Principle and Thermodynamic Process of the Compressor of Composite Gear Teeth

International Joumal of Plant Engineering and ManagementVol. 10 No.2June 2005Principle and Thermodynamic Process of the Compressorof Composite Gear TeethXIONG Wei , YU Xiao-ling , PENG Xue-yuan , FENG Quan-keSchool of Energy and Power Engineering , Xi' an Jiaotong University ,Xi'an , Shaanxi 710049 , P. R. ChinaAbstract : The compressor of composite gear teeth is a new type of rotor compressor with partial built-incompression process. Analysis of its thermodynamic process indicates that the built-in process is incom-plete. The thermodynamic process of the comupressor of composite gear teeth can be considered as fiveprocesses : the suction process , the isometric process , the compression process , the pressure-balanceprocess at high pressure and low pressure gas , and discharge process. Here ,it is necessary to explainfurther the pressure-balance process. The pressure-balance process is isometric process. It is found thatthe isometric process of gas in chamber A whose capacity is 83 percent of total work volume can be elim-inated basically through extending the discharge port to connect early the discharge port with the cham-ber B. By the above-mentioned method ,the loss of energy will be reduced.Key word : rotor compressor , pressure-balance , isometric process1 IntroductionThe gear pump is used extensively as a pumping-liquid mechanism. However , the gear pump trans-mits relatively lttle liquid in one rotation due to lttle inter-lobe area on the end face. For this prob-lem , Erich , proposed the mechanism of composite gear teeth in 19681. In the proposed mecha-nism , some of the small gear teeth are replaced by several big gear teeth respectively , correspond-ingly , some of the small grooves are replaced by several big grooves. By this way , the inter-lobe ca-pacity increases greatly ,resulting in high capacity transported in one rotation. The design refers to agear type rotary mechanism for transporting liquid , compressing and expending gas. It is composedof a case and a pair of gear-type rotors installed in the case. The driving shaft of the rotors is drivenby synchromesh gear which is installed out of the case for transmitting torque. In this design , thegear teeth do not contact with each other. Each gear includes several sets of small teeth and one ormore big teeth alternated with them.In fact , although the two rotors keep engaging with each other , they are out of actual metallic contactwith each other. Therefore , additional gears (中国煤化工be mounted out of thecase so as to drive the shaft of the rotor. Several kMYHC N M H Gned as the flank profileof the big teeth of the gear type rotor , without being the same as the small teeth. The effective areaused for fluid transferring by the rotors of the gear pump is greatly increased. Unfortunately , the seal .effect cannot be kept between the two big teeth , resulting in a great amount of backflow , thus the ef-Received 17 July 200490International Joumal of Plant Engineering and ManagementVol. 10 No.2June 2005ficiency of the fluid transmission is low , with nearly no function of compressing or expanding gas.The principle of an engaging rotor , proposed by Liao Zhenyf21 , in 1993 , resolved the transmissionof the gear composed of big gear teeth and small teeth. However , there are shortcomings in the prin-ciple , such as inflection point in the profile of the big teeth and imperfect seal. In the compressor ofcomposite gear teeth , suggested by Shen Jinfeng et al.C31 , in 1997 ,the inflection point between thebig teeth and the small teeth was eliminated , and the profile was replaced with none-symmetry pro-file to improve seal function. Subsequently , we carried out theoretic analysis and experiment of thiscompressor. An improved scheme was put forward according to the results of the theoretic analysisand experiment result.-Discharge pipe2 Construction of the prototype compressorDesigned for application in split type air conditioner , theprototype compressor which adopts hermetic upright con-Driving shaftostruction has the similar construction to a typical rotary air-Driven shaf修利主Discharge portconditioning compressor , except that it has two shafts , notDriving gc作期Upper capCylindersingle shaft. As shown in Figure 1. The manner of pumping Driven gear-oil in the lubricating system adapts differential pressureSuction pipeBottom cappumping and helical blade pumping consulting typical rota-ry air-conditioning compressor.Figure 1 Sctional view of the compressorThe compressor of composite gear teeth is composed of cyI-of composite gear teethinder , upper cap , bottom cap , driving gear and driven gear. As shown in Figure 2 ,a pair of en-gaged gear-type rotors is located in the cylinder , three big teeth are distributed evenly in circumfer-ential direction on the driving rotor , and three grooves on the driven rotor. A certain number of smallinvolute gear teeth on the two rotors are functioned as timing and torque transmission. The chambersurrounded by the three big teeth and grooves is used for gas compression. Evidently , the three bigteeth and grooves are also functioned as sealing and torque transmission.Suction portDriven gear ;中CylinderDChamber B1 Driving gearDischarge portChamber Aa)b)Figure2 Working principle of中国煤化工h”YHCNMHGThe suction port is so constructed that the inlet gas is drawn into the working chamber through thecylinder approximately in radial direction. The discharge port is arranged axially in the end plate.It is obvious that , compared with most of other positive displacement compressors , the compressor ofcomposite gear teeth has the advantages as below :Principle and Thermodynamic Process of the Compressor of Composite Gear Teeth9( 1 ) The compressor is composed of 5 parts :a pair of rotors , the case , the upper cap and the bottom .cap. Therefore , its construction is simple.(2 ) The inertia force of the compressor can be cancelled out completely. As a result , the compres-sor is always able to keep a minimum vibration and noise.( 3 ) The compressor seldom stops working , due to nonexistence of easily damaged components , thusthe compressor is high in reliability.3 Analysis on working processAs a new kind of machinery , the compressor of composite gear teeth has a unique working process il-lustrated in Figure 2 , in which its built-in compression is incomplete. Chamber A and chamber B inFigure 2( a ) form one pair of work volume , at that moment , the volume of chamber A is going to bedecreased. When the two rotors rotate , gas in chamber A is compressed but the capacity of chamberB is constant. When chamber A and chamber B join together , as shown in Figure 2( b ) , high pres-sure gas in chamber A flows partially into chamber B rapidly until the pressure of the two chambersbalances. Subsequently , the working chamber after pressure-balance opens to the discharge port.Because the pressure of mixed gas is lower than pressure in the discharge chamber , backflow takesplace until the pressure of mixed gas is equal to the pressure in the discharge chamber. Then thedischarge process begins. As the discharge process is in progress , a new working chamber formsgradually and opens to the suction port. Then the working chamber is divided into two chambers withrotation of the rotors , and the two chambers separate respectively from the suction port successively ,and the suction process ends up. However , gas in the two chambers will not be compressed untilthey reach the position ilustrated by chamber A and chamber B in Figure 2( a ).As analyzed before , the thermodynamic process of the compressor of composite gear teeth can be divided .to five processes : the suction process , the isometric process , the compression process , the pressure-bal-ance process of to high pressure and low pressure gas , and discharge process. According to the charac-teristic of rotor compressor with partial built-in compression process 1 , we deduce that the compressor ofcomposite gear teeth is a new type rotor compressor with partial built-in compression process.PtChamber APChamber BP.3V(a(b)Figure 3 Ideal working proce中国煤化工YHCNMHGFigure 3 shows the ideal working process of the compressor ot composite gear teeth. The thermody-namic characteristic of the compressor lies mainly in its pressure-balance process. As chamber Aand chamber B connect with each other , a pressure-balance process takes place because the pressurein chamber A is far higher than that in chamber B. The curve from point 2 to point 3 and the curveInternational Joumal of Plant Engineering and ManagementVol. 10 No.2June 2005from point 1' to point 2' stand for the pressure-balance process in the Figure 3. Because the pressureof gas after the pressure-balance process is lower than pressure in the discharge chamber , an isomet-ric compressing process takes place to enhance its pressure to discharge pressure. The curve frompoint 3 to point 4 and the curve from point 2' to point 3' stand for the isometric compressing process.And the curve from point 4 to point 5 stands for the discharge process.4 Analysis on P-V diagramWe obtained the P-V diagram including the compression process , pressure-balance process and theearly part of discharge process by dynamic pressure experiment”. The analysis of the work processwas identified by the result of experiment , that is to say , the isometric process exists in the workprocessof the compressor of composite gear teeth. As the main part of the discharge process can notbe measured , we analyzed the P-V diagram calculated by mathematical simulation , as shown in Fig-ure 4. The thermodynamic characteristics of the compressor of composite gear teeth are illustrated inFigure 4 : the pressure-balance process with constant volume , the isometric process due to backflowoverpressure at the beginning and at the end of discharge process.In the discharge process , the pressure of the work chamber is1.0-P:=0.1 MPadetermined by variety of its capacity and mass of work medi- Pc=0.8 MPa1m. The reduction of capacity results in increase in pressure ,0.8-N~and the reduction in mass due to discharge results in descentg 0.6-of pressure. In this compressor，the discharge port opens0.4gradually after the pressure-balance process , and the area of0.2-the discharge port enlarges gradually , so that the area of dis-0.0δ204060800120140160Angle 0/(°)charge port is relatively smaller in the early stage of dischargeprocess , causing overpressure. As shown in Figure 4，theFigure4 P-V diagram calculated bymathematical simulationmore serious overpressure happens at the end of dischargeprocess in which gas is discharged through slot while the discharge port has been closed. The sectionof the slot is 2mm X 0.5mm , and the remanent relative volume is 4 ~ 5 percent while the dischargeport is closed. The results of mathematical simulation shows that the max pressure of the work cham-ber reaches 1. 0Mpa , which ilustrates overpressure at the end of discharge process is very serious.Existence of overpressure in the discharge process causes high discharge resistance and high loss ofenergy. Enlargement of the section of the slot can eliminate the overpressure , but the clearancepocket will increase , therefore , an optimized size should be chosen by calculation.5 Improved scheme of the thermodyna中国煤化工npressorAs shown in the P-V diagram calculated by mathe:MYHC N M H Gmetric process exists inthe thermodynamic process. To be specific , there are 4 isometric processes in the whole workprocess of the compressor :( 1 ) The isometric expansion process of the gas in chamber A while chamber A connects with cham-ber B.Principle and Thermodynamic Process of the Compressor of Composite Gear Teeth93( 2 ) The isometric compression process of the gas in chamber A while chamber A connects with thedischarge port.( 3 ) The isometric compression process of the gas in chamber B while chamber B connects withchamber A.( 4 ) The isometric compression process of the gas in chamber B while chamber B connects with theThe isometric process causes additional loss of energy. On the other hand , the discharge process isarranged after the pressure balance process , then the discharge area is restricted to smaller size , sothe flow velocity passing the discharge port ishigh. All these result in high loss of energy.We put forward a better scheme to improve thethermodynamic process of the compressor of com-posite gear teeth according to the results of analy-sis and experiment , as shown in Figure 5.Enlarging the discharge area , the chamber B willSlotconnect with the discharge port before connectingOil chamberDischarge portOil injection holewith chamber A ,so that gas in chamber B will becompressed by the gas in discharge chamber beforeFigure 5 Construction of the improved compressormixing with gas in chamber A. The gas in chamberof composite gear teethA will be compressed to rated pressure by choosing proper parameter ,so ,gas in chamber A will mix withgas in chamber B without pressure diference. Then the mixed gas will be discharged subsequently. Con-necting the discharge port ahead of time , the discharge area will be enlarged effectively , the flow velocitypassing the discharge port will be descended , so ,the discharge loss will be reduced.Using this improved scheme , the compressor of composite gear teeth can be regard as a rotor compres-sor with partial built-in compression process. Gas in chamber A , whose capacity is 83 percent of totalwork volume , can be compressed completely ,and gas in chamber B , whose capacity is 17 percent oftotal work volume , will be compressed with constant volume. The ideal working process of the com-pressor of composite gear teeth with partial built-in compression process is shown in Figure 6.Chamber A2↑Chamber BPPg_2s1中国煤化工- V(a)0HCNMHGFigure 6 Ideal working process of une-mprovea compressor6 Conclusion( 1 ) We analyzed the work process of the compressor of composite gear teeth , and concluded that theInternational Joumal of Plant Engineering and ManagementVol. 10 No.2June 2005compressor of composite gear teeth was a new type of rotor compressor with partial builtin compres-sion process.( 2 ) The pressure-balance process of the compressor of composite gear teeth was composed of two proces-ses. ( a ) the isometric expansion process of the gas in chamber A and the isometric compression processof the gas in chamber B. ( b ) the isometric compression process of the gas in work chamber due to back-flow when the work chamber connected with discharge port. All these processes increase loss of energy.The work process of the compressor is as below : the suction process , the compression process of gas inchamber A , the pressure-balance process of gas in chamber A and chamber B , the isometric compressionprocess of gas in chamber A and chamber B , and discharge process.( 3 )It is found that the isometric process of gas in chamber A , whose capacity is 83 percent of totalwork volume , can be eliminated basically through extending the discharge port to connect early thedischarge port with the chamber B.(4 ) The study on this compressor indicates that the isometric process is the characteristic of rotorcompressor with partial built-in compression process.References[1 ] E. Martin , Gear-type rotary machine. United States Patent. US ,A ,3574491 , 1969.[2] Z. Y. Liao , Working principle of meshing rotors. China Patent , ZL93111972.3 ,1993( InChinese )[3] J. F. Shen ,et al. The composie gear-type machine. China Patent. CN 1181473A. 1997( In[4 ] D.G. Deng ,P. C. Su , Rotary compressor. Beijing : Machine Industry Press , pp. 205 ~ 208 ,1998 ( In Chinese )[5] W. Xiong , W. Zhou ,et al ,Experimental study on the indicating diagram of a hermetic com-posite gear-type compressor. Jourmal of Xi' an Jiaotong University , Vol.37 ,No. 1 ,pp. 33 ~36 , 2003( In Chinese )Brief BiographiesXIONG Wei received his doctor degree from Xi 'an Jiaotong University , china , in 2004. He is currentlya lecturer at School of Environmental & Municipal Engineering of Xi' an University of Architecture&Technology. His research interests include twin screw compressor and new type of rotary compressor.YU Xiao-ling is now a Ph. D candidate in Xi 'an Jiaotong University. Her research interests includeelectronics cooling and heat transfer.PENG Xue-yuan is now an assistant professor i中国煤化工His research interest isin compressors & refrigeration systems.MYHCNMHGFENG Quan-ke is now a professor in Xi' an Jiaotong University. His research include refrigerationmachinery & compressor working process.