COMPRESSIBLE FLOW ANALYSIS IN A CLUTCH PISTON CHAMBER

Masaru SHIMADA* , Hideharu YAMAMOTO*

* Hardware System Development Department, R&D Division JATCO Ltd

700-1, Imaizumi, Fuji City, Shizuoka, 417-8585 Japan (E-mail : masaru_shimada@jatco.co.jp)

ABSTRACT

In the automotive automatic transmission, the stagnated air in both the hydraulic circuit and the clutch controlling piston chamber have a bad influence on changing gears, so that understanding the mechanism of the flow field in the hydraulic system is very important. But there was no method to understand it except flow visualization experiment. So in this paper, we analyze the flow field with compressible VOF method calculation which includes an easy mesh morphing to move clutch piston. We also adapted the formulation of the boundary condition in order to reduce the calculation time. This calculation enables us to understand the mechanism of the flow field in the hydraulic system which contributes to improve controlling technology of changing gears. -- VOF method: popular computational technique for multi-fluid dynamics / mesh morphing: a technique of continuously deforming the CFD mesh by moving vertices

KEY WORDS

VOF, Compressible, Mesh morphing, Automatic Transmission

NOMENCLATURE

Ableed : Cross section of the air bleed [m2] Aorf : Cross section of the orifice [m2]

d : Diameter of the cylindrical clearance [m] h : Clearance height of the air bleed [m] l : Length of the cylindrical clearance [m]

Pat : Pressure in the transmission [Pa] (=0.0) pbleed : Pressure on the air bleed boundary [Pa]

Q : Flow rate from the air bleed [m3/s] μ : Viscosity [Pa s] ρ : Density [kg/m3] ζ : Loss coefficient

:=1.25 (Inlet:0.25 + Outlet:1.0) in Eq.(1) :=2.0 in Eq.(2)

INTRODUCTION

In the automotive automatic transmission (AT),

gear ratio is changed by engaging or releasing several clutches with the pistons. Since the pistons are controlled by oil pressure, highly accurate oil pressure controlling is essential for smooth and good response drive. The stagnated air in the hydraulic circuit and the clutch piston chamber has a bad influence on the hydraulic performance. Therefore, it is very important to understand the mechanism of the flow field in the hydraulic system. However, there was no method to predict the appearance (or disappearance) and the flow field of stagnated air in the hydraulic system when the clutch moves except flow visualization experiment. In this paper, we conduct the CFD with VOF method

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calculation which includes our various ideas and visualize the flow field of two types of clutch systems; one is a clutch which stops rotation (brake-type), another is a clutch which transmits rotation (rotary-type). We also compare the flow field of two clutch systems.

Computational fluid dynamics code STAR-CD is used in the calculation.

ANALYSIS SETTING

Outline

Fig.1 shows a computational domain of brake-type clutch. The schematic figure of all AT is shown in Fig.1 (a). The calculating clutch region is located in the end of AT which is inside the red line circle. The computational domain is composed of the output port and hydraulic circuit inside the control valve (C/V), hydraulic circuit inside the CASE, and the piston chamber. The piston surface is the green surface in the cross section as shown in Fig.1 (c). The piston surface is controlled by the spring force and moves to the left (right) when the oil pressure is high (low). The piston chamber is divided into outer and inner, and the inner

piston chamber contains an air bleeding hole (air bleed) which is shown inside the black circle. Air bleed is a cylindrical hole which has 15 [μm] clearance height (h), 4 [mm] diameter (d), and 7 [mm] length (l) approximately. From this hole, although air easily leaks, oil hardly leaks due to the difference of viscosity.

In this paper, the mechanism of the air flow from the piston chamber is considered with attention to the following points. 1) Air flow from the air bleed 2) Relation between the oil flow generated by the

stroke of piston and the air flow 3) Variation of the air volume by the oil pressure Solutions to the problems on the calculation

In this calculation, we added several ideas to VOF method as described below. 1) Compressible air flow

Since the oil pressure which controls the piston is up to 1.4[MPa] in AT, the compression and expansion of air should be taken into account. We applied the compressible VOF method to the calculation. Since it is considered that the heat has little influence to the flow field, we consider only density effect on the compressible air and ignore the heat. 2) Easy mesh morphing

Since the oil flow generated by the stroke of piston is very important for the air flow field in the piston chamber, it is necessary to deform the calculation mesh to realize the stroke of piston. However, the shape of piston chamber is so complicated that it is not easy to deform the calculation mesh. In order to solve this problem, we applied the morphing method explained below to deform the mesh without using a commercial mesh morphing program. Fig.2 shows a part of the cross section of the piston chamber.

1. Insert prism layers on the piston surface after making tetrahedral mesh

2. Deform only prism layers as solving the motion equation of the piston

Figure 2 Easy mesh morphing method

Piston Surface

Prism layer

Deform only Prism layer

(a) Original shape (b) Maximum deformation(b) Fluid domain (c) Cross section

Figure 1 Computational domain

Hydraulic Circuit

(C/V) (CASE)

Piston Chamber Air bleed

PistonSurface

Pressure boundary (Valve)

(a) Shape of AT

PistonCASE

Control Valve

Pull the fluid domain out

Piston motion

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This method enabled us to morph the mesh without breaking the topology and without making poor quality mesh. Fig.2 also shows the range of the motion. 3) Formulation of the air bleed

As mentioned above, the air bleed is a very narrow cylindrical hole in this hydraulic system. If we make grids as usual, both the number of mesh and the calculation time will be huge. In order to reduce the calculation time, we formulated the boundary condition to realize the air bleed.

The pressure loss of the air bleed is formulated as Equation (1). The first term means the friction loss of clearance and second term means the form loss of clearance inlet and outlet. Using this equation we calculated the flow rate Q from pressure at the boundary and applied it as the boundary condition. Density and viscosity are set depending on the volume fraction on the boundary. This formulation well expresses the characteristic of the air bleed such that air easily leaks and oil hardly leaks. Formulating the boundary condition enabled us to minimize the number of mesh and to reduce the calculation time.

(1)

4) Formulation of the control valve (C/V) Fig.4 shows the schematic diagram of C/V. Since

orifice and valve are located in the upstream of model (in C/V), we have to take their pressure characteristics into account to calculate pressure in the piston chamber accurately. However, the number of mesh and calculation time will be huge if we try to use CFD to solve the pressure loss of the hydraulic circuit in C/V and the valve motion. So we formulated the characteristics of C/V and applied the output pressure of C/V as the boundary condition.

We assumed the orifice is the main pressure loss element in C/V, and set the boundary pressure which is obtained by subtracting the loss formulated as

Equation (2) from the output pressure. Q is the flow rate into the piston chamber. Oil density is used because there is little air in C/V. We judge the state of valve by solving the motion equation of the valve spool, and set the output pressure as zero for the closed valve condition.

(2)

5) Δt control Finally we focus on the calculation time-step, since

reducing the calculation time is essential to apply this calculation to the development of AT.

In this hydraulic system, the oil velocity is high when the piston moves, but it is low when the piston stops. Therefore we tried to reduce the calculation time by controlling the time-step depending on the flow field. To be concrete, we changed the time-step depending on the maximum courant number. We set the time-step small when the courant number is high, and set the time-step large when the courant number is low. As a result, we were able to reduce the calculation time to 1/10 or 1/20 compared with the time when time-step is not controlled.

RESULTS & VERIFICATION

Stroke of piston and air bleed Fig.5 shows the transient data in 1-cycle of output

pressure of C/V. The data are pressure in the piston chamber, stroke of piston and flow rate into the piston chamber, respectively. The piston moves fast when the pressure is increasing, and moves relatively slowly when the pressure is decreasing. Although the graph of pressure looks like a shelf when the piston moves, this means that spring force and oil pressure force are balancing. From this figure, we can say that this

2

2

1

orfA

Qp

frompump

to piston chamber

Drain Orifice

Spool motion

controlpressure

Figure 4 Valve and orifice in the C/V

2

3 2

112

bleedatbleed A

QQ

dh

lpp

Figure 3 Air bleed

h

d

l

A bleed

from pistonchamber

to the air

p bleed

p at

401

calculation basically simulate the typical clutch motion.

Fig.6 shows the relation between the pressure in the piston chamber and the flow rate goes through the air bleed. The red line indicates the flow rate of air calculated by Eq. (1), the points indicate the flow rate (air and oil) calculated in CFD, and the bars indicate

the volume fraction of oil on the air bleed boundary. This graph means that the flow rate decreases when the oil reaches the boundary. Fig.7 shows the velocity vector which flow out through the air bleed, and the contour indicates the volume fraction; red is oil and blue is air. The vector shows that though air leaks, oil hardly leaks. These results mean that the formulated boundary condition simulates the characteristic of air bleed well. Comparison with the experiment

We conduct the experiments and calculations with two different cases and compare the relation between the stagnated air volume in the piston chamber and the response of oil pressure. In the first case, the air volume was checked before the response measurement. Fig.8 shows the volume fraction, and Fig.9 shows the pressure in the piston chamber compared with experimental results. The waveform of pressure rise is basically the same in both CFD and experiment, so we realize this calculation method is useful to visualize the flow field in the hydraulic system.

Figure 7 Velocity vector from the air bleedContour: volume fraction Red = Oil / Blue = Air

Air

Oil

0

0 . 5

1

1 . 5

2

2 . 5

3

0 0 . 2 0 . 4 0 . 6 0 . 8 1 1 . 2Pressure

Flow

rate

0

0 . 2

0 . 4

0 . 6

0 . 8

1

1 . 2

1 . 4

1 . 6

1 . 8

Vol

ume

frac

tion

Volume fraction (oil) CFD Eq.1

Figure 6 Flow rate from the air bleed

0 . 0 8

0 . 1

0 . 1 2

0 . 1 4

0 . 1 6

0 . 1 8

0 . 2

- 0 . 2 0 0 . 2 0 . 4 0 . 6 0 . 8 1 1 . 2

time [s]

Pres

sure

[Pa

]

Experiment CFD

Figure 9 Comparison of CFD and experiment(Air volume before the measurement is known)

Figure 8 CFD result: Volume fraction (Air volume before the measurement is known)

(a) Before the measurement (b) Final state

Figure 5 Transient data in 1-cycle

0

5 0 0

1 0 0 0

1 5 0 0

2 0 0 0

2 5 0 0

3 0 0 0

3 5 0 0

4 0 0 0

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 1 . 2 1 . 4 1 . 6 1 . 8 2 . 0time

Pres

sure

/ St

roke

- 1 . 2

- 0 . 9

- 0 . 6

- 0 . 3

0

0 . 3

0 . 6

0 . 9

1 . 2

Flow

rate

Pressure

Flow rate

Stroke of piston

typical shape like a shelf

appl

yre

leas

e

402

In the second case, the oil was fully discharged from the piston chamber initially, and then oil pressure was applied and released 5 times with the maximum range. The difference with the first case is that the air volume before the response measurement is unknown. Fig.10 shows the volume fraction, and Fig.11 shows the pressure in the piston chamber compared with experimental result. Compared with the first case the pressure rises faster because the air flows out from the piston chamber by applying and releasing oil pressure. Since the pressure rise rate seems to be the same in both CFD and experiment, we realize that this calculation method is useful to visualize the air flowing out from the piston chamber.

These results show this calculation method is very useful for the design of AT.

CONSIDERATION OF THE MECHANISM

(BRAKE CLUTCH)

We made calculations of two patterns of output pressure of C/V in order to understand how the stagnated air flows out from the piston chamber. Fig.12 shows pressure pattern diagram. We applied five times high pressure in the pattern1 and two times high pressure after once low pressure in the pattern2, and compared the flow field in the piston chamber which is shown in Fig.13. The timing of each figure is shown in Fig.12; 1)-4): the pressure applied, 5): after the pressure released, and 6): the final state.

With the air bleed (inner piston)

From Fig.13 (6), we can see that the difference of the air volume of final state in the inner piston chamber is large between two patterns. Paying attention to the oil flow, from Fig.13 (3), we can see that oil reaches the air bleed in pattern1. Once oil has reached the air bleed, air hardly leaks. As a result, the air bleed doesn't work effectively and the air stagnates in the piston chamber. In contrast, the oil level of pattern2 rises gradually, and compressed air leaks from the air bleed steadily. This means that the air bleed works effectively when the initial moderate oil injection is applied. From these results, it is important to apply low pressure and inject oil gradually at first in the case of piston chamber with the air bleed.

By the way, a little air must remain in the piston chamber even if the air bleed worked effectively as pattern2. It is because the compressed air stagnated in a volume above the air bleed (Fig.14) is expanded by releasing pressure. The stagnated air volume after releasing pressure can be calculated by Boyle’s law (pV=const.).

0

0 . 4

0 . 8

1 . 2

1 . 6

2

0 2 4 6 8 1 0 1 2

time [s]

Pres

sure

[Pa]

Pattern1 Pattern2

Figure 12 Pressure pattern

1)-4) 5) 6)

1)-4) 5) 6)

Figure 10 CFD result: Volume fraction (Air volume before the measurement is unknown)

(a) Initial state

(c) Final state

(b) Before the measurement

0 . 0 8

0 . 1

0 . 1 2

0 . 1 4

0 . 1 6

0 . 1 8

0 . 2

- 0 . 2 0 0 . 2 0 . 4 0 . 6 0 . 8 1 1 . 2

time [s]

Pres

sure

[Pa

]

Experiment CFD

Figure 11 Comparison of CFD and experiment(Air volume before the measurement is unknown)

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Without the air bleed (outer piston)

In the outer piston chamber which has no air bleeding hole, air is mixed by oil when applying pressure. Then, the mixed air flows out of the piston chamber as bubbles or the mass of air with the stream which is generated by stroke of piston and by expansion of air when releasing pressure. However, a large volume of air remains even after oil pressure is applied and released.

In order to understand the effect of outlet position on the flow field, we calculated two cases which are shown in Fig.15. In both cases, we can see that the air stagnates in upper part of the piston chamber after mixing with oil when the pressure is applied. When the pressure is released, a large volume of expanded air stagnates in the piston chamber in the case that the outlet is set at the bottom. On the other hand, the stagnated air flows out of the piston chamber in the case that the outlet is set at the top. This means that it is important to set the outlet as high as possible when a brake-type clutch is used.

These results gave us the following knowledge to

reduce the air volume in the piston chamber of brake-type clutch.

i. The outlet should be set as high as possible at the piston chamber.

ii. For the piston chamber with the air bleed a) Low pressure and initial moderate oil

injection should be applied. b) The volume above the air bleed should be

minimized.

Figure 14 Volume above the air bleed

Stagnation volume

Air bleed

Figure 13 Motion of oil and air (Red = Oil / Blue = Air)

(a) Pattern 1 (b) Pattern 2

1) Pressure apply-1

2) Pressure apply-2

3) Pressure apply-3

4) Pressure apply-4

5) Pressure release

6) Final state

AirOil

Air bleed

Flow outwith oil

Outlet (outer)

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APPLICATION TO THE OTHER PART

(ROTARY CLUTCH)

We applied the same calculation method to the rotary-type clutch as well as brake-type clutch. Fig.16 shows the results. In this case, the piston chamber and the shaft are rotating. Although the air stagnates in upper part of the piston chamber for the brake-type clutch, the air moves toward the shaft, which is rotation center, under the influence of centrifugal force for the rotary-type clutch. The stagnated air inside the shaft finally leaks from gap of the seal ring.

This calculation enabled us to visualize the flow field in the rotary clutch for the first time.

CONCLUSIONS In this calculation, we adapted the compressibility,

easy mesh morphing and formulation of the boundary conditions to the VOF method, so that we succeeded in visualizing the flow field inside the hydraulic system that conventionally required experiments. And it enabled us to understand the flow field and the air volume, and to get design knowledge of minimizing the stagnated air volume.

We are planning to apply this technology to the other parts in the transmission and achieve the performance improvement and the shortening of development period.

Figure 16 Motion of oil and air in the rotary clutch piston chamber

rotation

from C/V

shaft

Air moves toward the axis (shaft)

pres

sure

pres

sure

pres

sure

pres

sure

pres

sure

Figure 15 Difference by the outlet position

time

time

time

time

time

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