Non-sinusoidal vibration method for continuous casting mold

Abstract

The present invention relates to a non-sinusoidal vibration method for a continuous casting mold. In each vibration cycle, the vibration waveform consists of six segments of functions. By controlling the motion law of the mold driving device, the mold realizes non-sinusoidal vibration represented by six segments of functions; within 0 ≤ t ≤ t B , the mold moves upward at a constant speed, and the speed is a constant; within t B ≤ t ≤ t C , the mold moves upward with variable deceleration, and the speed curve is a parabola. When it moves to t C , the speed becomes 0; within t C ≤ t ≤ t D , the mold moves downward with variable acceleration, and the speed is a cubic curve; within t D ≤ t ≤ t E , the mold moves downward with variable deceleration, and the speed curve is a cubic curve. When it reaches t E , the speed becomes 0; within t E ≤ t ≤ t F , the mold moves upward with variable acceleration, and the speed curve is a parabola; within t F ≤ t ≤ t G , the mold moves upward at a constant speed, and the speed is a constant, which is a horizontal line.

Description

Technical Field

[0001] The present invention belongs to the technical field of continuous casting, and relates to a non-sinusoidal vibration method for a continuous casting mold. Background Art

[0002] Mold vibration is an indispensable process operation in continuous casting. Currently, the commonly used vibration forms are mainly sinusoidal and non-sinusoidal waveforms. Sinusoidal vibration with high-frequency and small-amplitude operation can reduce the surface oscillation mark depth of the slab by shortening the negative sliding time, thereby improving the quality of the slab. However, while shortening the negative sliding time, the positive sliding time is also correspondingly reduced, which is not conducive to the consumption of mold powder, that is, the lubrication effect between the slab and the mold wall is poor and the friction force is large. Non-sinusoidal vibration can obtain good process parameters. While reducing the negative sliding time, a longer positive sliding time is obtained, increasing the consumption of mold powder. In addition, a smaller positive sliding speed difference can be obtained, reducing the tensile stress of the primary shell, and a larger negative sliding amount, which is beneficial to the demolding of the slab. Therefore, non-sinusoidal vibration of the mold has become one of the key technologies for realizing high-efficiency continuous casting.

[0003] The vibration waveform is one of the core technologies of the non-sinusoidal vibration technology of the mold. With the rapid economic development and the increasing demand for the quality of steel products, surface oscillation marks, cracks, and even breakout accidents inevitably occur during the pursuit of high quality and high casting speed by each manufacturer. In order to reduce or even eliminate slab defects and improve productivity, it is urgent to develop a new non-sinusoidal vibration waveform function to meet the high efficiency and quality of continuous steel casting.

[0004] The non-sinusoidal vibration waveform functions mainly include integral functions and piecewise functions. Different waveform functions have different technological effects on the continuous casting billet. The currently known integral functions mainly include the Demag non-sinusoidal vibration waveform, and the non-sinusoidal vibration waveforms realized by inverse parallel four-link mechanisms, non-circular gears, double eccentrics, etc. Although these waveforms have good waveform dynamics characteristics, they are complex in structure, limited in adjustment range, difficult to solve process parameters, and not easy to control in practical applications. The piecewise function has a large adjustment range, a simple structure, and is easy to control, so it is widely used. The currently known piecewise functions mainly include two-segment, three-segment, four-segment, five-segment, and seven-segment functions. For the two-segment function non-sinusoidal vibration waveform given in Patent CN105081241A, the solution of its waveform parameters is complex, and an analytical expression cannot be given, making it difficult to apply in the process. For the three-segment waveform function constructed in CN1799727A, its displacement and velocity curves are continuous, but there are sudden changes in the acceleration curve, which is likely to cause impact on the equipment and affect its service life. For the non-sinusoidal vibration waveform constructed by the four-segment function given in CN105945249A, although the displacement, velocity, and acceleration curves are smooth and continuous, the process parameters of the waveform are not easy to solve, and a specific expression cannot be given, making it not easy to control. It was reported in the 1st issue of Volume 36 of the Chinese Journal of Mechanical Engineering in 2000 that for the non-sinusoidal vibration waveform constructed by the five-segment function, although specific expressions of the parameters are given, the positive sliding speed difference of the waveform is relatively large, which causes a large tensile stress on the initial solidified shell of the continuous casting billet and is prone to breakout. It was reported in the 24th issue of Volume 24 of China Mechanical Engineering in 2013 that for the non-sinusoidal vibration waveform constructed by the seven-segment function, its purpose is to keep the maximum acceleration unchanged when changing the waveform segregation rate, with less impact on the mechanism vibration. However, during the function construction process, there are many parameters, the solution is complex, and it is not easy to give specific expressions of the parameters, so it is not easy to adjust.

[0005] In summary, when constructing a non-sinusoidal vibration waveform, it is necessary to have a simple expression form, be easy to implement, have good control performance in practical applications, and also have good waveform dynamics characteristics and process characteristics. Summary of the Invention

[0006] Aiming at the deficiencies of the prior art, the present invention provides a non-sinusoidal vibration method for a continuous casting mold. By using a non-sinusoidal vibration waveform function, when the waveform slope increases, its positive sliding speed difference is lower than that of other non-sinusoidal vibration waveforms. Moreover, the waveform function has a simple form, strong control ability, and is easy to solve reasonable vibration process parameters and synchronous control models.

[0007] The present invention is implemented as follows:

[0008] A non-sinusoidal vibration method for a continuous casting mold, the specific process is as follows: By controlling the motion law of the mold driving device, the continuous casting mold is driven by the driving device to realize a non-sinusoidal vibration waveform determined by the following six-segment function in each vibration cycle:

[0009]

[0010] In the formula, v is the speed of the mold movement; t is the time; t B , t C , t D , t E , t F and t G are the time points of each stage of the non-sinusoidal vibration waveform respectively; v B is the speed at time t B ; v D is the speed when the mold moves to time t D ; δ and ψ are undetermined parameters, and f is the vibration frequency;

[0011] During each vibration period, the vibration process is divided into the following six stages, and each stage vibrates according to the following six-segment speed waveform respectively, so that the mold realizes the non-sinusoidal vibration represented by the above six-segment function:

[0012] Within 0 ≤ t ≤ t B , the mold moves upward at a constant speed, and the speed is a constant;

[0013] Within t B ≤ t ≤ t C , the mold moves upward with variable deceleration, and the speed curve is a parabola. When it moves to time t C , the speed becomes 0;

[0014] Within t C ≤ t ≤ t D , the mold moves downward with variable acceleration, and the speed curve is a cubic curve;

[0015] Within t D ≤ t ≤ t E , the mold moves downward with variable deceleration. When it reaches time t E , the speed becomes 0, and the speed curve within this time period is a cubic curve;

[0016] Within t E ≤ t ≤ t F , the mold moves upward with variable acceleration, and the speed curve is a parabola;

[0017] Within t F ≤ t ≤ t G , the mold moves upward at a constant speed, and the speed is a constant, which is a horizontal line.

[0018] Preferably, for the non-sinusoidal vibration of the mold,

[0019] Time point

[0020] where α is the waveform skew slope.

[0021] Preferably, the time point

[0022] Preferably, the time point Time point Time point

[0023] Preferably, t B The speed v at the moment B =-δ(t C -t B ) 2 .

[0024] Preferably, the parameter where h is the moving displacement of the mold from the 0 moment to the t C moment

[0025] Compared with the prior art, the present invention has the following beneficial effects:

[0026] 1. When the waveform skew rate of the non-sinusoidal vibration waveform function of the present invention increases, it can obtain a smaller positive sliding speed difference, reduce the upward friction force of the mold wall on the billet and the tensile stress in the solidified shell, so it plays an important role in increasing the drawing speed and reducing sticking breakout. The non-sinusoidal vibration waveform function constructed by the present invention has a simple form, strong regulation ability, smooth and continuous displacement and speed curves, no sudden change in acceleration, no rigid and flexible impacts, and has good waveform dynamics characteristics, ensuring the stable operation of the device.

[0027] 2. The amplitude, frequency and waveform skew rate of the present invention can be selected within a large range to meet the requirements of different steel grades. Compared with other waveform functions, under the same working conditions, it can reduce the positive sliding speed difference and is easy to solve reasonable vibration process parameters and synchronous control models. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 is the speed waveform curve of the present invention;

[0029] Figure 2 is the displacement curve diagram of non-sinusoidal vibration of the present invention under different waveform skew rates;

[0030] Figure 3 is the speed curve diagram of non-sinusoidal vibration of the present invention under different waveform skew rates; and

[0031] Figure 4 is the acceleration curve diagram of non-sinusoidal vibration of the present invention under different waveform skew rates. DETAILED DESCRIPTION OF THE INVENTION

[0032] Exemplary embodiments, features, and performance aspects of the present invention will be described in detail below with reference to the accompanying drawings. Identical reference numerals in the drawings denote functionally identical or similar elements. Although various aspects of the embodiments are shown in the drawings, the drawings do not have to be drawn to scale unless otherwise specified.

[0033] A non-sinusoidal vibration method for a continuous casting mold, the specific process being: by controlling the motion law of the mold driving device, the continuous casting mold is driven by the driving device to achieve a non-sinusoidal vibration waveform determined by the following six-segment function within each vibration cycle:

[0034]

[0035] In the formula, v is the speed of the mold movement; t is the time; t B , t C , t D , t E , t F and t G are the time points of each stage of the non-sinusoidal vibration waveform respectively; v B is the speed at the moment of t B ; v D is the speed when the mold moves to the moment of t D ; δ and ψ are undetermined parameters, and f is the vibration frequency;

[0036] Within each vibration cycle, the vibration process is divided into the following six stages, and each stage vibrates according to the following six-segment speed waveform respectively, so that the mold realizes the non-sinusoidal vibration represented by the above six-segment function:

[0037] Within 0 ≤ t ≤ t B , the mold moves upward at a constant speed, and the speed is a constant;

[0038] Within t B ≤ t ≤ t C , the mold moves upward with variable deceleration, and the speed curve is a parabola. When it moves to the moment of t C , the speed becomes 0;

[0039] Within t C ≤ t ≤ t D , the mold moves downward with variable acceleration, and the speed curve is a cubic curve;

[0040] Within t D ≤ t ≤ t E , the mold moves downward with variable deceleration. When it reaches the moment of t E , the speed becomes 0, and the speed curve within this time period is a cubic curve;

[0041] Within t E ≤ t ≤ t FInside, the mold moves upward with variable acceleration, and the velocity curve is a parabola;

[0042] At t F ≤ t ≤ t G Inside, the mold moves upward at a constant speed, and the speed is a constant, which is a horizontal line.

[0043] The following gives the calculation methods of each undetermined parameter in the waveform and the displacement, velocity, and acceleration waveforms of non-sinusoidal vibration:

[0044] The velocity function is:

[0045]

[0046] For the non-sinusoidal vibration of the mold, the general vibration frequency f and waveform skew slope α are known. The solution methods of each parameter in the above formula are as follows:

[0047] From the definition of the waveform skew slope, it can be known that And t B To be determined. When the mold moves at time t C , its velocity is 0, then

[0048] δ(t C - t B ) 2 + v B =0 (2)

[0049]

[0050] After arrangement, it can be obtained that

[0051] v B =-δ(t C - t B ) 2 (4)

[0052]

[0053] Since the acceleration of the mold is continuous at time t C , it can be obtained that

[0054]

[0055] After arranging formula (6), it can be obtained that

[0056]

[0057] When the mold moves from time t C to time, the displacement of the movement is -h, and it can be obtained that

[0058]

[0059] Rearranging Equation (8) and substituting Equation (5) gives

[0060]

[0061] The mold moves from time 0 for t C At time t, the displacement of the movement is h, and we get

[0062]

[0063] Rearranging Equation (10) gives

[0064]

[0065] Substituting Equations (4) and (7) into Equation (11) gives

[0066]

[0067] The displacement function is:[[]]

[0068]

[0069] The function of acceleration a is:[[]]

[0070]

[0071] Therefore, when the amplitude of the mold vibration h = 4 mm, the frequency f = 2 Hz, and the waveform skew slope takes different values, in the non-sinusoidal vibration wave form (1), the values of each parameter are shown in Table 1.[[]]

[0072] Table 1 Values of each parameter[[]]

[0073] α <![CDATA[t B > <![CDATA[t C > <![CDATA[t E > <![CDATA[t F > <![CDATA[v B > <![CDATA[v D > δ ψ 0.1 0.0847 0.1375 0.3625 0.4153 0.0334 0.0474 -11.9773 33.2957 α <![CDATA[t B > <![CDATA[t C > <![CDATA[t E > <![CDATA[t F > <![CDATA[v B > <![CDATA[v D > δ ψ 0.2 0.1137 0.15 0.35 0.3863 0.0290 0.0553 -22.0664 53.3333 α <![CDATA[t B > <![CDATA[t C > <![CDATA[t E > <![CDATA[t F > <![CDATA[v B > <![CDATA[v D > δ ψ 0.3 0.1337 0.1625 0.3375 0.3623 0.0259 0.061 -42.0965 90.9843 α <![CDATA[t B > <![CDATA[t C > <![CDATA[t E > <![CDATA[t F > <![CDATA[v B > <![CDATA[v D > δ ψ 0.4 0.1584 0.175 0.325 0.3416 0.0236 0.0711 -85.6964 168.5597

[0074] When the amplitude of the mold vibration h = 4 mm, the frequency f = 2 Hz, and the waveform skew slope α = 20%, the velocity waveform within one cycle of the mold vibration is obtained, as Figure 1 shown. The velocity waveform is smooth, continuous, and has no mutation points, and the device will not generate a rigid impact. In addition, the displacement, velocity, and acceleration curves of non-sinusoidal vibration under different skew slopes are also given, as Figures 2 to 4 shown. It can be seen from the figure that as the waveform skew slope increases, the characteristics of non-sinusoidal vibration become more obvious. The waveform skew slope can be adjusted within a large range to meet the requirements of different steel grades. The acceleration curve is continuous and has no mutation, and the equipment will not generate a flexible impact, ensuring its stable operation and having good dynamic performance.[[]]

[0075] Finally, it should be noted that the above-described embodiments are only used to illustrate the technical solutions of the present invention, rather than limiting them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A non-sinusoidal vibration method for continuous casting mold, Characterized in that: The specific process of the non-sinusoidal vibration method is as follows: By controlling the motion law of the mold driving device, the continuous casting mold is driven by the driving device to achieve a non-sinusoidal vibration waveform determined by the following six-segment function within each vibration cycle: where v is the speed of the mold movement; t is time; t B 、t C 、t D 、t E 、t F and t G are the time points of each stage of the non-sinusoidal vibration waveform respectively; v B is the speed at time t B ; v D is the speed when the mold moves to time t D ; δ and ψ are undetermined parameters, and f is the vibration frequency; Within each vibration cycle, the vibration process is divided into the following six stages, and each stage vibrates according to the following six-segment velocity waveform respectively, so that the mold realizes the non-sinusoidal vibration represented by the above six-segment function: Within \(0\leq t\leq t\) B the mold moves upward at a constant speed; At t B ≤ t ≤ t C within, the mold moves upward with variable deceleration, and the velocity curve is a parabola. When it moves to t C moment, the velocity becomes 0; At t C ≤ t ≤ t D Within, the mold moves downward with variable acceleration, and the velocity curve is a cubic curve; At time t D ≤t≤t E within, the mold moves downward with variable deceleration and reaches time t E when the speed becomes 0. The speed curve during this time period is a cubic curve; At t E ≤ t ≤ t F Within, the mold moves upward with variable acceleration, and the velocity curve is a parabola; At time t F where t G ≤ t ≤ t, the mold moves upward at a constant speed, which is a horizontal line segment; Among them, the parameter h is the movement displacement of the mold from the 0 moment to the t C moment.

2. The non-sinusoidal vibration method for continuous casting mold according to claim 1, Characterized in that: For the non-sinusoidal vibration of the mold, where α is the waveform slope deviation.

3. The non-sinusoidal vibration method for continuous casting mold according to claim 1, Characterized in that:

4. The non-sinusoidal vibration method for continuous casting mold according to claim 2 or 3, Characterized in that:

5. The non-sinusoidal vibration method for continuous casting mold according to claim 3, Characterized in that: t B Velocity at a moment: v B = -δ(t C - t B ) 2 。

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