1、05FTM11Low Loss Gearsby: B.- R. Hhn, K. Michaelis and A. Wimmer, TechnicalUniversity of Munich, FZGTECHNICAL PAPERAmerican Gear Manufacturers AssociationLow Loss GearsBernd- Robert Hhn, Klaus Michaelis and Albert Wimmer, TechnicalUniversity of Munich, FZGThe statements and opinions contained herein
2、are those of the author and should not be construed as anofficial action or opinion of the American Gear Manufacturers Association.AbstractIn most transmission systems one of the main power loss sources is the loaded gear mesh. High losses therelead to high energy consumption, high temperatures, ear
3、ly oil ageing, increased failure risk and high coolingrequirements. In many cases high efficiency is not the main focus and design criteria as load capacity orvibration excitation predominate the gear shape design. Those design criteria mostly counteract highestpossible efficiency.The influences of
4、gear geometry parameters on gear efficiency, load capacity, and excitation are shown.Thereof design instructions can be derived which lead to low loss gears with equivalent load capacity.According to the designers preference these guidelines can be followed to a varying extent which leads tomore or
5、less unconventional, but more efficient gear design.Low loss gears can save substantial energy in comparison to conventional gears. The power loss reduction isdependent on the operating conditions and can add up to some 70 % of the power loss of conventional gears.Such low loss gears have significan
6、t advantages in terms of energy consumption, heat development, andcooling requirements. For same load carrying capacity and adequate vibration excitation they have, however,to be designed with increased centre distance or face width.Copyright 2005American Gear Manufacturers Association500 Montgomery
7、 Street, Suite 350Alexandria, Virginia, 22314October, 2005ISBN: 1-55589-859-91LOW LOSS GEARS B.-R. Hhn, K. Michaelis, A. Wimmer FZG (Gear Research Centre), Technical University of Munich, Germany 1 INTRODUCTION Power losses occur in different components of a gearbox. Each gearbox element produces so
8、me power losses. The total power loss is the sum of the power losses of the single elements. Basic gearbox elements are bearings, gears, and seals. Their power losses are usually individually mentioned. Other potentially integrated elements, such as clutches or oil pumps, also produce losses, their
9、power losses are merged in auxiliaries. According to their types losses can be further divided into no-load losses and load-dependent losses. Equation (1) shows the summation of all power losses PVin a typical gearbox. Losses in bearings and gears usually predominate in a gearbox. No-load losses com
10、prise all losses which also exist when a gearbox is not transmitting power but rotating without power output. No-load losses derive from seals or from windage and churning etc. Load dependent losses occur only in elements which carry the transmitted power or portions of it, i. e. bearings and gears.
11、 They encompass all power losses that vary with the power transmission in the concerned element. They evolve when two surfaces under pressure move relatively to each other. Power losses in this case depend on the acting force between the solids, the sliding speed, and on the coefficient of friction
12、established in the contact of the surfaces. For the composition of total power losses PVin a gearbox the following four main components are investigated: no-load power losses in bearings load dependent power losses in bearings no-load power losses in gears load dependent power losses in gears The in
13、vestigations are based on calculations for which the FVA-software “WTplus” 1, “STplus” 13, and “RIKOR” 10 is used. Index Z: gears L: bearings D: seals X: auxiliaries 4876484764847648476VXVDVLPVL0VZPVZ0VPPPPPPP +=0: no-load P: load dependent (1)2 GEARING MODEL For the calculations a gearing model is
14、necessary. This is aligned to a existing test rig gearbox. Figure 1 (overleaf) shows the main data of the reference gearbox model and a transverse section of the reference gear shape on which the calculations are based. Starting from that gearing single modifications are applied in order to investig
15、ate the influence of one single parameter. Gearsmt=4 mmz2: z1= 23 : 23n= 20wt= 19.121: 2= 0.7 : 0.7b= 19b = 40 mma = 91.5 mmx m = -0.245Bearings4 ball bearingsd = 30 mmD = 90 mmOperating ConditionsT = 500 NmpC= 1180 N/mmlubricant FVA3A1)type injectionhOil= 60CFigure 1: Main data of reference gearing
16、 model and gear cross section. 1)mineral oil ISO VG 100 with 4% sulphur-phosphorus additive (Anglamol 99) 201234102030405060pitch line velocity m/spower losskWloss degree%gear, load dependent kWgear, no-load kWbearing, load dependent kWbearing, no-load kWtotal loss degree %load torqueT = 500 NmFigur
17、e 2: Power loss composition in the model gearbox vs. pitch line velocity. 3 POWER LOSS PORTIONS In Figure 2 the amount of power losses for each of the four considered components is depicted versus the rotational speed at the operating conditions given in Figure 1. The investigation of power loss com
18、position in Figure 2 is done with example of a modified reference gearing with spur gears ( = 0). It shows that the gear no-load losses increase progressively with speed, while the other components seem to depend fairly linearly on the speed. For the vast range of rotational speeds the main portion
19、of losses are load dependent gear losses. Only for very high speeds no-load losses prevail, though the load dependent gear losses may still occupy an important portion. Bearing losses have only subordinate portions of the total losses throughout the whole speed range. In addition, the sum of these l
20、osses is rated against the power transmission which results in the loss degree , the complement of the degree of efficiency : 1PPinV= (2)with PVtotal power loss W, Pininput power W, degree of efficiency -. The loss degree shows a significant minimum between 10 and 20 m/s rotational speed. This refle
21、cts the basic changes in the coefficient of friction in the mating gears from the mixed lubrication regime for low speeds towards elasto-hydrodynamic (EHD) friction at higher speeds. Depending on the geometry of the transmission and the operating conditions this minimum occurs at different speed ran
22、ges. The prevailing power loss portion is as well dependent on the operating conditions. However, in order to minimise the power losses a focus must always be set onto load dependent gear losses since their portion is always significant, but with increasing speed no-load losses of gears need to be c
23、onsidered increasingly. 4 BASICS OF LOAD DEPENDENT GEAR LOSSES The load dependent losses depend on both gear and lubricant properties. The calculation of load dependent power losses in gears is based on the law of friction according to Coulomb (3) FR= FN(3)PVP= FR vg= FN vg(4)with FRfriction force N
24、, coefficient of friction -, FNnormal force N, PVPload dependent power loss W, vgsliding speed m/s. 3Equation (4) is valid for a single point of contact. In order to receive the mean power loss of two mating gears all points of contact along the path of contact need to be regarded. The power loss is
25、 calculated by the integral of the product of sliding speed, coefficient of friction and load over the path of contact. PPVZP VZP=1pxdxet AE()(5)with pettransverse base pitch mm, AE path of contact mm. All three parameters (coefficient of friction, normal load, sliding speed) vary along the path of
26、contact (Figure 3). Sliding speed is a geometry parameter which is derived from the gear shape and can be calculated exactly. The load distribution along the path of contact can be approximately set to the total load resulting from the torque and be split up into the number of pairs of teeth in cont
27、act. This assumption is a simplistic approximation 9. The coefficient of friction over the path of contact is assumed to be approximately constant. Only at the pitch point C where sliding is zero and pure rolling takes place a steep decrease and increase of the coefficient of friction has to be cons
28、idered. This deviation of the coefficient of friction takes place where the sliding speed is zero. Hence, in the integral this deviation is negligible. The coefficient of friction is approximated according to the FVA project No. 166, done by Schlenk 11, with formula (6): L25.005.0oil2.0redCCtbmZXRav
29、b/F048.0=(6)with :mmean coefficient of friction -, Ftbcircumferential force at base circle N, vGCsum speed at operating pitch circle m/s, DredCreduced radius of curvature at pitch point mm, 0oildynamic oil viscosity at oil temperature mPas, Ra arithmetic mean roughness m, XLfactor for oil type -. Wi
30、th the introduced simplifications (constant coefficient of friction along the path of contact, equal load distribution onto mating pairs of teeth) equation (4) can be applied to gears and transformed into equation (7): PVZP= mZ HV PA(7)with HVgear loss factor -: ( )2221b1V1)cos(uz)1u(H +=for 1 2, 1/
31、2 pet(8)with u = z2/z1gear ratio -, z number of teeth (1 pinion, 2 wheel gear) -, bbase helix angle , =etpAEtransverse contact ratio -, 1=etpCEaddendum contact ratio of pinion, 2=etpACaddendum contact ratio of wheel gear. The gear loss factor HVwas introduced by Ohlendorf 9 and is only dependent on
32、gear geometry. These equations were set up for usual spur gear geometries (1 2 and 1/2 pet) and produce acceptable results in these cases. Extreme gear shapes, however, may result in calculated power losses which deviate significantly from actual power losses. By more detailed considerations a bette
33、r approximation to the real distribution of the load along the path of contact can be obtained by using sophisticated calculation methods as FEM or the FVA-programme RIKOR. This is proven by experimental investigations 14. Gear loss factors based on such methods are called local gear loss factors HV
34、L. Differences between HVand HVLare significant for high contact ratio, helical or gears with profile corrections, see Figure 4. The gear loss factors HV 9, or HVL14 respectively, comprise the integral of the product of the sliding speed and the load distribution. Here, for the calculation of load d
35、ependent power losses of gears the local gear loss factor HVLwith the more realistic load distribution according to the FVA-programme RIKOR 10 is used. For gear design power losses are often of subordinate interest compared to load capacity and excitation level. So, if gears are to be optimised in t
36、erms of efficiency, load capacity and excitation must not be neglected. For the 4evaluation of single gear geometry parameters their influence on power loss, load capacity, and excitation is investigated by the means of FVA-programmes according to Figure 5. Excitation is evaluated by the tooth force
37、 level which represents the dynamic load in the tooth contact without respect to the further environment. This load dynamics is cause of, but not equal to, real load dynamics, vibration and noise. Lubricant properties affect the power losses via the coefficient of friction and are not subject to thi
38、s investigation. Their influence is supposed to be constant here. Actual CalculationValid for1 21/2 petNot proven for helical gears correctionsHV=+ + +()cos()uzub1111222PPVZP VZP=1pxdxet AE()PVZP Z() () () ()xxFxvxNg= = mZ V AHPFNAB DC ExAB DC EFNxAB DC ExAB DC ExAB DC EvgxAB DC Evgxpower lossreduct
39、ionFigure 3: Tribological conditions along the path of contact. load distribution forspur gear, no correctionFNAB DC ELoad distribution acc. Ohlendorfload distribution for helical gear with correctionHuzuVb=+ + +()cos()1111222HFVLN=1pxvxFvdxetgNtbAE() ()modifiedcalculationFigure 4: Gear loss factors
40、 HVand HVL. 5Figure 5: Calculation methods for different parameters. 5 INFLUENCE OF GEARING GEOMETRY ON LOAD DEPENDENT POWER LOSSES Figure 6 to Figure 13 show the influences of gear geometry parameters on the gear load dependent power losses compared to the reference gears given in Figure 1. The inf
41、luence of these parameters on the coefficient of friction is included. For these parameter variations also the pitting and tooth fracture capacities are given referring to the reference gearing with capacities of 100%. In best case, hence, power loss and tooth force level is low while the safety fac
42、tors of load capacities are high. Most important geometric parameters are transverse contact ratio (Figure 6) and module size (Figure 7) whose influence on power losses is almost proportional. Less strong is the influence of the pressure angle (Figure 8), but its importance comes from the advantage
43、that in the given range a higher pressure angle has only advantageous effects both on power loss reduction and higher load capacities and no unfavourable effects on excitation. With helix angle (Figure 9) power losses increase generally, but to a limited extent. For minimum power losses with small t
44、ransverse contact ratio there has to be a significant overlap contact ratio ( 1) for proper load capacity and noise excitation. The influence of surface roughness (Figure 10) shows also only positive effects if it is reduced. Unfortunately, an improvement is usually subject to cost rise. Recent inve
45、stigations show that this effect is limited. Below a certain roughness there is no further improvement. Moreover, there are other effects of surface structure such as roughness orientation which are not expressed by surface roughness but can affect the power loss to a substantial extent. The paramet
46、ers gear ratio and face width (at constant load per face width) are usually constraints which hardly can be changed. Their effect on power loss, capacities, and excitation is shown in Figure 11 and Figure 13, respectively. Addendum transverse contact ratio (Figure 12) is best if equally split betwee
47、n both gears but small deviations have marginal impact. 05010015020000,511,522,5Safety Factor Tooth RootSafety Factor PittingSafety Factor ScuffingTooth Force LevelLoss Degree%transverse contact ratio g“-Figure 6: Influence of transverse contact ratio on power loss and load capacities. RIKOR load to
48、rque 500 Nm). In this example also the bearing type has been optimised, but is not relevant here. The main changes applied encompass the following: Bearings different type (ball taper roller) size (dm= 60 mm 43.5 mm) Gears module reduction (4 mm 2 mm) transverse pressure angle increase (19.1 41.5) transverse contact ratio reduction (1.4 0.6) face width increase (40 mm 80 mm) overlap contact ratio increase (1.18 4.73) For the optimised gears the module and the transverse contact ratio are radically cut back, compensated by a doubled face width. So, the optimised gears have a low tra
