Menu
Hydraulic transmission and control technology has developed to this day, and people have done a lot of theoretical research and discovered many laws—this is beyond doubt. However, the actual working conditions in application are complex and ever-changing. In order to have universal guiding significance, theory is always abstracted and idealized, and due to limitations in expression methods, many practical factors are ignored. Therefore, there is always a gap between theory and every actual working condition.
For example, Pascal’s Law, which serves as the theoretical foundation of hydraulic technology (hydrostatic transmission)—”pressure is transmitted equally in all directions in a fluid within a closed container”—has a prerequisite: the fluid must be stationary. However, if the fluid is stationary, it cannot transmit power! To transmit power, the fluid must flow! Therefore, simply applying Pascal’s Law in hydraulic technology violates its prerequisite.
The Euler equation (see Section 4.9) brilliantly summarizes the relationship between pressure and velocity for a micro-element volume in a fluid flow at a certain instant, under one-dimensional flow conditions. However, this equation does not consider the viscosity of the fluid. As mentioned earlier, modern hydraulics—oil hydraulics—was developed precisely by relying on the viscosity of oil. Therefore, the Euler equation cannot accurately calculate modern hydraulics.
The Navier-Stokes equations (see Section 4.9) brilliantly describe the three-dimensional unsteady motion of viscous compressible fluids, and therefore can theoretically be used to study vortex flows as well. These equations consider fluid viscosity, but assume that viscosity is a constant that does not change with time or position. However, all oils currently used in hydraulic technology have viscosity that changes with temperature: in a circuit, every time the oil passes through a hydraulic resistance, pressure drops, and the lost energy is basically converted into heat, causing the oil temperature to rise and viscosity to decrease. Therefore, even such seemingly comprehensive partial differential equations still have gaps with actual hydraulic system working conditions.
The Bernoulli equation, derived from the energy conservation principle of classical mechanics, obtains the relationship between flow velocity, pressure, and height under steady fluid motion. The expression is:
(v₁²)/(2g) + p₁/(ρg) + Z₁ = (v₂²)/(2g) + p₂/(ρg) + Z₂
Where:
This equation is very concise in form and can be applied to oil. However, it looks good but is not practical to use. Because to obtain one term from this formula, you must know all the other terms. For example, to find the pressure at point 2, you must know the pressure and velocity at point 1, as well as the velocity at point 2 (Z₁, Z₂ are often not difficult to know for hydraulic equipment in many situations). However, because fluid motion is often very complex, in turbulent flow, especially at places where the flow cross-sectional area changes, such as valve ports, orifices, etc., it is basically impossible to obtain analytical expressions for actual velocity, and thus impossible to obtain analytical expressions for pressure.
As mentioned in Section 4.10, by converting these differential equations that are difficult to solve analytically into difference equations, i.e., simulation models, and then inputting initial parameters and using computers for calculation—that is, performing simulation based on the aforementioned theoretical formulas—numerical descriptions of changes in pressure, flow rate, etc. can be obtained.
In hydraulic circuits, in the vast majority of cases, fluid flow velocity is relatively high and in a turbulent state: fluid molecular clusters collide with each other, merge, disperse, form vortices, and each goes its own way. Currently, hydraulic simulation models are far from reaching the level of simulating molecular clusters; hydraulic simulation only studies the motion laws of oil from a macroscopic statistical perspective. If the simulation model is not comprehensive and even one factor is ignored, then there is simply no way to know how much the simulation results differ from actual working conditions.
Simulation calculation results depend on the input initial values. If the initial data does not match reality, then the calculation results will not be true either. For example, as mentioned earlier, the bulk modulus of oil has a crucial influence on the pressure change process in a system. However, the actual bulk modulus of oil is not only affected by pressure and temperature, but also by the amount of undissolved air contained, the type of pipes used, and many other factors. Domestic university textbooks generally give 1400-2000 MPa, while according to a test by IFAS, it is approximately 1000-3500 MPa.
The above data was measured in the IFAS laboratory after vacuum treatment and careful removal of gases from the oil. In actual system operation, the turbulent waves at the tank return port will definitely continuously entrain some air into the oil, so the actual bulk modulus of the oil will certainly be even lower, because gas volume shrinks easily under pressure: volume is inversely proportional to pressure.
Additionally, modern hydraulic working pressures are often very high. When oil pressure increases, containers, especially pipes, and especially hoses, will expand, which also reduces the actual bulk modulus.
As mentioned in Chapter 4, most of the resistances affecting valve opening changes depend on actual machining factors, are limited by manufacturing process conditions, and basically cannot be determined by theoretical calculation. For example:
Furthermore, the flow calculation formula for long thin holes is only valid for laminar flow; the viscosity of hydraulic media changes with temperature and pressure, which affects the Reynolds number, and thus affects the determination of flow regime and calculation of hydraulic resistance; the inductance and hysteresis of electromagnets are nonlinear and vary with stroke.
Although the current-force characteristics of proportional solenoids are relatively regular, the accuracy requirements for them are also much higher; therefore, to accurately understand the actual response time of electro-proportional valves, one must consider the influence of many factors such as voltage, coil temperature, coil inductance, electromagnetic force, spool mass, spring force, flow force, friction force, etc.
There are many so-called distributed parameters in hydraulic circuits. For example, pressure in a pipeline gradually decreases, temperature gradually increases, and viscosity also gradually decreases—every millimeter is different. But to simplify calculations, one can only approximate by taking average values and treating them as lumped parameters.
For simulation, missing even one parameter won’t work. In the vast majority of actual application situations, much data, especially parameters of basic components, such as spring inertia, number of coil turns, etc., are generally not provided by suppliers and need to be requested one by one. This makes simulation not very realistic from both cost and time perspectives.
Additionally, computers can only calculate according to input parameters, but in actual applications, unexpected working conditions often occur. Computers don’t know about these unexpected conditions and therefore cannot calculate results that match reality.
Simulation of hydraulic components and systems, if used as a teaching tool for armchair strategizing, generally speaking, has some value in helping students understand and recognize the mutual influences of various components in hydraulic systems, especially transient characteristics. However, if simulation is used as a product development tool, where the purpose of simulation is to predict the characteristics of the simulated object and thereby improve and optimize it, then being “relatively true” is the most basic requirement for simulation.
To know whether it is “relatively true,” testing must be used for comparative verification. If the comparison shows small deviation, it means this simulation model and this set of parameters are relatively close to reality, relatively “true,” and can then be used to predict the performance of the simulation object and optimize on this basis, shortening development time. If the deviation is large, it means this simulation model still omits some important factors. The simulation model and parameters need to be studied and improved based on the deviation, which can also deepen understanding of the system.
Testing is like the number “1,” and simulation is like the number “0.” Without testing, simulation has little value; combined with testing, simulation can amplify the value of testing tenfold or a hundredfold.
Testing is the foundation. Only by doing simulation on the foundation of testing can one build skyscrapers; otherwise, it can only be castles in the air—just painting ghosts!
Professor Backé, the world authority in fluid dynamics, was an advocate of hydraulic simulation, but his principle was: no simulation without testing conditions! One must first create good testing conditions before starting simulation. Then compare simulation with testing to improve the simulation model and parameters, until the simulation results are close to the test results, and only then explore better solutions based on this simulation model.
Now, those world-class fluid technology companies do indeed use simulation, finite element analysis, flow field analysis, and other computer-aided tools during the design phase when developing new products, greatly accelerating the development process. But before this, they had conducted long-term massive testing, accumulated extremely rich data and experience. After simulation, they still compare with test results and make improvements.
“A leader in hydraulic technology, A convenient choice around you”
