Vibration Analysis of Refrigerant Compressor Shaft

Transcription

1 Purdue University Purdue e-pubs International Compressor Engineering Conference School of Mechanical Engineering 1984 Vibration Analysis of Refrigerant Compressor Shaft K. Nishioka T. Inagaki T. Kannon Follow this and additional works at: Nishioka, K.; Inagaki, T.; and Kannon, T., "Vibration Analysis of Refrigerant Compressor Shaft" (1984). International Compressor Engineering Conference. Paper This document has been made available through Purdue e-pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu for additional information. Complete proceedings may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratories at Herrick/Events/orderlit.html

2 VIBRATION ANALYSIS OF REFRIGERANT COMPRESSOR SHAFT Kazumitsu Nishioka, Ph.D., Group Leader, Mitsubishi Heavy Industries, Ltd. Air-Conditioning & Machinery Works, Nagoya, Japan Taiichi Inagaki, Mitsubishi Heavy Industries, Ltd., Takasago Technical Institute, Takasago, ~apan Tatsumi Kannon, Mitsubishi Heavy Industries, Ltd., Nagoya Technical Institute, Nagoya, Japan ABSTRACT An analysis of transverse vibrations of a compressor, using the modified Mykle stad-prohl method which is one of the transfer matrix methods, is explained. A 10 hp four-cylinder refrigerant compressor was used as an object. The shaft and the frame are modeled as beams which are coupled with the sets of a spring and a damper that are the models of bearing oil film, bearing pedestals or the magnetic pull force of the motor (the frame is supported with suspensions) The forces considered include unbalance forces and pressure forces. The experimental apparatus used to measure the vibrations of the shaft and the frame is described, and computed and measured traces illustrating the vibration amplitudes are presented. INTRODUCTION One of the most important problems in refrigerant compressor making is response problem of transverse shaft vibrations. Because, air conditioners with less vibrations and less noises are welcomed these days. Besides there are so many variable speed compressors driven by inverters. This paper presents an analysis of compressor shaft vibrations, taking an example of a 10 hp reciprocal refrigerant type, using multi level rotor dynamic calculation program, shown in Fig. l. METHOD The modified Myklestad - Prahl method is applied to calculate transverse vibrations in this analysis. The method is widely used in turbomachinery that the explanation is omitted. Shown in Fig. 2, the shaft and the frame are modeled as beams. They are coupaed in series with the sets of a spring and a damper which are connected at some points. These sets are the models of bearing oil film and those of bearing pedestals or the magnetic pull force of the motor. The frame is supported with suspensions. The vibrations of the shaft and the frame can be obtained by adding exciting forces. The forces consist of unbalances and gas pressures. A-A' surface in Fig. 2 is assumed to be a foundation. The assumption is valid when inner suspensions are very soft. SUCTION PIPE: PISCHARGE: CONDUIT MOTOR ROTOR MOTOR STATOR DISCHARGE: MUFFLER MAIN BEARING HOUSING PISTON VALVE: CYLINDER HE:AD CRANK PIN CYLINDER BLOCK CAGE; BEARING OIL CRANK SHAFT Fig. 1 Cross Section of Refrigerant Compressor 32

3 ~CONNECTING ROD MASS SHAFT, FRAME Fig. 2 Analytical Model of Four MODEL DEVELOPMENT Cylinder Refrigerant Compressor The modelings of the compressors components run as follows. (1) Rotor and Frame As shown in Fig. 3, the shaft and the frame are modeled as beams which consist of many finite elements. Each element has a concentric mass, a polar mass moment of inertia and a transverse mass moment of inertia at the station, and also it has a length, a linear density mass, a bending stiffness and a shear stiffness at the section. (2) Motor, Piston, Connecting Rod and Balance Weights. Those above are modeled as distributed masses which are jointed to the shaft or the frame. The motor and the balance weights have polar mass moments of inertia and transverse mass moments of inertia. (3) Bearing Oil Film The main and the cage bearings, which are the full journal bearings, have the spring and damper effects due to oil films. As the main bearing is too long, it is divided into two parts. The linearized bearing coefficients are restricted to infinitely small perturbations about a steady state position. But, the coefficients are believed useful for the shaft amplitude up to perhaps 40 percent of the bearing clearance. so it is assumed that the behaviour can be adequately represented by a set of eight linearized spring and damping coefficients as shown in Fig. 4. STATION SECTION ll1o : CONCENTRIC MASS ~J ; POLAR MASS MOMENT OF INERTIA S I : TRANSVERSE MASS MOMENT OF INERTIA : LENGTH A r ; LINEAR OCNSITY E I BENOING STIFFNESS GA : SHEAR STIFFNESS Fig. 3 Shaft and Frame Elements Fig. 4 Dynamic Representation of a Bearing by Spring and Damping Coefficient PEDESTAL SUPPORT X 83

4 . I j;:7' := =: --V-~ -~~~-... / -., g -~ :; 5 -' '.I.o A Kpxx w "" '/1 x (0.) I'"UI,I.J{l!/RN1\T, RF"I\RI~G L/Dr] Fig. 6 Pedestal Stiffness Fig. 5 Nondimensional Spring and Damping Coefficients Chart (L/D~l) 4 Consequently, the coefficients are given from charts of coefficients versus Sommerfeld number. One of them is presented in Fig. 5. The Sommerfeld number is obtained from the following equation. s~ (R/C) 2 pfdl/w Dimensional coefficients are obtained by multiplying the nondimensional coefficients of charts by C/W. (4) Bearing Pedestal It is modeled as a cantilever beam, as shown in Fig. 6. The stiffness is obtained by calculating the displacement under the unit load. (5) Suspension It is assumed that there are springs with rotational and translational restricts at supporting points. Then, values of spring coefficients are decided geometrically. On values of damping coefficients, 5 percent of those companions, (spring coefficients) are given from experiences. <6> Motor Force It is modeled as a spring which has a negative linearized coefficient. The spring connects the motor rotor and the motor stator at the center. The value is obtained by experiment of the motor. (7) Force Each of unbalance forces by the crank pin and the balance weights are added to each station of the elements of the shaft. - 6 ~o----7ro~--~12~0--~1~~--~2~4~o----s~oo----~~ co CRANK ANGLE ( oeg) d!' ' o':' Fig. 7 1,0 0.1 C t:l ~ CRDO:R NUMBER Gas Pressure Force About gas pressure of cylinders, a frequency constituent of the composed force is added to the elements stations of the shaft and the frame. In this case, the 84

5 resultant force of the opposed cylinders among 4 cylinders is added at the center of the crank pin and the frame. The moment forces are neglected. CBJ Others The spring effects of the compressed gasses and the effect of the lubricating friction forces between the pistons and cylinders are neglected. (2) In Fig. 12, the calculated values are smaller than the experimental ones. The reason for the difference seems to be caused from probable errors in manufacturing MEASuRED -----COMPUTED NONCONTACT EDDY CURRENT PROBE } Po- f's ~ 5.0 Kg/em' 2cll FFT ANALYSER COMPUTER N FREOUENCY CHz) Fig. 9 SN-Frequency Responce Chararacteristics of Shaft } fb-p5 ~ 2JJKg/cm 350 Fig. 8 Schematic Diagram of Experimental Apparatus 1 "' ~ K-1-~-1 Jltl'll;ll ~~'llftl.t2. 1~'iii:!i.,lll2 ~~(c;,) trj"ikl ~.K!i lit ~til-~ a l IQIIPillli ~~HI.!G~ D Ill,...qo.. 1 ~,... o t l.. <;ao.oqo..,,.. _ ~ EXPERIMENT The amplitudes at the tops of the shaft and the frame were measured, as it is difficult to measure the vibration modes. A schematic diagram of the experimental apparatus is shown in Fig. 8. A noncontact eddy-current probe was used to measure the displacement of the shaft, and an accelerometer was used to measure the vibration of the frame. For the comparison with theory, a 2-channel FFT analyzer was used. The compressor was operated with the air gas under the variable line frequency from 45 Hz to 65 Hz. IBM 360 computer was used to calculate the vibrations. The dimensions used for the calculations are shown in Table ~ AY;IICi 111~1~n ~l~r ttuh~.. lj).'< f.ft!~!--j.::l!.!-1~ to) SHAFT 1;;/\1011 1" 1 ~-2 1~1...,:1;1 ~~.,'I~J~-I~::iKG,\11~-.l~KCil fll~(;l 18.Kt:: IU 1 N:r.~ IIOT/11111~ ~~l>l - ~G:; 0 lt.t " ~""" _..,... 1r!<G<Imo: 111. RESULT (ll Shown in Fig. 9, the measured curve of amplitude and the computed one are approximately same. The vibration mode at the resonance frequency (about 270 Hzl in Fig. 9 is shown in Fig. 10. According to Fig. 11, the vibration mode of K = 104 "" los at 270 Hz can be said the first mode of the crank shaft. Fig. 10 Predicted Vibration Mode at 270 Hz 85

6 Td ;z:~- ~-~ ~-~ ~ * ~- ~ ;;;6oo ~- ~ W E 2 _j <( E "' <.) ~- _ iicjij8hqq f) I!! i ~.I_I_J..J.J..U -----'----J-'- 104 JQ5 GEARING STIFFNESS ( kgt /em) 30C 50 FRAME o~--~.o~------~5~o------~6~o~------~7o ln FilEOUENCY <llzl --t-ieaslllll D ----COt 1PUTHl [ IJy B!o'Oin~lrt~l~ Unll~ldf1Cl?5 Fig. ll Critical Speed - Bearing Stiffness Map Fig. 12 ln-frequency Responce Characteristics of Shaft and Frame CONCLUSION (ll The modified Myklestad - Prohl method is very useful for the analysis of transvers~ vibrations of the crank shaft, ~specially for telling critical speed of compressors. (2) The most important problem is the estimations of bearing coefficients at fluctuating loads, so it will be needed to research more thoroughly. (3) By improving the items, mentioned above, to develop this analysis, it will be possible to predict the transverse vibrations accurately. And that will enable to produce better compressors. NOTATION s D R L c p. w f (tj Kij Cij Kpii Cpii Pd Ps Pc Sommerfeld number shaft diameter D/2 bearing axial length bearing radial clearance viscosity static force on bearing shaft rotational frequency 21tf direct and cross-coupled spring coefficient for the oil film direct and cross-coupled damping coefficient for the oil film direct spring coefficient for the pedestal direct damping coefficient for the pedestal discharge pressure suction pressure pressure in a cylinder ( i, j=x or y l 86

7 BIBLIOGRAPHY 1. Kinney G. T., "Mathematical Simulation of the Vibration of a Refrigeration compressor", Masters Degree Thesis, Purdue University, Gerhold C. H., "Mathematical Model of a Single-Cylinder Compressor", Masters Degree Thesis, Purdue University, Imaichi K., Nishii N. and Imasu K., "A Vibration Source in Refrigerant Compressors", the Design Engineering Technical Conference, September, Lund J. w., "Analytical Methods in Rotor-Bearing Dynamics", Tribology International, Vol.l3, No.5, Oct. 1980, P McHugh J. D., "Estimating the Severity of Shaft Vibrations Within Fluid Film Journal Bearing", Journal of Lubrication Technology, Vol.lOS, July 1983, P Esaki J., Hurukawa T., Matsumoto I., "Experimental Research on the Stiffness and Damping Coefficients of Oil Film Journal Bearings", Mitsubishi Juko Giho, Vol.16, No.1, Table 1 Input Data (1) R1r (2 J R-22 Pd-Ps=2 Kg 'c.m 2 Pd-Ps=i6 r\~ :'1'' L f! 5 K:.x Kxy C"lGE kyx SEARING f(yy Cxx W C:<)' W Cy>o: W Cyy w Kpxx, f'.;yy Cpxx, Cp"iY L w s Kxx Kxy I-lAIN Kyx BEARING Kyy Cxx w Cxy w Cyx w Cyy w Kpxx,Kpyy Cpxx,Cpyy D CO~IMON c ).' 3.9 em 5.6 f<g 3.<J 0.' l x 10 4 Kgf /em 3.5 >.10 Kgf /cn1 [1.05 l<pxx 8.5 em 5.6 kgf ).;: l Ct'~l_~gf./~tll -1E , ,,8 x 105~(gf /em kpxx 0.05 f(pxx 300 em "\ x 10''1-.Jsec/m em 35.0 Kg 0.;J7 3.7 xicakgf/cm -8.~ ~., ~.' em 35.0 Kgf :: :.:ld4kgf/~rn -!5.8! ! ern 30. j)m 1.?x 112fSN!:ec/m:Z 87