Predicting cashew nut cracking using hertz theory of contact stress

Abstract

Abstract The cracking force is an important parameter in the design of cracking machines. A mathematical model for predicting the exact cracking force of cashew nut was presented based on the existing hertz’s theory of contact stress of two bodies under uniaxial compressive load. Hertz equation was adapted to loading of cashew nuts to cracking at three different loading orientations (X, Y, and Z) and two strain rates of 5 mm/min and 10 mm/min. The average moisture content of the dried cashew nuts was determined at 5% (db.). The physical properties of cashew nut varieties such as Length, Width, Thickness, mass, Geometric Mean diameter, Sphericity index, Surface area and Aspect ratio were 34.31 mm, 24.86 mm, 16.55 mm, 6.13 g, 24.13 mm, 0.70, 1834.65 mm 2 and 0.73 respectively. Some mechanical parameters such as cracking force, deformation and stiffness modulus at loading orientations (X, Y, and Z) (355,288 and 289 N), (1.396, 1.5002 and 1.815 mm) and (313, 195 and 160 N/mm) at 5 mm/min, and (458, 276 and 480 N), (2.28, 1.767 and 3.7197 mm) and (202, 162 and 146 N/mm) at 10 mm/min were also obtained from the force-deformation curve respectively. These physical and mechanical parameters were required in the derived model. The aspect ratio was introduced as a correcting factor to the stiffness modulus to improve the prediction of the hertz model. The highest value of mean cracking force (355 N) was determined at the X (Width) orientation at 5 mm/min while the highest value of mean cracking force (480 N) at 10 mm/min strain rate was found at the Z (Thickness) orientation. A two-sample t -test comparism of experimental cracking force values and that of the hertz model were acceptable at 5% probability level which gave good prediction of cracking force during compression. The force required for the design of suitable cashew nut shell cracking machine should be considered at the range of 400–500 N at X (width) and Z (thickness) loading orientations, therefore the magnitude of applied force with the loading orientation could determine the extent of mechanical damage and kernel recovery during cracking and separation processes.