrication.
OBJECTIVE OF RESEARCHES
The objective of researches was to determine the
sliding friction coefficient of coffee beans of different
varieties on the steel surfaces of different roughness under conditions of dry friction and under the presence of
lubrication.
METHODOLOGY OF RESEARCHES
The research used Arabica and Robusta coffee
beans. The value of relative humidity was obtained with
the help of drying preliminary moistened coffee beans
in the heat chamber at 100 оC by changing the drying
period.
92
R. Kuzminskyi, O. Sokolovskyi, R. Lozovyi, R. Sheremeta, V. Zholobko
а
b
Fig. 1. Device for determination of sliding friction coefficient (a) and bar with coffee beans (b):
1 – bar of the research material, 2 – carriage 3 – sliding surface, 4 – ruler,
5 – automatic recorder 6 – guide block
Determination of the angle φ and sliding friction
coefficient f was conducted using well-known structures
(Fig 1) [26, 27]. As sliding surfaces the flat surface of
steel parts, processed to a roughness Ra = 12,5 mcm, Ra
= 6,3 mcm, Ra = 2,5 mcm, Ra = 1,25 mcm are used.
Different roughness values that were determined according to the models of roughness are obtained due to
changing the surface processing mode (milling and
grinding).
The results of experimental researches were obtained up using the methods of mathematical statistics
[5, 18] calculated the mathematical expectation M[f],
average quadratic deviation σ[f] and variation coefficient υ[f] of values of sliding friction f, matched the distribution law, application of which was checked using
Pearson and Kolmohorov-Smirnov statistic fitting test.
The significance of the difference of obtained results of the sliding friction coefficient and geometrical
parameters for the different varieties of coffee beans
were checked using the Wilcoxon signed-rank test [5,
18].
The method of regression analysis [8] for obtaining
the dependencies of values of mathematical expectation
of sliding friction coefficient M[f] of different varieties
of coffee beans on steel surface roughness Ra in the
presence of lubrication was used. Checking of obtained
regression dependencies was conducted using the F-test.
RESULTS OF RESEARCHES
According to the results of determination of sliding
friction coefficient f the distribution of this random variable for Arabica and Robusta coffee beans for different
values of steel surface roughness Ra under conditions of
lubrication are obtained. (Fig 2).
The distribution parameters of obtained values of
sliding friction coefficient of coffee beans of these two
varieties on steel surfaces of different roughness under
condition of lubrication, namely the mathematical expectation M[f], average quadratic deviation [f] and variation coefficient [f] are defined.
Checking of received results according to the Wilcoxon signed-rank test showed that the difference of
values of sliding friction coefficient under condition of
dry friction and fс and under condition of lubrication fм
on steel surfaces of different roughness (1 – Ra = 1,25
mcm, 2 – Ra = 6,3 mcm, 3 – Ra = 12,5 mcm, 4 – Ra =
2,5 mcm.) is statistically significant for both varieties of
Arabica coffee beans (Fig. 3) and for Robusta coffee
beans (Fig 4).
With the help of regression analysis [8] dependencies of mathematical expectation of sliding friction coefficient M[f] of Arabica and Robusta coffee beans under condition of lubrication of steel surfaces roughness
Ra are obtained:
2
(1)
M [ f ]  c 0  c1  Ra  c 2 Ra ,
where: с0, с1 і с2 – regression coefficient; Ra – surface
roughness, mcm.
Checking of the regression model (1) according to
the F-test [5, 8, 18] did not give reasons for its rejection.
As we can see (Fig 5), at the same relative humidity
φ = 23-26 % for coffee beans of both varieties in case of
steel surfaces roughness decreasing starting with Ra =
12,5 mcm (turning) and to Ra = 1,25 mcm (grinding)
the values M [f] are reducing nonlinear.
LUBRICATION IMPACT ON THE VALUE OF FRICTION COEFFICIENT OF COFFEE
BEANS SLIDING EVER THE STEEL SURFACES OF VARIOUS ROUGHNESS
f
f
а
b
93
Fig. 2. The results of determination of distribution of values of the sliding friction coefficient of Arabica (a) and Robusta
(b) coffee beans of relative humidity φ = 23-26 % on steel surface roughness Ra = 6,3 mcm under condition of lubrication
Fig. 3. The results of checking of sampling values of sliding friction coefficient of Arabica coffee beans under condition of lubrication (fМ1, fМ2, fМ3, fМ4) and dry friction (fС1, fС2, fС3, fС4)on steel surfaces of different roughness according
to the Wilcoxon signed-rank test:1 – Ra = 1,25 mcm 2 – Ra = 6,3 mcm, 3 – Ra = 12,5 mcm, 4 – Ra = 2,5 mcm
94
R. Kuzminskyi, O. Sokolovskyi, R. Lozovyi, R. Sheremeta, V. Zholobko
Fig. 4. The results of checking of sampling values of sliding friction coefficient of Robusta coffee beans under
condition of lubrication (fМ1, fМ2, fМ3, fМ4) and dry friction (fС1, fС2, fС3, fС4)on steel surfaces of different roughness according to the Wilcoxon signed-rank test:1 – Ra = 1,25 mcm 2 – Ra = 6,3 mcm, 3 – Ra = 12,5 mcm, 4 – Ra = 2,5
mcm
а
b
Fig. 5. Dependencies of mathematical expectation of sliding friction coefficient M [f] of coffee beans on
steel surface roughness Ra: a – Arabica variety b – Robusta variety
CONCLUSIONS
1. The value of sliding friction coefficient of coffee
beans on steel surfaces should be considered as random
variables distributed according to normal or logarithmic
normal laws, the parameters of which significantly depend on the roughness of the processed steel surfaces
and the factor of lubrication that should be considered
during the project calculations of machines and equipment.
2. Under dry friction the increase of relative humidity of coffee beans influences the values change of sliding friction coefficient more significantly than the increasing of steel surface roughness.
3. The sliding friction coefficient of Arabica coffee
beans is much more sensitive to changes of frictional
surfaces roughness than for Robusta coffee beans, because of the differences of geometrical parameters of
different varieties of beans.
4. Lubrication significantly reduces the value of
sliding friction coefficient of coffee beans on steel surfaces with different processing quality.
5. Since the differences of obtained sampling values
of sliding friction coefficient for coffee beans of different varieties on steel surfaces with the same processing
quality were statistically significant, this index should
be given in the reference data taking into account the
sorts differences.
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LUBRICATION IMPACT ON THE VALUE OF FRICTION COEFFICIENT OF COFFEE
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