利用代数-阿基米德双螺线构建变截面涡旋齿组合型线

doi:10.16183/j.cnki.jsjtu.2022.532

上海交通大学学报 ›› 2024, Vol. 58 ›› Issue (8): 1282-1289.doi: 10.16183/j.cnki.jsjtu.2022.532

利用代数-阿基米德双螺线构建变截面涡旋齿组合型线

闫敏, 刘涛(), 麻德权, 党旭

兰州理工大学机电工程学院, 兰州 730050

收稿日期:2022-12-26 修回日期:2023-02-09 接受日期:2023-02-15 出版日期:2024-08-28 发布日期:2024-08-27
通讯作者: 刘涛,教授,博士生导师,电话(Tel.):0939-2973860;E-mail:liutao1971@lut.edu.cn.
作者简介:闫敏(1996-),博士生,从事涡旋机械复杂型面的设计研究.
基金资助:
国家自然科学基金(52265034)

Construction of Combined Variable-Section Scroll Tooth Profiles Using Algebraic-Archimedes Double Spiral

YAN Min, LIU Tao(), MA Dequan, DANG Xu

School of Mechanical and Electrical Engineering, Lanzhou University of Technology, Lanzhou 730050, China

Received:2022-12-26 Revised:2023-02-09 Accepted:2023-02-15 Online:2024-08-28 Published:2024-08-27

摘要/Abstract

摘要：

变截面涡旋机械组合型线由于不同类型曲线采用不同的模型参数,型线的数学模型较为复杂且连接条件不易通过显性计算获得.针对上述问题,提出由代数螺线-阿基米德螺线双螺线组合的新型涡旋型线.首先,基于共轭啮合理论求解螺线类涡旋型线曲线极角与主轴转角之间的关系,推导出螺线类涡旋型线的归一化数学方程.其次,根据组合型线的光滑连接条件建立双螺线涡旋型线连接点的约束方程,得到两类双螺线涡旋型线的几何模型.然后,定量分析了第一类双螺线组合型线参数(螺线指数、螺线系数和连接点极角)对涡旋齿几何性能的影响.最后,对比研究了双螺线组合涡旋型线的性能优势.结果表明:第一类双螺线组合型线几何表征简洁、无需进行齿头型线修正即可直接使用;在涡旋齿径向尺寸相同条件下,与传统圆渐开线涡旋齿相比,行程容积提升了7.61%,压缩比提升了27.42%,面积利用系数提升了7.61%.

关键词: 阿基米德螺线, 代数螺线, 螺线类涡旋型线, 双螺线组合型线, 变截面涡旋齿, 涡旋压缩机

Abstract:

The mathematical model of the profile is complicated and the connection conditions are not easily obtained by explicit calculation because different model parameters are used for different types of curves. To address the above problems, a new scroll profile is proposed by double spiral which is the combination of algebraic spiral and Archimedes spiral. First, based on the conjugate mesh theory, the relationship between the spindle angle and the pole angle of the curve is solved to derive the normalized mathematical model of the scroll line of the spiral type. Then, based on the smooth connection conditions of the combined profiles, the constraint equations of the connection points of the double spiral scroll profiles are established, and the geometric models of the two types of double spiral scroll profiles are obtained. Afterwards, the effects of the parameters of the first type of double spiral combined profile (spiral index, spiral coefficient, and pole angle of the connection point) on the geometric performance of the scroll teeth are quantitatively analyzed. Finally, the performance advantages of the two-screw combination scroll profile are comparatively studied. The results show that the geometry of the first type of double spiral combined profile is simple and can be directly used in production without head profile correction. The stroke volume is increased by 7.61%, the compression ratio is increased by 27.42%, and the area utilization factor is increased by 7.61% compared with the conventional circular involute scroll teeth at the same radial dimension of scroll teeth.

Key words: Archimedes spiral, algebraic spiral, spiral type scroll profile, double spiral combination profile, variable section scroll wraps, scroll compressor

中图分类号:

TH455

闫敏, 刘涛, 麻德权, 党旭. 利用代数-阿基米德双螺线构建变截面涡旋齿组合型线[J]. 上海交通大学学报, 2024, 58(8): 1282-1289.

YAN Min, LIU Tao, MA Dequan, DANG Xu. Construction of Combined Variable-Section Scroll Tooth Profiles Using Algebraic-Archimedes Double Spiral[J]. Journal of Shanghai Jiao Tong University, 2024, 58(8): 1282-1289.

图/表 12

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参数	第一类	第二类
a/mm	4π	-2π
b	2.87	2.15
t_c	3.25π	3.25π
c	8.24	0.61
k	0.7	1.4
R_or /mm	4	4
t_max	6π	6π

型线类型	型线参数				性能指标
型线类型	型线参数				V_s/mm³	V_d/mm³	ν	ε
圆渐开线	g=2.14 mm	α=0.2π	γ=0.48	λ=2.49	35 840.779	6 655.165	7.416	0.285 2
组合型线	a=7.3 mm	b=1.81	c=5.06	k=0.7	38 566.534	5 842.032	9.449	0.306 9
Δ/%	-	-	-	-	7.61	13.92	27.42	7.61

利用代数-阿基米德双螺线构建变截面涡旋齿组合型线

Construction of Combined Variable-Section Scroll Tooth Profiles Using Algebraic-Archimedes Double Spiral

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