Through the analysis and research of the friction force and friction work between the mold copper plate and the billet shell during the production process of the continuous casting machine, the mathematical model is obtained, and the bonding and crack leakage are predicted based on the changes in its characteristic values.
Keywords: continuous casting mold; friction force; friction work
Introduction
During the continuous casting production process, friction is generated due to relative motion between the solidified billet shell that is constantly moving downward and the copper plates of the mold that are vibrating up and down (hereinafter referred to as mold friction). The information source of mold friction can directly reflect the interaction between the billet shell and the mold copper plate during the continuous casting process. Once defects such as cracks and bonding are formed on the surface of the shell, the friction of the mold will change significantly. This paper focuses on determining the mold friction by detecting the pressure of the hydraulic servo cylinder and related motion parameters, and using the changing characteristics of the mold friction information source before the breakout to predict the breakout.
Calculation method of crystallizer friction force
The mold vibration table of the hydraulic servo vibration slab continuous casting machine of Steel Plant A is shown in Figure 1. The mold vibration system is a leaf spring vibration damping hydraulic servo vibration system. The synchronous control model is:
The vibration amplitude of the crystallizer is:
A=C₁+C₂Vc; Am=±9.5mm (1)
The crystallizer vibration frequency is:
f=C₃+C₄Ve (2)
The crystallizer vibration equation is:
y=A · sin2π/i (3)
Figure 1 Crystallizer hydraulic servo vibrating table of slab continuous casting machine
Crystallizer acceleration: a≤5m/s²
In the formula: A——the amplitude of the crystallizer, mm;
a——Acceleration of the crystallizer, m/s²;
C1——Amplitude when the pulling speed is zero, mm;
C2——Amplitude pulling speed coefficient, mm/m/min, C2>0;
C3——frequency when the pulling speed is zero, Hz;
C4——frequency pulling speed coefficient, mm/m/min, C4<0;
VC——casting machine casting speed, m/min.
Mathematical model of crystallizer friction
Each stream of the slab continuous casting machine in Steel Plant A has 2 mold hydraulic servo vibrating tables, 2 hydraulic servo cylinders (1 for each vibrating table), and 16 guide leaf springs (8 for each vibrating table). The hydraulic The servo vibration principle is shown in Figure 2. Install pressure sensors in the rodless cavity and rod cavity of the hydraulic servo cylinder respectively to measure the pressure P₁ of the rodless cavity and the pressure P₂ of the rod cavity at any time, the piston area A: through the rodless cavity and the piston of the rod cavity. The area A₂ can determine the external load force of the hydraulic servo cylinder piston rod at any time:
Fy=A₁P₁-A₂P₂(4)
Figure 2 Principle of hydraulic vibration system
A displacement sensor is installed on the piston rod to measure the stroke y of the piston. The mold friction force is determined using the detected piston rod load force and piston stroke. The hydraulic servo cylinder achieves sinusoidal vibration, and its movement pattern in the y direction is:
y=A · sin 2mfv ·t (5)
In the formula: y——displacement of the crystallizer of the hydraulic servo vibration system, mm;
A——The amplitude of the crystallizer of the hydraulic servo vibration system, mm;
f——Frequency of crystallizer vibration of hydraulic servo vibration system, Hz.
The change of each force with stroke in the mold hydraulic servo vibration system is shown in Figure 3. Then the motion equation of the system in the y direction is:
In the formula: M – equivalent load mass of the mold hydraulic servo vibration system, kg;
r—— viscous damping coefficient of the mold hydraulic servo vibration system, (N·S)/m;
h——Elastic coefficient of mold hydraulic servo vibration system, N/m;
g——gravitational acceleration, 9.8m/s²;
f——friction force, N.
Figure 3 The relationship between force and stroke during the vibration process of the mold hydraulic servo vibration system
In engineering applications, a mathematical model of the crystallizer friction force is established through numerical solutions of equations (4), (5), and (6). Through the data acquisition device, the rodless cavity pressure P₁ and rod cavity pressure P₂ of the hydraulic servo cylinder and the piston stroke y are obtained, and input into the mold friction mathematical model control system, the mold friction force f” at any time can be determined.
Determination of friction force and friction work of hydraulic servo vibrating mold
Pressure sensors are installed in the upper and lower chambers of the two hydraulic cylinders of the crystallizer hydraulic servo vibration system, and displacement sensors are installed on the piston rods. The friction force and friction work of the crystallizer at any time can be obtained. For this purpose, two different working states must be distinguished, namely hot and cold. The hot state refers to the vibration state of the crystallizer during normal casting; the cold state refers to the vibration state of the crystallizer when it is not casting, and its vibration parameters are the same as those in the hot state. Figure 4 shows the displacement time images of the hot and cold states, and Figure 5 shows the force and time images of the hot and cold states.
In the above image, curve a represents the hot state force, curve b represents the cold state force, and the difference between the hot state force and the cold state force represents the crystallizer at any time.
Friction (c curve). Its expression is:
f=F₁(t)-F₂(t) (7)
In the formula: F₁(t)——Thermal force at any time, N;
F₂(t)——cold force at any time, N;
f——Mold friction force at any time, N.
Figure 4 Displacement time images of hot and cold states
Figure 5 Hot and cold state force and time images
Figure 6 Hot and cold force and displacement images
Through the mold friction force and displacement image (as shown in Figure 6), the mold friction work at any time can be calculated as:
Conclusion
(1) Under normal working conditions of the crystallizer vibration table, the friction force and friction work at any time can be obtained through the pressure sensors and displacement sensors in the two chambers of the hydraulic cylinder, and the melting effect of the mold slag can be determined by online monitoring of their characteristic changes. , the air gap between the billet shell and the mold copper plate, the surface quality of the billet shell and prediction of related types of steel breakouts.
(2)Exploring the characteristic changes of friction force and friction work in the interaction between the mold copper plate and the billet shell, this information source predicts bonding and crack leakage. It is of great significance to reduce omissions and false alarms, improve slab surface quality, and increase the production capacity of continuous casting machines.
