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

Highlights

• Application of the reciprocal slope transformation (RST) was verified and described.

• Mechanical behaviour of Jatropha bulk seeds under compression loading was described by RST method.

• Equation describing Jatropha bulk seeds mechanical behaviour was determined.

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.

Introduction

The behaviour of Jatropha curcas L. bulk seeds in linear compression, where the characteristic behaviour of the dependency between compressive force and deformation curves is examined, requires detailed research to understand the compression process (Herak et al., 2010, Kabutey et al., 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 material 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 et al., 2009, Tumuluru et al., 2010) which need in-depth knowledge for optimisation. In the literature, densification theories have been applied on soil consolidation (Taylor, 1966) powder metallurgy 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 represented by functions expressing the relation between external pressure and density or other parameters describing the material porosity (Adapa et al., 2009, Talebi et al., 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. Balshin'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 and Kubát, 1987, Matthies and Busse, 1966). Generally, the mathematical description of densification process is useful 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 deformation characteristic curves of bulk Jatropha and other oilseeds (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 et al., 2013, Kabutey et al., 2013) it is difficult to describe the process. To solve this problem the tangent curve function (Herak et al., 2011, Herak et al., 2013), a finite element method (Petru, Novak, Herak, & Simanjuntak, 2012), using Marquardt–Levenberg 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 and Yanniotis, 2009, Błaszak and Sergyeyev, 2009) is utilised. The theory simply 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).

$$\left[F\right]=\frac{x}{F}$$

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).

$$F=\frac{x}{\left[F\right]}$$

It has been reported that the relationship of the new dependent of the RST and appropriate independent can simply be fitted by using the least square method for process simplification (Blahovec, 2011, Blahovec and 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.