# Development of Proportional Pressure Control Valve for Hydraulic Braking Actuator of Automobile ABS
## 1 Introduction  
To provide safer and more comfortable driving conditions for motorists, the anti-lock braking system (ABS) is currently basic equipment for automobiles. This system achieves improved control capability by connecting the electro-hydraulic brake (EHB) between master cylinder and wheel cylinder. As ABS starts to work, the hydraulic pressure (braking force) within the tire calipers is controlled by four groups of solenoid valves (inlet/outlet valve). Furthermore, there are three patterns of pressure variation, namely pressure increase, pressure holding, and pressure decrease [1; 2; 3; 4]. The hydraulic circuit of an EHB actuator is shown in Figure 1[5]. The braking capability of automobiles relies on characteristics of the tires, which are the only contact with the ground. The main factor determining this capability is the slip ratio of the tires and ground, defined as slip. \[S=\frac{V_{v}-V_{w}}{V_{v}} \tag{1}\]  
where \(S\) is the slip, \(V_{v}\) is the vehicle speed, and \(V_{w}\) is the wheel speed. When the slip is between 0.1 and 0.3, the braking action is most effective, and, if the slip is zero, the wheels are operating with no resistance. However, when slip is more than 0.3, the braking force may be reduced. The tires are completely locked when slip is 1, and the wheels would slide along the pavement [6; 7; 8; 9; 10; 11]. The results are shown in Figure 2[12]. An ABS braking system can prevent the improper sliding of tires and it has three functions:  
1. [label=(0)]
2. When encountering an obstacle or any road conditions, it can be actuated by the steering wheel to obtain suitable tracking performance. It can avoid excessive braking effects that can cause uncontrolled steering (if the front wheels are locked) or drifting (if the rear wheels are locked)
3. The electronic control braking effects can shorten the stopping distance. The general ABS drives the solenoid valve when it detects that the wheels are locked, and it operates the slip control in an on-off mode to release the calipers' pressure. Traditional solenoid valve patterns can only adjust the calipers' pressure through a fully open or closed valve port and have no accurate control for slip, so they cannot provided highly effective braking. However, an accident can occur when the ABS is actuating and high frequency vibration from the pedal make the driver panic and then release the pedal. To develop a brake actuator that uses a new pattern, and also considering the market differentiation and product performance, for the first time, a proportional pressure control valve was used for ABS to replace two solenoid valves. To improve the disadvantages of solenoid valve and achieve better slip control, the pressure to be released as determined by the corresponding input current and electromagnetic force. To improve braking quality, it can effectively control the calipers' pressure and then decide the appropriate braking force due to the stability of pressure release control, and no pressure oscillations are generated, as with a solenoid valve. A single proportional valve for each of the four wheels was substituted for the original two solenoid valves for each wheel. Figure 1: Hydraulic circuit of EHB actuator between master cylinder and wheel cylinder. Figure 2: Relationship between wheels and pavement. This reduces the cost and space requirements compared to the traditional EHB configuration. Figure 3 shows the novel hydraulic circuit for a proportional electro-hydraulic brake (PEHB) actuator. This research focused on the configuration design of the proportional electromagnet within the proportional valve, and its main function is to drive the armature. The development process was divided into three stages:  
1. Firstly, using electromagnetic theory and mathematical calculations, parameters of the new cone proportional electromagnet were analyzed, and then the electromagnet force using a simulation program was estimated. 2.