A Modeling Method for Shear Force in Crescent-Shaped Edge Cutting Shear

Abstract

This invention provides a modeling method for the shear force of a crescent-shaped shear blade, comprising the following steps: 1) expanding and parameterizing the theoretical shear blade arc into a function based on its formation process; 2) calculating the slope of each point on the arc; 3) determining the shear angle at each point on the arc based on the slope in step 2); 4) calculating the Nosari shear force using the shear blade shear's Nosari formula; 5) calculating the shear force at each point on the arc based on step 4); and 6) identifying the point with the maximum shear force within the range of the arc's values ​​as the design basis for the crescent-shaped shear blade. The data used in this modeling process are readily available, thus avoiding the impact of measurement errors on the shear force data, resulting in high calculation accuracy and precision. This invention solves the modeling problem for calculating the shear force of a crescent-shaped shear blade, transforming a complex model into a simple one, saving time, and offering low cost and high flexibility.

Description

Technical Field

[0001] This invention belongs to the field of modeling technology for shear force of edge-cutting shears; in particular, it relates to a method for modeling the shear force of crescent-shaped edge-cutting shears. Background Technology

[0002] In a continuous production line for cold-rolled strip, the shearing equipment used to cut the edges of the weld seam between the front and rear strips is usually called a shearing edge cutter. The shearing blade of this equipment is mostly crescent-shaped, hence the name crescent-shaped shearing edge cutter. A welding machine is essential in a continuous production line, used to weld the tail of the previous roll to the head of the next roll into one piece. A shearing edge cutter is essential after the welding machine to smoothly transition the width change of the strip. Therefore, the shearing edge cutter has become an essential process equipment in a continuous production line for strip and sheet. Because the crescent-shaped shearing edge cutter has a curve after the shearing line is unfolded, there has never been a systematic shearing force calculation model. In engineering design, stamping shearing is usually used to roughly calculate its shearing force, or a finite element model is used for calculation. Therefore, the existing production process still has the following shortcomings: (1) the theoretical deviation of stamping shearing is large and the calculation accuracy is low; (2) finite element calculation is time-consuming, expensive and inflexible; (3) there is no existing mature calculation process and formula. Summary of the Invention

[0003] The purpose of this invention is to provide a method for modeling the shearing force of a crescent-shaped edge-cutting shear.

[0004] This invention is achieved through the following technical solution:

[0005] This invention relates to a method for modeling the shear force of a crescent-shaped edge-cutting shear, comprising the following steps:

[0006] Step 1: Based on the formation process of the crescent-shaped shear blade, unfold the blade curve and establish the graphical coordinates of arc length and chord height;

[0007] Step 2: Establish the equations corresponding to the chord height and arc length based on the coordinates of the graph;

[0008] Step 3: Differentiate the equation to obtain the shear angle at the corresponding point on each arc length;

[0009] Step 4: Calculate the shearing force at each point on the crescent blade shears according to the calculation formula for oblique blade shears;

[0010] Step 5: Based on the shear force calculation formula, obtain the point of maximum shear force during shearing, which serves as the design basis for the crescent-shaped edge-cutting shear.

[0011] Preferably, in step 1, the formation process of the crescent-shaped shear blade is as follows: a pitch circle with radius R is cut by an inclined plane α, and the arc formed by the plane and the cylinder on the cylindrical surface is the shear blade arc, which is part of an ellipse.

[0012] Preferably, in step 1, the curve is a graph showing the relationship between the chord height and the arc after unfolding along the circumference with R as the central axis. For example... Figure 9 As shown

[0013] Preferably, in step 2, the process of establishing the equation corresponding to the chord height and arc length is as follows:

[0014] (1) X is the arc length along the elliptic curve, and the arc traversed is...

[0015] (2) The distance traveled on 2R corresponding to the arc length X is R-RcosB;

[0016] (3) The total height of the entire 2R is h = 2Rtanα;

[0017] (4) The height corresponding to X is

[0018] (5) Substitute into the above equation;

[0019] (6) Simplified to:

[0020] Where T is the radius of the model cylinder, and α is the inclination angle of the cutting cylinder plane.

[0021] Preferably, in step 4, the calculation process for the shearing angle at each point on the crescent-shaped scissors is as follows:

[0022] First, calculate the slope corresponding to each arc length point: Where RsinB is a constant, it can be replaced by A, then Therefore, the shear angles corresponding to each arc length point can be obtained as follows:

[0023] Preferably, in step 5, the shear force calculation formula is the Nossari formula, which is:

[0024]

[0025] Where, σ b —The shear strength limit of the strip steel, in kilograms per millimeter. 2 ;

[0026] h — the thickness of the strip being sheared, in millimeters;

[0027] δ5—Elongation;

[0028] z—depth of cut;

[0029] y — coefficient c represents the lateral clearance of the blade.

[0030] Generally speaking, when h ≤ 5 mm, c = 0.07h; when h = 10–20 mm, c = 0.5 mm.

[0031] α — Blade tilt angle (degrees);

[0032] x — coefficient n is the distance from the shearing plane to the pressure plate. In the preliminary calculation, x = 10.

[0033] K5 is the coefficient of influence of the blade becoming dull after use, and is generally taken as K5 = 1.1 to 1.3.

[0034] Preferably, in step 4, the shearing force at each point on the crescent-shaped shears is calculated using the Nossari formula.

[0035] The present invention has the following advantages:

[0036] (1) Based on the formation process of the shear blade arc, the present invention expands the shear blade curve and derives the shear blade arc curve function.

[0037] (2) The present invention derives the slope formula of the shearing curve by differentiating the shearing curve.

[0038] (3) This invention finds the point with the minimum slope within the shear blade region.

[0039] (4) Calculate the maximum shear force according to the Nosari formula for oblique blade shears.

[0040] (5) The method of this invention is the first to propose a calculation process and corresponding functions. The process is simple and the formula is accurate.

[0041] (6) The method of the present invention provides a template-style process for calculating the shear force of various types of excavation shearing. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of the layout of the edge-cutting shearing equipment involved in the modeling method of this invention during operation;

[0043] Figure 2 This is a product rendering of the edge-cutting shearing equipment involved in the modeling method of this invention after use;

[0044] Figure 3 This is a front view of the edge-cutting shearing device involved in the modeling method of this invention;

[0045] Figure 4 This is a three-dimensional view of the edge-cutting shearing device involved in the modeling method of this invention;

[0046] Figure 5 This is a schematic diagram of the upper shear blade of the edge-cutting shearing device involved in the modeling method of this invention;

[0047] Figure 6 This is a top view of the upper shear blade plane of the edge-cutting shearing device involved in the modeling method of this invention;

[0048] Figure 7 This is a schematic diagram of the lower shear blade plane elevation of the edge-cutting shearing device involved in the modeling method of this invention;

[0049] Figure 8 This is a top view of the lower shear blade plane of the edge-cutting shearing device involved in the modeling method of this invention;

[0050] Figure 9 This is a diagram illustrating the modeling method of the present invention;

[0051] In the attached diagram, 1-base, 2-waste conveying mechanism, 3-left shear body, 4-middle roller, 5-right shear body, 6-shearing hydraulic cylinder, 7-upper shear blade, 8-lower shear blade, 9-countersunk hole. Detailed Implementation

[0052] The present invention will now be described in detail with reference to specific embodiments. It should be noted that the following embodiments are merely further illustrations of the present invention, but the scope of protection of the present invention is not limited to the following embodiments.

[0053] Example

[0054] This embodiment relates to a modeling method for calculating the shear force of a crescent-shaped edge-cutting shear, including the following steps:

[0055] Step 1) Based on the formation process of the crescent-shaped shear blade, unfold the blade curve and establish the graphical coordinates of arc length and chord height, such as... Figure 9 As shown;

[0056] Step 2) Establish the equations corresponding to the chord height and arc length, as follows:

[0057] (1) Let X be the arc length along the elliptic curve, then the arc it travels is...

[0058] (2) The distance traveled on 2R corresponding to the arc length X is R-RcosB;

[0059] (3) The total height of the entire 2R is h = 2Rtanα;

[0060] (4) The height corresponding to X

[0061] (5) Substitute into the above equation;

[0062] (6) Simplified to:

[0063] Where T is the radius of the model cylinder, and α is the inclination angle of the cutting cylinder plane.

[0064] Step 3) Obtain the shear angle at each point along the arc length by differentiating the equation. The slope at each point along the arc length is: Where Rsinβ is a constant, it can be replaced by A, then Therefore, the shear angles corresponding to each arc length point can be obtained as follows:

[0065] Step 4) The shearing force at each point on the crescent shears can be calculated using the existing formula for calculating the shearing force of the oblique blade shears. The Nossari formula for calculating the shearing force of oblique blade shears is:

[0066]

[0067] σ b —Shear strength limit of strip (kg / mm) 2 );

[0068] h — the thickness of the strip being sheared (in millimeters);

[0069] δ5—Elongation;

[0070] z—depth of cut;

[0071] y — coefficient c represents the lateral clearance of the blade.

[0072] Generally speaking, when h ≤ 5 mm, c = 0.07h; when h = 10–20 mm, c = 0.5 mm.

[0073] α — Blade tilt angle (degrees);

[0074] x — coefficient n is the distance from the shearing plane to the pressure plate. In the preliminary calculation, x = 10.

[0075] K5—The coefficient of influence of blade dulling after use, generally taken as K5 = 1.1 to 1.3;

[0076] Step 5) Based on the shear force calculation in Step 4), the point of maximum shear force during shearing can be obtained. The shear force at this point serves as the design basis for the crescent-shaped edge-cutting shear.

[0077] like Figure 1 , Figure 3 and Figure 4As shown, a typical crescent-shaped edge-cutting shear from a certain manufacturer comprises: a base 1, a waste edge conveying mechanism 2, a left shearing machine body 3, a middle idler roller 4, a right shearing machine body 5, a shearing hydraulic cylinder 6, an upper shearing blade 7, and a lower shearing blade 8. The left and right shearing machine bodies 3 and 5 are fixed to the base 1 via linear guide rails and move left and right via the shearing hydraulic cylinder 6. The waste edge conveying mechanism 2 is located inside the base 1 and is used to convey the crescent-shaped waste edges cut by the left and right shearing machine bodies 3 and 5 to one side of the equipment. The middle idler roller 4 is fixed to the base 1 and is used to support the strip to be sheared. A product effect image of the edge-cutting shearing equipment after use is shown below. Figure 2 As shown.

[0078] The working process of the crescent-shaped shear is as follows: The shearing hydraulic cylinder 6 drives the upper shear blade 7, which is connected to the frame via a linear guide rail, to move up and down reciprocally. The lower shear blade 8 is fixed to the frame. When the upper shear blade 7 (equipped with multiple countersunk holes 9, with a spacing L of 125mm between the countersunk holes) and the lower shear blade 8 (equipped with multiple countersunk holes 9) overlap, there is a fixed shearing lateral clearance. When the upper shear blade 7 moves until the lower shear blade 8 is completely overlapped, the strip steel is sheared off. See Figures 5-8 As shown.

[0079] The principle of this invention is as follows:

[0080] This invention functionalizes the upper shear blade arc curve of a crescent-shaped edge-cutting shear, establishing a correlation function between arc length and chord height. The shear angle at each point on the shear blade arc can be calculated using this function. The shear force at each point is then calculated using Nosari's formula for oblique-blade shears. Finally, the maximum shear force within the shear blade range can be determined using the same function. This shear force serves as the design basis for the crescent-shaped edge-cutting shear. By modeling the shear force of the crescent-shaped edge-cutting shear using the above principles, accurate shear force calculations are obtained, providing a theoretical basis for the design of crescent-shaped edge-cutting shears and a template for calculating the shear force of various edge-cutting shears.

[0081] This invention solves the problem of calculating the shear force of crescent-shaped shear cutters, transforming complex models into simpler ones, saving time, and offering low cost and high flexibility.

[0082] This invention proposes for the first time a modeling method for shear force in a crescent-shaped shear cut. The various data used in the modeling process are readily available or can be obtained through queries. Therefore, the shear force data will not be affected by data measurement errors during the process, resulting in high calculation accuracy and precision.

[0083] The specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various modifications or variations within the scope of the claims, which do not affect the essence of the present invention.

Claims

1. A method of modeling the shearing force of a crescent-shaped undercutting scissors, characterized by, The method comprises the following steps: Step 1, according to the forming process of the cutting edge of the crescent-shaped edge cutting shear, the cutting edge curve is unfolded to establish a graphic coordinate of the chord height and the arc length; Step 2, an equation corresponding to the chord height and the arc length is established according to the graphic coordinate; Step 3, the derivative of the equation is obtained to obtain the shearing angle of the corresponding point on each arc length; Step 4, the shearing angle of each point on the crescent-shaped shear is calculated according to the oblique blade shear calculation formula; Step 5, the point of the maximum shearing force during shearing is obtained according to the shearing force calculation formula, which is used as the design basis of the crescent-shaped edge cutting shear; In step 1, the forming process of the cutting edge of the crescent-shaped edge cutting shear is that a division circle with a radius of R is cut by a plane with an inclined axis α, and the circular arc formed by the plane and the cylinder on the cylindrical surface is the cutting edge circular arc of the cutting edge, which is a part of an ellipse; In step 2, the process of establishing the equation corresponding to the chord height and the arc length is as follows: ; 1 X is the arc length along the elliptic curve, the arc length is ; ② X arc length corresponds to the distance walked on 2R is ; iii. The total height of the entire 2R is ; (4) the height corresponding to X is ; • the sum of the concentrations of the compounds of formula (I) and (II) is 100%, into the above formula ⑥ , which simplifies to ; Wherein, α is the inclination angle of the cutting cylindrical plane.

2. The method of claim 1, wherein the shear force of the crescent-shaped undercutting scissors is modeled by, In step 4, the calculation process of the shearing angle of each point on the crescent-shaped shear is as follows: First, the slope of each arc length point is calculated as: wherein is a constant, and A is replaced by Thus, the shear angle of each arc length point is: X∈(0, 2ΠR).

3. The method of claim 1, wherein the shear force of the crescent-shaped undercutting scissors is modeled by, In step 5, the shearing force calculation formula is the Norsali formula, which is as follows: wherein - the sheared strip strength limit in kg / mm 2 ; - thickness of the cut strip, in millimeters; - elongation; z is the cutting depth; - a coefficient, c is the side clearance of the blade; α is the inclination angle of the cutting cylindrical plane.

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