基于变径基圆渐开线涡旋压缩机的几何模型及优化研究

doi:10.16183/j.cnki.jsjtu.2022.129

摘要/Abstract

摘要：

针对现有变径基圆涡旋压缩机几何模型的定量分析及优化研究不够完善的问题,给出了变径基圆涡旋压缩机从吸气过程开始直到排气过程结束的完整工作腔容积变化规律.比较了格林定理法、图解法及法向等距法的容积计算差异性,分析了产生计算误差的原因,验证了几何模型的正确性.推导了齿面积利用率的计算公式,构建了行程容积及齿面积利用率的灵敏度模型,得出基圆半径变化系数及内侧型线发生角的影响尤为显著的结论.建立了一种考虑非线性约束且以行程容积与齿面积利用率为优化目标的多目标优化分析模型.结果表明:多目标遗传算法(NSGA-II)比多目标粒子群(MOPSO)算法综合性能更佳,且相较于优化前,某款汽车空调用变径基圆涡旋压缩机的行程容积提升了6.5%,齿面积利用率降低了4.27%.该研究能为变径基圆涡旋压缩机的优化设计及定量研究提供进一步的理论参考.

关键词: 涡旋压缩机, 变径基圆涡旋型线, 几何模型, 多目标优化, 算法对比

Abstract:

Considering the problems that quantitative analysis and optimization of the geometrical model of scroll compressor created from involute of circle with variable radii are incomplete, the changing trend of the working chamber volume from the beginning of the suction process to the end of the discharge process is given. The volume calculation differences of Green’s theorem method, the graphical method, and the normal isometric method are compared, the reasons for calculation errors are analyzed, and the correctness of the geometrical model is verified. The calculation formula of teeth area utilization rate is deduced, and the sensitivity models of suction volume and teeth area utilization rate are constructed. It is concluded that the influence of the base circle radius variation coefficient and the occurrence angle of the inner profile are particularly significant. A multi-objective optimization analysis model considering nonlinear constraints and taking the suction volume and teeth area utilization rate as the optimization goals is established. The results show that the multi-objective genetic algorithm NSGA-II has a better comprehensive performance than the multi-objective particle swarm algorithm MOPSO and the suction volume of the scroll compressor created from the involute of circle with variable radii for an automobile air conditioner has been increased by 6.5% and the teeth area utilization rate has been reduced by 4.27%. This paper can provide further theoretical reference for the optimal design and quantitative research of the scroll compressor constructed from involute of circle with variable radii.

Key words: scroll compressor, involute of circle with variable radii, geometrical model, multi-objective optimization, algorithm comparison

中图分类号:

TH455

彭斌, 刘慧鑫, 陶耀辉. 基于变径基圆渐开线涡旋压缩机的几何模型及优化研究[J]. 上海交通大学学报, 2023, 57(8): 1046-1054.

PENG Bin, LIU Huixin, TAO Yaohui. Geometrical Model and Optimization of Scroll Compressor Based on Involute of Circle with Variable Radii[J]. Journal of Shanghai Jiao Tong University, 2023, 57(8): 1046-1054.

图/表 12

表1

图1

图2

图3

表2

图4

图5

图6

图7

图8

表3

表4

参考文献 22

[1]	刘振全. 涡旋式流体机械与涡旋压缩机[M]. 北京: 机械工业出版社, 2009.
	LIU Zhenquan. The scroll type fluid machinery and scroll compressor[M]. Beijing: China Machine Press, 2009.
[2]	彭斌, 赵生显, 李要红. 新型无油涡旋压缩机性能[J]. 中国机械工程, 2018, 29(24): 2917-2924.
	PENG Bin, ZHAO Shengxian, LI Yaohong. Performances of new oil-free scroll compressors[J]. China Mechanical Engineering, 2018, 29(24): 2917-2924.
[3]	LIU Y G, HUNG C H, CHANG Y C. Study on involute of circle with variable radii in a scroll compressor[J]. Mechanism and Machine Theory, 2010, 45(11): 1520-1536. doi: 10.1016/j.mechmachtheory.2010.07.001 URL
[4]	LIU Y G, TANG Y H, CHANG Y H, et al. Optimum design of scroll profiles created from involute of circle with variable radii by using finite element analysis[J]. Mechanism and Machine Theory, 2012, 55: 1-17. doi: 10.1016/j.mechmachtheory.2012.04.002 URL
[5]	田亚永. 变径基圆渐开线涡旋型线的分析[D]. 兰州: 兰州理工大学, 2011.
	TIAN Yayong. Study on involute of variable circle radii in scroll compressor[D]. Lanzhou: Lanzhou University of Technology, 2011.
[6]	丁佳男, 张英莉, 岳向吉, 等. 涡旋压缩机的变基圆型线研究[J]. 东北大学学报(自然科学版), 2019, 40(05): 722-727.
	DING Jianan, ZHANG Yingli, YUE Xiangji, et al. Study on the circular profile of scroll compressors with changing radii[J]. Journal of Northeastern University (Natural Science), 2019, 40(05): 722-727.
[7]	王吉岱, 张臻臻, 魏军英. 变基圆半径渐开线涡旋膨胀机的研究[J]. 流体机械, 2014, 42(6): 33-36.
	WANG Jidai, ZHANG Zhenzhen, WEI Junying. Research of the scroll expander with variable base circle radius involute[J]. Fluid Machinery, 2014, 42(6): 33-36.
[8]	唐景春, 贾卿晨, 李晨凯. 变基圆半径渐开线涡旋齿形的修正[J]. 低温与超导, 2017, 45(2): 68-72.
	TANG Jingchun, JIA Qingchen, LI Chenkai. The modification on scroll wrap with involutes of variable radii[J]. Cryogenics & Superconductivity, 2017, 45(2): 68-72.
[9]	陈进, 张永栋, 宋立权, 等. 基于多目标遗传算法的涡旋型线形状优化[J]. 机械工程学报, 2005(1): 172-175.
	CHENG Jin, ZHANG Yongdong, SONG Liquan, et al. Profile optimization of scrolls based on multi-objective genetic algorithm[J]. Journal of Mechanical Engineering, 2005(1): 172-175.
[10]	彭斌, 蒋龙. 涡旋型线齿头修正的参数分析优化[J]. 华中科技大学学报(自然科学版), 2020, 48(9): 107-112.
	PENG Bin, JIANG Long. Parameter analysis and optimization of modification of tooth head of scroll profile[J]. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2020, 48(9): 107-112.
[11]	PENG B, LIU Z Q, ZHANG H S, et al. Scroll plate optimization based on improved genetic-particle swarm optimization algorithm[C]//2006 6th World Congress on Intelligent Control and Automation. Dalian, China: IEEE, 2006, 1: 3681-3685.
[12]	刘涛, 赵睿琦, 孙永吉. 基于自适应NSGA-II 算法的变截面涡旋盘优化[J]. 华中科技大学学报(自然科学版), 2021, 49(3): 63-68.
	LIU Tao, ZHAO Ruiqi, SUN Yongji. Optimization of variable cross-section scroll based on self-adaptive NSGA-II algorithm[J]. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2021, 49(3): 63-68.
[13]	彭斌, 蒋龙, 王永强. 变基圆半径涡旋膨胀机型线参数的优化选取[J]. 工程设计学报, 2020, 27(4): 463-468.
	PENG Bin, JIANG Long, WANG Yongqiang. Optimal selection of profile parameters of variable base circle radius vortex expander[J]. Chinese Journal of Engineering Design, 2020, 27(4): 463-468.
[14]	李雪琴, 王君. 涡旋压缩机的变径基圆渐开线型线研究[J]. 压缩机技术, 2011(4): 1-3.
	LI Xueqin, WANG Jun. Investigation of profile base circle involute with changing radius in scroll compressor[J]. Compressor Technology, 2011(4): 1-3.
[15]	DING J N, YUE X J, ZHANG Y L, et al. Accurate calculations of working chamber volume constructed from involute of variable radii circle with double arcs modification in a scroll type compressor[J]. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 2021, 235(5): 1652-1664. doi: 10.1177/09544089211013661 URL
[16]	BELL I H, GROLL E A, BRAUN J E, et al. Comprehensive analytic solutions for the geometry of symmetric constant-wall-thickness scroll machines[J]. International Journal of Refrigeration, 2014, 45: 223-242. doi: 10.1016/j.ijrefrig.2014.05.029 URL
[17]	王俊亭. 风冷无油涡旋空气压缩机热力学及涡盘变形研究[D]. 南昌: 南昌大学, 2014.
	WANG Junting. Research on thermodynamics and the scroll plate deformation of wind-cooling oil-free scroll air compressor[D]. Nanchang: Nanchang University, 2014.
[18]	贾卿晨. 涡旋压缩机变齿宽结构优化研究[D]. 合肥: 合肥工业大学, 2017.
	JIA Qingchen. Optimization study on scroll wrap with involutes of variable radii[D]. Hefei: Hefei University of Technology, 2017.
[19]	郝胜利, 马国远, 许树学, 等. 电动车空调用变壁厚涡旋压缩机的性能研究[J]. 流体机械, 2020, 48(4): 24-28. doi: 10.3969/j.issn.1005-0329.2020.04.005
	HAO Shengli, MA Guoyuan, XU Shuxue, et al. Research on performance of variable wall thickness scroll compressors for electric vehicle air conditioning[J]. Fluid Machinery, 2020, 48(4): 24-28. doi: 10.3969/j.issn.1005-0329.2020.04.005
[20]	张朋成, 彭斌, 张宇波. 圆渐开线变截面涡旋压缩机几何性能综合分析[J]. 机械工程学报, 2020, 56(23): 118-128. doi: 10.3901/JME.2020.23.118
	ZHANG Pengcheng, PENG Bin, ZHANG Yubo. Comprehensive analysis of geometric performance of circular involute variable thickness scroll compressor[J]. Journal of Mechanical Engineering, 2020, 56(23): 118-128. doi: 10.3901/JME.2020.23.118
[21]	侯才生, 刘涛. 基于Frenet标架的变截面涡旋型线构建与性能研究[J]. 上海交通大学学报, 2019, 53(12): 1495-1501.
	HOU Caisheng, LIU Tao. Construction and performance investigation of variable-cross section scroll profiles based on Frenet Frame[J]. Journal of Shanghai Jiao Tong University, 2019, 53(12): 1495-1501.
[22]	TIAN Y, CHENG R, ZHANG X Y. PlatEMO: A MATLAB platform for evolutionary multi-objective optimization[J]. IEEE Computational Intelligence Magazine, 2017, 12(4): 73-87.

参数	符号	取值
初始基圆半径	a₀/mm	3.675
基圆半径变化系数	δ₀/(mm·rad^-1)	-0.05
离散的多方指数	δ₁	1
回转半径	R_ob/mm	4.361 7
内侧型线发生角	α_in/rad	1.430 44
外侧型线发生角	α_ou/rad	0
内外侧型线展角	φ_in, φ_ou/rad	—
修正展角	Φ/rad	0.6π
终端渐开线展角	φ_e/rad	6π

计算方法	几何参数1	几何参数2^[18]	几何参数3^[19]
格林定理法	1 811.997 3	734.712 3	953.449 2
图解法	1 811.910 0	734.660 0	953.440 0
法向等距法	1 813.995 9	735.243 6	954.670 3

算法名称	种群大小	迭代次数	T/s	HV	IGD
NSGA-II	200	800	4.81	0.712 4	0.008 032
MOPSO	200	800	5.19	0	3.888 300

名称	δ₀	α_in/rad	V_s×10⁵/m³	ζ	ε
优化前	-0.020 0	1.317 8	2.316	0.276 7	4.315 6
优化型	-0.014 3	1.222 0	2.477	0.264 9	4.343 6