1、- STD-AGMA SbFTMB-ENGL Lb lal 0b7575 0004725 994 Thermal Rating of Gear Drives Balance Between Power Loss b b and Heat Dissipation by: Bernd-Robert Hhn, Klaus Michaelis and Thomas Vollmer, FZG TECHNICAL PAPER Thermal Rating of Gear Drives - Balance Between Power Loss and Heat Dissipation Bernd-Rober
2、t Hohn, Klaus Michaelis and Thomas Vollmer, FZG The statements and opinions contained herein are those of the author and should not be construed as an officiai action or opinion of the American Gear Manufacturers Association. Abstract From the balance between the generated heat in a gear box and the
3、 dissipated heat from the gear case surface the mean value for the expected lubricant temperature can be evaluated. The maximum oil temperature in a splash lubricated enclosed gear drive hits the transmittable power. High oil temperatures idluence wear, scuffing, micropitting and pitting load capaci
4、ty of the gears as weil as the gear oils service life. Experimental investigations of no-load and load dependent gear losses in cylindrical and bevel gears as a function of lubricant type and viscosity, load, speed and temperature are reported. The mean value for the coefficient of friction in a gea
5、r mesh is evaluated and compared to measurements in twin disk machines. A rating method for gear mesh power loss is derived. Investigations, using model and actual gear boxes, show the influence of radiation, free and forced convection as weil as conduction to the foundation on the heat dissipation
6、from the gear case surface. The influence of design, size, airvelocity, surface finish of the housing, etc., is reported. The results of such investigations together with accepted rating methods for bearing and seal power loss are introduced into a calculation method for the evaluation of the oil te
7、mperature in the sump of a gear box. in sample calculations the possibilities as well as the limits of this thexmal rating method is shown. Copyright O 1996 American Gear Manufacturers Association 1500 King Street, Suite 201 Alexandria, Virginia, 22314 , October, 1996 ISBN: 1-55589-675-8 - STDmAGMA
8、SbFTM-ENGL 199b Ub7575 0004917 7b7 THERMAL RATING OF GEAR DRIVES BALANCE BETWEEN POWER LOSS AND HEAT DISSIPATION Bernd-Robert Hhn, Professor Klaus Michaelis, Chief Engineer Thomas Vollrner, Research Assistant 1 Introduction The transmittable power of a splash lubricated gear drive is not only limite
9、d by the load carrying abilities but also by the maximum allowable oil temperature in the gear box. From the balance between the generated heat in the gear box and the dissipated heat from the gear case surface the mean value for the expected lubri- cant temperature can be evaluated. High oil temper
10、atures influence oil ageing as well as wear, scuffing, micro pitting and pitting load capacity of the gears. Therefor besides load carrying capacity rating also thermal rating of a gear drive is necessary. The paper deals with the evaluation of the differ- ent sources of power loss in a gear drive.
11、The main emphasis is laid on the determination of the gear mesh power loss. Also reported are measured data of heat dissipation from model testing and actual gear boxes in practice. 2 Thermal Balance The generated power loss in a gear box consists of the gear losses P, the bearing losses P, and the
12、seal losses PvD. in some cases additional losses P of auxiliary devices like e.g. oil pumps have to be taken into consideration. Gear and bearing losses include load de- pendent (e.g. gear mesh and roller contact) and non-load dependent (e.g. churning and cage friction) losses. “X Heat removal from
13、a splash lubricated gear drive is maintained by free and forced convection Qu, as well as radiation Qu.rad from the housing and rotating parts Q,t (e.g. shafts and couplings) and conduction to the foundation (4,“. Pvz + Pvl + Pvo + Pvx = Q, + Q, + Qt, (1) The thermal balance results in an temperatur
14、e equilibrium. As most of the parameters depend on oil temperature a solution of the equations is only possible by iteration. For too high temperatures additional cooling through external oil radiators is required with their re- spective enthalpy stream from the system (Fig. 11. output power input p
15、ower PA Fig. 1: Thermal balance of a gear unit 1 3 Determination of Power Loss Seal Losses in most cases the seal losses are less than 0.01 % of the nominal transmitted power and are thus negligible compared to other losses in a gear drive. Equations for their evaluation are given by the seal manufa
16、ctuers, as e.g. by Freudenberg I I. An approximation is given with: P, = 7.69 .lo4 - dt, - n (2) The seal power loss is independent of the trans- mitted power and can therefore be more relevant in the regime of partial power transmission. P, increases with tangential speed at the seal lip (Fig. 2).
17、Different prec- sure at the seal lip, which is designed into the seal, influ- ences the loss quite substantially. Different seal materi- als also influence the value of PvD. O io circumferential velocity Fig. 2: Lip oil seal power loss Bearina Power Losses For many anti-friction bearings the power l
18、oss is in the range of 0.1% of the transmitted power. For the often used tapered roller bearings the power loss can be much higher, it can also vary substantially with the ap- plied preloading and the grade of run-in of the bearing. From experimental data the bearing manufacturers provide approximat
19、ions for the evaluation of bearing power loss. These calculation methods are often derived from the equations of Eschmann 121, with a portion of non-load dependent TvLo and load dependent loss torque TvLpl (Fig. 3). For axially loaded roller and needle bear- ings an additional loss torque TVw2 has t
20、o be taken into account: TvL = T, + Tw, + T- (3) w-I I I I I taper roller ball bearing axial ball bearing cylindrical rolle bearing spherical ball bearing bearing I I I I I I 1 O 5 10 15 20 25 kN 30 I load F I Fig. 3: Friction torque of roller bearings The total power loss of an anti-friction bearin
21、g is then calculated from For the evaluation the SKF-method I31 is proposed with a portion of non-load dependent loss for woiin e ,2000 mm2/smin: for vaiin 2 2000 rnrn2/smin: Tu = 1 O-? - f, - ( vd n)yJ * dm (6) with fo as a function of the bearing type and the lubrica- tion (see Table 1). The load
22、dependent losses are calculated from: (7) TM = lo- f, P, d, where f, is again a function of the bearing type and P, is the equivalent bearing load (see Table 2) and: where f, can be approximated by f, = 0.006. Gear Power Loss Non-Load Dependent Gear Loss - The main influ- ence parameters on the chur
23、ning losses of the gear blanks are diameter, speed, immersion depth and gear oil viscosity. Additionally the internal gear box design can influence the no-load power loss of gears in a wide range. Fig. 4 shows the influence of circumferential speed and immersion depth on no-load gear power loss. Fig
24、. 5 shows the influence of different operating viscosi- ty of the oil on the no-load gear loss. It has to be men- tioned that the oil type has no influence on the no-load losses. 2 STD-AGHA SbFTM8-ENGL L79b E Ob87575 0004917 53T m Bearing design Deep-groove ball bearing single-row double-row Self-al
25、igning ball bearing Angular contact ball bearing single-row double-row Four-point contact bearing Cylind. roller bearing (cage) Series 10, 2, 3, 4 Series 22 Series 23 Cylind. roller bearing (full roller) sing le-ro w dou ble-row Needle roller bearing Self-aligning roller bearing Series 213 Series 22
26、2 Series 223, 230, 239 Series 231 Series 232 Series 240 Series 241 Taper roller bearing single-row Deep-groove ball thrust bearing Cylindrical roller thrust bearing Needle roller thrust bearing Self-alig. roller thrust bearing Series 292 E Series 292 Series 293 E Series 293 Series 294 E Series 294 T
27、able 1: Coefficient f, Type of lubrication Grease Oil mist Oil bath Oil injecti oil bath w vertical sh 0.75 . 2” 1 2 4 1,5 . 2” 0,7 . 12) 1,5 . 22) 3 . 42 3 2 4 8 2 1,7 3,3 6,6 4 3r4 63 13 6 2 6 9 O, 6 13 22 2) 08 2,1 3 33 1 2,8 4 43 54 _- 1 04 -_ 10 _ - 5 12 6 12 24 3,5 1,75 3,5 7 4 2 4 8 4,s 2,25
28、4,5 9 585 2,75 5,5 11 6 3 6 12 6,5 3,25 63 13 7 33 7 14 6 3 6 8 . IO2 585 O,8 115 3 9 -_ 3,5 7 14 - 5 11 _- 23 5 _ 3,7 7,4 _- 3 6 I - -_ 4,5 9 3,3 616 - 5 10 - - _ - - - ) 2, 4, The shown values are valid for steady condnions. For lately greased bearings i2 . 4) f, is to be used in the calculation.
29、The low values apply to the lightweight bearing. and the high values to the heavyweight bearings of a bore series. Valid for oil injection lubrication. For oil bath lubrication and vertical shaft the shown value is to be doubled. Valid for low rotation speed up to 20% of the reference rotation speed
30、 (see bearing tables). At higher rotation speed the fo value is to be doubled for the calculation. 3 STD-AGMA SbFTMB-ENGL 199b 9 Ob87575 0004920 251 m , Table 2: Coefficient f, and eauivalent bearinn load P, Bearing design P,” Deep-groove ball bearing (0,0006 . 0,0009) 3 Fa - 0,l F, (P/c) 21 Self-al
31、igning ball bearing 0,0003 (P0/Co)0r4 1,4 Y2Fa - O, 1 F, I I Angular contact ball bearing single-row o,oo i (PI) Fa -Oll F, double-row o,ooi (/qe 1,4 Fa - 0,l F, Four-point contact bearing o,ooi (P/O 1,5 Fa + 3,6 F, Cylind. roller bearing (cage) Series 10 0,0002 Fr:; F3) Series 2 0,0003 t31 Series 3
32、 0,00035 Seriesn 4, 22, 23 0,0004 Cylind. roller bearing (full roller) 0,00055 F,3) Needle roller bearing 0,002 Self-aligning roller bearing Series 213 Series 222 Series 223 Series 230,241 Series 231 Series 232 Series 239 Series 240 0,00022 0,0001 5 0,00065 0,001 0,00035 0,00045 0,00025 0,0008 1,35
33、Y2Fa, if F,/Fa -2, O. O I O C - 30 ,o no load loss Pvzo I Fig. 4: Influence of immersion depth on power loss “. o 5 io i5 20 25 30 mPas LO 0.8 Nm 0.7 5 0.6 ul 0.5 r - - O 01 - O o 3 0.L U O c v) 0.3 o 0.2 0.1 n O o - - 8 Fig. 5: No-load power loss for different lubricants Measurements of no-load gea
34、r power losses with a wide variety of operating conditions, speed, viscosity, internal gear box design etc. are reported by Walter i41 and Mauz 51. The hydraulic loss torque of each gear wheel is determined from: %.(A) TH = C,-C, .e where Csp (Fig. 6) depends on the immersion depth e, C, and C, on t
35、he face width b and the immersion depth e: e1 +e2 80 -eo c, = - + 0.2 (10) *G U I“ = - Fig. 6: Parameters for dip lubrication From these investigations the calculation of the no-load gear power loss Pw0 for splash lubrication can be determined from the angular velocity w and the hy- draulic torque T
36、,: (1 11 Load Dependent Gear Loss - The mean value for the gear mesh loss can be integrated along the path of contact from the local power loss (Fig. 7). It can be shown that the mesh power loss only depends on the transmitted power, the mean value of the coefficient of friction in the gear contact
37、and a gear loss factor li, which can be determined only from gear geometry. The problem is thus reduced to the determination of the mean value of the coefficient of gear friction. The load dependent gear power loss Pvzp is then: P, = PA * ccmZ * Hv (12) with the gear loss factor for cylindrical gear
38、 pairs: Sti3el 61 and later Michaelis 171 showed that friction measurements in a twin disk machine can be correlated to gear mesh friction. This makes it possible to use a twin disk machine for the independent investi- gation of main influence parameters on mesh friction. Fig. 8 shows an example of
39、the pressure influence on the coefficient of friction 7, 81. For small values of the slide ratio s = 10 % a constant degressive increase of the coefficient of friction can be assumed. For higher slide ratio s = 30 % which is more relevant for gear applications the influence of pressure decreases wit
40、h increasing pressure. Knauer 91 reports measured values of the coefficient of friction up to slide ratio s = 70 YO, without a visible influence of load. For the high sliding regime Stel 61 even finds decreasing values of the coefficient of friction with increasing pressure. 5 Fig. 7: Calculation of
41、 gear mesh loss 0,Ol- FVA 3 IS0 VG 100 o. 1 I 9- =gooc Oil - i 0.08 C O 0 .- c) E 0.06 u- O c. s s J .- 0.04 O u 0.02 1 disk contact 400 600 800 1000 1200 x2 1LOO Hemian stress PH Fig. 8: Influence of Hertzian stress on coefficient of friction (disk contact) o, 1 i 0.08 c O u - c - t 0.06 r c O - 5
42、F 0.04 O o 0.02 O O 5 10 15 mls 20 sum velocity VE Fig. 9: Influence of sum velocity and viscosity on coeffi- cient of friction (disk contact) Fig. IO: Influence of slide ratio on coefficient of friction (disk contact) Fig. 11: Influence of oil temperature on coefficient of friction (disk contact) F
43、ig. 9 shows the typical influence of the sum velocity on the coefficient of friction from investigations of Simon 8 and Prexler 9. The dependency is almost the same for different lubricants, different load, different temperature etc. Fig. 10 shows the influence of slide ratio respectively sliding ve
44、locity on the coefficient of friction. It can be seen that in the range of over 20 % slide ratio the coefficient of friction is almost indepen- dent of the sliding velocity. This influence can therefore be neglected. Fig. 11 shows the influence of oil temperature and thus oil viscosity on the coeffi
45、cient of friction 71. For low sum velocities the coefficient of friction increases with increasing temperature. This can be interpreted with boundary lubrication conditions as an increase in the amount of metal-to-metal contacts due to decreasing viscosity. For high sum velocities with elasto-hydrod
46、y- . 6 STD-ALMA SbFTM5-ENGL 1SSb Ob57575 0004723 Tb0 FVA L VG fi60 - Soil = 90 OC 0.1 - pH = 1300 Nlmm2 VE = 8 mls 0.08 _- 5 = 10 % .- O hmin= 0.8pm .c 80.0. . L .b .i r E - .- disk contact * O,06 I E 0.04 - direction of grinding maxial o circumferential o 0.02 - o- ! O 0.4 0.8 1.2 pm 1,6 arithmetic
47、 mean roughness Ra 04 I I I l 1.00 0.67 $50 O 2,OO specific film thickness h,in/Ra . Fig. 12: Influence of surface roughness and film thick- ness on coefficient of friction (disk contact) o. 1 % 0,08 E .- - E 0.06 L CI C .- 2 0.04 F o 0.02 IS0 VG220 gear type C and 212-1 Soil = 90 oc I -600 800 1000
48、 1200 1400 1600 f,1800 Hertzian stress p Fig. 13: Influence of Hertzian stress on coefficient of friction (gear contact) namic lubricating conditions the decrease in viscosity leads to less shear resistance and thus a decrease of the coefficient of friction. Fig. 12 shows the influence of the surfac
49、e rough- ness on the coefficient of friction. In a wide range of roughness and specific film thickness values for plateau- like run-in surfaces the coefficient of friction increases slightly with roughness. One of the main influence factors on gear tooth friction is the type of lubricant. This paper only deals with minerai oil based lubricants. The coefficient of fric- tion of polyalphaolefins is in the range of 80 to 90 %, of polyglycols in the range of 50 to 80 % and of esters in the rang
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