Hamada, T.

Okamoto, Y.

Shige, N.

English

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Purdue UniversityPurdue e-PubsInternational Compressor Engineering Conference School of Mechanical Engineering1986CAE Approach to the Development of RotaryCompressorsN. ShigeY. OkamotoT. HamadaFollow this and additional works at: https://docs.lib.purdue.edu/icecThis document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu foradditional information.Complete proceedings may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratories at https://engineering.purdue.edu/Herrick/Events/orderlit.htmlShige, N.; Okamoto, Y.; and Hamada, T., "CAE Approach to the Development of Rotary Compressors" (1986). InternationalCompressor Engineering Conference. Paper 560.https://docs.lib.purdue.edu/icec/560CAE APPROACH TO THE DEVELOPMENT OF ROLLING PISTON TYPE ROTARY COMPRESSORS Noriyoshi Sbigel ,Yoshio Okamoto! ,Tsuneaki Hamada2 'Daikin Industries. ,Ltd.,Sbiga Works.Kusatsu,Shiga,Japan 2Cae Center,Sakai,Osaka,Japan ABSTRACT This paper describes the computer aided engineering (CAE) approach to in,estigate the vibration of rolling piston type rotary compressors in the design and analysis stages. At first, the optimum design procedure for the compressor and piping system is presented. Then ,a compressor data base used for a dynamic simulation of the royary compressors are carried out. Finally, a practical application of the CAE approach to the optimum design of the rotary compressor is considered. INTRODUCTION Rolling piston type hermetic compressors have been used widely for room air-conditioners and unitary air-conditioners, because of high efficiency and reliability ,small size ,and light weight. Howe,er ,exciting forces generated by the rotary compressors are sometimes co•parable to the con,entional reciprocating compressors. Because,the motor and the components are directly fixed to the hermetic housing in order to reduce the size and improve the productivity. This means that an unbalanced inertia force around the crankshaft directly transmits to the hermetic housing which Is suspended with three coiled springs. Thetefore,it is important task to design the piping system connected to the rotary co•pressor in view of low vibration. A general concept of the CAE approach to the ptptng system in outdoor units has been established at DAIKIN and has already been 656 reported. [1] At our rotary compressor division we utilize the CAE approach to design the rotary compressoFs with reduced vibration. In this paper we introduce the CAE approach to the reduction of the excitation forces generated by the rotary compressors in operation. OPTIMUM DESIGN PROCEDURE FOR THE COMPRESSOR AND PIPING SYSTEM The optimum design procedure for the compressor and PIPing system is shown in Fig.l. Following are the key tasks in this procedure. (1) Solid modeling technique is employed to obtain precise geometries and mass properties of compressors, because it is a difficult task to measure the mass properties e1perimentally. (2) Kinematic simulations of compressors are carried out, in which excitation forces generated by the compressors are calculated based upon the unbalanced mass and the fluctuation of compression load. The results of prefious tasks (geometries,mass properties,and e1citation forces) are stored in a compressor data base. (3) Three dimensional piping design is performed using a 3-D CAD system. (4) Piping geometries are con•erted into Finite Element model. (5) Eigen•alue analysis is carried out with the p1p1ng systea model which comprises the beam elements and the rigid elements representing compressor and accumulator by Building Block Approach. (B) Calculated results are compared with modal testing data in the form of transfer function. (7) Dynamic responses on the piping system are calculated and local stress distribution is deri•ed from the displaceaent boundary condition. The alternative design cycles will be repeated until the optimum design is obtained which satisfies the design criterion. 657 CAE APPROACH TO THE DEVELOPMENT OF ROTARY COMPRESSORS Fig.2 shows a cross section of a rolling piston type rotary compressor in which the motor and the compressor components are each directly fixed to the upper or lower portion of the hermetic housing. Design process for a rotary compressor starts with performance evaluation of the compressor,which is followed by dynamic simulation of rolling piston and discharge valTe,and also lubrication analysis. In the view of vibration,the prediction of the the excitation forces is also a key factor in designing rotarY compressors,because dynamic responses of piping system depend upon the excitation forces. Therefore,before the detailed design of rotary compressors,the prediction of the ezcitation forces eust be carried out. THE PREDICTION OF EXCITATION FORCES Solid Modeling Of Compressors The graTity center and the moment of inertia (mass properties) are necessary parameters in calculating the excitation forces of the rotary compressors. HoweTer,it is a difficult task to measure the mass properties experimentally,because the geometric shapes of the compressor components are very complicated. Therefore,solid modeling technique is employed to obtain precise geometries and mass properties of compressors. In Fig.3 the computer model of 2 HP rotary compressor is shown. Fig.4 shows the computer models of several components which ars comprised in the compressor. And Table I shows the mass properties. E1citation Force Analysis (1) Momentu~ Equation The torque balance around the center of rotational a1is can be ~ritten as the following equation of ~otion. [2] Ir · jj =Tm -Tg -Tv where, Ir =moment of inertia of rotating co•ponents ()=crank angle Tm = 11otor torque 658 (1) Tg =loading torque due to the cylinder pressure Tv= loading torque due to the blade force In the momentum equation mentioned abofe,the loading torque due to the mechanical friction is neglected for the simplicity. Using the mass properties mentioned pre,iouslJ,the moment of inertia around the rotational azis, Ir , is obtained by the following equation. Ir = IMR + lcR +mRo ·e2 where, lMR =moment of motor-rotor inertia lcR =moment of crankshaft inertia 111\o =mass of roller e=eccentricih of crankshaft (2) Calculation Of E!citation Forces (2) On the coordinate system shown in Fig.5 ,each component of the force and the moment acting at the cylinder center can be written as the combination of unbalanced inertial forces. Fx =msu ·iisu +iiiRo ·iRo +meR ·iicR +IIIBL ·isL ry = -mv ·'jv +msu 'YBU +mRo 'JRO +meR ·YcR +meL 'JBL Fz =0 Mx=meu·Ysu·lsu +msL·JeL·lsL Mv =msu ·iieu ·leu +IIBL ·isL ·leL Mz =- lr · 0 where, msu =mass of upper balance weight IIBL =ma.ss of lower balance weight IICR =eccentric mass of crankshaft leu =gralih center of upper balance weight leL =gralih center of lower balance weight (3) (4) (5) (8) (?) (8) Therefore,eJcitation forces around the gra,ity center of the compressor, the location of which is (Xs, Ys ,ZG) in the oyl inder coordinate sJstem,can be written as follows. Fsx =Fx (9) Fsv =Fv (10) Msx ::Mx+ZG·FGY (11) Msv =Mv -Zs ·Fsx (12) Msz =Mz -Xs ·Fsv +Ys ·Fsx (13) 659 (3) Results Of Analysis rig.B shows the cylinder pressure fluctuation used for the analysis. rig.7 shows the loading torque fluctuations in steady state, in which the loading torque due to the cylinder pressure is dominant. rig.S shows the angular lelocitJ and acceleration around the rotational axis which calculated from equation (1). The excitation forces are calculated from the set of equations (3)~(13) using the mass properties as well as angular velocity and acceleration obtained abofe. The e1citation forces in both X andY a1es are shown in Fig.9,and the excitation moments around X,Y,and Z a1es are shown in Fig.lO. rig.ll and Fig.l2 show their Fourier transfor•ed data. It can be seen from rig.lO that the e1citation moment around Z azls is the largest component. Table 2 shows the ma1imum 'alues of the ezcitation force in each direction. APPLICATION TO THE OPTIMUM DESIGN Or THE ROTARY COMPRESSOR Optimum Design Of Balance Weight The unbalanced forces other than the inertia force of the blade can be canceled by the optimum design of upper and lower balance weights. The comparison between current design and the opti•um design is shown in Table 3 ,in which the balance weight specifications and the resultant elcitation forces are tabulated. Table 3 Comparison between Current Desigrl and Optimum Design of Balance Weights Current Doslu Opt l1um DeS\~n Upper Balinc• Wol«hl Thickness ( .. ) 5.5 •. 5 ------·-------Upper Balonce Woithl Hass (h) 0.0527 0. 04 31 Lo•er Balance Wel«hl Thickness ( .. ) 16.0 11. 717 -----·· Lover Balance Weight Hass (h) 0.1730 0. 1267 , ___ FGX (lai) ( N ) 100.079 8. 167 - -·~----FGY (•u) ( N ) 71.823 -16.089 ---HGX (1a1) ( N·• ) 4.344 -1. 286 HGY (lax) ( N ·I ) 5 .e97 0. 580 HGZ (lax) ( N·o ) 8. 208 7. 678 In Fig.l3 the fluctuations of the e:oitation forces are shown. It can be seen that all the excitation forces are reduced by the optimum design of the balance weights. 660 Influence Of Gra•ity Genter Change It is difficult to conform the gra~ity center of the rotary compressor to the cylinder center,because the motor is the largest mass in all the compressor components and is located in the upper portion of the compressor. Therefore,it is interesting problem to in•estigate how the e1citation forces are influenced by changing the gra•ity center. Fig.l4 shows the comparison between current design and aodified ones,in which the gravity center is changed. It can be seen that the eJcitation moments around the both X and Y aleS are reduced by conforming the gravity center to the cylinder center. Therefore. it is desirable to locate the gravity center as nearly as possible to the cylinder center. Influence Of Blade Inertia Force The blade is the only reciprocating element in the rotary compressor components. It can be seen in equation (() that the e1citation force in Y aais direction is influenced by the inertia force of the blade. We in•estigated the influence by changing the blade ~ass. In Fig.l5 the comparison between current design and •odified ones, in which the blade ~ass is changed,is shown. The e1citation force in Y a1is direction can be reduced by increasing the blade mass. CONCLUSIONS The CAE approach to the de•elopment of rolling piston type rotary compressors was introduced focusing on the investigation of the vibration characteristics,which is summarized as follows. (1) The loading torque due to tbe cylinder pressure is •ost dominant within the fluctuation of torques which generates the e1citation forces of rotary compressor,and the excitation mo•ent around the rotational a1is is the largest force component. (2) It was confirmed that the e1citation forces could be reduced by the optimum design of each component. (3) The results of this anal7sis are effecti,ely used for the opti~um design of the piping system in air conditioning units as a compressor data base. 661 The verification of the accuracy of the results remain as a future work. ACKNOWLEDGEMENT The authors would like to express their great thanks to Mr.Touru Hirano, Chief Engineer of CAE Center,for his support in carrying out this work. REFERENCES [l] T.Hirano,"CAE Approach to the Research and Development of Air Conditioning Units,"!Oth International Seminar on Modal Analysis,K.U. Leuven,Belgium,l885. [2] T.Yanagisawa et al. ,"Study on Vibration of Rolling Piston Type Rotary Compressor,"Transaction of the Japan Society of Mechanical Engineers (Series C),Vol.49.N0.444,1984. 662 0 SOLID MODELING 0 0 OF COMPRESSORS ft II • ~ ! I lr u II COMPRESSOR 0 n II SIMULATION II I '" I g. 1 I coMPRESSOR DATA BAsE'l IF"& ---..........l!9 GEOMETRIES ft ! 0 MASS PROPERTIES 0 II EXCITATION FORCES U I [BBA METHOD) I PIPING SYSTEM I [MODAL TESTING} I I DYNAMIC SIMULATION I •~---------1 VItRiFICATION OF I I THEORETICAL MODEL I t L-------' I I PIPING DYNAMIC MODEL I GEOMETRY GENERATION I r sPECIFICAtiON OF 1 I DISPLACEMENT I ! J BEND MODEL I I BOUNDARY CONDIT ION ~ I FEM MESH I I GENERATION ! fl t I a ~ I I zoolmm I STRESS IINALYSIS I OF THE J BEND I 3-D PIPING SYSTEM I I I "* I OESIGN & DRAWING f--J L--------' I INTERFERENCE CHECK I Fig.l Optimum Design Procedure for the Compressor and Piping System Fig.2 Cross Section of Rolling Piston Type Rotary Coapressor 663 rig.3 ComPUter Model of 2 HP RotarJ Compressor ~ ) ... ) ... ).. Sub-AssemblJ Motor Stator Motor Rotor !@hP ) .. . .... .l. CJlinder Crank Shaft Roller .l. Blade Front Head Rear Head ).. .l. ,.J Housing Top Housing Bottom Accumulator rig.4 Computer Models of Main Components 664 Table 1 Mass Properties of Compressor Components GRAVITY CENTER ( •• ) MOMENT OF INERTIA ( N· • ) COMPONENT I y z In Iyy Izz HOUSING TOP 1.306 11.719 281.462 14.634 13.080 24.441 .HOUSING BOTTOM 1.257 0.449 112.107 268.983 268.498 147.134 MOTOR STATOR 0. 000 0.000 183.067 200.709 198.273 187.004 MOTOR ROTOR 0. 420 0.000 182.624 25.7 90 25.788 12.050 FRONT HEAD 0. 639 0.836 99.821 2. 249 2.247 3. 709 REAR HEAD 0.593 ~1. 978 45.312 2.351 2.398 4.391 CRANl SHAFT ~1.122 0.010 113.Z73 1(.558 14.398 0.494 CYLINDER 2.388 ~3.824 71.984 14.464 22.040 33.461 ROLLER ~4. 000 0.000 71.975 0.550 0.550 0.672 BLADE 30 .126 10.916 72.000 0.039 0. 052 o. 018 ACCUMULATOR 118.288 0.000 204.356 31.989 32.029 9.354 2HP ROTARY 6. 754 0.267 151.494 1195.189 1317.142 569.344 ll/OPTJUN? COMP. PRESS VALUE [!] PRESS .... ~ 1~~ 2.~~ ~- ..... jtl ~:~F-~ ;1151'1. ... : 1. y ~ . '--• X Fig.5 Coordinate System used for Analysis 1!1 0 ~ + TORQUE DATA PRES:;; TO~~ 11Di0R TORQ ALL TO~GIUI;; BRQOE: TORGI !DEOl rig.7 Torque Fluctuation in Steady State J+_ ~~.~,-.~~~---,oor-~-.-r~~·,---r~ DEGREE tDEGl Fig.6 Cylinder Pressure Fluctuation used for Analysis 'OUOrTION'I THF.TA DATA 665 ACCEl.ERAT l~i VELOCITY •.l----r~...:;:,.~~.-.---r----r-.../-'-r--.----~r--l 6~ ~ IOEQl Fig.8 Angular Velocity and Acceleration 5.GEHH e.B!:HIO -5.El~H~ I -LBE+eL .. ·~ Tl11t OOHfl!l-l ~\ -"' u1' ~IM[-vb~c) "l'l 1110= 1 2/jD~ 2 FG x Fev Fig.9 Excitation Forces in Both X and Y Axes L. TIME DOI'IRHI e. eetee 1--t--t---rHf--t----t~+----r----1·1-·-t------1 e BEHle -• ""' H/·-\l\-lf-\!r-tilll'lf-1ol-t/-\lt-H-liHt-1HI-\ii--H1\JI-If+-----1 "'·"'3?e.'1,,1llr •• ~~TI > .. ~.-:w-.,~,-,~"-r 1-,"-,n"'-"'!a,t-,,~"~----,c,. d-=1'-.rt--,~_,_ ... llf[l= 3 2!10· t1 3/JD= S MG X __j MG y ____J KG l __j Fig.lO Excitation Moments around X,Y,and Z Azes 31-nr:w-F~taunrcv DOMRII-l "I r---=A;:::f~~ I I /' ,- --~ t: 1'-' --,., ''!. l.,OG Ffi1EIJUf;NC'i 0-1~) 1110= B 2/ID= 9 Fig.ll Fourier Transformed Data in Both X and Y Axes Fig.l2 Fourier Transfor~ed Data around X,Y,and Z Ages Table 2 Maximum Values of Excitation Forces ( Current Design ) Maximum Value FGX ( N) 100.079 1------. -----------1---------------.. -----------FGY ( N) 71.823 r-----· --------· ·----- . -------------------- .. , ... ____ ··--MGX ( N•m) 4.344 1-------·-----· ---· -------- ------... ---------------------MGY ( N·m ) 5.897 f----------... -.-- ----------··----···--·-- -·--MGZ ( N·m ) 8.208 666 ' SDI<'C_I-DEAS 2'-~S= El..cihtlon o~rlnl !ion TEST 31-11H f~~!j-1-DE:~S 2.SII• £xc:Jhtlon O.finltlon s.eE+IH 11+-+4-++41-4--H--+t-+H--+f--1+-H-f-----l D.eEtea 1'--\--f-+-f-l-lr-+-1'-4-+Hr-\--{-l--J'-\-lf-'lc-f---l -5 BE+BI 1-J~-+JL....\~..J-l---\++f--++-H--+IJ-++---J -LeE•s:e,J.,=>,,~~.,..,.J=n,,_.L_I~H-,TI-I.IMrnL,-(<15·-_,L,~nf.;.,j-"Ol~~'f:z,,.-.rOI• 1/ID= 1 2/IQ= 11 (a) Excitation Force in X Axis TJME IJQMAJH 4 BHBJ f\--l-J--f+--Jtt--f+-ft-+;1-#-l+ 1-+J-J--L....\ "·""" ft-~c-!r+lli-t-t-H--ll--hH·-lr-l--if-1-+----i _, """] f+,f-f+--+i'+-11+--l-l---1-1+-++--l+--++--i-.J----1 -e.BE+3 1a•<'"rnfl--'-''--fiH\--"__.._--y-ll,h,ji--.._]J._,.¥m'~~­LHl TIME (SEI;:) 1/JDc 2 2/JDc: 12 (b) Excitation force in Y Axis E>1~l t"'t)on Dcf In! tlt~n 31-t'\AY· ff~!j--1-DE~S 2 SB- Ex<:lht)en o~flnitlon !1-~'1'-'l.eEtBB \----f>~fi-.-J\---ifi-.-A--~\---1\--f\-fl\---f---J 2.eE+as i+---J--1.--i--l--11+-i--l-t++t--I++HI++---1 " ~ ' '"" 1-J-1-++HI H--1--H-N--J ~ -'-"''"" f-I-J--1-.J.IV-1~1+++-t++I+++V+H-li-H----l -< -"'" \-ljf--lf---\J+-H---\-i---"11+-H_.JI±---\tH;t-----" " '·.. ••• 1-1'-f--l-l---1+-l-l--t+-H---++--++-+11-++---1 ~ -3, "'" H-+1--++-tt+-+t-++-HI+-+t+f+l+----l -•. "'"' W----lt--\l--+!f--\1.---114-\1--11--\I-HI----l -b.li!E+:~·-·~),"""-~~--./-o .. J,L, __ "'_~l-JHL-f \,""·JM~E'-'lf%(j-IE~C~) ~.-...1._,,-,,-t-~L-., ,f-m .. o<- •9.B~•:BflJ"mir"'~~.c,_.,b, __ ,~l-JLH-, 'f'-,~i""'.!,,O< ••• ,.t,SE-CL)~TI""""' >lo-,j-•l~~-.j-,,_ .. ,. 1/ID= 3 2/J[I::r 13 1/ID= .t1 .Z/10• 11$ (c) Eacitation Moment around X Axis SDRC __ j-[)£~ 2 SB E"c I ht l on D~-1' I n1 Li o:>n TEST 9.eE+ee 6..0E+ae 3.eE+ee \--I 1 \1 ~ ~ ·•·"'G" "''"" , "·""' TIME OONFIJH I I I I i 1 I I 1/ I I v u ll ~ v ~ rNWi"'ITm ' 1110~ 5 ,-.. 2/UJ• 15 31-11AV (e) E1citation Moment around Z Axis (d) Excitation Moment around Y Axis Fig.13 Comparison between Current Design and Optimum Design of Balance Weights (): Current Design .c.: OptiiiUm Design 667 " n p 3. BI:.+BB 1\---1+-+J-1-l--1-1--/+-+1--+~-f t--1+-+-----l "-"'"" I-I-W---l---J--4j H++-J'---II---1---iH-+H+-1------J f -3 aE+ae e+J--1-1----W-l----I---I---I.J--l.J-+-++-++--I-ill---ll--l-------i ~ ' -9 .aE+S~e·.l-:~--eo~~----,,..._,,.lco,._2~_._,1~=--o o----J~---r-...J~=rt-~---+,J LIH TIME (SEC) 1/ID= 3 2/ID= 23 :3/10= 33 (a) Excitation Moment around X Axis TitlE D011n111 ---~--• .• , ·~• •. .J-.l\o.---.JL....jj.__,J.J,..,.--"-....;'.,.~-.~_1-I--"'---'---,Jl._ "...Jic.~ __ J-'--1:-rn _ LIH IM- (S~C) l/rD= 4 2/10= 24 (b) Excitation Moment around Y Axis () :Current Design, ~:15 mm Upper than Current Design, x:Gylinder Center Fig.i4 Comparison of Gravity Genter Change s.eE•eJ --~ - --S_Il(!OI 1--~l--l~t:l--1- H-+1-1~1-+1--1'1--rJI--l'l-----j (a) Excitation Force in Y Axis TIME OOMAIH ?.0E+913 6.BE+BB 3.9E+BB B.BI;"+F.IEl v v v v f "'" s; ~' LIH T !HE ~~~EC) = . l/!Dr S (c) Excitation Moment around 2 Axis b eEHlB a BE+BB -6.0£+(1['1 '·" 1 r-· f->--- ,_ >-l!IOc 3 TIME 0[1MRII~ -· ~ f- ----'---- 1--LIN TJn - ~5~[) - 7 ~liD= 53 (b) Excitation Moment around X Axis rig.l5 Comparison of Blade Mass Chage ():Current Design ~:Hea,y Blade Mass X :Light Blade Mass 668 

CAE Approach to the Development of Rotary Compressors

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CAE Approach to the Development of Rotary Compressors

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