Optimization of thick rubber part curing cycles

Figures & data

Figure 1. Schematic representation of a mould section.

Figure 2. Schematic diagram of the direct problem geometry.

Table 1. Thermophysical properties of the mould and part constituents.

	Material
	Ampco®	106	8800	370
	Deltherm®	0.25	1850	2500
	NR THERMEL1©	0.202	1042

Table 2. Kinetics parameters for THERMEL1 natural rubber.

k0	E (J mol^−1)	n	t0 (s)	(K)	(J kg^−1)
9.33 × 10^20	195,000	1.65	1.06 × 10^−9	11,216	6200

Figure 3. Example 1, cooling inside the mould – – Temperatures and vulcanization rate computed at different points of the part.

Table 3. Discretization of the prescribed temperatures.

k	1	2	3	4	5	6	7	8
tk (s)	0	1000	2000	3000	4000	5000	6000	7000
Tk (°C)	60	60	100	100	150	110	110	60

Figure 4. Experimental and theoretical temperature values achieved in different points of the moulded part during a moulding cycle.

Figure 5. Comparison between the vulcanization front position obtained experimentally (a) and calculated (b).

Figure 6. Example 2, 1000 s cooling outside the mould: , – temperatures and vulcanization rate computed at different points of the part.

Figure 7. Sensitivity evolution at the surface of the part.

Figure 8. Sensitivity evolution at the centre of the part.

Figure 9. Chemical reaction progress with the new model.

Figure 10. Sensitivity evolution at the surface of the part with the new model.

Figure 11. Sensitivity evolution at the centre of the part with the new model.

Figure 12. Optimization Example 1 – heating and cooling inside the mould. . fixed at . .

Figure 13. Example 1 – Residual error versus time – heating and cooling inside the mould.

Figure 14. Least squares criterion versus iteration numbers – a: Example 1 (N_t = 12); b: effect of the initial cycle; c: Example 1 (N_t = 1).

Figure 15. Influence of the initial cycle.

Figure 16. Progress residual error versus time.

Figure 17. Example 1 with N_t = 1.

Figure 18. Cooling within the mould – , fixed.

Figure 19. Least-squares criterion – a: cooling inside the mould; b: cooling outside the mould.

Figure 20. Vulcanization rate within the part thickness – a: desired vulcanization rate; b: vulcanization rate obtained with estimated cycle; c: vulcanization rate obtained with initial cycle.

Figure 21. Estimated cycle – cooling outside the mould between 4000 and 5000 s –, , , fixed.

Figure 22. Chemical reaction progress within the part thickness. Desired vulcanization rate: 0.9 – a: α obtained at the end of heating in the mould with the estimated cycle, b: α obtained at the end of heating in the mould with the initial cycle, c: α obtained at the end of cooling outside the mould with the estimated cycle, d: α obtained at the end of cooling outside the mould with the initial cycle.