Flow Pressure Coefficient in Hydraulic Networks

A comprehensive analysis of flow pressure characteristics in hydraulic systems, with particular emphasis on half-bridge resistance networks and their impact on system performance, including the torque of a hydraulic motor.

Flow-Pressure Characteristics

With γ as a parameter, the flow-pressure characteristic curve of q_v=f(p) is shown in Figure 2-7. The abscissa in the figure is p, the ordinate is q_v, and the value of the parameter γ ranges from -1 to 1. This family of curves represents the relationship between the dimensionless outlet pressure and the dimensionless outlet flow of the half-bridge hydraulic resistance network when y is constant. It is evident that when the dimensionless outlet pressure increases, the outlet dimensionless flow must decrease. The flatter the flow pressure characteristic curve, the smaller the influence of the external load on the dimensionless outlet flow, which directly affects the torque of a hydraulic motor.

The flow pressure coefficient of the half-bridge hydraulic resistance network is defined as the negative value of the slope of the q_v=f(p) curve at p=0.5 and y=0, denoted by the letter k_o. This coefficient plays a crucial role in determining system stability and efficiency, particularly when considering the torque of a hydraulic motor in various operating conditions.

Mathematical Formulation

From the partial derivative formula, we have:

For the partial derivative formula, there is:

By taking the partial derivative of equation (2-1), the flow pressure coefficient k_oA of the type A half-bridge hydraulic resistance network can be obtained as:

Similarly, by taking the partial derivative of equation (2-2), the flow pressure coefficient k_oB of the type B half-bridge hydraulic resistance network is:

Taking the partial derivative of equation (2-3) gives the flow pressure coefficient k_oC for type C half-bridge hydraulic resistance network:

It is evident that the flow pressure coefficients of the three types of half-bridge hydraulic resistance networks are the same. This is because when y=0, the resistances of the fixed and variable hydraulic resistances are set to be the same. If this assumption is not made and the resistances differ, the flow pressure coefficients of the three types of half-bridge hydraulic resistance networks would not be the same. This fundamental principle directly impacts system design considerations, including those affecting the torque of a hydraulic motor in practical applications.

Incremental Expressions

Using the incremental expressions for outlet pressure and outlet flow linearization given by equations (2-1), (2-2), and (2-3), we can observe the relationships between various parameters, which are critical for understanding how system changes affect the torque of a hydraulic motor.

For the zero operating condition (y=0, q_v=0, p=p₀/2), we can substitute the pressure gain, flow gain, and flow pressure coefficient into the above equations, resulting in formulations that are essential for predicting changes in the torque of a hydraulic motor under varying operating conditions:

Comparison of Half-Bridge Types

The flow gain, pressure gain, and flow pressure coefficient for the three types of half-bridge hydraulic resistance networks are summarized in Table 2-2. These parameters are critical for system designers when selecting the appropriate configuration for specific applications, especially those involving the torque of a hydraulic motor where precision and efficiency are paramount.

Detailed Analysis of Half-Bridge Configurations

As previously mentioned, a half-bridge hydraulic resistance network consists of two hydraulic resistances. Type A half-bridge features two variable hydraulic resistances, while Type B and Type C half-bridge hydraulic resistance networks each have only one variable hydraulic resistance. From Figure 2-2, it can be seen that when the valve core has displacement, Type A half-bridge always has one hydraulic resistance increasing while the other decreases. This characteristic affects the system's dynamic response and stability, which in turn influences the torque of a hydraulic motor in applications where precise control is required.

Clearly, the control characteristics of Type A half-bridge are superior to those of Type B and Type C half-bridges. Because of this, Type A half-bridges are commonly used in servo control valves, where their superior characteristics help maintain precise control over the torque of a hydraulic motor. The disadvantage of Type A half-bridge is that the two variable hydraulic resistances are controlled by one signal, requiring higher mechanical processing precision and correspondingly higher component costs.

Type B half-bridge has the advantages of simple structure, low price, and good sealing performance. It can be constructed using cone valves, nozzle flapper valves, etc. Type B half-bridge is widely used in the pilot oil circuit of pressure control valves, where it provides reliable performance without the high precision requirements, making it suitable for applications where the torque of a hydraulic motor does not require extremely fine control.

For Type C half-bridge, since the second hydraulic resistance is a fixed hydraulic resistance, when the hydraulic resistance R₁ is completely closed, the output control port is still connected to the oil tank through the fixed hydraulic resistance R₂. This means the controlled component cannot be isolated from the external environment, resulting in a certain degree of uncontrollability, which limits its application in systems where precise control of the torque of a hydraulic motor is necessary. Consequently, Type C half-bridge is not widely used.

Additionally, there is Type D half-bridge, where both hydraulic resistances are fixed. Therefore, both pressure gain and flow gain are zero. Type D half-bridge cannot be used alone as a control hydraulic resistance network, but when combined with other hydraulic resistance networks, it can form an effective control network. This configuration is sometimes used in auxiliary circuits that support the main control system affecting the torque of a hydraulic motor.

The selection of the appropriate half-bridge configuration depends on the specific application requirements, including factors such as control precision, cost constraints, and environmental conditions. In systems where the torque of a hydraulic motor is a critical performance parameter, the choice between these configurations becomes particularly important, as each type offers distinct advantages in different operational scenarios.

Understanding the flow pressure coefficient and its relationship with other system parameters allows engineers to optimize hydraulic systems for maximum efficiency and performance. Whether designing systems for industrial machinery, mobile equipment, or precision control applications, the flow pressure coefficient remains a fundamental concept that directly impacts the behavior and effectiveness of hydraulic components, including the torque of a hydraulic motor under various operating conditions.

Further research continues to explore innovative ways to enhance the performance of these half-bridge configurations, with particular focus on improving efficiency and control precision. These advancements aim to provide better control over critical parameters like the torque of a hydraulic motor, leading to more efficient and reliable hydraulic systems across various industries.

In summary, the flow pressure coefficient is a vital parameter in hydraulic system design, influencing everything from component selection to overall system performance. By understanding its characteristics and how it varies across different half-bridge configurations, engineers can make informed decisions that optimize system behavior, including the precise control of the torque of a hydraulic motor in complex hydraulic systems.