Study of the Endface Friction of the Revolving Vane Mechanism

Transcription

1 Pudue Univesity Pudue e-pubs Intenational Compesso Engineeing Confeene Shool of Mehanial Engineeing 010 Study of the Endfae Fition of the Revolving Vane Mehanism Alison Subiantoo Shool of Mehanial and Aeospae Engineeing Kim Tiow Ooi Shool of Mehanial and Aeospae Engineeing Follow this and additional woks at: Subiantoo, Alison and Ooi, Kim Tiow, "Study of the Endfae Fition of the Revolving Vane Mehanism" (010). Intenational Compesso Engineeing Confeene. Pape This doument has been made available though Pudue e-pubs, a sevie of the Pudue Univesity Libaies. Please ontat epubs@pudue.edu fo additional infomation. Complete poeedings may be aquied in pint and on CD-ROM dietly fom the Ray W. Heik Laboatoies at Heik/Events/odelit.html

2 1134, Page 1 Study of the Endfae Fition of the Revolving Vane Mehanism Alison SUBIANTORO 1 *, Kim Tiow OOI Nanyang Tehnologial Univesity, Shool of Mehanial & Aeospae Engineeing, Themal & Fluids Engineeing Division, Singapoe , alis0004@ntu.edu.sg, , mktooi@ntu.edu.sg ABSTRACT The Revolving Vane (RV) mehanism is diffeent fom othe otay mahines beause the oto and the ylinde otate togethe eentially. This podues a unique situation in the endfae gaps. A theoetial study on the fition behavio in these gaps has been onduted. It is found that due to the eentiity, a esultant foe is podued by the endfae fition. The powe loss is also found to be not only affeted by the veloity diffeene, but also by the eentiity. A egion in between the oto and the ylinde axis is found to suffe fom high fition loss due to high veloity diffeene ouing thee. Compaisons with ommon otay mahines show that RV mehanisms podue smalle endfae fition loss when the atio between the oto and the ylinde adii is less than INTRODUCTION Rotay mahines wee oiginally developed to solve the poblems faed by the moe established eipoating mahines. They inlude the vibation and noise issues. In thei futhe development, otay mahines have sine gained ineased populaity due to thei ompatness and good vibation haateistis. Howeve, otay mahines usually have issues with mehanial effiienies due to signifiant fitional losses aused by the high elative veloities among the sliding pats. Fo example, high elative speeds between sliding omponents suh as the eenti and the piston esult in signifiant loss in olling piston ompessos (Yanagisawa and Shimizu, 1985). The evolving vane (RV) mehanism was invented to solve these poblems (Teh and Ooi, 006). In this mehanism, the ylinde otates togethe with the oto at thei espetive axis of otation, esulting in muh edued elative veloities between the moving omponents. Futhe studies have shown that the mehanism indeed has supeio mehanial effiienies as ompaed to the moe established otay mahines (Teh and Ooi, 009a). Expeiments have also been onduted onfiming that the design onept an opeate suessfully (Teh and Ooi, 009b). The design onept has also been adopted fo expandes (Subiantoo and Ooi, 009, 010). Thee ae two endfaes gaps in the RV mehanism as an be seen fom Figue 1, iespetive of how the beaings ae aanged. In eah of these gaps, lubiant mixed with the woking fluid move due to shea and pessue, ausing fition on the endfae walls. One of the fitions that have been edued signifiantly by the RV mehanism is at these endfae gaps (Teh and Ooi, 009a). This is possible sine the elative veloity between the oto and the ylinde is now edued, esulting in smalle endfae fition loss. Howeve due to the eenti natue of the otations of the two omponents, it is possible that this endfae fition loss beomes signifiant when inappopiately designed. In addition, the fat that the ylinde and the oto otate togethe eentially in the RV mehanism podues an inteesting situation at the endfae gaps aely enounteed in typial otay mahines. It is the pupose of this pape to investigate in moe detail the fition behavios at the endfaes of the otating omponents of the RV mehanism. The study was onduted by analyzing the endfae fition of the mehanism theoetially. A ompaison with the endfae fition of a typial otay mehanism, suh as the sliding vane Intenational Compesso Engineeing Confeene at Pudue, July 1-15, 010

3 1134, Page mahine, whee only the oto is otating while the ylinde is stationay, will also be onduted to obseve how RV mehanism ompaes to a typial otay mahine. Figue 1: Side-view of the RV ompesso (Teh and Ooi, 009a). THEORETICAL MODEL OF THE RV MECHANISM The endfae aea oupied by the vane is elatively small and is negleted to simplify the analysis. Hene, the aeas of inteest an be eithe one of the two shapes shown as the shaded aeas in Figue. The lage ile is the ylinde wall while the smalle one is the oto wall. The x sign with a C next to it efes to the axis of the ylinde while the one with an R is the axis of the oto. The small hole onenti to the ylinde in Figue (a) epesents the ylinde shaft hole. The aea in Figue (a), whih is of the shape of a ile with a hole that is eenti fom the ente of the ile, is found at both the endfaes when the beaings ae aanged in the simply-suppoted aangement like Figue 1 o at the side with the oto shaft when the beaings ae aanged in the antileve-type aangement. The shape in Figue (b), whih is a solid ile, is found only at the side without the oto shaft when the beaings ae aanged in the antileve-type aangement. It is also impotant to emembe that the aea of inteest is atually appliable fo both the oto and ylinde endfaes and that thee ae two endfae gaps in a RV mahine. Figue : The two possible endfae aeas of inteest Intenational Compesso Engineeing Confeene at Pudue, July 1-15, 010

4 1134, Page 3 In this study, fo simpliity, the aea of inteest is taken to be the one shown in Figue (b) only. The oto is set to be the diving omponent and to otate at a onstant veloity in the lokwise dietion, ω, while the ylinde is the diven omponent. It is assumed that the fluid in the endfae gaps is a homogeneous lubiant with a onstant visosity, μ. The width of the endfae gaps, δ, is assumed to be unifom and onstant thoughout the opeation. It is also assumed that the gaps ae naow enough suh that pessue effet to the fluid flow is insignifiant. Instead, the fluid only flows due to shea aoding to the Couette flow model expessed by Equation (1). The veloity diffeene in Equation (1), ΔV, is the ylinde veloity veto minus the oto veloity veto when dealing with the oto endfae and is the opposite when dealing with the ylinde endfae. Fom Equation (1), the esultant foe and toque loss podued by the fluid fition in the endfae gaps an be deived and wee found to be as expessed by Equations () and (3) espetively. μ = ΔV δ τ (1) F = μ ΔV δ da μ T = ( ΔV ) da δ () (3) It is impotant to note that the moment am,, in Equation (3) is efeened to the oto axis when analyzing the oto endfae and is efeened to the ylinde axis when analyzing the ylinde endfae..1 Roto Endfae The analysis is stated at the oto endfae sine the aea of inteest is onenti to the oto endfae. Taking an abitay point A in the aea of inteest, a tiangle made of point A, the ylinde axis, C, and the oto axis, R, an be dawn as shown in Figue 3. Figue 3: The ACR tiangle Applying osine and sine ules to the ACR tiangle, the veloity diffeene veto at point A an be expessed as in Equation (4). V V = ( ω e ( ω ω ) x osθ ) xˆ + ( ω ω ) ( x sinθ )yˆ Obseving Figue 3 and Equation (4), it an be seen that the maximum veloity diffeene ous in the egion between the oto axis, R, and the ylinde axis, C. Hee, the oto veloity veto points to the positive x-dietion while the ylinde veloity veto points to the negative x-dietion. The maximum endfae fition loss will theefoe be lage in this egion. In light of this finding, it is advantageous to emove the fition fom this egion. This is the ase when ou aea of inteest is the one shown in Figue (a). (4) Intenational Compesso Engineeing Confeene at Pudue, July 1-15, 010

5 1134, Page 4 Substituting Equation (4) into Equations () and (3) gives the esultant foe and the toque podued by the endfae fition at the oto endfae whih ae expessed by Equations (5) and (6) espetively. F T μ = πω e xˆ + 0yˆ δ μ π 4 = ( ω ω ) zˆ δ (5) (6) It is inteesting to obseve that the esultant foe ating on the oto endfae does not have a y-omponent. It is simply a foe veto that always points to the negative x-dietion. The magnitude is also inteestingly popotional to the aea of the oto endfae multiplied by the tangential veloity of the ylinde ating at the oto axis. It is not a funtion of the veloity diffeene at all. To give some illustation on how stong this foe is, an 18 mm oto adius and 5 mm adius RV mahine with the oto tuning at a onstant angula veloity of 3000 pm is used. The endfae gap is 7.5μm and the lubiant visosity is Pa.s. With this onfiguation, the aveage esultant foe is found to be aound 1.0 N only. As fo the toque, the value an be eithe positive o negative depending on the diffeene between the ylinde and oto angula veloities. When the ylinde angula veloity is highe than the oto, it is as if the ylinde ties to pull the oto to move faste though the fluid in the gaps thus poduing a positive toque to the oto. On the othe hand, when the oto is tuning faste than the ylinde, it is as if the oto is pulling the ylinde and hene a negative toque, indiating a toque loss at the oto, is obtained.. Cylinde Endfae Pefoming a simila poedue desibed in setion.1 to the ylinde endfae gives the esultant foe and toque as expessed by Equations (7) and (8) espetively. T μ F = πωe xˆ + 0yˆ δ μ π = πωe + ω ω δ 4 ( ) (7) (8) Equation (7) shows that the esultant foe ating on the ylinde endfae is just the opposite of the one ating at the oto. This is expeted sine both the oto and the ylinde neve move lateally, only otationally. Meanwhile, Equation (8) shows that the toque on the ylinde endfae is equal to the negative of the toque ating on the oto endfae and a omponent whih is the esult of the eentiity between the oto and the ylinde axis. If the oto and the ylinde axis ae loated at the same loation, the eenti omponent of Equation (8) disappeas. This eenti omponent is also equal to the magnitude of the esultant foe multiplied with the eentiity, e..3 RV Mehanism Combining Equations (6) and (8) togethe with thei espetive angula veloities gives the total powe loss of the RV mehanism aused by the endfae fition expessed by Equation (9). μ P = πω e δ π + 4 ( ω ω ) (9) The negative sign in Equation (9) indiates that the powe is a loss, not a gain. Simila to the toque ating on the ylinde endfae, Equation (9) shows that the powe loss also has two omponents, namely the eenti and the veloity diffeene omponents. One example of this powe loss pofile is illustated by Figue 4. The data is obtained based on the RV mahine desibed in setion.. The aveage total endfae fition powe loss of this mahine is found to be.6 W. In Intenational Compesso Engineeing Confeene at Pudue, July 1-15, 010

6 1134, Page 5 patie, it is impotant to emembe that this powe loss is fo one side of the endfae only. Howeve, sine a RV mahine has two endfaes, the powe loss should be doubled. Figue 4 also shows that the eentiity omponent is moe dominant than the veloity diffeene one in this model. Howeve, this may hange fo diffeent RV mahine designs. Figue 4: Endfae powe loss of a RV mahine The aveage powe loss due to endfae fition is obtained by taking the aveage of Equation (9) fo one omplete opeating yle, expessed by Equation (10). π 1 μ 1 = π ω e + ω dϕ δ 0 P (10) The seond tem of Equation (10) whih ontains an integal tem is diffiult to solve analytially. The angula veloity, ω, itself is expessed by Equation (11) and plotted in Figue 5 (Subiantoo and Ooi, 009). Numeial integation may be pefomed to solve this integal tem. Anothe method is to appoximate the tem with a simple one. The seond method is hosen hee beause by obseving the ylinde angula veloity pofile of the RV mahine, the ylinde angula veloity seems to be able to be appoximated with a osine funtion expessed in Equation (1). = ω + ( ) ( ) + lv + lv e ω (11) ( ω ω0 ) osϕ whee ω 0 is the ylinde angula veloity when the opeating angle is zeo. ω ω (1) Compaing the aveages of the ylinde veloities of the RV mahine obtained fom Equations (11) and (1) shown in Figue 5 shows that they agee vey well. The oot mean squae diffeene is found to be only aound 0.3%. This indiates that Equation (1) appoximates Equation (11) vey well. Using the appoximated ylinde veloity in Equation (1), the aveage powe loss pe yle an now be solved analytially and is expessed by Equation (13). π μ ( ) P = e + ω δ (13) Intenational Compesso Engineeing Confeene at Pudue, July 1-15, 010

7 1134, Page 6 Using Equation (13), the aveage powe loss of the RV mahine pesented in Setion. is found to be.61 W whih diffes by only 0.3% fom the eal model. Figue 5: RV mehanism ylinde angula veloity 3. COMPARISON WITH STATIONARY CYLINDER MECHANISM Most of the ommonly found otay mahines have stationay ylindes. Theefoe, it is intuitive to ompae the RV mehanism esults with those of the stationay ylinde ones. The aea of inteest is still assumed to be a solid ile as shown by Figue (b). The endfae fition powe loss an then be expessed by Equation (14). μ π P0 ω δ 4 = (14) Unlike the RV mehanism powe loss, Equation (14) has only the veloity diffeene omponent and does not have the eentiity omponent. Of ouse the veloity diffeene is simply equal to the oto veloity sine the ylinde is stationay. In addition, sine the oto angula veloity is assumed to be onstant, the instantaneous powe loss is also the aveage powe loss. Theefoe, Equation (14) is also the aveage powe loss expession. It is also undestood that the endfae fition of the stationay ylinde mehanisms does not podue any esultant foe sine the elative veloity is puely otational in natue, unlike the RV mehanism. In ode to ompae the aveage powe loss between the RV mehanism with that of the stationay ylinde, Equations (13) and (14) should be ompaed, poduing a loss atio expessed by Equation (15). P P = (15) Fo the RV mahine desibed in setion., Equation (15) gives a value of 0.36, indiating that the RV endfae powe loss is signifiantly lowe as ompaed to that of the stationay ylinde. Plotting Equation (15) against the adius atio defined as the atio between of the oto and the ylinde adii (see Figue 6) shows that a RV mehanism podues lowe endfae loss than a stationay ylinde mehanism only if the adius atio is lage than 0.6. Below this value, RV mehanism podues moe endfae loss than those of the stationay ylinde. Intenational Compesso Engineeing Confeene at Pudue, July 1-15, 010

8 1134, Page 7 Figue 6: The loss atio ( P / P0 ) vs the adius atio ( / ) 4. CONCLUSIONS A theoetial study on the fition behavio in the RV mehanism endfae gaps has been onduted. It is found that unlike in the ases of the ommon otay mahines, a esultant foe is podued by the endfae fition in RV mehanisms. This foe is aused by the eentiity of the mehanism and is popotional to the aea of the oto endfae and the tangential veloity of the ylinde at the oto axis. The analysis also shows that thee is a egion in between the oto axis and the ylinde axis that suffes fom high fition loss due to sevee veloity diffeene ouing thee. The analysis on the powe loss found that the RV mehanism endfae fition powe loss is not only affeted by the veloity diffeene like those found in ommon otay mahines, but also by the eentiity. Compaisons with ommon otay mahines show that RV mehanisms podue lowe endfae fition loss only if the atio between the oto and the ylinde adii is highe than 0.6. NOMENCLATURE A aea (m ) Subsipts e eentiity (m) 0 stationay yl. F foe (N) ylinde l length (W) oto P powe (W) v vane adius (m) T toque (N.m) V veloity (m/s) x vaiable distane (m) δ endfae gap (m) ϕ angle (adian) μ dynami visosity (Pa.s) τ shea stess (N/m ) ω angula veloity (ad/s) Intenational Compesso Engineeing Confeene at Pudue, July 1-15, 010

9 1134, Page 8 REFERENCES Subiantoo, A., Ooi, K.T., 009, Intodution of the Revolving Vane Expande. HVAC&R Res., vol. 15, no. 4: p Subiantoo, A., Ooi, K.T., 010, Design Analysis of the Novel Revolving Vane Expande in a Tansitial Cabon Dioxide Refigeation System, Int. J. Refig., doi: /j.ijefig Teh, Y.L., Ooi, K.T., 006, Design and Fition Analysis of the Revolving Vane Compesso, Po. Pudue Comp. Conf., no. C046: p Teh, Y.L., Ooi, K.T., 009a, Theoetial Study of a Novel Refigeation Compesso - Pat I: Design of the Revolving Vane (RV) Compesso and Its Fitional Losses, Int. J. Refig., vol. 3, no. 5: p Teh, Y.L., Ooi, K.T., 009b, Expeimental Study of the Revolving Vane (RV) Compesso, Appl. Them. Eng., vol. 9, no : p Yanagisawa, T., Shimizu T., 1985, Fition Losses in Rolling Piston Type Rotay Compesso. III, Int. J. Refig., vol. 8, no. 3: p Intenational Compesso Engineeing Confeene at Pudue, July 1-15, 010