The Study of Drive Characteristic and Experimental Approach about Planetary Gearing Mechanism

Transcription

1 The Study f Drive Characteristic and Experimental Apprach abut Planetary Gearing Mechanism Feng Liu Schl f Mechanical Engineering, Tianjin University f Technlgy and Educatin N.1310, Da Gu Suth Street, He Xi District Tianjin, China darm@163.cm Chngning Li Schl f Mechanical Engineering, Tianjin University f Technlgy and Educatin N.1310, Da Gu Suth Street, He Xi District Tianjin, China Abstract The transmissin indexes which include transmissin errr and backlash are analyzed, it pints ut the reasns fr the frmatin f these indexes. The experimental principle and apprach abut transmissin accuracy and stiffness are intrduced based n the existing test bench f ur university. Keywrds: Planetary transmissin, Transmissin errr, Backlash, Stiffness 1. Intrductin Planetary gearing mechanism are applied t the dmain f aviatin, marine, autmbile and engineering plant, by the characteristics f large drive rati, high transmissin efficiency, cmpact structure and balanced mtin. Nwadays, with the flying develpment f ur technlgy, which in turn, places higher expectatins t equipment manufacturing industry, including the behavirs abut accuracy f manufacture, reliability, strength, rigidity and s n, and the accuracy f manufacture and reliability are particularly imprtant between them, they are the representative f manufacturing industry standard fr ne cuntry. The applicatin f technique abut industrial rbt heightened the manufacturing industry standard, and they serve as a supprt rle t accuracy f manufacture and reliability. A lt f high-precisin planetary gearing mechanisms are used in industrial rbt. S it is bviusly imprtant t research abut transmissin accuracy and its testing methd f planetary gearing mechanism. In this test, the testing principles and methds abut transmissin accuracy and stiffness f planetary gearing mechanism will be discussed linked with transmissin accuracy and its testing methd. And dynamic testing methd abut transmissin accuracy f high-precisin planetary gearing mechanisms. 2. Transmissin Accuracy Transmissin accuracy abut planetary gearing mechanism usually were cntrlled and measured with tw transmissin indexes, transmissin errr and the lst mtin, namely backlash. These tw errrs bth shw perating cnditin abut transmissin ff- ideal path. Backlash is the key abut dynamic respnse f transmissin chain, and als is the imprtant surce f psitinal errr. Transmissin errr is the measurement f distrted transmissin. Bth f them are generated with manufacturing and munting errrs abut mving parts and building-up members, which frm the whle system, and they are the cmbined respnse f many different factrs. 2.1 Transmissin errr and its testing Transmissin errr and its cause Transmissin errr which is als called rtary transmissin errr r angle drive errr is the angle errr f the factual angle f utput shaft in ne-way rtary transmissin cmpared with the academic angle. The mtin f the utput shaft has tw states with leading and delaying because f transmissin errr. Fr example, the rati f transmissin f a pair f meshing invlute gear is nt invariant. When gears were prcessing, as the reasns f cutter errrs, machine errrs, installatin and adjustment errrs and defrmatins, the gemetric parameters f gear must bring determinated errrs, which include tth frm, base pitch, circular pitch, tth thickness and tth alignment, it make meshing gears having crrespnding psitinal errrs in any time in the range f ne rund, as a result, the actual angle f meshing gear are different frm the academic angle, the deviatin value between them is called transmissin errr. Having it, the instantaneus transmissin rati is tiny diversificatin 164 ISSN E-ISSN

2 in factual transmissin prcess. The angles f utput and input shaft shuld accrd with the perfect linear relatinship in transmissin prcess accrding ideal transmissin thery, as fllw: i i (1) Where,i is verall transmissin rati f gearing mechanism. Frm it, it shws that the utput shaft will slew unifrmly while the input shaft slew at a unifrm speed. Once the input shaft reverses, the utput ne shuld reverses withut any angle f lag. Hwever, in fact, the relatin between the angles f input and utput is nn-linearity when transmissin errr exists in ne-way rtary transmissin, it is because f the manufacturing and fitting errrs t every parts frm system, besides, there are heat distrtin and elastic defrmatin while it wrking. It is a randm errr t transmissin errr, which is the synthesis frm the errrs abut every gear. The errr f gear in a brad sense mstly is the verall errr f the manufacturing and fitting errrs t gears and gearing mechanism. The higher the accuracy abut gears and gearing mechanism is, the littler the transmissin errr is. All f the pssible reasns fr engendering errrs must be taken int accunt t high-precisin planetary gearing mechanisms, there are three kinds f fremst reasns fr its errrs as fllw: 1 The prcess errr f gears which is inherent is a cmbinatin f factrs such as gemetrical errr, kinematic errr, tth prfile errr, pitch errr, tth alignment errr and s n. 2 The errrs caused by shaft eccentricity. 3 The errrs caused by eccentricity f fit clearance. Besides, the ther factrs affecting angular errr f gears as fllw: the eccentricity f bearing inner ring while it running at the time f uter ring fixed, the deflectin abut axis f the hle in gear bx casing. Smetimes it can be negligible Testing abut transmissin errr There are tw methds cntain dynamic measurement and static measurement fr testing abut transmissin errr. In the prcess f static measurement, the angle f input and utput shaft which are read in static state after turning a certain angle are cmpared with each ther, cnsequently, the transmissin errr can be read, viz., it is discntinuus fr the prcess f static measurement. While dynamic measurement is being carried ut, the angle are read in running state be appraching t nrmal perating cnditins, in a wrd, it is cntinuus fr the prcess f dynamic measurement. It can be fund ut that dynamic measurement can entirely describe the transmissin errr by and large. The dynamic measurement is being carried ut n the special test bench fr transmissin accuracy, which makes up f high-precisin rtary encder, precisin junctin bx, frame, data acquisitin system and s n. It has advantages fr simple structure, functinal agility, high-accuracy measuring, cnvenient peratin, lw cst etc. we chse S D-90-CC style grating encder made by Fagr cmpany in Spain, pulses/turn, the degree f accuracy is ±2"/pulse, it can meet the testing demand fr high-precisin gearing. The blck diagram f testing abut transmissin errr is shwn in Figure 1. Test underbed and bracing structure fr speed reducer are sealing-in tgether, tw frtified ribbed in the center f it, therefre, the plank is s rigid and steady. The sliding guide is used in the rt f the bracing structure fr speed reducer, s equipment can be fixed expediently, and it can be adjusted accrding different reducer. In rder t meet the testing fr different reducer, a big flange plate is fixed in the center f frame, different flange plate can be used accrding different type f machine. After thermal refining, higher hardness and strength it has. While testing is ging, the input shaft is running in stabilizing peratinal state, the actual angle f input shaft slewing in ne rund subtract the ideal ne, then, many numerical values are given, the minimum in them subtract frm the maximum give a number, that is the transmissin errr. The expressin f transmissin errr is shwn as fllw: (2) imax imin 2.2 backlash and its testing Backlash and its cause Backlash, namely the lst mtin, is the lag angle f utput shaft when input shaft turn frm psitive int negative, it can als be interpreted as any angle the utput can turn when the input fixed. T planetary gearing Published by Canadian Center f Science and Educatin 165

3 mechanism used in systems which ask fr precisin transmissin such as rbts and serv, backlash is a critical index, which directly affect the transmissin accuracy f transmissin system. It is anther errr that has bth links and differences with transmissin errr. Because f backlash, the utput shaft cannt turn back in pace with input shaft, a lag angle is generated after it reverses. The relatin between the angle f utput and input is shwn in Figure 2. The utput angle is zer at the beginning f input i running frward directin, the gears g int mesh with ther at a pint, after that, the fllwer will slew frward at a certain speed. The utput hld still fr a while after the input i turn back at b pint, then, the driver will turn the angle f clearance (frm b t c). Tw gears g int mesh with ther n anther flank f tth at c pint, after that, the fllwer will slew in ppsite directin at a certain speed. is nt zer when i get zer, slewing is ging, will reach zer at d pint. This curve is hysteresis curve f free play. Accrding characteristics, verall backlash f gear drive mechanism is made up f invariable backlash and flexible backlash. There are t many causes t generate backlash, and there are five parts fr planetary gearing mechanism n the whle. 1 design backlash. There must be necessary clearance t cmpensate fabricatin errr, installatin errr, heat distrtin and keep space fr lubricating film, and the lateral clearance frm fabricatin tlerance als shuld be taken int accunt. 2 tlerance backlash. As a result f tlerance f gear size and centre distance. It is the leading backlash. 3 backlash frm decentratin and gap f bearings. Thugh this kind f backlash is small, it is indispensable t high-precisin planetary gearing mechanism. 4 backlash frm bending and envirnment. That can nly be calculated frm the analysis f actual circumstantialities abut temperature and dynamic frce, but can nt be directly described in physical dimensin. 5 backlash frm tth runut. As a result f the decentratin between gear axis and spin axis. T a certain psitin, its number depends n phase angle, but average value is zer. Only in calculating an instantaneus verall backlash, must it be cnsidered. Amng five kinds f, the last is the nly flexible ne which changes with gears slewing. All f thers are invariable. Angle is the scale fr defining transmissin errr and backlash, s the units are expressed by arcmin r arcsec usually. There als is liner frm fr pitch circle f gears, usually expressed by micrns (um fr shrt). Then, the relatinship abut angular values f angle transmissin and its liner values n pitch circle is shwn in Frmula Lr 6.88 Ld arcmin (3) Where is angular value, L is liner value, r is pitch radius (mm) and d is pitch diameter (mm). Backlash is nt necessarily meaningful nly when the reverse, even a ne-way rtatin, hysteresis may affect the accuracy f the transmissin. Fr example, in ne-way rtatin, with the utput shaft suffering frm a large enugh external trque f rtating in the same directin, the utput shaft may have a leading angle due t backlash. Anther example is in the prcess f ne-way rtatin, if the shaking mment n utput shaft is large enugh, the utput shaft may have a leading angle while the input shaft slw dwn all at nce, which is because f backlash t Testing abut backlash The backlash f a gearbx can be defined (measured) at the utput (at lcked input) r at the input (at lcked utput), the relatinship between the backlash at the input and utput depends basically n the reductin rati. It is shwn as fllw: Sinput i Sutput (4) Where S is backlash and i is reductin rati. The abve equatin is theretical. Deviatins can be experienced when measuring, particularly with multiple stage gearbxes, since the effects f the individual clearances depend upn where the clearance is in the gear train furthermre the clearances are nt exactly the same in each mesh. Fig 3. shws the theretical diagram f testing abut backlash, testing abut backlash f a gearbx requires a 166 ISSN E-ISSN

4 prper test rig and instrumentatin. The fixture hlding the gearbx and its utput shaft shuld be as be as rigid as pssible. When testing is ging, ne shaft is fixed n the pedestal, the ther shaft cnnects circular grating encder with elastic jint, we chse S D-90-CC style grating encder made by Fagr cmpany in Spain, pulses/turn, the degree f accuracy is ±2"/pulse. As shwn in Fig 3, the input shaft f reducer is fixed, Then tw rtatin directins f the utput shaft are lading n durative rated trque, and then gradually unlading, the crrespnding phase angle in every mment is recrded by instruments, resulting curve is a clsed curve, backlash and trsinal stiffness f gearbx can be calculated frm it. This test uses direct displacement measurement, it is a measurement abut transmissin errr being cmpatible with the level f develpment abut sensr technlgy, electrnics and cmputer technlgy currently, In fact, hysteresis curve in Figure 2 shws as zigzag line in specific cnditins, factual line is smth in additin t the maximum and minimum at the utside. It s shwn in Figure 4. Because f frictin frce in gearbx, backlash regards as the angle difference f utput shaft between psitive and negative directins under the rated trque f 2% r 3%. 3. Testing abut stiffness Backlash is an index f the gearing mechanism measured withut lad, But fr high precisin planetary gear is cncerned, nly that is nt enugh, trsinal stiffness the index under rated burden must be cnsidered. Trsinal stiffness f the gearing mechanism is the rati f trsin mment in the rle f trque t crrespnding angle. It can be expressed by stiffness cefficient, namely the trsin mment that can make the utput shaft having ne curvature s trsinal deflectin with the input shaft nt mving. While the test abut stiffness is ging, tw rtatin directins f the utput shaft are respectively lading and unlading accrding t certain pririty with the input shaft fixed. The crrespnding trsin mment and angle are recrded at the same time. The test abut stiffness carries ut simultaneusly with the test abut backlash n test rig f backlash. Trsinal stiffness is getting frm hysteresis curve. The curve is nnlinear when trsin mment is small, and it can be seen as a straight line under the rated trque f 50% t 100%, as a result, trsinal stiffness can be btained frm that range in the way f liner regressin analysis. It is shwn as fllw: T Ct (5) Where T is the trsin mment between rated trque f 50% and 100%, is the angle between rated trque f 50% and 100% and C t is trsinal stiffness. 4. Cnclusins Transmissin errr f planetary gearing mechanism and its influence factrs are analyzed in this test, and the experimental principle and apprach abut transmissin accuracy and stiffness are intrduced. The detectin technique and devices abut transmissin accuracy and stiffness is an indispensable tl in the prcess f theretical research and prttype develpment abut high-precisin planetary transmissin. The accuracy in measurement is higher because f high-precisin sensr. It can meet the demands f research and prductin test abut planetary gearing mechanism. References CHEN, Hejuan. (2008). mechanical-electrical integratin system design. Beijing: Beijing Institute f Technlgy Press Gear Guide Editrial. (1990). Gear guide (final vlume). Beijing: Machinery Industry Press. 11. LI, Chngning, LIU, Jiyan & SUN Ta. (2001). Study n transmissin precisin f cyclidal pin gear in 2K-V planetary drives. Jurnal f chinese jurnal f mechanical engineering. 37(4), LI, Xijian. (2004). The Emulatin Prgramming Fr The Accuracy f Big Trque And High Acuracy And Big Velcity Rati. Qianhuangda: Yanshan University. NAN, B & CHENG, Dian translate. (1978). Precisin Gear Device-Thery And Practice. Beijing: Natinal Defence Industry Press. WU, Yuanyan. (2004). Precisin detectin f rigid transmissin chan and develpment f analysis system. Published by Canadian Center f Science and Educatin 167

5 Nanjing: Nanjing University f Science & Technlgy. YE, Qichuan & XU, Furen. (2003). Calculating the Return Stagnant Angle f the Gearing by Use f Prbability Statistic. Jurnal f Mechanical & Electrical Equipment.1, ,5 high-precisin rtary encder ; 2,4 precisin junctin bx ; 3 planetary gearing mechanism ; 6,10 ballscrew ; 7 data acquisitin system ; 8 frame ; 9 micr-driving mtr Figure 1. The Blck Diagram f Testing abut Transmissin Errr Φ c b d a Φ i Figure 2. The Hysteresis Lp Line high-precisin rtary encder ; 2 precisin junctin bx ; 3 gearbx ; 4 frame ; 5 lad pacer ; 6 damping bedstand ; 7 data acquisitin system Figure 3. The Blck Diagram f Testing abut Backlash 168 ISSN E-ISSN

6 η [arcmin] backlash ΔT ΔΨ -T [Nm] 50% 100% T [Nm] the rated trque f 2% r 3% -η [arcmin] Figure 4. The Hysteresis Curve Published by Canadian Center f Science and Educatin 169