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

doi:10.16183/j.cnki.jsjtu.2022.532

Abstract

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

CLC Number:

TH455

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.

Figures/Tables 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