AGMA 14FTM08-2014 The Efficiency of a Simple Spur Gearbox - A Thermally Coupled Lubrication Model.pdf

1、14FTM08 AGMA Technical Paper The Efficiency of a Simple Spur Gearbox - A Thermally Coupled Lubrication Model By A.I. Christodoulias, A.V. Olver, and A. Kadiric, Imperial College London, A.E. Sworski, A. Kolekar, and F.E. Lockwood, Valvoline/Ashland 2 14FTM08 The Efficiency of a Simple Spur Gearbox -

2、 A Thermally Coupled Lubrication Model Athanasios I. Christodoulias, Andrew V. Olver, and Amir Kadiric, Imperial College London, Adam E. Sworski, Anant Kolekar, and Frances E. Lockwood, Valvoline/Ashland The statements and opinions contained herein are those of the author and should not be construed

3、 as an official action or opinion of the American Gear Manufacturers Association. Abstract A thermally coupled efficiency model for a simple dip-lubricated gearbox is presented. The model includes elastohydrodynamic (EHL) friction losses in gear teeth contacts as well as bearing, seal and churning l

4、osses. An iterative numerical scheme is used to fully account for the effects of contact temperature, pressure and shear rates on EHL friction. The model is used to predict gearbox efficiency with selected transmission oils whose properties were first obtained experimentally through rolling-sliding

5、tribometer tests under representative contact conditions. Although the gearbox was designed using standard methods against a fixed rating, the model was used to study efficiency over a much wider range of conditions. Results are presented to illustrate the relative contribution of different sources

6、of energy loss and the effect of lubricant properties on the overall gearbox efficiency under varying operating conditions. Copyright 2014 American Gear Manufacturers Association 1001 N. Fairfax Street, Suite 500 Alexandria, Virginia 22314 October 2014 ISBN: 978-1-61481-100-8 3 14FTM08 The Efficienc

7、y of a Simple Spur Gearbox - A Thermally Coupled Lubrication Model Athanasios I. Christodoulias, Andrew V. Olver, and Amir Kadiric, Imperial College London, Adam E. Sworski, Anant Kolekar, and Frances E. Lockwood, Valvoline/Ashland Introduction The efficiency of drivetrain components is quickly beco

8、ming a significant research area pushed by the ever intensifying quest for improved fuel economy in automotive vehicles. Emission-controlling regulations are becoming stricter, owing mainly to environmental issues such as air contamination but also due to the depletion of oil deposits and the result

9、ing high fuel prices. Pursuing augmented efficiency of a drivetrain or its components can also have the positive side effect of decreasing the frictional heat that is generated inside the gearbox, differential or axle component therefore improving scuffing or pitting behavior. The drive train in pas

10、senger cars absorbs around six per cent of the total fuel energy in combined city-highway driving - equivalent to about thirty per cent of the mechanical energy delivered to the wheels 1. The biggest part of this energy loss ends up as heat in the axle or transmission lubricant resulting from fricti

11、on, windage and churning. As a result the reduction of lubricant-related losses in a vehicles drivetrain can lead to significant improvements in both the fuel economy and the environmental. Thus, this efficiency increase is a much sought-after goal for lubricant suppliers of OEM factory fill and aft

12、ermarket lubricants. Background The efficiency of spur gears is started receiving significant attention since about 1980s with the work of Anderson 2 3. Recent years have seen a boom in such publications owing mainly to the energy crisis. Li and Kahraman 4 and more recently Chang and Jeng 5 focused

13、on a spur gear pair while Michaelis 6 considered a more integrated approach which included churning losses as well as bearing and seal losses. Churning losses play a very important role in the prediction of a dip lubricated components efficiency and recent studies from Changenet and Velex 7 8 have s

14、hown that the accurate determination of churning losses and how these are affected by design parameters is a challenging problem. Thermal behavior of the components and thermal response of lubricants are dominant factors of efficiency enhancement. There are several published models of spur gear pair

15、s that analyze the thermal behavior of the pair like those developed by Long and Lord 9 and Taburdagitan 10 which use finite element methods to predict the overall and surface temperatures. A more integrated approach by Changenet and Velex 11 considered lump thermal elements to study and model a six

16、-speed gearbox, but with no experimental validation. In addition, the thermal response of transmission lubricants was extensively studied by Olver 12 who also developed a comprehensive model to predict traction in Elastohydrodynamic (EHL) contacts which included thermal effects 13. However, there ar

17、e currently no efficiency models that consider full spur gearbox including the all-important thermal coupling, taking into account the mesh and bulk temperature rise of all drivetrain components or that of the oil surrounding them as well as all sources of energy loss including bearings, seals, chur

18、ning and EHL traction. Additionally, the type of lubricant itself is a crucial factor in determining the efficiency of a drivetrain. Despite this, there is currently very limited ability to predict the relative fuel economy arising from the use of different drive train lubricants. Petry-Johnson 14 h

19、ave included more than one type of lubricants in their studies in an attempt to pinpoint the possible effect that a specific combination of lubricant, component design and operating condition may have on the overall gearbox efficiency. The results from their studies showed a linear relationship betw

20、een the gear power loss and the rotational speed of the gears and also highlighted the effect of surface finish on the efficiency of the gearbox. Their lubricant comparison used three different lubricants to indicate that there is a possible change in overall efficiency depending on the lubricant ty

21、pe. However, no complete method has been developed that is able to simultaneously account for specific lubricant characteristics under EHL contact conditions and relevant 4 14FTM08 gearbox parameters. Such an approach should be able to provide a more accurate estimation of the possible efficiency ga

22、in. The limitations of current approaches include limited treatment of gear churning losses and not accounting for the transient conditions arising from variable vehicle duty cycle. Kolekar and Olver 15 have recently worked on this issue concentrating on hypoid axles. A transient thermal model coupl

23、ed to a quasi-steady state lubricant traction and churning formulation has been used together with lubricant bench tests in order to predict the energy that is dissipated during specified drive cycles. The results highlight the high influence that the properties of axle oils have and that the rankin

24、g order of lubricant composition and properties depends greatly on the specified duty cycle, with high viscosity, friction modified oils being favored for high power use. In contrast, lower viscosity fluids than are currently in use provide lower losses for city and light highway duty. In addition t

25、o treating only the axle, this work has other significant shortcomings including the lumped mass axle temperature that does not capture the bulk lubricant temperature, the lack of a change gearbox model as well as the lack of provision to determine the effect of drive train efficiency on the engine

26、behavior and therefore on fuel consumption. The present work is designed to offer significant improvements in the accuracy of efficiency predictions for simple spur gearboxes including the effects of lubricant rheology on gearbox efficiency. The model accounts for EHL friction losses in gear teeth c

27、ontacts, bearing and seal losses, and losses due to oil churning. The EHL friction losses are calculated based on lubricant properties that have been obtained through extensive measurements on a ball-on-disk tribometer, while also fully accounting for the effect of thermal coupling so that any incre

28、ase in lubricant temperature (and the corresponding change in lubricant properties) due to power losses, is fed back to EHL friction calculations. The ambient temperature of the lubricant in the gearbox is calculated using a multi-physics finite element model which includes all conductive and convec

29、tive heat transfers within the gearbox. Such a holistic approach, particularly the inclusion of thermal coupling, will enable the model to account for the transient conditions due to particular usage history and therefore predict the efficiency for a given drive-cycle. Methods This section first out

30、lines the basics of the EHL model used to predict tooth frictional losses, followed by the methods to predict bearing, seal and churning losses. Finally the FEM approach used to calculate the ambient (oil bath) temperature rise, which is fed back to the EHL model, is outlined. The experimental metho

31、d used to extract lubricant characteristics that are used as input to the EHL model is also described. Basic EHL model A thermally coupled EHL model was devised adopting the approach of Olver and Spikes 13 which predicts the friction coefficient in the rolling-sliding EHL contact of a lubricated dis

32、c pair. The model uses the EHL regression equations developed by Chittenden 16 to calculate the minimum and central film thickness: 0.68 0.49 0.07303.63hUGWRx(1) 0.68 0.49 0.0734.30cxhUGWR(2)where h0is minimum EHL film thickness, m; Rxis reduced radius of contact, m; U is entrainment velocity, m/s;

33、G is gravitational acceleration, m/s2; W is total contact load, N; hcis central EHL film thickness, m. 5 14FTM08 Where the non-dimensional parameters 0xUUER(3) GE (4) LxWWWER L(5) are the speed, load (L = line contact) and material parameter respectively. where 0is inlet viscosity (at p = 0), Pa.s;

34、E is reduced modulus of elasticity, Pa; is pressure-viscosity coefficient; LWis total contact load in line of contact; L is length of EHL contact, m. The mean shear stress is calculated based on the Ree-Eyring approach as adapted by Evans and Johnson 17, and the traction regime is decided using the

35、following three-stage process described by Olver and Spikes which is based on the non-dimensional Deborah and S numbers (Figure 1). The friction coefficient is then predicted by means of a convergence loop; the loop is initiated by assuming an initial friction coefficient 0and then the temperature r

36、ise due to shear heating of the lubricant (Toil)avand contact of asperities (Tf)avare calculated using the approach developed by Olver 13. 1.061.061/210hf1hav11qTBqAk U (6) Figure 1. The rules for determination of the mean shear stress 13 (Dois Deborah number (= 0U/(2Ge), S is non-dimensional strain

37、 rate (= 0/E), * is non-dimensional shear stress (= /E) and cis the limiting shear stress) 6 14FTM08 88sc s coilavoil oilWU h U hTAk k (7) where his heat partition; q is heat generated by sliding in the contact,W; A is EHL contact area, m2; k is thermal conductivity, W/m-K; 1is thermal diffusivity o

38、f material, m2/s; 0is EHL semi contact width, m; B is transient thermal resistance; Usis sliding velocity, m/s; is shear stress, Pa; koilis thermal conductivity of the oil, W/m-K. Using these temperatures in conjunction with the skin (boundary) temperature rise, TB, calculated using a heat partition

39、 h between the two surfaces, the mean film temperature, T , can be calculated. 1.0621.06c22oilhc12 1 2oilhBMkAhBB MMkA (8) 1B1 2B2B12UT U TTUU(9) Bf oilav avTT T T (10) where M is steady state thermal resistance of contacting body. The temperatures are repeatedly evaluated until the desired converge

40、nce is achieved (usually within 0.1 C or less). Once these are known, the dissipated power in the form of heat can be calculated by simply multiplying the load with the friction coefficient and the sliding speed. The EHL model assumes that the basic lubricant properties do not change within the cont

41、act and are calculated either in respect to the inlet conditions or to the mean film temperature, based on the assumption by Evans 18. The lubricant properties that are used are based on a synthetic 75W90 type gear lubricant and they are calculated using a linear approach for the variation of densit

42、y and pressure viscosity coefficient with temperature. The shear modulus is calculated using an exponential approach quoted by Muraki 19. The ASTM equation based on the ASTM D341-722 standard is used to calculate the low shear rate viscosity of the lubricant, based on measurements at 40 C and 100 C.

43、 log log 0.7 logvbcT (11) where v is kinematic viscosity, m2/s; b is tooth face width, m; c is constant. The model can successfully predict the traction regime and friction coefficient of a combination of materials and lubricants. Roughness of the surfaces is also taken into account by means of the

44、non-dimensional lambda () value which necessitates the use of a boundary modified friction coefficient of the form shown below, suggested by Smeeth and Spikes 20 for m = 2. 7 14FTM08 1bfeff fm(12) where effis effective or mixed friction coefficient; fis fluid friction coefficient; bis boundary frict

45、ion coefficient. The model converges in less than 5 iterations for all but the most extreme conditions and can be used as a base to simulate a lubricated gear pair. The basic algorithm described here is summarized in the flowchart of Figure 2. Figure 2. Flowchart of the EHL model algorithm 8 14FTM08

46、 Extracting lubricant rheology coefficients The rheological characteristics of the lubricant play a crucial role in determining the thermal and frictional behavior. Previous studies 13 have shown that EHL contacts can operate at temperatures that are significantly higher than the ambient oil bath te

47、mperature. It is therefore necessary to produce an extended lubricant rheology database which will include the typically high temperatures that are encountered in practice. As stated earlier, the core of the EHL model is the Eyring model 21; it is therefore assumed that the lubricant is following th

48、e Eyring behavior where the relationship between the shear rate and the shear stress is described by the equation: sin00h(13) The viscosity in the second part of the equation is the high pressure, in-contact viscosity which is in turn described by either the Barus 22 or the Roelands equation. In thi

49、s case, the complete equation originally proposed by Roelands 23 which is both pressure and temperature corrected was used: 135log 1135z0rrrPsTpepTe (14) where Pis in-contact viscosity, Pa.s; is viscosity constant (= 0.0000631 Pas); ris measured viscosity at atmospheric pressure; p is pressure; pris reference pressure Tris reference temperature. 135 is temperat