Purdue Uiversity Purdue e-pubs Iteratioal Compressor Egieerig Coferece School of Mechaical Egieerig 008 Aalysis of the No-Load Characteristic of the Movig Coil Liear Compressor Yigbai Xie North Chia Electric Power Uiversity Xiuzhi Huag North Chia Electric Power Uiversity Liagmig Gui North Chia Electric Power Uiversity Zhouxua Xu North Chia Electric Power Uiversity Follow this ad additioal works at: http://docs.lib.purdue.edu/icec Xie, Yigbai; Huag, Xiuzhi; Gui, Liagmig; ad Xu, Zhouxua, "Aalysis of the No-Load Characteristic of the Movig Coil Liear Compressor" (008). Iteratioal Compressor Egieerig Coferece. Paper 1868. http://docs.lib.purdue.edu/icec/1868 This documet has bee made available through Purdue e-pubs, a service of the Purdue Uiversity Libraries. Please cotact epubs@purdue.edu for additioal iformatio. Complete proceedigs may be acquired i prit ad o CD-ROM directly from the Ray W. Herrick Laboratories at https://egieerig.purdue.edu/ Herrick/Evets/orderlit.html
, Page 1 Aalysis of the No-Load Characteristic of the Movig Coil Liear Compressor Yigbai XIE 1, Xiuzhi HUANG *, Liagmig GUI 3, Zhouxua XU 4 1,,3,4 Departmet of Power Egieerig, North Chia Electric Power Uiversity, Baodig, Hebei Chia Tel: 86-31-7588 Fax: 86-31-75440 1 xieyb@cepu.edu.c huag_xiuzhi@hotmail.com 3 guiliagmi006@163.com 4 steffie@sia.com ABSTRACT The liear compressor is drive by a liear motor. The efficiecy of the whole uit is higher tha that of the traditioal compressor. A movig coil liear compressor is take for a example to fid its o-load characteristic. The ope loop ad closed loop trasfer fuctios of the system i o-load coditio are obtaied derived from the equatio of system motio. The Matlab software is applied to aalyze the stability, time domai ad frequecy domai of the system. Result idicates that the movig coil liear compressor is almost stable at o-load stage, ad the characteristic of starig is relative fast, but the overshoot is relative high, ad the dampig ratio should be icrease to lower the overshoot. 1. INTRODUCTION A liear compressor is a pisto-type compressor i which the pisto is drive by a liear motor, rather tha by a rotary motor coupled to a coversio mechaism as i a covetioal reciprocatig compressor (Uger, R.Z., 1998). Liear motors are simple devices i which axial forces are geerated by currets i a magetic field. Because all the drivig forces i a liear compressor act alog the lie of motio, there is o sideways thrust o the pisto, substatially reducig bearig loads ad allowig the use of gas bearigs or low viscosity oil. The liear compressor is ow prove i a variety of hardware. Its efficiecy, modulatio, oil-free optio, ad features that should make it compete successfully with covetioal compressor over a wide rage of applicatios (Uger, R.Z., va der Walt, N.R., 1996). The chageability if the pisto stroke is oe of the characters of the liear compressor. It ca make the compressor easy start at differetial pressure ad adjust to the chage of the load. The chage of the pisto stroke ca lead to the chage of the pressure ratio, clearace ad dead poit of the compressor. This paper takes the movig coil liear compressor for example, by foudig motio equatios to aalysis stability, time ad frequecy of cotrol system.. DYNAMIC MODEL A schematic movig coil liear compressor is showed i figure 1. It uses permaet-maget to excite. Whe alterate curret flows though the coil, at the fuctio of magetic field, the coil geerates alterate axial force Iteratioal Compressor Egieerig Coferece at Purdue, July 14-17, 008
, Page which makes the pisto do reciprocatig motio to compress the gas. This compressor has may characteristics such as simple costructio, compact, high efficiecy, lower startig curret flow ad so o. Coil Refrigerat ilet Valve plate Pisto Refrigerat outlet Permaet maget The motio equatio of the system showed i figure 1 is Figure 1 The costructio of movig coil liear compressor M d X dt dx C dt KX BIL p (1) Where M is the mass of the movig coil ad pisto, C is dampig costat, K is sprig effect, B is magetic iductio itesity, L is the legth of coil. I equatio (1) P is the chage of the gas which belogs to disturb variable. Because we oly do research o the o-load characteristic of the system, take o accout of it. This system is a sigle iput ad sigle output (SISO) LTI system, i which the curret flow I is iput variable ad the displacemet X is output variable. Usig Laplace trasform, the ope loop trasfer fuctios of the mechaical system ca be obtai Figure is closed loop trasfer fuctios block diagram of the system. X ( s ) BL G ( s ) () I ( s ) Ms Cs K Figure The block diagram of vibratig system Accordig to the costructio characters ad optimizig computer results of liear compressor, choose the parameters M=0.3 kg, C=0.7 N.s/m, K=7.365 kn/m, B=0.5 T, L=4m. 3. ANALYSE OF SYSTEM PERFORMANCE All the characters of a system lies o the closed loop trasfer fuctios, stability lies o the pole, ad dyamic performace lies o the pole ad zero. Accordig to figure, the closed loop trasfer fuctio ca be obtaied from the ope loop trasfer fuctio G( s) H ( s) ( s) (3) 1 G( s) H ( s) Iteratioal Compressor Egieerig Coferece at Purdue, July 14-17, 008
, Page 3 Where H(s)=1, from the ormalized form of closed loop trasfer fuctio s 0 (4) We ca get the closed loop characteristic root s ad importat characteristic parameter such as dampig ratio =0.00745, udamped oscillatio frequecy =157rad/s ad so o. s 3.1 Time aalyse 3.1.1 Stability aalyse Pole determies the iherece movig attribute of the system. Its positio determies the stability ad rapidity of movig modality. Whe the pole has egative real part or is a egative real umber, the correspodig modality must be coverget. Through computer this system has a pair of cojugate complex (pole) of which the real part is egative s 1, = -1.17±157i. Sice the two root of the system both has egative real part, we ca estimate this system is steady. 3.1. Time domai respose Figure 3 is step respose of the system. The pole y=0.0041, delay time t d =0.007s, rise time t r =0.001s, pole time t p =0.004s, adjustig time t s =3s, overshoot %=95.9%. This system belogs to secod-order oscillatio segmet. Dyamic course aalyse: because 01 s 1, j 1 (5) Characteristic equatio has a pair of cojugate complex roots of which the real part is egative. Its roots correspod a pair of cojugate complex pole at the left of s plae. The characteristics of this periodic dampig secod-order system are (1) The overshoot is fuctio of dampig ratio, ad is idepedet of oscillatig frequecy. The smaller dampig ratio is, the bigger oscillatig frequecy is; () The smaller dampig ratio is, the smaller rise time is; (3) The respose speed of system is relative to the agular frequecy of udamped free oscillatio. The bigger is, the higher respose speed is. Accordig to the computig results, udersize of dampig ratio ca lead overshoot over. So it must be adjusted. Figure 3 Step respose of the system 3. Root locus aalyse Iteratioal Compressor Egieerig Coferece at Purdue, July 14-17, 008
, Page 4 Figure 4 is the root locus diagram. The root locus starts from the two symmetrical poles at ureal axis to ifiite distace with growig of closed loop gai k g. As both the closed loop poles are i the left part of s plae, the system is stability. But closed loop pole are both complex pole. Its uit-step respose is uderdamped oscillatio respose, ad the bigger k g. (closed loop gai) is, the bigger overshoot is. Figure 4 Root locus diagram of the system 3.3 Frequecy aalyse Frequecy characteristic is the frequecy related to the iput ad output complex sig ratio at steady state whe the liear system or segmet effected by sie fuctio. It attributes the dyamic law of system. Figure 5 is Bode diagram of system (the upper figure is magitude, the ether figure is phase). Its pole M t =0.081, harmoic frequecy r =156.7rad/s. The expressio of magitude is L( ) 0lg 1 (6) (1 ) 4 whe <<, L()-58dB; whe >>, L()-40lg/. Figure 5 Bode diagram of the system Iteratioal Compressor Egieerig Coferece at Purdue, July 14-17, 008
, Page 5 We ca see from Bode diagram, the frequecy of this oscillatio segmet is r. The magitude characteristic reaches the max at harmoic frequecy, ad the pole depeds o dampig ratio. If the harmoic frequecy of system is over, it ca cause the overshoot of dyamic respose over. It ca ifluece stability of system. The expressio of phase is whe =0, (0)=0; whe =,.( )=-90; whe, ( )=-180. ( ) arcta (7) 1 Dampig ratio ca ifluece the chage rate of () at the eighborhood of =. The smaller the dampig ratio is, the bigger the chage rate is. Figure 6 is Nyquist diagram. Because that the umber of pole of trasfer fuctio G(s) at s plae is zero, ad Nyquist diagram does ot eclose poit (-1,j0). Accordig to Nyquist criterio, the umber of pole of closed loop system at the right of s plae is zero. So the closed loop system is steady. Figure 6 Nyquist diagram of the system 4. CONCLUSIONS Accordig to the chrematistics of movig coil liear compressor, foud mathematic model of system. The Matlab software is applied to aalyze the stability, time domai ad frequecy domai of the system. (1) Accordig to stability aalyse, Nyquist diagram, we ca coclude that the movig coil liear compressor is almost stable at o-load stage; () Accordig to time-domai aalysis, root locus diagram ad Bode diagram, we ca get that the overshoot is relative high, ad the dampig ratio should be icrease to lower the overshoot. REFERENCES Huag, B.J, Che, Y.C., 00, System Dyamics ad Cotrol of a Liear Compressor for Stroke ad Frequecy Adjustmet, Joural of Dyamic Systems, Measuremet, ad Cotrol, vol. 5, o. 14: P. 176-181. Iteratioal Compressor Egieerig Coferece at Purdue, July 14-17, 008
, Page 6 Tae, W.C., Jug, R., 004, Aalysis ad cotrol for Compressor System Drive by PWM Iverter, The 30th Aual Cof. of the IEEE Idustrial Electroics Society, p. 63-67. Uger, R.Z., 1998, Liear Compressors for Clea ad Specialty Gases, Proc. of It. Compressor Egieerig Cof., Purdue Uiversity, West Lafayette, p. 334-339 Uger, R.Z., va der Walt, N.R., 1996, Liear Compressor for No-CFC Refrigeratio, It. Appliace Techical Cof.,Purdue Uiversity, West Lafayette, P. 44-60 Xie, J.F., 005, Theory ad Experimetal Research of the Movig-magetic Liear Compressor, Dr. Thesis of Zhejiag Uiversity, P. 7-9. Iteratioal Compressor Egieerig Coferece at Purdue, July 14-17, 008