CN114012048A - Non-sinusoidal vibration method for continuous casting crystallizer - Google Patents

Non-sinusoidal vibration method for continuous casting crystallizer Download PDF

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CN114012048A
CN114012048A CN202111316387.8A CN202111316387A CN114012048A CN 114012048 A CN114012048 A CN 114012048A CN 202111316387 A CN202111316387 A CN 202111316387A CN 114012048 A CN114012048 A CN 114012048A
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speed
crystallizer
vibration
sinusoidal
continuous casting
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周超
王芳
张兴中
于艳磊
李凤丽
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Yanshan University
Hebei Agricultural University
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Hebei Agricultural University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B22—CASTING; POWDER METALLURGY
    • B22D—CASTING OF METALS; CASTING OF OTHER SUBSTANCES BY THE SAME PROCESSES OR DEVICES
    • B22D11/00—Continuous casting of metals, i.e. casting in indefinite lengths
    • B22D11/04—Continuous casting of metals, i.e. casting in indefinite lengths into open-ended moulds
    • B22D11/053—Means for oscillating the moulds
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B22—CASTING; POWDER METALLURGY
    • B22D—CASTING OF METALS; CASTING OF OTHER SUBSTANCES BY THE SAME PROCESSES OR DEVICES
    • B22D11/00—Continuous casting of metals, i.e. casting in indefinite lengths
    • B22D11/16—Controlling or regulating processes or operations
    • B22D11/166—Controlling or regulating processes or operations for mould oscillation

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Abstract

The invention relates to a non-sinusoidal vibration method of a continuous casting crystallizer, wherein in each vibration period, a vibration waveform consists of six sections of functions, and the non-sinusoidal vibration expressed by the six sections of functions is realized by the crystallizer by controlling the motion rule of a crystallizer driving device; t is more than or equal to 0 and less than or equal to tBIn the process, the crystallizer moves upwards at a constant speed; at tB≤t≤tCThe crystallizer moves upwards in a speed-reducing mode, the speed curve is a parabola, and the crystallizer moves to tCAt that time, the speed becomes 0; at tC≤t≤tDThe crystallizer moves downwards with variable acceleration, and the speed is a cubic curve; at tD≤t≤tEThe crystallizer moves downwards at variable speed and reduced speed, the speed curve is a cubic curve and reaches tEAt that time, the speed becomes 0; at tE≤t≤tFThe crystallizer moves upwards in a variable acceleration mode, and a speed curve is a parabola; at tF≤t≤tGInternal and external crystallizer homogenizingThe speed moves upwards, and the speed is constant and is a section of horizontal line.

Description

Non-sinusoidal vibration method for continuous casting crystallizer
Technical Field
The invention belongs to the technical field of continuous casting, and relates to a non-sinusoidal vibration method of a continuous casting crystallizer.
Background
Crystallizer vibration is an indispensable technological operation of the continuous casting process, and the vibration forms commonly used at present are mainly sinusoidal and non-sinusoidal waveforms. The sinusoidal vibration adopts the operation of high frequency and small amplitude, and can reduce the surface vibration mark depth of the casting blank by shortening the negative sliding time, thereby improving the quality of the casting blank, but the process shortens the negative sliding time, correspondingly reduces the positive sliding time, is not beneficial to the consumption of the covering slag, namely the lubricating effect of the casting blank and the wall of the crystallizer is poor, and the friction force is large. And the non-sinusoidal vibration can obtain good process parameters, so that the negative sliding time is reduced, the longer positive sliding time is obtained, and the consumption of the covering slag is increased. In addition, a smaller positive sliding speed difference can be obtained, the tensile stress of the primary blank shell is reduced, and a larger negative sliding quantity is beneficial to demoulding of the casting blank. Therefore, the non-sinusoidal oscillation of the mold has become one of the key technologies for realizing efficient continuous casting.
The vibration waveform is one of the core techniques of the non-sinusoidal vibration technique of the crystallizer. With the rapid development of economy and the improvement of the quality requirement of steel products, accidents such as surface vibration marks, cracks, even steel leakage and the like can not be avoided in the process of pursuing high quality and high drawing speed by various manufacturers. In order to reduce or even eliminate the defects of casting blanks and improve the productivity, the development of a novel non-sinusoidal vibration waveform function is urgently needed to meet the high efficiency and high quality of continuous casting steel.
The non-sinusoidal vibration waveform function mainly includes an integral function and a piecewise function. Different wave functions have different technological effects on the casting blank. The existing known integral functions mainly comprise Damask non-sinusoidal vibration waveforms, non-sinusoidal vibration waveforms realized by an antiparallel four-bar linkage, a non-circular gear, double eccentricity and the like, and the waveforms have good waveform dynamics characteristics, but have complex structures, limited adjustment ranges, difficult solution of process parameters and difficult control in practical application. The piecewise function has a large adjusting range, a simple structure and is easy to control, so that the piecewise function is widely applied. At present, the known piecewise function mainly comprises two, three, four, five and seven segments. The two-segment function non-sinusoidal vibration waveform provided by the patent CN105081241A has complex waveform parameter solution, cannot provide an analytic expression, and has difficulty in process application. The displacement and speed curves of the three-section wave function constructed by CN1799727A are continuous, and the acceleration curve has sudden change, so that the equipment is easy to be impacted, and the service life of the equipment is influenced. CN105945249A gives out the non-sinusoidal vibration waveform constructed by four-segment function, although displacement, speed and acceleration curve are smooth and continuous, the technological parameter of waveform is not easy to solve, can not give out concrete expression, is not easy to control. In the report of No. 1 of volume 36 of the 2000 mechanical engineering report, a non-sinusoidal vibration waveform constructed by a five-segment function is adopted, although parameters give a specific expression of the parameters, the positive sliding speed difference of the waveform is large, the tensile stress on a primary billet shell of a casting blank is large, and steel leakage is easy to generate. In 24 th report of Chinese mechanical engineering in 2013, volume 24, a non-sinusoidal vibration waveform constructed by seven sections of functions aims to keep the maximum acceleration unchanged under the condition of changing the waveform segregation rate and has small vibration impact on a mechanism, but in the function construction process, parameters are more, the solution is complex, and a specific parameter expression is not easily given, so that the adjustment is not easy.
In a word, a non-sinusoidal vibration waveform is constructed, and the non-sinusoidal vibration waveform has the advantages of simple expression form, easiness in implementation, good practical application regulation and control performance, and good waveform dynamics characteristics and process characteristics.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a non-sinusoidal vibration method of a continuous casting crystallizer, which adopts a non-sinusoidal vibration waveform function, and when the waveform skewness is increased, the positive sliding speed difference is lower than other non-sinusoidal vibration waveforms. And the waveform function form is simple, the regulation and control capability is strong, and reasonable vibration technological parameters and a synchronous control model are easy to solve.
The invention is realized by the following steps:
a non-sinusoidal vibration method of a continuous casting crystallizer comprises the following specific processes: by controlling the motion law of the crystallizer driving device, the continuous casting crystallizer is driven by the driving device to realize a non-sinusoidal vibration waveform determined by the following six-segment function in each vibration period:
Figure BDA0003343820440000021
in the formula, v is the movement speed of the crystallizer, and t is time; t is tB、tC、tD、tFAnd tGRespectively, the time points of each stage of the non-sinusoidal vibration waveform, vBIs tBThe speed at the moment, delta and psi are undetermined parameters, and f is the vibration frequency;
in each vibration period, the vibration process is divided into the following six stages, and each stage vibrates according to the following six-stage speed waveform, so that the crystallizer realizes the non-sinusoidal vibration expressed by the six-stage function:
t is more than or equal to 0 and less than or equal to tBIn the process, the crystallizer moves upwards at a constant speed;
at tB≤t≤tCThe crystallizer moves upwards in a speed-reducing mode, the speed curve is a parabola, and the crystallizer moves to tCAt that time, the speed becomes 0;
at tC≤t≤tDThe crystallizer moves downwards in an accelerated mode, and a speed curve is a cubic curve;
at tD≤t≤tEThe crystallizer moves downwards at a variable speed and a reduced speed until tEAt the moment, the speed is changed into 0, and the speed curve in the time period is a cubic curve;
at tE≤t≤tFThe crystallizer moves upwards in a variable acceleration mode, and a speed curve is a parabola;
at tF≤t≤tGAnd the crystallizer moves upwards at a constant speed, and the speed is a section of horizontal line.
Preferably, for a non-sinusoidal oscillation of the crystalliser,
Figure BDA0003343820440000031
wherein f is the vibration frequency and alpha is the waveform skewness.
Preferably, the first and second electrodes are formed of a metal,
Figure BDA0003343820440000032
preferably, the first and second electrodes are formed of a metal,
Figure BDA0003343820440000033
preferably, t isBVelocity v of timeB＝-δ(tC-tB)2。
Preferably, the first and second electrodes are formed of a metal,
Figure BDA0003343820440000034
wherein h is the movement of the crystallizer from the moment 0 to tCThe movement displacement at the moment.
Compared with the prior art, the invention has the following beneficial effects:
1. when the waveform deflection rate is increased, the non-sinusoidal vibration waveform function can obtain smaller positive sliding speed difference, and reduces the upward friction force of the crystallizer wall on a casting blank and the tensile stress in a solidified blank shell, so the non-sinusoidal vibration waveform function plays an important role in improving the blank drawing speed and reducing cohesive breakout. The non-sinusoidal vibration waveform function constructed by the invention has the advantages of simple form, strong regulation and control capability, smooth and continuous displacement and speed curves, no sudden change of acceleration, no rigid and flexible impact, good waveform dynamics characteristics and capability of ensuring the stable operation of the device.
2. The amplitude, frequency and waveform skewness of the invention can be selected in a large range, and the requirements of different steel grades are met. Compared with other wave functions, under the same working condition, the positive sliding speed difference can be reduced, and reasonable vibration technological parameters and a synchronous control model are easy to solve.
Drawings
FIG. 1 is a velocity profile of the present invention;
FIG. 2 is a graph of the displacement of the non-sinusoidal vibrations of the present invention at different waveform skewness rates;
FIG. 3 is a graph of the velocity of a non-sinusoidal oscillation of the present invention at different waveform skewness rates; and
FIG. 4 is a graph of acceleration of a non-sinusoidal vibration of the present invention at different waveform skewness rates.
Detailed Description
Exemplary embodiments, features and performance aspects of the present invention will be described in detail below with reference to the accompanying drawings. In the drawings, like reference numbers can indicate functionally identical or similar elements. While the various aspects of the embodiments are presented in drawings, the drawings are not necessarily drawn to scale unless specifically indicated.
A non-sinusoidal vibration method of a continuous casting crystallizer comprises the following specific processes: by controlling the motion law of the crystallizer driving device, the continuous casting crystallizer is driven by the driving device to realize a non-sinusoidal vibration waveform determined by the following six-segment function in each vibration period:
Figure BDA0003343820440000041
in the formula, v is the movement speed of the crystallizer, and t is time; t is tB、tC、tD、tFAnd tGRespectively, the time points of each stage of the non-sinusoidal vibration waveform, vBIs tBThe speed at the moment, delta and psi are undetermined parameters, and f is the vibration frequency;
in each vibration period, the vibration process is divided into the following six stages, and each stage vibrates according to the following six-stage speed waveform, so that the crystallizer realizes the non-sinusoidal vibration expressed by the six-stage function:
t is more than or equal to 0 and less than or equal to tBIn the process, the crystallizer moves upwards at a constant speed;
at tB≤t≤tCThe crystallizer moves upwards in a speed-reducing mode, the speed curve is a parabola, and the crystallizer moves to tCAt that time, the speed becomes 0;
at tC≤t≤tDThe crystallizer moves downwards in an accelerated mode, and a speed curve is a cubic curve;
at tD≤t≤tEThe crystallizer moves downwards at a variable speed and a reduced speed until tEAt the moment, the speed becomes 0,the speed curve in the time period is a cubic curve;
at tE≤t≤tFThe crystallizer moves upwards in a variable acceleration mode, and a speed curve is a parabola;
at tF≤t≤tGAnd the crystallizer moves upwards at a constant speed, and the speed is a section of horizontal line.
The calculation method of each undetermined parameter in the waveform and the displacement, speed and acceleration waveforms of the non-sinusoidal vibration are given as follows:
the speed function is:
Figure BDA0003343820440000051
for non-sinusoidal vibration of the crystallizer, the general vibration frequency f and the waveform skewness alpha are known, and the solving method of each parameter in the above formula is as follows:
as can be seen from the definition of the waveform skew rate,
Figure BDA0003343820440000052
while
Figure BDA0003343820440000053
tBAnd (5) waiting for solving. Movement t of the moldCAt the moment, its speed is 0, then
δ(tC-tB)2+vB＝0 (2)
Figure BDA0003343820440000054
Can be obtained by finishing
vB＝-δ(tC-tB)2 (4)
Figure BDA0003343820440000055
Since the crystallizer is at tCThe acceleration at the moment is continuous, can obtain
Figure BDA0003343820440000056
Can be obtained by finishing the formula (6)
Figure BDA0003343820440000057
The crystallizer consisting ofCMove to at all times
Figure BDA0003343820440000058
At the moment, the displacement of the motion is-h, and can be obtained
Figure BDA0003343820440000061
By arranging formula (8) and substituting formula (5), the compound can be obtained
Figure BDA0003343820440000062
The crystallizer moves from the 0 moment tCAt the moment, the displacement of the motion is h, which can be obtained
Figure BDA0003343820440000063
Finishing formula (10) to obtain
Figure BDA0003343820440000064
By substituting the formulae (4) and (7) for the formula (11)
Figure BDA0003343820440000065
The displacement function is:
Figure BDA0003343820440000066
the function of the acceleration a is:
Figure BDA0003343820440000071
therefore, when the amplitude h of the mold oscillation is 4mm, the frequency f is 2Hz, and the waveform deviation rate has different values, the values of the parameters in the non-sinusoidal oscillation waveform formula (1) are shown in table 1.
TABLE 1 values of the parameters
α tB tC tE tF vB vD δ ψ
0.1 0.0847 0.1375 0.3625 0.4153 0.0334 0.0474 -11.9773 33.2957
α tB tC tE tF vB vD δ ψ
0.2 0.1137 0.15 0.35 0.3863 0.0290 0.0553 -22.0664 53.3333
α tB tC tE tF vB vD δ ψ
0.3 0.1337 0.1625 0.3375 0.3623 0.0259 0.061 -42.0965 90.9843
α tB tC tE tF vB vD δ ψ
0.4 0.1584 0.175 0.325 0.3416 0.0236 0.0711 -85.6964 168.5597
When the amplitude h of the crystallizer vibration is 4mm, the frequency f is 2Hz, and the waveform skewness alpha is 20%, the velocity waveform of the crystallizer vibration in one period is obtained, as shown in FIG. 1, the velocity waveform is smooth and continuous without abrupt points, and the device does not generate rigid impact. In addition, displacement, speed and acceleration curves of non-sinusoidal vibration under different deflection rates are also given, as shown in FIGS. 2-4. It can be seen from the figure that the characteristic of non-sinusoidal vibration is more obvious along with the increase of the waveform deflection rate, the waveform deflection rate can be adjusted in a larger range so as to meet the requirements of different steel types, the acceleration curve is continuous and has no sudden change, the equipment can not generate flexible impact, the stable operation of the equipment is ensured, and the dynamic performance is better.
Finally, it should be noted that: the above-mentioned embodiments are only used for illustrating the technical solution of the present invention, and not for limiting the same; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (6)

1. A non-sinusoidal vibration method of a continuous casting crystallizer is characterized by comprising the following steps: the non-sinusoidal vibration method comprises the following specific processes: by controlling the motion law of the crystallizer driving device, the continuous casting crystallizer is driven by the driving device to realize a non-sinusoidal vibration waveform determined by the following six-segment function in each vibration period:
Figure FDA0003343820430000011
in the formula, v is the movement speed of the crystallizer, and t is time; t is tB、tC、tD、tFAnd tGRespectively, the time points of each stage of the non-sinusoidal vibration waveform, vBIs tBThe speed at the moment, delta and psi are undetermined parameters, and f is the vibration frequency;
in each vibration period, the vibration process is divided into the following six stages, and each stage vibrates according to the following six-stage speed waveform, so that the crystallizer realizes the non-sinusoidal vibration expressed by the six-stage function:
t is more than or equal to 0 and less than or equal to tBIn the process, the crystallizer moves upwards at a constant speed;
at tB≤t≤tCThe crystallizer moves upwards in a speed-reducing mode, the speed curve is a parabola, and the crystallizer moves to tCAt that time, the speed becomes 0;
at tC≤t≤tDThe crystallizer moves downwards in an accelerated mode, and a speed curve is a cubic curve;
at tD≤t≤tEThe crystallizer moves downwards at a variable speed and a reduced speed until tEAt the moment, the speed is changed into 0, and the speed curve in the time period is a cubic curve;
at tE≤t≤tFThe crystallizer moves upwards in a variable acceleration mode, and a speed curve is a parabola;
at tF≤t≤tGAnd the crystallizer moves upwards at a constant speed, and the speed is a section of horizontal line.
2. The non-sinusoidal oscillation method of a continuous casting mold according to claim 1, characterized in that: for a non-sinusoidal oscillation of the crystalliser,
Figure FDA0003343820430000012
wherein f is the vibration frequency and alpha is the waveform skewness.
3. The non-sinusoidal oscillation method of a continuous casting mold according to claim 2, characterized in that:
Figure FDA0003343820430000021
4. the non-sinusoidal oscillation method of a continuous casting mold according to any one of claims 1 to 3, comprising:
Figure FDA0003343820430000022
5. the non-sinusoidal oscillation method of the continuous casting mold according to claims 1 to 4, characterized in that:
Figure FDA0003343820430000023
Figure FDA0003343820430000024
Figure FDA0003343820430000025
6. the non-sinusoidal oscillation method of a continuous casting mold according to claim 5, characterized in that:
tBvelocity of time of day
vB＝-δ(tC-tB)2。
CN202111316387.8A 2021-11-08 2021-11-08 Non-sinusoidal vibration method for continuous casting crystallizer Pending CN114012048A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115106497A (en) * 2022-06-14 2022-09-27 河钢乐亭钢铁有限公司 Method for controlling vibration mark defect of continuous casting slab

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115106497A (en) * 2022-06-14 2022-09-27 河钢乐亭钢铁有限公司 Method for controlling vibration mark defect of continuous casting slab

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