﻿ 空间RSSR机构在舰船舱门设计中的应用
 舰船科学技术  2019, Vol. 41 Issue (6): 143-146 PDF

Application of mechanism RSSR in the ship cabin designbased on the method of Genetic Algorithm
LIU Jian-wei, GENG Kai-zhen
The 713 Institute of CSIC, Zhengzhou 450015, China
Abstract: At present, along with the domestic ship developing, the ship cabin mechanism presents multiple structural forms, and also possess the feature of smalling space and carrying large. This article put forward the design method based on the genetic algorithm method, and successfully used in the ship cabin mechanism design, gained better design result.
Key words: genetic algorithm     ship cabin mechanism     RSSR mechanism     pressure angle
0 引　言

1 空间RSSR机构基本原理

 图 1 空间RSSR机构组成 Fig. 1 The composition of RSSR mechanism

 \begin{aligned} & {x_{\text{B}}} = {l_1}\cos {\varphi _{01}}, \\ & {y_{\text{B}}} = {l_1}\sin {\varphi _{01}}, \\ & {z_{\text{B}}} = {s_0}, \\ & {x_{\text{C}}} = {l_3}\cos {\varphi _{03}} + {h_0}, \\ & {y_{\text{C}}} = {l_3}\cos {\lambda _{30}}\sin {\varphi _{03}} + {s_3}\sin {\lambda _{30}}, \\ & {z_{\text{C}}} = - {l_3}\sin {\lambda _{30}}\sin {\varphi _{03}} + {s_3}\cos {\lambda _{30}} \text{。} \end{aligned}

 $\begin{split} & \left( {{s_0}\sin {\lambda _{30}}/{l_1} - \cos {\lambda _{30}}\sin {\varphi _{01}}} \right)\sin {\varphi _{03}} + \left( {{h_0}/{l_1} - \cos {\varphi _{01}}} \right) \!\!\!\!\!\!\!\!\!\\ & \quad \quad \quad \quad \cos {\varphi _{03}} + \frac{{l_1^2 + l_3^2 + s_0^2 + s_3^2 + h_0^2 - l_2^2}}{{2{l_1}{l_3}}} - \\ &\quad \frac{{{s_3}\sin {\lambda _{30}}\sin {\varphi _{01}} + {h_0}\cos {\varphi _{01}} + {s_0}{s_3}\cos {\lambda _{30}}}}{{{l_3}}} = 0 \text{。}\!\!\!\! \end{split}$ (1)

2 遗传优化算法在舰船舱门机构中的设计应用

2.1 空间RSSR机构的优化设计过程

1）设计变量的确定

 $X = [{l_1},{l_2},{l_3},{s_0},{s_3}]\text{。}$ (2)

2）目标函数的确定

 \begin{aligned} & {v_{{\text{B}}x}} = - \sin ({\varphi _{01}}), \\ & {v_{{\text{B}}y}} = \cos ({\varphi _{01}}), \\ & {v_{{\text{B}}z}} = 0, \\ & {v_{{\text{C}}x}} = - \sin ({\varphi _{03}}), \\ & {v_{{\text{C}}y}} = 0, \\ & {v_{Cz}} = \cos ({\varphi _{03}}) \text{。} \end{aligned} (3)

 $\frac{{\overrightarrow {{F_{12}}} }}{{\left| {\overrightarrow {{F_{12}}} } \right|}} = \frac{{\left[ {{x_{\rm{C}}},{y_{\rm{C}}},{z_{\rm{C}}}} \right] - \left[ {{x_{\rm{B}}},{y_{\rm{B}}},{z_{\rm{B}}}} \right]}}{{{l_2}}}\text{。}$ (4)

 \begin{aligned} & {\alpha _1} = {\rm arc}\sin \left( {\left| {\frac{{\overrightarrow {{F_{12}}} }}{{\left| {\overrightarrow {{F_{12}}} } \right|}} \times \overrightarrow {{V_{\rm{B}}}} } \right|} \right) \times 180/{\rm{ {\text{π}}}}\;\text{，}\\ & {\alpha _2} = {\rm arc}\sin \left( {\left| {\frac{{\overrightarrow {{F_{23}}} }}{{\left| {\overrightarrow {{F_{23}}} } \right|}} \times \overrightarrow {{V_{\rm{C}}}} } \right|} \right) \times 180/{\rm{{\text{π}} }}\text{。} \end{aligned}

 $f\left( X \right) = \sum\limits_{j = 1}^t {{\omega _j}{f_j}\left( X \right) }(j = 1,2, \cdots t)\text{。}$ (5)

 ${\omega _j} = \frac{1}{{{f_j}({X^*})}} (j = 1,2, \cdots ,t)\text{，}$ (6)

 $\begin{split} & f = \sum\limits_{j = 1}^{30} {{\omega _j}\left( {\left| {\left| {\left( {{\rm arc}\sin \left( {\left| {\frac{{\overrightarrow {{F_{12}}} }}{{\left| {\overrightarrow {{F_{12}}} } \right|}} \times \overrightarrow {{V_{\rm{B}}}} } \right|} \right) \times 180/ {\text{π}} } \right)\left( j \right)} \right| - 30} \right|} \right. } + \\ & \left. {\left| {\left| {\left( {{\rm arc}\sin \left( {\left| {\frac{{\overrightarrow {{F_{23}}} }}{{\left| {\overrightarrow {{F_{23}}} } \right|}} \times \overrightarrow {{V_{\rm{C}}}} } \right|} \right) \times 180/{\text{π}}} \right)\left( j \right)} \right| - 30} \right|} \right) \text{，} \\ & (j = 1,2, \cdots 30)\text{。} \end{split}$ (7)

3）约束函数的定义

 ${\varphi _{03}} = 2a\tan \left( {(A + \sqrt {{A^2} + {B^2} - {C^2}} )/(B - C)} \right)\text{。}$ (8)

 $A = {s_0}\sin {\lambda _{30}}/{l_1} - \cos {\lambda _{30}}\sin {\varphi _{01}}\text{，}$
 $B = {h_0}/{l_1} - \cos {\varphi _{01}}\text{，}$
 $\begin{gathered} C = \frac{{l_1^2 + l_3^2 + s_0^2 + s_3^2 + h_0^2 - l_2^2}}{{2{l_1}{l_3}}} - \\ \frac{{{s_3}\sin {\lambda _{30}}\sin {\varphi _{01}} + {h_0}\cos {\varphi _{01}} + {s_0}{s_3}\cos {\lambda _{30}}}}{{{l_3}}}\text{。} \end{gathered}$

4）边界条件的定义

 $\begin{split} & {l_1} = \left[ {80,120} \right],{l_2} = \left[ {120,250} \right],{l_3} = \left[ {90,130} \right] \\ &{s_3} = \left[ {20,150} \right],{s_0} = \left[ {20,200} \right] \text{，} \end{split}$ (9)
2.2 遗传优化算法的求解

 $\begin{split} &\left[ {{\rm{xf,endPop,beestSols,trace}}} \right] = \\ &\rm{ga}(\rm{bounds},'\rm{RSSR}\_1',\left[ {} \right],\rm{startPop},\left[ {} \right], \\ & '\max \rm{GenTerm}',300, \\ & '\rm{normGeomSelect}',\left[ {0.08} \right], \\ & \left[ {'\rm{arithXover}'} \right],\left[ {2} \right],'\rm{nonUniMutation}', \\ & \left[ {2\;300\;3} \right]) \end{split}$ (10)

 图 2 空间RSSR机构目标函数最优解和平均值的变化曲线 Fig. 2 Optimal solution and average value′s varying curve of RSSR mechanism
3 空间RSSR机构参数设计结果的正确性检验

 图 3 输出参数 ${\varphi _{03}}$ 求解结果 Fig. 3 The calculation results of output parameter

 图 4 ${l_1}$ 和 ${l_2}$ 间压力角变化曲线 Fig. 4 The pressure angle of varying curve between ${l_1}$ and ${l_2}$

 图 5 ${l_3}$ 和 ${l_2}$ 间压力角变化曲线 Fig. 5 The pressure angle of varying curve between ${l_3}$ and ${l_2}$

4 结　语

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