变截面涡旋压缩机数学模型的研究
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摘要
涡旋压缩机是一种新型高效的流体机械，具有节能、高效、可靠的特点。目前已在制冷、空调、各种气体压缩、发动机增压以及增压泵等领域得到广泛应用，有着广阔的应用前景和市场。目前国内外的研究主要集中于圆渐开线的等截面涡旋压缩机，压缩比通常较小，如果增大压缩比则需要增加渐开线的圈数，圈数增加会引起型线加工困难、气体在腔体内停留时间过长而导致涡旋盘整体温度过高、整机尺寸过大等诸多问题。而采用新型等距组合型线的变截面涡旋压缩机则可以采用很少的圈数就实现高压比。
本文构建了一种以渐开线和高次曲线为基线的新型组合型线，以较少的圈数实现了涡旋压缩机的高压比。提出了变截面涡旋压缩机的数学模型，通过对数学模型的详细研究得到了整机的性能特点。
论文基于微分几何学的共轭曲线啮合原理，建立了变截面涡旋齿基线，进而生成了变截面内外壁型线，再进行了双圆弧修正，然后根据基线法原理进行了相应的容积计算；通过对变截面涡旋压缩机气体力（轴向力、径向力和切向力）、力矩、动盘受力、曲轴受力和十字环受力的分析，建立了动力学模型的迭代方程组，采用Newton-Raphson数值方法进行了求解；在机械摩擦损失部分，主要研究了主轴承、曲柄销、止推轴承和十字环的损失模型，对机械效率和输入轴功进行了详细分析，通过与动力学模型的联立求解，获得了变截面涡旋压缩机的功率损失、机械效率和轴功的变化规律，这些规律经归纳总结，主要表现在：
1）主轴承的摩擦损失是影响机械效率的主要因素，在优化和实际生产中应予以重视；
2）机械效率因摩擦损失功的影响，随转速的升高而有一定的降低，但下降幅度平缓，说明此变截面涡旋压缩机运转具有可靠性。
通过对实验数据和数值计算结果的详细对比分析，验证了本文提出的变截面涡旋压缩机数学模型的正确性。
Scroll compressor is new and efficient fluid machinery with its advantages ofenergy-saving, efficiency, and reliability. At present, Scroll compressor has alreadybeen extending application in many kinds of fields, such as refrigeration,air-condition fields, gas compression, engine booster, and booster pumps, etc, anddestined for a broad application prospects and good future. Nowadays, the research onthe conventional same thickness scroll compressor has been the main aspects of study,both domestic and abroad, which has a relatively lower pressure ratio. The number ofturns must be added if the higher pressure ratio is to be wanted from the conventionalsame thickness scroll compressor, and problems must be followed with the addednumber of turns, such as, the added difficulty of vane production, the risingtemperature of the whole machine because of the long time stay of the compressedmass of gas, the bigger size and the heaver weight of the whole machine. However, allproblems will be solved if variable thickness scroll compressor with combinationprofile is been used instead of the conventional same thickness one.
A new type combination profile has been established in this thesis which is madeup of circle involute and high times curve. The high pressure ratio has been achievedwith the fewer number of turns. Mathematical model has been built with this kind ofscroll compressor and the performance of the whole plate has been analyzed anddiscussed.
The process of research in this thesis has been showed as follow. First, thebaseline of combination profile of variable thickness scroll compressor has beenfounded depend on conjugation theory of conjugacy curve in infinitesimal geometry,and combination profile has been created with twin-circular arc profile modification.Second, volume has been calculated depend on baseline principle. Third, equations ofdynamics has been built including gas forces, moment, force on the orbiting scroll,force on crank journal and force on Oldham ring, and been solved with the method ofNewton-Rophson. Fourth, mechanical frictional losses model has been createdincluding crank journal, crank pin, thrust bearing and Oldham ring. Mechanicalefficiency and available shaft work rate has been detailedly analyzed, too. The law ofchange in power consumptions, mechanical efficiency and available shaft work ratehas been get with the solving of the model. The law to sum-up mainly displays in:
1) The main bearing friction loss is the main factors of influencing mechanical efficiency and should attach importance in the optimization and actual production.
2) Mechanical efficiency has some fall with the rising speed because of frictionloss. But the fall is slow and shows that the variable thickness scroll compressor has areliable running.
Mathematical modeling of variable thickness scroll compressor has been provedcorrect in this thesis with the comparison and analysis about the result fromexperiment study and numerical analysis.
本文构建了一种以渐开线和高次曲线为基线的新型组合型线，以较少的圈数实现了涡旋压缩机的高压比。提出了变截面涡旋压缩机的数学模型，通过对数学模型的详细研究得到了整机的性能特点。
论文基于微分几何学的共轭曲线啮合原理，建立了变截面涡旋齿基线，进而生成了变截面内外壁型线，再进行了双圆弧修正，然后根据基线法原理进行了相应的容积计算；通过对变截面涡旋压缩机气体力（轴向力、径向力和切向力）、力矩、动盘受力、曲轴受力和十字环受力的分析，建立了动力学模型的迭代方程组，采用Newton-Raphson数值方法进行了求解；在机械摩擦损失部分，主要研究了主轴承、曲柄销、止推轴承和十字环的损失模型，对机械效率和输入轴功进行了详细分析，通过与动力学模型的联立求解，获得了变截面涡旋压缩机的功率损失、机械效率和轴功的变化规律，这些规律经归纳总结，主要表现在：
1）主轴承的摩擦损失是影响机械效率的主要因素，在优化和实际生产中应予以重视；
2）机械效率因摩擦损失功的影响，随转速的升高而有一定的降低，但下降幅度平缓，说明此变截面涡旋压缩机运转具有可靠性。
通过对实验数据和数值计算结果的详细对比分析，验证了本文提出的变截面涡旋压缩机数学模型的正确性。
Scroll compressor is new and efficient fluid machinery with its advantages ofenergy-saving, efficiency, and reliability. At present, Scroll compressor has alreadybeen extending application in many kinds of fields, such as refrigeration,air-condition fields, gas compression, engine booster, and booster pumps, etc, anddestined for a broad application prospects and good future. Nowadays, the research onthe conventional same thickness scroll compressor has been the main aspects of study,both domestic and abroad, which has a relatively lower pressure ratio. The number ofturns must be added if the higher pressure ratio is to be wanted from the conventionalsame thickness scroll compressor, and problems must be followed with the addednumber of turns, such as, the added difficulty of vane production, the risingtemperature of the whole machine because of the long time stay of the compressedmass of gas, the bigger size and the heaver weight of the whole machine. However, allproblems will be solved if variable thickness scroll compressor with combinationprofile is been used instead of the conventional same thickness one.
A new type combination profile has been established in this thesis which is madeup of circle involute and high times curve. The high pressure ratio has been achievedwith the fewer number of turns. Mathematical model has been built with this kind ofscroll compressor and the performance of the whole plate has been analyzed anddiscussed.
The process of research in this thesis has been showed as follow. First, thebaseline of combination profile of variable thickness scroll compressor has beenfounded depend on conjugation theory of conjugacy curve in infinitesimal geometry,and combination profile has been created with twin-circular arc profile modification.Second, volume has been calculated depend on baseline principle. Third, equations ofdynamics has been built including gas forces, moment, force on the orbiting scroll,force on crank journal and force on Oldham ring, and been solved with the method ofNewton-Rophson. Fourth, mechanical frictional losses model has been createdincluding crank journal, crank pin, thrust bearing and Oldham ring. Mechanicalefficiency and available shaft work rate has been detailedly analyzed, too. The law ofchange in power consumptions, mechanical efficiency and available shaft work ratehas been get with the solving of the model. The law to sum-up mainly displays in:
1) The main bearing friction loss is the main factors of influencing mechanical efficiency and should attach importance in the optimization and actual production.
2) Mechanical efficiency has some fall with the rising speed because of frictionloss. But the fall is slow and shows that the variable thickness scroll compressor has areliable running.
Mathematical modeling of variable thickness scroll compressor has been provedcorrect in this thesis with the comparison and analysis about the result fromexperiment study and numerical analysis.
引文
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[2]荒田哲者.制冷压缩机的现状和发展方向[J].流体工程,1989,3:54-61.
[3]刘志经.制冷涡旋压缩机及其应用[J].制冷,1998,4:25-28.
[4] Winandy, Eric, O．, Claudio Saavedra, Lebrun, Jean. Experimental analysis andsimplified modeling of a hermetic scroll refrigeration compressor[J]. AppliedThermal Engineering.2002,22(2):107-120.
[5]卜啸华.涡旋式制冷压缩机.动力机械通讯[J].1989(49):30-62.
[6][日]森下悦生,杉原正浩.涡旋压缩机的设计问题[J].压缩机技术,1988,4:11-20.
[7]李连生,束鹏程,郁永章,等.涡旋型线对涡旋压缩机性能的影响[J].西安交通大学学报,1997,31(2):45-50.
[8]李连生.线段渐开线涡旋压缩机的几何理论[J].流体机械,1994,22(12):22-28.
[9]黄允东,郁永章.半圆偏心涡旋压缩机的几何理论[J].压缩机技术,1997,1:3-6.
[10]王君,刘振全,李超.涡旋压缩机渐开线和圆弧组合型线的设计计算[J].流体机械,2004,32(10):10-13.
[11]王国梁,李连生,张薇,等.一种新型涡旋型线的几何理论研究[J].西安交通大学学报,2003,37(5):499-503.
[12] T. Hirano. Scroll profiles for scroll fluid machines[J]. MHI Tech ReV(1990),27(1):35-41.
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