基于启发式算法的附件传动系统轻量化设计

路凯屹; 刘怀举; 廖常军; 卢泽华; 魏沛堂

doi:10.13224/j.cnki.jasp.20220911

基于启发式算法的附件传动系统轻量化设计

doi: 10.13224/j.cnki.jasp.20220911

1.
重庆大学高端装备机械传动全国重点实验室，重庆 400044
2.
中国航发四川燃气涡轮研究院，成都 610500

基金项目: 国家重点研发计划项目（2022YFB3402801）

详细信息

作者简介:
路凯屹（1999-），男，硕士生，主要从事航空齿轮传动系统智能设计

通讯作者:
刘怀举（1986-），男，教授，博士，主要从事高性能齿轮设计制造研究。E-mail：huaijuliu@cqu.edu.cn

中图分类号: V233.1⁺4
计量
- 文章访问数: 505
- HTML浏览量: 345
- PDF量: 53
- 被引次数: 0
出版历程
- 收稿日期: 2022-11-27
- 网络出版日期: 2024-12-13

Lightweight design of accessory transmission based on heuristic algorithm

1.
State Key Laboratory of Mechanical Transmissions for Advanced Equipment，Chongqing University，Chongqing 400044，China
2.
Sichuan Gas Turbine Establishment，Aero Engine Corporation of China，Chengdu 610500，China

摘要

摘要:
为解决因航空发动机功率密度、轻量化水平的不断提高所带来的常规设计方法难以满足附件传动系统高可靠、轻量化、低成本等综合性能设计需求的问题，提出了一种采用基于启发式搜索的非支配排序算法（HS-NSGA Ⅱ）的传动系统结构轻量化设计方法，开展了某航发附件机匣传动系统结构参数的优化设计，发现优化齿轮齿宽和腹板结构对传动系统轻量化程度最为显著，而引入喷丸强化等表面强化工艺可进一步提高传动系统服役性能，实现相比初始方案，齿轮组质量最大降低了21.0%，系统最大相对滑动率降低11.4%，为航空发动机附件齿轮传动系统轻量化设计提供了方法支撑。
- 附件机匣 /
- 传动系统 /
- 多目标优化 /
- 轻量化 /
- 启发式算法
Abstract:
To solve the problem that conventional design methods are unable to meet the comprehensive performance design requirements of accessory transmission systems, such as high reliability, lightweight, and low cost, due to the continuous improvement of power density and lightweight level of aero-engines, a lightweight design method of transmission structure based on the heuristic search non-dominated sorting genetic algorithm Ⅱ (HS-NSGA Ⅱ) was proposed, and the optimal design of structural parameters of an aero-engine accessory gearbox transmission was launched. It was found that the optimization of gear tooth number and displacement had the most significant effect on the lightweight degree of transmission. The introduction of surface hardening processes, such as shot peening, can further improve the service performance of the transmission. Compared with the initial design, the maximum weight of the gear set was reduced by 21.0%, and the maximum relative slip rate of the system was reduced by 11.4%. This can provide a methodological support for the lightweight design of the aero-engine accessory gear transmission.
- accessory gearbox /
- transmission /
- multi-objective optimization /
- lightweight /
- heuristic algorithm

HTML

图 1 某航发附件机匣齿轮传动系统结构示意图

Figure 1. Structure diagram of an aero-engine accessory gearbox transmission

下载: 全尺寸图片幻灯片

图 2 HS-NSGA Ⅱ遗传算法流程图

Figure 2. Flow chart of HS-NSGA Ⅱ genetic algorithm

下载: 全尺寸图片幻灯片

图 3 成组交叉、成组变异策略

Figure 3. Group mutation and group crossover strategy

下载: 全尺寸图片幻灯片

图 4 轴系分布图

Figure 4. Shafting distribution diagram

下载: 全尺寸图片幻灯片

图 5 薄腹板齿轮结构示意图

Figure 5. Schematic diagram of thin web gear structure

下载: 全尺寸图片幻灯片

图 6 1000组原始可行设计方案

Figure 6. 1000 sets of original feasible design schemes

下载: 全尺寸图片幻灯片

图 7 目标函数迭代变化

Figure 7. Iterative change of objective function

下载: 全尺寸图片幻灯片

图 8 初始方案与结构优化方案安全系数对比

Figure 8. Comparison of safety factors between initial scheme and structural optimization scheme

下载: 全尺寸图片幻灯片

图 9 喷丸前后齿轮2、齿轮3接触温度变化

Figure 9. Contact temperature change of gear 2 and gear 3 before and after shot peening

下载: 全尺寸图片幻灯片

图 10 工艺优化方案与材料优化方案安全系数对比

Figure 10. Comparison of safety factors between process optimization scheme and material optimization scheme

下载: 全尺寸图片幻灯片

图 11 不同设计方案的轻量化和安全性结果

Figure 11. Lightweight and safety results of different design schemes

下载: 全尺寸图片幻灯片

表 1 该航发附件机匣运转工况

Table 1. Operating conditions of the aero-engine accessory gearbox

工况参数		数值
输入转速n/（r/min）		40000
输出转速/（r/min）	输出轴A	14000
	输出轴B	18200
	输出轴C	14600
输出功率/kW	输出轴A左端	14
	输出轴A右端	4
	输出轴B	2
	输出轴C	5

下载: 导出CSV

表 2 齿轮传动系统初始设计方案

Table 2. Initial design scheme of gear transmission

参数	齿轮1		齿轮2		齿轮3		齿轮4		齿轮5
模数m/mm	1.5		1.5		1.5		1.5		1.5
齿数z	48		37		27		35		46
齿宽b/mm	4		5		6		5		4
压力角α/（°）	25		25		25		25		25
变位系数x /mm	0		0		0		0		0
接触安全系数S_h	1.58		1.44		1.39		2.63		2.75
弯曲安全系数S_f	4.29		4.67		5.43		14.42		12.19
胶合安全系数S_ins	3.81		3.16		3.16		4.38		4.58
轴系角度安装角度α_shaft/（°）		5		10		3		30
选用材料	一代航空齿轮钢

下载: 导出CSV

表 3 材料疲劳极限值（99%可靠度下）

Table 3. Material fatigue limit value （under 99% reliability）

材料	弯曲疲劳极限σ_flim/MPa	接触疲劳极限σ_hlim/MPa	胶合极限温度/℃
一代航空齿轮钢	500	1500	296
喷丸强化一代齿轮钢	600	1600	296
二代航空齿轮钢	650	1700

下载: 导出CSV

表 4 结构优化方案

Table 4. Structural optimization scheme

参数	齿轮1	齿轮2	齿轮3	齿轮4	齿轮5
模数m/mm	1.5	1.5	1.5	1.5	1.5
齿数z	48	37	27	37	43
齿宽b/mm	3	4	5	4	3
压力角α/（°）	25	25	25	25	25
变位系数x/mm	0.026	−0.026	0.026	−0.026	0.026
接触安全系数S_h	1.42	1.30	1.26	2.34	2.38
弯曲安全系数S_f	3.48	3.77	4.74	11.39	9.28
胶合安全系数S_ins	3.53	2.80	2.80	4.23	4.48
轴系角度安装角度α_shaft/（°）		5	10	3	30

下载: 导出CSV

表 5 结构优化方案优化效果

Table 5. Optimization effect of structural optimization scheme

参数	初始设计方案	结构优化方案	变化率/%
最小重合度ε	1.476	1.479	0.2
最大相对滑动率η	1.054	0.998	−5.3
齿轮组质量M/kg	0.781	0.698	−10.6

下载: 导出CSV

表 6 腹板优化方案减重效果

Table 6. Lightweight effect of web optimization scheme

齿轮/方案	质量/kg		减重率/%
齿轮/方案	结构优化方案	腹板优化方案	减重率/%
齿轮1	0.228	0.213	6.8
齿轮2	0.117	0.097	14.9
齿轮3	0.059	0.059	0
齿轮4	0.087	0.065	25.3
齿轮5	0.209	0.200	4.3
齿轮组	0.698	0.635	9.0

下载: 导出CSV

表 7 工艺优化方案优化效果

Table 7. Optimization effect of process optimization scheme

参数	腹板优化方案	工艺优化方案	变化率/%
齿宽b/mm	5	4.5	−10
齿轮组质量M/kg	0.635	0.617	−2.8
最大相对滑动率η	0.998	0.934	−6.4
最小接触安全系数S_h	1.26	1.26	0
最小弯曲安全系数S_f	3.48	3.59	3.2
最小胶合安全系数S_ins	2.80	2.58	−7.9

下载: 导出CSV

参考文献(26)

[1]	《航空发动机设计手册》总编委会. 航空发动机设计手册: 第12 册[M]. 北京: 航空工业出版社,2002: 553-573.
[2]	ZOLFAGHARI A,GOHARIMANESH M,AKBARI A A. Optimum design of straight bevel gears pair using evolutionary algorithms[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering,2017,39(6): 2121-2129. doi: 10.1007/s40430-017-0733-9
[3]	TAMBOLI K,PATEL S,GEORGE P M,et al. Optimal design of a heavy duty helical gear pair using particle swarm optimization technique[J]. Procedia Technology,2014,14: 513-519. doi: 10.1016/j.protcy.2014.08.065
[4]	HOFSTETTER M,LECHLEITNER D,HIRZ M,et al. Multi-objective gearbox design optimization for xEV-axle drives under consideration of package restrictions[J]. Forschung Im Ingenieurwesen,2018,82(4): 361-370. doi: 10.1007/s10010-018-0278-9
[5]	THOMPSON D F,GUPTA S,SHUKLA A. Tradeoff analysis in minimum volume design of multi-stage spur gear reduction units[J]. Mechanism and Machine Theory,2000,35(5): 609-627. doi: 10.1016/S0094-114X(99)00036-1
[6]	PARMAR A,RAMKUMAR P,SHANKAR K. Macro geometry multi-objective optimization of planetary gearbox considering scuffing constraint[J]. Mechanism and Machine Theory,2020,154: 104045. doi: 10.1016/j.mechmachtheory.2020.104045
[7]	SEDAK M,ROSIĆ B. Multi-objective optimization of planetary gearbox with adaptive hybrid particle swarm differential evolution algorithm[J]. Applied Sciences,2021,11(3): 1107. doi: 10.3390/app11031107
[8]	LIU Genshen,LIU Huaiju,ZHU Caichao,et al. Design optimization of a wind turbine gear transmission based on fatigue reliability sensitivity[J]. Frontiers of Mechanical Engineering,2021,16(1): 61-79. doi: 10.1007/s11465-020-0611-5
[9]	YOKOTA T,TAGUCHI T,GEN M. A solution method for optimal weight design problem of the gear using genetic algorithms[J]. Computers & Industrial Engineering,1998,35(3/4): 523-526.
[10]	CHONG T H,LEE J S. A design method of gear trains using a genetic algorithm[J]. International Journal of Precision Engineering and Manufacturing,2000,1(1): 62-70.
[11]	DEB K,JAIN S. Multi-speed gearbox design using multi-objective evolutionary algorithms[J]. Journal of Mechanical Design,2003,125(3): 609-619. doi: 10.1115/1.1596242
[12]	FU Guozhong,HUANG Hongzhong,LI Yanfeng,et al. Multi-objective design optimization for a two-stage transmission system under heavy load condition[J]. Mechanism and Machine Theory,2018,122: 308-325. doi: 10.1016/j.mechmachtheory.2017.12.024
[13]	PATIL M,RAMKUMAR P,KRISHNAPILLAI S. Multi-objective optimization of two stage spur gearbox using NSGA-Ⅱ[R]. Warrendale,US: SAE Technical Paper,2017.
[14]	PATIL M,RAMKUMAR P,SHANKAR K. Multi-objective optimization of the two-stage helical gearbox with tribological constraints[J]. Mechanism and Machine Theory,2019,138: 38-57. doi: 10.1016/j.mechmachtheory.2019.03.037
[15]	MAPUTI E S,ARORA R. Multi-objective optimization of a 2-stage spur gearbox using NSGA-Ⅱ and decision-making methods[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering,2020,42(9): 1-22.
[16]	郭梅,邢彬,史妍妍. 航空发动机附件机匣结构设计及齿轮强度分析[J]. 航空发动机,2012,38(3): 9-11. GUO Mei,XING Bin,SHI Yanyan. Structural design and strength analysis of accessory gearbox system for aeroengine[J]. Aeroengine,2012,38(3): 9-11. (in Chinese doi: 10.3969/j.issn.1672-3147.2012.03.004 GUO Mei, XING Bin, SHI Yanyan. Structural design and strength analysis of accessory gearbox system for aeroengine[J]. Aeroengine, 2012, 38(3): 9-11. (in Chinese) doi: 10.3969/j.issn.1672-3147.2012.03.004
[17]	王琳,徐可君,王永旗. 航空发动机最优翻修间隔评定研究[J]. 燃气轮机技术,2007,20(4): 57-60. WANG Lin,XU Kejun,WANG Yongqi. Study on evaluation of the best overhaul interval for aero engine[J]. Gas Turbine Technology,2007,20(4): 57-60. (in Chinese doi: 10.3969/j.issn.1009-2889.2007.04.014 WANG Lin, XU Kejun, WANG Yongqi. Study on evaluation of the best overhaul interval for aero engine[J]. Gas Turbine Technology, 2007, 20(4): 57-60. (in Chinese) doi: 10.3969/j.issn.1009-2889.2007.04.014
[18]	王颖,王三民,郭家舜. 高速重载齿轮传动多目标优化设计研究[J]. 机械设计与制造,2012(9): 7-9. WANG Ying,WANG Sanmin,GUO Jiashun. Research on multi-objective optimization design of high-speed and heavy-duty gear transmissions[J]. Machinery Design & Manufacture,2012(9): 7-9. (in Chinese WANG Ying, WANG Sanmin, GUO Jiashun. Research on multi-objective optimization design of high-speed and heavy-duty gear transmissions[J]. Machinery Design & Manufacture, 2012(9): 7-9. (in Chinese)
[19]	刘大响. 一代新材料,一代新型发动机: 航空发动机的发展趋势及其对材料的需求[J]. 材料工程,2017,45(10): 1-5. LIU Daxiang. One generation of new material,one generation of new type engine: development trend of aero-engine and its requirements for materials[J]. Journal of Materials Engineering,2017,45(10): 1-5. (in Chinese LIU Daxiang. One generation of new material, one generation of new type engine: development trend of aero-engine and its requirements for materials[J]. Journal of Materials Engineering, 2017, 45(10): 1-5. (in Chinese)
[20]	ZHENG Yong,WANG Xuejun. A survey of recommender systems with multi-objective optimization[J]. Neurocomputing,2022,474: 141-153. doi: 10.1016/j.neucom.2021.11.041
[21]	WANG Bingchuan,LI Hanxiong,ZHANG Qingfu,et al. Decomposition-based multiobjective optimization for constrained evolutionary optimization[J]. IEEE Transactions on Systems,Man,and Cybernetics: Systems,2021,51(1): 574-587. doi: 10.1109/TSMC.2018.2876335
[22]	GEEM Z W,KIM J H,LOGANATHAN G V. A new heuristic optimization algorithm: harmony search[J]. SIMULATION,2001,76(2): 60-68. doi: 10.1177/003754970107600201
[23]	QIU Wenbo,ZHU Jianghan,WU Guohua,et al. Ensemble many-objective optimization algorithm based on voting mechanism[J]. IEEE Transactions on Systems,Man,and Cybernetics: Systems,2022,52(3): 1716-1730. doi: 10.1109/TSMC.2020.3034180
[24]	WU Jizhan,LIU Huaiju,WEI Peitang,et al. Effect of shot peening coverage on residual stress and surface roughness of 18CrNiMo7-6 steel[J]. International Journal of Mechanical Sciences,2020,183: 105785. doi: 10.1016/j.ijmecsci.2020.105785
[25]	WU Jizhan,WEI P,LIU Huaiju,et al. Evaluation of pre-shot peening on improvement of carburizing heat treatment of AISI 9310 gear steel[J]. Journal of Materials Research and Technology,2022,18: 2784-2796. doi: 10.1016/j.jmrt.2022.03.163
[26]	CHEN Taimin,WEI P,ZHU Caichao,et al. Experimental investigation of gear scuffing for various tooth surface treatments[J]. Tribology Transactions,2022 (just-accepted): 1-19.