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

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Abstract

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.

Original languageEnglish
Pages (from-to)343-351
Number of pages9
JournalProceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
Volume216
Issue number3
DOIs
Publication statusPublished - 2002 Jan 1

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Compressors
Rotors
Mathematical models
Machining

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering

Cite this

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title = "A mathematical model of the rotor profile of the single-screw compressor",
abstract = "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.",
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N2 - 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.

AB - 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.

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