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

摘要/Abstract

摘要：

根据圆渐开线的性质，提出一种由不同圆渐开线组合的新型变截面涡旋齿的建立方法。详细论述了型线的生成方法，阐述了建立基线的基本条件，推导出型线的一般方程，给出2种计算容积的方法，讨论正确生成内、外壁型线的控制变量取值范围。根据不同要求可快速建立一系列圆渐开线变截面涡旋齿的几何模型，为变截面涡旋齿型线的研究拓宽了思路。研究结果表明：相比传统的变截面涡旋齿几何模型的建立方法，提出的新型变截面涡旋齿的建立方法不但具有传统变截面涡旋齿的优点，而且减少了建立变截面涡旋齿的计算量，在一定程度上降低了变截面涡旋齿的加工难度，扩大了变截面涡旋压缩机或膨胀机的实际应用。

关键词: 机械设计, 圆渐开线, 涡旋齿, 变截面, 几何模型, 涡旋压缩机, 涡旋膨胀机

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

中图分类号:

TH45

张朋成,彭斌,张宇波. 基于圆渐开线建立变截面涡旋齿的方法与理论[J]. 吉林大学学报(工学版), 2022, 52(4): 789-798.

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.

图/表 13

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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）