The relationship between closed chamber and pressure flow rate
Hydraulic technology is the use of oil to transmit power through pressurized flow in a closed space consisting of pipelines, pumps, cylinders, motors, control valves, etc. (rather than open channels such as water channels, rivers, and canals), in order to safely, accurately, quickly, and efficiently achieve various cyclic action requirements required by machine equipment. The role of modern hydraulic technology on the host is similar to that of the human blood system and nervous system. Therefore, studying the characteristics of oil in a closed chamber is the foundation for researching hydraulic technology, designing, using, and maintaining hydraulic equipment.
Overall, there are two types of closed chambers encountered in hydraulic technology: steady-state closed chambers and dynamic closed chambers. It should be noted that the oil in the enclosed chamber can be compressed (represented by elastic modulus, steel is 2.1 X 10 ^ 5MPa, and hydraulic oil is 1.4-2 X 10 ^ 3MPa, with a difference of 100 times between the two).
1、 Steady state closed cavity
Its characteristic is that the oil inside it basically does not flow, that is, there is neither oil flowing out of the chamber nor oil being replenished from the outside into the chamber. In this closed chamber, the famous Pascal's principle applies, which states that when the outside world applies pressure to the closed chamber (connector) through an interface, the pressure generated will be simultaneously and equally transmitted to the walls of the closed chamber. The jack shown in the attachment is the most typical application example of force amplification using the equal pressure transmission characteristics of a closed chamber. This type of enclosed cavity is generally easier to understand.
Basic formula for pressure of steady-state closed chamber
When the pressure in a closed chamber is P, the volume is V; When the pressure is increased to P+Δ P, the volume is V - Δ V. Therefore:
ΔP=Ee×ΔV/V
In the formula, Ee -- effective bulk modulus of elasticity (including the equivalent modulus of elasticity of the oil itself, as well as the enclosed cavity wall, etc., which is greatly influenced by the gas content).
Note: This only considers the steady-state pressure changes caused by volume changes, without the factor of time, so it is a steady-state consideration.
2、 Dynamic closed cavity
Its characteristic is that the oil inside is flowing, that is, both oil flows into the chamber and oil flows out from the chamber. The basic pressure formula is very similar to the steady-state closed chamber pressure formula mentioned above, but the meaning of the symbols is different.
Formula for dynamic closed chamber pressure
ΔP=Ee×Δq×t/V
In the equation, the meanings of Ee and V are the same as those of a steady-state closed cavity, while the rest have changed:
Ee: Effective bulk modulus of elasticity
V: The total volume of the enclosed chamber;
Δ q: The difference in liquid flow rate between the inflow and outflow of the enclosed chamber in time t (no longer a change in volume)
Δ P: The change (either increase or decrease) in the closed chamber pressure during time t;
And (Δ P/t) is commonly referred to as the rate of pressure rise (change in pressure per unit time). It can be seen that there are three main factors that affect the pressure changes in a closed chamber: Ee, V, and Δ q.
3、Several key points that still need attention
3.1 Oil is compressible
In hydraulic systems, it is generally necessary to consider that oil can be compressed, but the values may vary depending on different pressure levels and usage scenarios. Do not believe too much that some books state that low pressure is incompressible;
3.2 No matter what system, there are dynamic problems with different levels
When designing any system or analyzing system failures, it is important to pay attention to this issue and calculate it using the closed chamber pressure formula.
There used to be a large pressing machine that used carbon rods to press steel furnaces. When there were slight changes in the ore raw materials, the main pressing hydraulic cylinder often operated abnormally, stopping and running, and all the waste was discharged. Upon on-site inspection, it was found that the rodless chamber from the hydraulic pump to the main compression cylinder is actually a closed chamber. Due to insufficient flow, the thrust of the hydraulic cylinder (with a diameter of about 1.5m and a stroke of about 15m) is often lower than the load force. As soon as the hydraulic cylinder stops, the enclosed chamber temporarily does not increase, and the pump continues to supply oil, causing the pressure in the enclosed chamber to rise again, thus overcoming the load and moving forward. But when the hydraulic cylinder piston moves, the total volume of the enclosed chamber increases, and when the oil pressure drops, the piston stops moving.
In fact, the oil source flow rate of the system is in an edge state that cannot meet the system requirements, and it is estimated that the calculation of the closed chamber parameters has not been carried out at all. The movement speed of the main hydraulic cylinder in this system is very low, and it is not considered a dynamic problem according to convention. However, it is actually a dynamic problem (the pressure changes slower than required over time), and the problem needs to be solved by relying on the concept of dynamic enclosed chambers. There are three factors in the formula: E, V, and Δ q, but in practice, there is no way to increase the elastic modulus of the oil; To carry out pipeline renovation on the massive system of steel piles to reduce the total volume of enclosed chambers, time and production losses cannot be incurred (the entire production line is imported from abroad).
Finally, we can only seek help from Δ q, which is to increase the oil source flow rate. The result was to change 2 out of the original 3 variable pumps with synchronized variables to fixed input values (equivalent to a quantitative pump), leaving 1 as a feedback variable (all 3 cannot keep up with the feedback speed, and it is unnecessary), which only solved a key problem in production by performing a small operation on the electronic controller.
3.3 Among the factors affecting the effective bulk modulus of elasticity, the presence of air in the oil has the greatest impact
The impact on gas content should be distinguished between air dissolved in the oil or air mixed into the oil.
(1) Air dissolves in oil
1) Air dissolves in oil - it has no effect on the properties of the liquid, and its compressibility and viscosity remain unchanged!
2) The solubility is directly proportional to the absolute pressure of the air above the oil; When the pressure increases, some of the air mixed in will dissolve in the liquid; The air dissolved in the liquid will escape with the decrease of pressure (carbon dioxide will escape when opening the water bottle);
3) Dissolving takes time! The dissolution rate is determined by the pressure of the oil, and if the oil is stirred, the bubble dissolution rate is faster.
(2) Air mixed into the oil
1) Has a small impact on viscosity, but can significantly reduce the bulk modulus of elasticity! There is data indicating that mixing 1% air causes the effective bulk modulus of elasticity to decrease from 1449MPa to 1077.5MPa.
2) At high rates of pressure change, bubbles in oil are unstable and may be crushed under high pressure. This produces what is known as gas cavitation, where the pressure generated when bubbles break is large enough to cause damage to the machine, often occurring at the high-pressure oil discharge port of a gear pump.
3.4 Distinguish between static and dynamic bulk modulus of elasticity
Static modulus of elasticity - refers to the elastic modulus of an oil that is stationary or moving at a low speed.
Dynamic elastic modulus - When designing a control system, if the oil needs to flow out at high speed from the ports of servo valves, proportional valves, throttle valves, and pressure reducing valves, the amount of air pockets in the oil will increase significantly, resulting in a significant decrease in the elastic modulus of the oil. The elastic modulus of the oil in this state is called dynamic elastic modulus.