基于改进EHO算法的主轴承组合结构多结构特性协同优化设计方法

doi:10.12382/bgxb.2023.1135

摘要/Abstract

摘要：

随着柴油机功率密度的提升,主轴承组合结构将面临主轴承变形加剧、关键部件强度下降等可靠性问题。以主轴承组合结构作为优化设计对象,将强度、刚度、接触强度和轻量化表现作为优化目标,构建多结构特性协同优化设计数学模型。针对传统快速和精英保留多目标遗传算法(Non-dominated Sorting Genetic Algorithm II,NSGA-II)在求解小种群规模、有限进化代数的复杂工程问题时计算效率低的问题,基于Pareto优化理论,引入自适应策略及固定候选集随机测试算法,提出改进的大象放牧优化(Elephant Herding Optimization,EHO)算法用于求解多结构特性协同优化设计数学模型,并对算法性能及协同优化设计方案进行试验验证。研究结果表明:在小种群规模和有限进化代数下,改进EHO算法的求解能力更强,计算效率更高;在质量波动仅为0.6%的情况下,机体和主轴承座的应力分别降低18.67%和11.06%;各考察截面失圆度平均值降低14.39%;机体与主轴承座接触面最大接触压力降低18.92%。

关键词: 主轴承组合结构, 多目标优化, 协同设计, 改进EHO算法

Abstract:

As the power density of diesel engines increases,the main bearing assembly structure may suffer from reliability problems such as the increased deformation of main bearing and the decreased strength of key components.The strength,stiffness,contact strength and lightweight performance of main bearing assembly structure are taken as the optimization objectives,and a mathematical model for the collaborative optimization design of multi-structural characteristics is constructed.Aiming at the poor computational efficiency of the traditional non-dominated sorting genetic algorithm II(NSGA-II) in solving the complex engineering problems with small population size and restricted evolutionary generations,an improved elephant herding optimization(EHO) algorithm is proposed for solving the reliability matching mathematical model for the main bearing assembly structure based on the Pareto optimization theory by introducing the adaptive strategy and fixed sized candidate set random testing algorithm.Furthermore,the performance of the improved EHO algorithm and the reliability matching design scheme are experimentally verified.The results show that the improved EHO algorithm has stronger solving ability and higher computational efficiency with small population size and restricted evolutionary generations.After optimization,the first principal stresses in the stress-concentrated areas of engine block and main bearing cover are decreased by 18.67% and 11.06%,respectively,with a mass fluctuation of only 0.6%; and the average out-of-roundness in each examined section is decreased by 14.39%; and the maximum contact pressure on the contact surface between the engine block and the main bearing cover is decreased by 18.92%.

Key words: main bearing assembly structure, multi-objective optimization, collaborative design, improved EHO algorithm

中图分类号:

TK422

赵鑫, 苏铁熊, 马富康, 史建华, 柴常. 基于改进EHO算法的主轴承组合结构多结构特性协同优化设计方法[J]. 兵工学报, 2025, 46(1): 231135-.

ZHAO Xin, SU Tiexiong, MA Fukang, SHI Jianhua, CHAI Chang. Collaborative Optimization Design Method of Main Bearing Assembly Structure with Multi-structural Characteristics Based on Improved EHO Algorithm[J]. Acta Armamentarii, 2025, 46(1): 231135-.

图/表 28

图1 主轴承组合结构半气缸几何模型

Fig.1 Half-cylinder geometric model of main bearing assembly structure

图2 曲轴载荷示意图

Fig.2 Schematic diagram of crankshaft load

表1 网格无关性验证方案及结果

Table 1 Grid independence verification schemes and results

方案序号	网格数量/10⁵	机体应力/MPa	15mm 截面失圆度/mm	-15mm 截面失圆度/mm
1	5.6	210.9	0.1035	0.0974
2	14.9	187.6	0.0896	0.08793
3	20.3	145.7	0.0738	0.0729
4	31.4	147.1	0.0742	0.0764
5	43.8	142.8	0.0748	0.0750

表2 设计变量及其取值范围

Table 2 Design variables and their value ranges

设计变量名称	最小值	最大值
单个竖向螺栓载荷x₁/kN	100	250
单个横向螺栓载荷x₂/kN	50	200
主轴瓦过盈量x₃/mm	0.12	0.20
主轴承座装配侧隙x₄/mm	0.05	0.15
机体隔板厚度x₅/mm	40	48
主轴承座厚度x₆/mm	36	44
机体侧壁竖加强筋厚度x₇/mm	30	50

图3 机体高应力区域

Fig.3 Stress concentration area of engine block

图4 主轴承座高应力区域

Fig.4 Stress concentration area of main bearing cover

图5 强度目标函数的影响因素及规律

Fig.5 Influencing factors and rules of strength objective functions

图6 主轴瓦考察截面

Fig.6 Investigated sections of main bearing shell

图7 刚度目标函数的影响因素及规律

Fig.7 Influencing factors and rules of stiffness objective function

图8 机体与主轴承座接触面

Fig.8 Contact surface between engine block and main bearing cover

图9 接触强度目标函数的影响因素及规律

Fig.9 Influencing factors and rules of contact strength objective function

图10 FSCS-ART算法基本原理

Fig.10 FSCS-ART algorithm fundamentals

表3 多目标EHO算法伪代码

Table 3 Pseudo-code of multi-objective EHO algorithm

算法1:多目标EHO算法
1	设种群规模为N
2	对父代种群P按照支配等级和拥挤度进行排序
3	for每个氏族i,i=1,2,…,n,n为种群N中氏族的数量
4	for每个氏族中的大象个体j,j=1,2,…,N/n
5	将父代种群P中第10(j-1)+i个个体作为第i个氏族中的第j个大象个体
6	end_for
7	end_for
8	建立临时矩阵Temp,依次放入各氏族大象个体的设计变量
9	设置氏族更新每个氏族保留优秀个体数量为keep
10	for每个氏族i,i=1,2,…,n
11	执行氏族更新
12	确保氏族更新生成的大象个体处于全局空间
13	进行非支配排序与拥挤度计算
14	end_for
15	for每个氏族i,i=1,2,…,n
16	执行基于自适应策略的个体分离
17	确保个体分离生成的大象个体处于全局空间
18	替换氏族中适应度差(排序最后)的大象个体
19	end_for
20	合并各氏族的大象个体作为子代种群S

图11 改进EHO算法流程图

Fig.11 Flow chart of the improved EHO algorithm

图12 改进EHO和NSGA-II测试结果对比

Fig.12 Comparison of test results of improved EHO and NSGA-II algorithms

图13 联合仿真信息传递路径

Fig.13 Information transfer path of co-simulation

表4 协同优化设计结果

Table 4 Reliability matching design results

序号	x₁	x₂	x₃	x₄	x₅	x₆	x₇	F_s,1	F_s,2	F_r	F_c	F_l
1	210512.6	106276.5	0.185	0.103	42.93	43.12	32.11	0.234	0.781	0.242	0.329	0.019
2	225853.8	167072.6	0.181	0.088	43.76	43.92	32.60	0.229	0.775	0.245	0.326	0.016
3	151323.9	69629.7	0.204	0.052	42.70	42.83	38.92	0.338	0.863	0.121	0.556	0.024
4	168681.2	111287.0	0.180	0.107	43.01	43.95	32.51	0.157	0.832	0.189	0.475	0.018
5	200141.3	138133.5	0.185	0.105	36.46	36.48	32.59	0.241	0.722	0.183	0.295	0.036
6	200141.3	138133.5	0.185	0.105	36.46	36.48	32.59	0.241	0.722	0.183	0.295	0.036
7	177335.5	79778.9	0.178	0.070	36.19	36.09	38.72	0.378	0.726	0.142	0.357	0.039
8	150582.5	111464.8	0.174	0.103	42.78	42.82	32.80	0.196	0.883	0.120	0.509	0.025

表5 优化前后设计参数

Table 5 Design parameters before and after optimization

参数名称	初值	优化值
单个竖向螺栓载荷x₁/kN	200.0	210.5
单个横向螺栓载荷x₂/kN	98.0	106.3
主轴瓦过盈量x₃/mm	0.160	0.185
主轴承座装配侧隙x₄/mm	0.050	0.103
机体隔板厚度x₅/mm	44.0	42.9
主轴承座厚度x₆/mm	40.0	43.1
机体侧壁竖加强筋厚度x₇/mm	30.0	32.1

图14 原方案及协同优化设计方案仿真结果

Fig.14 Simulated results of original scheme and collaborative optimization design scheme

图15 强度测试示意图(左为应力集中区域仿真结果,右为应力集中区域强度测试图)

Fig.15 Diagram of strength testing(left:the simulated result of stress concentration area,right:the strength test diagram of stress concentration area)

图16 应变片位置示意图

Fig.16 Diagram of strain gauge positions

图17 主轴瓦测点位置

Fig.17 Measuring point locations of main bearing shell

图18 主轴瓦周向正应变测量原理(左为测量过程示意图,右为测量装配示意图)

Fig.18 Principle of circumferential vertical strain measurement of main bearing shell(left:the diagram of measurement process,right:the diagram of measurement assembly)

图19 最大接触压力测量

Fig.19 Maximum contact pressure measurement

图20 试验样机及测量对象示意图

Fig.20 Schematic diagram of test specimen and measured objects

表6 机体应力仿真值与测量值

Table 6 Simulaed and measured values of stresses of engine block

方案	仿真值/MPa	测量值/MPa	相对误差/%
原方案	143.48	150.3	4.5
改进方案	116.69	140.5	16.9

表7 径向变形仿真值与测量值对比

Table 7 Comparison of simulated and measured radial deformations

被测截面	测点	原方案		改进方案
被测截面	测点	仿真值/ mm	测量值/ mm	仿真值/ mm	测量值/ mm
15 mm 轴向截面	1	0.039	0.042	0.035	0.031
	2	0.040	0.039	0.034	0.034
	3	0.036	0.033	0.036	0.033
	4	0.043	0.040	0.035	0.032
-15 mm 轴向截面	1	0.037	0.034	0.034	0.030
	2	0.038	0.039	0.033	0.032
	3	0.040	0.037	0.035	0.034
	4	0.036	0.035	0.036	0.032

图21 原方案和改进方案最大接触压力

Fig.21 Maximum contact pressures of the original scheme and improved scheme

参考文献 22

[1]	REITZ H R, OGAWA H, PAYRI R, et al. IJER editorial:the future of the internal combustion engine[J]. International Journal of Engine Research, 2019, 21(1):146808741987799.
[2]	PRASAD N S, GANESH N, KUMARASAMY A. Technologies for high power density diesel engines[J]. Defence Science Journal, 2017, 67(4):370.
[3]	姬亚萌, 张卫正, 原彦鹏, 等. 高强化柴油机活塞加速热疲劳与等效寿命评估方法[J]. 兵工学报, 2022, 43(12):3008-3019.
	JI Y M, ZHANG W Z, YUAN Y P, et al. Study of equivalent and influence laws of accelerated thermal fatigue life of aluminum alloy pistons in highly strengthened diesel engines[J]. Acta Armamentarii, 2022, 43(12):3008-3019. (in Chinese)
[4]	周玮, 廖日东. 高功率密度柴油机主轴承热弹流混合润滑分析[J]. 内燃机学报, 2016, 34(4):370-378.
	ZHOU W, LIAO R D. Thermo-elasto-hydrodynamic mixed lubrication analysis of main bearings for high power-density diesel engine[J]. Transactions of CSICE, 2016, 34(4):370-378. (in Chinese)
[5]	ZHAO X M, LIU R L, WANG H, et al. Effects of charge motion on knocking combustion under boosted high load condition of a medium-duty gasoline engine[J]. Fuel, 2022,326:125040.
[6]	GAO J B, TIAN G H, JENNER P, et al. Preliminary explorations of the performance of a novel small scale opposed rotary piston engine[J]. Energy, 2020,190:116402.
[7]	郭圣刚, 王建平, 赵忠诚, 等. 金属掺杂对高强化柴油机活塞销类金刚石薄膜涂层摩擦学性能的影响[J]. 兵工学报, 2021, 42(4):715-722.
	GUO S G, WANG J P, ZHAO Z C, et al. The effect of metal doping on the friction performance of DLC coating for piston pins of highly strengthened diesel engine[J]. Acta Armamentarii, 2021, 42(4):715-722. (in Chinese)
[8]	欧阳光耀. 船用高速大功率柴油机运行可靠性与再设计技术[J]. 内燃机学报, 2008, 26(增刊1):40-46.
	OUYANG G Y. Techniques of re-design and operation reliability in high-speed and high-power diesel engine[J]. Transactions of CSICE, 2008, 26(S1):40-46. (in Chinese)
[9]	刘若辰, 李建霞, 刘静, 等. 动态多目标优化研究综述[J]. 计算机学报, 2020, 43(7):1246-1278.
	LIU R C, LI J X, LIU J, et al. A survey on dynamic multi-objective optimization[J]. Chinese Journal of Computers, 2020, 43(7):1246-1278. (in Chinese)
[10]	孟令烁. 柴油机机体组结构协调性设计技术研究[D]. 济南: 山东大学, 2018.
	MENG L S. Research on block assembly’s structure design compatibility of diesel engines[D]. Jinan: Shandong University, 2018. (in Chinese)
[11]	马明旭, 王成恩, 张嘉易, 等. 复杂产品多学科设计优化技术[J]. 机械工程学报, 2008, 44(6):15-26.
	MA M X, WANG C E, ZHANG J Y, et al. Multidisciplinary design optimization for complex product review[J]. Chinese Journal of Mechanical Engineering, 2008, 44(6):15-26. (in Chinese)
[12]	任培荣, 左正兴, 程颖. 内燃机主承力结构响应协调性评价体系研究[C]// 2018中国汽车工程学会年会暨展览会. 上海: 中国汽车工程学会,2018:762-768.
	REN P R, ZUO Z X, CHENG Y. Study on the response coordination assessment system of internal combustion engine main loaded structure[C]//Proceedings of China Society of Automotive Engineers.Congress and Exbition. Shanghai: China Society of Automotive Engineers,2018:762-768. (in Chinese)
[13]	唐佳桃, 雷基林, 雷启铭, 等. 柴油机活塞环组动力学特性分析及多目标优化设计[J]. 内燃机工程, 2023, 44(2):73-80.
	TANG J T, LEI J L, LEI Q M, et al. Dynamic characteristic analysis and multi-objective optimization design of piston ring set of a diesel engine[J]. Chinese Internal Combustion Engine Engineering, 2023, 44(2):73-80. (in Chinese)
[14]	ZHAO X, SU T X, LIU X Y, et al. Research on coordination design method of main bearing assembly structure based on the maximum radial deformation of bearing bush[J]. International Journal of Engine Research, 2022, 23(11):1795-1813.
[15]	赵鑫. 基于改进NSGA-Ⅱ算法的主轴承组合结构协调匹配设计方法研究[D]. 太原: 中北大学, 2023.
	ZHAO X. Research on coordinated matching design method of main bearing assembly structure based on improved NSGA-II[D]. Taiyuan: North University of China, 2023. (in Chinese)
[16]	WANG G G, DEB S, COELHO L D S. Elephant herding optimization[C]//Proceedings of the 2015 3rd International Symposium on Computational and Business Intelligence.Bali, Indonesia:IEEE, 2015.
[17]	LI J, LEI H, ALAVI A H, et al. Elephant herding optimization:variants,hybrids,and applications[J]. Mathematics, 2020, 8(9):1415.
[18]	ELSHAARAWY I A, HOUSSEIN E H, ISMAIL F H, et al. An exploration-enhanced elephant herding optimization[J]. Engineering Computations, 2019,36:3029-3046.
[19]	DEB K, PRATAP A, AGARWAL S, et al. A fast and elitist multiobjective genetic algorithm:NSGA-II[J]. IEEE Transactions on Evolutionary Computation, 2002, 6(2):182-197.
[20]	李金忠, 夏洁武, 曾小荟, 等. 多目标模拟退火算法及其应用研究进展[J]. 计算机工程与科学, 2013, 35(8):77-88.
	LI J Z, XIA J W, ZENG X H, et al. Survey of multi-objective simulated annealing algorithm and its applications[J]. Computer Engineering & Science, 2013, 35(8):77-88. (in Chinese)
[21]	DEB K. Multi-objective genetic algorithms:problem difficulties and construction of test problems[J]. Evolutionary Computation, 1999, 7(3):205-230.
[22]	章恩泽. 多目标粒子群优化算法及其应用研究[D]. 南京: 南京理工大学, 2018.
	ZHANG Z E. Research on multi-objective particle swarm optimization algorithm and applications[D]. Nanjing: Nanjing University of Science and Technology, 2018. (in Chinese)