Method for operating continuous casting machine

Abstract

A primary object of this invention is to provide a method for operating a continuous casting machine with which a mold can oscillate with a predetermined oscillation waveform since the start of operation of an oscillator. This invention is a method for operating a continuous casting machine, the method comprising: withdrawing a slab from a mold while vertically oscillating the mold with an oscillation waveform represented by the following formula (1) by selecting a value of according to a value of b so that the following formula (1) satisfies r(0)=0:
r(t)=(S/2){sin(t+)+b cos 2(t+)+b}(1)
where r(t): displacement of the mold (mm), S: vibration stroke of the mold S (mm), : angular velocity (=2f) (rad/s), f: oscillation frequency of the mold (Hz), t: time(s), : initial phase (), and b: non-sine coefficient (0<b0.25).

Claims

1. A method for operating a continuous casting machine where a slab is withdrawn from a mold for continuous casting while the mold is oscillated in a vertical direction, the method comprising: oscillating the mold so as to satisfy the following formula (2) with an oscillation waveform represented by the following formula (1): $\begin{array}{cc}\left[\mathrm{Math}.1\right]& \\ r\left(t\right)=\left(S/2\right)\left\{\sin \left(t+\right)+b\cos 2\left(t+\right)+b\right\}& \left(1\right)\\ ={\tan }^{-1}\left\{\frac{1}{\sqrt{2}}\sqrt{\left(1+16b^2\right)-1}\right\}& \left(2\right)\end{array}$ wherein r(t) is displacement of the mold (mm), S is an oscillation stroke of the mold (mm), is angular velocity (=2f) (rad/s), f is oscillation frequency of the mold (Hz), t is time(s), is the initial phase (rad), and b is a non-sine coefficient (0<b0.25).

2. The method for operating a continuous casting machine according to claim 1, wherein 0.15b.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) FIG. 1 is a cross sectional view showing an example of the structure of a continuous casting machine to which the operation method of this invention can be applied.

(2) FIG. 2 shows oscillation waveforms when b=0.40 and =33.66 (oscillation waveforms of Reference Example).

(3) FIG. 3 shows oscillation waveforms when b=0.15 and =16.08 in this invention.

(4) FIG. 4 shows oscillation waveforms when b=0.20 and =20.535 in this invention.

(5) FIG. 5 shows oscillation waveforms when b=0.25 and =24.46 in this invention.

(6) FIG. 6 shows the maximum frictional force per oscillation waveform.

DESCRIPTION OF EMBODIMENTS

(7) FIG. 1 is a cross sectional view showing an example of the structure of a continuous casting machine to which the operation method of this invention can be applied. A tundish 1 is stocked with molten steel 6 supplied from a ladle not shown. A tubular mold 3 having an opening at each top and bottom thereof is arranged below the tundish 1. The molten steel 6 is poured from the tundish 1 via the immerged nozzle 2 into the mold 3 through the opening at the top of the mold 3.

(8) An oscillator 20 is connected to the mold 3. The oscillator 20 is electro-hydraulic, and can vertically oscillate the mold 3. The oscillator 20 includes a controlling part. Parameters of waveforms can be inputted to the controlling part. The oscillator 20 can generate oscillation having various waveforms based on inputted parameters. Oscillation having a waveform generated by the way described above is applied to the mold 3 during continuous casting.

(9) Powder is put into the molten steel 6 in the mold 3. Powder melts with heat of the molten steel 6, to become molten powder, and spreads over the surface of the molten steel 6 in the mold 3. In the molten steel 6, a contact portion with or a portion in the vicinity of a part facing the mold 3 are cooled, solidified, to be a tubular solidified shell 7. The molten powder is supplied to a space between the mold 3 and the solidified shell 7. Whereby, frictional force between the mold 3 and the solidified shell 7 is decreased.

(10) The inside of the solidified shell 7 is filled with the molten steel 6. The molten steel 6 is not completely solidified by passing through the mold 3, to be an unsolidified slab including an unsolidified part. The unsolidified slab is cooled by cooling water jetted out of secondary cooling spray nozzles arranged below the mold 3, which are not shown. Whereby, the solidified shell 7 enlarges.

(11) As being supported by foot rolls 4 arranged right under the mold 3 and plural of roller aprons 5 arranged in the downstream side of the foot rolls 4 in the direction where the unsolidified slab travels (hereinafter just referred to as downstream side), the unsolidified slab is withdrawn by pinch rolls 8 arranged in the downstream side of the roller aprons 5. The unsolidified slab is reduced by reduction rolls 9 arranged in the downstream side of the pinch rolls 8, to be a slab that does not substantially contain any unsolidified part.

(12) As described above, in the method for operating a continuous casting machine of this invention, the mold oscillates with the oscillation waveform represented by the formula (1). While the waveform of the formula (X) in the prior art is a composite waveform that is the combination of only sine waves of different cycles, the waveform of the formula (1) is a composite waveform of a sine wave and a cosine wave. Further, the formula (1) is significantly different from the formula (X) in introduction of the initial phase and r(0)=0.

(13) In the formula (1), let =0. The displacement of the mold r(t) is the maximum value (S/2) when t=/2, and is the minimum value (S/2) when t=/2. The maximum value and the minimum value of the displacement of the mold r(t) do not depend on the initial phase . Thus, a neutral position does not shift in the oscillation waveform represented by the formula (1). Therefore, poor lubrication and involvement of powder into the molten steel can be prevented not only in vertical type continuous casting but also curved type continuous casting.

(14) The formula (3) below has to be satisfied in order for the displacement of the mold to be 0 when the time t=0. The formula (3) below is obtained by substituting 0 for t, to be r(0)=0 in the formula (1):
0=sin +b cos 2+b(3)

(15) Using the formula of a trigonometric function, cos 2=12 sin.sup.2 , the formula (3) can be rewritten into the formula (4) below:
2b sin.sup.2 sin 2b=0 (b>0)(4)

(16) Since |sin |1, the following formula (5) is obtained if sin is made to be the subject of the formula (4):
sin ={1(1+16b.sup.2).sup.1/2}/4b(5)

(17) If is made to be the subject of the formula (5) using the formulae of a trigonometric function, tan =sin /cos and cos =(1sin.sup.2 ).sup.1/2, the above formula (2) is obtained.

(18) That is, satisfaction of the formula (2) makes the displacement of the mold r(0) 0 when the time t=0. Therefore, it becomes possible to oscillate the mold with a predetermined oscillation waveform since the start of operation of the oscillator that oscillates the mold, and to well seal the opening of the mold with a dummy bar.

(19) Two values of are determined by the formula (2). If a direction of the movement of the mold at the start of oscillation is upward, that satisfies cos >0 may be employed since dr(0)/dt>0.

(20) A non-sine coefficient b is any value within the range of 0<b0.25.

(21) b is a coefficient of cos 2(t+) in the term of b cos 2(t+), and determines magnitude of the term of b cos 2(t+) to the term of sin(t+). In a case of 0.25<b, the term of b cos 2(t+) is too large compared to the term of sin(t+), which arises a problem that the mold descends when t+=(+2n) (n is 0 or a positive integer), where the mold should ascend most. Thus, b0.25. For your reference, FIG. 2 shows the waveforms when b=0.4 and the initial phase =33.66. As shown in FIG. 2, in the case of b=0.4 that satisfies 0.25<b, the mold descends when t+=(+2n) (n is 0 or a positive integer), where the mold should ascend most. Therefore, in this invention, b0.25.

(22) On the other hand, when b is 0, the waveform of the displacement of the mold r(t) shows simple harmonic motion. In this case, compared with the case of 0<b, the inflow of the molten powder into a space between the mold and the solidified shell cannot be increased. Thus, in this invention, 0<b. Preferably 0.15b in this invention in order to increase the inflow of the molten powder enough compared with the case of the simple harmonic motion.

(23) Table 1 shows values of the initial phase determined by the formula (2) in each case where the non-sine coefficient b is 0.15, 0.20 and 0.25. It makes r(0)=0 possible that a value of the initial phase that satisfies the formula (2) is employed according to a value of the non-sine coefficient b.

(24) TABLE-US-00001 TABLE 1 Non-sine Coefficient (b) 0.15 0.20 0.25 Initial Phase () 16.08 20.535 24.46

(25) FIGS. 3 to 5 show waveforms based on the formula (1) (relation between the time t and the displacement of the mold r(t)) when the combination shown in Table 1, that is, (b=0.15, =16.08), (b=0.20, =20.535), (b=0.25, =24.46) are employed as values of the non-sine coefficient b and the initial phase .

(26) In FIGS. 3 to 5, the part of sin(t+) in the formula (1) is shown as a primary waveform, the part of b cos 2(t+) therein is shown as a secondary waveform, and r(t) therein is shown as a composite waveform, where S=4 mm and =2rad/s.

(27) In each composite waveform shown in FIGS. 3 to 5, change in movement speed in the vicinity of the maximum displacement (peak) is small, and that in the vicinity of the minimum displacement (bottom) is large compared to the case where an oscillation waveform is a sine wave. As the non-sine coefficient b is larger, time when the change in movement speed in the vicinity of the maximum displacement is small is longer. The movement speed of the mold (ascending speed and descending speed) is fast during the time between the vicinity of the minimum displacement and the vicinity of the maximum displacement, compared to the case where an oscillation waveform is a sine wave.

(28) The fast descending speed of the mold makes the amount of the molten powder that is pushed (pumped) into a space between the mold and the solidified shell increase. The fast ascending speed of the mold makes the powder possible to reach closer area to the inner wall surface of the mold (makes it possible to broaden the flow path of the powder). The long time when change in the movement speed of the mold in the vicinity of the maximum displacement is small makes it possible to keep the state where the flow path of the powder broadens long. Therefore, the lubricity between the mold and the solidified shell can be improved by vertical oscillation of the mold with any composite waveform shown in FIGS. 3 to 5.

(29) The displacement of the mold in the case of t=0 is at the middle position between the maximum displacement (2 mm) and the minimum displacement (2 mm), that is, at a neutral position in every composite waveform shown in FIGS. 3 to 5. Whereby, troubles at the initial stage of casting such as seal leakage can be prevented. The neutral position does not shift. So, the effect of suppressing poor lubrication in the mold and involvement of the powder into the molten steel can be stably brought about.

(30) While the lubricity between the mold and the solidified shell can be more improved as the non-sine coefficient b is larger, some kinds of physical properties of the powder cause the molten powder to be easily involved into the molten steel. In view of the above, preferably, a proper value of the non-sine coefficient b is employed according to physical properties of powder, or powder of proper physical properties is employed correspondingly to the value of the non-sine coefficient b. For example, when the value of the non-sine coefficient b is large, involvement of the molten powder into the molten steel can be suppressed efficiently if powder of a high solidification point, and in a molten state, of high viscosity is employed.

(31) Difference in performance of the lubricity of powder of different oscillation waveforms were examined. As oscillation waveforms, a sine wave, the waveform shown in FIG. 3 (b=0.15) and the waveform shown in FIG. 5 (b=0.25) were used. Continuous casting was carried out as a mold oscillated vertically with each waveform using an electro-hydraulic oscillator. The powder of the same properties (solidification point: 1154 C., viscosity of the molten powder at 1300 C.: 0.14 Pa.Math.s) was used for every case where the mold oscillated with the above mentioned oscillation waveform. Load when the mold oscillated, which was the maximum load during the time when the mold ascended (hereinafter simply referred to as max load), was measured by the above electro-hydraulic oscillator.

(32) The performance of the lubricity was evaluated by the maximum frictional force. The maximum frictional force F was represented by
F=(L1L2)/S,
where L1 is the max load at the casting (when the molten steel existed in the mold);

(33) L2 is the max load when the casting was not carried out (when the molten steel did not exist in the mold; and

(34) S is an area of a part that touched or faced the molten steel in the inner face of the mold.

(35) FIG. 6 shows the maximum frictional force for the oscillation waveforms. The maximum frictional force is small in the case the waveforms shown in FIGS. 3 and 5 were used as oscillation waveforms compared to the case where the sine wave is used. That is, the performance of the lubricity of the powder between the mold and the solidified shell was high in the case where the waveform of the formula (1) (b=0.15, 0.25) compared to the case where the sine wave was used. The performance of the lubricity was higher in the case of b=0.25 than the case of b=0.15.

REFERENCE SIGNS LIST

(36) 3 . . . mold 20 . . . oscillator