Cracking Force Analysis for Apricot Pit Decortication Based on Mathematical Model of Hertz’s Theory

Figures & data

FIGURE 1 Compressive loading of wild apricot pit between two parallel plates on the texture analyzer machine: (a) longitudinal loading; (b) transverse loading.

TABLE 1 Some physical properties of apricot pit samples used in the experiments

Property	Measurements for particle on sieve size, mm
	12	11	10	<10	SD	SS	F-value	Significance
Size distribution, % retained	10.36	56.19	23.59	9.86	21.74	1.4365	5.9504	**
Axial dimensions, mm
Major diameter, a	23.40	22.12	21.16	20.86	1.14	0.0697	0.1378	ns
Intermediate diameter, b	18.25	17.26	16.76	16.01	0.94	0.0226	0.048	ns
Minor diameter, c	11.36	10.52	9.62	8.96	1.05	0.0489	0.0365	ns
Geometric mean diameter, mm	16.92	15.89	15.05	14.41	1.09	0.0061	0.0107	ns
Sphericity	0.723	0.719	0.711	0.691	0.01	0.0003	0.2738	ns
Average mass, g	1.57	1.36	1.46	1.03	0.23	0.0953	0.1367	ns
Shell thickness, mm	2.6	2.5	2.7	2.7	0.10	0.0156	0.6598	ns

ns: non-significant;

**significant at 5% level of confidence.

FIGURE 2 Force-deformation curves for two sizes of apricot pits along transverse axes at 5 mm/min loading rate of texture analyzer showing three stages of biomaterial deformation: I: transient; II: apparent linear elastic; III: plastic to failure point.

TABLE 2 Comparison of predicted and measured force required in apricot pit decortication

Sieve size retaining pit, mm	Physical characteristics			Force, n
	Average mass, g	GMD, mm	Equivalent contact area, m^2	Hertzian model	Axial compression	Falling impact
12	1.57	16.92	0.105816	542.36^a	523.83^a	542.42^a
11	1.36	15.89	0.098203	525.59^b	514.25^abc	529.23^ab
10	1.46	15.05	0.091379	511.51^bc	508.37^abc	524.11^abc
<10	1.03	14.41	0.084378	500.52^c	502.84^c	519.78^bc

Values are (mean) of three replicates;

Values followed by the same superscript letter in the same row and column are not significantly different (p < 0.05).

Table

A	Coefficient	M	Mass of the nut, kg
Ae	Equivalent contact area, m^2	R	Radius of rotor, m
A0	Actual contact area, m^2	Ri	Minimum radius of curvature of body, m
A	Major diameter of palm nut, m	R’i	Maximum radius of curvature of body, m
B	Intermediate diameter of palm nut, m	S	Stiffness modulus, Nm^–1
C	Minor diameter of palm nut, m	W	Drop weight, N
D	Elastic deformation, m	α	Major axis of elliptic contact area, m
d	Diameter of a spherical body, m	β	Minor axis of elliptic contact area, m
da	Apparent diameter of irregularly shaped body, m	γ	Sphericity
E	Modulus of elasticity, Nm^–2	σmax	Maximum contact stress, Nm^–2
F	Force, N	υ	Poisson’s ratio
k;m;n	Factors depending on the principal curvature of the body	ω	Rotational speed of rotor, rpm s^–1