Comparison of Tangent Curve Method and Reciprocal Slope Transformation Method for Describing Mechanical Behaviour of Jatropha Curcas L. Bulk Seeds Under Compression Loading

Year 2014, Volume: 10 Issue: 2, 83 - 86, 01.04.2014

David Herak Abraham Kabutey Petr Hrabe

Abstract

The study investigates the use of two different methods for the description of

deformation characteristics of Jatropha curcas L. bulk seed in linear compression. These methods

include the tangent curve and reciprocal slope transformation. The merits and limitations of both

methods were also compared. The different methods were used for development of mathematical

equations for fitting experimental data describing the mechanical behaviour of Jatropha bulk seed.

Pressing vessel diameter 60 mm was used to compress the bulk Jatropha seed which was

measured at pressing height 80 mm. For tangent curve method, the experimental data was fitted

by using the Marquardt Levenberg process whiles the Least Square Method (LSM) satisfies the

reciprocal slope transformation method. Statistical analysis of both experimental and fitted data

coefficients of reciprocal slope transformation and tangent curve methods indicated significant

results with high coefficient of determination which suggests the suitability of both methods for the

description of deformation characteristic of Jatropha curcas L. bulk seed in linear compression.

Keywords

Oil bearing bulk seed, mathematical model, force deformation curve, Marquardt Levenberg Process

References

• Blahovec J., 2008. Agromaterials. CULS Prague.
• Blahovec J., 2011. Reciprocal slope transformation applied to physical problems. Applied Mathematics Letters, 24 (12): 2038 – 2041.
• Blahovec J., S. Yanniotis, 2009. Modified classification of sorption isotherms. Journal of Food Engineering, 91: 72 – 77.
• Herak D., J. Blahovec, A. Kabutey, 2014. Analysis of the axial pressing of bulk Jatropha curcas L. seeds using reciprocal slope transformation. Biosystems Engineering, 121: 67 – 76.
• Herak D., A. Kabutey, M. Divisova, S. Simanjuntak, 2013. Mathematical model of mechanical behaviour of Jatropha curcas L. seeds under compression loading. Biosystems Engineering, 114 (3): 279-278.
• Kabutey A., D. Herak, R. Choteborsky, O. Dajbych, M. Divisova, W. E. Boatri, 2013. Linear pressing analysis of Jatropha curcas L seeds using different pressing vessel diameters and seed pressing heights. Biosystems Engineering, 115 (1): 42–49.
• Fasino O. O., O. O. Ajibola, 1990. Development of equations for the yield of oil expressed from conophor nut. Journal of Agricultural Engineering Research, 46: 45-53.
• Marquardt D. W., 1963. An Algorithm for the Least-Squares Estimation of Nonlinear Parameters, SIAM. Journal of Applied Mathematics, 11 (2): 431-441.
• Mrema, G. C., P. B. Mc Nulty, 1985. Mathematical model of mechanical oil expression from oilseeds. Journal of Agricultural Engineering Research: 31 (4), 361-370.
• Petru M., O. Novak, D. Herak, S. Simanjuntak, 2012. Finite element method model of the mechanical behaviour of Jatropha curcas L. seed under compression loading. Biosystems Engineering, 111 (4): 412-421.
• Willems P., N. J. M. Kuipers, A. B. De Haan, 2008. Hydraulic pressing of oilseeds: Experimental determination and modeling of yield and pressing rates. Journal of Food Engineering, 89 (1): 8-16.
• Zheng Y., D. P. Wiesenborn, K. Tostensona, N. Kangasa, 2005. Energy analysis in the screw pressing of whole and dehulled flaxseed. Journal of Food Engineering, 66 (2): 193-202.