基于圆渐开线建立变截面涡旋齿的方法与理论

doi:10.13229/j.cnki.jdxbgxb20200881

Abstract

Abstract:

According to the nature of the circle involute， a new method of variable thickness scroll composed of different circle involutes is proposed. The method of generating the profile is discussed in detail. The basic conditions for establishing the baseline are expounded. The general equations of the profile are derived. Two methods for calculating the volume are given. The range of control variables for correctly generating the inner and outer profiles is discussed. According to different requirements， a series of geometric models of circle involute variable thickness scroll can be quickly established， which broadens the research on variable thickness profile. The results show that， compared with the traditional method of establishing the variable thickness scroll geometry model， the new method not only has the advantages of traditional variable thickness scroll， but also reduces the calculation of establishing variable cross-section scroll， reduces the machining difficulty of variable cross-section scroll to a certain extent， and expands the practical application of variable thickness scroll compress or expander.

Key words: mechanic design, circle involute, scroll, variable thickness, geometric model, scroll compressor, scroll expander

CLC Number:

TH45

Peng-cheng ZHANG,Bin PENG,Yu-bo ZHANG. Method and theory of establishing variable thickness scrolls based on circle involute[J].Journal of Jilin University(Engineering and Technology Edition), 2022, 52(4): 789-798.

Figures/Tables 13

Table 1

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Table 2

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Table 3

References 23

1	Peng B, Zhu B G, Vincent L. Theoretical and experimental analysis of scroll expander[C]∥The 23rd International Compressor Engineering Conference at Purdue, West Lafayette, Indiana, USA, 2016: 1-12.
2	王怀信, 王大彪, 张圣君. 低温有机朗肯循环系统参数的理论与实验优化[J]. 天津大学学报, 2014, 47(5): 408-413.
	Wang Huai-xin, Wang Da-biao, Zhang Sheng-jun. Theoretical and experimental optimization of low-temperature organic rankine cycle system parameters[J]. Journal of Tianjin University, 2014, 47(5): 408-413.
3	陈进, 王立存, 李世六. 通用涡旋型线理论研究与深入分析[J]. 机械工程学报, 2006, 42(5): 11-15.
	Chen Jin, Wang Lin-cun, Li Shi-liu. Study and profound analysis on general profile theory of scrolls[J]. Journal of Mechanical Engineering, 2006, 42(5): 11-15.
4	王立存, 李世六, 明勇, 等. 涡旋压缩机型线耦合机理动态性研究[J]. 哈尔滨工业大学学报, 2009, 41(7):187-189.
	Wang Li-cun, Li Shi-liu, Ming Yong, et al. Dynamics of joggling principle for scroll profiles of scroll compressor[J]. Journal of Harbin Institute of Technology, 2009, 41(7): 187-189.
5	彭斌, 李要红, 赵生显. 涡旋膨胀机的性能模拟[J].中国机械工程, 2018, 29(8):965-970, 978.
	Peng Bin, Li Yao-hong, Zhao Sheng-xian. Performance simulation for scroll expanders[J]. China Mechanical Engineering, 2018, 29(8): 965-970, 978.
6	Shaffer B R, Groll E A. Variable wall thickness scroll geometry modeling with use of a control volume approach[J]. International Journal of Refrigeration, 2013, 36(7): 1809-1820.
7	Bell I. Theoretical and experimental analysis of liquid flooded compression in scroll compressors[D]. West Lafayette: Purdue University, 2011.
8	Morishita E, Sugihara M, Inabat T, et al. Scroll compressor analytical model[C]∥Proceedings of International Compressor Engineering Conference 1984. Purdue University, West Lafayette, Indiana, USA, 1984:487-495.
9	李连生. 线段渐开线涡旋压缩机的几何理论[J] .流体机械, 1994, 22(12): 22-28.
	Li Lian-sheng. Geometric theory of line involute scroll compressor[J]. Fluid Machinery, 1994, 22(12): 22-28.
10	李雪琴, 王君. 一种涡旋压缩机的圆弧线段等壁厚组合型线[J] .流体机械, 2010, 38(8): 27-30.
	Li Xue-qin, Wang Jun. A novel combined profile of arc and line segment for scroll compressor[J]. Fluid Machinery, 2010, 38(8): 27-30.
11	王君, 官华, 戴克文. 多涡旋齿圆渐开线和圆弧组合型线构建[J] .流体机械, 2008, 36(5): 14-17, 29.
	Wang Jun, Guan Hua, Dai Ke-wen. Construction of involute and arc combination profile for multi-wrap scroll compressor[J]. Fluid Machinery, 2008, 36(5): 14-17, 29.
12	彭斌, 孙迎. 变截面涡旋压缩机数学模型及试验研究[J].机械工程学报, 2015, 51(14): 185-191.
	Peng Bin, Sun Ying. Investigation of mathematical modeling and experiment for variable thickness scroll compressor [J]. Journal of Mechanical Engineering, 2015, 51(14): 185-191.
13	彭斌, 张朋成. 一种变截面涡旋膨胀机的几何模型及容积变化[J].机械设计与制造, 2019, 56(6): 5-8.
	Peng Bin, Zhang Peng-cheng. Geometric model and volume change of a variable cross section scroll expander[J]. Machinery Design＆Manufacture, 2019, 56(6): 5-8.
14	孙永吉, 刘涛. 涡旋压缩机复杂变截面涡旋型线高速加工研究[J].现代制造工程, 2017, 39(7): 25-30.
	Sun Yong-ji, Liu Tao. Research on high speed machining complex scroll profiles of scroll compressor[J]. Modern Manufacturing Engineering, 2017, 39(7): 25-30.
15	李新, 何传江. 矩阵理论及其应用[M]. 重庆: 重庆大学出版社, 2005.
16	刘涛, 邬再新, 刘振全. 法向等距线法生成涡旋压缩机型线的研究[J]. 机械工程学报, 2004, 40(6): 55-58.
	Liu Tao, Wu Zai-xin, Liu Zhen-quan. Study on generating profile with nomal-equidistant-curve method for scroll compressor[J]. Journal of Mechanical Engineering, 2004, 40(6): 55-58.
17	孙迎. 变截面涡旋压缩机数学模型的研究[D]. 兰州: 兰州理工大学温州泵阀工程研究院, 2012.
	Sun Ying. Research on the mathematical modeling of variable thickness scroll compressor[D]. Lanzhou: Wenzhou Pump and Valve Engineering Research Institute, Lanzhou University of Technology, 2012.
18	王君, 刘振全. 涡旋压缩机渐开线类型线的双圆弧修正[J]. 机械工程学报, 2005, 41(9): 202-206.
	Wang Jun, Liu Zhen-quan. Double circle arc of involute type wrape of scroll compressor[J]. Journal of Mechanical Engineering, 2005, 41(9): 202-206.
19	Peng B, Lemort V, Legros A, et al. Variable thickness scroll compressor performance analysis-Part I: geometric and thermodynamic modelling[J]. Proceedings of the Institution of Mechanical Engineering, 2016, 231 (4): 633-640.
20	王国梁. 基于对称圆弧修正的单元组合型线涡旋压缩机特性研究[J]. 机械工程学报, 2011, 47(16): 139-142.
	Wang Guo-liang. Investigation of wrap profile modification based on symmetric arc shaped curves for the scroll compressor with unit combined profile[J]. Journal of Mechanical Engineering, 2011, 47(16): 139-142.
21	王珺. 等距曲线的有理逼近新方法[D]. 合肥: 合肥工业大学巢湖学院数学系, 2009.
	Wang Jun. New algorithms for rational approximation of offset curves[D]. Hefei: Department of Mathematics, Chaohu College, Hefei University of Technology, 2009.
22	李国龙, 任唯贤, 谢天明, 等. 求解共轭齿形的轮转曲线等距偏移法[J].重庆大学学报, 2019, 42(5): 10-18.
	Li Guo-long, Ren Wei-xian, Xie Tian-ming, et al. An equidistant offset algorithm of rotation curve to solve conjugate gear profile[J]. Journal of Chongqing University, 2019, 42(5): 10-18.
23	梁栋. 共轭曲线齿轮啮合理论研究[D]. 重庆: 重庆大学机械传动国家重点实验室, 2015.
	Liang Dong. Research on meshing theory of conjugate-curve gear transmission[D]. Chongqing: State Key Laboratory of Mechanical Transmission, Chongqing University, 2015.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed

Comments

Recommended 0

No Suggested Reading articles found!

变量θ	差值X^'₂-X₁	差值Y^'₂-Y₁
0.7π	10	18.85
0.75π	10	15.71
0.8π	10	12.57
0.85π	10	9.42
0.9π	10	6.28
0.95π	10	3.14
π	10	0
1.05π	10	-3.14
1.1π	10	-6.28
1.15π	10	-9.42
1.2π	10	-12.57
1.25π	10	-15.71
1.3π	10	-18.85

R₁	R₂	n₁	n₂	φ₁	φ₂	θ_M	R_or
R₁	2R₁	2	1	φ₁	φ₁/2	φ₁/2	（0， πR₁）
R₁	3R₁	3	1	φ₁	φ₁/3	2φ₁/3	（0， πR₁）
R₁	3R₁/2	3	2	φ₁	2φ₁/3	φ₁/3	（0， πR₁）
R₁	4R₁	4	1	φ₁	φ₁/4	3φ₁/4	（0， πR₁）
R₁	2R₁	4	2	φ₁	φ₁/2	φ₁/2	（0， πR₁）
R₁	4R₁/3	4	3	φ₁	3φ₁/4	φ₁/4	（0， πR₁）
R₁	5R₁	5	1	φ₁	φ₁/5	4φ₁/5	（0， πR₁）
R₁	5R₁/2	5	2	φ₁	2φ₁/5	3φ₁/5	（0， πR₁）
R₁	5R₁/3	5	3	φ₁	3φ₁/5	2φ₁/5	（0， πR₁）
R₁	5R₁/4	5	4	φ₁	4φ₁/5	φ₁/5	（0， πR₁）

[1]	Cai-sheng HOU,Tao LIU,Li-xian GUO. Construction theories of a new type of variable wall thickness scroll profile [J]. Journal of Jilin University(Engineering and Technology Edition), 2020, 50(5): 1627-1634.
[2]	Yan-qin ZHANG,Ya-nan FENG,Peng-rui KONG,Xiao-dong YU,Xiang-bin KONG. Temperature field and experiment of hydrostatic bearing oil film based on hot oil carrying [J]. Journal of Jilin University(Engineering and Technology Edition), 2019, 49(4): 1203-1211.

Method and theory of establishing variable thickness scrolls based on circle involute

RICH HTML

PDF (PC)

Abstract

Cite this article

share this article

Figures/Tables 13

References 23

Related Articles 2

Metrics

Comments

Recommended 0