JP7183064B2 - Mold vibrating device, continuous casting slab manufacturing method, and mold vibrating method - Google Patents

Description

TECHNICAL FIELD The present disclosure relates to a mold vibrating device, a method for manufacturing a continuously cast slab, and a mold vibrating method.

Patent Literature 1 discloses a continuous casting facility that continuously casts slabs by pouring molten metal into a mold. A known technique for continuous casting is to add a lubricant (for example, mold powder) to the molten metal in the mold and to vibrate the mold vertically (in the casting direction). The vibration of the mold makes it easier for the lubricant to flow between the mold and the molten metal, thereby suppressing seizure between the mold and the slab. There is also known a technique for improving the stability of drawing a slab from a mold by causing the mold to vibrate in accordance with a non-sinusoidal waveform (for example, vibration in which the descending speed is faster than the ascending speed).

Japanese Patent Application Laid-Open No. 2003-211256

However, non-sinusoidal waves may be composed of multiple harmonic components. If this harmonic component resonates with the vibration mechanism that vibrates the mold, the mold cannot operate as desired. Therefore, in Patent Document 1, in order to eliminate the influence of the natural frequency of the vibration mechanism, feedback control is performed based on the state estimation amounts of the mold and the actuator. In order to observe the state estimator, it is necessary to construct a state observer (observer) and perform complex matrix arithmetic processing. A controller capable of such processing is generally expensive.

Therefore, the present disclosure describes a mold vibrating device, a continuously cast slab manufacturing method, and a mold vibrating method that can realize stable continuous casting of a slab with an extremely simple method.

Example 1. A mold vibrator according to one aspect of the present disclosure provides a predetermined non-sinusoidal target waveform for a mold configured to cool poured molten metal and continuously cast a billet. By correcting each of the plurality of sine wave components constituting the target waveform based on the vibration generator configured to generate vibration according to the vibration of the mold and the deformation of the vibration generator caused by the vibration of the mold, the plurality of a correcting unit configured to generate a corrected waveform; and a synthesizing unit configured to combine a plurality of corrected waveforms to generate one combined waveform and output a signal of the combined waveform to the vibration generator. Prepare. In this case, the correcting section obtains a plurality of corrected waveforms in which the deformation occurring in the vibration generator is preliminarily included. Therefore, when a composite waveform obtained by synthesizing the plurality of correction waveforms is output to the mold via the vibration generator, the composite waveform changes due to the deformation caused by the vibration generator, and the waveform after this change is Act on the mold. Therefore, ideal vibration can be generated in the mold without using the state estimator. As a result, stable continuous casting of slabs can be achieved by an extremely simple method.

Example 2. In the apparatus of Example 1, the correcting unit adjusts the plurality of correction waveforms so that each waveform after the amplitude and phase of each of the plurality of correction waveforms has changed due to deformation substantially matches the corresponding plurality of sinusoidal components. It may be configured to generate a correction waveform. In this case, when a composite waveform obtained by synthesizing the plurality of correction waveforms is output to the mold via the vibration generator, the composite waveform changes to a waveform equivalent to the target waveform under the influence of deformation by the vibration generator. Then, the waveform after this change acts on the mold. Therefore, it is possible to vibrate the mold more accurately.

Example 3. In the apparatus of Example 2, the amplitude and phase may be calculated based on the resonant angular frequency and damping constant of the vibration generator. In this case, the resonance angular frequency and the damping constant can be obtained relatively easily through experiments or the like. Therefore, it is possible to perform arithmetic processing by the correction unit more easily and at high speed.

Example 4. In the apparatus of any of Examples 1-3, the plurality of sinusoidal components may include two or three sinusoidal components. In this case, the number of components to be subjected to correction arithmetic processing by the correcting unit can be reduced. Therefore, it is possible to perform arithmetic processing by the correction unit more easily and at high speed.

Example 5. In the apparatus of any of Examples 1-4, each of the plurality of sinusoidal components may include angular frequencies that are integral multiples of the fundamental angular frequency and that are multiples that are different from each other.

Example 6. In the apparatus of any one of Examples 1 to 5, the vibration generator includes a linearly movable drive unit, and an arm supported by a rotation fulcrum and connected to different locations between the drive unit and the mold. may contain.

Example 7. According to another aspect of the present disclosure, there is provided a method for producing a continuously cast slab, in which vibration is generated in accordance with a predetermined non-sinusoidal target waveform in a mold by a vibration generator, and vibration is generated in accordance with the vibration of the mold. generating a plurality of corrected waveforms by respectively correcting a plurality of sine wave components forming the target waveform based on the deformation occurring in the machine; and generating a single composite waveform by synthesizing the plurality of corrected waveforms. and continuously casting a billet by pouring molten metal into the mold while vibrating the mold by outputting a composite waveform signal to a vibration generator. In this case, the same effect as in Example 1 is obtained.

Example 8. According to another aspect of the present disclosure, a method of oscillating a mold configured to cool poured molten metal to continuously cast billets is directed to a predetermined non-sinusoidal target waveform. When the corresponding vibration is generated by the vibration generator, the plurality of sine wave components constituting the target waveform are respectively corrected based on the deformation generated in the vibration generator due to the vibration of the mold, and the plurality of corrected waveforms are generated. synthesizing a plurality of correction waveforms to generate one synthesized waveform; and outputting a signal of the synthesized waveform to a vibration generator to vibrate the mold. In this case, the same effect as in Example 1 is obtained.

Advantageous Effects of Invention According to the mold vibrating device, the continuously cast slab manufacturing method, and the mold vibrating method according to the present disclosure, it is possible to achieve stable continuous casting of slabs by an extremely simple technique.

FIG. 1 is a side view schematically showing an example of continuous casting equipment. FIG. 2 is a side view showing an example of the mold vibrating device. FIG. 3 is a schematic diagram mainly showing the hardware configuration of the controller. FIG. 4 is a block diagram showing an example of a mold vibration device. FIG. 5 is a diagram showing examples of a target waveform, a plurality of sine wave components, and a plurality of correction waveforms. FIG. 6 is a diagram showing examples of a composite waveform, a plurality of distorted waveforms, and a vibration waveform, respectively. FIG. 7 is a diagram showing an example of a model of the vibration generator 110 and the mold 14. As shown in FIG. 8(a) shows an example of mold displacement when the entire drive arm is rigid, and FIGS. 8(b) and 8(c), respectively, where the drive arm is partially rigid. FIG. 8D is a diagram showing an example of displacement of the mold in this case, and FIG. 8D is a diagram showing an example of displacement of the mold when the drive arm is not rigid. FIG. 9(a) is a graph showing a piston rod position command and its actual position according to the example, and FIG. 9(b) is a graph showing a mold position command and its actual position according to the example. is. FIG. 10(a) is a graph showing a piston rod position command and its actual position according to a comparative example, and FIG. 10(b) is a graph showing a mold position command and its actual position according to a comparative example. is.

An example of an embodiment according to the present disclosure will be described below in more detail with reference to the drawings. In the following description, the same reference numerals will be used for the same elements or elements having the same functions, and redundant description will be omitted.

[Configuration of continuous casting equipment]
First, the configuration of the continuous casting facility 1 will be described. The continuous casting facility 1 includes a ladle 10, a tundish 12, a mold 14, a plurality of cast piece support rolls 16, and a mold vibration device 100, as shown in FIG.

The ladle 10 is a container in which molten metal (molten metal; molten steel) M is stored. A tundish 12 is arranged below the ladle 10 . The tundish 12 is configured to store the molten metal M flowing out from the outlet of the nozzle provided on the bottom wall of the ladle 10 .

A mold 14 is arranged below the tundish 12 . The mold 14 is configured to mold the molten metal M into a predetermined shape while cooling the molten metal M poured from a nozzle provided on the bottom wall of the tundish 12 . A plurality of cast piece support rolls 16 are arranged below the mold 14 . The plurality of slab support rolls 16 are configured to further cool the slab S pulled out from the mold 14 and convey it downstream.

The cast slab S immediately after being molded by the mold 14 includes a solidified shell S1 whose surface portion is solidified and an unsolidified portion S2 filled inside the solidified shell S1. The unsolidified portion S2 is molten metal in an unsolidified state and has fluidity. The cast slab S is cooled toward the downstream side, the unsolidified portion S2 gradually solidifies, and the solidified shell S1 grows. That is, as the solidified shell S1 grows, the unsolidified portion S2 shrinks and the thickness of the solidified shell S1 increases. The slab S is completely solidified before reaching the slab reduction device (not shown).

The mold vibrating device 100 is configured to vibrate the mold 14 according to a predetermined target waveform. The mold vibration device 100 includes a vibration generator 110, a sensor 120, a servo valve 130, and a controller 140 (control section), as shown in FIG.

Vibration generator 110 includes drive unit 111 and link mechanism 112 . Drive portion 111 includes a main body 113 and a piston rod 114 . The main body 113 is attached to the floor via a rotation fulcrum P1 and can swing around the rotation fulcrum P1. The piston rod 114 is slidably attached to the main body 113 . The drive unit 111 may be, for example, a hydraulic cylinder, an electric cylinder combining a ball screw and a servomotor, or a linear motor.

Link mechanism 112 includes base 115 , drive arm 116 (arm), and auxiliary arm 117 . The pedestal 115 is fixed with respect to the floor. The drive arm 116 is attached to the lower portion of the pedestal 115 via a rotation fulcrum P2 in the vicinity of its center. Therefore, the drive arm 116 can swing around the rotation fulcrum P2. One end of the drive arm 116 is attached to the tip of the piston rod 114 via a rotation fulcrum P3. The other end of the drive arm 116 is connected to the lower portion of the mold 14 via a rotation fulcrum P4. One end of the auxiliary arm 117 is attached to the upper part of the pedestal 115 via the rotation fulcrum P5. The other end of the auxiliary arm 117 is attached to the upper part of the mold 14 via the rotation fulcrum P6.

Since the driving portion 111 and the mold 14 are connected via the link mechanism 112, when the piston rod 114 advances outward, the driving arm 116 swings clockwise around the rotational fulcrum P2, thereby moving the mold. 14 moves downwards. On the other hand, when the piston rod 114 retreats toward the main body 113, the drive arm 116 swings counterclockwise around the rotation fulcrum P2, and the mold 14 moves upward. Therefore, the mold 14 vibrates up and down by repeating the advance and retreat of the piston rod 114 .

Sensor 120 is configured to detect the position of piston rod 114 relative to body 113 . Sensor 120 may be, for example, a linear encoder such as a rod sensor. Sensor 120 may be built in drive unit 111 . Data detected by sensor 120 is transmitted to controller 140 .

The servo valve 130 is configured to open and close the valve based on a control signal from the controller 140 to control the flow direction and flow rate of hydraulic oil to the main body 113 . When the servo valve 130 changes the flow direction of hydraulic oil, the movement direction of the piston rod 114 changes. When the servo valve 130 changes the flow rate of hydraulic oil, the moving speed of the piston rod 114 changes.

Controller 140 is configured to process data received from sensor 120 to control operation of servo valve 130 .

The hardware of the controller 140 is configured by, for example, one or more control computers. The controller 140 has, as a hardware configuration, for example, as shown in FIG. part). The controller Ctr may consist of electrical circuitry.

The processor Ctr1 cooperates with the memory Ctr2 to execute a program and input/output signals via the input port Ctr3 and the output port Ctr4, thereby configuring each functional module described later. That is, processor Ctr1 is configured to generate an output signal for driving servo valve 130 based on the input signal from sensor 120 . The memory Ctr2 is configured to store programs, input signals, output signals, and the like. Input port Ctr3 is configured to transmit an input signal from sensor 120 to processor Ctr1. Output port Ctr4 is configured to transmit the output signal generated by processor Ctr1 to servo valve 130 .

As shown in FIG. 4, the controller 140 includes, as functional modules, a target waveform setter 141, a fundamental wave generator 142, a compensator 143 (compensator), a synthesizer 144 (synthesizer), and a comparator. 145 and amplifier 146 . Note that these functional modules may be realized on software by a program, or may be realized by an electric circuit element (for example, a logic circuit) or an integrated circuit in which these are integrated.

The target waveform setter 141 is configured to set conditions of a predetermined target waveform W1 for vibrating the mold 14, for example, based on an input from an operator. The conditions for the target waveform W1 are output to the fundamental wave generator 142 . The target waveform W1 may be non-sinusoidal. The target waveform W1 may be, for example, a waveform that causes the mold 14 to vibrate such that the downward speed of the mold 14 is faster than the upward speed, as shown in FIG. 5(a). If the target waveform W1 is a non-sinusoidal wave, the conditions for the target waveform W1 may include, for example, amplitude and non-sine rate or distortion coefficient. In this specification, the non-sinusoidal rate refers to the ratio of the peak-to-trough variation time of a non-sinusoidal wave in a half cycle to the variation time of a non-sinusoidal wave in a half cycle. do. In this specification, the distortion coefficient refers to the ratio of the amplitude of cos2ωt to the amplitude of sinωt.

Fundamental wave generator ₁₄₂ generates a plurality of sine wave components W2 ₁ , W2 ₂ , . ) is configured to generate A plurality of generated sine wave components W2 ₁ , W2 ₂ , . . . , W2 _N are output to the corrector 143 . Of these, an arbitrary sine wave component W2 _n (where n is a natural number from 1 to N) is, for example, equal to the nth term (nth harmonic) when the target waveform W1 is expanded into a Fourier series. The number of sinusoidal components forming the target waveform W1 is not particularly limited, but may be, for example, two or three. FIG. 5(b) shows an example in which the target waveform W1 is decomposed into three sine wave components W2 ₁ , W2 ₂ and W2 ₃ .

The corrector 143 corrects the plurality of sine wave components W2 _{1 ,} W2 ₂ , . By doing so, a plurality of correction waveforms W3 ₁ , W3 ₂ , . . . , W3 _N are generated. The plurality _of correction waveforms W3 ₁ , W3 ₂ , .

By the way, when a composite waveform W4 of a plurality of correction waveforms W3 ₁ , _{W3 2} , . _{Therefore , a} plurality of distorted waveforms W5 ₁ , W5 ₂ , _. output to _{Therefore ,} the corrector 143 provides _a plurality of distortion waveforms W5 ₁ , W5 _{2 ,} . It may be configured to generate correction waveforms W3 ₁ , W3 ₂ , . . . , W3 _N. FIG. 5(c) shows an example of three corrected waveforms W3 ₁ , W3 ₂ and W3 ₃ in which the three sine wave components W2 ₁ , W2 ₂ and W2 ₃ are corrected in consideration of the deformation of the vibration generator 110. show. A more detailed correction calculation method will be described later.

The combiner 144 is configured to combine the plurality of corrected waveforms W3 ₁ , W3 ₂ , . . . , _W3N generated by the corrector 143 to generate one combined waveform W4. The generated composite waveform W4 is output to comparator 145 . The composite waveform W4 may be, for example, a sum of a plurality of corrected waveforms _{W3 1} , W3 ₂ , . . . , W3 _N (W4=W3 ₁ +W3 ₂ + . FIG. 6A shows an example of a synthesized waveform W4 obtained by synthesizing three correction waveforms W3 ₁ , W3 ₂ and W3 ₃ .

The comparator 145 is configured to calculate the deviation E between the current value (target value) X of the composite waveform W4 and the current value Y of the position of the piston rod 114 detected by the sensor 120 . That is, the comparator 145 calculates the deviation E by subtracting the current value Y from the target value X (E=XY). The calculated deviation E is output to amplifier 146 .

The amplifier 146 is configured to multiply the deviation E calculated by the comparator 145 by a predetermined proportional gain Kp to calculate the output value Q (Q=Kp×E). The output value Q calculated by amplifier 146 is output to servo valve 130 . The piston rod 114 of the drive unit 111 advances and retreats (elevates) by the servo valve 130 that operates based on the output value Q, and the mold 14 vibrates via the link mechanism 112 . _At this time, _as described _above , the plurality _of corrected waveforms W3 ₁ , W3 ₂ , . acts on mold 14 .

FIG. 6(b) shows an example of three distorted waveforms W5 ₁ , W5 ₂ and W5 ₃ after the three correction waveforms W3 ₁ , W3 ₂ and W3 ₃ are distorted through the link mechanism 112 . The three distorted waveforms W5 ₁ , W5 ₂ and W5 ₃ approximately match the three sine wave components W2 ₁ , W2 ₂ and W2 ₃ respectively. FIG. 6(c) shows an example of the vibration waveform W6 of the mold 14 when the composite wave of the three strain waveforms W5 ₁ , W5 ₂ and W5 ₃ acts on the mold 14 . This vibration waveform W6 substantially matches the target waveform W1.

[Correction calculation method]
(1) Modeling of Vibration Generator 110 and _Mold 14 A calculation method for obtaining a corrected waveform W3n such that the distorted waveform _W5n approximately matches the sine wave component _W2n will be described. For purposes of illustration, the vibration generator 110 and mold 14 are modeled as shown in FIG. Specifically, parameters L ₁ , L ₂ , A ₁ , A ₂ , and m ₂ are defined as follows. The portion of the drive arm 116 between the one end on the drive section 111 side (input side) and the rotation fulcrum P2 is called a "drive arm 116 ₁ ", and the other end on the mold 14 side (output side) and the rotation fulcrum P2. The portion of drive arm 116 between is referred to as "drive arm 116 ₂ ". Also, the upward direction in FIG. 7 is assumed to be positive.

L ₁ : Length of drive arm 116 ₁ [m]
L ₂ : Length of drive arm 116 ₂ [m]
A ₁ : Amplitude of piston rod 114 (one end of drive arm 116) [m]
A ₂ : Amplitude [m] of the mold 14 (the other end of the drive arm 116)
m ₂ : mass of mold 14

また、モールド１４の変位をｘ_２とするとｘ_１：Ｌ_１＝ｘ_２：Ｌ_２が成り立つので、変位ｘ_２について式２が得られる。なお、式２において、Ａ_２は変位ｘ_２の振幅である。

ここで、式２より、Ａ_２について式３が成り立つ。

(2) When the entire drive arm 116 is a rigid body First, it is assumed that the entire drive arm 116 is a rigid body and does not deform (see FIG. 8A). In this case, when a sinusoidal vibration is applied to one end of the drive arm 116 by the drive unit 111, the displacement _x1 of the one end is expressed by Equation (1). In Equation 1, the parameters ω, t, θ ₁ are
ω: Angular frequency [rad/sec]
t: time [sec]
θ ₁ : initial phase of displacement x ₁ [rad]
is.

Also, if the displacement of the mold 14 is _x2 , then _x1 : _L1 = _x2 : _L2 holds, so Equation ₂ is obtained for the displacement x2. Note that in Equation 2, _A2 is the amplitude of the displacement _x2 .

Here, from Equation 2, Equation 3 holds for _A2 .

ここで、ａ_２は、式２を２階微分することにより得られる（式５参照）。

式５を式４に代入すると、式６が得られる。

(3) When the drive arm _116-1 is not rigid Next, it is assumed that the drive arm _116-2 is rigid but flexible (is a leaf spring) instead of being rigid (FIG. 8 ₎ . (b)). In this case, the equation of motion of the drive arm 116 is represented by Equation 4. In Equation 4, the parameters k ₁ , c ₁ , a ₂ , a ₂₁ , v ₂₁ , x ₂₁ are
k ₁ : Spring constant of drive arm 116 ₁ [N/m]
c ₁ : damping coefficient of drive arm 116 ₁ [N·sec/m]
a ₂ : Acceleration [m/sec ² ] generated in the mold 14 by the operation of the drive unit 111
a ₂₁ : Acceleration generated in mold 14 due to deflection of drive arm 116 ₁ [m/sec ² ]
v ₂₁ : Velocity generated in mold 14 by deflection of drive arm 116 ₁ [m/sec]
x ₂₁ : Displacement [m] produced in mold 14 due to deflection of drive arm 116 ₁
is.

where a ₂ is obtained by second-order differentiation of Equation 2 (see Equation 5).

Substituting Equation 5 into Equation 4 yields Equation 6.

ただし、減衰定数ｈ_１は測定によって得られる値であり、共振角周波数ω_ｎ１及びパラメータＺ_１はそれぞれ式１０及び式１１にて定義される。

Formula 6 is one form of the equation of motion of forced vibration, and when enough time has passed (t→∞), the general solution of the equation of motion of forced vibration becomes equal to the special solution. Therefore, parameters A ₂₁ , φ ₁ , h ₁ , ω _n1 are respectively A ₂₁ : amplitude of displacement x ₂₁ [m]
φ ₁ : Lag phase of displacement x ₂₁ [rad]
h ₁ : damping constant (damping ratio)
ω _n1 : resonance angular frequency [rad/sec]
, the special solution of Equation 6 is expressed by Equation 7, the amplitude _A21 is expressed by Equation 8, and the lag phase _φ1 is expressed by Equation 9. However, θ ₂₁ =θ ₁ -φ ₁ is defined.

However, the damping constant _h1 is a value obtained by measurement, and the resonance angular frequency ω _n1 and the parameter _Z1 are defined by equations 10 and 11, respectively.

式５を式１２に代入すると、式１３が得られる。

(4) When the drive arm _116-2 is not rigid Next, it is assumed that the drive arm _116-1 is rigid but flexible (is a leaf spring) ( _FIG . 8). (c)). In this case, the equation of motion of the drive arm 116 is represented by Equation 12. In Equation 12, the parameters k ₂ , c ₂ , a ₂ , a ₂₂ , v ₂₂ , x ₂₂ are
k ₂ : Spring constant of drive arm 116 ₂ [N/m]
c ₂ : damping coefficient of drive arm 116 ₂ [N·sec/m]
a ₂ : Acceleration [m/sec ² ] generated in the mold 14 by the operation of the drive unit 111
a ₂₂ : Acceleration generated in mold 14 by deflection of drive arm 116 ₂ [m/sec ² ]
v ₂₂ : Velocity generated in mold 14 by deflection of drive arm 116 ₂ [m/sec]
x ₂₂ : Displacement [m] produced in mold 14 by deflection of drive arm 116 ₂
is.

Substituting Equation 5 into Equation 12 yields Equation 13.

ただし、減衰定数ｈ_２は測定によって得られる値であり、共振角周波数ω_ｎ２及びパラメータＺ_２はそれぞれ式１７及び式１８にて定義される。

Equation 13 is one form of the equation of motion of forced vibration, and when enough time has passed (t→∞), the general solution of the equation of motion of forced vibration becomes equal to the special solution. Therefore, the parameters A ₂₂ , φ ₂ , h ₂ , ω _n2 are respectively A ₂₂ : amplitude of displacement x ₂₂ [m]
φ ₂ : Lag phase of displacement x ₂₂ [rad]
h ₂ : damping constant (damping ratio)
ω _n2 : resonance angular frequency [rad/sec]
, the special solution of Eq _. 13 is expressed by Eq. 14, the amplitude A ₂₂ is expressed by Eq. However, θ ₂₂ =θ ₁ -φ ₂ is defined.

However, the damping constant _h2 is a value obtained by measurement, and the resonance angular frequency _ωn2 and the parameter _Z2 are defined by Equations 17 and 18, respectively.

(5) When both drive arms 116 ₁ and 116 ₂ are not rigid Next, let us consider the case where both drive arms 116 ₁ and 116 ₂ are not rigid (actual drive arm 116) (see FIG. 8(d)). . That is, assume that the entire drive arm 116 is a leaf spring. The actual displacement x ₀ of the mold 14 at this time is, as shown in Equation 19, the displacement x ₂ of the mold 14 when the drive arm 116 is not flexed and the displacement x 2 of the mold 14 when the drive arm 116 ₁ is flexed. It can be expressed by the superposition of the displacement _x21 and the displacement _x22 of the mold 14 when the drive arm 1162 is flexed _.

式１９に、式２、式７、式１４及び式２０を代入すると、式２１が得られる。

ここで、加法定理を用いて式２１の右辺を展開すると、式２２が得られる。

ただし、式２２において、パラメータａ，ｂは以下の式２３及び式２４とおりである。

If the amplitude of the displacement _x0 is _A0 and the initial phase of the displacement _x0 is _θ0 , then the displacement _x0 is given by Eq.

Substituting Equation 2, Equation 7, Equation 14 and Equation 20 into Equation 19 yields Equation 21.

Here, when the right side of Equation 21 is expanded using the addition theorem, Equation 22 is obtained.

However, in Equation 22, parameters a and b are as shown in Equations 23 and 24 below.

From Equations 23 and 24, A ₀ , sin θ ₀ and cos θ ₀ are represented by Equations 25 to 27, respectively.

式２８をＡ_１について解くと、式２９が得られる。

Substituting Equation 3, Equation 8, Equation 9, Equation 15 and Equation 16 into Equation 25 yields Equation 28.

Solving Equation 28 for A ₁ yields Equation 29.

式３０に式３、式８、式９、式１５及び式１６を代入して、θ_１について整理すると、式３１が得られる。

On the other hand, when the initial phase θ ₀ on the mold 14 side is used as a reference (θ ₀ =0), since sin θ ₀ =0, Equation 30 is obtained from Equation 27.

Equation 31 is obtained by substituting Equation 3, Equation 8, Equation 9, Equation 15 and Equation 16 into Equation 30 and arranging for θ ₁ .

By the way, in Equations 9, 11, 16 and 18, ω is the ideal frequency of vibration to be caused in the mold 14, and is determined by setting. In Equation 29, _A0 is the ideal vibration amplitude to be caused in the mold 14, and is determined by setting. Therefore, according to Equations 9, 11, 16, 18, 29, and 31, the unknowns included in A ₁ and θ ₁ are ω _n1 , ω _n2 , h ₁ , and h ₂ . . From the above, by substituting these variables ω _n1 , ω _n2 , h ₁ , h ₂ and the ideal vibration amplitude A ₀ and frequency ω to be caused in the mold 14 into the equations 29 and 31, , the amplitude A ₁ and the initial phase θ ₁ of the piston rod 114 for causing the mold 14 to ideally vibrate can be obtained.

(6) Method of Measuring Unknowns ω _n1 , ω _n2 , h ₁ , h ₂ The unknowns ω _n1 , ω _n2 may be measured, for example, as follows. First, the actual vibration generator 110 and the mold 14 are prepared. Next, an impulse signal is output from the controller 140 to the servo valve 130 while the vibration generator 110 and the mold 14 are stationary. That is, the piston rod 114 is moved with a predetermined stroke amount in a very short period of time. Next, the displacement caused in the mold 14 by the input of the impulse signal is measured. Next, the period of damped free vibration of the mold 14 is measured from the measured displacement of the mold 14 . As a result, the unknowns ω _n1 and ω _n2 are obtained. On the other hand, the unknowns h ₁ and h ₂ may be measured by various known methods such as the half width method, attenuation factor method, impedance method, and the like.

[Manufacturing method of slab]
Next, a method for manufacturing the slab S (method for vibrating the mold 14) will be described. First, the resonance angular frequency _ωn and the damping constant h of the vibration generator 110 and the mold 14 are measured in advance. Next, the operator inputs ideal vibration data to be generated in the mold 14 into the controller 140 . The target waveform setter 141 generates a target waveform W1 corresponding to the vibration based on the input and outputs the target waveform W1 to the fundamental wave generator 142 .

Next, the fundamental wave generator 142 decomposes the target waveform W1 into a plurality of sine wave components W2 ₁ , W2 ₂ , . . . , W2 _N . This gives the amplitude ⁿ A ₀ and the angular frequency ⁿ ω of any sinusoidal component W2 _n . The fundamental wave generator 142 outputs these sine wave components W2 ₁ , W2 ₂ , . . . , W2 _N to the corrector 143 . When the fundamental angular frequency is ω ₀ , the angular frequency ⁿ ω may be an integral multiple of the fundamental angular frequency ω ₀ as shown in Equation (32). The magnitude of the fundamental angular frequency ω ₀ may be set according to the actual machines of the vibration generator 110 and the mold 14 . For example, the value of ω ₀ /2π may be set to 6 Hz or less.

Next _, the corrector 143 calculates the sine wave components _{W2 1} , W2 ₂ , _. W2 ₂ , . . . , W2 _N are corrected to generate _a plurality of corrected waveforms W3 ₁ , W3 ₂ , . For example, the amplitude ⁿ A ₁ and the initial phase ⁿ θ ₁ of an arbitrary correction waveform W3 _n can be calculated from Equations 29 and 31, respectively. Therefore, the displacement ⁿ x ₁ of an arbitrary correction waveform W3 _n is obtained by Equation 33 by substituting the amplitude ⁿ A ₁ and the initial phase ⁿ θ ₁ into Equation 1. The corrector 143 outputs the generated plural corrected waveforms W3 ₁ , W3 ₂ , . . . , W3 _N to the synthesizer 144 .

Next, the synthesizer 144 synthesizes a plurality of correction waveforms W3 ₁ , W3 ₂ , . . . , W3 _N to generate one synthesized waveform W4. The displacement _x1 of the composite waveform W4 is expressed by Equation 34 using Equation 33.

The synthesized waveform W4 generated by the synthesizer 144 is output to the servo valve 130 after undergoing comparison processing by the comparator 145 and amplification processing by the amplifier 146 . As a result, the servo valve 130 operates the driving portion 111, and the link mechanism 112 is oscillated according to the composite waveform W4. In the course of the vibration propagating through the link mechanism 112, the combined waveform W4 is distorted due to the deformation of the drive arm 116, and vibration corresponding to the target waveform W1 is generated in the mold 14. FIG. When the molten metal M is poured from the tundish 12 into the vibrating mold 14 corresponding to the target waveform W1, the molten metal M is cooled by the mold 14 and formed into a predetermined shape. When the slab S pulled out from the mold 14 is further cooled and completely solidified, the slab S is completed.

[Action]
According to the above example _, the corrector 143 obtains a plurality of corrected waveforms W3 ₁ , W3 ₂ , . Therefore, when a composite waveform _W4 obtained by synthesizing these plurality of correction waveforms W3 ₁ , W3 ₂ , . The composite waveform W4 is affected by this change, and the waveform after this change (composite wave of a plurality of distorted waveforms W5 ₁ , W5 ₂ , . . . , _W5N ) acts on the mold 14 . Therefore, ideal vibration can be generated in the mold 14 without using the state estimator. As a result, it becomes possible to realize stable continuous casting of the slab S by an extremely simple method. Further, in this case, since the arithmetic processing by the corrector 143 is extremely simplified, it becomes possible to perform the arithmetic processing at low cost and at high speed using, for example, a commercially available controller.

According _to the above example, even if the angular frequencies ω of the plurality of correction waveforms W3 ₁ , W3 ₂ , . Abnormal vibration of the mold 14 can be suppressed.

According to the above example, the amplitude _A1 and the phase _θ1 are calculated based on the resonance angular frequencies _ωn1 , _ωn2 and the damping constants _h1 , _h2 of the vibration generator 110 (drive arm 116). The resonant angular frequencies ω _n1 , ω _n2 and the damping constants h ₁ , h ₂ can be obtained relatively easily through experiments or the like. Therefore, it becomes possible to perform arithmetic processing by the corrector 143 more easily and at high speed.

In the above example, the actual displacement _x0 of the mold 14 when both of the drive arms 116 ₁ and 116 ₂ are not rigid bodies was examined. A displacement X ₀ may be calculated. Examples of such other elements include a piston rod 114, a base 115, an auxiliary arm 117, and the like.

[Test results]
In order to confirm that the mold 14 vibrates according to the target waveform W1 when the mold 14 is vibrated using the vibration generator 110 and the mold 14 according to the above example, a test was conducted using an actual machine. (Example). Specifically, the waveform of the position command for the mold 14 (see the dashed line in FIG. 9B) was used as the target waveform W1, corrected by the corrector 143, the mold 14 was vibrated, and the change in the position of the mold 14 was measured. As a result, the actual position waveform of the mold 14 (see the solid line in FIG. 9B) vibrating according to the waveform corresponding to the composite waveform W4 (see the broken line in FIG. 9A) is the actual position command for the mold 14. It substantially coincided with the waveform (see the dashed line in FIG. 9(b)). Therefore, it was confirmed that the mold 14 vibrates according to the target waveform W1.

In this test, the resonance frequency ω _n /2π was 18.5 Hz and the damping constant h was 0.087. Further, in the fundamental wave generator 142, with a fundamental frequency of 370 cpm (cycles per minute), three frequencies of 370 cpm (≈6.17 Hz), 740 cpm (≈12.33 Hz) and 1110 cpm (=18.5 Hz) are generated. A sinusoidal component was generated from the target waveform W1.

On the other hand, a similar test was conducted without correction by the corrector 143 (comparative example). Specifically, by operating the piston rod 114 with a waveform (see the dashed line in FIG. 10(a)) obtained by inverting the waveform (see the dashed line in FIG. 10(b)) of the position command for the mold 14, the mold 14 was measured. As a result, the actual position waveform of the mold 14 (see the solid line in FIG. 10B) was greatly distorted and did not match the position command waveform of the mold 14 (see the broken line in FIG. 10B).

[Modification]
Although the embodiments according to the present disclosure have been described in detail above, various modifications may be made to the above embodiments without departing from the scope and spirit of the claims. For example, _the compensator 143 may provide a plurality of amplitudes and phases of the plurality of compensation waveforms W3 ₁ , W3 ₂ , . _The distorted _waveforms W5 _{1 , W5 2 , .} , . . . , W3 _N. In this case, when a composite waveform _W4 obtained by synthesizing a plurality of correction waveforms W3 ₁ , W3 ₂ , . In response, the composite waveform W4 changes to a waveform W6 equivalent to the target waveform W1, and the waveform W6 after this change acts on the mold 14. Therefore, it is possible to vibrate the mold 14 more accurately.

Fundamental generator 142 may be configured to decompose target waveform W1 into 2-5 sinusoidal components, and may be configured to decompose target waveform W1 into 2-3 sinusoidal components. may be In this case, the number of components to be subjected to correction arithmetic processing by the corrector 143 can be reduced. Therefore, it becomes possible to perform arithmetic processing by the corrector 143 more easily and at high speed.

The angular frequencies of the plurality of sine wave components W2 ₁ , _{W2 2} , .

In the above example, the drive unit 111 is connected to the mold 14 via the link mechanism 112, and the drive arm 116 swings according to the advance and retreat of the piston rod 114, thereby vibrating the mold 14 up and down. . However, the driving part 111 may be directly or indirectly connected to the mold 14 without the link mechanism 112 . In this case, the advancement and retraction of the piston rod 114 immediately causes the mold 14 to move up and down.

DESCRIPTION OF SYMBOLS 1... Continuous casting equipment 14... Mold, 100... Mold vibration apparatus, 110... Vibration generator, 111... Drive part, 112... Link mechanism, 116... Drive arm (arm), 120... Sensor, 130... Servo valve, 140 141 Target waveform setter 142 Fundamental wave generator 143 Corrector (corrector) 144 Synthesizer (synthesizer) M Molten metal P2 Rotation fulcrum S ... slab, W1 ... target waveform, W21 _{, W22} , ..., _W2N ... sine wave component _{, W31} , _W32 , ..., _W3N ... correction waveform, W4 ... composite waveform.

Claims (7)

A vibration generator configured to generate vibrations according to a predetermined non-sinusoidal target waveform in a mold configured to cool poured molten metal and continuously cast billets. machine and
a correction unit configured to generate a plurality of corrected waveforms by correcting a plurality of sine wave components constituting the target waveform based on the deformation of the vibration generator caused by the vibration of the mold; ,
a synthesizing unit configured to synthesize the plurality of correction waveforms to generate one synthesized waveform and output a signal of the synthesized waveform to the vibration generator ;
The correcting unit adjusts the plurality of corrected waveforms so that each waveform after the amplitude and phase of each of the plurality of corrected waveforms have changed due to the deformation substantially coincides with the corresponding plurality of sinusoidal wave components. A mold vibration device configured to generate a waveform . 2. The apparatus of claim 1 , wherein said amplitude and phase are calculated based on the resonant angular frequency and damping constant of said vibration generator. 3. The apparatus of claim 1 or 2 , wherein the plurality of sinusoidal components comprises two or three sinusoidal components. 4. The apparatus according to any one of claims 1 to 3 , wherein each of said plurality of sinusoidal components includes angular frequencies which are integral multiples of the fundamental angular frequency and which are multiples different from each other. The vibration generator is
a drive unit capable of linear motion;
5. The apparatus according to any one of claims 1 to 4 , comprising an arm supported by a rotational fulcrum and connected to the driving part and the mold at different points. When a vibration generator is used to generate a vibration corresponding to a predetermined non-sinusoidal target waveform in the mold, a plurality of the target waveforms are formed based on the deformation that occurs in the vibration generator due to the vibration of the mold. correcting each of the sinusoidal components of to generate a plurality of corrected waveforms;
synthesizing the plurality of correction waveforms to generate one synthesized waveform;
continuously casting a billet by pouring molten metal into the mold while vibrating the mold by outputting the composite waveform signal to the vibration generator ;
Generating the plurality of correction waveforms is performed so that each waveform after the amplitude and phase of each of the plurality of correction waveforms has changed due to the deformation substantially matches the corresponding plurality of sine wave components. 2. A method for producing a continuously cast slab, comprising generating the plurality of correction waveforms . When the vibration generator generates vibration according to a predetermined non-sinusoidal target waveform to the mold configured to cool the poured molten metal and continuously cast the steel billet, generating a plurality of corrected waveforms by respectively correcting a plurality of sine wave components constituting the target waveform based on the deformation of the vibration generator caused by the vibration of the mold;
synthesizing the plurality of correction waveforms to generate one synthesized waveform;
outputting the composite waveform signal to the vibration generator to vibrate the mold ;
Generating the plurality of correction waveforms is performed so that each waveform after the amplitude and phase of each of the plurality of correction waveforms has changed due to the deformation substantially matches the corresponding plurality of sine wave components. and generating said plurality of correction waveforms .

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