JPH10291068A - Method for restraining waving of liquid surface - Google Patents

Abstract

PROBLEM TO BE SOLVED: To simply restrain the vibration of liquid surface and to improve the accuracy of poured molten metal quantity and the molten metal pouring pattern by executing the modeling with double pendulum system while using a vessel and the liquid surface therein as each of the pendulums and calculating a vessel tilting angle of the still liquid surface from a vessel tilting angle speed and a liquid surface vibrating angle speed. SOLUTION: Molten metal is poured by tilting a ladle 3 through a servo motor 5, and after completing the pouring of molten metal, the ladle 3 is quickly turned back and stopped to tilt the ladle. By this method, the molten metal is vibrated in the ladle 3. The ladle tilting angle θ1 with an encorder 7 and the molten metal vibrating angle θ2 with a liquid surface range finder 6, are detected and fetched into a computer 8 for control. Therein, the modeling of the double pendulums is executed by using the ladle 3 as the fist pendulum and the molten metal surface 4 as the second pendulum. A servo system is constituted by executing a linear approximation of the double pendulums at the last target position of this ladle 3. Further, the ladle tilting angle speed and the molten metal surface vibrating angle speed are calculated from θ1 and θ2 , and the tilting angle of the first pendulum is calculated so as to still the second pendulum by executing the feedback, and the output voltage V of the servo motor 5 is obtd. based on this calculation to control the vibration of molten metal surface.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a technique for suppressing the waving of a liquid level generated in a liquid contained in a container when the container is tilted, and more particularly, to a technology for generating a ladle containing a molten metal during automatic pouring. This is a suitable technique for suppressing waves.

[0002]

2. Description of the Related Art In a ladle tilting type automatic pouring, when pouring of a predetermined weight is completed after pouring is completed, reversing is rapidly performed, and outflow of molten metal is completed during reversing. However, since the reversal is rapid, when the ladle is stopped after the reversal, the molten metal surface is waved by the reaction. If there is a ripple, when pouring with a short tact, the next pouring will be performed with the ripple. If pouring is started in the presence of undulations, the timing of hot water detection will vary due to the undulations,
It causes variation in pouring time. Also, the flow of the molten metal may be cut off due to the wave of the molten metal during the pouring, which may affect the quality of the cast product.

In order to solve the above-mentioned problem, Japanese Patent Laid-Open Publication No. Hei 6-19054 has a tilting shaft provided with a shaft for raising and lowering, and the tilting axis is moved up and down so that the tilting motion of the pouring ladle is substantially equal to that of the molten metal. There is disclosed a device which can be performed at the center of gravity and which realizes a pouring with less flow motion and less waving of molten metal when tilting forward and backward.

[0004]

Problems to be Solved by the Invention
In the method of (1), the configuration of the entire apparatus becomes complicated because it is necessary to add a rising axis to the tilt axis. In addition, complicated control for setting the center of the tilting movement at the center of the melt, such as raising and lowering movement control, tilt correction by raising and lowering, front and rear control, and responding to changes in the weight of the molten metal in the ladle, is required.

[0005]

SUMMARY OF THE INVENTION The present invention is a method for suppressing liquid surface waviness, which suppresses waviness of a liquid surface generated in a liquid contained in a container when the container is tilted by controlling the tilting operation of the container. Then, modeling is performed with a double pendulum using the container containing the liquid as the first pendulum and the liquid surface as the second pendulum, and a linear approximation of the double pendulum system is performed at the final target position of the container, and the servo system is constructed. Configure, calculate the vibration angle of the liquid level based on the tilt angle of the container and the height of the liquid level, calculate and add the container tilt angular velocity and the liquid level vibration angular velocity, and perform feedback, and perform the second pendulum. Calculate the tilt angle of the first pendulum to make it stand still,
It is characterized by suppressing the vibration of the liquid level in the container.

[0006]

FIG. 2 shows an example of the configuration of an apparatus for realizing the present invention. The tilting of the ladle 3 is controlled by the servomotor 5. Information on the ladle tilt angle θ ₁ and the molten metal surface vibration angle θ ₂ is taken into the control computer 8. The control computer 8 calculates a servo motor output voltage V to be output to the servo motor 5 based on the ladle tilt angle θ ₁ , the melt surface vibration angle θ _2, and the melt surface target angle θ _2r . Hereinafter, a method by which the control computer 8 calculates the servo motor output voltage V will be described.

The ladle 3 and the ripples in the ladle are shown in FIG.
Modeling is performed using a double pendulum. Ripple vibration is dominant in the lowest frequency component, and the other high frequency components are ignored because they are smaller than the whole wave. The first pendulum 1 is a ladle 3, and the second pendulum 2 is a molten metal surface 4. By controlling the first pendulum 1 by setting the state in which the second pendulum 2 swings to the state in which the melt surface is wavy, the second pendulum 2 is stopped at a vertical angle in FIG. This model is equivalent to damping the molten metal surface 4 in the actual ladle.

[0008] τ ₁ is the torque applied to the pendulum 1, θ ₁ is the ladle-shaped moving angle, θ ₂ is the vibration angle of the molten metal surface, the relative angle of the molten metal surface 4 from the ladle 3, and D is the angle of the first pendulum 1. The length and L are the length of the second pendulum 2, m ₁ is the weight of the entire ladle 3, and m ₂ is the equivalent mass of vibration of the molten metal surface 4. D is when operating a theta _1, determined as the size of the molten metal surface vibration angle theta ₂ which occurs to the actual device of FIG. 2 matches the measured values. For example, when θ ₂ is smaller than the actually measured value, D is increased to increase the generation of waves. Conversely, if the measured value is large, D is decreased. L is adjusted so that the cycle of the melt surface vibration angle θ ₂ matches the generation cycle of the actual apparatus in FIG. For example, if the period of the actual measurement value is large, L is increased, and if it is small, L is decreased. The system shown in FIG. 3 is solved using Lagrange's equation of motion, and the viscosity term is added. D gm ₁ sin (θ ₁ ) + gm ₂ {D sin (θ ₁ ) + L sin (θ ₁ + θ ₂ )} + D ² m ₁ θ ₁ ⁽²⁾ + m ₂ {−2 DL sin (θ ₂ ) θ ₁ ⁽¹⁾ θ ₂ ⁽¹⁾ −DL sin (θ ₂ ) θ ₂ ^{(1) 2} + D ² θ ₁ ⁽²⁾ + L ² θ ₁ ⁽²⁾ +2 DL cos (θ ₂ ⁽¹⁾ ) θ ₁ ⁽¹⁾ + L ² θ ₂ + DL cos (θ ₂ ) θ ₂ } + μ ₁ θ ₁ = τ ₁ ............ Equation 1 L m ₂ {g sin (θ ₁ + θ ₂ ) + D sin (θ ₂ ) + D sin (θ ₂ ) θ ₁ ^{(1) 2} + Lθ ₁ ⁽²⁾ + D cos (θ ₂ ) θ ₁ ⁽²⁾ + Lθ ₂ ⁽²⁾ } + μ ₂ (θ ₁ ^{(1 )} + θ ₂ ⁽¹⁾ ) = 0 Equation 2 Note that the number in parentheses such as θ ₁ ⁽²⁾ is the angle θ _{1 of the} pendulum ₁
Represents the second derivative with respect to time. Hereinafter, the differentiation will be expressed in this manner. Assuming that the target stop position of the ladle 3 corresponding to the first pendulum 1 is θ _1r , the target stop position of the second pendulum 2 is θ _2r = −θ _1r . θ _1r is the angle at which the ladle is to be finally stopped. Θ _2r becomes the target angle of θ ₂ .

[0009] Number 1, with respect to the number 2, to linearize the trigonometric function about the angle theta ₁₀ and theta ₂ of an angle theta ₂₀ with theta _1. Usually θ ₁₀ θ ₂₀ to θ _1r is to θ _2r. Further, when the square terms are ignored and a linear approximation is performed to represent a matrix, Equation 3 is obtained. ^{V x (1) = A x} + b u + q ...... number 3 except _{x = {θ 1 θ 2 θ} 1 θ 2} T = {x 1 x 2 x 3
x ₄ ｝ ^T Here, when a character is underlined, it represents a vector. Hereinafter, the vector will be expressed in this manner.
T represents transposition. Also, θ ₁₀ = x ₂₀ , θ
₂₀ = a x _20, u = τ _1. Here, V, A, b , and q are represented as follows. Multiplying from the left with V ^-1 to the number 3 on both sides ^{x (1) = V -1 A} x + V -1 b u + V -1 q Furthermore s = -A ^-1 q Distant converts the following Expression 4 and variables. z = x − s Equation 4 From this, the following equation is obtained. ^{z (1) = V -1 A} z + V -1 b u summarized this becomes as follows. z ⁽¹⁾ = A ^* z + b ^* u Here, s is represented by the following. In the case of the device shown in FIG.
Corresponding to theta _1, theta ₂ is theta ₁ shown in FIG. 7, a theta _2,
The number used in the calculation by the control computer 8 uses z converted by equation (4). For Figure 7, the counterclockwise is positive, theta ₁ because they relate to the vertical line is negative.

The target of the control is to quickly suppress the angle θ ₂ of the molten metal surface 4 to the target angle θ _2r . Since the variable conversion represented by Equation 4 is performed, in the calculation by the control computer 8, z _2r = θ _2r -θ ₂₀ -tan with respect to z ₂ described later.
Servo control is performed with the target of (θ ₁₀ ) = θ _2r -x ₂₀ + tan (x ₁₀ ). That z _2r = theta become _{2r -x 20 + tan (x 10} ) as a target value of z _2. The placing and _{^{e (1) = z 2r -z}} 2. u = - perform f ^T z + he and feedback, so that the number of 5 to constitute a type 1 servo system.

(Equation 5) However _{f = [f 1 f 2 f} 3 f 4] T Distant, f and h is the feedback factor. here far. So as to stabilize the A ^~, by adjusting the f and h, z ₂ converges to z _2r is the target. Therefore, the actual melt surface vibration angle θ _{2 in} FIG. 2 is θ _2r and the ladle tilt angle θ ₁ is θ
Converge to _1r

FIG. 1 is a block diagram showing an algorithm calculated by the control computer 8 described above. FIG.
The calculation shown in FIG. 1 is performed in the square box 10 in the control computer 8 in the step (1). Ladle tilt angle θ in FIG.
₁ is calculated by converting to z ₁ , and the molten surface vibration angle θ ₂ is converted to z ₂ for calculation. The converted melt surface vibration angle z ₂ and the converted ladle tilt angle z ₁ are measured by a distance meter 6 from the melt surface 4 and an encoder 7 attached to the servomotor 5. By differentiating z ₁ and z ₂ , a converted molten metal surface angular velocity z ₄ and a converted ladle tilt angular velocity z ₃ are calculated. E is the integral of the difference between z _2r and z ₂
Also calculate. U is calculated using f and h calculated in advance so as to stabilize Equation 5, and the target ladle angle is set to z _h3 by the ladle target tilt angular acceleration z ₃ ⁽¹⁾ (i + 1) at the next time. (I + 1) = z ₃ (i) + z ₃ ⁽¹⁾ (i + 1) T... _Equation 6 z _h1 (i + 1) = z ₁ (i) + z _h3 (i + 1) T... Here, T is the sampling time of the control computer 8. The calculated z _h1 (i + 1) is targeted. V = KK (Σ (z _h1 (i + 1) −z ₁ ) + KI (z _h1 (i + 1) −z ₁ )) (8) The servo motor output voltage V to be output to the servo motor 5 by the equation (8) calculate. Here, V is the output voltage, and KK and KI are feedback parameters for calculating the voltage.

[0012]

EXAMPLE The result of an experiment using water with the apparatus configuration shown in FIG. 2 will be described. An ultrasonic sensor was used as a distance meter for measuring the distance from the water surface. Based on the measured distance from the water surface and the ladle tilt angle, the water surface angle, the water surface angular velocity, and the ladle tilt angular velocity are calculated. Based on this, the torque is calculated, the ladle angular acceleration is calculated from Equation 5, the target ladle tilt angle is calculated from Equations 6 and 7, and finally the servo motor 5 is calculated using Equation 8. Calculate and output the output voltage. By repeating the above, ripples are suppressed.

Using the distance meter 6 in FIG.
The calculation method to ₂ is described. Since the rotation is based on the positive direction in the counterclockwise direction and the lower side of the vertical line, in FIG.
Is negative. The distance meter 6 is tilted by the angle δ, and the difference L2 between the distance when the molten metal surface vibration angle at the ladle tilt angle θ ₁ measured in advance is horizontal and the actually measured value is calculated. The height h of the water surface is calculated from L2. Further calculating a theta ₂ by ^{_{θ 2 = tan -1 (2h /}} W) + π / 2-θ 1. The reason why π / 2 is added here is that when the pendulum is stationary, the string of the weight is vertical, but the water surface is horizontal, so correction by π / 2 is necessary. The output voltage V is further converted into z , and the output voltage V is calculated by the control computer 8.

The results of an experiment using water are shown. FIG.
Shows the tilting pattern of the ladle 3 before the reversal. The time at which the inversion is completed is set to 0. The tilting is started from the time of −28 seconds and water is injected. Inversion is performed rapidly at a time of −2.5 seconds, and the injection is terminated. FIG. 5 shows the state of vibration of the water surface when it stops after tilting in the pattern shown in FIG. Even after 10 seconds or more, the wave does not attenuate and continues to vibrate at an amplitude of about 0.8 ° C.

For this system, using an ultrasonic sensor,
Fig. 6 shows the result of feedback control of the water level.
Shown in The ladle 3 was controlled from time 0 shown in FIG. The value at time 0 is the target stop angle of the ladle, and is also the center of linearization. Time 0
If the control is started earlier, it will deviate from the center of linearization, so the control is started at time 0. The parameters of the apparatus used in the experiment were D = 0.612 and L = 0.1643. The coefficients used for the feedback are: f ₁ = 31969.8, f ₂ = −8099.75, f ₃ =
−2369.72 f ₄ = −8547.85, h = −97253.4. Ladle 3 tilts slightly after the water surface wave, and the water surface wave is decreasing.

Further, f and h need to be changed according to the target angle θ _{1r of the} ladle. It is because the actual ladle tilting angle theta ₁ with the center theta ₁₀ in which the linearization come displaced, because the parameters of the 2 centroid pendulum model comes shifted. Actually, f and h are calculated in advance based on the value of θ _1r and stored in the control computer 8. Control computer 8
_Are feedback parameters f and h according to the value of θ _1r
Change the value of.

[0017]

According to the present invention, when pouring with a short tact time, the influence of the wave caused by the last pouring can be eliminated, which is effective in improving the pouring accuracy and the pouring pattern.

[Brief description of the drawings]

FIG. 1 is a control block diagram.

FIG. 2 Example of device configuration

FIG. 3 is a double pendulum model

FIG. 4 Ladle reversal explanatory diagram

FIG. 5 without control

FIG. 6 When controlled

FIG. 7 is an explanatory diagram of angle calculation.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Pendulum 1 2 Pendulum 2 3 Ladle 4 Melt surface 8 Control computer

Claims (1)

[Claims] A method for suppressing waviness of a liquid surface generated in a liquid contained in a container when the container is tilted by controlling the tilting operation of the container, comprising: The first pendulum and the liquid surface are modeled with a double pendulum as the second pendulum, and a servo system is constructed by performing linear approximation of the double pendulum system at the final target position of the container. Calculate the vibration angle of the liquid surface based on the height of the liquid surface, calculate and add the container tilt angular velocity and the liquid surface vibration angular velocity, and perform feedback, and make the first pendulum to stop the second pendulum A liquid surface waving suppressing method characterized by calculating a tilt angle of a liquid and suppressing vibration of a liquid surface in a container.