COMPRESSIBLE FLOW ANALYSIS IN A CLUTCH PISTON CHAMBER Masaru SHIMADA*, Hideharu YAMAMOTO* * Hardware System Development Department, R&D Division JATCO Ltd 7-1, 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. 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 A bleed : Cross section of the air bleed [m ] A orf : Cross section of the orifice [m ] d : Diameter of the cylindrical clearance [m] h : Clearance height of the air bleed [m] l : Length of the cylindrical clearance [m] P at : Pressure in the transmission [Pa] (=.) p bleed : Pressure on the air bleed boundary [Pa] Q : Flow rate from the air bleed [m 3 /s] μ : Viscosity [Pa s] ρ : Density [kg/m 3 ] ζ : Loss coefficient :=1.5 (Inlet:.5 + Outlet:1.) in Eq.(1) :=. in Eq.() 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, highly accurate oil 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
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 is high (low). The piston chamber is divided into outer and inner, and the inner (a) Shape of AT Piston Chamber Piston Air bleed CASE Control Valve Pull the fluid domain out 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 ) Relation between the oil flow generated by the stroke of piston and the air flow 3) Variation of the air volume by the oil 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 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. ) 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. shows a part of the cross section of the piston chamber. 1. Insert prism layers on the piston surface after making tetrahedral mesh. Deform only prism layers as solving the motion equation of the piston Hydraulic Circuit (C/V) (CASE) Piston motion Deform only Prism layer Piston Surface Piston Surface Prism layer Pressure boundary (Valve) (b) Fluid domain (c) Cross section Figure 1 Computational domain (a) Original shape (b) Maximum deformation Figure Easy mesh morphing method
This method enabled us to morph the mesh without breaking the topology and without making poor quality mesh. Fig. 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 will be huge. In order to reduce the calculation, we formulated the boundary condition to realize the air bleed. The 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 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. from pump Orifice Spool motion Drain Figure 4 Valve and orifice in the C/V control to piston chamber Equation () from the output. 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 as zero for the closed valve condition. p bleed p at 1l 1 Q 3 dh Q A bleed (1) 1 p Q A orf () from piston chamber p bleed A bleed Figure 3 Air bleed 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 characteristics into account to calculate in the piston chamber accurately. However, the number of mesh and calculation will be huge if we try to use CFD to solve the loss of the hydraulic circuit in C/V and the valve motion. So we formulated the characteristics of C/V and applied the output of C/V as the boundary condition. We assumed the orifice is the main loss element in C/V, and set the boundary which is obtained by subtracting the loss formulated as l h d p at to the air 5) Δt control Finally we focus on the calculation -step, since reducing the calculation 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 by controlling the -step depending on the flow field. To be concrete, we changed the -step depending on the maximum courant number. We set the -step small when the courant number is high, and set the -step large when the courant number is low. As a result, we were able to reduce the calculation to 1/1 or 1/ compared with the when -step is not controlled. RESULTS & VERIFICATION Stroke of piston and air bleed Fig.5 shows the transient data in 1-cycle of output of C/V. The data are in the piston chamber, stroke of piston and flow rate into the piston chamber, respectively. The piston moves fast when the is increasing, and moves relatively slowly when the is decreasing. Although the graph of looks like a shelf when the piston moves, this means that spring force and oil force are balancing. From this figure, we can say that this
4 35 3 5 15 1 5... 4. 6. 8 1. 1. 1. 4 1. 6 1. 8. 3. 5 1. 5 1. 5 1.. 9. 6. 3 -. 3 -. 6 -. 9-1. 1. 8 1. 6 1. 4 1. 1. 8. 6. 4... 18. 16. 14. 1. 1. 8 calculation basically simulate the typical clutch motion. Fig.6 shows the relation between the 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 Pressure / Stroke Stroke of piston Pressure Flow rate typical shape like a shelf Figure 5 Transient data in 1-cycle apply release 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. In the first case, the air volume was checked before the response measurement. Fig.8 shows the volume fraction, and Fig.9 shows the in the piston chamber compared with experimental results. The waveform of 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. Volume fraction (oil) CFD Eq.1 Flow rate Volume fraction Flow rate.. 4. 6. 8 1 1. Pressure Figure 6 Flow rate from the air bleed (a) Before the measurement (b) Final state Figure 8 CFD result: Volume fraction (Air volume before the measurement is known) Air Experiment CFD Oil Pressure [Pa] -... 4. 6. 8 1 1. [s] Figure 7 Velocity vector from the air bleed Contour: volume fraction Red = Oil / Blue = Air Figure 9 Comparison of CFD and experiment (Air volume before the measurement is known)
.. 18. 16. 14. 1. 1. 8 1. 6 1.. 8. 4 4 6 8 1 1 In the second case, the oil was fully discharged from the piston chamber initially, and then oil was applied and released 5 s with the maximum range. The difference with the first case is that the air volume before the response measurement is unknown. Fig.1 shows the volume fraction, and Fig.11 shows the in the piston chamber compared with experimental result. Compared with the first case the rises faster because the air flows out from the piston chamber by applying and releasing oil. Since the 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 of C/V in order to understand how the stagnated air flows out from the piston chamber. Fig.1 shows pattern diagram. We applied five s high in the pattern1 and two s high after once low in the pattern, and compared the flow field in the piston chamber which is shown in Fig.13. The timing of each figure is shown in Fig.1; 1)-4): the applied, 5): after the released, and 6): the final state. 1)-4) Pattern1 Pattern 5) 6) Pressure [Pa] (a) Initial state (b) Before the measurement (c) Final state Figure 1 CFD result: Volume fraction (Air volume before the measurement is unknown) Pressure [Pa] Experiment CFD -... 4. 6. 8 1 1. [s] Figure 11 Comparison of CFD and experiment (Air volume before the measurement is unknown) [s] 1)-4) 5) 6) Figure 1 Pressure pattern 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 pattern 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 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 pattern. It is because the compressed air stagnated in a volume above the air bleed (Fig.14) is expanded by releasing. The stagnated air volume after releasing can be calculated by Boyle s law (pv=const.).
Air Oil Stagnation volume 1) Pressure apply-1 Air bleed Outlet (outer) ) Pressure apply- 3) Pressure apply-3 4) Pressure apply-4 Flow out with oil 5) Pressure release Air bleed Figure 14 Volume above the air bleed Without the air bleed (outer piston) In the outer piston chamber which has no air bleeding hole, air is mixed by oil when applying. 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. However, a large volume of air remains even after oil 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 is applied. When the 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 and initial moderate oil injection should be applied. b) The volume above the air bleed should be minimized. 6) Final state (a) Pattern 1 (b) Pattern Figure 13 Motion of oil and air (Red = Oil / Blue = Air)
rotation shaft from C/V Air moves toward the axis (shaft) Figure 16 Motion of oil and air in the rotary clutch piston chamber CONCLUSIONS Figure 15 Difference by the outlet position 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. 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.