A mathematical model of the rotor profile of the single-screw compressor

2002 ◽  
Vol 216 (3) ◽  
pp. 343-351 ◽  
Author(s):  
S-C Yang
Keyword(s):  
Mathematical Model ◽  
Parameter Family ◽  
Cutting Edge ◽  
Screw Compressor ◽  
Single Screw ◽  
Rotor Profile ◽  
The Family ◽  
Screw Rotor ◽  
The One ◽  
Screw Rotors

This paper presents a method for determining the basic profile of a single-screw compressor including a gate rotor and a screw rotor. The inverse envelope concept for determining the cutting-edge curve of the gate rotor is presented. Based on this concept, the required cutter for machining the screw rotor can be obtained by an envelope of the one-parameter family of obtained screw rotors. The obtained screw rotor is an envelope of the family of gate rotor surfaces. Let the obtained envelope of the one-parameter family of gate rotor surfaces become the generating surface. The inverse envelope can be used to obtain the envelope of the family of generating surfaces. Then, the profile of the gate rotor with the cutting-edge curve can be easily obtained. The proposed method shows that the gate rotor and the screw rotor are engaged along the contact line at every instant. This is essential to reduce the effect of leakage on compressor performance. In this paper, a mathematical model of the meshing principle of the screw rotor with the gate rotor is established. As an example, the single-screw compressor for a compressor ratio of 11:6 is determined with the aid of the proposed mathematical model. Results from these mathematical models should have applications in the design of single-screw compressors.

A mathematical model of a cc-type single-screw compressor

2004 ◽  
Vol 218 (4) ◽  
pp. 437-448 ◽  
Author(s):  
S-C Yang
Keyword(s):  
Mathematical Model ◽  
Cutting Edge ◽  
Screw Compressor ◽  
Contact Lines ◽  
Full Size ◽  
Single Screw ◽  
The Family ◽  
Screw Rotor ◽  
Design And Manufacture ◽  
Further Development

In this paper, a method is proposed for determining a basic profile of a cc-type single-screw compressor including the gate rotor and the screw rotor. The cc-type has a cylindrical screw and two cylindrical gate rotors. Based on this method, a mathematical model of the meshing principles of a cc-type screw rotor meshed with a gate rotor, that has either straight edge teeth or conical teeth, is presented. The inverse envelope concept is used to determine the cutting-edge curve of a gate rotor. Based on this concept, the required cutter for machining a cc-type screw rotor can be obtained by the envelope of a one-parameter family. The obtained screw rotor is an envelope to the family of the gate rotor's surfaces. The obtained envelope becomes the generating surface. The inverse envelope can be used to obtain the envelope to the family of generating surfaces. Then the profile of a gate rotor cutting-edge curve can be easily obtained. The surface analysis including contact lines is shown for the design and manufacture of a screw compressor. As an example, the cc-type single-screw compressor with a compressor ratio of 11:6 was determined with the aid of the proposed mathematical model. Using rapid prototyping (RP) and manufacturing technology, a cc-type single-screw rotor with a gate rotor was designed. The RP primitives provide an actual full-size physical model that can be analysed and used for further development. Results from these mathematical models should have applications in the design of cc-type single-screw compressors.

MODELING AND MANUFACTURING OF PP-TYPE SINGLE SCREW COMPRESSOR

2007 ◽  
Vol 31 (2) ◽  
pp. 219-234 ◽  
Author(s):  
Yang Shyue-Cheng ◽  
Tsang-Lang Liang
Keyword(s):  
Mathematical Model ◽  
Stress Analysis ◽  
Surface Analysis ◽  
Compression Ratio ◽  
Geometric Model ◽  
Screw Compressor ◽  
Generation Process ◽  
Single Screw ◽  
Screw Rotor ◽  
Design And Manufacture

A geometric model and a mathematical model of a PP-type single screw rotor with planar gate rotor are derived from the gate-rotor generation process and gear theory. The teeth of gate rotor are planar. Based on the inverse envelope concept, the cutter required for machining the single screw rotor can be obtained using an inverse envelope of a one-parameter family of screw surfaces. The surface of the proposed screw rotor is analyzed using the developed mathematical model. A surface analysis, including stress analysis, of the design and manufacture of the screw compressor is presented. Finally, a numerical example demonstrates the geometric model of the PP-type single screw rotor with a compression ratio of 11:6.

STUDY OF A SINGLE SCREW COMPRESSOR WITH A CONICAL TEETH GATE ROTOR

2008 ◽  
Vol 32 (3-4) ◽  
pp. 333-352
Author(s):  
Yang Shyue-Cheng ◽  
Tsang-Lang Liang
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Software Package ◽  
Analytical Procedure ◽  
Conjugate Problem ◽  
Screw Compressor ◽  
Main Rotor ◽  
Conjugate Pair ◽  
Single Screw ◽  
Envelope Theory

From a geometric viewpoint, a mathematical model of a single screw compressor with a conjugate pair of meshing conical teeth gate rotor is a conjugate problem. Coordinate transformation and envelope theory are applied to determine the sets of spatial points of the contacting surfaces that define the main rotor of a single screw compressor. Envelope theory and analytical procedure are used to derive mathematical models of a gate rotor and a main rotor. Stress analysis for the single screw compressor mechanism is performed. PowerMILL software package is used to simulate the manufacture of a main rotor. A numerical example with a compressor ratio of 11:6 is presented to demonstrate the application of the mathematical models developed in this paper.

Research on Processing Technology and Cutting Parameter of the Spiral Surface of Screw Rotor

2011 ◽  
Vol 314-316 ◽  
pp. 543-546
Author(s):  
Xing Wei Sun ◽  
Guang Lv ◽  
Ke Wang
Keyword(s):  
Cutting Parameters ◽  
Element Model ◽  
Milling Process ◽  
Screw Compressor ◽  
Processing Quality ◽  
Excellent Performance ◽  
Single Screw ◽  
Screw Rotor ◽  
Spiral Surface ◽  
The Finite Element Model

The key components of the single screw compressor are rotor screw and two star-wheels which are symmetrical arrangement. The rotor screw and two star-wheels have composed a special spatial meshing pair. The high meshed precision is the guarantee of its excellent performance. In this paper, we will study the milling technology of screw milling cutter to the rotor screw, and establish the finite element model of the cutter, and analyze the cutter’s stress situation during the milling process, make the cutting parameters of the screw optimization, In this paper, we will also study the influence of the Milling depth and cutting width to tool in displacement and stress, in order to provide a theoretical reference of selecting of appropriate cutting parameters ,improving of processing quality and reducing wear of the tool.

Geometric Design Investigation of Single Screw Compressor Rotor Grooves Produced by Cylindrical Milling

2009 ◽  
Vol 131 (7) ◽  
Author(s):  
Weifeng Wu ◽  
Quanke Feng ◽  
Xiaoling Yu
Keyword(s):  
Mathematical Simulation ◽  
Surface Profile ◽  
Geometric Design ◽  
Screw Compressor ◽  
Machining Efficiency ◽  
Gas Leakage ◽  
Single Screw ◽  
Compressor Rotor ◽  
Compressed Gas ◽  
Screw Rotor

Cylindrical milling of a screw rotor groove in a single screw compressor has higher machining efficiency than turning. However, the screw groove bottom produced by the flat end of the milling cutter fails to mesh hermetically with the flat tooth tip due to the oversized clearance between them. The clearance forms two leakage paths leading to a compressed gas leakage. The shape of the path is roughly the same as that of two parallel oblate divergent nozzles in an inverse orientation. A mathematical simulation is presented for the surface profile of the screw groove bottom for a single screw compressor generated using several cylindrical milling cutters. The results contribute to improving the design of the meshing pairs in the single screw compressor.

scholarly journals Study on screw rotor thermal machining method of single screw compressor

2021 ◽  
Vol 1180 (1) ◽  
pp. 012011
Author(s):  
S Y Wang ◽  
Z L Wang ◽  
H W Shi ◽  
Z M Wang ◽  
M M Hao ◽  
...  
Keyword(s):  
Screw Compressor ◽  
Single Screw ◽  
Screw Rotor

scholarly journals Mating quadratic maps with the modular group II

2019 ◽  
Vol 220 (1) ◽  
pp. 185-210
Author(s):  
Shaun Bullett ◽  
Luna Lomonaco
Keyword(s):  
Modular Group ◽  
Parameter Family ◽  
Quadratic Polynomial ◽  
Complex Parameter ◽  
Rational Maps ◽  
Quadratic Maps ◽  
The Family ◽  
The One ◽  
Holomorphic Correspondences ◽  
Connectedness Locus

Abstract In 1994 S. Bullett and C. Penrose introduced the one complex parameter family of (2 : 2) holomorphic correspondences $$\mathcal {F}_a$$Fa: $$\begin{aligned} \left( \frac{aw-1}{w-1}\right) ^2+\left( \frac{aw-1}{w-1}\right) \left( \frac{az+1}{z+1}\right) +\left( \frac{az+1}{z+1}\right) ^2=3 \end{aligned}$$aw-1w-12+aw-1w-1az+1z+1+az+1z+12=3and proved that for every value of $$a \in [4,7] \subset \mathbb {R}$$a∈[4,7]⊂R the correspondence $$\mathcal {F}_a$$Fa is a mating between a quadratic polynomial $$Q_c(z)=z^2+c,\,\,c \in \mathbb {R}$$Qc(z)=z2+c,c∈R, and the modular group $$\varGamma =PSL(2,\mathbb {Z})$$Γ=PSL(2,Z). They conjectured that this is the case for every member of the family $$\mathcal {F}_a$$Fa which has a in the connectedness locus. We show here that matings between the modular group and rational maps in the parabolic quadratic family $$Per_1(1)$$Per1(1) provide a better model: we prove that every member of the family $$\mathcal {F}_a$$Fa which has a in the connectedness locus is such a mating.

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