﻿ 基于Pareto遗传算法和TRIZ理论的数控加工参数优化

# 基于Pareto遗传算法和TRIZ理论的数控加工参数优化Optimization of CNC Machining Parameter Based on Pareto Genetic Algorithm and TRIZ Theory

Abstract: Based on the CNC machine parameter optimization, an algorithm was proposed of Pareto genetic algorithm and TRIZ theory. First, a multi-objective optimization model was built of cutting efficiency, tool life and processing cost as the optimization objectives, and the Pareto optimal solutions were generated based on the Pareto genetic algorithm. Second, based on TRIZ theory, technical contradiction was analyzed on the Pareto optimal solutions and contradiction matrix was built, and the optimal solution was decided based on technical problem-solving principles; at last, this algorithm was proved feasible and effective by experiments results. This method effectively avoids the drawbacks of experience and preference, and the good combination of reasonable optimization and rational decision was achieved.

1. 引言

2. 改进型Pareto遗传算法

TRIZ能够有效解决产品创新中遇到的问题，解决矛盾和冲突是产品创新的核心 [12] ，科学运用RIZ理论中的矛盾解决策略能够有效消除产品创新过程中出现的技术冲突和物理冲突。TRIZ理论提出了39个工程参数的抽象描述方法，而且这些描述方法能够有效解释对象冲突的本质，TRIZ理论还提出了39个通用的工程参数，构建了用于分析参数问题的冲突矩阵模型，其中“列”所描述的是需要改善的一方，而“行”所针对的则是恶化的一方，而后基于一定的规则，将40条发明原理视为参考解列入其中，从而得到冲突解决原理表。在实际应用过程中，为了促使问题实现抽象化，还需要借助参数来进行定义描述，并在矩阵表中确定对应的原理号 [13] ，根据解决原理号及原理内容，结合实际，分析、提炼和总结，最终找到解决问题的方法。TRIZ理论的39个通用工程参数及其40条发明原理是针对所有问题基础上的提炼和通用，从而保证了应用的科学性。

Figure 1. Improved Pareto genetic algorithm flow chart

3. 建立数学模型

3.1. 设计变量

3.2. 目标函数

$E\left(v,f\right)=\frac{1}{{t}_{m}}=\frac{1000vfZ}{\pi dL}$ (1)

$T\left(v,f\right)=\frac{{C}_{\epsilon }}{{v}^{\alpha }{f}^{\beta }{a}_{p}^{\gamma }}$ (2)

$C\left(v,f\right)={t}_{m}\cdot M+{t}_{ct}\cdot \frac{{t}_{m}}{T\left(v,f\right)}\cdot M+\frac{{t}_{m}}{T\left(v,f\right)}\cdot {C}_{t}+{t}_{ot}\cdot M$ (3)

3.3. 约束参数

1) 主切削力约束

${h}_{1}\left(v,f\right)={F}_{Z}-{F}_{Z\mathrm{max}}=9.81{C}_{FZ}{a}_{p}^{{x}_{FZ}}{f}^{{y}_{FZ}}\left(60v\right){n}_{FZ}{K}_{FZ}-{F}_{Z\mathrm{max}}\le 0$ (4)

2) 机床功率约束

${h}_{2}\left(v,f\right)=\frac{{F}_{z}v}{60000}-\eta {P}_{\mathrm{max}}=\pi dn{F}_{Z}-\eta {P}_{\mathrm{max}}\le 0$ (5)

3) 工件表面粗糙度约束

${h}_{3}\left(v,f\right)={f}^{2}/\left(8{r}_{\epsilon }\right)-{R}_{\mathrm{max}}\le 0$ (6)

4) 切削用量范围约束

3.4. Pareto最优解集

Figure 2. Cam model

$E\left({x}_{1},{x}_{2}\right)=\frac{1000{x}_{1}{x}_{2}×Z}{\pi ×d×L}$ (7)

$T\left({x}_{1},{x}_{2}\right)={C}_{{}_{Z}}/{a}_{p}^{\gamma }{x}_{1}^{\alpha }{x}_{2}^{\beta }$ (8)

$C\left({x}_{1},{x}_{2}\right)={t}_{m}\cdot M+{t}_{ct}\cdot \frac{{t}_{m}}{T\left({x}_{1},{x}_{2}\right)}\cdot M+\frac{{t}_{m}}{T\left({x}_{1},{x}_{2}\right)}\cdot {C}_{t}+{t}_{ot}\cdot M$ (9)

Figure 3. Pareto solution set of cam cutting parameters

Table 1. Optimization results of cam

Table 2. Selected machining parameters based on experience of cam

4. 最优解决策

4.1. 确定矛盾

4.2. 确定问题解决原理

4.3. Pareto最优解的理性决策

Figure 4. Analysis process based on TRIZ

5. 加工实验验证

Figure 5. Machining test process of cam

Figure 6. Machined surface roughness values of three groups parameters of cam

Table 4. Comparison between theoretical and actual measurement value of cam machining experiment

6. 结论

NOTES

*通讯作者。

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