1、98FTM10Local Coefficients of Friction inWorm Gear Contactsby: B.-R. H6hn and K. Steingr6ver, Gear Research Centre, FZG,GermanyAvAmerican Gear Manufacturers AssociationTECHNICALPAPERLocal Coefficients of Friction in Worm Gear ContactsBernd-Robert HOhn and Karl Steingrtver, Gear Research Centre, FZG,G
2、ermanyThe statements and opinions contained herein are those of the author and should notbe construed as an official action oropinion of the American Gear Manufacturers Association.AbstractThe friction conditions in the mesh of worm gear drives have big influence on the efficiency of worm gears. Bec
3、ause thefriction conditions of worm gears cant be determined directly, a special test rig (three disk test rig) was built to simulatethe contact conditions for discrete points along the contact lines of a worm gear.The highest values of the local coefficient of friction occur under poor lubricating
4、conditions with the vector of the rollingspeed in direction of the contact line, normally in the center of aworm gear flank, the lowest coefficients of friction in thearea of the outlet.Furtheron the local coefficients of friction strongly depend on the type of lubricant and material combination and
5、 to aminor extent on load, lubricant viscosity and oil temperature.The investigations at the three disk test rig offer a cost saving possibility to examine the different influences on thecoefficient of friction of worm gears.Copyright 1998American Gear Manufacturers Association1500 King Street, Suit
6、e 201Alexandria, Virginia, 22314October, 1998ISBN: 1-55589-728-2iwLocal Coefficients of Friction in Worm Gear ContactsBernd-Robert H6hn and Karl Steingr6verGear Research Centre, FZG, Germanythe axis of one disk could be made skewed for some- 1 Introduction degrees. Boring motion was simulated by usi
7、ng conicalv disks instead of cylindrical. Between the disks, which bothImportant influence on the performance of worm gears is were made of steel, there was point contact. In a wormtheir efficiency. When calculating the efficiency the gear - worm made of steel, wheel made of bronze - therecoefficien
8、t of friction must be known. The main influence is line contact. These investigations did also not take intoparameters on the coefficient of friction in the contact of account the sliding velocity of the worm flank relative toworm gears are the materials of the worm and the wheel, the wheel flank al
9、ong a contact line. So the results ofthe lubricant, the Hertzian stress, the sliding conditions investigatons in a twin disk machine cannot easily bealong the contact lines and the equivalent diameters, transferred to worm gears.Ueno/6/and Octrue /7/ described test rigs, which allowInvestigations on
10、 worm gears of Neupert/1/, Steingr_iver to investigate the influence of sliding in direction of the/2/and Rank/3/show the dependence of the efficiency contact line on friction and wear. They determined theon sliding velocity, geometry and lubricant although the coefficient of friction and wear rates
11、 for different contactmain interest of these investigations were wear, scurfrag conditions. These investigations were mainly made toand pitting. Fundamental investigations about the deter- optimize the position of the wheel relative to the wormmination of the coefficient of friction in general were
12、and to determine characteristic material values. Systematicmade by St6Bel /4/ on a twin disk machine. This test rig investigations on worm gear friction are not reported.consists mainly of two disks with parallel axes, with The above mentioned investigations show, that there arecentre distance a = 8
13、0 mm. For the investigation of no formulas, based on test results, which allow to cal-sliding conditions as they occur in e.g. traction drives the culate coefficients of friction in worm gear drives.A test rig was modified by Gaggermeier /5/ in that way, that Therefore a three disk test rig was desi
14、gned and built to-1-simulate the conditions in worm gear contacts and inves-tigatethecoefficientof frictionunder slidingconditionsof _ _anypointalongthecontactlines.2 Test Rig _ _ -_/2.1 Comparison of Velocities _The test rig consists mainly of a large plane disk, whichsimulates the worm, and a roll
15、er, which simulates thewheel. Figure 1 shows the velocities in a contact point of Fig. 2: Test Rig (Schematic View)a worm gear compared to the velocities in a contact pointof the test rig. The velocities in an arbitrary contact pointB are characterized by the flank velocities v 1 of the surement of
16、the coefficient of friction. Disk (1) is con-neeted through the flexible coupling (6) with a variableworm, v2 of the wheel and the angle IL The angle 8 is theangle between the vectors of the flank velocities vI of the speed motor (7) and rotates around the axis a - a. Rollersdisk and v2 of the rolle
17、r. Different contact conditions (2) and (3) are driven by the variable speed motors (8)along a contact line of a worm gear can be simulated in and (9) and rotate around their axes b - b and c - c. Thethe test rig by positioning the axis of the roller at different whole drive system of the rollers (2
18、) and (3) in their hou-angles fL sings (10) and (11) are pivoted. They can be rotatedaround axis d - d and can be fixed in any desired position.,_/,o,e, Roller (3) is connected to the load cell (12) and fixed withthe leaf springs (13) and (14). The contact pressure is/coo,oct ,_- - - t - applied by
19、the hydraulic cylinder (15)._i!_ _ _ To achieve equal load distribution along the contact line/ t:2_acg-_-d _ roller (2) can be adjusted by swiveling around link (16),/ _/ roller (3) by adjusting the leaf spring (17). Parallel ad-justment of the roller is achieved by the setting deviceworm gear test
20、 rig (18). An overall view of the test rig is shown in Figure 3.Fig. 1: Comparision of Velocities2.3 Measurement2.2 Test Rig DesignTo determine the coefficient of friction it is necessary toThe principle of the test rig is shown in Figure 2. measure the frictional force and the normal force in theDi
21、sk (1) simulates the worm, the two rollers (2) and (3) contact.each simulate one wheel (see Figure I). Disk (1) is sup- The frictional force is determined by measuring the torqueported intwo cylindrical roller bearings (4) and (5) in that of disk (1). For this reason disk (1) is built as a spokes-wa
22、y that disk 1 can move freely in axial direction. Thus wheel. On the surface of the spokes resistive wire strainthe axial forces in the two roller contacts can be compen- gages were applied. The torque, generated by the fric-sated. By using an axial bearing instead of the second tional force causes
23、a bending deflection of the spokes,roller the loss of this bearing would influence the mea- which is measured by the strain gages. The advantage of-2-Fig. 3: Test Rig (Overall View)this method of measuring the frictional force is that no * polyglycole ISO VG 680 high additivatedother losses like los
24、ses of beatings etc. influence the ($6/680)measurment. Because disk (1) is axially floating there is material of disk/rollers:_ no adulteration of the signal by transverse forces. The * 100Cr6/GZ-CuSnl2Ni (steel/bronze)v signals of the strain gages are recorded through a mercury * 100Cr6/GGG (steel/
25、spheroidal graphite iron)slip ring and an amplifier. The force applied by the The following parameters were left constant:hydraulic cylinder (15) is measured by the load cell (12). Hertzian pressure: PI-I = 300 N/ram 2The coefficient of friction can now be determined from virtual radius of curvature
26、: Pers = 30 mmthe normal load and the frictional force as a function ofthe angle B and the angle between v 1 und Vg.4 Test Results3 Test Program The test results are presented as a function of the slip s,according to/4/:Tests were made with the following variable parameters:- different tangential sp
27、eeds vl of the disk and v2 s = Ivll - Iv21 with Ivxl Iv21 (1)of the rollers Ivxl- different angles 13,which means different loca- Advantage of this is, that the velocities of disk and rollerstions of the speed vectors relative to the contact can be directly taken from the diagrams. Additionally atli
28、ne slip s = 10, 50, and 90 % the vectorsof the rolling- lubricants: velocityv_ and the sliding velocityVgrelativeto the* EP mineral oils ISO VG 460 (IA/460) and ISO contact line are shown. The vector of the rolling velocityVG 680 (L4/680, similar to AGMA #8) characterizes the conditions for developi
29、ng of an oil film,- * polyglycole ISO VG 220 with mild additives the amount of the sliding velocity characterizes together($2/220) with the frictional force the power loss in the contact.34.1 Influence of Angle fl and Velocity on Coef- curves show comparably high coefficients of friction withficient
30、 of Friction a maximum and then decreasing values with increasingslip s. At high slip rates (range of worm gears) theFigures 4 to 7 show the coefficient of friction g for highest absolute coefficients of friction were measured atdifferent angles g and different velocities. High angles # angles g = 9
31、0*.characterize the inlet area, low angles/_ the outlet area ofreal worm gears.0,08 0,08lOOCr6/GZ-CuSn 12Ni IOOCr6/GZ-CuSn 12Niangle: /Y=70“ _ angle: _=95“0,06 oil: polyglycole $2/220 0,06 oil: polyglycole $2/220=L %n= 80“C =t _ _oll = 80“C .c PH = 300 N/mm 2 _) J PH = 300 N/ram 2._ 0,04 u 0,04 re-“
32、_ _ .-0“ _ _ 0 V1 = 0,5 m/s _ “_D._. 0 v1 = 0,5 m/s v 1 = 1,0 m/s “6 _ .-,C_.:_ _ v! = 1,0 m/s“_ .o-o- _ _ “i 2,0 /s *_vq vg ,_ VgO,O 0,00 20 40 60 _ 100 0 20 40 60 7_ 100slip s _ slip sFig. 4: Coefficient of Friction tt Over the Slip s at an Fig. 6: Coefficient of Friction # Over the Slip s at anAn
33、gle B = 70 Angle g = 95 0,08 0,08100Cr6/GZ-CuSnl2Ni -f “_ lOOCr6/GZ-CuSn12Niangle: #=85“ _ angle: /Y=110“0,06 oil: polyglycole $2/220 0,06 “_ oil: polyglycole S2/220:L oil = 80“ C _. ,.,.I- %_) / pH = .500 N/mm z oc .0./ -0 _ “_o, = 80“ C= “-= 41 %_ PH = ,300 N/ram 2_ 0,04 .u_0,04,_ 0._._00.-. -X_;:
34、;il“lll;l=l= 0 V, = 0,5 m/s _ _1_ 0 v I _ 0,5 m/s_e_,:_tl_I,_,l_: “ vI = 1,0 m/s _ vI = 1,0 m/s0,02 13 vt = 2,0 m/s _ vI = 2,0 m/s“.3 vl = 2,5 m/s rj 0,02 =o u vg “g I0,0 0,00 20 40 60 _. 100 0 20 40 60 7. 100slip s _ slip sFig. 5: Coefficient of Friction # Over the Slip s at an Fig. 7: Coefficient
35、of Friction F Over the Slip s at anAngle g = 85 Angle fi = 110 From these Figures the following conclusions can be - Influence of the sliding in direction of the contact line:drawn: TheslidingvelocityvLalongthe contactlineis increasedonly by the angle B (vL = v 1 sin B) and independent- Influence of
36、 the tangential speed vl: from the slip s. In general a higher coefficient of frictionAt all angles g the coefficient of friction decreases with is measured for higher sliding in direction of the contactincreasingtangentialspeedv1. line.- Influence of the slip s and the angle/3: The tests with other
37、 conditions of lubrication and materialAt angles B 90 the4.2 Evaluation of the Coefficient of Friction for In this Figure the lubricant film thickness acc. /8/alongWorm Gear Contacts the contact lines for the conditions as in Figure 8 isshown. Here it can be seen that the lubricant film thick-From t
38、he measured coefficients of friction, presented in ness along the contact lines - beginning from the inlet -chapter 4.1, the local coefficient of friction along the steadily decreases to the center of the flank. There itcontact lines of a worm gear can be determined. The reaches theoretically the va
39、lue 0 and then steadily tends tocoefficient of friction along the contact lines of a worm higher values at the outlet. Further this Figure shows, thatgear with centre distance a = 100 mm und ratio i = 20.5 the differences in the lubricant film thickness betweenis shown in Figure 81). It is assumed t
40、hat there is constant different contact lines are of minor importance.pressure PH along the contact lines. The comparably high coefficients of friction in the center _ of the fiank (see Figure 8) correspond withthe pooro.o8 lubrication conditions because of the low rolling velocityz_0.06 inthatarea.
41、0.04Jc q_5 002 J outlet 4.3 Influence of speed on the coefficient of frictionO.00.X_ intet steel/bronzeto mineral oil L4/460n1= 1000 rpm In Figure 10 the coefficients of friction along one contacta = 100 mm (3.9 in) PH = 300 N/ram 2i = 20.5 %i, = 80% line at different speeds are displayed 1).Fig. 8:
42、 Distribution of the Coefficient of Friction Along o.lo I /the Contact Lines of a Worm Gear I0,08 500 1=_ This Figure shows, that the coefficient of friction along _. L./f -, m o = 1o0 r_m(3.9 in)0,06 i = 20,5- the contact lines- beginning from the inlet- steadily in- _-g- _J _/ X_ _ m0Cr6/GZ-CuSn,a
43、Nicreases to the centre of the flank. There it reaches its o.o “-._f =_.,. mineral oil L4/460maximum and then drops to lower values at the outlet. “_ _ %,= 8o“cn1 = 1000 rpm0,02 j OH = .500N/turn2Furtheron the Figure shows, that there are practically no _ inlet outletdifferences in the coefficient o
44、f friction between the - o,0 I Idifferent contact lines. The reason for the higher coef- o 10 20 mm 3owheel widthficients of friction in the center of the flank can be Fig. 10: Coefficients of Friction Along a Contact Line atexplainedby Figure91). DifferentSpeeds_- 020 _m- From this Figure the follo
45、wing statements can be made:-50_2-E 0.80- - The coefficient of friction drops down to lower valueso40- with increasing speed. This can be observed for all areasc inlet$ o.oo _ on the gear flank (the analysis of the tests for other condi-._ steel/bronzemineral oil L4/450 tions of lubrication and mate
46、rial showed comparable re- o = 100 mm (5.9 in) nl= 1000 rpmi= 205 PH = 300 N/mm 2 suits)._o,I = 80“CFig. 9: Distribution of the Lubricant Film Thickness_ Along the Contact Lines of a Worm Gear1) Main geometrical data of the worm gear drivesee Chapter 9-5-4.4 Influence of the Kind of Lubricant on the
47、 5 Comparison with Real Worm GearsCoefficient of FrictionFrom the local coefficients of friction, measured at theIn Fig. 11 test results with different lubricants (mineral three disk test rig, a mean value over all discrete points at -oil, low and high additivated polyglycole) are shown 1). all cont
48、act lines can be calculated. Such mean values cano,ao I I be compared to mean coefficients of friction/Zzm , whichinlet outlet are determined from measured efficiencies at real worm+o,0 I/_ a = 100 mm (3,9 in) gears. This comparison is shown in Figure 12 for dif-.mineral oil i = 20,5o,o6 / L4/680 fe
49、rent material combinations and different 1)lubricants .oc j_/_,_ “,_ 100Cr6/0Z-CuSnl2Ni:_ n1= 250 rpm 0,10 oH = 300 N/ram 2.o_ J / %,= 40“c lOO“_ 0,04 p_ol_g I _ o = rnmi = 20,5“6 lycolel_ N _ OH = 300 N/rnrn 2 +sz/,_ _ 0,08 %: 80“c0,02 E _ _ .N _3 O _7 /Zzm from rneosurementpolyglycole. 7“- _h.% _ at three disk test rigo_ 0,06 - /Zzrn from meosurernentS6/680 “- “%“o 0,0 _ . _ _ ot worm cjear test rig0 10 20 ram 30 _oD.04 _y_ worm: 16MnCrSE_ JL wheel: GGG 40w
