1、91 FTM 10vDynamic Measurements of Gear ToothFriction and Loadby: B. Rebbechi, F. B. Oswald and D. P. TownsendNASA, Lewis Research Center_AV,American Gear Manufacturers Association:_ TECHNICAL PAPERDynamic Measurements of Gear Tooth Friction and LoadB. Rebbechi, F. B. Oswald and D. TownsendNASA, Lewi
2、s Research CenterTheStatements andopinionscontainedherein arethoseof theauthor andshould notbe construedas an officialaction oropinion of the American GearManufacturers Association.ABSTRACT:A program to experimentally and theoretically study fundamental mechanisms of gear dynamic behavior is beingco
3、nducted at the NASA Lewis Research Center in supportof a joint research program between NASA and the U. S.Army. Thispaper presents theresults ofdynamic tooth-fillet straingage measurementsfrom theNASA gear-noise rig,and it inlroduces a technique for using these measurementsto separate thenormaland t
4、angential(friction) componentsof the load at the tooth contact -_-Copyright 1991American Gear ManufacturersAssociation1500 King Slreet, Suite 201Alexandria, Virginia, 22314October, 1991ISBN: 1-55589-607-3Dynamic Measurements of Gear Tooth Frictionand LoadBrian Rebbechl , Fred B. Oswald, andDennis P.
5、 TownsendNational Aeronautics and SpaceAdministrationLewis Research CenterCleveland, Ohio 44135i. INTRODUCTION problems. Anderson and Lowenthal 4 com-puted overall losses due to friction and_ The dynamic forces at the point of found good agreement between theoreticaltooth contact are of considerable
6、 interest predictions and experimental data. Krantzto the designers of high-speed, light- and Handschuh 5 applied a similar tech-weight gearing. Accurate prediction of the nique to an epicyclic gear rig, obtainingdynamic loads can assist in minimizing the good correlation at low oil temperatures,siz
7、e and weight of a transmission. In a but poorer correlation at higher oil tem-helicopter application, where the transmis- peratures. However, this technique cannotsion is a significant fraction of vehicle detect the variation in friction during theweight, such a reduction would be an impor- tooth en
8、gagement cycle. There is also thetant factor in overall vehicle performance, problem of separating the power loss due toA program to experimentally and theo- gear tooth friction from power losses dueretically study fundamental mechanisms of to other sources such as bearings, windage,gear dynamic beh
9、avior is being undertaken and so forth.at the NASA Lewis Research Center in sup- Extensive measurements of lubricationport of a joint research program between conditions at a sliding-rolling contactNASA and the U.S. Army. This paper pre- have been carried out on disk machines 6 .sents the results of
10、 dynamic tooth-fillet These experiments are of considerable valuestrain gage measurements from the NASA in confirming the existence of elastohydro-gear-noise rig, and it introduces a tech- dynamic lubrication and in identifying thenique for using these measurements to separate regimes of lubrication
11、 that pre-separate the normal and tangential vail under the various slide-to-roll(friction) components of the load at the ratios. However, the usefulness of thetooth contact. Resolution of the contact modes of behavior and friction coefficientsforce is desirable for several reasons, in predicting lu
12、brication conditions at anTwo of these reasons are the following: actual tooth contact, where the degree of(I) A primary output of analytical sliding changes throughout the toothmodels of gear dynamic behavior is typi- engagement cycle (typical duration,cally the normal force at the point of 250 _se
13、c), needs to be verified. In thiscontact (e.g., I and 2). short period of time, large changes occur(2) The measurement of dynamic in the lubricant temperature, shear, andfriction of meshing gears does not appear viscosity at pressures up to 1.4 GPato have yet been carried out successfully. (200 000
14、ibf-in. _). Dyson 7 reportedAn interesting trial was carried out temperatures up to 400 C and oscillatoryA by Benedict and Kelly 3, but it was dis- shear rates up to l0 T sec -I These con-continued because of dynamic response ditions cannot readily be produced outsideof an actual tooth mesh.Visiting
15、 scientist from AustralianAeronautical Research Laboratory.Friction at the tooth contact is tooth-root fillets on both the loadedimportant for determining not only power (tensile) and unloaded (compression) sideloss and efficiency, but also for under- of two adjacent teeth on the outputstanding gear
16、-tooth scoring and wear. An (driven) gear (Fig. 4). To measure maximumimportant parameter in scoring is the fric- tooth bending stress, the gages were placed _tion coefficient 3. Friction greatly at the 30 tangency location 9.affects the heat input to the lubricant Strain gage signals were condition
17、edwhen sliding velocities are high. by two methods: for static calibration andThis report presents dynamic, gear- measurement, a strain gage (Wheatstone)tooth strain measurements from low-contact- bridge was used; for dynamic measurements,ratio spur gears tested in the NASA gear- the strain gages we
18、re connected via a slip-noise rlg. The technique used to convert ring assembly to a set of constant-currentthese strain measurements into normal and strain gage amplifiers.tangential (friction) tooth loads is A 4-channel, 14-bit digital datadescribed. Plots of normal and tangential acquisition syste
19、m was used to record theforces, for both static and dynamic condi- dynamic strain data. Sample rates of 20 totions, are presented for a representative 50 kHz per channel were used, depending onrange of loads and speeds. The normal test gear speed.force and dynamic strain data have been An optical en
20、coder was mounted on theused to verify a gear dynamics code in input shaft to measure roll angle and henceanother related report 8. determine load location; the position ofthe encoder was adjusted so it would pro-2. APPARATUS duce 1 pulse/revolution at a known rollangle.2.1 Test Facility3. TEST PROC
21、EDUREThese tests were conducted in the NASALewis gear-noise rig (Fig. i). This rig 3.1 Calibrationcomprises a simple gearbox powered by a150-kW (200-hp) variable speed electric Calibration of the strain gages on themotor, with an eddy-current dynamometer instrumented (driven) gear was conducted toth
22、at loads the output shaft. The gearbox provide a matrix of strain output versuscan be operated at speeds up to 6000 rpm. applied load. Before commencing the strainThe rig was built to carry out fundamental gage calibration, the gears were demagne-studies of gear noise and of dynamic tized. This dema
23、gnetization reduced thebehavior of gear systems. It was designed apparent strain resulting from the gages Ato allow testing of various configurations moving through the magnetic field of theof gears, bearings, dampers, and supports, adjacent gear. At normal gear operatingA poly-V belt drive served a
24、s a speed speeds, magnetic effects can induce anincreaser between the motor and input error signal in the gage.shaft. A soft coupling was installed on For calibration, the instrumented gearthe input shaft to reduce input torque was meshed with a special gear whose adja-fluctuations caused by a nonun
25、iformity of cent teeth had been ground away; this per-the belt at the splice, mitted loading of a single tooth only. TheTest gear parameters are shown in calibration was carried out for each of theTable I, test rig parameters in Table 2, two instrumented teeth for roll anglesand gear tooth profile t
26、races in Fig. 2. ranging from 12 to 30 . At each test po-The tooth surface roughness was measured by sition (roll angle) the torque was appliedusing an involute-gear-checking machine at three levels - 45 percent, 88.5 percent,with a diamond stylus of approximately and 132 percent of the nominal valu
27、e of10-_m (0.0003-in.) radius. The surface 71.8 N-m (635 in.-ib). At each of theseroughness varied along the length of the load levels the sliding direction wastooth, with the region near the root reversed (by reversing roll direction), andappearing to be lightly polished. The a linear curve was fit
28、 to the data for eachmaximum surface roughness was estimated to sliding direction. By reversing the rollbe 1.3 and second, to provide informationon load sharing characteristics of the gearassembly. A strain gage bridge circuit wasused to record strains for roll angles from!2 to 40 relative _o tooth
29、2. Torquelevels of 37, 88, I00, and !32 percent were app!ied_ but unlike the single-tooth case,i_near curve-fitting of these data was notappropriate because of the kinematic non-lineari_ies introduced by load sharing whenmore than one pair of zeeth are in contact.8_-I_7c_ As for the singie-too_h cas
30、e, these meas-urements were carried ouz for the instru-_qu_S.-S_n_a_r_m_. mended gear acting as bo_h the driven anddriving gear, thus reversing the sliding2000_,_ D_vingge_ direction.I_ D_v_g_r 3.2.2 Dynamic s_rain data. - DynamicI_0 b_ strains were recorded for the 4 gages, for-_ a speed-load matri
31、x of 28 points: 4 speeds_ _orque levels (16_ 31, 47, 63, 79, 94,_0 and !0 percent of the nominal value of71.8 N-m (635 in.-ib). The data were0 recorded by 14-bit data recorders via a(a)Gage2,_iles_in._ slip-ring assembly. S_Dle rates used were_ 50 000 Hz per channel for the 2000-, 4000-,_ F_ and 600
32、0-rDm speeds, and 20 000 Hz per_-1_o _-_ channel for zhe 800-rpm speed. A continu-._ ous recordt consisting of !0 000 data_-1500 scans, was made at each speed so as to givea record length of 0.2 sac at 50 000 Hz,-_oo and 0.5 sac at 20 000 Hz. Because of theinterest in comparing tensile and com-_ I I
33、 I I _ I I I Dressive strains on each tooth, data from28 _ 24 _ _ 18 16 i_ 12Roll_gle. d_ these two gages were simultaneouslyrecorded along with _he encoder signal.(b)Gage1,_mpr_si_ s_in. This procedure was repeated for the second_gu_ 6.-S_ s_-_n gage_m, sin_le_o_ _0aoing instrumented tooth.on_om 1(
34、am_ws_owmil_on). The da_a were then digitallyresa_pled, by using linear interpolation,at either !000 or 2000 samples per revolu-D_vinggear t_O TM. (depend_nc_ on speed) and synchronously40| _ “-:-. - Ddvenge_ _. averaged. Time domain synchronous averag-_ _ _ a technicue now _ _ide use in20 _ ._ -“_
35、_ - - gear_ _ diagnostics !0_, was used here to reduce01 I I I I I I I I I noise effects (especially from the torquefluctuation caused by the belt drive). Its(a)_age4._nsiles_in. implementation requires two data channels -Ci one for timing signal data and one foro_- _._. _ strain data. The timing si
36、gnal data pro-_ _ vided resample intervals for exactly one-15_revolution.-,30 28 26 24 _ _ 18 16 14 12 4. ANALYS I SRoll _gle, degb)Gage3, compmssives_in. For a single tooth, measurement of the_gu_7.-Sm_cs_ingage_mme_u_d_o_2 strain outputs S and S of gages- _rsingl_o_loa_ng on _o_ 1 (_sshow roll mou
37、nted on the compresslve and tensiledirec_on), sides of the tooth respectively (Fig. 4)- will, in principle, enable resolution ofthe tooth forces Fn (normal) and Fz(tangential), provlded that the response of 5. RESULTS AND DISCUSSIONthese two gages to the two forces islinearly independent. The respon
38、se of the 5.1 Calibrationgages can then be expressed asTooth-fillet strains for 100-percentSc = anF _ + az2Ff (4.1) torque were evaluated by fitting a linear -curve to the calibration data for the threeSt = az_Fn + az2F f (4.2) torque levels. These strains at gages I to4 are plotted in Figs. 6 and 7
39、 as a func-tion of roll angle, for loading of tooth I.or simply as Notable from these curves is the signifi-cant influence of static friction on strainS = a_ (4.3) output; the tensile gage (see Fig. 6(a)shows a difference in strain between thedriving- and driven-gear cases (when slid-I ing direction
40、 reverses) that is 27 percentwhere S = S of the mean strain reading. The signifi-cance of this is twofold: first, it ist difficult to establish a “no-friction“curve; and second, and possibly more impor-tant, these curves (particularly the ten-F mile curve) illustrate the effect that_ = Fn tooth fric
41、tion has on the results. It isapparent from Fig. 6 that the compressivef gage is much less influenced by frictionand, thus, would be expected to give thebest indication of normal force if only oneand ai is the strain influence coeffi- gage were used. This is further confirmedcient; _that is, the str
42、ain at i due to aunit normal force (j = I) or a unit fric- by the tooth strain influence coefficientstion force (j = 2). (see Appendix).The strain influence coefficients aj 5.2 Static Meshingare evaluated by alternately setting Fand Ff in equations (4.1) and (4.2) to Measured strain is plotted in Fi
43、g. 8zero. In practice, neither F nor FIcan actually be zero because annormal force as a function of roll angle for staticmeshing of the gears (i.e., for multiple-between the teeth is a prerequisite for a tooth contact) This figure shows thesliding force to develop. However, becausestrain values were
44、 recorded for both direc- average strain (mean of driving- andtions of sliding (that is, for the instru- driven-gear values) for 37-, 88-, I00-, andmented gear acting as both driving and 132-percent torque. Figure 9 shows indriven gear) at each roll angle value, we greater detail the tooth-fillet st
45、rains forinferred that the average of these two _ge2 _ge4strain values is equivalent to the fric- 2_0- _ml _m2 _r_e_v_.tionless case, and that the effect of fric- /-_rc_ltet eo w uos, coe.- ,., ._-_ficients az2 and a22 (which relate to i_0friction) are evaluated from half the _._y, -_k _,_difference
46、 between the driving gear and 5oo .“-_-_ Piiqdriven gear curves of Fig. 6. Likewise, 0the strain coefficients an and a2z I I J J J I J I(which relate to normal force) are eval- _ (a)_a_d_nsiles_msi_of_om.uated from the average of these two curves.The solution for F and F_ is found bypremultiplying b
47、othnsides of equation (4.3) m 5_ - _0m_ge11 _mG_e32by a-1; hence 0=Eal-(s (4.4) -=oThe analysis presented above ignores _ _ythe influence on strains S and St due -I_0to loading on adjacent teeth. In the case -2_0 k./ J I J I _ I I I Jof thin-rim gears II, this effect can be 3230282624222018161412on
48、the order of 12 percent. For the thick- RoUanglefor_oth2. degrim gears used here, however, the influence 111111111from adjacent teeth is at most 3 percent 2e_ 24_ 2018161412(compare Figs. 6 and 7). In the data pre- Rollang_f_oml. degsented in this paper, the influence of (b) Unl_dcompmssi_s_insi_oft
49、_m.adjoining teeth has been included. Thecomputational procedure is outlined in the Rgure8.-Av_g_ sm_cs_indamon_0 _ccessiveAppendix. _“gages 1 to 4 at 100-percent torque, with The total normal force between thethe instrumented gear acting as both driven one- or two-tooth pairs in mesh should beand driving gear. The curves of Fig. 9 are equal to 1718 N (386 ibf). This value isthe averaged result of three trials. From the torque divided by the base circlethe results of Fig. 9, and the influence radi
