Machine type curve of cycloid continuous bending straightening arc-shaped continuous casting machine

Abstract

The invention discloses a cycloid continuous bending straightening arc-shaped continuous casting machine model curve, which belongs to the technical field of continuous steel casting and comprises a vertical straight line section, a continuous bending section, a continuous straightening section and a horizontal straight line section which are sequentially connected. Wherein the continuous bending section and the continuous straightening section are integrally symmetrical about a straight line forming an included angle of 45 degrees with the horizontal direction, and each of the continuous bending section and the continuous straightening section is composed of a cubic curve and a cycloid. Aiming at the situation that an original arc section casting blank does not deform and has no curvature change, the continuous bending straightening section is introduced to replace an original bending straightening arc section, the deformation of the casting blank is dispersed into the whole curve, the strain rate is extremely low, creep bending straightening can be achieved, the internal quality of the casting blank is improved, and the crack defect is avoided.

Description

Technical Field

[0001] This invention relates to the field of continuous steel casting technology, and in particular to a cycloidal continuous bending and straightening arc-shaped continuous casting machine curve. Background Technology

[0002] Continuous casting technology is a core process in modern steel production, and the design of the continuous casting machine's profile curve directly affects the quality of the cast billet and production efficiency. Straight-arc continuous casting machines, due to their ability to accommodate inclusions floating in the vertical section and their relatively low equipment height, are widely used in the production of high-quality billets such as slabs and large square billets. The profile curve of a traditional straight-arc continuous casting machine typically consists of a vertical section, a bending section, a basic circular arc section, a straightening section, and a horizontal section. The bending and straightening deformation of the continuously cast billet is concentrated in the bending and straightening sections, which are relatively short. Conversely, the billet does not undergo any bending or straightening deformation in the long circular arc section. This results in defects in the profile curve of traditional straight-arc continuous casting machines, such as unreasonable deformation distribution and high strain rates. Summary of the Invention

[0003] To address the shortcomings of traditional straight-arc continuous casting machine designs, such as unreasonable deformation distribution and high strain rates, this invention provides a cycloidal continuous bending straightening arc continuous casting machine design curve. Through parametric design, it achieves continuously controllable curvature, process self-adaptation, and optimized equipment height, fundamentally solving the inherent defects of traditional straight-arc continuous casting machine designs.

[0004] The technical solution adopted by the present invention for the arc-shaped curve of a cycloidal continuous bending straightening continuous casting machine is as follows:

[0005] A cycloidal continuous bending and straightening arc-shaped continuous casting machine curve includes a vertical straight section, a continuous bending section, a continuous straightening section and a horizontal straight section connected in sequence; wherein, the continuous bending section and the continuous straightening section are symmetrical about a straight line at an angle of 45° to the horizontal direction, and both the continuous bending section and the continuous straightening section are composed of a cubic curve and a cycloid.

[0006] A further improvement to the technical solution of this invention lies in that: the parametric equations of the vertical straight line segment and the continuous curved segment are,

[0007]

[0008] in,

[0009] r = a·[π - t0 - sinint0 + sin(2t0)]

[0010] Equation (1) is the equation of the vertical straight line segment, where δ∈[r,r+η], and η is the length of the vertical straight line segment in mm; Equation (2) is the equation of the cubic curve of the continuous curved segment; and Equation (3) is the equation of the cycloid of the continuous curved segment. The unit is rad, representing the connection point between the cubic curve of the continuous bending segment and the cycloid. 'a' can be calculated using the following formula.

[0011]

[0012] In the formula, R0 is the main radius of the traditional straight arc continuous casting machine, in mm.

[0013] A further improvement to the technical solution of this invention is that: the curvature at the intersection of the vertical straight line segment and the cubic curve of the continuous curved segment is 0; the slope of the tangent at the intersection of the cubic curve of the continuous curved segment and the cycloid is... The magnitude of curvature is

[0014] A further improvement to the technical solution of this invention lies in that: the curve parametric equations of the horizontal straight line segment and the continuous straightening segment are,

[0015]

[0016] in,

[0017] r = a·[π - t0 - sinint0 + sin(2t0)]

[0018] Equation (4) is the equation of the horizontal straight line segment, where δ∈[-r-λ,-r], and λ is the length of the horizontal straight line segment in mm; Equation (5) is the equation of the cubic curve of the continuous straightening segment; and Equation (6) is the equation of the cycloid of the continuous straightening segment. The unit is rad, representing the position where the cubic curve of the continuous straightening segment connects with the cycloid. 'a' can be calculated using the following formula.

[0019]

[0020] In the formula, R0 is the main radius of the traditional straight arc continuous casting machine, in mm.

[0021] A further improvement to the technical solution of this invention is that: the curvature at the intersection of the horizontal straight line segment and the cubic curve of the continuous straightening segment is 0; the slope of the tangent at the intersection of the cubic curve of the continuous straightening segment and the cycloid is... The magnitude of curvature is

[0022] A further improvement to the technical solution of this invention lies in that: the slope of the tangent at the intersection of the continuous bending segment and the continuous straightening segment is 1, and the magnitude of the curvature is...

[0023] A further improvement of the technical solution of the present invention is that it is applicable to the continuous casting steel production of slabs and large square billets.

[0024] The technological advancements achieved by this invention due to the adoption of the above technical solutions are as follows:

[0025] This invention replaces the bending section, basic arc section, and straightening section of traditional models with continuous bending and straightening sections, eliminating the basic arc section of traditional models. This evenly distributes the bending and straightening deformation of the billet throughout the entire continuous bending and straightening process, significantly extending the deformation range. Compared to the traditional model where billet deformation is concentrated in the short bending and straightening section, this invention significantly reduces the strain rate of the billet, effectively avoiding crack defects caused by stress concentration and improving the internal quality of the billet.

[0026] In this invention, both the continuous bending and straightening sections are smoothly connected by cubic curves and cycloids, and the intersections of each curve segment satisfy the same tangent slope and equal curvature, achieving continuous curvature change throughout the entire curve and satisfying the continuity of the second derivative. This design fundamentally solves the problem of high billet strain rate caused by the short bending and straightening deformation zone in traditional models, and also eliminates the problem of abrupt changes in billet strain at each bending and straightening point in traditional multi-point bending and straightening models, ensuring a smooth and continuous billet deformation process.

[0027] This invention defines the machine model curves through explicit parametric equations and provides a quantitative calculation method for the connection positions of each curve, providing an accurate parametric model for continuous casting machine design, which facilitates precise manufacturing and debugging in engineering practice.

[0028] This invention, due to the extremely low strain rate of the continuous bending and straightening section, can fully utilize the creep characteristics of the high-temperature cast billet, achieving slow stress release during bending and straightening, and reducing the risk of internal cracks in the billet. Simultaneously, the low strain rate characteristic creates favorable conditions for increasing the casting speed of the continuous casting machine, thus contributing to improved production efficiency.

[0029] The continuous straightening section and continuous bending section of this invention adopt a cycloidal design. Utilizing the characteristic of the cycloidal "rapidest descent line", the downward force generated by the weight of the billet can be used to assist in billet pulling, reducing the driving force requirement of the billet pulling equipment, reducing the pulling force and tensile stress in the billet. At the same time, the overall height of the equipment is reduced by curve optimization, which reduces the amount of billet bulging deformation caused by the weight of molten steel. Attached Figure Description

[0030] Figure 1 Curve diagram of a traditional five-point bending and five-point straightening straight arc continuous casting machine;

[0031] Figure 2 This invention relates to a cycloidal continuous bending straightening arc-shaped continuous casting machine model curve;

[0032] Figure 3 This invention provides a graph showing the relationship between the curvature and rate of change of curvature of the arc curve of a cycloidal continuous bending straightening arc continuous casting machine as a function of arc length.

[0033] Figure 4This is a comparison chart of the curve of a traditional five-point bending and five-point straightening arc continuous casting machine and the curve of a cycloidal continuous bending and straightening arc continuous casting machine of the present invention. Detailed Implementation

[0034] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings. In the following description, descriptions of well-known structures and technologies are omitted to avoid unnecessarily obscuring the concept of this invention.

[0035] This invention provides a cycloidal continuous bending and straightening arc-shaped continuous casting machine curve, which includes a vertical straight line segment, a continuous bending segment, a continuous straightening segment, and a horizontal straight line segment. There is no basic circular arc segment, and the entire machine curve is smoothly connected.

[0036] The aforementioned continuous bending section and continuous straightening section are symmetrical about a straight line at a 45° angle to the horizontal direction, and each is composed of a cubic curve and a cycloid.

[0037] The parametric equations for the above-mentioned vertical straight line segment and continuous curved segment are:

[0038]

[0039] in,

[0040] r = a·[π - t0 - sinint0 + sin(2t0)]

[0041] Equation (1) is the equation of the vertical straight line segment, where δ∈[r,r+η], and η is the length of the vertical straight line segment in mm; Equation (2) is the equation of the cubic curve of the continuous curved segment; and Equation (3) is the equation of the cycloid of the continuous curved segment. The unit is rad, representing the connection point between the cubic curve of the continuous bending segment and the cycloid. 'a' can be calculated using the following formula.

[0042]

[0043] In the formula, R0 is the main radius of the traditional straight arc continuous casting machine, in mm.

[0044] The curvature at the intersection of the vertical straight segment and the cubic curve of the continuous curved segment is 0; the slope of the tangent at the intersection of the cubic curve of the continuous curved segment and the cycloid is... The magnitude of curvature is

[0045] The parametric equations for the above horizontal straight segment and continuous straightening segment are:

[0046]

[0047] in,

[0048] r = a·[π - t0 - sinint0 + sin(2t0)]

[0049] Equation (4) is the equation of the horizontal straight line segment, where δ∈[-r-λ,-r], and λ is the length of the horizontal straight line segment in mm; Equation (5) is the equation of the cubic curve of the continuous straightening segment; and Equation (6) is the equation of the cycloid of the continuous straightening segment. The unit is rad, representing the position where the cubic curve of the continuous straightening segment connects with the cycloid. 'a' can be calculated using the following formula.

[0050]

[0051] In the formula, R0 is the main radius of the traditional straight arc continuous casting machine, in mm.

[0052] The curvature at the intersection of the horizontal straight segment and the cubic curve of the continuously straightened segment is 0; the slope of the tangent at the intersection of the cubic curve of the continuously straightened segment and the cycloid is... The magnitude of curvature is

[0053] After obtaining the cubic curves of the vertical straight segment, the continuous bending segment, and the continuous bending segment cycloidal curve from equations (1), (2), and (3), and obtaining the cubic curves of the horizontal straight segment, the continuous straightening segment, and the continuous straightening segment cycloidal curve from equations (4), (5), and (6), the vertical straight segment, the continuous bending segment, the continuous bending segment cubic curve, and the continuous bending segment cycloidal curve are translated with the horizontal straight segment, the continuous straightening segment cubic curve, and the continuous straightening segment cycloidal curve. This allows the two curves to connect at the bending end point (i.e., the straightening start point). This ensures that the two curves have a common tangent and equal radii of curvature at the connection point, achieving a smooth connection. The final cycloidal continuous bending straightening arc continuous casting machine model curve is obtained, such as... Figure 2 As shown. The slope of the tangent at the intersection of the continuous bending segment and the continuous straightening segment is 1, and the magnitude of the curvature is...

[0054] Taking the R9300mm straight arc continuous casting machine as an example, the machine model is as follows: Figure 1 As shown, its basic arc radius is 9300mm, the continuous casting billet thickness is 230mm, the casting speed is 1.5m / min, the continuous casting machine height is 12305.55mm, and it adopts a five-point bending and five-point straightening method. The vertical section length is 1465mm, the bending section arc length is 1030mm, the basic arc section arc length is 13300mm, and the straightening section arc length is 1520mm. The cycloidal continuous bending and straightening arc continuous casting machine model designed for this continuous casting machine type is as follows: billet thickness 230mm, a is 2500mm, t0 is 3.4rad, η is 1000mm, λ is 18447.32mm, R0=9300mm. The parametric equation expressions for the vertical straight section and the continuous bending section curve are:

[0055]

[0056] The parametric equations for the horizontal straight segment and the continuous straightening segment curve are as follows:

[0057]

[0058] The obtained cycloidal continuous bending straightening arc continuous casting machine model is as follows: Figure 2 As shown. The intersection of the horizontal straight line segment and the cubic curve of the straightening segment has a common tangent, with a slope of 0 and a curvature of 0; the intersection of the cubic curve of the straightening segment and the cycloid of the straightening segment also has a common tangent, with a slope of 0.1299 and equal curvature of 1.008 × 10⁻⁶. -4 The intersection of the straightened cycloid and the curved cycloid has a common tangent with a slope of 1 and equal curvature of 1.414 × 10⁻⁶. -4 The intersection of the cycloid and the cubic curve of the curved segment has a common tangent with a slope of 7.698 and equal curvature of 1.008 × 10⁻⁶. -4 The intersection of the cubic curve of the curved segment and the vertical straight segment has a common tangent with a slope of +∞ and equal curvature of 0. The length of the vertical straight segment is 1000mm, and the casting machine height is 13068mm. A comparison of the designed cycloidal continuous bending straightening arc-shaped continuous casting machine curve with the original R9300mm straight arc-shaped continuous casting machine curve is shown in the figure below. Figure 4 As shown, compared with the original R9300mm model, the height of the new model casting machine is reduced by 236.56mm, and all sections of the curve of the entire model are smoothly connected.

[0059] The curvature and rate of change of curvature of the new model's curves vary with arc length as follows: Figure 3 As shown, the maximum curvature of the model curve is 1.414 × 10⁻⁶. -4 Located at the junction of the continuous bending section and the continuous straightening section, the maximum rate of curvature change is 4.11 × 10⁻⁶. -8 Located at the junction of the vertical straight segment and the cubic curve of the bending segment, and at the junction of the horizontal straight segment and the cubic curve of the straightening segment, the maximum strain rate on the surface of the continuously cast billet is 7.89 × 10⁻⁶. -5 Because the new model eliminates the basic circular arc segment, its continuous bending and straightening sections are very long. The bending and straightening deformation of the billet is distributed within these sections, resulting in very low strain and strain rate. In contrast, the original R9300mm straight-arc continuous casting machine, employing five-point bending and five-point straightening, had its billet bending and straightening deformation distributed within shorter bending and straightening sections, leading to large strain peaks and abrupt strain rate changes. Therefore, the cycloidal continuous bending and straightening machine's curve exhibits extremely low strain rates, which can improve the internal quality of the billet and prevent crack defects, demonstrating the feasibility and superiority of this method.

[0060] In the above embodiments, the present invention provides a cycloidal continuous bending and straightening arc-shaped continuous casting machine curve. The present invention replaces the bending section, basic arc section, and straightening section of the traditional machine with a continuous bending section and a continuous straightening section, eliminating the basic arc section of the traditional machine. This evenly distributes the bending and straightening deformation of the billet throughout the entire continuous bending and straightening process, significantly extending the deformation range. Compared to the traditional machine where billet deformation is concentrated in the short bending and straightening section, the present invention significantly reduces the strain rate of the billet, effectively avoiding crack defects caused by stress concentration and improving the internal quality of the billet. Both the continuous bending section and the continuous straightening section of the present invention use cubic curves to smoothly connect with the cycloid, and the intersection points of each curve segment satisfy the same tangent slope and equal curvature, achieving continuous curvature change throughout the entire curve and satisfying the continuity of the second derivative. This design fundamentally solves the problem of high billet strain rate caused by the short bending and straightening deformation zone in traditional machines, and also eliminates the problem of abrupt changes in billet strain at each bending and straightening point in traditional multi-point bending and straightening machines, ensuring a smooth and continuous billet deformation process.

[0061] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the concept and scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the inventive concept should fall within the protection scope of the present invention. All technical contents for which protection is sought in this invention are fully described in the claims.

Claims

1. A curve of a trochoidal continuous bend straightening arc continuous caster machine type, characterized in that: The curve comprises a vertical straight line segment, a continuous bending segment, a continuous straightening segment and a horizontal straight line segment connected in sequence; the continuous bending segment and the continuous straightening segment are symmetric about a straight line with a 45° angle with the horizontal direction as a whole, and the continuous bending segment and the continuous straightening segment are both composed of a cubic curve and a trochoid.

2. The curve of a trochoidal continuous bending and straightening arc-shaped continuous caster model according to claim 1, characterized in that: The parameter equation of the vertical straight line segment and the continuous bending segment curve is, wherein, r=a·[π-t0-sint0+sin(2t0)] Wherein (1) is a vertical straight line equation, wherein δ∈[r, r+η], η is the length of the vertical straight line, in mm; (2) is a cubic curve equation of the continuous curved section, and (3) is a cycloid equation of the continuous curved section, wherein rad, representing the connection position of the cubic curve of the continuous curved section and the cycloid, and a can be calculated by the following formula, In the formula, R0 is the main radius of a traditional straight arc continuous caster, with the unit of mm.

3. The trochoidal continuous bend straightening arc continuous caster machine model curve according to claim 2, characterized in that: The curvature at the intersection point of the vertical straight segment and the continuous curved segment cubic curve is 0; the tangent slope at the intersection point of the continuous curved segment cubic curve and the cycloid is The curvature size is 4. The curve of a trochoidal continuous bending and straightening arc-shaped continuous caster model according to claim 1, characterized in that: The parameter equation of the horizontal straight line segment and the continuous straightening segment curve is, wherein, r=a·[π-t0-sint0+sin(2t0)] wherein (4) is a horizontal straight line segment equation, in which δ ∈ [-r-λ, -r], λ is the length of the horizontal straight line segment, in units of mm; (5) is a cubic curve equation of the continuous straightening segment, and (6) is a cycloid equation of the continuous straightening segment, in which in units of rad, representing the connection position of the cubic curve of the continuous straightening segment and the cycloid, and a can be calculated by the following formula, In the formula, R0 is the main radius of a traditional straight arc continuous caster, with the unit of mm.

5. The trochoidal continuously curved straightening arc continuous caster machine model curve of claim 4, wherein: The curvature at the intersection of the horizontal straight segment and the continuous straightening cubic curve is 0; and the tangent slope at the intersection of the continuous straightening cubic curve and the cycloid is The curvature size is 6. The trochoidal continuously curved straightening arc continuous caster machine model curve of claim 1, wherein: The tangent slope at the intersection of the continuous bending section and the continuous straightening section is 1, and the curvature size is 7. A trochoidal continuous bend straightening arc continuous caster machine model curve according to any one of claims 1 to 6, characterised in that: The continuous steel casting machine is suitable for the continuous casting production of slab and bloom.

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