# Improvement in DCT Shaft Lubrication through CFD Method.

IntroductionTransmission lubrication system is directly related to transmission internal shafts, gears, bearings, synchronizers, and other component working performances and life cycles. Good lubrication can effectively reduce transmission component surface contact friction, gear rattle, and power loss [1, 2, 3]. It is also one of the most important prerequisites for transmission working and endurance.

In terms of vehicle powertrain performance, transmission lubrication is significant in improving durability and reducing power losses under all circumstances. Liu et al. [4] investigated a single-stage gearbox oil distribution and churning losses by using the finite volume method. The simulation results compared with test rig results affirmed to be in unison. Hohn et al. [5] tested the lubricant immersion level effects on gear scuffing, power losses, and temperature variations. The experimental results and calculation methods were also discussed. Luke and Olver [6] measured a range of single-gear churning torques and compared its losses with different parameters, such as speeds, lubricants, and temperatures. Liu et al. [7] studied a mathematical method to calculate an electric oil pump effects on increasing automatic transmission working efficiency and decreasing hydraulic system leakage. Currently, the most adopted test methods are the following two ways during the transmission lubrication system development process. One is to observe lubricant real-time morphology under transparent plastic housings. Another is to evaluate component lubrication results with colored oil and check part fast deconstruction after the test. However, no matter which test method to employ, detailed quantitative data cannot be approached.

The objectives of this work were (1) to build an accurate computational fluid dynamics (CFD) model in STAR-CCM+ software to simulate a dual-clutch transmission (DCT) lubricant morphology, (2) explore a quantitative approach to monitor transmission component oil volume changes, and (3) improve transmission output shaft 1 (OSl)-insufficient lubrication conditions according to simulation results.

Numerical Approach

Governing Equations

As for typical fluid, the basic governing equations obey the following two laws: the law of conservation of mass and the law of conservation of momentum [8].

Conservation of mass:

[[[partial derivative][[rho].sub.m]]/[partial derivative]t] + [nabla] * ([[rho].sub.m][U.sub.m]) = 0 Eq. (1)

Conservation of momentum:

[mathematical expression not reproducible] Eq. (2)

Here, [rho] is the density of fluid, U is the velocity vector of the fluid, subscript m is the gas-phase and the liquid-phase mixture extent, and p is the pressure field. Assume that both phases share the same pressure field. g is the acceleration under gravity, and f is the body force imparted to the fluid. The mixture density, [[rho].sub.m], and the coefficient of viscosity, [[mu].sub.m], are estimated using the volume fraction of the liquid phase, and F as synthetic quantities weighted for the volume fraction of each phase, as shown below:

[[rho].sub.m] = F[[rho].sub.liquid] + (1 - F) [[rho].sub.gas] (Eq.) (3)

[[mu].sub.m] = F[[mu].sub.liquid] + (1 - F) [[mu].sub.gas] (Eq.) (4)

The volume of fluid (VOF) method is used to analyze oil surface behaviors. The VOF transport equation is shown as follows:

[[partial derivative]F/[partial derivative]t] + [nabla] * (FU) = S, Eq. (5)

where S is a source term for suction and discharge. Given that the transmission is a closed space in this calculation, S is assumed to equal 0.

Considering the disturbance of the transmission lubrication system, the k-[epsilon] turbulence model is used for lubrication analysis. In the standard k-[epsilon] model, the eddy viscosity is determined from a single turbulence length scale, whereas in reality all scales of motion will contribute to the turbulent diffusion. The above problems can be solved using the re-normalization group (RNG) k-[epsilon] turbulence model.

For turbulent kinetic energy k:

[[partial derivative]([rho]k)/dt] + [[[partial derivative]([rho]k[u.sub.i])]/[partial derivative][x.sub.i]] = [[partial derivative]/[partial derivative][x.sub.j]] [[[alpha].sub.k][[mu].sub.eff][[partial derivative]k/[partial derivative][x.sub.i]]]+[G.sub.k] -[[rho].sub.[epsilon]] Eq. (6)

For dissipation [epsilon]:

[mathematical expression not reproducible] Eq. (7)

where k is turbulent kinetic energy, [epsilon] is energy dissipation, [[mu].sub.t] is eddy viscosity, [[mu].sub.t] = [rho][C.sub.[mu]][k.sup.2]/[epsilon], [[mu].sub.eff] is a modified form of RNG k-[epsilon] turbulent model eddy viscosity, and [[mu].sub.eff] = [mu] + [[mu].sub.t]. [G.sub.k] is average velocity gradient caused by turbulent kinetic energy k source term, calculated by the following function:

[mathematical expression not reproducible] Eq. (8)

[C*.sub.1[epsilon]] is a correction coefficient of RNG k-[epsilon] turbulent model constant [C.sub.1[epsilon]], which can be calculated by the following equation:

[C*.sub.1[epsilon]] = [C.sub.1[epsilon]] -[[[eta](1 - [eta]/[[eta].sub.0])]/1+[beta][[eta].sup.3]], Eq. (9)

where

[eta] = [(2[E.sub.ij][E.sub.ij] ).sup.1/2] k/[epsilon] Eq. (10)

[E.sub.ij] = ([partial derivative][u.sub.i]/[partial derivative][x.sub.j] +[partial derivative][u.sub.j]/[partial derivative][x.sub.i])/2 Eq. (11)

[C.sub.[mu]], [[alpha].sub.k], [[alpha].sub.[epsilon]], [C.sub.1[epsilon]], [C.sub.2[epsilon]], [[eta].sub.0], and [beta] are constants of RNG k-[epsilon] turbulent model, [C.sub.[mu]] = 0.085, [[alpha].sub.k] = [[alpha].sub.[epsilon]] = 1.39, [C.sub.1[epsilon]] = 1.42, [C.sub.2[epsilon]] = 1.68, [[eta].sub.0] = 4.377, [beta] = 0.012.

For flow near-wall region and low Reynolds number flow, the wall function is shown as follows:

[[mu].sub.+] = [1/k]ln ([Ey.sup.+]) Eq. (12)

[y.sup.+]= [[DELTA][y.sup.p][C.sup.1/4.sub.[mu]][C.sup.1/2.sub.p]/[mu]] Eq. (13)

where [[mu].sub.+] and [y.sup.+] are dimensionless parameters that represent velocity and distance, respectively. [k.sub.p] is turbulent kinetic energy of node p, [DELTA][y.sub.p] is the distance between node p and wall surface, [mu] is fluid viscosity, and E is a constant related to roughness, for smooth wall surface, E = 9.8.

During the transmission working process, assume that the numerical model conforms to the following assumptions:

a. Lubricant and air should be two exclusive phase interfaces.

b. Only consider transmission internal oil churning and oil bath lubrication, excluding external oil pump and dual-clutch active lubrication.

c. Do not consider the transmission working process heat transfer.

d. Fluid has no-slip boundary condition on the wall.

Boundary Conditions and Initial Definitions

On the basis of the abovementioned assumptions and the CFD model simulation methods [9, 10, 11, 12], the following specific boundary conditions and initial definitions were derived:

a. Assume transmission housing internal wall surface, pipeline internal wall surface, and gear surface as no-slip surface. Fluid velocity at the wall surface is defined as 0.

b. Assume that lubricant and air were mutually exclusive phases and their interface is defined as the free surface while using the VOF method to analyze the oil surface behavior.

c. Assume that all non-slipping wall surface contact angles with fluid were 120[degrees].

d. At the breather valve position, set the fluid pressure equal with valve exit pressure. The valve exit pressure is the standard atmospheric pressure 101.325 kPa.

e. Assume that there is no heat transfer during the transmission lubrication process and that lubricant properties adopt a certain brand oil under 80[degrees]C condition.

f. Assume that transmission lubricant and air density were constant.

g. The mounted transmission simulation model has the same angle with the mounted transmission on the vehicle. The transmission bottom side was set horizontal.

h. Shafts, gears, bearings, synchronizers, and other rotating component speeds were calculated according to transmission working conditions.

i. The simulation time stepping was defined as constant, 6e-05 second. The total simulation time was defined as 4 seconds.

j. The surface tension model was activated and defined surface tension value as 0.03 N/m.

The convergence is confirmed when momentum variable residuals reached below 1e-03 and energy variable residuals reached below 1e-06. Meanwhile, the monitored quantities stay steady values. However, these requirements are only for reference. For simulation model which is too complex, some of above requirements can be compromised.

Model Creation

The DCT lubrication simulation model should keep the same dimension with the design model. The simulation model simplified detailed structures for finite element mesh generation (Figure 1).

The grid analysis was conducted along with CFD software setting procedures. The following steps are grid size setting procedures and requirements:

First, implement automatic surface repair and define the minimum proximity as 0.05 and minimum quality as 0.01. Then, define the number of prism layers as 2, prism layer stretching as 1.5, and prism layer thickness as 0.89 mm. Next, define the relative minimum surface size as 1.75 mm and relative target surface size as 3.75 mm.

For gears, oil guide components implemented volumetric control, defined grid size between 1.5 and 2.5 mm.

The total number of grid cells is 2.49 million. The cell number at the interface should be approximately the same.

The transmission lubricant properties are shown as follows.

To create complicated DCT model and simulate DCT lubrication process, the following modifications were implemented.

Gear Mesh

For specific gear pairs, which have a large lubrication effect, the gear geometry remains to be unchanged. Large-wheel gear dimensions were kept unchanged and small-pinion gear dimensions were decreased proportionally, as shown in Figure 2(a). For specific gear pairs, which have little lubrication effects, gear geometry was simplified to cylinder, as shown in Figure 2(b).

According to references [4-5, 9, 13] and experimental investigations, two types of gears have large lubrication effects. One is gears that were immersed in the oil, such as differential ring gear and large idler gears on output shaft 2 (OS2). These gears directly churned oil. Another is gears that mesh with the oil churning gears. They could receive sufficient lubricant and meanwhile churned lubricant into other component surfaces. These two types of gears have good lubrication effects.

For gears that were mounted above the oil level and not directly meshed with oil churning gears, they could not obtain enough oil lubrication. In this case, these gears would be modeled as the simplified cylinder gears.

Interface Settings

Set the interface of dynamic zone and static zone (Figure 3). Different zones were, respectively, defined in different rotation speeds. To effectively use computer resource, the following principles were suggested for interface settings:

a. The interface quantity is the same with computer central processing unit (CPU) quantity. This setting made CPU use maximum and calculation time minimum.

b. The grid cell numbers of each interface keep almost the same.

Monitor Zone and Model Change

The transmission mount attitude was shown in Figure 4. The OS1 mount position was above the lubricant level that made OS1 lubrication difficult. The simulation focused on OS1 area lubricant flow morphology. Four oil bores on the OS1 were monitored. Each oil bore corresponds with one needle bearing on OS1, as shown in Figure 5.

Two attempts of the transmission lubrication system were implemented to solve OS1-insufficient lubricant phenomenon. One attempt was to unblock the housing lubrication channel that made oil flow directly to the bearing area, as shown in Figure 6. Another attempt was to change oil guide component structure. The oil guide side walls were extended to collect more churned oil. Meanwhile, the oil guide component was divided into two individual parts for better assembly, as shown in Figure 7.

Simulation Results

The transmission input shaft was set at the speed of 2000 rpm at the seventh gear ratio, with oil being approximately 4 liters and a running time of 2 minutes. Accordingly, the simulation results were generated. Figure 8 shows the transmission lubricant transient morphology pictures. The morphology pictures indicated the oil flow trend and estimated lubrication effect provided that intuitive references for lubrication system evaluation emerge.

Figure 9 shows the local housing structure and lubricant transient morphology at the oil guide area.

The lubricant flowed into the hollow output shaft internal channel under the centrifugal force effect, and the churned oil flowed outside through four bores on the shaft. The churned oil reached the needle bearings, synchronizers, gears, and other components on the shaft. Figure 10 shows the OS1 oil churning process.

Figure 11 reflects the oil volume change curves of the four monitors. Given that the shaft rotated in a certain speed, the oil flow displayed a periodical change. Monitors 1 and 4 had a relatively large amplitude of oil flow volumes, whereas monitors 2 and 3 had a relatively small amplitude of oil flow volumes. On the basis of the cited references [14-16] and engineering experiences, the needle bearing under the oil volume more than 15 mL/h will meet lubrication requirements. Given that the oil density was 787 kg/[m.sup.3] known (Table 1), 1 kg of oil approximately equaled 1270 mL. Thus, 15 mL/h equaled the 3.3*[10.sup.-6] kg/s oil flow volume. The minimum amplitude of monitor 4 (Figure 11) was approximately 0.0001 kg/s, which is considerably larger than 3.3*[10.sup.-6] kg/s oil flow volume requirement. Therefore, under this simulation condition, all the needle bearings on OS1 could obtain sufficient lubrication.

Experimental

Method

The transmission mounted on the test rig kept the same angle with transmission mounted on the vehicle, as shown in Figure 12. Three kinds of lubrication test conditions were implemented: vehicle uphill test, vehicle downhill test, and vehicle turn test.

Test lubricant used the Shell transmission oil with the same oil properties used in the simulation, colored with special additive, with an oil volume of 3.5 L-4.0 L, a clutch immersion depth of 9-19 mm, and an oil level of 105-115 mm from the clutch zero plane, as shown in Figure 13. Set test input speed as 2000 rpm at the seventh gear ratio. Set test running time as 2 minutes.

Results and Discussion

The simulated 3D lubrication morphology was compared with an actual transmission lubrication test process to validate its reliability. The test transmission was assembled with a transparent plastic plate instead of aluminum housing material at the position of OS2 bearing area. Figure 14 showed high correlation between the 3D simulation morphology and the real test result.

Figures 15 and 16 showed lubrication system component structure changes. Figure 15 shows the housing oil channel and the modified housing oil channel had no block and directly flowed to the housing bearing area. Figure 16 shows the oil guide structure comparison; the new oil guide increased side wall for collecting and reserving more oil. The outlet was also widened to increase oil flow speed.

The simulation model defined the total volume of lubricant as 4 liters. In this work, only high position OS1 existed lubrication problem; thus the study focused on OS1 oil volume investigation. Before the lubrication system structure modification, the transmission oil had no effective path flow into the hallow shaft, and the lubrication test results were not acceptable. The needle bearings, gears, and synchronizer rings on the OS1 had no colored oil, as shown in Figure 17(a). After the lubrication system structure changed, the lubricant could effectively flow into the hollow shaft, such as the morphology simulation presented. The test results had a good lubrication performance. The needle bearings, idler gears, and synchronizer rings obtained sufficient lubrication, as depicted in Figure 17(b).

In the perspective of simulation, the four monitored bore oil volumes on the output shaft were sufficient enough to meet the four needle bearing lubrication requirements. As for the actual test results, the hollow output shaft also obtained sufficient lubrication as the four needle bearing assembly positions on the shaft had no friction or abrasion. Figure 18 displays the output shaft lubrication result.

Conclusions

A DCT lubrication model was created and simulated based on CFD method. The transmission internal lubricant morphology was displayed accurately. Oil volume changes with time at key positions on OS1 were monitored. The detailed data calculated in the simulation provided guidance for solving lubrication problems.

The test results were consistent with simulation morphology. By changing oil guide structure and housing structure, OS1 lubrication problem was solved. The simulation predictions were validated with actual test results.

Definitions/Abbreviations

DCT - Dual-clutch transmission

CFD - Computational fluid dynamics

OS1 - Output shaft 1

OS2 - Output shaft 2

References

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Zhan Cao, Hebei University of Technology, China; China Automotive Technology and Research Center Co., Ltd., China

Yong Chen, Hebei University of Technology, China; Geely Powertrain Research Institute, China

Ting Su, Geely Powertrain Research Institute, China

Hai Liu and Libin Zang, Hebei University of Technology, China

Keywords

Dual-clutch transmission, Lubrication, Computational fluid dynamics, Simulation, Structure optimization

Citation

Cao, Z., Chen, Y., Su, T., Liu, H. et al., "Improvement in DCT Shaft Lubrication through CFD Method," SAE Int. J. Fuels Lubr. 11(3):219-227, 2018,

doi:10.4271/04-11-03-0011.

History

Received: 20 May 2018

Revised: 31 Jul 2018

Accepted: 24 Aug 2018

e-Available: 25 Oct 2018

doi:10.4271/04-11-03-0011

TABLE 1 Lubricant properties. Temperature sViscosity Density Heat conductivity Specific ([degrees]C) s(Pa*s) (kg/[m.sup.3]) coefficient heat s (W/m*K) (J/kg*K) s 80 s0.00739 787 0.136 2150

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Author: | Cao, Zhan; Chen, Yong; Su, Ting; Liu, Hai; Zang, Libin |
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Publication: | SAE International Journal of Fuels and Lubricants |

Article Type: | Technical report |

Date: | Nov 1, 2018 |

Words: | 3443 |

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