SuperWASP-N Extra-solar Planet Candidates from Fields 06hr RA 16hr
a r X i v :0711.2581v 1 [a s t r o -p h ] 16 N o v 2007
Mon.Not.R.Astron.Soc.000,000–000(0000)Printed 2February 2008
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SuperW ASP-N Extra-solar Planet Candidates from Fields
06hr S.R.Kane 1,2,W.I.Clarkson 4,9,R.G.West 8,D.M.Wilson 5,D.J.Christian 3,A.Collier Cameron 1,B.Enoch 4,T.A.Lister 1,5,11,R.A.Street 3,11,A.Evans 5,A.Fitzsimmons 3,C.A.Haswell 4,C.Hellier 5,S.T.Hodgkin 6,K.Horne 1,J.Irwin 6,F.P.Keenan 3,A.J.Norton 4,J.Osborne 8,N.R.Parley 4,D.L.Pollacco 3,R.Ryans 3,I.Skillen 7,P.J.Wheatley 10 1School of Physics &Astronomy,University of St Andrews,North Haugh,St Andrews,Fife KY169SS,UK 2Department of Astronomy,University of Florida,211Bryant Space Science Center,Gainesville,FL 32611-2055,USA 3School of Mathematics and Physics,Queen’s University,Belfast,University Road,Belfast,BT71NN,UK 4Department of Physics &Astronomy,The Open University,Milton Keynes MK76AA,UK 5Astrophysics Group,School of Chemistry &Physics,Keele University,Sta?ordshire ST55BG,UK 6Institute of Astronomy,University of Cambridge,Madingley Road,Cambridge CB30HA,UK 7Isaac Newton Group of Telescopes,Apartado de correos 321,E-38700Santa Cruz de la Palma,Tenerife,Spain 8Department of Physics &Astronomy,University of Leicester,Leicester LE17RH,UK 9Space Telescope Science Institute,3700San Martin Drive,Baltimore,MD 21218,USA 10Department of Physics,University of Warwick,Coventry CV47AL,UK 11Las Cumbres Observatory Global Telescope,Goleta,CA 93117,USA 2February 2008 ABSTRACT The Wide Angle Search for Planets (WASP)survey currently operates two instal-lations,designated SuperWASP-N and SuperWASP-S,located in the northern and southern hemispheres respectively.These installations are designed to provide high time-resolution photometry for the purpose of detecting transiting extra-solar plan-ets,asteroids,and transient events.Here we present results from a transit-hunting observing campaign using SuperWASP-N covering a right ascension range of 06hr 1INTRODUCTION More than 30extra-solar planets are now known to transit their parent stars,most of which were discov-ered through photometric monitoring.Transit surveys which use a narrow-?eld and a large magnitude depth have had some success;most notably that of the OGLE transiting planets (e.g.,Konacki et al.(2003)).Surveys which utilise the “wide and shallow”technique of mon-itoring relatively bright ?eld stars have achieved re-cent rapid success,including the discoveries of TrES-3 (O’Donovan et al.2007),XO-2b (Burke et al.2007),and several new HATNet planets (Kov′a cs et al.(2007)for ex-ample).The transit technique has matured through over-coming serious obstacles which were impeding the data analysis,such as improved optimal photometric methods for wide-?eld detectors (Hartman et al.2004)and reduc-tion of correlated (red)noise (Pont,Zucker,&Queloz 2006;Tamuz,Mazeh,&Zucker 2005). The Wide Angle Search for Planets (WASP)project currently operates two SuperWASP instruments (Pollacco et al.2006),one in the northern hemisphere on 2S.R.Kane et al. La Palma(SuperWASP-N)and the other(SuperWASP-S)located at South African Astronomical Observatory (SAAO).The relatively large?eld-of-view(FOV)of the SuperWASP design allows each instrument to monitor a substantial amount of the visible sky with relatively high time resolution.SuperWASP-N has been acquiring data since late-2003,achieving photometric precision of1%for stars brighter than V～11.5. The process of extracting reliable transit signatures from the SuperWASP data involves a systematic approach of removing trends from the photometry,employing an ef-?cient transit detection algorithm(Collier Cameron et al. 2006),and performing spectroscopic follow-up using both low-medium resolution and high resolution spectrographs to identify false-positives and con?rm planetary candidates. This method has already been used successfully on Super-WASP data to detect the planets WASP-1b and WASP-2b (Collier Cameron et al.2007a).However,this process typi-cally begins with millions of lightcurves from which many transit candidates are found and provides an extremely use-ful reference source for future surveys which monitor the same?elds.For this reason,the transit candidates detected in several RA ranges have been published for the bene-?t of the transit survey community(Christian et al.2006; Clarkson et al.2007;Lister et al.2007;Street et al.2007). We present the results of a photometric search for exo-planetary transits using data from SuperWASP-N,covering the?elds in the range06hr 2.1Observations and Recovery Rate The SuperWASP-N instrument is a robotic observatory de-signed to provide precision photometry for large areas of sky.First light was achieved in November2003and ob-servations have continued until the present time.The in-strument consists of a fork mount which is able to support up to eight lens/detector combinations simultaneously,de-scribed in more detail in Pollacco et al.(2006).When the instrument is operating at full capacity,the sky coverage becomes substantial leading to a total FOV of482square degrees.with a pixel scale of13.7arcsec per pixel.During the2003/2004(hereafter referred to as2004)observing sea-son,?ve out of the eight detectors were installed.Even so, the data rate from those?ve cameras exceeded the elec-tronic transfer capability of the ethernet connection on La Palma at that time and so data was stored via a tape(DLT) autoloader then mailed to data reduction sites. The observing strategy during the2004observations was given careful consideration,mostly in an e?ort to re-duce the false-alarm rate due to blended eclipsing binaries Table1.Fields observed using SuperW ASP-N during2004in the range06hr 0616+312637627128284239362800 1043+312631653150142775610 1044+242732654163652785180 1116+312631584142342459720 1117+232631653155212586390 1143+3126511200139072508800 1144+2427521203154002591781 1144+394445908149852285320 1216+3126511111151772592770 1217+2326511200130452460820 1243+31268623781508226051151 1244+24278523821328725471610 1244+39447819851506524101110 1316+31268622771525925661470 1317+23268723861220724081340 1342+382410328461479227241390 1342+464210126891592825561550 1343+312610128421535726161150 1417+382410228481550928711540 1418+302510328541637429331670 1443+312612540181684730711670 1444+242711339181950231801310 1444+394411735031747632852890 1516+312612338812012534482530 1517+232612339862124234682451 1543+312613047752318039632080 1544+242711345602273739071790 1544+394412242712009738742960 1616+312612746262862751333812 1617+232612947223004351104331 1643+312612953333544362333630 1644+242711249693326663782740 1644+3944121488329958630390 SuperWASP-N Extra-solar Planet Candidates3 to extract suitable stars for transit hunting.These include extracting only stars whose lightcurves have an RMS pre-cision better than0.01mag and whose baseline contains at least500frames spread over at least10nights.A summary of the?elds observed in this dataset is shown in Table1. Of the56?elds,23did not meet the baseline criteria for lightcurve extraction and so are not included in Table1.A total of130,566stars were extracted for transit hunting from the729,335remaining stars using the above criteria. The lack of baseline coverage su?ered by many of the ?elds due to the visibility of the?elds over the observing campaign was particularly acute at small RA.Consequently, the sensitivity to planetary transits varies greatly over the RA range in this dataset.This is illustrated by the transit recovery plots shown in Figure1.Transit signatures were randomly generated with periods in the range1 A transit signature is considered“recovered”if both the ingress and egress of the transit is observed.Figure1shows the results of this simulation for four?elds which span the range of RA in this dataset;in each case using2,4,and6 transits as the requirement for detection.The reduction in transit recovery rate is clearly quite dramatic for?eld which are observed for less than～60nights. 2.2Data Reduction Reduction of the SuperWASP-N data required producing milli-magnitude photometry whilst managing a high data rate.An automated reduction pipeline was constructed which was able to achieve this goal and is described in more detail in Pollacco et al.(2006).This description will concentrate on the main factors to consider when reducing wide-?eld data from instruments such as SuperWASP.Wide-?eld issues such as vignetting,point-spread function(PSF) distortion,and spatial dependence were encountered with the WASP0prototype instrument(Kane et al.2004).The WASP0dataset provided an excellent starting point around which to solve the same wide-?eld issues that would a?ect the SuperWASP data and pipeline. The calibration frames include bias,dark,and?at-?eld frames which are generally acquired on a nightly basis when the automated enclosure commences operations at dusk. These frames are handled by the pipeline through a se-ries of statistical tests which are able to classify them and create master frames.To create the master?at-?eld,a vi-gnetting map and a shutter time correction map are created and then combined with the?at-?eld through an inverse variance weighted linear least-squares?t.Iterative sigma-clipping and smoothing via spline-?tting leads to an accu-rate representation of the sky brightness for the wide-?eld. Rather than?t the spatially-variable PSF shape of the stellar images,weighted aperture photometry is used to compute the?ux in a circular aperture of tunable ra-dius.This is achieved by implementing a?ux-weighted as-trometric?t which uses an automatically extracted subset of the Tycho-2(H?g et al.2000)catalogue,then?xing the aperture locations based on entries within the USNO-B1.0 (Monet et al.2003)catalogue with a2nd epoch red magni-tude brighter than15.0.This also allows the correction of spatially-dependent aspects which are normally assumed to be constant across the frame,for example the airmass and heliocentric time correction.The vignetting and barrel dis-tortion produced by the camera optics can result in serious blending e?ects for stars whose neighbours possess signi?-cantly distorted stellar pro?les.It has been shown by Brown (2003)and Torres et al.(2004)that blending can have a detrimental e?ect on transit searches.Stars which are sig-ni?cantly a?ected by blending are identi?ed by computing blending indices B1=(F3?F1)/F1and B2=(F3?F2)/F2 where F1,F2,and F3are the?ux measurements from aper-ture radii of2.5,3.5,and4.5respectively.The comparison of these indices leads to an e?ective exclusion of blended stars as described by Kane et al.(2005). The photometric data which is produced by the pipeline is further re?ned by applying corrections for primary and secondary extinction through an iterative process which is explained in detail by Collier Cameron et al.(2006).The instrumental magnitudes are then transformed to Tycho-2 magnitudes by using local calibrators observed on excep-tional nights.These corrected data are stored as FITS bi-nary tables and ingested into the SuperWASP Data Archive which is located at the University of Leicester. 3HUNTING FOR TRANSITS This section describes the methodology used to sift the archived photometric data for transit signatures.The de-scription here is based upon the principles suggested by Collier Cameron et al.(2006)and Collier Cameron et al. (2007b)with applications to these particular data in mind. 3.1De-trending Lightcurves Achieving the photometric accuracy necessary to be sensi-tive to transiting extra-solar planets is a major challenge for wide-?eld instruments such as SuperWASP.The stel-lar lightcurves which are extracted from the archive typi-cally have systematic errors which have the strong poten-tial to produce false-alarms when scanned for transit signa-tures.The severity of the e?ects of correlated noise on the planet yield was demonstrated by Pont et al.(2006).The SysRem algorithm proposed by Tamuz et al.(2005)is e?ec-tive at identifying and removing correlated noise and was the method adopted for the SuperWASP data prior to transit hunting. As shown by Collier Cameron et al.(2006),the SysRem algorithm identi?ed four basis functions,each of which rep-resents a distinct systematic noise pattern,which were used to model the global systematic errors.The frequency struc-ture of the noise outside of transit was found to be corre-lated and characterised by a power-law.As a result of this frequency dependence,the entire correlated noise is referred to as red noise.Applying the deduced correction to the Su-perWASP data reduced the RMS amplitude of the red noise from0.0025magnitude to0.0015magnitudes.These basis functions were representations of such e?ects as colour cor-rections,extinction,and the vignetting function.Further ba-sis functions were identi?ed but these were not applied to the error model to avoid the risk of removing real variabil-ity.The resulting de-trended lightcurves are then ready to be analysed for periodic variability including transit signa-tures. 4S.R.Kane et al. 0 0.2 0.4 0.6 0.8 1 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.2 0.4 0.6 0.8 1 F r a c t i o n o f t r a n s i t s r e c o v e r e d Period (days) Field SW0616+3126 2 transits 4 transits 6 transits 0 0.2 0.4 0.6 0.8 1 1 1.5 2 2.5 3 3.5 4 4.5 5 0.2 0.4 0.6 0.8 1 F r a c t i o n o f t r a n s i t s r e c o v e r e d Period (days) Field SW1216+3126 2 transits 4 transits 6 transits 0 0.2 0.4 0.6 0.8 1 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.2 0.4 0.6 0.8 1 F r a c t i o n o f t r a n s i t s r e c o v e r e d Period (days) Field SW1417+3824 2 transits 4 transits 6 transits 0 0.2 0.4 0.6 0.8 1 1 1.5 2 2.5 3 3.5 4 4.5 5 0.2 0.4 0.6 0.8 1 F r a c t i o n o f t r a n s i t s r e c o v e r e d Period (days) Field SW1644+3944 2 transits 4 transits 6 transits Figure 1.Transit recovery rate for the ?elds SW0616+3126,SW1216+3126,SW1417+3824,and SW1644+3944;observed for 37,51,102,and 121nights respectively.The solid line represents the recovery of 2transits,the dashed line 4transits,and the dotted line 6transits. 3.2Transit Detection Algorithm The automation of transit detection algorithms for very large datasets has presented a major challenge for the transit survey teams,prompting extensive studies into optimal solutions (eg.,DeFa¨y ,Deleuil,&Barge (2001);Kov′a cs,Zucker,&Mazeh (2002)).The transit model which is applied needs to be optimised to correctly balance the computational time and the e?ciency of avoiding false-positive detections.The hybrid algorithm suggested by Collier Cameron et al.(2006)uses a re?ned version of the Box Least-Squares (BLS)algorithm to perform a search on a coarse grid of transit epochs.The algorithm then re-jects candidates based upon such features as strong vari-ability,the number of transits,and signi?cant gaps in the phase-folded lightcurve.This removes more than 95%of the search sample,allowing for a ?ner grid search on the remaining stars using the Newton-Raphson method of Protopapas,Jimenez,&Alcock (2005).Recall also from sec-tion 2.1that a requirement imposed before transit searching was that each star have ≥500measurements obtained over ≥10nights with an RMS precision ≤0.01mag.In practise,the RMS restriction results in the inclusion of stars with Tycho V <～13. For the SuperWASP ?elds,a coarse grid search was con-ducted with periods in the range 0.9≤P ≤5.0.The ?ne grid search to the remaining stars yields a candidate list which includes measurements of basic transit ?t parame-ters;such as the period,duration,depth,and epoch of ?rst transit.Additionally provided are the delta chi-square of the ?t ?χ2,the ratio of the best-?t transit model to that of the best-?t anti-transit model ?χ2/?χ2?(Burke et al.2006),the signal to red noise ratio S red (as described by Pont et al.(2006)),and the signal-to-noise of the ellipsoidal variation S /N ellip to reduce false-alarms due to eclipsing bi-naries (Sirko &Paczy′n ski 2003).The combination of these statistics allows for a powerful analysis tool in sifting transit candidates from the list. 3.3Candidate Selection Criteria The evolution of the candidate list provided by the detec-tion algorithm and the ?nal list of candidates proceeds in three distinct stages.The ?rst stage is the visual inspec-tion of the folded lightcurves,a process by which we are able to discard many of the candidates for which there is clear evidence of a secondary eclipse.In addition,candi-dates whose best-?t period is closely correlated with an integer number of days are rejected in order to minimise the number of aliases.This stage is also used to dis-card those whose data are of exceptionally poor quality.It SuperWASP-N Extra-solar Planet Candidates5 should be emphasised that this step is not to select tran- sit candidates,rather it is to reject obvious false-alarms. Through this visual inspection stage,also employed using identical criteria by the other SuperWASP-N2004candi- date releases(Christian et al.2006;Clarkson et al.2007; Lister et al.2007;Street et al.2007),generally over95%of the candidates are rejected. The second stage of candidate sifting uses the quanti- ties computed by the detection algorithm.Candidates were systematically removed from the list if any of the following are true:(i)the signal to red noise ratio is low(S red<8.0), (ii)there are signi?cant～1days aliases(P<1.05days), (iii)less than3transits are observed,(iv)the anti-transit ratio is low(?χ2/?χ2?<2.0),or(v)the ellipsoidal varia- tion is high(S/N ellip >8.0).The surviving candidates are combined together and sorted by RA so that any close com-panions can be easily identi?ed. The third stage ingests the candidates from the second stage into the Variable Star Investigator(VSI) which is an automated query tool developed by the SuperWASP consortium to provide colour information from existing photometric catalogues.The VSI tool re-turns photometric information from such catalogues as Tycho-2and2MASS(Skrutskie et al.2006)via VIZIER (Ochsenbein,Bauer,&Marcout2000).The information is used to provide estimates of basic stellar parameters,such as spectral type,e?ective temperature(see Street et al. (2007)),and radius R?.The transit depth then translates into a direct estimate of the planetary radius R p.The transit parameters allow a calculation of the exoplanet diagnostic parameterηp which serves as a measure of the candidate reli-ability and is described by Tingley&Sackett(2005).More-over,?ndercharts from DSS(Cabanela et al.2003)are used to reveal the presence of any close companions within a 48′′aperture.Candidates are removed from the list if ei-ther(i)there is a brighter object within the48′′aperture, or(ii)if the estimated radius is too large(R p>～1.6R J). This radius cuto?was selected to remain consistent with the previous SuperWASP candidate papers and also the rel-atively large radius of the recently discovered planet TrES-4 (Mandushev et al.2007). 4RESULTS This section presents results from the transit search for the 33?elds monitored in the6hr 4.1Planetary Transit Search As described in section2.1,we required that a number of conditions be satis?ed before subjecting the data to the tran-sit search algorithm.A total of729,335stars from33?elds achieved the baseline requirement for transit hunting,and 130,566of these stars also met the photometric precision re-quirement.These stars were processed by the detection algo-rithm,yielding an output of?t parameters and lightcurves folded on the best-?t period.This output contained5,445 stars which were selected by the detection algorithm as hav-ing transit signatures that require further investigation.Ta-ble1lists the number of stars extracted for transit hunting N e,the initial number of candidates detected N i,and the ?nal number of candidates N f per?eld. The?rst stage(visual inspection)of the candidate sift-ing process yielded36candidates from the original list of 5,445.Table2presents these candidates in order of increas-ing RA.Only those candidates for which a clear transit was visible were selected to populate this list.The criteria de-scribed in section3.3for the second stage of candidate sift-ing were then applied to this list,using the information dis-played in the table.The code in the?nal column of the table shows which test from the second stage was failed by that star.In the instance where more than one test is failed by a star,the?rst test failed is shown.Half of those which failed to pass through the second stage were elimi-nated due to the degree of ellipsoidal variation in the out-of-transit lightcurve,emphasising the potential contamination by grazing eclipsing binary stars. The18candidates which passed through the second stage were then subjected to further analysis using VSI. These candidates are listed in Table3along with the rel-evant information extracted from VSI,including the num-ber of brighter stars N bri and fainter stars N f ai(<5mag) within the48′′aperture.Since the Tycho-2catalogue is in-complete below V～11.5,the USNO-B1.0catalogue is used to identify individual objects within the aperture.Two of the candidates were rejected due to their sharing the aper-ture with at least one brighter object.The colours from the photometric catalogues returned by VSI combined with the ?t parameters provided by the detection algorithm are suf-?cient to calculate approximate values of stellar parameters for the host star.The code column of Table3shows that most of the candidates have a predicted planet size that is signi?cantly larger than one would expect,and are therefore excluded from the?nal list. Shown in Figure2is a plot of the depth produced by orbiting extra-solar planets of radii0.5,1.0,and1.5R J as a function of stellar radius.The transit candidates from Table 3are shown on the plot;the surviving candidates as solid 5-pointed stars and the rejected candidates as open circles. The candidate host stars are predominantly F–G–K stars as expected of the spectral distribution amongst?eld stars, hence there does not appear to be a signi?cant bias towards early or late-type stars.Therefore,although bloated gas-giant planets transiting late-type stars can result in transit depths of～25%,these kinds of detections from wide-?eld surveys such as SuperWASP will be quite rare. 4.2Transit Candidates Presented here is a brief discussion for each of the six surviv-ing candidates from the third stage of the transit sifting pro-cess.The de-trended and phase-folded lightcurves of these candidates along with their respective BLS periodograms are shown in Figures3and4.These?gures also include phase-binned average lightcurves weighted by1/σ2i where σ2i is the total estimated variance on each datapoint. 1SW ASP J115718.66+261906.1:This candidate has7transits observed with a period of～1.22days(the shortest period of the?nal candidates)and a2.78hour duration.However,the periodogram reveals that there are signi?cant peaks at longer periods,especially at2.45days. 6S.R.Kane et al. Table2.List of candidates that passed the visual inspection(?rst stage)of the transit candidates detected by the BLS algorithm.The ?nal column lists a rejection code for those which were rejected according to the information available from the BLS search,as described in section3.3.The codes are as follow:(R)signal to red noise ratio S red,(P)period,(A)anti-transit ratio,and(E)signal-to-noise of ellipsoidal variation S/N ellip. J113655.81+281708.50.9604300.0344 2.5923127.54138336.2065 5.3844 3.9539.181P J115418.56+351211.5 1.4279040.2355 2.1843127.954361672.444014.0745 3.81415.175 J115718.66+261906.1 1.2268040.0170 2.7843128.16437140.30187.6224 2.21412.916 J120214.02+332920.4 2.5894060.1456 3.6963126.519353569.546412.8868 2.51510.962 J120933.96+335637.2 1.1676740.0278 2.0403128.148481131.8057 1.581335.97210.319A J121653.45+263804.10.9826130.0301 1.1523128.3462390.3980 5.2886 1.98512.937P J122557.80+334651.1 1.3624620.0811 2.5683127.7017134330.117224.383115.72514.670E J122600.12+274221.5 1.3665170.0265 1.8963127.62775124.4934 2.7044 3.3877.215R J122640.99+310203.0 1.3378580.0139 1.3683127.8386763.7055 1.88590.13310.476A J122812.01+324132.3 3.0904370.0874 2.3763126.747642586.749024.344411.98020.691E J124428.08+255631.5 2.7630640.0547 1.8003127.8606480.7336 1.69150.03119.010A J125704.45+320657.4 2.8995150.0196 2.6883127.5493636.5989 1.3138 1.6708.645A J130303.23+423223.7 2.8580610.0829 2.2083125.720951505.2094 3.2609 5.61010.246 J130322.00+350525.4 2.6742070.0179 3.2643127.36086304.3417 5.6491 2.0018.467 J130409.52+201138.5 1.0842500.1161 1.2003127.5449101827.665412.90698.68913.746E J133022.79+330746.7 3.6269030.0863 2.5683125.312051229.325035.52550.67710.713 J133156.81+460026.6 3.1664820.0844 5.0883128.2366101924.863610.2625 5.18612.102 J133623.52+283745.30.9595610.0586 2.7123127.6365253638.79968.463422.66615.258P J141558.71+400026.7 2.4509240.0397 1.6323126.73248281.4857 3.5665 2.99913.474 J142947.03+230708.4 4.2194850.0868 2.9763125.006182755.398732.12537.45318.133 J144659.77+285248.3 3.7987680.1094 3.0483125.3835113284.560327.9419 4.25020.591 J151508.36+301413.7 1.3947740.2315 2.2803128.11231513151.546911.02428.32823.730E J152131.01+213521.3 1.3380180.0259 2.9523127.790821579.25807.1841 1.34213.865 J152645.62+310204.3 1.4091020.0297 1.2483127.3904161648.0901 3.516513.72912.944E J153135.51+305957.1 4.4672240.0367 4.0803128.3252101652.430817.8900 5.46818.038 J153741.83+344433.40.9635140.0296 1.3203127.823024253.6837 2.0412 2.37619.644P J160211.83+281010.4 3.9415540.0238 2.3523127.0391111176.7375 3.6554 1.89613.653 J160242.43+290850.1 1.3046930.0454 1.8723127.2471231878.1125 2.5227 4.07914.767 J160944.95+202609.7 1.6442430.0917 2.7843127.76031620028.279325.34758.78915.681E J161644.68+200806.8 3.9671350.1608 4.1763124.448083263.724932.0755 5.04330.317 J161732.90+242119.0 1.4537380.0157 1.4403127.679916325.0795 4.49740.80112.968 J162437.86+345723.8 4.4238510.0238 2.9523124.56136514.216611.82620.75519.494 J163245.61+321754.9 3.5381880.0928 2.8083128.34011024310.101672.417713.17623.421E J163844.53+411849.0 3.8598970.1098 3.5523125.8313107159.120626.135110.46739.587E J165424.59+241318.7 2.5711730.0434 2.1603127.117914755.804110.8147 2.24716.440 J165949.13+265346.1 2.6824130.0206 1.8483128.172111957.7991 4.561514.61614.128E SuperWASP-N Extra-solar Planet Candidates 7 Table 3.List of candidates that passed the second stage tests and were subsequently subjected to catalogue-based tests,as described in section 3.3.The rejection codes shown in the ?nal column are as follows:(B)brighter object within the speci?ed aperture,and (S)the estimated size (radius)of the planet.A total of six candidates pass all of the tests. J115418.56+351211.512.994 1.160.3290.070 1.00 5.470.6401S J115718.66+261906.111.116 1.060.1770.037 1.32 1.55 1.0602J120214.02+332920.412.533 1.630.2900.060 1.08 3.23 1.0900S J130303.23+423223.711.657 1.560.2350.055 1.21 2.580.6701S J130322.00+350525.410.893 1.770.2750.099 1.12 1.06 1.2100J133022.79+330746.712.529 1.780.2680.081 1.12 2.330.7600S J133156.81+460026.612.627 2.130.4660.1040.78 1.98 1.7301S J141558.71+400026.712.393 1.440.2110.063 1.25 1.900.5300S J142947.03+230708.412.149 1.570.2810.060 1.10 2.610.7900S J144659.77+285248.312.726 1.730.2860.084 1.08 2.680.8601S J152131.01+213521.312.188 1.360.2400.046 1.19 1.62 1.1701J153135.51+305957.111.778 1.280.2520.060 1.16 2.03 1.0001S J160211.83+281010.411.319 1.790.3380.0740.98 1.210.7600J160242.43+290850.112.417 1.990.3800.0510.91 1.530.8801J161644.68+200806.812.352 1.770.5870.1560.69 3.18 1.1213B J161732.90+242119.011.959 2.610.4770.1220.770.760.7700J162437.86+345723.810.764 1.190.2000.072 1.28 1.710.7501S J165424.59+241318.712.774 1.190.3510.0990.96 2.310.6313 B SW ASP ID Period Depth Duration Epoch (1SW ASP+)(days)(mag)(hours) (2450000+) Figure 2.The transit depth for planets of radii 0.5,1.0,and 1.5R J as a function of stellar radius.The rejected transit candidates from Table 3are shown on the diagram as open circles and the ?nal accepted candidates are shown as solid 5-pointed stars. of 3.94days and estimated radius of 1.21R J are in good agreement with the values reported by McCullough et al. (2006).A more detailed analysis of the SuperWASP-N XO-1b data may be found in Wilson et al.(2006). 1SW ASP J160242.43+290850.1:This relatively faint candidate has 23observed transits with a best-?t pe-riod of ～1.30days and a duration of 1.87hours.Based upon the spectral type of the host star,the estimated radius of the planet is 1.53R J .However,there is a fainter object within the aperture and the transit is “V-shaped”which means that this is possibly due to a grazing eclipsing binary rather than a true planetary transit.Additionally,there is a second dominant peak in the periodogram at ～2.61days.Folding the data on this longer period reveals two eclipses of slightly di?erent depth.This further evidence indicates that this candidate is most likely not due to a planet. 1SW ASP J161732.90+242119.0:There are 16tran-sits observed for this candidate with a period of ～1.45days and a duration of 1.44hours.The ellipsoidal variation is extremely low and there are no detected faint companions within the aperture.The large colour index of this star in-dicates a late-K spectral type which leads to a relatively small estimate for the planet radius of 0.76R J .The promis-ing nature of this candidate led to spectroscopic follow-up observations,described in section 4.3. 8S.R.Kane et al. Figure 3.Final transit candidates 1–3,showing the unbinned and binned lightcurves (left)and the BLS periodograms (right). 4.3Follow-up of Transit Candidates The major source of transit mimics amongst candidates are eclipsing binaries.These can be either grazing eclipsers of ～1%depth or blended eclipsers contributing ～1%of light (Brown 2003).Wide-?eld surveys such as SuperWASP and WASP0generally su?er from heavily undersampled stellar pro?les due to the large pixel sizes.In most cases,eclips-ing binaries can be excluded through photometric analysis,the catalogue queries provided by VSI,or straightforward multi-colour observations using a higher angular resolution telescope to resolve blended objects. The techniques described in section 3were used on all the SuperWASP-N 2004?elds to construct a list of high priority candidates.Further study of these candidates re-quired precision radial velocity measurements to test the planet hypothesis of the observed transit events.A sample of the high priority candidates were subsequently observed using the SOPHIE cross-dispersed echelle spectrograph on the 1.93m telescope at the Observatoire de Haute-Provence SuperWASP-N Extra-solar Planet Candidates 9 Figure 4.Final transit candidates 4–6,showing the unbinned and binned lightcurves (left)and the BLS periodograms (right). (Collier Cameron et al.2007a).SOPHIE achieved ?rst light on 31st July,2006and so the follow-up campaign under-taken by the SuperWASP consortium was amongst the ?rst science applications of the instrument. Amongst these candidates observed during these runs was the last of the candidates shown in Table 4:1SWASP J161732.90+242119.0.A single narrow-lined cross-correlation function (CCF)was observed for each of the spectra obtained.Evidence of pressure broadening was seen in the Na I D and Mg I D lines with slight asymmetry and red-shifted emission in the H αline.A radial velocity varia-tion of only a few m/s determined from three spectra were used to conlude that there is no signi?cant evidence of radial velocity induced behaviour due to the presence of a planet.Hence,this candidate has been ruled out as a transiting planet from the SOPHIE observations.The remainder of the candidates have been assigned priorities and await further observations. 10S.R.Kane et al. 4.4Rejected Candidates Presented here is a brief discussion for a subset of the re-jected candidates shown in Tables2and3.The purpose of this discussion is to highlight the quality of these candi-dates and hence the potential for false-alarms being need-lessly observed with spectroscopic follow-up.The lightcurves and BLS periodigrams for these six examples are shown in Figures5and6.These exhibit strong transit-like signatures but the information available for the majority of the rejected candidates from stages two and three of the sifting process indicated that the size of the secondary is too large to be a planetary companion. 1SW ASP J122557.80+334651.1:This candidate was very high in the list from the12h?elds,as can be seen from the high?χ2in Table2.A total of13transits were observed and folding the data on the strongest periodogram peak～1.36days yields a?at-bottomed transit lightcurve, as shown in Figure5.However,binning the data reveals the out-of-eclipse variation which is further supported by the high value of S/N ellip ,although the value of?χ2/?χ2?is very high due to the depth of the eclipse.This candidate was rejected on the basis of its high ellipsoidal variation. 1SW ASP J152645.62+310204.3:A total of16tran-sits observed with a well-constrained period of～1.41days favoured this candidate.A relatively high ellipsoidal varia-tion,however,excluded this candidate from passing through the second stage of selection criteria.Indeed,the out-of-eclipse variation becomes especially apparent when the data is binned. 1SW ASP J153135.51+305957.1:This appears to be a promising candidate with a strong signal to red noise ratio and10transits observed.The?at-bottomed transits in the lightcurve folded on a period of～4.47days appear to be very convincing and the candidate passed through to the third stage of candidate sifting.Even though the exo-planetary disgnosticηp is unity for this candidate,the es-timated size of the planet based upon the spectral type is 2.03R J and so was excluded from appearing in the?nal list. A brown dwarf companion,though possible,is only likely for relatively young ages where ongoing contraction allows for a large radius(Stassun,Mathieu,&Valenti2006).De-tection of low-mass stellar companions such as OGLE-TR-122b(Pont et al.2005)and HAT-TR-205-103(Beatty et al. 2007)have shown that even low mass stars can have radii comparable to or even less than giant planets.This target will be the subject of further observations in a low-mass eclipsing binary study. 1SW ASP J160944.95+202609.7:A large transit depth,or which16were observed,contributed to this star having a very high?χ2and?χ2/?χ2?.Additionally,the period of～1.64days is well determined by the strong peak in the periodogram.However,the transits are distinctly “V-shaped”in appearance and the ellipsoidal variation is slightly too large to prevent exclusion from the list of can-didates. 1SW ASP J163245.61+321754.9:This candidate was one of the strongest candidates selected by the detection algorithm and the subsequent visual inspection.The?χ2,?χ2/?χ2?,and signal to red noise ratio are all exception-ally high.Indeed,the relative strength of the primary peak in the periodogram at a period of～3.54days is striking.The transits are?at-bottomed and there is little evidence of out-of-eclipse variation for the10eclipses observed,although there is slight evidence for a secondary eclipse in the binned lightcurve.The measured ellipsoidal variation for this star is more than enough for it to be excluded from the candi-date list,strengthening the case of this candidate being an eclipsing binary star. 1SW ASP J165949.13+265346.1:This lightcurve is a good example of a transit mimic in that it is a subtle dip in the lightcurve with a small depth,which is generally the signature one would expect from a transiting planet.The 11observed transits folded on the period of～2.68days look convincing even when binned.However,once again the ellipsoidal variation reveals that this star is also likely to be either a blend of an eclipsing binary or a grazing eclipsing binary system. 5DISCUSSION The preceding sections have described how130,566stars were extracted from729,335for transit searching;and how the yield of5,445candidates was reduced to a list of6can-didates through the stringent selection criteria.The criteria were largely designed to aggressively remove the primary source of false-alarms,eclipsing binary stars,from the can-didate list.In this sense,the criteria proved to be very suc-cessful since,for example,the ellipsoidal variation criteria dealt a devastating blow against the kinds of false-alarms during the second stage and was the major cause for elim-ination.Though this removed some very promising looking candidates from the list,the evidence presented by closer ex-amination of a subset of the rejected candidates shows that there is indeed clear eclipsing binary behaviour in the binned lightcurves,if not in the unbinned data.The major source of elimination during the third stage of candidate sifting was an excessive estimate of the planet size,also generally due to an eclipsing binary star.Some?exibility was allowed in the size criteria,particularly in view of the recent detection of the large exoplanet TrES-4(Mandushev et al.2007). The detection of XO-1b by the transit detection algo-rithm and the subsequent passing of all the selection criteria is an important test for the transit sifting process.However, the recent discovery of HAT-P-3b(Torres et al.2007)was cause for concern since it was observed in one of the13h ?elds and has the identi?er1SWASP J134422.58+480143.2. The period of～2.9days is within the parameter space which was searched by the detection algorithm.Based upon the ephemeris information provided by Torres et al.(2007), the star was observed numerous times by SuperWASP-N during at least5predicted transits during the2004observ-ing season.However,examination of the data show that the S/N for this star is exceptionally low which resulted in a correspondingly low?χ2during the?tting https://www.sodocs.net/doc/57435221.html,-bining the data with that from the2006/2007seasons will undoubtedly yield a better result for this star. Considering the large amount of sky surveyed in the RA range presented in this paper,it is worth investi-gating the number of extra-solar planet candidates one should expect and the practical limitations on achieving this number.Analysis of radial velocity surveys such as Santos et al.(2003)and Fischer&Valenti(2005)has shown SuperWASP-N Extra-solar Planet Candidates 11 Figure 5.Example rejected candidates,showing the unbinned and binned lightcurves (left)and the BLS periodograms (right). that planet host-stars are preferentially higher in metal-licity.The ?eld stars surveyed in these ?elds are predom-inantly F–G–K dwarfs in the solar neighbourhood and so solar metallicity is a reasonable approximation.Based upon the Besan?c on model (Robin et al.2003)constructed by Smith et al.(2006),～46%of the stars in typical Su-perWASP ?elds are of F–G–K type and are therefore of small enough size to produce detectable transit dips.Of the 130,566stars in the 06h–16h ?elds searched for tran-sits,around 60,000stars will meet this criteria.It has been noted before by such papers as Kane et al.(2005)that the frequency of hot Jupiters and the geomet-ric consideration of randomly oriented orbits will result in ～0.1%of stars having an observable transiting planet in a 1 12S.R.Kane et al. Figure 6.Example rejected candidates,showing the unbinned and binned lightcurves (left)and the BLS periodograms (right). to detect multiple transits.The probability plots shown in Figure 1demonstrate this clearly with even the 14h ?elds only having a 20%chance of observing 4transits of a 5day period planet.Given this limitation for transit hunting in this dataset,the ?nal number of 6transit candidates is not an unreasonable detection rate.The eventual combination of several years of SuperWASP data will greatly help to al-leviate this de?ciency for this particular RA range.Though the criteria used to remove eclipsing binary stars was generally very successful,the problem of blended eclipsing binaries (as discussed by Brown (2003))is more dif-?cult to solve.O’Donovan et al.(2006)gives a particularly tricky example in which the light from a K dwarf binary system was blended with the light from a late F dwarf star.Avoiding confusion with these kinds of systems requires the use of careful spectroscopic follow-up to identify blended light.The strategy adopted for SuperWASP targets was to obtain high-resolution spectroscopic snapshots of high pri-ority candidates for fast and e?cient elimination of blends (described in detail by Street et al.(2007)and Lister et al. SuperWASP-N Extra-solar Planet Candidates13 (2007)).The follow-up campaign during2006/2007is con-tinued photometric monitoring,medium-resolution spectra for blend elimination,two-colour precision photometry at the predicted times of transit,and?nally precision radial velocity monitoring using such instruments as SOPHIE. 6CONCLUSIONS This paper has described the acquisition,analysis,and re-sults from the transit-hunting SuperWASP-N2004observ-ing campaign covering a right ascension range of06hr From the?nal list of6transit candidates,the pho-tometry alone indicates that1SWASP J160242.43+290850.1 is in fact likely to be the signature of a eclipsing binary rather than a planet.Furthermore,follow-up spectroscopy of 1SWASP J161732.90+242119.0shows that there is no signif-icant radial velocity variation,resulting in its rejection as a planet candidate.Further follow-up observations,both pho-tometric and spectroscopic,are being undertaken for these and other?elds from the2004SuperWASP observing cam-paign.However,the real strength of the06–16h range will be realised when the2004data is combined with that of sub-sequent years to create an exceptional baseline for transit hunting. ACKNOWLEDGEMENTS The WASP consortium consists of representatives from the Queen’s University Belfast,University of Cambridge(Wide Field Astronomy Unit),Instituto de Astro?sica de Canarias, Isaac Newton Group of Telescopes(La Palma),University of Keele,University of Leicester,Open University,and the University of St Andrews.The SuperWASP-N instrument was constructed and operated with funds made available from the Consortium Universities and the Particle Physics and Astronomy Research Council.SuperWASP-N is located in the Spanish Roque de Los Muchachos Observatory on La Palma,Canary Islands which is operated by the Instituto de Astrof′?sica de Canarias(IAC).The data reduction and analysis described in this made extensive use of the Star-link Software Collection,without which this project would not have been possible.This research also made use of the SIMBAD database and VIZIER catalogue service,operated at CDS,Strasbourg,France.In addition we made use of data products from the Two Micron All Sky Survey,which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California In-stitute of Technology,funded by the National Aeronautics and Space Administration and the National Science Foun-dation. 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Torres,G.,et al.,2007,ApJ,666,L121 Wilson,D.M.,et al.,2006,PASP,118,1245 目录 一．绪论 (3) 1．引言 (3) 2．本文的主要内容 (3) 二．拟定传动方案及相关参数 (4) 1．机构简图的确定 (4) ２．齿形与精度 (4) ３．齿轮材料及其性能 (5) 三．设计计算 (5) 1．配齿数 (5) 2．初步计算齿轮主要参数 (6) （1）按齿面接触强度计算太阳轮分度圆直径 (6) （2）按弯曲强度初算模数 (7) 3．几何尺寸计算 (8) 4．重合度计算 (9) 5．啮合效率计算 (10) 四．行星轮的的强度计算及强度校核 (11) １．强度计算 (11) ２．疲劳强度校核 (15) 1．外啮合 (15) 2．内啮合 (19) ３．安全系数校核 (20) 五．零件图及装配图 (24) 六．参考文献 (25) 一．绪论 1．引言 渐开线行星齿轮减速器是一种至少有一个齿轮绕着位置固定的几何轴线作圆周运动的齿轮传动，这种传动通常用内啮合且多采用几个行星轮同时传递载荷，以使功率分流。渐开线行星齿轮传动具有以下优点:传动比范围大、结构紧凑、体积和质量小、效率普遍较高、噪音低以及运转平稳等，因此被广泛应用于起重、冶金、工程机械、运输、航空、机床、电工机械以及国防工业等部门作为减速、变速或增速齿轮传动装置。 渐开线行星齿轮减速器所用的行星齿轮传动类型很多，按传动机构中齿轮的啮合方式分为:NGW、NW、NN、NGWN、ZU飞VGW、W.W等，其中的字母表示:N—内啮合，W—外啮合，G—内外啮合公用行星齿轮，ZU—锥齿轮。 NGW型行星齿轮传动机构的主要特点有: 重量轻、体积小。在相同条件下比硬齿面渐开线圆柱齿轮减速机重量减速轻1/2以上，体积缩小1/2—1/3; 传动效率高; 传动功率范围大，可由小于1千瓦到上万千瓦，且功率越大优点越突出，经济效益越高; 装配型式多样，适用性广，运转平稳，噪音小; 外齿轮为6级精度，内齿轮为7级精度，使用寿命一般均在十年以上。 因此NGW型渐开线行星齿轮传动已成为传动中应用最多、传递功率最大的一种行星齿轮传动。 2．本文的主要内容 NGW型行星齿轮传动机构的传动原理:当高速轴由电动机驱动时，带动太阳轮回转，再带动行星轮转动，由于内齿圈固定不动，便驱动行星架作输出运动，行星轮在行星架上既作自转又作公转，以此同样的结构组成二级、三级或多级传动。NGW型行星齿轮传动机构主要由太阳轮、行星轮、内齿圈及行星架所组成， 1 绪论 行星齿轮传动与普通定轴齿轮传动相比较，具有质量小、体积小、传动比大、承载能力大以及传动平稳和传动效率高等优点，这些已被我国越来越多的机械工程技术人员所了解和重视。由于在各种类型的行星齿轮传动中均有效的利用了功率分流性和输入、输出的同轴性以及合理地采用了内啮合，才使得其具有了上述的许多独特的优点。行星齿轮传动不仅适用于高速、大功率而且可用于低速、大转矩的机械传动装置上。它可以用作减速、增速和变速传动，运动的合成和分解，以及其特殊的应用中；这些功用对于现代机械传动发展有着重要意义。因此，行星齿轮传动在起重运输、工程机械、冶金矿山、石油化工、建筑机械、轻工纺织、医疗器械、仪器仪表、汽车、船舶、兵器、和航空航天等工业部门均获得了广泛的应用[1-2]。 1．1 发展概况 世界上一些工业发达国家，如日本、德国、英国、美国和俄罗斯等，对行星齿轮传动的应用、生产和研究都十分重视，在结构优化、传动性能，传动功率、转矩和速度等方面均处于领先地位，并出现一些新型的行星传动技术，如封闭行星齿轮传动、行星齿轮变速传动和微型行星齿轮传动等早已在现代化的机械传动设备中获得了成功的应用。行星齿轮传动在我国已有了许多年的发展史，很早就有了应用。然而，自20世纪60年代以来，我国才开始对行星齿轮传动进行了较深入、系统的研究和试制工作。无论是在设计理论方面，还是在试制和应用实践方面，均取得了较大的成就，并获得了许多的研究成果。近20多年来，尤其是我国改革开放以来，随着我国科学技术水平的进步和发展，我国已从世界上许多工业发达国家引进了大量先进的机械设备和技术，经过我国机械科技人员不断积极的吸收和消化，与时俱进，开拓创新地努力奋进，使我国的行星传动技术有了迅速的发展[1-8]。 1．2 3K型行星齿轮传动 在图4所示的3K型行星齿轮传动中，其基本构件是三个中心轮a、b和e，故其传动类型代号为3K[10]。在3K型行星传动中，由于其转臂H不承受外力矩的作用，所以，它不是基本构件，而只是用于支承行星轮心轴所必需的结构元件， 目录 一．绪论 (1) 二．拟定传动方案及相关参数 (3) 1.机构简图的确定 (3) 2.齿形与精度 (3) 3.齿轮材料及其性能 (4) 三．设计计算 (4) 1．配齿数 (4) 2．初步计算齿轮主要参数 (5) 3．几何尺寸计算 (8) 4．重合度计算 (9) 四．太阳轮的强度计算及强度校核 (10) 1.强度计算 (10) （1）外载荷 (12) （2）危险截面的弯矩和轴向力 (12) 2.疲劳强度校核 (14) （1）齿面接触疲劳强度 (14) （2）齿根弯曲疲劳强度 (18) 3.安全系数校核 (21) 五．零件图和装配图 (25) 六．参考文献 (26) 一．绪论 渐开线行星齿轮减速器是一种至少有一个齿轮绕着位置固定的几何轴线作圆周运动的齿轮传动，这种传动通常用内啮合且多采用几个行星轮同时传递载荷，以使功率分流。渐开线行星齿轮传动具有以下优点:传动比范围大、结构紧凑、体积和质量小、效率普遍较高、噪音低以及运转平稳等，因此被广泛应用于起重、冶金、工程机械、运输、航空、机床、电工机械以及国防工业等部门作为减速、变速或增速齿轮传动装置。 渐开线行星齿轮减速器所用的行星齿轮传动类型很多，按传动机构中齿轮的啮合方式分为:NGW、NW、NN、NGWN、ZU飞VGW、W.W等，其中的字母表示:N—内啮合，W—外啮合，G—内外啮合公用行星齿轮，ZU—锥齿轮。 NGW型行星齿轮传动机构的主要特点有: 1、重量轻、体积小。在相同条件下比硬齿面渐开线圆柱齿轮减速机重量减速轻1/2以上，体积缩小1/2—1/3; 2、传动效率高; 3、传动功率范围大，可由小于1千瓦到上万千瓦，且功率越大优点越突出，经济效益越高; 4、装配型式多样，适用性广，运转平稳，噪音小; 5、外齿轮为6级精度，内齿轮为7级精度，使用寿命一般均在十年以上。因此NGW型渐开线行星齿轮传动已成为传动中应用最多、传递功率最大的一种行星齿轮传动。 NGW型行星齿轮传动机构的传动原理:当高速轴由电动机驱动时，带动太阳轮回转，再带动行星轮转动，由于内齿圈固定不动，便驱动行星架作输出运动，行星轮在行星架上既作自转又作公转，以此同样的结构组成二级、三级或多级传动。NGW型行星齿轮传动机构主要由太阳轮、行星轮、内齿圈及行星架所组成，以基本构件命名， 行星齿轮机构原理及应用 我们熟知的齿轮绝大部分都是转动轴线固定的齿 轮。例如机械式钟表、普通机械式变速箱、减速器，上面所有的齿轮尽管都在做转动，但是它们的转动中心（与圆心位置重合）往往通过轴承安装在机壳上，因此，它们的转动轴都是相对机壳固定的，因而也被称为"定轴齿轮"。 有定必有动，对应地，有一类不那么为人熟知的称为"行星齿轮"的齿轮，它们的转动轴线是不固定的，而是安装在一个可以转动的支架（蓝色）上（图中黑色部分是壳体，黄色表示轴承）。行星齿轮（绿色）除了能象定轴齿轮那样围绕着自己的转动轴（B-B）转动之外，它们的转动轴还随着蓝色的支架（称为行星架）绕其它齿轮的轴线（A-A）转动。绕自己轴线的转动称为"自转"，绕其它齿轮轴线的转动称为"公转"，就象太阳系中的行星那样，因此得 名。 也如太阳系一样，成为行星齿轮公转中心的那些轴线固定的齿轮被称为"太阳轮"，如图中红色的齿轮。在一个行星齿轮上、或者在两个互相固连的行星齿轮上通常有两个啮合点，分别与两个太阳轮发生关系。如右图中，灰色的内齿轮轴线与红色的外齿轮轴线重合，也是太阳轮。 轴线固定的齿轮传动原理很简单，在一对互相啮合的齿轮中，有一个齿轮作为主动轮，动力从它那里传入，另一个齿轮作为从动轮，动力从它往外输出。也有的齿轮仅作为中转站，一边与主动轮啮合，另一边与从动轮啮合，动力从它那里通过。 在包含行星齿轮的齿轮系统中，情形就不同了。由于存在行星架，也就是说，可以有三条转动轴允许动力输入/输出，还可以用离合器或制动器之类的手段，在需要的时候限制其中一条轴的转动，剩下两条轴进行传动，这样一来，互相啮合的齿轮之间的关系就可以有多种组合： 第二章 原始数据及系统组成框图 （一）有关原始数据 课题: 一种行星轮系减速器的设计 原始数据及工作条件： 使用地点：减速离合器内部减速装置； 传动比：p i =5.2 输入转速:n=2600r/min 输入功率：P=150w 行星轮个数：w n =3 内齿圈齿数b z =63 第五章 行星齿轮传动设计 （一）行星齿轮传动的传动比和效率计算 行星齿轮传动比符号及角标含义为： 123i 1—固定件、2—主动件、3—从动件 1、齿轮b 固定时（图1—1），2K —H （NGW ）型传动的传动比b aH i 为 b aH i =1-H ab i =1+b z /a z 可得 H ab i =1-b aH i =1-p i =1-5.2=-4.2 a z =b z /b aH i -1=63*5/21=15 输出转速： H n =a n /p i =n/p i =2600/5.2=500r/min 2、行星齿轮传动的效率计算： η=1-|a n -H n /(H ab i -1)* H n |*H ψ H ψ=*H H H a b B ψψψ+ H a ψ为a —g 啮合的损失系数，H b ψ为b —g 啮合的损失系数，H B ψ为轴承的损失系数，H ψ 为总的损失系数，一般取H ψ=0.025 按a n =2600 r/min 、H n =500r/min 、H ab i =-21/5可得 η=1-|a n -H n /(H ab i -1)* H n |*H ψ=1-|2600-500/(-4.2-1)*500|*0.025=97.98% (二) 行星齿轮传动的配齿计算 1、传动比的要求——传动比条件 即 b aH i =1+b z /a z 可得 1+b z /a z =63/5=21/5=4.2 =b aH i 所以中心轮a 和内齿轮b 的齿数满足给定传动比的要求。 2、保证中心轮、内齿轮和行星架轴线重合——同轴条件 为保证行星轮g z 与两个中心轮a z 、b z 同时正确啮合，要求外啮合齿轮a —g 的中心距等于内啮合齿轮b —g 的中心距，即 w (a )a g - =()w b g a - 称为同轴条件。 对于非变位或高度变位传动，有 m/2(a z +g z )=m/2(b z -g z ) 得 g z =b z -a z /2=63-15/2=24 3、保证多个行星轮均布装入两个中心轮的齿间——装配条件 想邻两个行星轮所夹的中心角H ?=2π/w n 中心轮a 相应转过1?角，1?角必须等于中心轮a 转过γ个（整数）齿所对的中心角， 即 1?=γ*2π/a z 式中2π/a z 为中心轮a 转过一个齿（周节）所对的中心角。 p i =n/H n =1?/H ?=1+b z /a z 将1?和H ?代入上式，有 2π*γ/a z /2π/w n =1+b z /a z 经整理后γ=a z +b z =（15+63）/2=24 满足两中心轮的齿数和应为行星轮数目的整数倍的装配条件。 4、保证相邻两行星轮的齿顶不相碰——邻接条件 在行星传动中，为保证两相邻行星轮的齿顶不致相碰，相邻两行星轮的中心距应大于两轮齿顶圆半径之和，如图1—2所示 行星齿轮机构和工作原理 一、 简单的行星齿轮机构的特点 行星齿轮机构的组成： 简单（单排）的行星齿轮机构是变速机构 的基础，通常自动变速器的变速机构都由两排 或三排以上行星齿轮机构组成。简单行星齿轮 机构包括一个太阳轮、若干个行星齿轮和一个 齿轮圈，其中行星齿轮由行星架的固定轴支 承，允许行星轮在支承轴上转动。行星齿轮和 相邻的太阳轮、齿圈总是处于常啮合状态，通 常都采用斜齿轮以提高工作的平稳性（如图l 所示）。 如图2表示了简单行星齿轮机构，位于行星齿轮机构中心的是太阳轮，太阳轮和行星轮常啮合，两个外齿轮啮合旋转方向相反。正如太阳位于太阳系的中心一样，太阳轮也因其位置而得名。行星轮除了可以绕行星架支承轴旋转外，在有些工况下，还会在行星架的带动下，围绕太阳轮的中心轴线旋转，这就像地球的自转和绕着太阳的公转一样，当出现这种 情况时，就称为行星齿轮机构作用的传动 方式。在整个行星齿轮机构中，如行星轮 的自转存在，而行星架则固定不动，这种 方式类似平行轴式的传动称为定轴传动。 齿圈是内齿轮，它和行星轮常啮合，是内 齿和外齿轮啮合，两者间旋转方向相同。 行星齿轮的个数取决于变速器的设计负 荷，通常有三个或四个，个数愈多承担负 荷愈大。 简单的行星齿轮机构通常称为三构件机构，三个构件分别指太阳轮、行星架和齿圈。这三构件如果要确定相互间的运动关系，一般情况下首先需要固定 其中的一个构件，然后确定谁是主动件，并确定主动件的转速和旋转方向，结 果被动件的转速、旋转方向就确定了。 二、 单排行星齿轮机构的工作原理 根据能量守恒定律，三个元件上输入和输出的功率的代数和应等于零，从而得到单排行星齿轮机构一般运动规律的特性方程。 特性方程：n1+an2-(1+a)n3=0 n1——太阳轮转速，n2——齿圈转速，n3——行星架转速，a——齿圈与太阳轮齿数比。 由特性方程可以看出，由于单排行星齿轮机构具有两个自由度，在太阳轮、环形内齿圈和行星架三个机构中，任选两个分别作为主动件和从动件，而使另一个元件固定不动，或使其运动受一定的约束（即该元件的转速为某定值），则机构只有一个自由度，整个轮系以一定的传动比传递动力。下面分别讨论三种情况。 1、齿圈固定，太阳轮为主动件且顺时针转动，而行星架则为被动件。太阳轮顺时针转动时，太阳轮轮齿必给行星轮齿A一个推力F 1 ，则行星轮应为逆时针 转动，但由于齿圈固定，所以齿圈轮齿必给行星轮齿B一个反作用力F 2 ,行星轮 在F 1和 F 2 合力作用下必绕太阳轮顺时针旋转，结果行星轮不仅存在逆时针自 转，并且在行星架的带动下，绕太阳轮中心轴线顺时针公转。在这种状态下，就出现了行星齿轮机构作用的传动方式，而且被动件行星架的旋转方向与主动件同方向。在这里，太阳轮是主动件而且是小齿轮，被动件行星架没有具体齿数的传动关系，因此定义行星架的当量齿数等于太阳轮和齿圈齿数之和。这样，太阳轮带动行星架转动仍属于小齿轮带动最大的齿轮，是一种减速运动且有最大的传动比。因为此时n2=0，故传动比 i13=n1?n3=1+a。（如图3） 1．绪论 1.1课题研究的背景和意义 “十一五”期间我国将按照国家储备与企业储备相结合，以国家储备为主的方针，统一规划，分批建设国家战略石油储备基地。为了快速建立起我国独立的石油储备基地，根据我国国情石油储备形式以大型工业油罐为主。 在使用大型油罐进行原油储备的过程中，遇到最关键的问题就是油泥的问题，储运重未经提炼制的原油重平均约含2.2%的油泥，即对一个10万立方的储罐来说，灌满原油后其中约有2200立方的油泥成点在油罐底部。如不及时清除，再次加入原油是油泥将继续累积在一起，形成硬块，为油罐的检查及清洗增加困难。而且数量如此巨大的油泥存在于油罐底部，不经减小油罐的有效储存空间，降低储存周期寿命，造成进出阀的阻塞，而且较厚的油泥层使浮顶灌的浮顶不能不下降到底而引起浮顶倾斜，对储油安全造成威胁。因此大型原油储罐在建立时就必须增设油泥防止和消除系统，以增加油罐的储油效率，提高储油安全性，减小清灌难度。 大型原油储罐灌底油泥的防止和消除方法主要是在灌内增加油泥的混合搅拌系统，使油泥破碎细化，便于通过管线输出，我们选用了旋转喷射搅拌器。但是，其喷嘴口径相对于大型储罐的直径而言是很小的，喷嘴固定是射流束的搅拌范围是有限的，于是，在旋转喷射器入口处设置轴流涡轮，考循环油泵加压后的原油流动带动轴流涡轮高速旋转，旋转的涡轮通过主轴带动结构上完全隔绝的传动箱内一系列的减速传动使喷嘴缓慢旋转，而且通过传动箱内有关参数的选择来调节喷嘴旋转的速度，是从喷嘴喷出的射流也随之缓慢旋转，射流可打击到油罐底周向任一位置的油泥，实现彻底清除油泥，不留死角的功能。 可见，旋转喷射器中减速箱是工业油罐底油泥旋转喷射混合系统中重要的一部分。高速旋转的涡轮带动喷水嘴低速的转动，中间需要一个传动比很大的减速器连接。 1.2行星齿轮减速器研究现状及发展动态 行星齿轮传动与普通定州齿轮传动相比较，具有质量小，体积小，传动比大，承载能力大以及传动平稳和传动效率高等优点，这些已经被我过越来越多的机械工程技术人员所了解和重视。由于在各种类型的行星齿轮传动种均有效地利用了功率分流性和输入，输出地同轴性以及合理的采用了内啮合，才使得其具有了上述的许多独特的优点。行星齿轮传动不仅适用于高速，大功率而且可用于低速，大转矩的机械传动装置上。它可以用作减速，增速和变速传动，运动的合成和分解，以及其特殊的应用中： 一、填空题。 1、单排行星齿轮机构是由一个太阳轮、一个齿圈、一个行星架和支承在行星架上的几个行星齿轮（一般3-6个）组成的，成为一个行星排。 2. 行星齿轮机构一般由太阳轮、行星齿轮、行星架和齿圈四个基本构件组成。 3.双排辛普森式行星齿轮变速器通常具有四个独立元件，分别是前排齿圈、前后太阳轮组件、后排行星架、前行星架和后齿圈组件。 4.拉维娜行星齿轮机构的主要组成有大太阳轮、小太阳轮、长行星轮、短行星齿轮和齿圈。 5、传动比等于从动齿轮的齿数除以主动齿轮的齿数。 6、倒档的实现是通过在两个齿轮之间附加一个惰轮。 7、当一个小齿轮驱动一个大齿轮时，转矩增大而转速降低。 · 8、在行星齿系中，如果齿圈固定和以太阳齿轮为主动件，则可以形成减速档。 9、如果行星齿轮机构中任意两元件以相同转速和相同方向转动，则第三元件与前二者一起同速转动，而形成直接档。 10、双行星轮式行星齿轮机构：太阳轮和齿圈之间有两组互相啮合的行星齿轮，其中外面一组行星齿轮和齿圈啮合，里面一组行星齿轮和太阳轮啮合。 二、简答题。 1. 简述单排行星齿轮机构的结构及其变速原理. 答：单排行星齿轮机构是由太阳轮,行星架(含行星轮),齿圈组成.固定其中任意一个件其它两个件分别作为输入输出件就得到一种传动比,这样有8种组合方式;当其中任两件锁为一体时相当于直接挡,一比一输出;当没有固定件时相当于空挡,无输出动力。 ^ / 2、请画出单排行星齿轮机构简图。 3、请画出辛普森式行星齿轮机构简图。 1-前齿圈；2-前行星轮；3-前行星架和后齿圈组件4-前后太阳轮组件；5-后行星轮；6-后行星架 ￥ 行星齿轮传动原理 每一部汽车上都有行星齿轮，少了它们，汽车就不能自由行走。汽车上的行星齿轮主要用在两个地方，一是驱动桥减速器、二是自动变速器。很多网友都想知道，行星齿轮有什么功能，为什么汽车少不了它。 我们熟知的齿轮绝大部分都是转动轴线固定的齿轮。例如机械式钟表，上面所有的齿轮尽管都在做转动，但是它们的转动中心（与圆心位置重合）往往通过轴承安装在机壳上，因此，它们的转动轴都是相对机壳固定的，因而也被称为"定轴齿轮"。有定必有动，对应地，有一类不那么为人熟知的称为"行星齿轮"的齿轮，它们的转动轴线是不固定的，而是安装在一个可以转动的支架（蓝色）上（图1中黑色部分是壳体，黄色表示轴承）。行星齿轮（绿色）除了能象定轴齿轮那样围绕着自己的转动轴（B-B）转动之外，它们的转动轴还随着蓝色的支架（称为行星架）绕其它齿轮的轴线（A-A）转动。绕自己轴线的转动称为"自转"，绕其它齿轮轴线的转动称为"公转"，就象太阳系中的行星那样，因此得名。 也如太阳系一样，成为行星齿轮公转中心的那些轴线固定的齿轮被称为"太阳轮"，如图2中红色的齿轮。在一个行星齿轮上、或者在两个互相固连的行星齿轮上通常有两个啮合点，分别与两个太阳轮发生关系。如右图中，灰色的内齿轮轴线与红色的外齿轮轴线重合，也是太阳轮。 轴线固定的齿轮传动原理很简单，在一对互相啮合的齿轮中，有一个齿轮作为主动轮，动力从它那里传入，另一个齿轮作为从动轮，动力从它往外输出。也有的齿轮仅作为中转站，一边与主动轮啮合，另一边与从动轮啮合，动力从它那里通过。 在包含行星齿轮的齿轮系统中，情形就不同了。由于存在行星架，也就是说，可以有三条转动轴允许动力输入/输出，还可以用离合器或制动器之类的手段，在需要的时候限制其中一条轴的转动，剩下两条轴进行传动，这样一来，互相啮合的齿轮之间的关系就可以有多种组合： 动力从其中一个太阳轮输入，从另外一个太阳轮输出，行星架通过刹车机构刹死；动力从其中一个太阳轮输入，从行星架输出，另外一个太阳轮刹死； 动力从行星架输入，从其中一个太阳轮输出，另外一个太阳轮刹死； 两股动力分别从两个太阳轮输入，合成后从行星架输出； 两股动力分别从行星架和其中一个太阳轮输入，合成后从另外一个太阳轮输出；动力从其中一个太阳轮输入，从另外一个太阳轮和行星架分两路输出； 动力从行星架输入，分两路从两个太阳轮输出； 我们知道，汽车发动机只有一个，而车轮有四个。发动机的转速扭矩等特性与路面行驶需求大相径庭。要把发动机的功率适当地分配到驱动轮，可以利用行星齿轮的上述特性。如自动变速器，也是利用行星齿轮的这些特性，通过离合器和制动器改变各个构件的相对运动关系而获得不同的传动比 文献综述 机械设计制造及其自动化 行星齿轮减速器设计 一．前言 齿轮及齿轮变速箱作为机械传动中的关键零部件，几乎在所有的机械设备中都能看到它的身影。因此从某种程度上说，中国的齿轮行业是我国机械制造业的基础，齿轮行业的发展对我国机械行业有着至关重要的作用。我国齿轮行业经过“九五”结构调整与科技攻关，取得了长足的进步。 行星齿轮传动技术是齿轮传动技术的一个重要分支，采用行星齿轮传动技术开发的各类行星齿轮减速箱与行星齿轮增速箱，较之于一般的定轴式齿轮箱，在传递同样的功率与扭矩时，具有更小的体积、更轻的重量以及更高的效率，因而也更易于进行传动系统的布置和便于降低造价及运输和检修成本，因此在水泥、冶金、煤炭、矿山及石化等许多行业得以普遍运用。 行星齿轮传动的发展概况： 我国早在南北朝时代（公元429-500年），祖冲之发明了有行星齿轮的差动式指南车。因此我国行星齿轮传动的应用比欧美各国早1300多年。 1880年德国第一个行星齿轮传动装置的专利出现了。19世纪以来，随着机械工业特别是汽车和飞机工业的发展，对行星齿轮传动的发展有很大的影响。1920年首次成批制造出行星齿轮传动装置，并首先用于汽车的差速器。1938年起集中发展汽车用的行星齿轮传动装置。二次世界大战后，高速大功率船舰、透平发电机组、透平压缩机组、航空发动机及工程机械的发展，促进行星齿轮传动的发展。 高速大功率行星齿轮传动广泛的实际应用，于1951年首先在德国获得成功。1958年后，英、意、日、美、苏、瑞士等国亦获得成功，均有系列产品，并已成批生产，普遍应用。英国Allen齿轮公司生产的压缩机用行星减速器，功率25740kW；德国Renk公司生产的船用行星减速器，功率11030kW。低速重载行星减速器已由系列产品发展到生产特殊用产品，如法国Citroen生产用于水泥磨、榨糖机、矿山设备的行星减速器，重量达125t，输出转矩3900kW·m；德国Renk公司生产矿井提升机的行星减速器，功率1600kW，传动比13，输出转矩350 kW·m；日本宇都兴产公司生产了一台3200 kW，传动比720/280，输出转矩2100 kW·m的行星减速器。 我国从20世纪60年代起开始研制应用行星齿轮减速器，20世纪70年代制定了NGW型渐开线行星 目录 第一章概述 (1) 第二章要求分析 (2) （一） ............................................................... 原始数据2（二） ........................................................... 系统组成框图2 第三章方案拟定 (4) 第四章传动系统的方案设计 (5) 传动方案的分析与拟定 (5) 1. 对传动方案的要求 (5) 2. 拟定传动方案 (5) 第五章行星齿轮传动设计 (6) （一）行星齿轮传动比和效率计算 (6) （二）行星齿轮传动的配齿计算 (6) 1. 传动比条件 (6) 2. 同轴条件 (6) 3. 装配条件 (7) 4. 邻接条件 (7) （三）行星齿轮传动的几何尺寸和啮合参数计算 (8) （四） ............................................... 行星齿轮传动强度计算及校核10 1 、行星齿轮弯曲强度计算及校核 (10) 2、................................................... 齿轮齿面强度的计算及校核11 3、..................................................... 有关系数和接触疲劳极限11 （五） .................................................. 行星齿轮传动的受力分析13（六） .......................................... 行星齿轮传动的均载机构及浮动量15（七） ................................................... 轮间载荷分布均匀的措施15第六章行星轮架与输出轴间齿轮传动的设计 (17) （一）................................................... 选择齿轮材料及精度等级17（二）..................................................... 按齿面接触疲劳强度设17（三）................................................... 按齿根弯曲疲劳强度计算18 行星齿轮机构和工作原理 §3-3 行星齿轮机构和工作原理 Ⅰ授课思路：在初步了解行星齿轮机构的组成的基础上，通过单排行星齿轮机构一般运动规律的特性方程结合力和反作用力的作用原理使学生掌握单排行星齿轮的工作原理。拓展学生的能力，使学生概括出单排行星齿轮的基本特征。Ⅱ过程设计： 1．提问问题，复习上次课内容（约3min） ⑴导轮单向离合器有哪几种？（楔块式、滚柱式） ⑵锁止离合器的作用？（提高传动效率，使液力变矩器有液力传动变为机械 传动） 2．导入新课（约1min） 自动变速器是怎样实现自动换挡的呢？这就是我们这节课讲的主要内容3．新课内容：具体内容见“授课内容”（约73min） 4．本次课内容小结（约2min） 5．布置作业（约1min） Ⅲ讲解要点：单排行星齿轮的工作原理和单排行星齿轮的基本特征这一主线进行讲解。 Ⅳ授课内容： 一、简单的行星齿轮机构的特点 行星齿轮机构的组成： 简单（单排）的行星齿轮机构是变速机构 的基础，通常自动变速器的变速机构都由两排 或三排以上行星齿轮机构组成。简单行星齿轮 机构包括一个太阳轮、若干个行星齿轮和一个齿轮圈，其中行星齿轮由行星架的固定轴支承，允许行星轮在支承轴上转动。行星齿轮和相邻的太阳轮、齿圈总是处于常啮合状态，通常都采用斜齿轮以提高工作的平稳性（如图l所示）。 如图2表示了简单行星齿轮机构，位于行星齿轮机构中心的是太阳轮，太阳轮和行星轮常啮合，两个外齿轮啮合旋转方向相反。正如太阳位于太阳系的中心一样，太阳轮也因其位置而得名。行星轮除了可以绕行星架支承轴旋转外，在有些工况下，还会在行星架的带动下，围绕太阳轮的中心轴线旋转，这就像地球的自转和绕着太阳的公转一样，当出现这种 情况时，就称为行星齿轮机构作用的传动 方式。在整个行星齿轮机构中，如行星轮 的自转存在，而行星架则固定不动，这种 方式类似平行轴式的传动称为定轴传动。 齿圈是内齿轮，它和行星轮常啮合，是内 齿和外齿轮啮合，两者间旋转方向相同。 行星齿轮的个数取决于变速器的设计负 荷，通常有三个或四个，个数愈多承担负 荷愈大。 简单的行星齿轮机构通常称为三构件机构，三个构件分别指太阳轮、行星架和齿圈。这三构件如果要确定相互间的运动关系，一般情况下首先需要固定其中的一个构件，然后确定谁是主动件，并确定主动件的转速和旋转方向，结果被动件的转速、旋转方向就确定了。 二、单排行星齿轮机构的工作原理 根据能量守恒定律，三个元件上输入和输出的功率的代数和应等于零，从而得到单排行星齿轮机构一般运动规律的特性方程。 特性方程：n1+an2-(1+a)n3=0 n1——太阳轮转速，n2——齿圈转速，n3——行星架转速，a——齿圈与太阳轮齿数比。 由特性方程可以看出，由于单排行星齿轮机构具有两个自由度，在太阳轮、环形 一、简单行星轮系转矩关系 简单行星轮系(Planetary Gear Set)由太阳轮(Sun Gear)、行星架(Planet Carrier)、齿圈(Ring Gear)和行星轮(Planet Gear)构成，太阳轮S、齿圈R和行星架C有共同的回转中心，为行星轮系3个基本传动构件，如下图： 设发动机转矩由行星架C输入，FC为输入转矩在行星架上行星轮P的回转中心点的作用力，FS、FR分别为太阳轮S和齿圈R受到的外部阻力矩作用于行星轮P节圆上的反力， rS、rR分别为太阳轮S、齿圈R的节圆半径（到共同回转中心），rC为行星架上行星轮P 的回转中心点到共同回转中心的半径，rP为行星轮P的节圆半径，TS、TC、TR分别为太阳轮S、行星架C、齿圈R对行星轮P的作用力点对共同回转中心的转矩。ZS、ZR分别为太阳轮S和齿圈R的齿数， 因两齿轮齿数比等于其节圆半径比，故有：ZR∕ZS＝rR∕rS，设α= ZR ∕ZS＝rR∕rS，（α>1，称为行星轮系结构参数） 忽略轮系各转轴内摩擦力及各齿轮啮合摩擦力，根据作用力与反作用力定理及行星轮P平面力系平衡条件有： FC=－（FR+FS）（1） TC=－（TR+TS）（2） FR=FS （3） FC=－2FR=－2FS （4） （事实上，由于行星轮P与太阳轮S及齿圈R是通过轮齿接触传力，而与行星架C是通过转轴连接，因此当太阳轮S或齿圈R作为主动构件，行星架C作为从动构件时，（3）、（4）式的受力关系仍然成立。（1）、（2）式当然更是成立。） 即FS∕FR∕FC =1∕1∕－2 （5） 由rS、rR、rC的几何关系可知： rS∕rR∕rC =1∕α∕（1+α）÷2 （6） 第一章概述 行星轮系减速器较普通齿轮减速器具有体积小、重量轻、效率高及传递功率范围大等优点，逐渐获得广泛应用。同时它的缺点是：材料优质、结构复杂、制造精度要求较高、安装较困难些、设计计算也较一般减速器复杂。但随着人们对行星传动技术进一步的深入地了解和掌握以及对国外行星传动技术的引进和消化吸收，从而使其传动结构和均载方式都不断完善，同时生产工艺水平也不断提高，完全可以制造出较好的行星齿轮传动减速器。 根据负载情况进行一般的齿轮强度、几何尺寸的设计计算，然后要进行传动比条件、同心条件、装配条件、相邻条件的设计计算，由于采用的是多个行星轮传动，还必须进行均载机构及浮动量的设计计算。 行星齿轮传动根据基本够件的组成情况可分为：2K—H、3K、及K—H—V三种。若按各对齿轮的啮合方式，又可分为：NGW型、NN型、WW型、WGW型、NGWN型和N型等。我所设计的行星齿轮是2K—H行星传动NGW型。 第二章原始数据及系统组成框图 （一）有关原始数据 课题: 一种自动洗衣机行星轮系减速器的设计 原始数据及工作条件： 使用地点：自动洗衣机减速离合器内部减速装置； 传动比：p i=5.2 输入转速:n=2600r/min 输入功率：P=150w n=3 行星轮个数： w z=63 内齿圈齿数 b （二）系统组成框图 洗涤：A制动，B放开，运动经电机、带传动、中心齿轮、行星轮、行星架、波轮 脱水：A放开，B制动，运动经电机、带传动、内齿圈（脱水桶）、中心齿轮、行星架、 波轮与脱水桶等速旋转。 第三章减速器简介 减速器是一种动力传达机构，利用齿轮的速度转换器，将马达的回转数减速到所要的回转数，并得到较大转矩的机构。 减速器降速同时提高输出扭矩，扭矩输出比例按电机输出乘减速比，但要注意不能超出减速器额定扭矩。降速同时降低了负载的惯量，惯量的减少为减速比的平方。 一般的减速器有斜齿轮减速器(包括平行轴斜齿轮减速器、蜗轮减速器、锥齿轮减速器等等)、行星齿轮减速器、摆线针轮减速器、蜗轮蜗杆减速器、行星摩擦式机械无级变速机等等。按传动级数主要分为：单级、二级、多级；按传动件类型又可分为：齿轮、蜗杆、齿轮-蜗杆、蜗杆-齿轮等。 1）蜗轮蜗杆减速器的主要特点是具有反向自锁功能，可以有较大的减速比，输入轴和输出轴不在同一轴线上，也不在同一平面上。但是一般体积较大，传动效率不高，精度不高。 2）谐波减速器的谐波传动是利用柔性元件可控的弹性变形来传递运动和动力的，体积不大、精度很高，但缺点是柔轮寿命有限、不耐冲击，刚性与金属件相比较差。输入转速不能太高。 3）行星减速器其优点是结构比较紧凑，回程间隙小、精度较高，使用寿命很长，额定输出扭矩可以做的很大。 行星齿轮传动比计算 在《机械原理》上，行星齿轮求解是通过列一系列方程式求解，其求解过程繁琐容易出错，其实用不着如此，只要理解了传动比e ab i 的含义，就可以很快地直接写出行星齿轮的传动比，其关键是掌握几个根据e ab i =ab i (E 是指固定件，即是固定的太阳轮，A 为主动件，B 为被动件)说明：H ab i =(Na-NH)/(Nb-NH),那么如果H 一开始是E ，那么e ab i =(Na-NE)/(Nb-NE)=Na/Nb=ab i NE 的转速为0........由于的含义推导出来公式，随便多复杂的行星齿轮传动机构，根据这几个公式都能从头写到尾直接把其传动比写出来，而不要象《机械原理》里面所讲的方法列出一大堆方程式来求解。 一式求解行星齿轮传动比有三个基本的公式 1=+c ba a bc i i ――――――――――――――――――――――――1 a cx a bx a bc i i i = ―――――――――――――――――――――――――2 a c b a b c i i 1= ――――――――――――――――――――――――――3 熟练掌握了这三个公式后，不管什么形式的行星齿轮传动机构用这些公式代进去后就能直接将传动比写出来了。关键是要善于选择中间的一些部件作为参照，使其最后形成都是定轴传动，所以这些参照基本都是一些行星架等 在此例中，要求出e ab i ＝？，如果行星架固定不动的话，这道题目就简单多了，就是一定轴传动。所以我们要想办法把e ab i 变成一定轴传动，所以可以根据公式a cx a bx a bc i i i =将x 加进去， 所以可以得出：e bx e ax e ab i i i =要想变成定轴传动，就要把x 放到上面去，所以这里就要运用第 一个公式1=+c ba a bc i i 了，所以)1()1(x be x ae e bx e ax e ab i i i i i --==所以现在e ab i 就变成了两个定轴传动之间的关系式了。定轴传动的传动比就好办了，直接写出来就可以了。 即)1()1())1(1())1(1()1()1(01 c e b d a e c e b d c e a c x be x ae e bx e ax e ab Z Z Z Z Z Z Z Z Z Z Z Z Z Z i i i i i ?-+=?--?--=--== 再例如下面的传动机构： 已知其各轮的齿数为z 1=100，z 2=101，z 2’ =100 ，z 3=99。其输入件对输出件1的传动比i H1 行星齿轮机构传动比计算方法 Key words: epicyclic gear train; speed ratio; compute way. 随着行星齿轮减速器以及行星齿轮传动在变速箱中的广泛应用，对行星齿轮传动的了解和掌握已成为工程技术人员的必要技能。但是，对于刚接触行星齿轮传动的工程技术人员来说，行星齿轮传动的速比计算比较不容易理解和掌握。本文通过对各类参考资料及教科书中的行星齿轮传动速比计算方法进行总结归纳，并针对常用的最具代表性的2K-H型行星齿轮传动，分别用不同方法对其传动特性方程进行了推导论证。 行星齿轮传动或称周转轮系。根据《机械原理》[1]上的定义，我们可把周转轮系分为差动轮系和行星轮系。为理解方便，本论文所讨论限于2K-H型周转轮系。 关于行星齿轮传动（周转轮系）的速比计算方法，归纳起来有两大类四种方法，分别为由行星架固定法和力矩法组成的分析法；由速度图解法和矢量法组成的图解法[2]。矢量图解法一般适用于圆锥齿轮组成的行星齿轮传动，在此不作介绍；下面分别运用其它三种计算方法对2K-H型周转轮系的传动特性方程（1）进行推导。 1－太阳轮 2－行星轮 3－内齿圈 H －行星架 图1 行星齿轮传动 Fig 1 Epicyclic gear train 0)1(31=++-αωωαωH （1） 结合图1，式中1ω为太阳轮1的转速、H ω为行星架H 转速、3 ω为内齿圈3转速、α为内齿圈3与太阳轮1的齿数比即1 3 Z Z =α。 1 行星架固定法 机械专业教科书上一般介绍的都是此种方法，也可叫转化机构法。其理论是一位名叫Wlies 的科学家于1841年提出的，即“一个机构整体的绝对运动并不影响其内部各构件间的相对运动” [3]，就像手表的时针、分针、秒针的相对运动不会因带表人的行动而变化。 如图2所示，其中太阳轮1、行星轮2、内齿圈3、行星架H 的转速分别为H ωωωω、、、321。我们假定整个行星轮系放在一个绕支点O 旋转的圆盘上，此圆盘的转速为 H ω-。那么，此时行星架的转速为()0=-+=H H H H ωωω，相当于行星 行星齿轮传动的特点 行星齿轮传动与普通齿轮传动相比较，它具有许多独特的优点。它的最显著的特点是：在传递动力时它可以进行功率分流；同时，其输入轴与输出轴具有同轴性，即输出轴与输入轴均设置在同一主轴线上。所以，行星齿轮传动现已被人们用来代替普通齿轮传动，而作为各种机械传动系统中的减速器、增速器和变速装置。尤其是对于那些要求体积小、质量小、结构紧凑和传动效率高的航空发动机、起重运输、石油化工和兵器等的齿轮传动装置以及需要差速器的汽车和坦克等车辆的齿轮传动装置，行星齿轮传动已得到了越来越广泛的应用。 行星齿轮传动的主要特点如下。 (1)体积小、质量小，结构紧凑，承载能力大由于行星齿轮传动具有功率分流和各中心轮构成共轴线式的传动以及合理地应用内啮合齿轮副，因此可使其结构非常紧凑。再由于在中心轮的周围均匀地分布着数个行星轮来共同分担载荷，从而使得每个齿轮所承受的负荷较小，并允许这些齿轮采用较小的模数。此外，在结构上充分利用了内啮合承载能力大和内齿圈本身的可容体积，从而有利于缩小其外廓尺寸，使其体积小，质量小，结构非常紧凑，且承载能力大。一般，行星齿轮传动的外廓尺寸和质量约为普通齿轮传动的1/2～1/5 (即在承受相同的载荷条件下)。 (2)传动效率高由于行星齿轮传动结构的对称性，即它具有数个匀称分布的行星轮，使得作用于中心轮和转臂轴承中的反作用力能互相平衡，从而有利于达到提高传动效率的作用。在传动类型选择恰当、结构布置合理的情况下，其效率值可达0.97~0.99。 (3)传动比较大，可以实现运动的合成与分解只要适当选择行星齿轮传动的类型及配齿方案，便可以用少数几个齿轮而获得很大的传动比。在仅作为传递运动的行星齿轮传动中，其传动比可达到几千。应该指出，行星齿轮传动在其传动比很大时，仍然可保持结构紧凑、质量小、体积小等许多优点。而且，它还可以实现运动的合成与分解以及实现各种变速的复杂的运动。 (4)运动平稳、抗冲击和振动的能力较强由于采用了数个结构相同的行星轮，均匀地分布于中心轮的周围，从而可使行星轮与转臂的性力相互平衡。同时，也使参与啮合的齿数增多，故行星齿轮传动的运动平稳，抵抗冲击和振动的能力较强，工作较可靠。 总之，行星齿轮传动具有质量小、体积小、传动比大及效率高（类型选用得当）等优点。因此，行星齿轮传动现已广泛地应用于工程机械、矿山机械、冶金机械、起重运输机械、轻工机械、石油化工机械、机床、机器人、汽车、坦克、火炮、飞机、轮船、仪器和仪表等各个方面。行星传动不仅适用于高转速、大功率，而且在低速大转矩的传动装置上也已获得了应用。它几乎可适用于一切功率和转速范围，故目前行星传动技术已成为世界各国机械传动发展的重点之一。 随着行星传动技术的迅速发展，目前，高速渐开线行星齿轮传动装置所传递的功率已达到2000KW，输出转矩已达到4500KNm。据有关资料介绍，人们认为目前行星齿轮传动技术的发展方向如下。 行星齿轮传动2CV T 机构的参数模型和分析 Param etr ic M odeli ng and Analysis of A planetary Gear -CVT M echan is m V ictor H .M ucino 3 J am es E .Sm ith 3 B en Co w an 33M a rek Km icik ie w icz 33 [摘要]本文研究行星齿轮传动和无级变速器(CV T )综合功能,用太阳轮和齿圈与可变节距的带轮相连接形 成一个循环功率控制元件。该机构简单,工作时不需离合器。 参数方法是用一个数学模型去完成参数灵敏度分析。优化过程的一个特徵参数是系统最有影响的参数和功能比,以它为基础去估算可变传动和功率控制元件。用三种不同的传动比和二个独立设计参数可完全确定系统的结构。这些是:行星齿轮系速比(F g )、CV T 传动速比(F c )和控制输出齿轮速比(F gc )。二个独立参数是:a ,行星轮转臂、太阳轮、内齿圈和b ,控制齿圈和输出齿轮其中之一的半径。 [ABSTRACT ] T he m echan is m con sidered here ,com b ines the functi on s of a p lanetary g ′ ear train and a con tinuou sly variab le tran s m issi on (CV T )system ,th rough a circu lating pow er con tro l un it ,w h ich resu lts by connecting the sun 2gear shaft and the ring 2gear ro tati on th rough a variab le p itch pu lley system .T he m echan is m is si m p le and does no t requ ire clu tches fo r its operati on . A param etric app roach is u sed to generate a model that can be u sed to perfo rm param etric sen sitivity analysis .In the op ti m izati on p rocess ,a param etric characterizati on is m ade based on the mo st sign ifican t param eters and functi onal rati o s of the system to evaluate the perfo rm ance of the variab le tran s m issi on and pow er con tro l un it .T h ree differen t tran s m issi on rati o s and tw o independen t design param eters fu lly define the configu rati on of the system .T hese are :the p lanetary gear train rati o (F g ),the CV T tran s m issi on rati o (F c ),and the con tro l to ou tpu t gear rati o (F gc ).T he tw o independen t param eters can be selected from the radii of tw o group s of elem en ts (one from each ),that include a )the p lanetary gear carrier ,the sun gear ,the in ternal ring gear and b )the con tro l ring gear ,and the ou tpu t gear . 关键词:行星传动 无级变速器CV T 参数模型 功率分流 功率反馈 Key w o rds :p lanetary gear train con tinuou sly variab le tran s m issi on CV T Param etric modeling pow er sp lit Pow er 2Feedback 3W est V irginia U niv .33CK Engineering 引言 行星齿轮机构和无级变速箱的综合已有很多成功的应用实例,本文仅述及由行星齿轮系和CV T 直接组合提供变速的传动装置。这两个主要部件(行星传动和CV T )的综合特性是不要求采用离合器和链传动,这种的机构的三种主要结构简称为“行星2CV T ”,一般布置为二个功率反馈和一个功率分流。 本文研究的系统如图1所示,按其特徵参数确 I n troduction P lanetary gear train m echan is m s and con tinu 2ou sly variab le tran s m issi on s have been u sed suc 2cessfu lly in m any types of app licati on s .T he m echa 2n is m p resen ted in th is paper u ses on ly a p lanetary gear train system and a CV T un it directly connect 2ed to p rovide a variab le tran s m issi on un it .T he com b ined featu res of the tw o m ain componen ts (p lanetray and CV T )do no t requ ire the u se of clu 2NGW型行星齿轮减速器——行星轮的设计
行星齿轮传动设计详解
(完整word版)NGW型行星轮中太阳轮的设计和计算要点
行星齿轮机构原理及应用
行星齿轮设计【模板】
行星齿轮结构及工作原理
3Z型行星齿轮减速器设计
行星齿轮机构练习答案
行星齿轮传动原理
行星齿轮减速器设计【文献综述】
行星减速器设计
行星齿轮结构和工作原理
行星轮系基本关系
行星轮系减速器设计说明书
行星齿轮传动比计算
行星齿轮机构传动比计算方法
行星齿轮传动的特点
行星齿轮传动_CVT机构的参数模型和分析