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In this paper, to realize the pressure stability control of high-pressure oil pipe, the dynamic differential equation of fuel oil inlet and outlet is established based on the theory of mass conservation. According to the change of the pressure in the high-pressure tubing, an optimization model is established to achieve precise control of the working time of each part of the high-pressure oil pipe.

Fuel entering and ejecting high-pressure fuel pipe is the basis of many fuel engines. When the high-pressure fuel system is working, fuel enters the high-pressure fuel pipe from the oil inlet valve and then ejects from the fuel injector at the other end. The intermittent working process of fuel entering and ejecting will lead to the change of the pressure in the high-pressure oil pipe, which will cause the deviation of the quantity of fuel ejected, thus affect the working efficiency of the engine, and even cause the direct economic loss due to the fault [

In this paper, a dynamic differential equation of fuel oil inlet and outlet is established based on the theory of mass conservation and a Matlab visual simulation tool is developed. To be more specific, three questions are answered: (1) How to determine the oil supply time of the one-way oil inlet valve? (2) How to determine cam angular velocity? (3) How to adjust the oil supply strategy if adding another injection nozzle?

The following example is used to illustrate the model development and problem-solving process. Figure

Schematic diagram of the high-pressure oil pipe.

The oil supply time is controlled by the one-way valve switch, which closes for 10 ms after each opening. The injector works 10 times per second, and the injection time is 2.4 ms each time. When the injector is working, the injection rate from nozzle B to the outside is shown in Figure

Schematic diagram of injection rate.

To solve the pressure control problem of high-pressure oil pipe, He et al. [

In this paper, an algorithm based on the differential equation, optimization model, and simulation model was developed. This algorithm can minimize pressure fluctuations and make the solution more accurate.

In order to facilitate the study of the problem and simplify the process of solution, some symbols are uniformly defined and assumptions are made which are consistent with the actual situation.

The symbols and their explanation are provided in Table

Symbols and explanation.

Symbol | Explanation | Unit |
---|---|---|

_{A} | The oil supply quantity at the oil supply end A in t time | m^{3}/s |

_{B} | Output of fuel injection end in one injection time | m^{3}/s |

Density of fuel | mg/mm^{3} | |

The area of the small circular hole area | m^{2} | |

Modulus of elasticity | ||

_{1} | Supply end pressure | Pa |

_{2} | Total volume of high-pressure oil pipe | Pa |

Pressure variation function in tube | Pa | |

Internal pressure of high-pressure oil pipe | m^{3} | |

One working cycle of high-pressure oil pump | s |

The pressure in the high-pressure oil pipe is uniform, regardless of the viscous resistance of the oil

The influence of the change of fuel temperature on the model during the operation of the high-pressure oil pipe is not considered

There will be no fuel leakage in the whole working system

The one-way valve and oil nozzle both work properly

The working condition of the oil nozzle has nothing to do with its position

The opening and closing of the valve are completed instantaneously

The pressure of oil pipe in unit time is determined by the quantity of oil in _{2} are obtained. Based on the given relationship between the injection rate and time at the fuel injector B, the quantity of oil injected

According to the speed of the oil supply end and the oil outlet end about time

To unify the dimension in the calculation and derivation process, the following conversion formulas are used to convert the unit:

Unit conversion:

Circle area formula:

Column volume formula:

When the pressure in the pipe is stable at

Step 1. Calculate the quantity of oil

According to the flow formula, the oil supply quantity is calculated:

where flow coefficient

According to the data that indicates the relationship between the elastic modulus

Then, based on the fact that the pressure change of fuel is proportional to the density change and the ratio coefficient is

The simplified expression is

To sum up, within the time period

Step 2. Calculate the oil output

According to the graph of oil injection rate and time, as shown in Figure

According to the integration of time

Step 3. Establish the dynamic pressure equation in the high-pressure oil pipe.

Based on the quantity of oil in and out, the dynamic pressure equation in the high-pressure oil pipe can be expressed as

where

By fitting the search function, the change of

When the pressure in the pipe increases to

Then, formula (

Finally, the high-pressure oil pipe enters the next working state. In the stable state, the working principle of the tubing is similar to the previous analysis. Based on the quantity of oil in and out, the dynamic pressure equation in the high-pressure pipe is established as follows:

By fitting the search function, the change is kept as small as possible so that the pressure in the high-pressure tubing is maintained at about

The equation is established by converting the pressure difference into the mass difference:

It can be seen that the opening time of the oil pipe is reduced when the pressure in the pipe increases from 100 MPa to

The elastic modulus

The functional relationship between the elastic modulus and the pressure is obtained:

Figure

It can be seen from the fitting comparison chart that the fitting curve has a high degree of agreement with the original data set, and the cubic fitting effect is good, which can accurately describe the functional relationship between elastic modulus

Comparison between the fitting curve and original data.

Calculation of oil output

The flow rate function integrates the time

Bring in dynamic pressure equation (

With Matlab, it could be found that

When the pressure in the high-pressure oil pipe is stable at 150 MPa, if working process of the high-pressure oil pump is divided into the adjustment stage and the balance stage, then the working rules of the oil pump under the three adjustment stages are as follows:

The adjustment process is as follows:

The adjustment process is as follows:

The adjustment process is as follows:

To sum up, see Table

Adjustment plan.

Status time | 2 s | 5 s | 10 s |

Adjustment status (ms/time) | 0.898 | 0.752 | 0.532 |

Stable status (ms/time) | 0.761 | 0.761 | 0.761 |

When the pressure and other factors change, the constant is the quality of the liquid in the fuel supply end and the quality of the liquid out of the fuel injection end. In a working cycle of the high-pressure oil pipe system, in order to maintain the stability of the pressure in the pipe, the quality of the fuel in and out is equal.

For problem 2, the fuel supply end compresses the low-pressure fuel oil by the rotation of the cam. Firstly, according to the relationship between the cam edge curve and the angle, combined with the working data of the plunger system, the movement range of the plunger is 0 to 10.626 mm. The rotation angle of the plunger from the compression to the low point, after the compression to the high point, then back to the low point is

In the whole working system of high-pressure oil pipe, the pressure in the pipe can be kept stable only when the mass of injected fuel is always equal. The following gives the concept of conservation of mass and its application formula.

Conservation of mass: in any isolated system, the total mass remains unchanged no matter what changes or processes occur. In other words, any changes, including chemical reaction and nuclear reaction, can not eliminate substances but changes the original form or structure of substances, so this law is also known as the law of material immortality [

Liquid mass, density, volume relationship:

Calculate the mass

Fit the relationship between the cam edge curve and the angle, and the result is shown in Figure

The maximum compression value of cam is

When the plunger is at a low point, the fuel pressure is

Schematic diagram of the high-pressure oil pump.

Fitting curve of polar diameter and polar angle.

Calculate the mass

The schematic diagram of the injector nozzle is shown in Figure

In the initial stage, that is, when the needle valve is closed, the height _{2}, that is to say, the area of the circular ring formed by the bottom of the needle valve and the inner surface of cone S is equal to the area of a small hole, the flow rate reaches the maximum. At this time, the outer radius

Performing three times fitting for the given needle method motion, the fitting curve is shown in Figure

According to the rising height node of needle valve, the time node of flow rate change can be obtained, and then the functional relationship between flow rate and ring area can be obtained:

To sum up, the quality of oil ejected in unit time is

Structure of the fuel injection nozzle.

Curve of moving distance and time of needle valve.

Balance stage.

To make the pressure in the high-pressure oil pipe at _{A} = _{B}; then,

The angular velocity of the cam is

The speed curve of the injection end is shown in Figure

The results obtained by taking the known data into formula (

Curve of velocity versus time.

If adding another injection nozzle with the same working rule based on the model developed in Problem 2, without considering the influence of its position distribution. Then installing another pressure relief valve to control the pressure in the high-pressure oil pipe. According to the previous analysis, the pressure relief valve is opened and the fuel returns when the pressure in the high-pressure oil pipe is greater than

Schematic diagram of high-pressure oil pipe.

In the calculation of high-pressure oil pump, a function is used to fit the change of oil supply pressure.

Fitting is to connect a series of points on a plane with a smooth curve. Generally, the fitting curve can be expressed by function, and a commonly used fitting method is the least square curve fitting method. In Matlab, polyfit can also be used to fit polynomials.

Adding an injector with the same working rule, that is, there are two injectors in the system, which are recorded as

The starting working time of two fuel injection nozzles is the same.

Adding an injector with the same working rule based on problem 2, in this case, it can be considered that the oil output in the same time is 2 times that in question 2, and the time to achieve stable oil pressure in the pipe is 1/2 of the original.

In unit time, the quality of the oil out of the injector end is

And the angular velocity of the cam is

The starting working time of two fuel injection nozzles is inconsistent.

If nozzle

In the whole process of pressure regulation, the minimum pressure fluctuation of a system is the optimal objective, and the objective function is

The constraints are

A single objective programming model is established, the optimal angular velocity of the cam is 245.63 rad/s in a system cycle, and the initial working time difference of the two nozzles is 1/2 cycle.

When adding a pressure reducing valve, if taking time as an independent variable, the fuel oil pressure input and nozzle injection could be calculated. By multiplying the difference by the elastic modulus

It is simulated circularly and the image is drawn. The simulation results are shown in Figure

It can be seen from Figure

After opening, the pressure in the pipe tends to be stable, and the pressure reducing valve plays an important role in stabilizing the air pressure in the tubing when the working time is about

Simulation results of internal pressure.

Air pressure simulation diagram after adding single pressure reducing valve.

Inspection idea: during the working process of high-pressure oil pipe, when the pressure inside the oil pipe fluctuates within a certain range, it can be regarded as stable, which can increase the service life of the whole oil supply system. In this paper, the real-time monitoring of the pressure in the tube during the working process of the oil tube is carried out, and the change curve of the pressure in the tube with time

Real-time pressure.

It can be seen that, during the working process of high-pressure oil pipe, the air pressure in the pipe always changes periodically between 96 MPa and 104 MPa, and the pipe can be regarded as a stable state, which shows that the model has precise control on all parts of the oil pipe, thus making the whole oil supply system more stable.

In the dynamic differential equilibrium equation model of question 1, the time is subdivided, the relation between the oil supply rate and the pressure difference and time is fully considered, and the oil supply end is precisely controlled by the flow rate of the oil injection end; in the adjustment state, the linear function is used to fit the pressure change in the high-pressure oil pipe, which simplifies the solution.

In the process of solving the second problem, based on the conservation of mass, a dynamic equation model with mass as the link is established, and a constant quantitative equation is established in many variable quantities to eliminate the interference of temperature and other factors on the solution process.

In the process of solving problem 3, this paper adopts the method of function fitting to eliminate the influence of the irregular change of oil supply of high-pressure oil pump on the solution of the problem and improve the efficiency of the solution.

Finally, for the model testing, the simulation model is established to test the working system of high-pressure oil pipes one by one [

In the process of solving problem one, because of the particularity of solving a differential equation, the analytical solution is difficult to solve. In this paper, the numerical solution is used for approximate substitution, resulting in errors.

In this paper, the change of system temperature caused by friction and other factors is not considered in the model.

To sum up, the purpose of this paper is to study the pressure control problem of the high-pressure oil pipe of the fuel engine, with the known parameters to calculate the pressure density and other indexes by using the numerical solution of differential equation flexibly. The fluid density and pressure model of high-pressure oil pipe are established, and the pressure stability of high-pressure oil pipe is maintained by using visual simulation tools. At the same time, the control scheme of fuel injection nozzle and pressure relief valve is studied to precisely control the working time of each part of high-pressure oil pipe, so as to improve the service life of engine.

In reality, there will be differences in the pressure in the high-pressure oil pipe, which is related to the elastic deformation in the pipe, the transmission mode of fuel in the pipe, and other factors. The function of the pressure in the pipe can be constructed to refine the change of the pressure in the pipe, to quantify the injection rate at the injection end more accurately, as to precisely regulate the oil supply end.

In the solution model of problem 2, the fuel supply end drives the plunger to pressurize the low fuel oil through the cam rotation. In this process, due to the influence of friction, the volume and pressure of fuel oil will be affected. Therefore, the temperature influence factor can be added in the process of solving the fuel supply quality to eliminate the influence of temperature change.

In question 3, the position of the fuel injector will affect the injection rate [

In the working system of high-pressure oil pipe, the model in this paper realizes the mutual correlation and precise regulation of various components. In the era of the rapid development of big data, the model can be applied to the sensing process of the robot, self-regulation of medical instruments and correction equipment, etc. [

The cam edge curve, needle valve motion curve, and elastic modulus pressure data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.