CN112338155B - Non-sinusoidal vibration waveform of continuous casting crystallizer - Google Patents

Non-sinusoidal vibration waveform of continuous casting crystallizer Download PDF

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CN112338155B
CN112338155B CN202011028728.7A CN202011028728A CN112338155B CN 112338155 B CN112338155 B CN 112338155B CN 202011028728 A CN202011028728 A CN 202011028728A CN 112338155 B CN112338155 B CN 112338155B
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sinusoidal vibration
waveform
vibration
crystallizer
sinusoidal
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CN112338155A (en
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张康晖
马建超
李强
冯孔方
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Jiangsu Shagang Iron and Steel Research Institute Co Ltd
Zhangjiagang Rongsheng Special Steel Co Ltd
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Jiangsu Shagang Iron and Steel Research Institute Co Ltd
Zhangjiagang Rongsheng Special Steel Co Ltd
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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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  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Continuous Casting (AREA)
  • Apparatuses For Generation Of Mechanical Vibrations (AREA)

Abstract

The invention discloses a non-sinusoidal vibration waveform of a continuous casting crystallizer, which has the characteristics of non-sinusoidal vibration and the advantages of sinusoidal vibration. And constructing a non-sinusoidal vibration mode through a five-segment function to control the crystallizer driving device. The non-sinusoidal vibration waveform function constructed by the invention is simple in form and easy to realize, and can meet different vibration requirements; meanwhile, displacement and speed curves are continuous and smooth, an acceleration curve is continuously changed, no sudden change or no limit value exists, rigid and flexible impact on a driving device is avoided, and the dynamic characteristic is good.

Description

Non-sinusoidal vibration waveform of continuous casting crystallizer
Technical Field
The invention relates to the field of continuous casting, in particular to a non-sinusoidal vibration waveform of a continuous casting crystallizer.
Background
The crystallizer vibration technology is one of the core technologies of high-efficiency continuous casting, and the main purpose is to prevent the blank shell from being adhered to the wall of the crystallizer. With the acceleration of production rhythm and the improvement of the surface quality requirement of the casting blank, the surface quality of the casting blank needs to be ensured while the demoulding is realized, which puts higher requirements on a crystallizer vibration device and a control technology.
The crystallizer mainly has two modes of sinusoidal vibration and non-sinusoidal vibration. Sinusoidal vibration completely depends on two parameters of vibration frequency and amplitude, and has limited regulation and control capacity on vibration waveform, so that the sinusoidal vibration has the defects of long negative sliding time, large positive sliding speed difference and the like, particularly under the condition of high pulling speed. Compared with sinusoidal vibration, the non-sinusoidal vibration increases independent parameters, enhances the regulation and control capability of the waveform, and has the following characteristics: the negative sliding time is short, so that the vibration mark depth is favorably reduced; the forward sliding time is long, so that the protective slag can permeate into a gap between the crystallizer and a casting blank, and the lubricating effect of the wall of the crystallizer is improved; the positive sliding speed difference is reduced, the tension fracture and the leakage are reduced, and the surface quality of the casting blank is improved; the negative sliding speed difference is increased, so that the demolding of the casting blank is facilitated; amplitude, vibration frequency and skewness can be adjusted on line to meet different vibration requirements.
Typical non-sinusoidal vibration methods of the crystallizer include a combined function model of an austenite-steel union, a composite function model of a demark and the like. The quality of the non-sinusoidal vibration is mainly judged by investigating whether the displacement and the speed of the crystallizer are continuous and smooth or not and whether the acceleration is monotonous and continuous or not in the vibration process. The acceleration of the combined function model has sudden change in a transition region, so that flexible impact is caused on a driving device; the patent CN106311995A constructs a non-sinusoidal vibration waveform through seven sections of functions, and has more related parameters, complex function construction and poor regulation and control capability; patent CN101642801 constructs a non-sinusoidal vibration waveform by three-segment function, however, there is abrupt change in acceleration, which produces impact effect on the equipment and causes flutter.
Therefore, the non-sinusoidal vibration waveform is constructed, so that not only can all characteristics of non-sinusoidal vibration be met, the expression form is simple and easy to realize, different vibration requirements are met, but also good dynamic characteristics are achieved, and mechanical damage to a driving device is reduced.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a non-sinusoidal vibration waveform of a continuous casting crystallizer, the expression form of the function is simple and easy to realize, and different vibration requirements can be met; meanwhile, displacement and speed curves are continuous and smooth, an acceleration curve is continuously changed, no sudden change or no limit value exists, rigid and flexible impact on a driving device is avoided, and the dynamic characteristic is good.
In order to achieve the purpose, the invention provides the following technical scheme:
a non-sinusoidal oscillation waveform of a continuous casting crystallizer, the velocity waveform curve of which is composed of a horizontal straight line and a parabola, a crystallizer driving device is controlled by a waveform function, and the velocity waveform in each period is as follows:
Figure BDA0002701422820000021
wherein v (t) is the vibration speed (mm/s) of the crystallizer, t is the non-sinusoidal vibration time(s), k1、k2A, B is a constant value, tb、tc、td、te、tf、tgRespectively at different times(s) of the non-sinusoidal vibration velocity waveform.
The velocity wave curve is continuous and smooth, the slope of each point is continuously changed, and the ascending displacement and the descending displacement are equal. Parabolas with upward and downward openings in the curve, the opening degrees of which are linked, i.e. k1＝N*k2N denotes broadly k1And k2Functional relationship between them. From the above constraints, the following relationship can be obtained:
Figure BDA0002701422820000031
Figure BDA0002701422820000032
where f is the vibration frequency (cpm) and α is the slope.
The following limiting relationship exists between N and α:
Figure BDA0002701422820000033
point c is the highest point of displacement, so the amplitude (i.e., half of the vibration path h) is as follows:
Figure BDA0002701422820000034
the velocity wave function is derived, and the acceleration wave function in each period is as follows:
Figure BDA0002701422820000035
the velocity waveform function is integrated, and the displacement waveform function in each period is as follows:
Figure BDA0002701422820000041
when the drawing speed is VCThen, the negative slip time t can be obtainedNAnd the negative slip displacement amount NSA is:
Figure BDA0002701422820000042
Figure BDA0002701422820000043
the invention has the beneficial effects that:
(1) the non-sinusoidal vibration waveform function constructed by the invention is simple in form and easy to realize, and different vibration requirements can be met by adjusting the vibration frequency, the amplitude and the skewness;
(2) the displacement and speed curves are continuous and smooth, the acceleration curve is continuously changed, no sudden change or no limit value exists, rigid and flexible impact on the driving device is avoided, and the dynamic characteristic is good.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a velocity diagram of a five-segment function forming a non-sinusoidal vibration waveform in accordance with the present invention.
FIG. 2 is a graph of displacement within one cycle of a non-sinusoidal vibration waveform in an embodiment of the present invention.
FIG. 3 is a velocity profile for one cycle of a non-sinusoidal vibration waveform in an embodiment of the present invention.
FIG. 4 is a graph of acceleration during one cycle of a non-sinusoidal vibration waveform in an embodiment of the present invention.
Wherein, the ab segment and the fg segment are horizontal straight segments and move upwards at a constant speed; the bc section and ef section are open degree phaseThe same parabolic segment moves upwards in a variable speed; the ce section is a parabolic section and moves downwards at variable speed; t is tNA negative slip time(s); vCThe pull rate (mm/s) is used.
Detailed Description
The embodiment provides a non-sinusoidal vibration waveform of a continuous casting crystallizer.
A non-sinusoidal oscillation waveform of a continuous casting crystallizer, the velocity waveform curve of which is composed of a horizontal straight line and a parabola, a crystallizer driving device is controlled by a waveform function, and the velocity waveform in each period is as follows:
Figure BDA0002701422820000051
wherein v (t) is the vibration speed (mm/s) of the crystallizer, t is the non-sinusoidal vibration time(s), k1、k2A, B is a constant value, tb、tc、td、te、tf、tgRespectively at different times(s) of the non-sinusoidal vibration velocity waveform.
The velocity wave curve is continuous and smooth, the slope of each point is continuously changed, and the ascending displacement and the descending displacement are equal. Parabolas with upward and downward openings in the curve, the opening degrees of which are linked, i.e. k1＝N*k2N denotes broadly k1And k2The relation between the two can be an integer or other non-linear relation. From the above constraints, the following relationship can be obtained:
Figure BDA0002701422820000061
Figure BDA0002701422820000062
where f is the vibration frequency (cpm) and α is the slope.
The following limiting relationship exists between N and α:
Figure BDA0002701422820000063
point c is the highest point of displacement, so the amplitude (i.e., half of the vibration path h) is as follows:
Figure BDA0002701422820000064
the velocity wave function is derived, and the acceleration wave function in each period is as follows:
Figure BDA0002701422820000065
the velocity waveform function is integrated, and the displacement waveform function in each period is as follows:
Figure BDA0002701422820000071
when the vibration frequency f is 120cpm, the amplitude h/2 is 4mm, and the skewness α is 0, 0.2, and 0.4, the displacement, velocity, and acceleration curves are shown in fig. 2, 3, and 4, respectively.
Take the drawing speed of 1.2m/min as an example. When the deflection rate alpha is 0, the vibration is sinusoidal vibration, the negative sliding time is 0.191s, the positive sliding time is 0.309s, the maximum positive sliding speed difference is 68mm/s, and the maximum negative sliding speed difference is 28 mm/s; and when the deflection rate alpha is 0.4, namely non-sinusoidal vibration, the negative sliding time is 0.130s, which is about 31.9 percent reduced, the positive sliding time is 0.370s, which is about 19.7 percent increased, the maximum positive sliding speed difference is 43.9mm/s, which is about 35.4 percent reduced, and the maximum negative sliding speed difference is 60mm/s, which is about 135.7 percent increased. The method has obvious significance for reducing the depth of the vibration mark, improving the demoulding effect of the casting blank and improving the surface quality of the casting blank.
It should be understood that the above examples are only for clarity of illustration and are not intended to limit the embodiments. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. And obvious variations or modifications therefrom are within the scope of the invention.

Claims (1)

1. A non-sinusoidal vibration waveform of a continuous casting crystallizer is characterized in that: the speed waveform curve is composed of a horizontal straight line and a parabola, the crystallizer driving device is controlled through a waveform function, and the speed waveform in each period is as follows:
Figure FDA0003363521350000011
wherein v (t) is the vibration speed of the crystallizer and the unit is mm/s; t is non-sinusoidal vibration time in units of s; k is a radical of1、k2A, B is a constant value; t is tb、tc、td、te、tf、tgRespectively different moments of the non-sinusoidal vibration speed waveform, and the unit is s;
the speed wave curve is continuous and smooth, the slope of each point is continuously changed, and the ascending displacement and the descending displacement are equal; parabolas with upward and downward openings in the curve, the opening degrees of which are linked, i.e. k1＝N*k2N denotes broadly k1And k2Functional relationship between; from the above constraints, the following relationship can be obtained:
Figure FDA0003363521350000012
Figure FDA0003363521350000013
wherein f is the vibration frequency and the unit is cpm; alpha is the skewness; the following limiting relationship exists between N and α:
Figure FDA0003363521350000021
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CN114012054B (en) * 2021-11-08 2023-06-09 河北农业大学 Non-sinusoidal vibration method of continuous casting crystallizer
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ES2034073T3 (en) * 1987-08-29 1993-04-01 Nippon Steel Corporation METHOD TO ROCK A MOLD FOR CONTINUOUS CASTING AT HIGH FREQUENCIES AND MOLD MADE TO ROCK BY SUCH A METHOD.
CN1150072A (en) * 1995-11-10 1997-05-21 东北重型机械学院南校 Mould non-sinusoidal oscillation curve (mode) and oscillating apparatus thereof
KR100364131B1 (en) * 1996-12-06 2003-02-11 주식회사 포스코 Method for oscillating mold of continuous caster
CN102847894B (en) * 2012-09-11 2014-06-25 中冶南方工程技术有限公司 Waveform adjustable non-sinusoidal vibration method of continuous casting crystallizer
CN103600043B (en) * 2013-11-27 2015-06-17 东北大学 Continuous-casting crystallizer vibration simulation test unit and non-sine vibration control method thereof
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JP2017104772A (en) * 2015-12-07 2017-06-15 大同特殊鋼株式会社 Vibrator
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