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Research Paper Analysis of the axial pressing of bulk Jatropha curcas L. seeds using reciprocal slope transformation David Hera ´k a, *, Ji rı´ Blahovec b , Abraham Kabutey a a Department of Mechanical Engineering, Faculty of Engineering, Czech University of Life Sciences Prague, Kamycka 129, Prague, Czech Republic b Department of Physics, Faculty of Engineering, Czech University of Life Sciences Prague, Kamycka 129, Prague, Czech Republic article info Article history: Received 9 October 2013 Received in revised form 14 January 2014 Accepted 19 February 2014 Published online 13 March 2014 A reciprocal slope transformation (RST) with the least squares method (LSM) was used to develop mathematical equations to describe dependency between compressive force and deformation characteristic curves of Jatropha bulk seeds of varying initial pressing height from 30 mm, 40 mm, 50 mm, 60 mm, 70 mm and 80 mm in linear compression. The experimental data derived from a compression test was done using compression device (ZDM, model 50, Germany) and pressing vessel diameter, 60 mm at compression speed of 1 mm s 1 and compressive force between 0 kN and 100 kN. Statistical analysis of both experimental and fitted data coefficients of third order polynomial function was significant (p > 0.05) with high coefficient of determination (R 2 ). The RST method provides the fundamental step for the development of generalised model in future research where varying effect of compression factors such as moisture content, friction, compression speed and pressing temperature would be considered. ª 2014 IAgrE. Published by Elsevier Ltd. All rights reserved. 1. Introduction The behaviour of Jatropha curcas L. bulk seeds in linear compression, where the characteristic behaviour of the de- pendency between compressive force and deformation curves is examined, requires detailed research to understand the compression process (Herak, Gurdil, Sedlacek, Dajbych, & Simanjuntak, 2010; Kabutey, Herak, & Sedlacek, 2011). This knowledge can be transformed to understand the non-linear oil expression process involving mechanical screw presses or expellers for the optimisation of oil recovery efficiency and energy requirement. In the linear compression process, the boundary conditions are that zero force relates to zero deformation and when the compressive force approaches infinity, the deformation characteristic curve of the bulk ma- terial also increases with respect to the initial pressing height until maximum deformation is reached (Herak, Kabutey, Sedlacek, & Gurdil, 2011). Similarly, densification of biomass material properties relates to the axial and non-linear linear compression processes (Adapa, Tabil, & Schoenau, 2009; Tumuluru, Wright, Kenny, & Hess, 2010) which need in- * Corresponding author. E-mail address: [email protected] (D. Hera ´ k). Available online at www.sciencedirect.com ScienceDirect journal homepage: www.elsevier.com/locate/issn/15375110 biosystems engineering 121 (2014) 67 e76 http://dx.doi.org/10.1016/j.biosystemseng.2014.02.009 1537-5110/ª 2014 IAgrE. Published by Elsevier Ltd. All rights reserved.

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Page 1: Analysis of the axial pressing of bulk Jatropha curcas L. seeds using reciprocal slope transformation

ww.sciencedirect.com

b i o s y s t em s e ng i n e e r i n g 1 2 1 ( 2 0 1 4 ) 6 7e7 6

Available online at w

ScienceDirect

journal homepage: www.elsev ier .com/locate/ issn/15375110

Research Paper

Analysis of the axial pressing of bulk Jatrophacurcas L. seeds using reciprocal slopetransformation

David Herak a,*, Ji�rı Blahovec b, Abraham Kabutey a

aDepartment of Mechanical Engineering, Faculty of Engineering, Czech University of Life Sciences Prague,

Kamycka 129, Prague, Czech RepublicbDepartment of Physics, Faculty of Engineering, Czech University of Life Sciences Prague, Kamycka 129,

Prague, Czech Republic

a r t i c l e i n f o

Article history:

Received 9 October 2013

Received in revised form

14 January 2014

Accepted 19 February 2014

Published online 13 March 2014

* Corresponding author.E-mail address: [email protected] (D. Hera

http://dx.doi.org/10.1016/j.biosystemseng.201537-5110/ª 2014 IAgrE. Published by Elsevie

A reciprocal slope transformation (RST) with the least squares method (LSM) was used to

develop mathematical equations to describe dependency between compressive force and

deformation characteristic curves of Jatropha bulk seeds of varying initial pressing height

from 30 mm, 40 mm, 50 mm, 60 mm, 70 mm and 80 mm in linear compression. The

experimental data derived from a compression test was done using compression device

(ZDM, model 50, Germany) and pressing vessel diameter, 60 mm at compression speed of

1 mm s�1 and compressive force between 0 kN and 100 kN. Statistical analysis of both

experimental and fitted data coefficients of third order polynomial function was significant

(p > 0.05) with high coefficient of determination (R2). The RST method provides the

fundamental step for the development of generalised model in future research where

varying effect of compression factors such as moisture content, friction, compression

speed and pressing temperature would be considered.

ª 2014 IAgrE. Published by Elsevier Ltd. All rights reserved.

1. Introduction

The behaviour of Jatropha curcas L. bulk seeds in linear

compression, where the characteristic behaviour of the de-

pendency between compressive force and deformation curves

is examined, requires detailed research to understand the

compression process (Herak, Gurdil, Sedlacek, Dajbych, &

Simanjuntak, 2010; Kabutey, Herak, & Sedlacek, 2011). This

knowledge can be transformed to understand the non-linear

oil expression process involving mechanical screw presses

k).14.02.009r Ltd. All rights reserved

or expellers for the optimisation of oil recovery efficiency and

energy requirement. In the linear compression process, the

boundary conditions are that zero force relates to zero

deformation and when the compressive force approaches

infinity, the deformation characteristic curve of the bulk ma-

terial also increases with respect to the initial pressing height

until maximum deformation is reached (Herak, Kabutey,

Sedlacek, & Gurdil, 2011). Similarly, densification of biomass

material properties relates to the axial and non-linear linear

compression processes (Adapa, Tabil, & Schoenau, 2009;

Tumuluru, Wright, Kenny, & Hess, 2010) which need in-

.

Page 2: Analysis of the axial pressing of bulk Jatropha curcas L. seeds using reciprocal slope transformation

Nomenclature

a coefficients of the polynomial function

(N�1 mm�2)

b coefficients of the polynomial function

(N�1 mm�1)

c coefficients of the polynomial function (N�1)

CV coefficient of variation (%)

d coefficients of the polynomial function

(N�1 mm)

D inner diameter of pressing vessel (mm)

F compressive force (N)

Fcrit critical value that compares a pair of models (e)

Frat value of the F test (e)

H initial pressing height of bulk Jatropha seeds

(mm)

Mc moisture content (% d.b.)

ms mass of bulk seeds (g)

Pf porosity (%)

Pvalue hypothesis of the study outcomes significant

level (e)

R2 coefficient of determination (e)

T amount of reciprocal slope transformation

(mm N�1)

Tmax maximal value of reciprocal slope

transformation (mm N�1)

V initial volume of pressing vessel (m3)

x deformation of bulk seeds (mm)

xm deformation in local maximum of reciprocal

slop transformation function (mm)

rb bulk density (kg m�3)

rt true density (kg m�3)

3m strain in local maximum of reciprocal slope (e)

b i o s y s t em s e n g i n e e r i n g 1 2 1 ( 2 0 1 4 ) 6 7e7 668

depth knowledge for optimisation. In the literature, densifi-

cation theories have been applied on soil consolidation

(Taylor, 1966) powdermetallurgy and ceramics (Balshin, 1972).

Compression densification can also be described by models

focused on the simplified analysis of processes that follow the

pressing of particles inside the compressed materials. These

models, based on Balshin’s Laws (Balshin, 1972), are repre-

sented by functions expressing the relation between external

pressure and density or other parameters describing the ma-

terial porosity (Adapa et al., 2009; Talebi, Tabil, Opoku, &

Shaw, 2011). Mathematically, the Balshin’s first law, which is

also known as Walker model (Walker, 1923), is expressed by

exponential relationship between pressure and density. Bal-

shin’s second law is expressed by a power relation between

the same parameters, usually used for description of the

compression of straw and is similar to Skalweit’s Law

(Blahovec & Kubat, 1987; Matthies & Busse, 1966). Generally,

the mathematical description of densification process is use-

ful for understanding the inner processes connected with oil

and fibre separation from oilseeds such as in plant extruders

(Herak, Gurdil, et al., 2010). There has been some published

information describing the mechanical behaviour and defor-

mation characteristic curves of bulk Jatropha and other oil-

seeds (Kabutey et al., 2011). In such studies the behaviour of

the force and deformation function and the border conditions

of the compression process lack mathematical understanding

since using the standard least squares method (Herak,

Kabutey, Divisova, & Simanjuntak, 2013; Kabutey, Herak,

et al., 2013) it is difficult to describe the process. To solve

this problem the tangent curve function (Herak et al., 2011,

2013), a finite element method (Petru, Novak, Herak, &

Simanjuntak, 2012), using MarquardteLevenberg process

(Lourakis, 2005; Marquardt, 1963), rheological models

(Ocenasek & Voldrich, 2009) and non-linear equations

(Blahovec & Yanniotis, 2009) have been used, but further

research is necessary to develop suitable mathematical

models do describe the compression process. In this respect,

the reciprocal slope transformation (RST) theory involving two

separate variables (Blahovec, 2011; Blahovec & Yanniotis,

2009; Błaszak & Sergyeyev, 2009) is utilised. The theory sim-

ply identifies two distinct variables, the independent and

dependent. The application of the theory on the linear

compression process can be described as the deformation of

bulk seeds, x (mm) being the independent variable whiles

compressive force F (N) as the dependent variable. But the

transformation of the dependent variable can produce a new

dependent [F], which is defined by equation (Eq. (1)) (Blahovec,

2011).

½F� ¼ xF

(1)

Based on Eq. (1) the description of the relationship between

compressive force and deformation by the reciprocal slope

transformation can be used in the form given by Eq. (2).

F ¼ x½F� (2)

It has been reported that the relationship of the new

dependent of the RST and appropriate independent can sim-

ply be fitted by using the least square method for process

simplification (Blahovec, 2011; Blahovec & Yanniotis, 2009).

Therefore the aim of this study was to investigate the use of

RST method to describe the mechanical behaviour of J. curcas

L. bulk seeds in axial pressing.

2. Materials and methods

2.1. Sample

Bulk samples of J. curcas L. seeds, variety IPB2, obtained from

North Sumatra, Indonesia were used for the experiment. The

general physical properties of the oilseed crop are given in

Table 1. The moisture content Mc (% d.b.) of the samples was

determined using standard moisture measurement equip-

ment (Farm Pro, model G, Czech Republic) which was cali-

brated by the ASAE method (ASAE S410.1 DEC97) (ASAE, 1998;

Sirisomboon, Kitchaiya, Pholpho, & Mahuttanyavanitch,

2007). Samples of 100 g mass from a batch of Jatropha seeds

were randomly selected for the moisture content determina-

tion. Themass of each samplems (g) was determined using an

electronic balance (Kern 440-35, Kern & Sohn GmbH, Balingen,

Germany). The porosity Pf (%) was calculated from the rela-

tionship between the bulk and true densities (Blahovec, 2008).

Page 3: Analysis of the axial pressing of bulk Jatropha curcas L. seeds using reciprocal slope transformation

Fig. 1 e Schematic diagram of the pressing vessel.

Table 1 e Physical properties of Jatropha bulk seeds; datain the table are means ± SD.

H (mm) V (mm3) ms (g) Mc (% d.b.) Pf (%)

30 84,834 � 5650 30.04 � 0.90 8.5 � 0.2 63.49 � 3.22

40 113,112 � 4600 45.20 � 0.29 8.5 � 0.2 58.80 � 2.86

50 141,390 � 3800 54.83 � 0.74 8.5 � 0.2 60.02 � 2.99

60 169,668 � 6200 66.56 � 1.03 8.5 � 0.2 59.56 � 3.42

70 197,946 � 4800 75.16 � 1.62 8.5 � 0.2 60.86 � 3.12

80 226,224 � 6340 88.04 � 1.55 8.5 � 0.2 59.88 � 3.61

H e initial pressing height, V e volume, ms e mass, Mc e moisture

content, Pf e porosity.

b i o s y s t em s e ng i n e e r i n g 1 2 1 ( 2 0 1 4 ) 6 7e7 6 69

However, it is important to note that the bulk density rb

(kg m�3) was determined from themass of the sample divided

by initial pressing volume V (m3) which was calculated as the

area of pressing vessel multiplied by initial pressing height

(Table 1). The true seed density rt ¼ (980 � 12) kg m�3 was

determined gravimetrically (Blahovec, 2008). This means that

the mass of individual samples (10 seeds from a batch of

Jatropha, randomly selected and measured using an elec-

tronic balance (Kern 440-35, Kern & Sohn GmbH, Balingen,

Germany)), was divided by the volume of sample. However the

volume of the individual sample was determined by weighing

the sample in toluene and applying the principle of buoyancy

(Sirisomboon et al., 2007). The results obtained were

expressed as mean of three replicates.

2.2. Compression test

To determine the relationship between compressive force and

deformation characteristic curves, a compression device

(ZDM, model 50, Germany) was used to record the course of

deformation function. A single pressing vessel diameter,

60 mm with plunger (Fig. 1) was used whereby six different

initial pressing heights from 30, 40, 50, 60, 70 and 80 mm of

Jatropha bulk seeds were tested with a compression speed of

1 mm s�1 under temperature of 20 �C. The compressive force

was between 0 and 100 kN. The experiment was repeated

three times where deformationwas expressed by strain as the

ratio of deformation to that of initial height of the compressed

Jatropha bulk seeds.

2.3. Reciprocal slope transformation (RST)

The dependency between compressive force, F (N) and corre-

sponding deformation, x (mm) was transformed using recip-

rocal slope transformation (Eq. (1)) into the form given by Eq.

(3):

T ¼ x

F(3)

where T (mm N�1) is the transformed compressive force. The

obtained relation T(x) was approximated by a third order

polynomial function (Eq. (4)):

TðxÞ ¼ ax3 þ bx2 þ cxþ d (4)

The coefficients of the polynomial function, a (N�1mm�2), b

(N�1mm�1), c (N�1) and d (N�1mm),were calculatedby the least

squares method (LSM) using MathCAD software (MathCAD 14,

PTCSoftware,Needham,MA,USA).Thecompressive force,F (N)

Eq. (5) was then expressed from the product of Eqs. (3) and (4):

FðxÞ ¼ xax3 þ bx2 þ cxþ d

(5)

In Eq. (5), the compressive, F (N) and deformation, x (mm)

can also be substituted using stress and strain as reported by

Blahovec (2008) where the stress is determined as compres-

sive force divided by area of pressing vessel and strain is

determined as deformation divided by initial height of

pressing.

3. Results and discussion

In this study, the physical properties namely porosity,

Pf¼ (59.98 � 1.26)% and moisture content, Mf¼ (8.5 � 0.2)% in

dry basis (d.b.) of the Jatropha bulk seeds were constant (Table

1) therefore these parameters did not influence the results

obtained from the experiment. The dependence between the

compressive force and deformation characteristic curve and

the initial seed pressing heights are illustrated in Figs. 2e7. It

was observed that these dependencies were consistent with

the results previously published by Herak et al. (2013) and

Kabutey, Herak, et al. (2013). The above experimental datawas

transformed using Eq. (3) where their theoretical de-

pendencies were described using reciprocal slope trans-

formation (RST) of force and deformation data (Figs. 2e7).

These data were fitted by Eq. (4) using the least squares

method. The coefficients obtained from Eq. (3) for fitting the

above dependencies are presented in Table 2 which indicated

very high correlation. An analysis of variance (ANOVA) sta-

tistical analysis using MathCAD software (MathCAD 14, PTC

Software, Needham, MA, USA) of both experimental and fitted

or theoretical predicted data obtained fromEq. (5) showed that

Page 4: Analysis of the axial pressing of bulk Jatropha curcas L. seeds using reciprocal slope transformation

-1)

Compressive force

Fitted compressiveforce

RST

Polynomial (RST)

T max

Fig. 2 e Dependency between compressive force and deformation at initial height, 30 mm. (The bars denote coefficient of

variation and Tmax is RST maximal value.)

b i o s y s t em s e n g i n e e r i n g 1 2 1 ( 2 0 1 4 ) 6 7e7 670

the dependency between compressive force and deformation

can experimentally and theoretically be described. The sig-

nificance of the ANOVA analysis results was based on values

of Fcrit higher than Frat values. In addition, values of Pvalue were

greater than 0.05 (Table 3). Clearly, the predicted data using

Eq. (5) were obtained within the range of experimental data

coefficients of variations (Table 2). The values of coefficients of

the polynomial function (Eqs. (4) and (5)) of the reciprocal

slope transformation for each initial bulk seed pressing height

are shown in (Table 2). These amounts show that the devel-

oped mathematical equations take into account the experi-

mental boundary conditions of the linear compression of

T max

Fig. 3 e Dependency between compressive force and deformati

variation and Tmax is RST maximal value.)

Jatropha bulk seeds for themechanical behaviour description.

The boundary conditions means that the origin of the defor-

mation curve starts from zero force and zero deformation and

is followed by an increasing function within the whole range

of pressing.When compressive force approaches infinity then

deformation reaches a maximum limit (Herak et al., 2011,

2013; Kabutey, Herak, et al., 2013). Deformation values in the

local maximum of the reciprocal slope transformation func-

tion (Eq. (4)) were transformed into strain values. The local

maximum for the initial pressing height of Jatropha bulk seeds

was observed at a strain value 3m ¼ 0.25 � 0.02 as shown in

Table 3 and Fig. 8. There was similarity in the mechanical

-1)

Compressive force

Fitted compressiveforceRST

Polynomial (RST)

on at initial height, 40 mm. (The bars denote coefficient of

Page 5: Analysis of the axial pressing of bulk Jatropha curcas L. seeds using reciprocal slope transformation

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

0 5 10 15 20 25 30 35 40

Deformation (mm)

Com

pres

sive

forc

e (N

)

0

0.001

0.002

0.003

0.004

0.005

0.006

Am

ount

of t

he r

ecip

roca

l slo

pe tr

ansf

orm

atio

n (m

m N

-1)

Compressive force

Fitted compressiveforceRST

Polynomial (RST)

T ma x

Fig. 4 e Dependency between compressive force and deformation at initial height, 50 mm. (The bars denote coefficient of

variation and Tmax is RST maximal value.)

b i o s y s t em s e ng i n e e r i n g 1 2 1 ( 2 0 1 4 ) 6 7e7 6 71

behaviour of the initial pressing height implying the accuracy

of the RST method to describe the mechanical behaviour of

Jatropha bulk seeds of varying initial pressing height. The

relationship between fitted values of the reciprocal slope

transformation and initial pressing height for strain values of

0.1, 0.25, and 0.5 is also presented in Fig. 9. The values of RST

for the corresponding initial pressing height in relation to

strain showed a linear function in describing the mechanical

behaviour of Jatropha bulk seeds. In Fig. 10 is shown the

maximum RST value corresponding to the minimum slope

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

0 5 10 15 20 25

Deformatio

Com

pres

sive

forc

e (N

)

T max

Fig. 5 e Dependency between compressive force and deformati

coefficient of variation and Tmax is RST maximal value.)

value of the secant line connecting the point 0 of the force

deformation curve increasing to point 1 with high coefficient

of determination. It was seen that the dependencies of RST

and strain (Fig. 8) showed similarity with the theoretical de-

pendency presented in Fig. 10 based on the RST reciprocal

slope transformation distribution function (Blahovec, 2011).

The RST coefficients (Eq. (4)) values determined also implied

the inverse value of the rigidity of bulk seeds (Blahovec, 2008;

Neckar & Das, 2012) where the individual coefficients can be

described.

30 35 40 45 50

n (mm)

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

Am

ount

of t

he r

ecip

roca

l slo

pe tr

ansf

orm

atio

n (m

m N

-1)

Compressive force

Fitted compressiveforceRST

Polynomial (RST)

on at initial pressing height, 60 mm. (The bars denote

Page 6: Analysis of the axial pressing of bulk Jatropha curcas L. seeds using reciprocal slope transformation

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

0 10 20 30 40 50

Deformation (mm)

Com

pres

sive

forc

e (N

)

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

Am

ount

of t

he r

ecip

roca

l slo

pe tr

ansf

orm

atio

n (m

m N

-1)

Compressive force

Fitted compressiveforceRST

Polynomial (RST)

T max

Fig. 6 e Dependency between compressive force and deformation at initial pressing height, 70 mm. (The bars denote

coefficient of variation and Tmax is RST maximal value.)

b i o s y s t em s e n g i n e e r i n g 1 2 1 ( 2 0 1 4 ) 6 7e7 672

In addition, the coefficients of the third order polynomial

function (Eq. (4)), based on RST, also influence the description

of the mechanical behaviour. Furthermore, the amount of

reciprocal transformation (Eq. (4)) is, in essence, the inverse of

bulk seed rigidity which is described by the compliance of the

system (Blahovec, 2008; Neckar & Das, 2012). The coefficients,

d denotes the initial compliance; cx as the linear compliance;

bx2 a real compliance and ax3 is the volume compliance ac-

cording to the theory published by Neckar and Das (2012) for

the structure and mechanics of fibrous materials. However,

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

0 10 20 30

Deformatio

Com

pres

sive

forc

e (N

)

T max

Fig. 7 e Dependency between compressive force and deformati

coefficient of variation and Tmax is RST maximal value.)

based on the experimental results which were verified by Eqs.

(4) and (5), the mechanical behaviour of Jatropha bulk seeds

can be described as by small deformations at both the initial

and linear compliances; and at moderate deformations can be

described by initial, linear and real compliances. The combi-

nation of all the above compliances constitutes themaximum

deformation (Figs. 2e8 and 10). The RST method thus can

more accurately describe the deformation characteristic

curves of Jatropha bulk seeds than other methods previously

published by Herak et al. (2013). Most importantly, the

40 50 60

n (mm)

0

0.002

0.004

0.006

0.008

0.01

0.012

Am

ount

of t

he r

ecip

roca

l slo

pe tr

ansf

orm

atio

n (m

m N

-1)

Compressive force

Fitted compressiveforceRST

Polynomial (RST)

on at initial pressing height, 80 mm. (The bars denote

Page 7: Analysis of the axial pressing of bulk Jatropha curcas L. seeds using reciprocal slope transformation

Table 2 e Coefficients of Eq. (4) for different initial pressing heights of Jatropha bulk seeds.

H (mm) a (10�7 N�1 mm�2) b (10�5 N�1 mm�1) c (10�3 N�1) d (10�5 N�1 mm) R2 (e) CV (%)

30 21.76 �9.95 1.14 8.07 0.995 5.0

40 10.98 �6.34 0.89 55.84 0.992 4.5

50 5.61 �4.37 0.84 4.00 0.992 5.2

60 5.60 �4.97 1.11 �5.29 0.991 5.3

70 3.04 �3.28 0.87 44.02 0.994 5.0

80 2.14 �2.85 0.93 16.34 0.993 5.0

H e initial pressing height, a, b, c, d e coefficient of polynomial function of RST, R2 e coefficient of determination, CV e coefficient of variation of

measured characteristics.

Table 3 e Statistical analysis of general deformation curve for different initial pressing heights of Jatropha bulk seeds.

H (mm) Frat (e) Fcrit (e) Pvalue (e) R2 (e) xm (mm) 3m (e) Tmax (mm N�1)

30 0.032 3.936 0.859 0.982 8.48 0.28 0.003919

40 0.086 3.938 0.77 0.969 8.51 0.21 0.004218

50 0.391 3.926 0.533 0.934 12.64 0.25 0.004809

60 0.008 3.916 0.93 0.999 14.95 0.25 0.007409

70 0.008 3.92 0.93 0.991 18.12 0.26 0.007247

80 0.062 3.919 0.803 0.984 20.59 0.26 0.009098

He initial pressing height, Frat value of the F test, Fcrit test statistic for test rejection, Pvalue, hypothesis of the study outcomes significant level (e),

R2 e coefficient of determination, xm e RST deformation in local maximum, 3m e RST strain in local maximum, Tmax e RST maximal value.

b i o s y s t em s e ng i n e e r i n g 1 2 1 ( 2 0 1 4 ) 6 7e7 6 73

relationship between compressive force and deformation is

also dependent on moisture content and pressing tempera-

ture (Herak, Gurdil, et al., 2010; Kabutey et al., 2011). Thus,

these compression factors can also influence the individual

coefficients of the RST (Eq. (4)). The effect of friction among

seeds, as well as friction between the seeds and walls of the

pressing vessel, could also affect the coefficients of third order

polynomial function (RST) (Eq. (4)). Clearly, this model (Eq. (5))

can be used as background information for further research

which will focus on the determination of a generalised

mathematical model for the description of mechanical

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

0 0.1 0.2 0.3

The

fitt

ed a

mou

nt o

f rec

ipro

cal t

rans

form

atio

n (m

m N

-1)

Fig. 8 e Dependency between fitted RST and st

behaviour of bulk seeds. In such follow up study, it will be

important to determine mathematical equations which will

describe the relationship between amounts of individual co-

efficients of RST function (Eq. (4)) andmoisture content aswell

as friction. For the development of ideal mathematical

models, the friction between seeds and also friction between

seeds and wall of pressing vessel needs to be considered. For

instance, the results published by Herak, Gurdil, et al. (2010),

Kabutey et al. (2011) and Herak, Sedlacek, and Kabutey (2010)

showed that the change of moisture content, pressing tem-

perature and stage of maturity of bulk oilseeds of Jatropha

0.4 0.5 0.6 0.7Strain (-)

H = 30 mmH = 40 mmH = 50 mmH = 60 mmH = 70 mmH = 80 mmTmaxMean strain Tmax

rain as function of initial pressing height.

Page 8: Analysis of the axial pressing of bulk Jatropha curcas L. seeds using reciprocal slope transformation

R² = 0.9169

R² = 0.9021

R² = 0.8492

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

20 30 40 50 60 70 80 90

Initial pressing height (mm)

The

fitt

ed a

mou

nt o

f rec

ipro

cal t

rans

form

atio

n (m

m N

-1)

T0.25T0.1T0.5

Fig. 9 e Dependency between fitted RST and initial pressing height for strain values 0.1, 0.25, and 0.5.

b i o s y s t em s e n g i n e e r i n g 1 2 1 ( 2 0 1 4 ) 6 7e7 674

influenced the shape and position of the deformation curve as

well the energy demand for obtaining the oil. Nevertheless,

the oil leakage during compression process has also been re-

ported as having no influence on the dependency between the

force and deformation characteristic curves in relation to

varying pressing vessel diameters and bulk seed pressing

heights Herak et al. (2013) and Kabutey, Herak, et al. (2013).

Generally, the results of the present study were in agreement

with the results published by Braga, Couto, Hara, and Neto

(1999), Guner, Dursun, and Dursun (2003), Faborode and

Favier (1996) and Kabutey, Divisova, et al. (2013) for the

0

1

2

3

4

5

6

7

8

0 0.1 0.2 0.3 0.4

Strain (-)

Com

pres

sive

forc

e (k

N)

T

1

Fig. 10 e Dependency of compressi

description of mechanical behaviour of Jatropha bulk seeds

and other bulk oilseeds such as rapeseed in linear compres-

sion. However, it is important to highlight that the RST

method (i.e. Eqs. (4) and (5)) has the advantage of using LSM for

fitting experimental data compared methods used in earlier

published studies. It is evident that using transformation

processes as previously described by Herak, Sedlacek, et al.

(2010), the results from the present mathematical model can

be transformed into a non-linear mechanical behaviour such

as screw extruders and other processing technologies. A

combination of these models with additional information

0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

Am

ount

of r

ecip

roca

l slo

pe tr

ansf

orm

atio

n (m

m k

N-1

)

FT

ve force and RST versus strain.

Page 9: Analysis of the axial pressing of bulk Jatropha curcas L. seeds using reciprocal slope transformation

b i o s y s t em s e ng i n e e r i n g 1 2 1 ( 2 0 1 4 ) 6 7e7 6 75

such as oil point, juice point or compressibility which requires

processing technology with maximal energy efficiency, could

also be designed.

4. Conclusion

An experimental study of the dependency between the

compressive force and deformation characteristic curves of

Jatropha bulk seeds with varying initial pressing heights in

axial or linear compression loading was carried out. The re-

sults were fitted using the RST and LSM methods where the

dependency between RST and deformation was also

described. Statistical analysis of experimental and RST fitted

data using a third order polynomial function were significant

(p > 0.05) with a high coefficient of determination (R2). The

validity of RST equation was limited from zero to the

maximum deformation of the bulk Jatropha seeds with vary-

ing initial pressing height. The RST method provides a

fundamental step forward for the development of more

generalised mathematical models where parameters

including varying pressing vessel diameter, moisture content,

maturity stage and variety of bulk oilseeds, friction, oil point

pressure, pressing temperature could be considered. This in-

formation could be transformed to investigate the non-linear

pressing involving mechanical screw presses or expellers for

the optimisation of oil recovery efficiency and energy

requirements.

Acknowledgement

The research has been supported by Grant Agency of CULS

Prague e CIGA 31130/1313/313127.

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