Transient State in Hydraulic Systems
A comprehensive analysis of static, steady-state, and transient conditions in hydraulic systems, with special focus on valve dynamics and performance characteristics
1. Definitions: Static, Steady-State, and Transient
Static Condition
The Chinese mechanical industry standard JB/T7033-2007 defines static condition as "a condition where parameters do not change with time."
Steady-State Condition
A condition where the mean value of a variable does not change with time, or variations follow a predictable cyclic pattern.
Transient Condition
The state between two steady-states, where system parameters are changing as the system adapts to new conditions.
1.1 Static Condition
The Chinese mechanical industry standard JB/T7033-2007 "General Rules for Hydraulic Transmission Measurement Technology" (modified from ISO 9110-1:1990) defines: static condition as "a condition where parameters do not change with time." In actual hydraulic systems, however, all hydraulic pumps discharge flow with more or less pulsation, which encounters fluid resistance and causes pressure pulsation as well. Therefore, whenever the system is operating, the pressure and flow in pump ports, pipelines, hydraulic valves, and hydraulic cylinders are variable and rarely exhibit parameters that remain constant over time. Consequently, this condition is not particularly worthy of investigation, especially when considering critical components like the hydraulic valve seal which inherently creates some resistance and potential for minor fluctuations.
Even with a perfectly designed hydraulic valve seal, the inherent nature of fluid dynamics prevents truly static conditions in operating systems. The hydraulic valve seal itself, while designed to maintain consistent performance, can contribute to minimal pressure variations due to minute deformations under different pressure conditions, further supporting the notion that true static conditions are theoretical rather than practical in hydraulic systems.
1.2 Steady-State Condition
Steady-state, as the name suggests, refers to stability. Because parameters such as pressure and flow are always changing in actual operating systems, the aforementioned standard makes a compromise by defining steady-state conditions as "conditions where the mean value of a variable does not change with time, or the variation of an instantaneous value of that variable is cyclic and can be described by a simple mathematical expression." In other words, as long as the average value remains essentially unchanged, it can be considered a steady-state. It should be noted that the variable here should not be interpreted as all variables in the system. For example, as long as an object has a non-zero velocity, its displacement (average value) will definitely change over time.
According to the original text in ISO 9110-1:1990: "Conditions under which the mean of a variable does not change with time and the variation of an instantaneous value of that variable is cyclic and can be described by a simple mathematical expression," it should be understood as "a certain variable." GB/T 17446-2012 "Fluid Power Systems and Components Terminology" (equivalent to ISO 5598:2008) translates it as related parameters, which can also avoid misunderstanding.
Figure 1: Example of steady-state pressure variations with consistent mean value, including effects from hydraulic valve seal performance
In practical hydraulic technology, when we say, for example, that the pressure at a certain point in the system is 15MPa, or the flow rate in a certain channel is 40L/min, these generally refer to steady-state values, i.e., average values. Static conditions can be considered a special case of steady-state: when the flow into a hydraulic cylinder is zero, the velocity of the hydraulic cylinder is zero, and therefore, the position of the load remains unchanged.
It is generally believed that steady-state performance refers to the performance of hydraulic components or systems under steady-state conditions. The following characteristics of hydraulic valves are all steady-state performances, many of which are directly influenced by the quality and design of the hydraulic valve seal:
- Flow-pressure difference performance of directional control valves, where the hydraulic valve seal plays a critical role in maintaining consistent pressure differentials
- Pressure-flow performance of relief valves, with the hydraulic valve seal affecting pressure retention capabilities
- Pressure difference-flow performance of flow control valves, where the hydraulic valve seal contributes to leak prevention and pressure stability
The hydraulic valve seal is particularly important for maintaining steady-state conditions as it prevents unwanted leakage that would otherwise cause pressure fluctuations and deviations from the desired mean values. A high-quality hydraulic valve seal ensures that the steady-state parameters remain within acceptable ranges for longer periods, reducing the energy losses that would occur with poor sealing performance.
1.3 Transient Condition
The state of a system after leaving one steady-state and before entering another steady-state is called transient, also known as dynamic. Figure 4-101 shows a measured pressure change process from steady-state to transient and back to steady-state. This transition period is where the hydraulic valve seal's dynamic response characteristics become particularly important, as it must adapt to changing pressures and flow rates.
Figure 2: Example of pressure transitioning from one steady-state to another through a transient state, demonstrating the importance of hydraulic valve seal responsiveness
Generally understood, the transient state is a process of finding a new equilibrium point, during which not only pressure but also many other parameters (spool movement speed, opening, flow rate, etc.) change. The transient response performance of components and systems to changes in load, interference, and commands is called transient response performance, or simply transient performance or dynamic performance.
Components and systems with good transient performance can quickly adapt to changes and enter a new steady-state. If a component or system requires a long adaptation time, has significant overshoot, or even oscillates continuously and cannot enter a steady-state at all, its transient performance is generally considered poor. The hydraulic valve seal's ability to respond to rapid pressure changes without excessive leakage or delay is a key factor in determining overall system transient performance.
The transient performance of a hydraulic system depends on both the components used and the system configuration. Hydraulic systems do not remain in a single steady-state indefinitely. The task of hydraulic transmission is to change the state of the load: from stationary to moving, from moving to stationary, from slow movement to fast movement, and from fast movement to slow movement. In a word, it is to change the state.
Currently, the primary way to accomplish these tasks is by controlling the movement of the valve spool, changing its position relative to the valve body, thereby changing the opening. The hydraulic valve seal must accommodate these spool movements while maintaining appropriate sealing, which can create dynamic friction forces that influence transient behavior.
Theoretically perfect valve closed-loop control that can achieve desired targets actually involves continuous adjustment of the opening. When the opening changes, the flow rate through it also changes. When the flow rate changes, the pressure will also change, but there are delays, which depend on the transient response performance of the valve and system. The hydraulic valve seal contributes to these delays through friction and pressure-dependent deformation, making its design a critical consideration in optimizing transient response.
2. Force Analysis Summary
The various control forces and resistances acting on the valve spool have been analyzed earlier. Figure 4-102 provides a general overview of these forces and their influencing factors, including those related to the hydraulic valve seal which creates friction forces between moving parts.
Figure 3: Forces acting on a valve spool and their influencing factors, including friction from the hydraulic valve seal
The resistances to spool movement include oil pressure, spring force, friction force, and gravity. Oil pressure is mainly determined by the valve structure and the position of the spool, and can be estimated, but it is also affected by fluid force, making accurate estimation difficult. The hydraulic valve seal contributes significantly to the friction force, especially as pressure differentials change during transient conditions.
Fluid force is determined by the pressure difference across the opening and the flow rate through the opening. Spring force is mainly determined by the amount of compression of the spring, including the displacement of the spool, and can be estimated.
Friction force mainly varies with the relative movement speed of the spool with respect to the valve body, but is affected by many factors such as machining shape deviation, combined clearance conditions, surface roughness of contact surfaces, lubrication conditions, and oil contamination. Therefore, it is basically impossible to calculate theoretically. The hydraulic valve seal is a primary source of this friction, with its material properties and design directly impacting the magnitude and variability of frictional forces during spool movement.
Although gravity may also affect spool movement, it is often negligible compared to other forces in modern hydraulics. All objects have mass, and valve spools are no exception. Although the weight of the spool can often be ignored, its mass cannot be ignored when considering the transient performance of the valve. For a translating solid, its inertia is its mass (as mentioned, rotating spools are rarely used at present, and their rotation speed is generally low, so the effect of inertia is not significant. Therefore, the following discussion only applies to translating spools), and inertia resists changes in motion state, somewhat like a resistance, which is therefore often called inertial force. In fact, the resistance of inertia to object motion is fundamentally different from friction, spring force, etc.: inertia does not affect the resultant force.
Control forces generally include mechanical, manual, and electronic control. When these forces are insufficient or for other reasons, hydraulic and pneumatic assistance may be used. The hydraulic valve seal can influence the effectiveness of these control forces by creating variable friction that must be overcome during spool movement.
Control force reflects the operator's expectation, while the actual opening of the valve is the reality. There is always a lag between expectation and reality. Because the difference between control force and resistance, divided by inertia, is only the acceleration of the spool movement. The accumulation of acceleration is velocity, and the accumulation of velocity is the displacement of the spool. Only when the position of the spool changes can the opening change.
The pressure difference across the opening and the opening itself determine the flow rate, which is sometimes also affected by oil viscosity. The flow rate and the size of the opening determine the flow velocity at the opening, and the flow will reduce the oil pressure, the so-called fluid force. The process of spool movement under the action of these control forces and resistances, including those from the hydraulic valve seal, determines the transient performance of the valve and thus affects the transient conditions of the system.
Key Considerations for Hydraulic Valve Seal in Force Analysis
The hydraulic valve seal plays a multifaceted role in the force dynamics of valve operation:
- It creates variable friction forces that change with pressure and velocity
- It must maintain sealing integrity during rapid pressure changes in transient conditions
- Its material properties affect response time and energy losses
- Wear on the hydraulic valve seal over time can significantly alter force dynamics
- Properly designed hydraulic valve seal reduces hysteresis in transient response
3. Spool Movement Process
For a spool to move from one position to another, from rest to motion, its velocity must increase from zero, which requires acceleration. The acceleration of the spool = (control force acting on the spool - resistance) / spool inertia. Therefore, as long as there is inertia, acceleration cannot be infinite, and velocity cannot be infinite.
Therefore, no matter how light the spool is, it takes time to move. Even for on-off valves, where the spool moves relatively quickly, although the movement time is generally not a concern under normal circumstances, there is still a process involved. This process is definitely not uniform. The hydraulic valve seal contributes to both the resistance forces and the dynamic behavior during this movement, as its friction characteristics change with velocity and pressure.
Figure 4: Example of uniform acceleration start and uniform deceleration stop for spool movement, showing the phases where hydraulic valve seal friction has varying effects
During the initial acceleration phase, the control force must overcome both the static friction from the hydraulic valve seal and the inertial resistance. As the spool begins to move, the hydraulic valve seal transitions from static to dynamic friction, which typically results in a lower frictional force. This transition can create a non-linear response in the early stages of movement, affecting the precision of transient control.
The hydraulic valve seal's lubrication properties also play a crucial role during spool movement. Inadequate lubrication can lead to increased friction and uneven movement, while proper lubrication, often provided by the hydraulic fluid itself, allows the spool to accelerate more uniformly. The interaction between the hydraulic valve seal and the fluid creates a complex boundary layer that influences both friction and movement characteristics during transients.
As the spool approaches its target position, deceleration begins. During this phase, the hydraulic valve seal's dynamic friction characteristics again become important, as the reducing velocity can cause changes in frictional resistance. This can lead to overshoot if not properly accounted for in the system design. Modern hydraulic systems often incorporate feedback mechanisms to compensate for these friction variations caused by the hydraulic valve seal, improving transient response accuracy.
The material composition of the hydraulic valve seal directly impacts its behavior during spool movement. Elastic materials may deform under pressure, creating variable friction forces that change with the pressure differential across the valve. Rigid materials, while providing consistent friction characteristics, may not seal as effectively during rapid pressure changes common in transient conditions. The optimal hydraulic valve seal material selection involves balancing these competing requirements based on the specific transient performance needs of the system.
Temperature effects on the hydraulic valve seal must also be considered in transient analysis. As the hydraulic fluid temperature changes during system operation, the properties of the hydraulic valve seal material can vary, altering friction characteristics. This thermal sensitivity adds another layer of complexity to predicting transient behavior, especially in systems with wide operating temperature ranges.
In high-frequency transient applications, the hydraulic valve seal's response time becomes critical. The seal must adapt quickly to rapidly changing spool positions without causing excessive damping or滞后 (hysteresis). Specialized low-friction hydraulic valve seal designs are often employed in these applications to minimize their impact on transient response times.
Aging and wear of the hydraulic valve seal over time can significantly alter spool movement characteristics. As the seal wears, friction forces may decrease due to reduced contact pressure, or increase due to uneven wear patterns. This gradual change in the hydraulic valve seal's performance can lead to degradation in system transient response over the operational life of the hydraulic component, making regular maintenance and replacement of the hydraulic valve seal an important consideration for maintaining consistent transient performance.
Understanding the complex interactions between the hydraulic valve seal and spool movement during transient conditions is essential for optimizing system design. Computational fluid dynamics (CFD) simulations often include detailed models of the hydraulic valve seal behavior to accurately predict transient responses. These models account for the seal's material properties, contact mechanics, and fluid interaction to provide insights into how different hydraulic valve seal designs will perform under various transient scenarios.