CN114921598A - A method and system for modeling motion trajectory of blast furnace top charge - Google Patents

Abstract

The invention discloses a modeling method and a system for movement tracks of furnace burden on the top of a blast furnace, which establish a static coordinate system which is static relative to the blast furnace and a moving coordinate system which rotates together with a chute, establish a mathematical model for discharge of a burden throttling valve according to the discharge mode of the burden at a blanking tank, establish a mathematical model for free fall of the burden at a central throat, establish an initial movement mathematical model of the burden on the chute after the burden collides with the chute according to the collision recovery coefficient of the burden and the chute, establish a mathematical model for chute movement of the burden in the chute and obtain a mathematical model for movement tracks of the burden from the throttling valve to the tail end of the chute of single-particle burden according to the mathematical model for chute movement, thereby obtaining the mathematical model for movement tracks of the burden on the top of the whole blast furnace, solving the technical problem of low calculation precision of the movement tracks of the burden on the top of the blast furnace in the existing blast furnace, realizing the calculation of the movement tracks of the burden on the top of the blast furnace in different initial movement states, the calculation precision of the furnace charge motion trail is improved.

Description

A method and system for modeling motion trajectory of blast furnace top charge

technical field

The invention mainly relates to the technical field of blast furnace smelting, in particular to a method and a system for modeling the motion trajectory of a blast furnace top charge.

Background technique

Blast furnace ironmaking is a key process in the iron and steel production process. It is a production process of continuous blasting, batch distribution, periodic iron tapping, accompanied by complex physical and chemical reactions, violent material and phase transformation, and high-intensity energy transfer and transfer. The three-dimensional shape of the blast furnace top surface is the most important basis for optimizing and adjusting the distribution of blast furnace gas flow, and it is also an important basis for assisting blast furnace smelting experts to detect abnormal furnace conditions in time, adjust the distribution system appropriately, and avoid further deterioration of furnace conditions. The trajectory of the charge on the top of the blast furnace directly determines the three-dimensional shape of the material surface. Successfully predicting the trajectory of the three-dimensional trajectory of the charge on the top of the blast furnace is of great significance to promote the stability of the blast furnace, improve the utilization rate of gas, and ensure the quality of molten iron. Due to the harsh environment of the blast furnace roof, high temperature and high pressure, high dust and weak light, it is difficult for the existing mechanical probes, radar probes, laser probes and industrial endoscopes to detect the shape of the material surface stably for a long time in this environment. Therefore, based on the motion mechanism of the charge, it is necessary to analyze the whole process movement of the charge from the unloading tank to the material surface, establish a three-dimensional mathematical model of the charge movement trajectory, and calculate the charge trajectory and drop point position under different blast furnace distribution operating parameters.

The charge transferred from the silo to the inside of the blast furnace will pass through the charging tank, the discharging tank, the central throat, and the rotating chute successively on the top of the blast furnace, and finally fall to the material surface to form a new material surface shape. On the top of the tandem-type bellless blast furnace, the movement of the charge from the charging tank to the unloading tank has almost no influence on the operation of the charging material distribution. Therefore, the trajectory model of the charge on the top of the blast furnace can be divided into five parts. First is the throttle discharge model leaving the end of the discharge tank; then the free-fall motion model at the central throat; then the collision model with the chute; then the 3D helical motion model on the rotating chute; A model of the oblique throw motion in the empty area. At present, there are many models about the movement trajectory of the charge, but they only take the charge as a particle for force analysis, and the obtained charge trajectory is the movement trajectory of the particle, which cannot characterize the position and velocity distribution of the charge when it leaves the chute. Therefore, the present invention proposes a method for modeling the motion trajectory of the blast furnace top charge, which realizes the accurate calculation of the motion trajectory of the blast furnace top charge, and is of great significance to the precise distribution operation of the blast furnace.

The patent with publication number CN 103131809 A discloses a multi-ring distribution mathematical model of blast furnace without material bell. The invention comprehensively considers the influence of factors such as the position of the material line, the movement distance of the charge on the chute and the change of the inclination angle of the chute. The initial distribution of the charge in the furnace is analyzed, and the collision velocity model of the charge passing through the central throat and the chute, the velocity model of the charge moving out of the chute, and the force model of the charge moving in the furnace throat cavity are proposed to realize the multi-ring distribution of the bellless blast furnace.

However, in this invention, the material flow is modeled as a mass point, and the obtained material flow trajectory is a single-point motion trajectory, so it is difficult to obtain the position and velocity distribution of the entire material flow at the end of the chute; It is also a single point, and it is difficult to obtain the distribution of the charge on the material surface.

The patent with publication number CN112176136B discloses a method and system for modeling the motion trajectory of the charge on the U-shaped chute of a blast furnace. The invention is mainly aimed at the modeling method of the motion trajectory of the charge on the U-shaped chute, and establishes a static coordinate system and a dynamic coordinate system. , analyze the force of the charge in the U-shaped chute, and obtain the mathematical model of the movement trajectory of the charge relative to the U-shaped rotary chute according to Newton's second law. After the initial motion state of the particles on the U-shaped chute is set, the motion trajectory of the charge on the U-shaped chute can be obtained.

However, in this invention, the initial movement state of the charge particles in the chute is artificially set, and the influence of the initial position of the charge at the throttle valve on the charge movement trajectory is not considered, making it difficult to calculate the blast furnace top charge movement trajectory.

SUMMARY OF THE INVENTION

The method and system for modeling the motion trajectory of the blast furnace top charge provided by the invention solve the technical problem of low calculation accuracy of the existing blast furnace top charge motion trajectory.

In order to solve the above-mentioned technical problems, the method for modeling the motion trajectory of the blast furnace top charge proposed by the present invention includes:

Establish a static coordinate system that is stationary relative to the blast furnace and a dynamic coordinate system that rotates with the chute;

According to the discharge mode of the charge at the unloading tank, a mathematical model of the discharge of the charge throttle valve is established;

The free-fall mathematical model of the charge in the central throat is established, and the free-fall mathematical model is used to obtain the velocity and position in the static coordinate system at the moment before the charge and the chute collide;

According to the collision recovery coefficient of the collision between the charge and the chute, a mathematical model of the initial movement of the charge on the chute after the collision between the charge and the chute is established. The collision recovery coefficient includes the normal recovery coefficient and the radial recovery coefficient;

According to the mathematical model of the initial movement of the charge on the chute after the collision between the charge and the chute, the mathematical model of the chute movement of the charge in the chute is established;

According to the mathematical model of the chute movement, the mathematical model of the movement trajectory of the single particle charge from the throttle valve to the end of the chute is obtained, and then the mathematical model of the movement trajectory of the entire blast furnace top charge is obtained.

Further, establishing a static coordinate system that is stationary relative to the blast furnace and a moving coordinate system that rotates with the chute includes:

According to the right-hand rule, a static coordinate system that is stationary relative to the blast furnace is established, wherein the origin of the static coordinate system is the intersection between the horizontal connection line of the two implicated points of the chute and the central throat and the symmetry axis of the blast furnace;

According to the right-hand rule, rotate the static coordinate system around the two coordinate axes in the static coordinate system in turn to obtain the moving coordinate system that rotates with the chute;

Solve the coordinate transformation matrix between the static coordinate system and the moving coordinate system.

Further, the establishment of the free-fall mathematical model of the charge in the central throat includes:

Obtain the coordinates in the static coordinate system when the charge leaves the throttle valve according to the mathematical model of the discharge of the charge throttle valve;

According to the coordinates in the static coordinate system when the charge leaves the throttle valve, the mathematical model of the free fall of the charge in the central throat is established, and the specific calculation formula of the mathematical model of the free fall of the charge in the central throat is:

R为溜槽半径。Among them, r ₁ and v ₁ are the velocity and position in the static coordinate system at the moment before the charge and the chute collide, respectively, x ₀ , _{y 0} , and ha are the X-axis, y 0 , and ha respectively in the static coordinate system when the charge leaves the throttle valve. The coordinates of the Y-axis and Z-axis, hw is the distance from the end of the central throat to the contact point between the charge and the chute, v ₀ is the Z-axis _velocity when the charge leaves the throttle valve, g is the acceleration of gravity, and e is the tilting distance of the chute , β ₀ and γ ₀ are the horizontal rotation angle and inclination angle of the chute relative to the initial position when the charge collides with the chute, θ ₀ is the included angle between the charge and the axis of symmetry of the chute, and

R is the radius of the chute.

Further, according to the collision recovery coefficient of the collision between the charge and the chute, the initial movement mathematical model of the charge on the chute after the collision between the charge and the chute is established, including:

Transform the speed and position in the static coordinate system before the collision between the charge and the chute into the moving speed and moving position in the moving coordinate system;

Obtain the normal phase vector of the collision point on the chute according to the moving position in the moving coordinate system at the moment before the charge and the chute collide;

According to the moving speed in the moving coordinate system before the collision between the charge and the chute, obtain the incident velocity before the charge and the chute collide;

Calculate the angle between the normal phase vector of the collision point on the chute and the incident velocity before the charge and the chute collide to obtain the first angle;

According to the collision recovery coefficient and the first angle when the charge collides with the chute, obtain the initial velocity constant of the charge moving on the chute after collision with the chute;

According to the initial velocity constant of the charge and the chute moving on the chute after the collision, the ejection velocity after the charge and the chute collide is calculated.

Further, the specific formula for calculating the ejection velocity after the collision between the charge and the chute is:

n为溜槽上碰撞点的法相向量。Among them, v′ ₁ is the incident velocity before the charge and the chute collide, v′ ₂ is the exit velocity after the charge and the chute collide, ||·|| represents the operation of taking the die length, and e _n is the normal direction when the charge and the chute collide coefficient of restitution, θ _int is the first angle, θ _out is the angle between the normal phase vector of the collision point on the chute and the exit velocity after the charge collides with the chute, and

n is the normal vector of the collision point on the chute.

Further, according to the initial velocity constant of the charge on the chute after the collision between the charge and the chute, the calculation formula for calculating the ejection velocity after the charge and the chute collide is:

v ₂ ′=av ₁ ′+bn,

Among them, v′ ₁ is the incident velocity before the charge and the chute collide, v′ ₂ is the exit velocity after the charge and the chute collide, a and b are the initial velocity constants of the charge moving on the chute after the collision with the chute, and n is the velocity on the chute The normal vector of the collision point.

Further, according to the mathematical model of the initial movement of the charge on the chute after the collision between the charge and the chute, establishing the mathematical model of the chute movement of the charge in the chute includes:

According to the mathematical model of the initial movement of the charge on the chute after the collision between the charge and the chute, the initial movement position and the initial movement speed of the charge on the chute are obtained;

According to the initial motion position and initial motion speed of the charge on the chute, based on the compound motion of points, the relative motion and implicated motion of the charge relative to the chute are analyzed respectively, and then the absolute motion of the charge in the blast furnace is analyzed, and the charge is established according to Newton's second law. Mathematical model of the chute movement in the chute;

According to the mathematical model of the chute movement, the moving speed and movement position of the charge from the throttle valve to the end of the chute are obtained.

Further, according to the mathematical model of the chute movement, after obtaining the end movement speed and end movement position of the charge from the throttle valve to the end of the chute, it also includes:

A mathematical model of the motion of the furnace throat empty area is established, and the calculation formula of the mathematical model of the furnace throat empty area motion is:

Among them, S _x , S _y and S _z represent the distance that the charge moves in the X-axis, Y-axis and Z-axis of the furnace throat empty area, t is the movement time of the charge from the end of the chute to the material surface, v _cx , v _cy , v _cz Respectively represent the moving speed of the charge leaving the end of the chute;

According to the mathematical model of the motion of the empty zone of the furnace throat, the position of the falling point of the charge is obtained, and the calculation formula of the position of the falling point of the charge is:

Among them, r _xc , r _yc and r _zc respectively represent the moving position of the charge leaving the end of the chute.

The blast furnace top charge movement trajectory modeling system provided by the present invention includes:

A memory, a processor and a computer program stored in the memory and running on the processor, when the processor executes the computer program, implements the steps of the method for modeling the motion trajectory of the blast furnace top charge provided by the present invention.

Compared with the prior art, the advantages of the present invention are:

The method and system for modeling the motion trajectory of the charge on the top of the blast furnace provided by the present invention are based on the establishment of a static coordinate system relative to the blast furnace and a dynamic coordinate system that rotates with the chute, and a charge throttle valve is established according to the discharge method of the charge at the unloading tank. The mathematical model of discharge is established, and the mathematical model of the free fall of the charge in the central throat is established. The mathematical model of the initial movement on the chute, establish the mathematical model of the chute movement of the charge in the chute, and obtain the mathematical model of the movement trajectory of the single particle charge from the throttle valve to the end of the chute according to the mathematical model of the chute movement, and then obtain the entire blast furnace top charge The mathematical model of the motion trajectory of the present invention solves the technical problem of low calculation accuracy of the motion trajectory of the existing blast furnace top charge. It can not only realize the function of the traditional material flow trajectory model, but also calculate the position of the entire material flow at the end of the chute according to the movement trajectory of the particles in different initial motion states. and velocity distribution, and then find out the drop point position of the entire material flow on the blast furnace charge surface.

Specifically, the present invention aims to provide a method and a system for modeling the motion trajectory of the charge on the top of the blast furnace, which are used to accurately calculate the motion trajectory of the charge on the top of the blast furnace. The movement of the charge on the top of the blast furnace is in the form of material flow. The current movement trajectory of the charge is mainly to consider the charge as a mass point for force analysis. The speed and the collision recovery coefficient and model coefficient of the contact between the charge and the chute are related. At the same time, the traditional material flow trajectory model considers that the initial movement position of the charge on the chute is only related to the inclination distance of the chute and the inclination angle of the chute, and the movement speed is only along the longitudinal direction of the chute. In fact, the initial motion state of the charge on the chute after the collision with the chute is not only related to the initial motion state of the charge particles when they leave the throttle valve, but also to the motion state of the chute during the free fall of the charge in the central throat. Therefore, the accuracy of the charge trajectory predicted by the traditional charge trajectory model is low. In view of the deficiencies of the traditional charge trajectory model, the present invention proposes a method for mathematical modeling of the charge trajectory of the blast furnace top based on coordinate transformation. And establish the transformation matrix between the static coordinate system and the moving coordinate system to realize the position and speed transformation of the charge between the static coordinate system and the moving coordinate system. At the same time, the vectorized analysis of the charge motion model reduces the complexity of the force analysis during the charge motion process and improves the calculation accuracy of the charge motion trajectory.

The purpose of the invention is to comprehensively consider the initial motion state of the single particle charge and the motion state of the rotary chute, so as to realize the calculation of the motion trajectory of the charge particles in different initial motion states on the top of the blast furnace. The invention can realize the function of the traditional material flow trajectory model, and can also obtain the position and velocity distribution of the entire material flow at the end of the chute according to the motion trajectory of the particles in different initial motion states, and then obtain the entire material flow on the blast furnace charge surface. drop location.

The invention proposes a method for modeling the movement trajectory of the top charge of a tandem bellless blast furnace based on coordinate transformation. The chute motion model and the oblique throwing motion model of the furnace throat empty area; the invention establishes a static coordinate system and a dynamic coordinate system, and calculates the descending height of the charge in the central throat based on the coordinate transformation matrix, and then calculates the three-dimensional motion speed after the charge and the chute collide; the The invention takes into account the influence of the initial motion state of the charge particles and the motion state of the chute on the motion trajectory of the charge, and can calculate the position distribution and velocity distribution of the material flow at the end of the chute, which meets the requirements of the batch-type bellless blast furnace for distribution, and has great application value. .

Key points of the present invention include:

(1) A method for mathematical modeling of the movement trajectory of the charge on the top of a tandem bellless blast furnace based on coordinate transformation is proposed to achieve accurate calculation of the movement trajectory of the charge on the top of the blast furnace;

(2) The static coordinate system relative to the blast furnace and the dynamic coordinate system relative to the blast furnace movement are constructed, and the three-dimensional movement position and speed of the collision point in the chute when the charge and the chute collide are calculated based on the coordinate transformation matrix;

(3) The vectorized modeling of the charge movement process, and the analysis of the relationship between the relative motion, implicated motion and absolute motion of the charge in the chute based on point compound motion, reducing the complexity of the load force analysis and improving the math of the charge movement trajectory model accuracy;

(4) The calculation of the trajectory of the charge particles on the top of the blast furnace with different initial motion states is realized, and the model can obtain the position distribution and velocity distribution of the charge at the end of the chute.

Description of drawings

Fig. 1 is a schematic diagram of the top of a bellless blast furnace in a second embodiment of the present invention;

Fig. 2 is the relational diagram between the static coordinate system and the dynamic coordinate system of the second embodiment of the present invention;

Fig. 3 is the flow chart of the method for modeling the motion trajectory of blast furnace top charge in Embodiment 2 of the present invention;

4 is a schematic diagram of the position of the charge relative to the chute according to the second embodiment of the present invention;

5 is a schematic diagram of the O'X'Z' plane of the charge particles in the chute according to the second embodiment of the present invention;

6 is a schematic diagram of the O'Y'Z' plane of the charge particles in the chute according to the second embodiment of the present invention;

7 is a flowchart of a method for modeling the motion trajectory of blast furnace top charge in Embodiment 3 of the present invention;

FIG. 8 is a structural block diagram of a system for modeling the motion trajectory of a blast furnace top charge according to an embodiment of the present invention.

Reference number:

1. Weighing tank; 2. Throttle valve; 3. Central throat; 4. Rotary chute; 5. Furnace throat; 6. Material surface; 7. Charge particles; 8. Static coordinate system; 9. Material flow; 10. Memory; 20. Processor.

Detailed ways

In order to facilitate the understanding of the present invention, the present invention will be described more comprehensively and in detail below with reference to the accompanying drawings and preferred embodiments of the specification, but the protection scope of the present invention is not limited to the following specific embodiments.

The embodiments of the present invention are described in detail below with reference to the accompanying drawings, but the present invention can be implemented in many different ways as defined and covered by the claims.

Example 1

The method for modeling the motion trajectory of a blast furnace top charge provided in Embodiment 1 of the present invention includes:

Step S101, establishing a static coordinate system relative to the blast furnace and a dynamic coordinate system rotating with the chute;

Step S102, according to the discharge mode of the charge at the unloading tank, establish a mathematical model for the discharge of the charge throttle valve;

Step S103, establishing a free-fall mathematical model of the charge in the central throat, and the free-fall mathematical model is used to obtain the speed and position in the static coordinate system at the moment before the charge and the chute collide;

Step S104, according to the collision recovery coefficient of the collision between the charge and the chute, establish a mathematical model of the initial movement of the charge on the chute after the charge and the chute collide;

Step S105, according to the initial movement mathematical model of the charge on the chute after the collision between the charge and the chute, establish a mathematical model of the chute movement of the charge in the chute;

Step S106, according to the mathematical model of the chute movement, obtain the mathematical model of the movement trajectory of the single particle charge from the throttle valve to the end of the chute, and then obtain the mathematical model of the movement trajectory of the entire blast furnace top charge.

In the method for modeling the motion trajectory of the charge on the top of the blast furnace provided by the embodiment of the present invention, by establishing a static coordinate system relative to the blast furnace and a dynamic coordinate system rotating together with the chute, and according to the discharge mode of the charge at the discharge tank, a charge throttle valve is established. The mathematical model of discharge is established, and the mathematical model of the free fall of the charge in the central throat is established. The mathematical model of the initial movement on the chute, establish the mathematical model of the chute movement of the charge in the chute, and obtain the mathematical model of the movement trajectory of the single particle charge from the throttle valve to the end of the chute according to the mathematical model of the chute movement, and then obtain the entire blast furnace top charge The mathematical model of the motion trajectory of the present invention solves the technical problem of low calculation accuracy of the motion trajectory of the existing blast furnace top charge. It can not only realize the function of the traditional material flow trajectory model, but also calculate the position of the entire material flow at the end of the chute according to the movement trajectory of the particles in different initial motion states. and velocity distribution, and then find out the drop point position of the entire material flow on the blast furnace charge surface.

Specifically, the movement of the charge on the top of the blast furnace is in the form of material flow. The current movement trajectory of the charge is mainly to consider the charge as a particle for force analysis, and the obtained movement trajectory of the charge is only related to the initial speed of the charge and the angle of inclination of the chute. , the rotation speed of the chute, and the collision recovery coefficient and model coefficient of the contact between the charge and the chute. At the same time, the traditional material flow trajectory model considers that the initial movement position of the charge on the chute is only related to the inclination distance of the chute and the inclination angle of the chute, and the movement speed is only along the longitudinal direction of the chute. In fact, the initial motion state of the charge on the chute after the collision with the chute is not only related to the initial motion state of the charge particles when they leave the throttle valve, but also to the motion state of the chute during the free fall of the charge in the central throat. Therefore, the accuracy of the charge trajectory predicted by the traditional charge trajectory model is low. In view of the deficiencies of the traditional charging trajectory model, the embodiment of the present invention proposes a method for mathematical modeling of the charging trajectory of the blast furnace top based on coordinate transformation. The method establishes a static coordinate system relative to the blast furnace and a dynamic coordinate rotating together with the chute. system, and establish a transformation matrix between the static coordinate system and the dynamic coordinate system to realize the position and speed transformation of the charge between the static coordinate system and the dynamic coordinate system. At the same time, the vectorized analysis of the charge motion model reduces the complexity of the force analysis during the charge motion process and improves the calculation accuracy of the charge motion trajectory.

Embodiment 2

The embodiment of the present invention discloses a coordinate transformation-based mathematical model for the movement trajectory of the charge on the top of a tandem-type bellless blast furnace. Throttle valve 2, central throat 3, rotary chute 4, furnace throat 5, material surface 6, charge particles 7, static coordinate system 8, material flow 9. Figure 2 is a diagram showing the relationship between the static coordinate system and the moving coordinate system. Fig. 3 is the implementation step of solving the mathematical model of the motion trajectory of the single-particle charge of the blast furnace top proposed by the present invention, including the following steps:

(1) According to the right-hand rule, establish a static coordinate system OXYZ relative to the blast furnace and a dynamic coordinate system O'X'Y'Z' that rotates with the chute, and solve the coordinate transformation matrix between the static coordinate system and the dynamic coordinate system;

(2) Establish a mathematical model for the discharge of the charge throttle valve according to the discharge mode of the charge at the unloading tank;

(3) Calculate the total drop height of the charge in the central throat when the charge leaves the throttle valve in a certain initial motion state according to the coordinate transformation matrix, and establish a mathematical model for the free fall of the charge in the central throat;

(4) Convert the motion information of the charge in the static coordinate system into the moving coordinate system, and establish a mathematical model of the initial movement of the charge on the chute after the collision between the charge and the chute according to the velocity loss coefficient of the collision between the charge and the chute;

(5) On the basis of the known initial movement position and movement speed of the charge on the chute, based on the compound motion of points, analyze the relative motion of the charge relative to the chute, the implicated movement of the chute, and then analyze the absolute motion of the charge in the blast furnace , and establish the mathematical model of the charge in the chute according to Newton's second law;

(6) According to the mathematical model of the charge movement trajectory of the single particle charge from the throttle valve to the end of the chute, analyze the charge movement trajectory of the charge particles on the top of the blast furnace when the charge particles with different initial movement positions and moving speeds leave the throttle valve, forming the entire charge movement trajectory. Mathematical model of motion trajectory.

(7) Taking the moving position and moving speed of the charge at the end of the chute as the initial conditions, analyze the force of the charge at the throat of the blast furnace, and establish a mathematical model for the movement of the charge in the empty area of the throat.

The specific implementation scheme is as follows:

(1) Establish static coordinate system, dynamic and static coordinate system, and coordinate transformation matrix

In order to describe the moving trajectory of the charge on the top of the bellless blast furnace, a static coordinate system OXYZ relative to the blast furnace and a moving coordinate system O'X'Y'Z' relative to the blast furnace are established according to the right-hand coordinate system rule.

(a) Establish the static coordinate system OXYZ:

Take the symmetrical center line of the blast furnace as the Z-axis of the static coordinate system, and the vertical downward direction as the positive direction of the Z-axis of the static coordinate system; The intersection point is the origin O of the static coordinate system; the horizontal line perpendicular to OZ and intersecting with point O is the X axis, and the horizontal rightward direction is the positive direction of the X axis of the static coordinate system; perpendicular to the OXZ plane, the line intersecting with point O is Y Axis, perpendicular to the paper surface outward as the positive direction of the Y-axis of the static coordinate system, as shown in the coordinate system OXYZ in Figure 1.

(b) Establish a moving coordinate system OX′Y′Z′:

According to the actual operation of the blast furnace chute, it can be known that any position of the blast furnace chute during operation can be reached through two rotations through the original static state. According to the right-hand rule, first take the positive direction of the OZ axis as the positive direction of rotation around the axis, take the OX axis as the initial position, the rotation angle β, the unit is rad, to reach the one-time rotation coordinate system OX _r Y _r Z _r ; On the basis of the second rotation, take the positive direction of the OY _r axis as the positive direction of the second rotation around the axis, take the OZ _r axis as the initial position of the second rotation, the rotation angle γ, the unit is rad, and reach the moving coordinate system O'X 'Y'Z', the schematic diagram of the specific coordinate transformation is shown in Figure 2.

(c) Calculate the coordinate transformation matrix:

When the coordinate system is transformed, when the coordinate system is rotated around a certain axis, it is actually only a plane perpendicular to the rotation axis and located there. Therefore, the relationship between the charge in the static coordinate system and the dynamic coordinate is:

分别表示坐标系绕Y轴和Z轴旋转时的坐标变换矩阵。Among them, (x, y, z) is the motion state information of the charge in the static coordinate system, and (x', y', z') is the motion state information of the charge in the dynamic coordinate system.

Represents the coordinate transformation matrix when the coordinate system rotates around the Y-axis and Z-axis, respectively.

(2) Mathematical model of throttle valve discharge

The discharge method of the charge at the unloading tank is "funnel type", which can be calculated by the hydraulic continuity equation, which is described in the static coordinate system as:

Among them, Q is the mass flow rate of the charge when it leaves the throttle valve, the unit is kg/s, ρ is the bulk density of the charge, S is the projected area of the throttle valve, L _s is the length of the periphery of the throttle valve, and d is the diameter of the charge. The position of the charge in the static coordinate system when it leaves the throttle valve is expressed as:

r ₀ =(x ₀ , _{y 0} ,ha ) ^T (3)

where x ₀ , _{y 0} , and ha are the coordinates of the X-axis, Y-axis, and Z-axis in the static coordinate system when the particles leave the throttle valve, respectively.

(3) Mathematical model of free fall of central throat

At the opening of the throttle valve, the charge particles will move vertically downward at v ₀ under the action of gravity, and fall on the rotating chute after passing through the central throat. The position where the charge and the chute collide can be expressed as

r ₁ =(x ₀ , y ₀ , h _w ) ^T (4)

Where x ₀ and y ₀ are the X-axis coordinates and Y-axis coordinates respectively when the particles leave the throttle valve, and h _w is the distance from the end of the central throat to the point of contact between the charge and the chute. If the charge collides with the chute, the chute rotates β ₀ horizontally and tilts γ ₀ relative to the initial position, then h _w can be described as:

为炉料颗粒与溜槽对称轴之间的夹角，当θ₀在Y′轴负半轴时为正值。炉料在中心喉管运动期间，只受到重力的作用，因此，炉料即将与溜槽碰撞前的运动速度表示为：where e is the tilting distance of the chute, R is the radius of the chute,

is the included angle between the charge particles and the axis of symmetry of the chute, and is a positive value when θ ₀ is in the negative semi-axis of the Y' axis. During the movement of the central throat, the charge is only affected by gravity. Therefore, the moving speed of the charge before it collides with the chute is expressed as:

Where v ₀ is the Z-axis speed when the charge leaves the throttle valve, and g is the acceleration of gravity.

(4) Mathematical model of collision between charge and chute;

When the charge collides with the chute, the chute rotates β around the Z axis and γ around the Y axis relative to the static coordinate system. Therefore, the velocity v ₁ and the position r ₁ at the moment before the charge and the chute collide are respectively expressed in the moving coordinate system as:

Among them, v ₁ ′ represents the moving speed in the moving coordinate system when the charge and the chute are about to collide, and r ₁ ′ represents the position of the collision point between the charge and the chute in the moving coordinate system, that is, the initial position of the charge moving on the chute. Since the horizontal velocity of the charge moving in the central throat is negligible, the direction of the incident velocity before the charge and the chute collide can be represented by the direction of v ₁ '. In the moving coordinate system, the surface of the chute can be expressed as f(x', y', z'), then the normal phase vector of the collision point r ₁ ' on the chute is expressed as:

The angle θ _int between the incident velocity before the charge and the chute collide and the normal vector of the chute is expressed as:

Assuming that the ejection velocity after the collision between the charge and the chute is v ₂ ′=(v _{x, 2} ′, v _{y, 2} ′, v _{z, 2} ′), the size of the ejection velocity of the charge is expressed as

where v′ _2,x , v′ _2,y and v′ _2,z represent the velocity components of the exit velocity in the X-axis, Y-axis and Z-axis, respectively. The angle between the exit velocity after the charge and the chute collide with the normal vector of the collision point is expressed as

After the charge collides with the chute, both the normal and tangential velocities are lost, and the magnitude of the velocities after the collision is related to the collision recovery coefficient. The collision recovery coefficient between the charge and the chute is expressed as:

where e _n is the normal restitution coefficient when the charge and the chute collide, which is related to the material of the collision body and is a fixed value, and e _t is the tangential restitution coefficient when the charge and the chute collide, which is related to the material of the collision body and the collision angle, It can be expressed as:

e _t =1-μ(1 ₊ en )cotθ _int (14)

where μ is the sliding friction coefficient between the charge and the chute. According to formulas (13) and (14), the angle between the exit velocity and the normal vector of the collision point can be obtained, which is expressed as:

Therefore, according to formulas (12) and (15), the ejection velocity after the collision between the charge and the chute can be calculated as:

At the same time, the exit velocity after the collision between the charge and the chute is in the same plane as the incident velocity before the collision and the normal vector of the collision point, that is, it satisfies:

v ₂ ′=av ₁ ′+bn (17)

Converting formula (17) into a scalar expression is:

According to the previous known parameters and formulas (10), (11) and (18), the initial velocity constants a, b and v ₂ ′=(v _{x, 2} ′ can be obtained after the charge collides with the chute moving on the chute , v _{y, 2} ′, v _{z, 2} ′).

(5) Mathematical model of rotary chute movement

When the chute rotates, the charge on the chute is subjected to gravity, support force, friction force and Coriolis force, etc. Among these forces, except for the direction and magnitude of gravity, the other four forces will follow the movement of the charge on the chute. varies by location. Therefore, a point-based compound motion method is proposed to analyze the three-dimensional motion mathematical model of the charge in the rotary chute.

(a) Relative motion:

The position of the charge P relative to the chute is shown in Figure 4. The position of the charge P relative to the chute can be represented by P(x', θ), where x' represents the projection of the charge P on the O'X' axis in the moving coordinate system O'X'Y'Z', as shown in Figure 5, θ is the angle between the charge P and the axis of symmetry of the chute, as shown in Figure 6. Then the vector radius of the charge P relative to the moving coordinate system O'X'Y'Z' is expressed as:

为炉料在溜槽上的偏析角度，规定θ在Y′轴负方向为正角度偏析，在Y′轴正方向为负角度偏析，e为溜槽的倾动距。在动坐标系O′X′Y′Z′中，炉料P的相对速度表示为：where R is the radius of the chute,

For the segregation angle of the charge on the chute, it is specified that θ is a positive angle segregation in the negative direction of the Y' axis, a negative angle segregation in the positive direction of the Y' axis, and e is the tilting distance of the chute. In the moving coordinate system O'X'Y'Z', the relative velocity of the charge P is expressed as:

The relative acceleration of charge P is expressed as:

(b) Implicated Movement:

In the moving coordinate system, the moving coordinate system that coincides with the moving point and the pipeline point become the implicated point, and the vector radius of the implicated point relative to the dynamic coordinate system is the same as that of the charge P relative to the dynamic coordinate system, both of which are r'. The vector radius of the implicated point relative to the static coordinates is expressed as:

r _e =r _o′ +r′ (22)

Among them, r _o' represents the position of the origin O' of the moving coordinate system in the static coordinate system, which is zero here. Taking the time derivative of formula (22), the implicated velocity _ve of the moving point can be obtained, which is expressed as:

v _e =ω×r′ (23)

where ω is the rotational angular velocity of the chute. The time derivative of formula (23) can be obtained to obtain the implicated acceleration a _e of the moving point, which is expressed as:

a _e = a×r′+ω×ω×r′ (24)

where a is the rotational angular acceleration of the chute.

(c) Absolute motion:

When the chute rotates, the absolute motion of the moving point is equal to the vector sum of relative acceleration, implicated acceleration and Coriolis acceleration, expressed as:

a _a = a _r + a _e + a _c (25)

where a _c is the Coriolis acceleration of the charge P, expressed as:

a _c = 2ω×v _r (26)

Substituting equations (21), (24) and (26) into (25), the absolute acceleration can be obtained:

in

(d) Force analysis:

In the moving coordinate system, the charge is subjected to gravity, support force and frictional force. The gravity of the charge can be expressed as:

Where m is the mass of the charge P, the unit is kg, and g is the acceleration of gravity, m/s ² . The support force received by the charge is expressed as:

Among them, F _N is the support force received by the charge P. The sliding friction force on the charge is expressed as:

where μ is the dynamic friction factor between the charge P and the U-shaped chute. Therefore, the resultant external force F _Σ that the charge receives in the moving coordinate system is expressed as:

F _Σ =G′+F _N ′+F _f ′ (31)

According to Newton's second law, the relationship between the absolute acceleration of the charge P and the resultant external force can be obtained, which is expressed as:

F _Σ = ma _a (32)

Substituting equations (27) and (31) into equation (32) and simplifying to:

采用四阶Runge-Kutta算法即可求出炉料在溜槽上不同时刻的运动位置、速度和加速度。进一步的，根据公式(19)和(20)即可求出第i时刻炉料在溜槽上的位置r_i′和速度v_ri。再根据公式(7)即可求出炉料在静坐标系中的位置和速度：in

The fourth-order Runge-Kutta algorithm can be used to obtain the moving position, velocity and acceleration of the charge on the chute at different times. Further, according to formulas (19) and (20), the position ri ' and velocity v _ri of the charge on the chute at the _ith moment can be obtained. Then according to formula (7), the position and speed of the charge in the static coordinate system can be obtained:

(6) Mathematical model of motion of furnace throat empty area.

When there is no influence of gas flow, the charge is only subjected to vertical downward gravity in the empty area of the furnace throat, so the charge moves at a uniform speed in the X and Y axes, and performs uniform acceleration in the Z axis. The three-dimensional movement distance of the charge in the empty area Expressed as:

where t is the movement time of the charge from the end of the chute to the material surface, and v _cx , v _cy , and v _cz represent the moving speed of the charge leaving the end of the chute, respectively. The drop position of the charge can be expressed as:

Among them, r _xc , r _yc , and r _zc respectively represent the moving position of the charge leaving the end of the chute.

(7) Mathematical model of charge movement trajectory

The charge at different positions of the throttle valve forms different charge motion trajectories on the top of the blast furnace, and the collection of the motion trajectories of the material flow formed by all particles on the top of the blast furnace is called the mathematical model of the material flow trajectory.

In the method for modeling the motion trajectory of the charge on the top of the blast furnace provided by the embodiment of the present invention, by establishing a static coordinate system relative to the blast furnace and a dynamic coordinate system rotating together with the chute, and according to the discharge mode of the charge at the discharge tank, a charge throttle valve is established. The mathematical model of discharge is established, and the mathematical model of the free fall of the charge in the central throat is established. The mathematical model of the initial movement on the chute, establish the mathematical model of the chute movement of the charge in the chute, and obtain the mathematical model of the movement trajectory of the single particle charge from the throttle valve to the end of the chute according to the mathematical model of the chute movement, and then obtain the entire blast furnace top charge The mathematical model of the movement trajectory of the present invention solves the technical problem of low calculation accuracy of the existing blast furnace charge movement trajectory. It can not only realize the function of the traditional material flow trajectory model, but also calculate the position of the entire material flow at the end of the chute according to the movement trajectory of the particles in different initial motion states. and velocity distribution, and then find out the drop point position of the entire material flow on the blast furnace charge surface.

Further, the method for modeling the motion trajectory of the top charge of a tandem-type bellless blast furnace based on coordinate transformation proposed in the embodiment of the present invention includes a throttle valve discharge model, a central throat descending model, a charge and chute collision model, and a rotating chute movement. Model, the oblique throwing motion model of the furnace throat empty area, by establishing a static coordinate system and a dynamic coordinate system, based on the coordinate transformation matrix to calculate the falling height of the charge in the central throat, and then calculate the three-dimensional movement speed of the charge and the chute after collision, considering the charge particles The influence of the initial motion state and the chute motion state on the charging trajectory can be calculated, and the position distribution and velocity distribution of the material flow at the end of the chute can be calculated to meet the distribution requirements of the tandem bellless blast furnace, which has great application value.

Embodiment 3

The third embodiment of the present invention takes a domestic ^2650m3 large-scale bellless blast furnace as the experimental platform, applies the mathematical model of the charge movement trajectory to the top of the tandem-type bellless blast furnace to estimate the charge movement, and constructs the charge movement trajectory as shown in Figure 3 Computational model. The specific implementation steps for completing the calculation of the trajectory model of the top charge of the bellless blast furnace of the tandem can refer to Fig. 7, and the details are as follows:

Step1: According to the specific physical parameters of a ^2650m3 large-scale bellless blast furnace in China, initialize the calculation model, including the fixed physical parameters of the geometry: the diameter of the central throat D, the height of the central throat H, the tilting distance e of the chute, the radius of the chute R, the length of the chute L , the normal recovery coefficient _{en and tangential recovery coefficient e t when} the charge and the chute collide, the sliding friction coefficient μ between the charge and the chute, etc.; the initial motion state of the charge particles: initial motion position and speed; : the initial position of the charge in the dynamic coordinate system and the static coordinate system; the initial motion state of the chute: the initial motion speed in the dynamic coordinate system and the static coordinate system; the initial position of the charge: the initial position in the dynamic coordinate system and the static coordinate system ;The initial motion state of the charge: the initial speed in the moving coordinate system and the static coordinate system; the single-step running time of the charge is h, and the running time of the charge at this moment is set to 0;

Step2: Input the initial motion state of the particles, that is, the initial motion position r ₀ of the particles at the throttle valve, and input the motion state parameters of the U-shaped chute, including the initial motion position of the chute when the particles leave the throttle valve (β ₀ , γ _{0 )} ), the horizontal rotation angular velocity ω ₁ and the angular acceleration α ₁ of the chute, the angular velocity ω ₂ and the angular acceleration α ₂ of the inclined rotation of the chute;

Step3: According to the opening size of the throttle valve, calculate the different moving positions of the charge at the throttle valve {r ¹ , r ² ... r ⁿ }, where n represents the number of charge particles at the throttle valve. Initialize the movement position ri when the particle leaves the throttle valve, let ⁱ =1;

Step3: Calculate the initial movement speed v ₀ of the charge i when it leaves the throttle valve according to the material flow discharge model;

和初始速度

以及溜槽的运动状态，包括初始位置(β₀,γ₀)及旋转速度(ω₁,ω₂)，计算炉料颗粒离开节流阀至于溜槽碰撞过程所耗时间t₀，进而求出颗粒在中心喉管下降总高度h_a+h_b、颗粒在碰撞点的运动速度v₁、碰撞点的位置r₁、溜槽的位置(β₁,γ₁)。Step4: According to the initial motion state of the charge i when it leaves the throttle valve, including the initial position

and initial velocity

And the motion state of the chute, including the initial position (β ₀ , γ ₀ ) and the rotational speed (ω ₁ , ω ₂ ), calculate the time t ₀ for the charge particles to leave the throttle valve and collide with the chute, and then find out that the particles are in the center The total descending height of the throat h _a +h _b , the velocity v ₁ of the particle at the collision point, the position r ₁ of the collision point, and the position of the chute (β ₁ , γ ₁ ).

和速度

以及碰撞时溜槽的位置(β₁,γ₁)，计算出炉料在动坐标系内的位置

和速度

并根据炉料与溜槽的碰撞数学模型，计算出炉料与溜槽碰撞后的位置

和速度

Step5: According to the position of the charge when it collides with the chute

and speed

and the position of the chute at the time of collision (β ₁ , γ ₁ ), calculate the position of the charge in the moving coordinate system

and speed

And according to the collision mathematical model between the charge and the chute, the position after the collision between the charge and the chute is calculated.

and speed

和速度

为炉料在溜槽上的初始运动状态，根据炉料在溜槽上的运动数学模型，求解炉料离开溜槽时的位置

和速度

并根据坐标变换矩阵计算炉料离开溜槽时在静坐标系内的位置

和速度

Step6: Take charge position

and speed

is the initial motion state of the charge on the chute, according to the mathematical model of the motion of the charge on the chute, to solve the position of the charge when it leaves the chute

and speed

And calculate the position in the static coordinate system when the charge leaves the chute according to the coordinate transformation matrix

and speed

和速度

为炉料在炉喉空区的初始运动状态，根据炉料在空区的斜抛运动模型求解炉料在料面的落点位置。Step7: According to the charge position

and speed

It is the initial motion state of the charge in the empty area of the furnace throat, and the position of the drop point of the charge on the material surface is solved according to the oblique throwing motion model of the charge in the empty area.

Step8: Determine whether i is greater than n, if it is greater, go to Step9; otherwise, go to Step3;

Step 9: Output the drop position of the charge on the blast furnace charge surface, and finish.

Referring to FIG. 8 , the blast furnace top charge trajectory modeling system proposed by the embodiment of the present invention includes:

The memory 10, the processor 20, and the computer program stored in the memory 10 and running on the processor 20, wherein, when the processor 20 executes the computer program, the steps of the method for modeling the motion trajectory of the blast furnace top charge proposed in this embodiment are implemented .

The specific working process and working principle of the blast furnace top charge motion trajectory modeling system in this embodiment may refer to the working process and working principle of the blast furnace top charge motion trajectory modeling method in this embodiment.

The above are only preferred embodiments of the present invention, and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims (9)

1. a blast furnace top charge trajectory modeling method, is characterized in that, described method comprises: Establish a static coordinate system that is stationary relative to the blast furnace and a dynamic coordinate system that rotates with the chute; According to the discharge mode of the charge at the unloading tank, a mathematical model of the discharge of the charge throttle valve is established; A free-fall mathematical model of the charge in the central throat is established, and the free-fall mathematical model is used to obtain the velocity and position in the static coordinate system at the moment before the charge and the chute collide; According to the collision restitution coefficient of the collision between the charge and the chute, establish a mathematical model of the initial movement of the charge on the chute after the collision between the charge and the chute, and the collision restitution coefficient includes a normal restitution coefficient and a radial restitution coefficient; According to the mathematical model of the initial movement of the charge on the chute after the collision between the charge and the chute, the mathematical model of the chute movement of the charge in the chute is established; According to the mathematical model of the chute movement, the mathematical model of the movement trajectory of the single particle charge from the throttle valve to the end of the chute is obtained, and then the mathematical model of the movement trajectory of the entire blast furnace top charge is obtained. 2. blast furnace top charge trajectory modeling method according to claim 1, is characterized in that, establishing the static coordinate system that is stationary relative to blast furnace and the moving coordinate system that rotates together with chute comprises: According to the right-hand rule, a static coordinate system that is stationary relative to the blast furnace is established, wherein the origin of the static coordinate system is the intersection between the horizontal connection line of the two implicated points of the chute and the central throat and the symmetry axis of the blast furnace; According to the right-hand rule, rotate the static coordinate system around two coordinate axes in the static coordinate system in turn to obtain a moving coordinate system that rotates with the chute; Solve the coordinate transformation matrix between the static coordinate system and the moving coordinate system. 3. blast furnace top charge motion trajectory modeling method according to claim 1, is characterized in that, establishing the free-fall mathematical model of charge at central throat comprises: Obtain the coordinates in the static coordinate system when the charge leaves the throttle valve according to the mathematical model of the discharge of the charge throttle valve; According to the coordinates in the static coordinate system when the charge leaves the throttle valve, a mathematical model of the free fall of the charge in the central throat is established, and the specific calculation formula of the mathematical model of the free fall of the charge in the central throat is:

Among them, r ₁ and v ₁ are the velocity and position in the static coordinate system at the moment before the charge and the chute collide, respectively, x ₀ , _{y 0} , and ha are the X-axis, y 0 , and ha respectively in the static coordinate system when the charge leaves the throttle valve. The coordinates of the Y-axis and Z-axis, hw is the distance from the end of the central throat to the contact point between the charge and the chute, v ₀ is the Z-axis _velocity when the charge leaves the throttle valve, g is the acceleration of gravity, and e is the tilting distance of the chute , β ₀ and γ ₀ are the horizontal rotation angle and inclination angle of the chute relative to the initial position when the charge collides with the chute, θ ₀ is the included angle between the charge and the axis of symmetry of the chute, and

R is the radius of the chute. 4. the method for modeling blast furnace top charge motion trajectory according to claim 1 and 3, is characterized in that, according to the collision recovery coefficient of the collision of charge and chute, establishes the initial movement mathematical model of charge on chute after charge and chute collide include: Transform the speed and position in the static coordinate system before the collision between the charge and the chute into the moving speed and moving position in the moving coordinate system; Obtain the normal phase vector of the collision point on the chute according to the moving position in the moving coordinate system at the moment before the charge and the chute collide; According to the moving speed in the moving coordinate system before the collision between the charge and the chute, obtain the incident velocity before the charge and the chute collide; Calculate the angle between the normal phase vector of the collision point on the chute and the incident velocity before the charge and the chute collide to obtain the first angle; According to the collision recovery coefficient and the first included angle when the charge collides with the chute, obtain the initial velocity constant of the charge moving on the chute after the collision with the chute; According to the initial velocity constant of the charge and the chute moving on the chute after the collision, the ejection velocity after the charge and the chute collide is calculated. 5. blast furnace top charge motion trajectory modeling method according to claim 4, is characterized in that, the concrete formula that calculates the ejection velocity after charge and chute collide is:

Among them, v′ ₁ is the incident velocity before the charge and the chute collide, v′ ₂ is the exit velocity after the charge and the chute collide, ||·|| represents the operation of taking the die length, and e _n is the normal direction when the charge and the chute collide coefficient of restitution, θ _int is the first angle, θ _out is the angle between the normal phase vector of the collision point on the chute and the exit velocity after the charge collides with the chute, and

n is the normal vector of the collision point on the chute. 6. blast furnace top charge motion trajectory modeling method according to claim 5, is characterized in that, according to the initial velocity constant of moving on chute after charge and chute collide, calculate the calculation formula of the ejection velocity after charge and chute collide for: v ₂ ′=av ₁ ′+bn, Among them, v′ ₁ is the incident velocity before the charge and the chute collide, v′ ₂ is the exit velocity after the charge and the chute collide, a and b are the initial velocity constants of the charge moving on the chute after the collision with the chute, and n is the velocity on the chute The normal vector of the collision point. 7. blast furnace top charge motion trajectory modeling method according to claim 6, is characterized in that, according to the initial movement mathematical model of charge on the chute after charge and chute collide, establishing the chute movement mathematical model of charge in the chute comprises : According to the mathematical model of the initial movement of the charge on the chute after the collision between the charge and the chute, the initial movement position and the initial movement speed of the charge on the chute are obtained; According to the initial motion position and initial motion speed of the charge on the chute, based on the compound motion of points, the relative motion and implicated motion of the charge relative to the chute are analyzed respectively, and then the absolute motion of the charge in the blast furnace is analyzed, and the charge is established according to Newton's second law. Mathematical model of the chute movement in the chute; According to the mathematical model of the chute movement, the movement speed and movement position of the charge from the throttle valve to the end of the chute are obtained. 8. The method for modeling the motion trajectory of blast furnace top charge according to claim 7, wherein, according to the chute motion mathematical model, after obtaining the end motion speed and end motion position of the charge from the throttle valve to the end of the chute. include: A mathematical model of the motion of the furnace throat empty area is established, wherein the calculation formula of the mathematical model of the furnace throat empty area motion is:

Among them, S _x , S _y and S _z represent the distance that the charge moves in the X-axis, Y-axis and Z-axis of the furnace throat empty area, t is the movement time of the charge from the end of the chute to the material surface, v _cx , v _cy , v _cz Respectively represent the moving speed of the charge leaving the end of the chute; According to the mathematical model of the motion of the furnace throat empty area, the position of the drop point of the charge is obtained, wherein the calculation formula of the drop position of the charge is:

Among them, r _xc , r _yc and r _zc respectively represent the moving position of the charge leaving the end of the chute. 9. A motion trajectory modeling system for a blast furnace top charge, the system comprising: A memory (10), a processor (20) and a computer program stored on the memory (10) and executable on the processor (20), characterized in that the processor (20) is implemented when the computer program is executed The steps of the method of any of the preceding claims 1 to 8.

Images