汽車減速器殼加工工藝及專用機(jī)床設(shè)計(jì)【鉆8φ20H7孔及鉆14-φ12H7孔】【說明書+CAD+3D】

汽車減速器殼加工工藝及專用機(jī)床設(shè)計(jì)【鉆8φ20H7孔及鉆14-φ12H7孔】【說明書+CAD+3D】,鉆8φ20H7孔及鉆14-φ12H7孔,說明書+CAD+3D,汽車減速器殼加工工藝及專用機(jī)床設(shè)計(jì)【鉆8φ20H7孔及鉆14-φ12H7孔】【說明書+CAD+3D】,汽車,減速器,加工,工藝,專用,機(jī)床 Transactions of Tianjin UniversityISSN100624982pp1632168Vol.13No.3Jun. 2007Design and Dynamics Simulation of a NovelDouble2Ring2Plate Gear Reducer3ZHANGJun(張 俊) , SONG Yimin(宋軼民) , ZHANG Ce(張 策)(School of Mechanical Engineering , Tianjin University , Tianjin 300072 , China)Abstract:A patented double2ring2plate gear reducer was designed and its dynamic performancewas simulated.One unique characteristic of this novel drive is that the phase angle difference be2tween two parallelogram mechanisms is a little less than180degree and four counterweights on twocrankshafts are designed to balance inertia forces and inertia moments of the mechanisms.Its oper2ating principle,advantages,and design issues were discussed.An elasto2dynamics model was pr2esented to acquire its dynamic response by considering the elastic deformations of ring2plates,gears,bearings,etc.The simulation results reveal that compared with housing bearings,planetarybearings work in more severe conditions.The fluctuation of loads on gears and bearings indicatesthat the main reason for reducer vibration is elastic deformations of the system rather than inertiaforces and inertia moments of the mechanisms.Keywords:double2ring2plate gear reducer;planetary transmission;elasto2dynamicsAccepted date : 2006211228.ZHANGJun , born in 1981 , male , doctorate student.3Supported by theKey Project of Ministry ofEducation of China (No. 106050) , National Natural Science Foundation of China(No. 50205019) , and Doctoral Foundation of Ministry of Education of China(No. 20040056018) .Correspondence to ZHANGJun , E2mail : zhang-jun tju. edu. cn.Three2ring gear reducer , an internal gear planetarytransmission , claims many advantages , including largetransmission ratio , high loading capacity , and compactvolume1. However , there still exist some disadvantages inits application. One is the unbalanced inertia moments ex2erted on the housing bearingsof crankshafts during its work2ing process. The unbalanced moments , named the shakingmoments, may produce negative vibration and noise2.And with the increase of input speed , the vibration getsmore severe. Another one is the fretting wear of eccentricsleeves3. The six eccentric sleeves on crankshafts bringnot only assembling difficulties but also premature fatigue ofplanetary bearings.T o eliminate the above disadvantages , Xinet al4proposed a fully2balanced three2ring gear reducer.Thephase angle differences between middle ring2plate and twoside ones are both 180 degree , and the thickness of middlering2plate is twice the side ones. Thus , the inertia forcesand inertia moments of three phases of mechanisms are fullybalanced.However , from the viewpoint of mechanism ,such an internal gear planetary transmission is a combina2tion of three parallelogram linkages and internal gear trans2missions juxtaposed , whose motion will be uncertain whenthe coupler is collinear with the cranks. And this position isoften named“dead point”. As the phase angle differencebetween two adjacent mechanisms is 180 degree , threephases of parallelogram mechanisms will reach the“deadpoint”at the same time. Therefore , to overcome the“deadpoint”, this device needs two additional timing belts todrive the crankshafts simultaneously , which makes thestructure of the reducer more complicated. Besides thecomplexity of structure , the fretting wear of eccentricsleeves still remains. T o solve the problems concerning ec2centric sleeves , Tanget alpresented a similar double2ring2plate gear reducer5. Four counterweights are fixed on twocrankshafts to balance the inertia moments. Similarly , thephase angle difference between the juxtaposed parallelogrammechanisms is 180 degree. Because of the problem of“dead point”, an additional bridge gear pair is needed todivert the input into two crankshafts. The both drives men2tioned above need a first stage transmission to overcome the“dead point”, which makes the structure of the drive com2paratively incompact.In this paper , a novel double2ring2plate gear reduc2 1994-2007 China Academic Journal Electronic Publishing House. All rights reserved. http:/er6is designed and the afore2mentioned disadvantages ofinternal gear planetary transmission are eliminated. By con2sidering elastic deformations of the parts , a systematic elas2to2dynamic model is developed to reveal its dynamic perfor2mance.1Mechanism design111Structure and operating principleThe basic structure of the double2ring2plate gear re2ducer is shown in Fig. 1.Fig.1Schematic of a double2ring2plate gear reducerThe two corresponding eccentrics on each crankshaftand one ring2plate form a parallelogram mechanism. Whenthe input shaft is driven , the ring2plate will perform a trans2lational motion. Through the meshingof internal gear on thering2plate with external gear on the output shaft , the poweris output with a large transmission ratio.One unique feature of this drive is that the phase angledifference between two parallelogram mechanisms is a littleless than 180 degree. When one parallelogram mechanismis at the“dead point”where the coupler is collinear withthe cranks , the other one is at“regular position”. Throughthe gear meshing , the mechanism at“regular position”willcarry the other mechanism through the“dead point”suc2cessfully. Thus the reducer can rotate continuously with asingle power input. Compared with previous internal gearplanetary transmissions1 ,4 ,5, this drive needs no first stagetransmission. Therefore , the volume is much more com2pact. Moreover , the cancellation of eccentric sleeves helpsto eliminate the fretting wear.112Calculation for counterweightsAs mentioned above , the phase angle difference be2tween two parallelogram mechanisms is a little less than 180degree. So when the reducer works , the inertial forces andinertial moments of two parallelogram mechanisms cannot bebalanced ,which will produce both shaking forces and shak2ing moments on housing bearings of two crankshafts ,leadingto vibration and noise. Hence , four counterweights are de2signed to eliminate the shaking forces and moments.Let the inertia force produced by each parallelogrammechanism beFi(i= 1 ,2) , and we haveFi= (015mb+mH)e2(1)wherembandmHrepresent the mass of the ring2plate andthe tumbler , ande,stand for eccentric of the sleeves(orthe crank length) and angular velocity of input shaft ,re2spectively.According to the dynamic balance theory for rigid ro2tor , we can choose two balance planes , named I and II , inwhich the shaking forces and moments are balanced bycounterweights. The balance condition is described as fol2lows:F1+F2+Fe1= 0F1+F2+Fe2= 0(2)whereFi,Fiare the components ofFiin balanceplanes I and II respectively , whileFe1,Fe2are the in2ertia forces yielded by counterweights in related balanceplanes.By solving Eq. (2) , we can obtain the mass of coun2terweightmeiand the eccentric radiusrpiusing the follow2ing formula :Fei=meirpi2(3)2Elasto2dynamics analysisT o evaluate the performance of the drive , an elasto2dynamics model is developed to simulate its dynamic re2sponse.A prototype of the double2ring2plate gear reducer isdesigned for case study. Its main parameters are listed inTab. 1 , where the nomenclatures are explained as follows:ADistance between input shaft and output shaft ,mm;z1,z2T ooth number of external gear and internalgear , respectively;mModule of gear pair , mm;eEccentric of the sleeves , mm;Phase angle difference between two parallelogrammechanisms , degree ;461Transactions of Tianjin UniversityVol. 13No. 32007 1994-2007 China Academic Journal Electronic Publishing House. All rights reserved. http:/x1,x2Modification coefficient of gear pair respec2tively; Meshing angle of gear pair , degree ;diRadius of crankshafts , mm;nInput speed of crank , rmin;mbMass of ring2plate , kg;mHMass of tumbler , kg;moMass of output shaft , kg;meMass of counterweight , kg;Jxb,JzbInertia moments of ring2plate aboutxandzaxis respectively , kgm2;Jxo,JzoInertia moments of output shaft aboutx,andzaxis respectively , kgm2;JsInertia momentsof support shaft aboutzaxis , kgm2;kpStiffness of planetary bearing , 108Nm;kmStiffness of gear meshing , 108Nm;koStiffness of housing bearing on output shaft , 108Nm;ToRated output torque , kNm.Tab.1Main parameters of prototypeAz1z2me200515345121761603 8x1x2 dinmb0166211164431985 2401 5002918mHmomeJxbJzbJxo3152381761152012350197301191JzoJskpkmkoTo0119401000 5514019410It is necessary to point out that the phase angle differ2enceis 31396 2 degree less than 180 degree , whichequals a half of tooth angle of the internal gear. As men2tioned before , to overcome“dead point”, the phase angledifference between two parallelogram mechanisms must notequal 180 degree. Theoretically , anyunequal to 180 de2gree can make the mechanisms get through the“deadpoint”. But ifis too close to 180 degree , the errors ofmanufacturing and assembling may bring unpredictable trou2bles. On the other hand , ifis much less than 180 de2gree , the inertia forces and inertia moments of the mecha2nisms will increase and a larger mass of counterweights isneeded , which mayprobably bring difficulty to structure de2sign issues.211ModelingThe double2ring2plate gear reducer is an over2con2strained mechanism , which requires some coordinate rela2tions when a dynamics analysis is made. Therefore , someelastic deformations are taken into consideration to derivethe coordinate relations. The deformations include those ofcrankshafts, gearings , bearings , ring2plates and errors ofeccentrics.Fig.2 shows the elastic deformations of one phase ofparallelogram mechanism. The dashed lines represent theactual position of the mechanism while the solid lines indi2cate the theoretical position. Here ,OIAandOSBare the2oretical lengths of input eccentric and support eccentric ;OIOIandOSOSare bending deformations of input shaftand support shaft ;OIA1andOSB1are positions of eccen2trics on input shaft and support shaft without any errors;A1A2andB1B2are run2out error and indexing error of ec2centrics on input shaft and support shaft , respectively;A2A3andB2B3denote elastic deformations of input plane2tary bearing and support planetary bearing , respectively ,andiis the crank angle of theith parallelogram mecha2nism.Fig.2Deformations of one phase of parallelogram mechanismT o simplify the analysis , the overall transmission is di2vided into several subsystems. The dynamic model for eachsubsystem is developed separately and then assembled withthe coordinate relations to get the global dynamics equation.The process is a little similar to Yangs derivation1.However , in Yangs model the ring2plates were merely con2sidered as rigid bodies while in this model the elastic defor2mations of ring2plates are taken into account. Previous re2searches revealed that the elasticities of ring2plate played asignificant role in ring2plate type gear reducers dynamicperformance7 ,8. By considering all these deformations , wederive some alternative coordinate relations as follows.From thevectorloops ofOIOIA1A2A3AandOSOSB1B2B3B, we can derive the following equations:Uax=G1Xn1+G2Xn2-XI-G3+G4561ZHANG Jun et al :Design and Dynamics Simulation of a Novel Double2Ring2Plate Gear Reducer 1994-2007 China Academic Journal Electronic Publishing House. All rights reserved. http:/Uay=H1Yn1+H2Yn2-YI-H3-H4(4)Ubx=G5Xn1+G6Xn2+Es-XS-G7+G8Uby=H5Yn1+H6Yn2-Ec-YS-H7-H8(5)whereXni,Yniare the tensile compression and bending de2formations of theith ring2plate , respectively; andXI,YI,XS,YSdenote the bending deformations of input shaft andsupport shaft inxandydirections , respectively;Uax,Uay,Ubx,Ubyrepresent the elastic deformations of plane2tary bearingson input shaft and support shaft inxandydi2rections respectively;is the elastic angular displacementof support shaft with respect to its initiative position.As to the deformations of gear meshing , we namepithe relative displacement of meshing pair along the actionline for theith ring2plate and we finally have :pi=L1iXni+L2iYni+L3iXo(6)whereXois the displacement of output shaft.In Eqs.(4)(6) , the variant vectors have the same meaning as inYangs1, but the compositions of coefficient matrixes suchasG,H,Lare different. The detailed elements of thosematrixes and vectors will not be listed here for content limi2tation.By inserting the coordinate relations into the dynamicequations of subsystems , we obtain the global dynamicequation for this novel drive as follows:MX+KX=Q(7)whereM,K,X,Qrepresent global mass matrix , globalstiffness matrix , vector of global generalized coordinates ,and vector of global excitations , respectively. Their compo2sitions are as follows:M= diag(Mi)i=1 ,10K=K11K16K17K22K28K29K33K35K36K37K44K45K48K49K55K56K57K58K59K66K68K6 ,10sym.K77K79K7 ,10K88K8 ,10K99K9 ,10K10 ,10X= XI,YI,XS,YS,Xn1,Xn2,Yn1,Yn2,XoTQ= QiTi=1 ,10The global dynamic equation consists of 32 second2order differential equations with periodically time2variantstiffness matrix and excitation vector.It is worthy to point out that the elements in mass ma2trix and stiffness matrix are different from those in Yangsmodel1because of the different coordinate relations wehave deduced.212SimulationBy solving the global dynamic equations , we can ob2tain the dynamic responses of the double2ring2plate gear re2ducer.The dynamic forces of gear meshing are shown in Fig.3 where the horizontal axis represents the rotation angle ofthe first crank. Obviously , the dynamic responses betweentwo parallelogram mechanisms are similar but with a littledifference in amplitude and phase angle , which indicatesthat the load distribution is unequal between two phases ofmechanisms.The unequal load sharing may attribute toelastic deformations of the parts in this over2constrainedtransmission system. And this unequal load distribution ismuch more apparent when the mechanisms reach the regionsaround“dead point”.Fig.3Dynamic forces acting on gearsThe dynamic reactions on planetary bearings of the in2put shaft are shown in Fig.4. It can be seen that two paral2lelogram mechanisms share similar dynamic responses. Thepeaks indicate that the reactions on planetary bearings varyquite severely. The varyingof planetary bearing reactions isdue to the elastic deformations of the transmission systemunder the external load.Fig. 5 shows the dynamic reactions on two housingbearings of the input shaft. Herein , the solid curve denotesthe forward housing bearing of the shaft while the dashedone stands for the backward housing bearing.By comparing Figs. 4 and 5 , we can find that the re2actions of planetary bearings are much greater than those ofhousing bearings. This accountsfor the premature fatigue ofplanetary bearings in this type of planetary gearing. There2fore , roller bearing is strongly recommended as the plane2tary bearing because of its high loading capacity.Though the counterweights are designed to balance the661Transactions of Tianjin UniversityVol. 13No. 32007 1994-2007 China Academic Journal Electronic Publishing House. All rights reserved. http:/Fig.4Dynamic reactions on planetary bearings of input shaftFig.5Dynamic reactions on housing bearings of input shaftinertia forces and inertia moments of the mechanisms , thereactions on housing bearings still fluctuate greatly. Notic2ing that all the reactions of housing bearings are finallytransferred to the reducer case and may cause negative vi2bration , we need to calculate the shaking moments producedby those reactions.The shaking momentsof the reducer produced by reac2tions of all housing bearings are demonstrated in Fig. 6.Herein, Figs. 6 (a) and (b) are the shaking momentsaboutxaxis andyaxis , respectively. And the solid curvesrepresent the shaking moments of the reducer produced bydynamic reactionsof housing bearings while the dashedonesstand for the inertia moments of the mechanisms before thecounterweights are fixed.Apparently, the mechanismsinertia moments aremuch smaller than the reducers shaking moments in bothdirections. Therefore , it can be further predicated that themain reason for reducer vibration is not the inertia forces orinertia moments of the mechanisms but the elastic deforma2tions of the parts produced by the external load.Even though the inertia forces and inertia moments arefully balanced by the well2designed counterweights , whichmeans the dashed curves in Fig. 6 become straight lineswith zero amplitude , the fluctuation of reducers shakingFig.6Shaking moments of the reducermoments still remains noticeable. Inother words , insteadofeliminating the vibration of reducer case , the design ofcounterweights can only suppress it to some extent.3ConclusionsA novel double2ring2plate gear reducer is designed andits dynamic performance is simulated with an elasto2dynam2ics model. This drive is featured by non2180 degree phasedifference. This provides the feasibility of single power in2put and makes a compact volume for the reducer. T o bal2ance the inertia forces and inertia moments of the mecha2nisms , four counterweights are designed on the crankshafts.The dynamic simulation results indicate that comparedwith the housing bearings , the planetary ones work in moresevere conditions. Different from the prevailing viewpointthat the inertia forces and inertia moments are main vibra2tion resource of ring2plate type gear reducers2, this inves2tigation reveals that the vibration of this novel double2ring2plate gear reducer is mostly caused by elastic deformationsof the parts rather than by inertia forces and inertia mo2ments.References1Yang Jianmin , Zhang Ce , Qin Datonget al. Elasto2dy2761ZHANG Jun et al :Design and Dynamics Simulation of a Novel Double2Ring2Plate Gear Reducer 1994-2007 China Academic Journal Electronic Publishing House. All rights reserved. http:/namic analysis of three2ring reducersJ .Chinese Journalof Mechanical Engineering, 2000 , 36 (10) : 5458 (inChinese) .2Cui Jiankun , Zeng Zhong. Calculation and balance forshaking force and shaking moment of three2ring gear reduc2erJ .Machine Design and Research, 1996 (3) : 3940(in Chinese) .3Cui Jiankun , Zhang Guanghui. Study on fretting wear ofeccentric sleeves in three2ring2plate gear reducer J .Journal of Machine Design, 1996 (10) : 3133(in Chi2nese) .4Xin Shaojie , Li Huamin , Liang Y ongsheng.Study onequilibrating load mechanism of oil film floating on a newtype of three2ring gear reducerJ .Mechanical Science andTechnology, 2000 , 19(4) : 581583(in Chinese) .5Tang Guoliang , Wang Shuhao. Double Crank Double2Ring2Plate Gear Reducer with Few T ooth Number DifferenceP. CN: 2118208U , 1992210207(in Chinese) .6Zhang Ce , Song Y imin , Zhang Jun. Double2Ring2PlateGear ReducerP. CN: Z L 20042008568610 , 2005212207(in Chinese) .7Zhang Y ongxin. Elasto2Static Analysis of Three2Ring GearReducer in Consideration ofGear2Coupler DeformationsD. Tianjin: School of Mechanical Engineering , TianjinUniversity , 2005(in Chinese) .8Zhang Guanghui , Han Jielin , Long Hui. Stress analysis ofdriving ring board of three2ring type gear reducerJ .Chi2nese Journal of Mechanical Engineering, 1994 , 30 (2) :5863(in Chinese) .861Transactions of Tianjin UniversityVol. 13No. 32007 1994-2007 China Academic Journal Electronic Publishing House. All rights reserved. http:/