## 4 Results and Discussion
### Analysis of Leakage Flow  
Leakage is one of the inevitable problems for the automatic transmission which would give rise to pressure loss, waste of ATF, fluid insufficient, etc. The leakage flow has an important influence on the direct operating solenoid valve. Firstly, the leakage flow will directly affect the response characteristics of the solenoid valves, including pressure response and output flow. If the leakage flow is too large, the actual output flow will be less than the control flow which can't meet the requirement of both the flow and the pressure. At this point, the oil filling time of the clutch will be extended which leads to the delay of the pressure response time. As a result, the shifting time will be prolonged and the shifting quality will be reduced. Secondly, large leakage in the solenoid valve will reduce the efficiency of the automatic transmission. Thereby, it affects the fuel consumption of the vehicle. Although a small leakage has been achieved in the direct operating solenoid valve, it cannot be completely avoided. The leakage in the direct operating solenoid valve is mainly caused by the clearance between the spool and the sleeve. The clearance height which is the most important  
Figure 19: Spool displacement for different clearance. parameter affecting the leakage flow in the solenoid design is usually between 20 \(\upmu\)m-40 \(\upmu\)m. A good clearance design is actually accurate design of the machining tolerance and the assembly tolerance of both the valve spool and the sleeve. Small clearance height will raise the requirements of the processing technique and the assembly technique, so it will significantly increase the cost. Meanwhile, it is averse to the quality control because high processing requirements will increase the product reject ratio which brings down the production efficiency. It is hard for small clearance to keep the oil slick between the spool and the sleeve. Once the oil slick is broken during relative motion, the surface of the components is easily scratched because of dry friction. In addition, small clearance would frequently result in clamping stagnation. Thus, the solenoid valve falls into control failure. Although big clearance could not only decrease the cost but cut down the risk of clamping stagnation, the unavoidable large leakage will greatly reduce energy efficiency and bring about poor pressure response. Since the clearance height between the spool and the sleeve has a direct effect on the performance of the direct operating solenoid valve. It is necessary to balance the energy efficiency, manufacturing technique and quality control. In order to analyze the effect of the clearance, the leakage from different height of clearance is depicted in Figure 20.  
Figure 20 describes that the maximum leakage in 30 \(\upmu\)m is 0.06 L/min and the leakage reduces rapidly with the decrease of the clearance. It is observed that the solenoid valve with smaller clearance height has not only less leakage but faster pressure response when considering both Figures 15 and 20. The leakage flow is of same variation trend with the control pressure at the same clearance height. To make a further study, the clearance between the spool and the sleeve could be considered as an orifice when controlling the other variables constant. The pressure difference between the control port and the exhaust port will increase with the growing control pressure, and vice versa. According to Equation (18),  
\[Q_{\mathit{o}rifice}=C_{d}\uptau r_{\mathit{o}rifice}^{2}\sqrt{\frac{2}{\rho} |\Delta p|} \tag{25}\]  
where \(Q_{\mathit{o}rifice}\) is the flow through the orifice, \(r_{\mathit{o}rifice}\) is the radius of the orifice, \(\Delta p\) is the pressure difference at both ends of the orifice. Hence, the flow is in proportion to the pressure difference at both ends of the orifice. As a result, the leakage flow changes with the control pressure. Figure 20: Leakage flow characteristics in the direct operating solenoid valve for different clearance.