﻿ 翼型结构蒙皮厚度优化设计方法及规律研究
 舰船科学技术  2018, Vol. 40 Issue (8): 33-36, 132 PDF

1. 中国人民解放军92942部队，北京 100161;
2. 海军工程大学 舰船工程系，湖北 武汉 430033

Research on optimization method and regularity for thickness of airfoil skin
LIU Ling1, LI Hua-dong2, MEI Zhi-yuan2
1. No. 92942 Unit of PLA, Beijing 100161, China;
2. Department of Naval Architecture, Naval University of Engineering, Wuhan 430033, China
Abstract: In order to improve cross-sectional inertia moment and obtain optimum strength and stiffness characteristics, airfoil structure is usually designed with local thickening skin. The area-inertia moment ratio is proposed as a concept, and the calculating formulas is derived as well as the main influencing factors is analyzed. Then, variety law of the area-inertia moment ratio is studied. Based on the principle of maximum moment of inertia, the optimization method for thickness of airfoil skin is proposed. The range of optimal thickened section is determined, and drawn into curves for common ship rudder profiles. Finally, a numerical example describes the use of the curves, and verifies the effectiveness of the method.
Key words: airfoil structure     area-inertia moment ratio     local thickening     optimal design
0 引　言

1 比惯性矩及其影响因素

 图 1 翼剖面及坐标系 Fig. 1 Wing profile and coordinate system

AB段为例（AC段计算方法相同），假设AB段的型线函数 $y = {f_1}(x),x \in [0,{x_B}]$ ，计算剖面对于中线BC的比惯性矩如下：

AE加厚段长度、面积及惯性矩分别为

 ${l_{AE}} = \int_0^{x_1} {\sqrt {1 + y{'^2}} } {\rm{d}}x\text{，}$
 ${s_{AE}} = {l_1} \cdot {t_1}\text{，}$
 ${j_{AE}} = \int_0^{{x_1}} {\sqrt {1 + y{'^2}} } \cdot {t_1} \cdot {({y_B} - y)^2}{\rm{d}}x\text{。}$

EB未加厚段长度、面积及惯性矩分别为

 ${l_{EB}} = \int_{{x_1}}^{{x_B}} {\sqrt {1 + y{'^2}} } {\rm{d}}x\text{，}$
 ${s_{EB}} = {l_2} \cdot {t_2}\text{，}$
 ${j_{EB}} = \int_{{x_1}}^{{x_B}} {\sqrt {1 + y{'^2}} } \cdot {t_2} \cdot {({y_B} - y)^2}{\rm{d}}x\text{。}$

AB段比惯性矩为

 $\begin{split}&j/s = \frac{{{j_1} + {j_2}}}{{{s_1} + {s_2}}} =\\&\frac{{{t_1}/{t_2} \cdot \int_0^{{x_1}} {\sqrt {1 + y{'^2}} } \cdot {{({y_B} - y)}^2}{\rm{d}}x + \int_{{x_1}}^{{x_B}} {\sqrt {1 + y{'^2}} } \cdot {{({y_B} - y)}^2}{\rm{d}}x}}{{{t_1}/{t_2} \cdot \int_0^{{x_1}} {\sqrt {1 + y{'^2}} } {\rm{d}}x + \int_{{x_1}}^{{x_B}} {\sqrt {1 + y{'^2}} } {\rm{d}}x}}\end{split}\text{。}$

 ${d_i} = \sqrt {{{({x_i} - {x_{i - 1}})}^2} + {{({y_i} - {y_{i - 1}})}^2}} \text{，}$

AE段面积与惯性矩为

 ${s_A} = \sum\limits_{i = 1}^M {{d_i}} \cdot {t_1}\text{，}$
 ${j_A} = \sum\limits_{i = 1}^M {{d_i} \cdot {t_1} \cdot {{\Bigr({y_{\max }} - \frac{{{y_i} + {y_{i - 1}}}}{2}\Bigr)}^2}} \text{。}$

EB段面积与惯性矩为

 ${s_B} = \sum\limits_{i = M + 1}^N {{d_i}} \cdot {t_2}\text{，}$
 ${j_B} = \sum\limits_{i = M + 1}^N {{d_i} \cdot {t_2} \cdot {{\Bigr({y_{\max }} - \frac{{{y_i} + {y_{i - 1}}}}{2}\Bigr)}^2}} \text{。}$

AB段比惯性矩为

 $j/s = \frac{{{t_1}/{t_2} \cdot \sum\limits_{i = 1}^M {{d_i} \cdot {{\Bigr({y_B} - \frac{{{y_i} + {y_{i - 1}}}}{2}\Bigr)}^2}} + \sum\limits_{i = M + 1}^N {{d_i} \cdot {{\Bigr({y_B} - \frac{{{y_i} + {y_{i - 1}}}}{2}\Bigr)}^2}} }}{{{t_1}/{t_2} \cdot \sum\limits_{i = 1}^M {{d_i}} + \sum\limits_{i = M + 1}^N {{d_i}} }}\text{。}$
2 比惯性矩变化规律研究

 图 2 比惯性矩/分点坐标曲线 Fig. 2 Specific moment/point coordinate curve

 图 3 最优比惯性矩/厚度比曲线 Fig. 3 Optimal specific moment/thickness ratio curve
3 蒙皮厚度优化方法与分点图谱

 图 4 最优惯性矩/厚度比曲线 Fig. 4 Optimal moment of inertia / thickness ratio curve

 图 5 最优分点坐标图谱 Fig. 5 Optimal point coordinate map
4 算例分析 4.1 算例描述

x1=146.0×2.4=350.4（mm），x2=247.5×2.4=594.0（mm）；

x1=144.6×1.6=231.4（mm），x2=247.2×1.6=395.5（mm）。

4.2 结果分析

 图 6 优化前后舵叶模型 Fig. 6 Comparison of rudder model before and after optimization

 图 7 优化前后舵叶位移 Fig. 7 Comparison of rudder deformation before and after optimization

 图 8 优化前后蒙皮应力 Fig. 8 Comparison of skin stress before and after optimization
5 结　语

1）在翼型与加厚比 ${t_1}/{t_2}$ 一定的情况下，随着分点EF位置坐标的增大，比惯性矩先增大或减小，其间存在最优分点位置使比惯性矩最大。

2）随着厚度比 ${t_1}/{t_2}$ 的增大，最佳分点坐标x1x2逐渐变小，即分点往中间移动，加厚段范围变小；随着翼型系数e/b的增大，x1x2逐渐变大，即分点往两边移动，加厚段范围变大。

3）随着翼型系数e/b的增大，同一厚度比的分点坐标x1x2呈现线性变化，这说明对于变截面变翼型（厚度比不变）的船用舵，只需确定两端面的最优分点位置，即可线性确定其他舵剖面的分点，极大地扩展了该方法的实用性和适用范围。

 [1] 胡燕平, 戴巨川, 刘德顺. 大型风力机叶片研究现状与发展趋势[J]. 机械工程学报, 2013, 49(20): 140–147. http://www.cqvip.com/qk/86583b/201110/39568309.html [2] 冯消冰, 孙树力. 2 MW风机叶片梁帽与腹板的强度优化设计[J]. 合成材料老化与应用, 2015, 44(2): 21–27. http://www.cqvip.com/QK/93456A/201502/664572732.html [3] VITALE A J, ROSSI A P. Computational method for the design of wind turbine blades[J]. International Journal of Hydrogen Energy, 2008, 33(13): 3466–3470. [4] 李丹, 姚卫星. GFRP风机叶片结构设计的二级优化方法[J]. 南京航天航空大学学报, 2011, 43(5): 598–601. http://or.nsfc.gov.cn/bitstream/00001903-5/72867/1/1000004601243.pdf [5] 廖猜猜, 王建礼, 石可重, 等. 风力叶片截面刚度优化设计[J]. 工程热物理学报, 2010, 31(7): 1127–1130. http://www.oalib.com/paper/4856035 [6] CAI Xin, ZHU Jie, PAN Pan, et al. Structural optimization design of horizontal-axis wind turbine blades using a particle swarm optimization algorithm and finite element method[J]. Energies, 2012, 5(11): 4683–4696. [7] 梅琴生. 船用舵[M]. 北京: 人民交通出版社, 1981. [8] QUYANG X, YU X Q, WANG Y. Flutter analysis for wing structure using finite element modeling with equivalent stiffness[J]. Journal of Vibroengineering, 2014, 16(3): 1483–1493. [9] 王宇, 欧阳星, 余雄庆. 采用等效有限元模型的复合材料机翼结构优化[J]. 复合材料学报, 2015, 32(5): 1487–1494. http://www.cqvip.com/QK/95343A/201501/664032299.html