Optimization of laying time for in-situ photocuring of composites
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摘要: 紫外光固化技术存在可固化厚度有限的问题，而原位光固化工艺以层层叠加、逐层固化的方式，在固化较大厚度的复合材料方面有着独特优势。为了在原位光固化工艺中实现各层同时完成固化且固化度分布均匀的目标，首先给出单层紫外光固化的数学模型，基于该模型建立一个描述原位光固化过程的数学模型，进而对铺层时间进行优化，使用遗传算法结合梯度下降算法的方式求解出优化后的铺层时间，对原位光固化过程进行有限元仿真。仿真结果表明：与其他固化方式相比，原位光固化工艺优化铺层时间后，到达固化结束时间时，各层均能完成固化，固化度均在以期望固化度为中值的区间内且分布均匀，通过玻璃纤维增强树脂基复合材料层合板固化实验对算法及仿真进行验证，实验结果与仿真对照表明，优化后的原位光固化工艺能够实现同步固化的效果。Abstract: Ultraviolet (UV) curing technology has the problem of limited curable thickness. However, the in-situ photocuring process has a unique advantage in curing large thickness composite materials by stacking and curing layer by layer. In order to achieve the goal of simultaneous curing and uniform curing degree of each layer in the in-situ photocuring process, the mathematical model of single layer UV curing was presented. Based on this model, a mathematical model was established, which could describe the entire in-situ photocuring process. The time to add each layer was then optimized, the optimal layering time was solved by genetic algorithm combined with gradient descent algorithm. In addition, the in-situ photocuring process was simulated by finite element method. The simulation results show that compare with other curing methods, after optimizing the layering time of in-situ photocuring process, each layer will complete curing when the curing end time is reaching, and the curing degree is uniformly distributed within the median of the desired curing degree. The algorithm and simulation are verified by curing experiment of glass fiber reinforced resin matrix composite laminates. The comparison between experimental results and simulation results shows that the optimized in-situ photocuring process can achieve the goal of simultaneous curing.
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图 1 梯度下降算法流程图
Figure 1. Flow chart of gradient descent algorithm
H—Hamiltonian; τ—Layering time; ξ—Step factor; J—Objective function value; i—Number of layers; N—Total number of layers; k—Iteration count; k is used as the upper corner symbol to represent the current number of iterations, i is used as the lower corner symbol to represent the number of layers
图 3 添加新层的间隔时间分布
Figure 3. Distribution of the interval time required for adding each layer
图 5 优化铺层时间后的原位光固化工艺中固化度的演变
Figure 5. Evolution of curing degree in in-situ UV curing process after optimizing laying time
图 6 优化铺层时间后的原位光固化工艺中温度的演变
Figure 6. Evolution of temperature in in-situ UV curing process after optimizing laying time
图 7 采用不同固化方法的COMSOL仿真固化度结果
Figure 7. COMSOL simulation results using different curing processes
图 9 各层固化度COMSOL仿真曲线
Figure 9. Curing degree curves of each layer obtained by COMSOL simulation
图 10 层边界处温度的COMSOL仿真曲线和实验曲线
Figure 10. Temperature curves at the boundary of the layer obtained by COMSOL simulation and experiment
表 1 仿真中使用到的参数
Table 1. Parameters used in the simulation
Parameter Value ${\rho _{\rm{r}}}/({\rm{kg}} \cdot {{\rm{m}}^{{\rm{ - 3}}}})$ $1.1 \times {10^3}$ ${c_{\rm{r}}}/({\rm{J}} \cdot {\rm{k}}{{\rm{g}}^{{\rm{ - 1}}}} \cdot {{\rm{K}}^{{\rm{ - 1}}}})$ $1.674 \times {10^3}$ ${V_{\rm{r}}}$ 0.6 ${\rho _{\rm{f}}}/({\rm{kg}} \cdot {{\rm{m}}^{{\rm{ - 3}}}})$ $2.54 \times {10^3}$ ${c_{\rm{f}}}/({\rm{J}} \cdot {\rm{k}}{{\rm{g}}^{{\rm{ - 1}}}} \cdot {{\rm{K}}^{{\rm{ - 1}}}})$ $0.8 \times {10^3}$ ${k_{\rm{y}}}/({\rm{W}} \cdot {{\rm{m}}^{ - 1}} \cdot {{\rm{K}}^{ - 1}})$ $0.35$ $h/({\rm{W}} \cdot {{\rm{m}}^{ - 2}} \cdot {{\rm{K}}^{ - 1}})$ $20$ ${H_{\rm{r}}}/({\rm{J}} \cdot {\rm{k}}{{\rm{g}}^{ - 1}})$ $3.35 \times {10^5}$ $s/{\rm{wt\% }}$ $0.05$ $\lambda /{\rm{c}}{{\rm{m}}^{ - 1}}$ $2$ $E/({\rm{kJ}} \cdot {\rm{mo}}{{\rm{l}}^{ - 1}})$ $12.7$ $R/({\rm{J}} \cdot {\rm{mo}}{{\rm{l}}^{ - 1}} \cdot {{\rm{K}}^{ - 1}})$ $8.314$ ${C_0}/{{\rm{s}}^{ - 1}}$ $0.631$ ${T_0},{T_{\inf }}/^\circ {\rm{C}}$ $20$ $\vartheta $ 0.85 $m$ 0.7 $n$ 1.3 $p$ 0.8 $q$ 0.7 Notes: ${\rho _{\rm{r}}}$—Density of resin; ${c_{\rm{r}}}$—Specific heat capacity of resin; ${V_{\rm{r}}}$—Volume fraction of resin; ${\rho _{\rm{f}}}$—Density of fiber; ${c_{\rm{f}}}$—Specific heat capacity of fiber; ${k_{\rm{y}}}$—Thermal conductivity of composite materials; $h$—Convective heat transfer coefficient; ${H_{\rm{r}}}$—Heat of polymerization; $s$—Concentration of photoinitiator; $\lambda $—UV absorption coefficient of composite materials; $E$—Activation energy; $R$—Gas constant; ${C_0}$—Preexponential factor; ${T_0},{T_{\inf }}$—Ambient temperature; $\vartheta $—Coefficient of surface absorption of UV radiation; $m$, $n$—Reaction order; $p$, $q$—Exponential constant. 
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表 2 不同固化方式对应的铺层时间
Table 2. Different curing methods correspond to the time of adding layers
Serial number of layer Laying time for one-shot
direct curing/sLaying time for equal interval
layering time curing/sLaying time for optimized
in-situ UV curing/s1 0 0 0 2 0 25 26 3 0 50 48 4 0 75 67 5 0 100 86
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表 3 固化度测试得到的各层平均固化度
Table 3. Average curing degree of each layer obtained by curing degree experiment
Serial number of each layer Average degree of curing/% 1 92.2 2 89.4 3 88.6 4 88.1 5 90.7
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