Modeling of carrot root radial press process for different shapes of loading elements using the finite element method

Figures & data

Figure 1. Method of taking a sample for the study.

Figure 2. Geometrical disc-type model – the load and the boundary conditions.

Table 1. Parameters used to the FEM model building - COSMOS/M.

Layer and direction of load	E (MPa) Modulus	ν (−) Poisson’s ratio
core × X	4.76	0.473
core × Y	4.62	0.482
core × Z	4.88	0.468
bark × X	4.22	0.479
bark × Y	4.04	0.474
bark × Z	4.83	0.478
kambium × X	4.49	0.475
kambium × Y	4.33	0.475
kambium × Z	4.85	0.477

Figure 3. Geometrical disc-type model – the load and the boundary conditions.

Figure 4. Optical system for measurement of displacement using ESPI.

Figure 5. (a) Real object – measurement of ESPI (b) Disc model – MES. Contours of u_y displacement obtained during the contact with the flat l₁ = 3 mm.

Figure 6. The u_y displacement distributions in the Y direction obtained during the contact with a flat l₁ = 3 mm.

Figure 7. Dispersion of the obtained results of the displacement u_y (ESPI) in comparison to the predicted FEM values, during the contact with the flat l₁ = 3 mm in width.

Figure 8. (a) Real object – measurement of ESPI (b) Membrane model – FEM Contours of u_y displacements obtained during the contact with the flat l₂ = 7 mm in width being under load.

Figure 9. Distributions of displacements u_y in the Y direction obtained during contact with a flat (l₂ = 7 mm in width).

Figure 10. Dispersion of the measured values of the displacement u_y (ESPI) compared to the predicted values FEM during contact with a flat (l₁ = 7 mm in width).

Figure 11. Contours of u_y displacements obtained during the contact with the flat l₂ = 7 mm in width being under load.

Table 2. Comparison of displacement distributions uy in the direction of the Y axis (Fig. 6).

n	Type of deviation	Dimension	Average	Min	Max	Standard deviation
25	Relative	%	8.19	0	13.18	5.96
	Absolute	µm	0.92	0	1.48	0.67

Table 3. The comparison of displacement distributions uy in the direction of Y axis (Fig. 9).

n	Type of deviation	Dimension	Average	Min	Max	Standard deviation
25	Relative	%	3.31	0	13.09	6.41
	Absolute	µm	0.39	0	1.51	0.74

Figure 12. Displacement distributions u_y in the direction of Y axis obtained during the contact with cylindrical element of R = 28 mm.

Table 4. The comparison of displacement distributions uy in the direction of Y axis (Fig. 12).

n	Type of deviation	Dimension	Average	Min	Max	Standard deviation
25	Relative	%	4.8	0	17.7	5.4
	Absolute	µm	0.09	0	0.34	0.1

Figure 13. Dispersion of measured displacement u_y values (ESPI) in the comparison to the predicted MES model values during the contact with cylindrical loading element of R = 28 mm.