[机械模具数控自动化专业毕业设计外文文献及翻译]【期刊】螺杆压缩机的几何抽象的热力学优化-外文文献

/Engineering ScienceEngineers, Part C: Journal of Mechanical Proceedings of the Institution of Mechanical/content/225/6/1399The online version of this article can be found at:DOI: 10.1177/095440621039588413992011 225:Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering ScienceJ Hauser and A BrmmerGeometrical abstraction of screw compressors for thermodynamic optimizationPublished by:On behalf of:Institution of Mechanical Engineerscan be found at:ScienceProceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical EngineeringAdditional services and information for /cgi/alertsEmail Alerts: /subscriptionsSubscriptions: /journalsReprints.navReprints: /journalsPermissions.navPermissions: /content/225/6/1399.refs.htmlCitations: What is This?- May 25, 2011Version of Record at ZHEJIANG UNIVERSITY on March 28, 2012Downloaded from GeometricalabstractionofscrewcompressorsforthermodynamicoptimizationJHauserand ABrmmerDepartment of Fluidics, Technical University Dortmund, Dortmund, GermanyThe manuscript was received on 17 May 2010 and was accepted after revision for publication on 17 November 2010.DOI: 10.1177/0954406210395884Abstract: The construction and development of different rotor profiles is an important area inconnection with the development of screw compressors for specific applications. Geometricalperformance figures (using criteria to describe interdependencies of geometrical parameters forscrew compressors) for profile optimization are used in order to achieve specific improvementsin performance. During this process, rotor profiles and spatial parameters are the main factors.Compared to data derived from the front section of rotor profiles, these figures which also takespatial parameters into account provide a better evaluation of gap conditions and operatingefficiency of the compressors under examination.Keywords: screw compressor performance, profile optimization, new design concepts1 INTRODUCTIONThe operational behaviour of a screw compressorcan be examined experimentally but also by meansof comprehensive simulation procedures 1,2. Thecomplexity of the simulation, the need for trial runs,and the need to achieve the closest possible par-allels to a real compressor do lead to valid results,but the process is very time-consuming. Computer-aided optimization by comprehensive simulation istherefore undesirable, despite leading to valid results.With a view to finding a compromise between pre-cision and calculation time, evaluation and analysisby means of abstracted geometrical performance fig-ures is a reasonable approach. The main feature of thisapproach is intended to be a reduction in develop-ment time by using geometrical codes to characterizethe thermodynamic performance behaviour of a screwcompressor.Within the field for developing geometrical per-formance figures, there have been attempts to eval-uate the gap conditions for various front-sectionCorresponding author: Department of Fluidics, Technical Uni-versity Dortmund, Leonhard-Euler-Strasse 5, D-44227 Dortmund,Germany.email: jan.hausertu-dortmund.degeometries 3. This approach has proved useful inspite of the two-dimensional (2D) viewpoint, anddemonstrates that direct profile modification tak-ing into account application-orientated requirementsseems to be effective. However, this approach doesnot provide direct comparability of 3D rotor geome-tries, as a pure profile abstraction inevitably ignoresspatial geometrical parameters. These exercise con-siderable influence on gap conditions, and thus onthermodynamic processes in the compressor.The aim of this study is to link geometrical param-eters with their effects in terms of performance. Theinterrelationships will be integrated in geometricalperformance codes, which can then be used to reduceinternal leakages and, to some extent, improve theenergy conversion efficiency of screw compressors.Ascertaining general trends for geometrical optimiza-tion will be carried out via a purely geometricalevaluation of the compressors, independent of anyactual operating situation. In order to compare thegeometries, it is only necessary to decide whichmechanical and operational parameters it is advis-able to keep constant. It will be necessary to ascertainwhether simple geometrical data are capable of replac-ing extensive measurements and simulations in afirst assessment of the energy conversion efficiencyof differing compressor designs, for example, withinthe framework of a computer-aided optimizationprocess.Proc. IMechE Vol. 225 Part C: J. Mechanical Engineering Science1399at ZHEJIANG UNIVERSITY on March 28, 2012Downloaded from JHauserandABrmmerFig.1 Gap situation of a screw compressor. Above: casing and front gap, below: profile intermeshgap (left), blow hole (right)2 INTERRELATIONSHIPSBETWEENGEOMETRICALPARAMETERSThe selection of the geometrical parameters of a com-pressor, such as rotor diameter, length, rotor wrapangle, and compression ratio, influences gap interac-tion and the resulting degree of energy conversion. Thesettings for the casing, front, and profile intermesh areresponsible for the internal leakage characteristics ofthe compressor, and are mainly responsible for gapflow losses (Fig. 1). If gap flow losses are increased,efficiency suffers. The types of gaps have differentinfluences on the energy conversion efficiency of ascrew compressor. A general view of gap priorities withregard to the relative rates of mass flow at the gaps with respect to the current pressure situation andthe respective gap lengths is provided by 1,4 thefollowing.1. Profile intermesh gap (between male and femalerotor).2. Casing gap at (depending on number of teeth):(a) male rotor;(b) female rotor (larger number of teeth than themale rotor).3. Blow hole.4. Front gap at:(a) high-pressure side;(b) low-pressure side.The order above refers basically to the overpres-sure area of a screw compressor. For a machine ofthis type used in mechanical compression applica-tions, this order of priorities is confirmed by Kauderand Janicki 4. Results for gap priorities in expansionapplications are not available at present. The energyconversion assessment is carried out via mechanicalefficiency as the principal performance figure. A fur-ther important item is the volumetric efficiency forrotational displacement machines.The framework of the geometrical assessment doesnot include factors which have no direct influenceon the rotor geometry. The level of volumetric effi-ciency thus represents the influence of the gap massflows. Volumetric efficiency is influenced by geomet-rical parameters such as the way rotor tooth countsare paired, length of the rotor, wrap angle, lengthdiameter ratio, and the settings of the gap heights.In addition, profile design plays a major role,because it is the form of the profile which influencesthe main types of gap 3,4. Based on a referencecompressor, the influence of the profile form on thevolumetric efficiency of the compressor is variable.Every change in the profile form directly influencesthe gap configuration and the order of priority amongthe gaps, which in turn has a direct influence on leak-ages in the compressor. The fact that changing theprofile directly affects the size of the machine (i.e. themaximum delivery volume) should also be taken intoProc. IMechE Vol. 225 Part C: J. Mechanical Engineering Science1400at ZHEJIANG UNIVERSITY on March 28, 2012Downloaded from Geometricalabstractionofscrewcompressorsaccount. The smaller the delivery volume, the largerthe effect of the gaps, as the increase in length is lin-ear, while the delivery volume increases at the powerof three related to the size of the compressor.3 GAPS:AGEOMETRICALEXAMINATIONWithin the framework of profile development for dry-running rotational displacement machines, geometri-cal performance figures are helpful in carrying out acomparative assessment of different profiles. This canbe done using either thermodynamic or mechanicalflow values. Ignoring rotor length and wrap angles ofthe rotor under examination, rotor profiles with 2Dperformance figures (e.g. with 2Dgap lengths in rela-tion to the scoop surface), have so far been physicallycharacterized. However, the part played by the spatialgap lengths is not taken into account. It seems desir-able to transfer the geometrical compressor parame-ters (wrap angle and rotor length) to the resulting gapsituation. Gap priority now depends on the settingsof the gap height and the profile contour itself. Conse-quently, various approaches to a description of the gapconditions should be set up and validated within theframework of a computer-aided profile optimizationprocedure.3.1 GeometricalgapsituationAn assessment of 3D gap interrelationships can beeffectively represented by means of a rotor diagram(Fig. 2). The rotor position is determined by the lead-ing chamber, where the volume has just reached zero.As the influence of the front gap on the low-pressureside is small, this is not taken into account in theperformance figures. A comparison of different wrapangles shows that as the angles increase, the num-bers and also the total lengths of the gaps increase.Where there is an identical pressure ratio, greater wrapangles will result in a more constant pressure gradient,which should result in higher volumetric efficiency.This assessment only applies if there is a constanttheoretical mass flow in comparable compressors.Gap conditions can be derived from the representa-tion of the rotors, as a single gap alteration (e.g. in thelength or the height), changes its priority and its influ-ence on volumetric efficiency. Based on the referencecompressor (compressor with subscript 11), simplycombining values for the surfaces of the respectivegaps produces an approximation of the performancerelation Pi11, because it is assumed that the volumet-ric efficiency will fall in proportion to the gap area(equation (1). The gap area AGapis arrived at by addingthe gap lengths, multiplied in each case by the gapheight. Comparability of different compressors can beMale Rotor (MR) Female Rotor (FR)CG1HP-PortCG2CG3CG1CG2CG3CG4IMC2BH1IMC1CGMale Rotor (MR) Female Rotor (FR)CG1HP-PortCG2CG3CG1CG2CG3CG4IMC3BH2CG5BH1IMC2CG4IMC1CGFig.2 Rotor intermesh diagram demonstrating the gap analysis for a specified rotor position.Above: small wrap angle, below: large wrap angle. CG, casing gap; BH, blow hole; IMC,intermesh clearance; HP, high pressureProc. IMechE Vol. 225 Part C: J. Mechanical Engineering Science1401at ZHEJIANG UNIVERSITY on March 28, 2012Downloaded from JHauserandABrmmerachieved with reference to the delivery volume (i.e.depending on the number of teeth)Pi11(Pi11)11=AGap(AGap)11(VmaxzMR)11VmaxzMR(1)withAGap=summationdisplay(hIMClIMC) + Sigma1ABH+parenleftBigsummationdisplay(hCGlCG) +summationdisplay(hFGlFG)parenrightBigMR+parenleftBigsummationdisplay(hCGlCG) +summationdisplay(hFGlFG)parenrightBigFRThis approach only provides a rough estimate of thevolumetric efficiency in an assessment of profile char-acteristics with different wrap angles. This is becausegap area does not necessarily change along with thewrap angle, whereas volumetric efficiency develops inan approximately anti-proportional way.Gap influences tend to reduce as wrap anglesincrease, with the total number of gaps increasing.We can conclude from this that the gap count tendsto develop in an approximately anti-proportional waycompared with the gap area, so the equation can beextended as followsPi12(Pi12)11=Pi11(Pi11)11(iGap)11iGap(2)withiGap=summationdisplay(iIMC+ iBH+ (iCG+ iFG)MR+ (iCG+ iFG)FR)The performance code Pi12thus represents the rela-tionship between a moderate gap area for all gaps ofthe compressor and the theoretical delivery volume.The number of gapsiGapis arrived at by adding togetherthe total gaps for the machine. The total gap countbroadly corresponds with the weighting of the gaps ina screw compressor. As the number of individual gaptypes does not change at the same rate (e.g. the wrapangle), it is desirable to carry out an assessment of theindividual gap types.3.2 AssessmentofgaptypesThe previous calculations do not directly cater for gapareas dependent on wrap angles and rotor length. Thismeans that the actual significance of the different gapsis not taken into account. The performance figureswill be augmented by internal and external weightingfactors for the respective gap areas (3)Pi13(Pi13)11=summationtext(Gap,esummationtext(Gap,iAGap,Type,i)parenleftbigsummationtext(Gap,esummationtext(Gap,iAGap,Type,i)parenrightbig11(VmaxzMR)11VmaxzMR(3)withGap,e=Sigma1AGap,TypeAGapiGapiGap,Typeand Gap,i=AGap,Type,iSigma1AGap,TypeInternal weighting factors are revealed by examininga single gap, with changes in the machine parametersalso leading to changes in the number of gaps, andalso in the total area of the gap under examination.The factor Gap,irelates the specific area of a gap typeto the total area of a gap type. At constant pressure,gaps with higher values have a positive effect on per-formance. External weighting factors for a particulargap type result from the machine gaps, evaluated viathe gap area and count. The factor Gap,etherefore rep-resents the relationship between the mean area of eachgap of a particular type and the mean area of all gaps.This performance code therefore combines all impor-tant gap-geometrical and variable values, which varyaccording to the profile form and intermesh charac-teristics. As by the creation of these codes the area of agap type is entered in quadratic form, the surface com-ponent of the gap as a whole only in linear form, thereis an extreme lack of proportion between the areasof the gap types, which results in an unsatisfactoryrepresentation of gap priorities.3.3 Evaluationofasingle-chamberexaminationThe working chamber, which is mainly responsible forthe compression process, exercises a decisive influ-ence on volumetric efficiency.With an increase in wrapangle, the total area of the gap increases, but the gaparea of the process chamber is further reduced. Con-sequently, an examination of the high-pressure (HP)chamber in the previously defined rotor position canhelp to provide further gap performance values.The generation of these values, referred to as Pi11,OCMand Pi13,OCM, is carried out in the same way as Pi11andPi13. Code Pi11,OCMevaluates only the gap surfaces of theHP chamber, and does not take into account variationsin rotor length with suitably modified wrap ratios (4)Pi11,OCM(Pi11,OCM)11=AGap,1(AGap,1)11(VmaxzMR)11VmaxzMR(4)withAGap,1= AIMC,1+ ABH,1+ (ACG,1+ AFG,1)MR+ (ACG,1+ AFG,1)FRThe gap area AGap,1results from combining the indi-vidual gaps of the HP chamber, but this does notallow gap priorities to be ascertained. This influenceis included via code Pi13,OCM, with a weighting factorproduced by the relationship between the HP side ofthe gap and the total area of the gap (equation (5).With constant wrap angles, increasing the rotor lengthProc. IMechE Vol. 225 Part C: J. Mechanical Engineering Science1402at ZHEJIANG UNIVERSITY on March 28, 2012Downloaded from Geometricalabstractionofscrewcompressorsinevitably leads to a more uniform pressure distri-bution throughout the machine, as there are morechambers between the high- and low-pressure sidesPi13,OCM(Pi13,OCM)11=summationtext(Gap,iAGap,Type,1)parenleftbigsummationtext(Gap,iAGap,Type,1)parenrightbig11(VmaxzMR)11VmaxzMR(5)withGap,i=AGap,Type,1summationtextAGap,TypeThe weighting factor Gap,ithus expresses the rela-tionship of the HP gap-type area to the total gap-typearea of the machine. It seems desirable to work thisout, as with constant wrap angles, tooth pairings withdifferent numbers of teeth can be compared. As thenumber of teeth increases, the weighting factor Gap,iisreduced, which corresponds to a reduction in the gappriority of the individual gap types, and a consequentimprovement in volumetric efficiency.All these performance figures are basically suitablefor a qualitative assessment of machines based ontheir gap areas and values, but not for a quantita-tive representation of the volumetric efficiency or theoverall efficiency of the compressor. They serve as afirst step in the relative geometrical assessment of dif-ferent compressor designs (e.g. in a computer-aidedoptimization process).4 APPLICATIONINPROFILEOPTIMIZATIONAfter implementing the performance codes definedabove, it is necessary to examine their validity incomputer-aided profile generation. For this purpose,an optimization strategy for screw rotor profiles usingevolutionary approaches is employed 5. The repre-sentation of the rotor flanks is carried out by means ofa non-uniform rational basis spline (NURBS) curve 6.The geometrical parameters of the reference machineare listed in Table 1.Further the general requirements for the optimiza-tion process are a sample size of 30 rotors and amaximum of 100 000 optimization steps. The curve ofTable 1 Parameters of the reference machine (sub-script 11)Rotor length 100 mmTooth relation (malefemale rotor) 3/5Wrap angle (malefemale rotor) 200/120Gap height setting 0.1 mmParameters for optimization Male rotor profile, curvewith 12 control points,polynomial degree:3, rolling circle fixed,crown and root circlesnot fixedthe rotor profile of a tooth is represented by a polyno-mial degree of 3, and 12 control points. The intermeshconditions for profile generation follow the generalgearing law. Because of the varying influences of thegap types on the general course of the process dur-ing the compression phase, the front rotor gaps on thelow-pressure side are ignored during the generation ofthe performance figures. The