A heart-line based hot mill cutting edge and method of designing the same

Abstract

The application discloses a hot mill grinding piece based on a heart curve and a design method thereof, and belongs to the technical field of hot mill grinding pieces. The design method of the hot mill grinding piece based on the heart curve comprises the following steps: S1, determining an inner circle radius R1 and an outer circle radius R2 of the hot mill grinding piece; S2, determining an origin of the heart curve as a center O of the hot mill grinding piece; S3, defining an arbitrary point P on the heart curve, a grinding tooth starting point P1, a grinding tooth ending point P2, a rotary radius p1 of the grinding tooth starting point, a sliding angle a of the arbitrary point on the heart curve, and a polar angle theta of the arbitrary point on the heart curve; and S4, obtaining a heart curve equation of the hot mill grinding piece. The hot mill grinding piece provided by the application can improve fiber separation quality, reduce energy consumption and prolong tool life. The design method of the hot mill grinding piece based on the heart curve designs a grinding tooth profile of the hot mill grinding piece as a curve function, which is convenient for design expression and mathematical analysis of tooth blade stress.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of hot mill grinding plate, and more particularly to a hot mill grinding plate based on a cardioid and a design method thereof. BACKGROUND

[0002] Fiberboard is widely used in furniture, packaging and other industries due to its homogeneous material, small difference in strength, and resistance to cracking. At present, the demand for fiberboard is very strong. The hot mechanical method is the most commonly used method for separating fibers. The raw material is treated with hot water or saturated steam to soften or partially dissolve the intercellular layer of the fiber, and then separated into fibers by a hot mill under normal or high pressure conditions. When the wood chips are subjected to the shearing force of a pair of relatively rotating grinding plates, the wood chips will undergo dissociation. With the continuous separation, the wood fibers will eventually be dissociated. The dissociation of wood fibers uses a sliding cutting method, that is, there is a certain angle (i.e., a sliding angle) between the cutting speed and the cutting force, which can reduce energy consumption. The hot mill grinding plate is a key component for separating fibers, and has a significant impact on separation quality and energy consumption.

[0003] At present, the patents related to hot mill grinding plates are represented by the Chinese invention patent "Design method of tooth shape structure of circular ring partitioned large diameter stage hot mill grinding plate" with application number CN201210437023.X and the Chinese invention patent "Design method of tooth shape structure of hot mill grinding plate" with application number CN201910891957.2. The grinding plate is divided into a crushing zone, a coarse grinding zone, a fine grinding zone, and other zones. The parameters of each zone are set according to the hot mill raw material, which improves the separation quality and reduces the energy consumption to a certain extent. However, the sliding angle of these existing patents is constant, which does not completely match the actual demand. Each zone has independent structural parameters, and the structure expression is relatively cumbersome. SUMMARY

[0004] In order to design the grinding tooth profile of the hot mill grinding plate as a curve function, facilitate design expression, and facilitate mathematical analysis of the stress of the tooth edge, the present application provides a hot mill grinding plate based on a cardioid and a design method thereof.

[0005] To solve the above technical problems, the technical solutions of the present application are as follows:

[0006] The present application provides a hot mill grinding plate based on a cardioid, wherein the tooth edge profile of the hot mill grinding plate is a cardioid,

[0007] The cardioid equation of the hot mill grinding plate is:

[0008] ρ=a·(1-cosθ)

[0009] wherein ρ is the distance from any point on the cardioid to the origin of the cardioid, i.e., the polar radius; a is a parameter of the cardioid, representing the shape of the cardioid; and θ is the polar angle of any point on the cardioid, i.e., the angle between the polar axis and the x-axis at that point.

[0010] The horizontal coordinate and the vertical coordinate of the point on the cardioid line of the tooth edge profile of the hot mill grinding blade are as follows:

[0011] x=a*(1-cosθ)*cosθ

[0012] y=a*(1-cosθ)*sinθ

[0013] wherein x and y are respectively the horizontal coordinate and the vertical coordinate of the point on the cardioid line; a is a parameter of the cardioid line, representing the shape of the cardioid line; θ is the polar angle of any point on the cardioid line, that is, the included angle between the polar axis and the x-axis at the point.

[0014] Further, the polar angle θ satisfies θ∈(θ1, θ2), θ1 is the polar angle of the starting point of the cardioid line, and θ2 is the polar angle of the terminal point of the cardioid line; wherein the polar angle θ1 of the starting point of the cardioid line ranges from 28° to 60°.

[0015] The application further provides a design method of a hot mill grinding blade based on a cardioid line, comprising the following steps:

[0016] S1, determining the inner circle radius R1 and the outer circle radius R2 of the hot mill grinding blade;

[0017] The outer circle radius R2 ranges from 400 mm to 2000 mm, and the expression of the inner circle radius R1 is as follows:

[0018] R1=C1*R2 (1)

[0019] wherein C1 is a constant, and the range of C1 is from 0.4 to 0.6;

[0020] S2, determining that the origin of the cardioid line is the center O of the hot mill grinding blade;

[0021] S3, defining any point P on the cardioid line, the starting point P1 of the grinding tooth, the terminal point P2 of the grinding tooth, the rotation radius ρ1 of the starting point of the grinding tooth, the sliding angle α of any point on the cardioid line, and the polar angle θ of any point on the cardioid line;

[0022] The any point P on the cardioid line is the intersection point of the cardioid line and the straight line where the radius of the hot mill grinding blade is located;

[0023] The starting point P1 of the grinding tooth is the intersection point of the cardioid line and the inner diameter of the hot mill grinding blade;

[0024] The terminal point P2 of the grinding tooth is the intersection point of the cardioid line and the outer diameter of the hot mill grinding blade;

[0025] The expression of the rotation radius ρ1 of the starting point of the grinding tooth is as follows:

[0026] ρ1=R1 (2)

[0027] The sliding tangent angle a of any point on the cardioid is the included angle between the polar axis at the point and the tangent line at the point, the sliding tangent angle of the starting point of the cardioid is denoted by a1, the sliding tangent angle of the terminal point of the cardioid is denoted by a2, and the sliding tangent angle a1 of the starting point of the cardioid ranges from 14° to 30°;

[0028] The polar angle θ of any point on the cardioid is the included angle between the polar axis at the point and the x-axis, the polar angle of the starting point of the cardioid is denoted by θ1, and the polar angle of the terminal point of the cardioid is denoted by θ2;

[0029] S4, obtain the cardioid equation of the hot mill grinding piece;

[0030] The cardioid equation of the hot mill grinding piece is ρ=a·(1-cosθ), θ∈(θ1, θ2);

[0031] Wherein, ρ is the distance from any point on the cardioid to the origin of the cardioid, that is, the polar radius; a is the parameter of the cardioid, representing the shape of the cardioid; θ is the polar angle of any point on the cardioid, that is, the included angle between the polar axis at the point and the x-axis; θ1 is the polar angle of the starting point of the cardioid; θ2 is the polar angle of the terminal point of the cardioid.

[0032] Further, step S4 specifically comprises:

[0033] S41, set the parameter equation of the cardioid;

[0034] The parameter equation of the cardioid is:

[0035] ρ=a·(1-cosθ) (3)

[0036] x=a·(1-cosθ)·cosθ (4)

[0037] y=a·(1-cosθ)·sinθ (5)

[0038] S42, calculate the polar angle θ1 of the starting point of the cardioid;

[0039] Derive the derivatives of formula (4) and formula (5) with respect to the polar angle θ, respectively, to obtain formula (6) and formula (7);

[0040]

[0041]

[0042] Derive the derivative of y with respect to x, which is equal to the tangent slope corresponding to the polar angle θ on the cardioid, as formula (8):

[0043]

[0044] From formula (8), we have:

[0045]

[0046] According to formula (9) and the range of the slide angle of the heart line starting point α1 being 14° to 30°, the range of the polar angle θ1 of the heart line starting point is 28° to 60°;

[0047] S43, the value of a is obtained;

[0048] Let:

[0049] a = C2·R2 (10)

[0050] By combining formula (1), (2), (3), (10), we get:

[0051] C1·R2 = C2·R2·(1-cosθ1) (11)

[0052] We get:

[0053]

[0054] From the range of C1 being 0.4 to 0.6 and the range of the polar angle θ1 being 28° to 60°, we get the range of C 2MAX and C 2MIN :

[0055]

[0056]

[0057] The range of C2 is 0.8 to 5.0, which is brought into formula (10) to obtain the value of a;

[0058] S44, the polar angle θ2 of the heart line ending point is obtained;

[0059] From the following formula

[0060] R2 = a·(1-cosθ2) (13)

[0061] We get:

[0062]

[0063] The heart line equation of the hot mill grinding piece is obtained, and the heart line equation of the hot mill grinding piece is:

[0064] ρ = a·(1-cosθ), θ ∈ (θ1, θ2) (15)

[0065] Wherein, ρ is the distance from any point on the cardioid to the origin of the cardioid, that is, the polar radius; a is the parameter of the cardioid, representing the shape of the cardioid; θ is the polar angle of any point on the cardioid, that is, the angle between the polar axis and the x-axis at the point; θ1 is the polar angle of the starting point of the cardioid; θ2 is the polar angle of the terminal point of the cardioid.

[0066] Further, the cardioid segment P1P2 formed by the grinding tooth starting point P1 and the grinding tooth terminal point P2 is the grinding tooth profile of the hot mill grinding plate.

[0067] Further, the cardioid segment P1P2 is arranged in a circumferential array to obtain a complete hot mill grinding plate.

[0068] Compared with the prior art, the beneficial effects of the technical scheme of the present application are:

[0069] The present application provides a hot mill grinding plate based on a cardioid and a design method thereof. The hot mill grinding plate based on the cardioid provided by the present application has gradually increasing slide angles from the inner circle to the outer circle, which are matched with gradually increasing cutting rates and gradually decreasing cutting forces, thereby improving the fiber separation quality, reducing energy consumption, and prolonging the tool life. The grinding tooth profile of the hot mill grinding plate is designed as a curve function, which is convenient for design expression and mathematical analysis of the stress of the tooth edge. BRIEF DESCRIPTION OF DRAWINGS

[0070] In order to more clearly illustrate the technical schemes in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor on the basis of these drawings.

[0071] Figure 1 It is a cardioid diagram of the hot mill grinding plate based on the cardioid of the present application; wherein, point O is the center of the hot mill grinding plate, which is also the origin of the cardioid; R1 is the inner circle radius of the hot mill grinding plate; R2 is the outer circle radius of the hot mill grinding plate; P is any point; ω is the rotation direction of the hot mill grinding plate; P1 is the grinding tooth starting point; P2 is the grinding tooth terminal point; α is the slide angle; α1 is the slide angle of the grinding tooth starting point; α2 is the slide angle of the grinding tooth terminal point; θ1 is the polar angle of the grinding tooth starting point; θ2 is the polar angle of the grinding tooth terminal point; the cardioid segment P1P2 is the tooth edge;

[0072] Figure 2 It is a tooth profile structure diagram of the hot mill grinding plate based on the cardioid of the present application, and the tooth edge profile is a cardioid;

[0073] Figure 3 It is a flow chart of the design method of the hot mill grinding plate based on the cardioid of the present application. Detailed Implementation

[0074] To better understand the purpose, structure, and function of this invention, the technical solution of this invention will be further described in detail below with reference to the accompanying drawings and specific preferred embodiments.

[0075] In the description of this invention, it should be understood that the terms "left side," "right side," "upper part," "lower part," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. "First," "second," etc., do not indicate the importance of components, and therefore should not be construed as a limitation of the invention. The specific dimensions used in the embodiments are only for illustrating the technical solutions and do not limit the scope of protection of the invention. It is understandable that some well-known structures and their descriptions may be omitted in the accompanying drawings for those skilled in the art.

[0076] Unless otherwise expressly specified and limited, the terms "installation," "setting," "connection," and "fixation" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.

[0077] Example 1:

[0078] like Figures 1-2 As shown, the present invention provides a technical solution: a thermal grinding disc based on a heart-shaped profile, wherein the tooth profile of the thermal grinding disc is a heart-shaped profile.

[0079] The equation of the heart line of the hot grinding mill disc is:

[0080] ρ=a·(1-cosθ)

[0081] Where ρ is the distance from any point on the cardiac line to the origin of the cardiac line, i.e., the polar radius; a is a parameter of the cardiac line, representing the shape of the cardiac line; θ is the polar angle at any point on the cardiac line, i.e., the angle between the polar axis and the x-axis at that point.

[0082] The x and y coordinates of the points on the cardioid line formed by the tooth profiles of the hot grinding mill disc are:

[0083] x = a·(1-cosθ)·cosθ

[0084] y = a·(1-cosθ)·sinθ

[0085] Where x and y are the abscissa and ordinate of a point on the cardiac line, respectively; a is a parameter of the cardiac line, representing the shape of the cardiac line; θ is the polar angle of any point on the cardiac line, that is, the angle between the polar axis and the x-axis at that point.

[0086] Furthermore, the polar angle θ satisfies θ∈(θ1, θ2), where θ1 is the polar angle at the starting point of the cardiac line and θ2 is the polar angle at the ending point of the cardiac line; wherein, the polar angle θ1 at the starting point of the cardiac line ranges from 28° to 60°.

[0087] The hot grinding disc provided in this embodiment has a sliding angle that gradually increases with the radius, which matches the actual needs; the tooth profile is expressed by only one function, which is simple; the design of the heart line tooth profile can improve the cutting force distribution during the cutting process, reduce the concentration of cutting force, reduce grinding heat and tool wear on the workpiece surface, and improve cutting performance.

[0088] Specifically, the hot mill grinding disc provided in this embodiment has a gradually increasing slip angle from the inner circle to the outer circle, which matches the gradually increasing cutting rate. The gradually increasing slip angle also matches the gradually decreasing cutting force, thereby improving fiber separation quality, reducing energy consumption, and extending tool life.

[0089] Example 2:

[0090] like Figure 3 As shown, the present invention also provides a design method for a thermal grinding disc based on a heart-shaped wire, comprising the following steps:

[0091] S1. Determine the inner radius R1 and outer radius R2 of the grinding disc of the hot mill;

[0092] The outer radius R2 ranges from 400 to 2000 mm, and the expression for the inner radius R1 is:

[0093] R1=C1·R2 (1)

[0094] Where C1 is a constant, and the range of C1 is 0.4-0.6;

[0095] S2. Determine the origin of the cardiac line as the center O of the grinding disc of the hot mill;

[0096] S3. Define any point P on the cardiac line, the starting point P1 of the molar, the ending point P2 of the molar, the radius of rotation ρ1 where the starting point of the molar is located, the sliding angle α of any point on the cardiac line, and the polar angle θ of any point on the cardiac line.

[0097] Any point P on the cardiac line is the intersection of the cardiac line and the straight line containing the radius of the hot grinding mill disc.

[0098] The grinding starting point P1 is the intersection of the cardiac line and the inner diameter of the grinding disc of the hot grinding mill;

[0099] The tooth grinding termination point P2 is the intersection point of the cardioid and the outer diameter of the hot mill grinding plate;

[0100] The expression of the rotation radius p1 where the tooth grinding starting point is located is:

[0101] p1=R1 (2)

[0102] The sliding angle a of any point on the cardioid is the included angle between the cutting speed and the cutting force at the point, and the sliding angle a of any point on the cardioid is embodied in the included angle between the polar axis at the point and the tangent at the point in the attached figure, the sliding angle of the starting point of the cardioid is represented by a1, and the sliding angle of the termination point of the cardioid is represented by a2, and the sliding angle a1 of the starting point of the cardioid ranges from 14° to 30°; Figure 1

[0103] The polar angle θ of any point on the cardioid is the included angle between the polar axis at the point and the x-axis, and the polar angle of the starting point of the cardioid is represented by θ1, and the polar angle of the termination point of the cardioid is represented by θ2;

[0104] S4, obtaining the cardioid equation of the hot mill grinding plate;

[0105] The cardioid equation of the hot mill grinding plate is ρ=a·(1-cosθ), θ∈(θ1, θ2);

[0106] Wherein, ρ is the distance from any point on the cardioid to the origin of the cardioid, i.e. the polar radius; a is the parameter of the cardioid, representing the shape of the cardioid; θ is the polar angle of any point on the cardioid, i.e. the included angle between the polar axis at the point and the x-axis; θ1 is the polar angle of the starting point of the cardioid; θ2 is the polar angle of the termination point of the cardioid.

[0107] Further, step S4 specifically comprises:

[0108] S41, setting the parameter equation of the cardioid;

[0109] The parameter equation of the cardioid is:

[0110] ρ=a·(1-cosθ) (3)

[0111] x=a·(1-cosθ)·cosθ (4)

[0112] y=a·(1-cosθ)·sinθ (5)

[0113] S42, calculating the polar angle θ1 of the starting point of the cardioid;

[0114] Deriving the derivatives of formula (4) and formula (5) with respect to the polar angle θ, respectively, to obtain formula (6) and formula (7);

[0115] ​

[0116]

[0117] Take the derivative of y with respect to x, which equals the tangent slope of the polar angle θ on the cardioid, as shown in equation (8):

[0118]

[0119] From equation (8), we have:

[0120]

[0121] According to equation (9) and the range of the tangent angle α1 of the starting point of the cardioid being 14° to 30°, the range of the polar angle θ1 of the starting point of the cardioid is 28° to 60°;

[0122] From equation (9), we can see that the tangent angle increases with the increase of the polar angle, i.e., increases with the increase of the separation radius;

[0123] From equation (9), we can also see that when the polar angle is as large as 90°, the tangent angle is 45°, which is also within the allowable range;

[0124] S43, obtain the value of a;

[0125] Let:

[0126] a = C2·R2 (10)

[0127] By combining equations (1), (2), (3), and (10), we have:

[0128] C1·R2 = C2·R2·(1-cosθ1) (11)

[0129] We have:

[0130]

[0131] From the range of C1 being 0.4 to 0.6 and the range of the polar angle θ1 being 28° to 60°, we obtain the ranges of C 2MAX and C 2MIN :

[0132]

[0133]

[0134] The range of C2 is 0.8 to 5.0, which is brought into equation (10) to obtain the value of a;

[0135] S44, obtain the polar angle θ2 of the termination point of the cardioid;

[0136] From the following equation

[0137] R2 = a · (1 - cos θ2) (13)

[0138] The heart line equation of the hot mill grinding piece is obtained as follows:

[0139]

[0140] The heart line equation of the hot mill grinding piece is obtained as follows:

[0141] ρ = a · (1 - cos θ), θ ∈ (θ1, θ2) (15)

[0142] wherein ρ is the distance from any point on the heart line to the origin of the heart line, i.e. the polar radius; a is the parameter of the heart line, representing the shape of the heart line; θ is the polar angle of any point on the heart line, i.e. the angle between the polar axis at the point and the x-axis; θ1 is the polar angle of the starting point of the heart line; θ2 is the polar angle of the terminal point of the heart line.

[0143] Further, the heart line segment P1P2 formed by the gear tooth starting point P1 and the gear tooth terminal point P2 is the gear tooth profile of the hot mill grinding piece.

[0144] Further, the heart line segment P1P2 is arranged in a circumferential array to obtain a complete hot mill grinding piece.

[0145] The design method of the hot mill grinding piece based on the heart line provided in the embodiment makes the gradually increasing slide angle of the hot mill grinding piece from the inner circle to the outer circle match the gradually increasing cutting speed and the gradually increasing slide angle match the gradually decreasing cutting force, thereby improving the fiber separation quality, reducing the energy consumption, and prolonging the tool life; the gear tooth profile of the hot mill grinding piece is designed as a curve function, which is convenient for design expression and mathematical analysis of the stress of the gear blade.

[0146] Embodiment 3:

[0147] Based on the embodiment 2, the embodiment provides three specific embodiments of the design method of the hot mill grinding piece based on the heart line, including a specific embodiment a, a specific embodiment b, and a specific embodiment c; the specific embodiment a illustrates the specific design steps, the specific design steps of the specific embodiment b and the specific embodiment c are similar to those of the specific embodiment a, so the results of the specific embodiment b and the specific embodiment c are given in the form of a table, please refer to Table 1 for details;

[0148] The specific embodiment a is as follows:

[0149] First step: determining the inner circle radius and the outer circle radius of the hot mill grinding piece;

[0150] The inner circle radius is R1 and the outer circle radius is R2.

[0151] The R2 takes 800mm;

[0152] The inner diameter is:

[0153] R1 = C1 R2 (1)

[0154] The C1 takes 0.45, and R1 = 360mm.

[0155] Second step: determine the origin of the heart line;

[0156] The origin of the heart line is set as the center of the grinding disc O;

[0157] Third step: definition of an arbitrary point of the heart line, the starting point, the turning radius of the starting point, the sliding angle, and the polar angle:

[0158] (1) An arbitrary point of the heart line: the intersection of the heart line and the straight line where the radius of the hot mill grinding disc is located, represented by point P;

[0159] (2) Starting point: the intersection of the heart line and the inner diameter of the hot mill grinding disc, represented by P1;

[0160] (3) The turning radius of the starting point is defined as p1, which has

[0161] p1 = R1 (2)

[0162] (4) Sliding angle of an arbitrary point of the heart line: the angle between the cutting speed and the cutting force at that point, which is represented by the angle between the polar axis at that point and the tangent at that point, represented by a, the sliding angle of the starting point of the heart line is represented by a1, and the range is 14° to 30°, and the sliding angle of the terminal point of the heart line is represented by a2; Figure 1

[0163] (5) Polar angle of an arbitrary point of the heart line: the angle between the polar axis at that point and the x-axis, represented by θ, the polar angle of the starting point of the heart line is represented by θ1, and the polar angle of the terminal point of the heart line is represented by θ2.

[0164] Fourth step: obtain the equation of the heart line;

[0165] (1) Let the parameter equation of the heart line be

[0166] p = a (1 - cos θ) (3)

[0167] x = a (1 - cos θ) cos θ (4)

[0168] y = a (1 - cos θ) sin θ (5)

[0169] (2) Find the polar angle θ1 of the starting point of the heart line

[0170] Take the derivative of equation (4) and equation (5) with respect to the polar angle θ, respectively, to obtain equation (6) and equation (7);​

[0171]

[0172]

[0173] The derivative of y with respect to x is equal to the tangent slope of the polar angle θ on the cardioid, as shown in equation (8):

[0174]

[0175] From equation (8), we have:

[0176]

[0177] From equation (9) and the sliding tangent angle α1 of 16° at the starting point of the cardioid, we can determine that the polar angle θ1 of the starting point of the cardioid is 32°.

[0178] From equation (9), we can see that the sliding tangent angle increases with the increase of the polar angle, that is, it increases with the increase of the separation radius.

[0179] From equation (9), we can also see that when the polar angle is as large as 90°, the sliding tangent angle is 45°, which is also within the allowable range.

[0180] (3) Obtain the value of a

[0181] Let:

[0182] a = C2·R2 (10)

[0183] By combining equations (1), (2), (3), and (10), we have:

[0184] C1·R2 = C2·R2·(1-cosθ1) (11)

[0185] We have:

[0186]

[0187] Then the range of c2 is (0.8-5.0), and by substituting it into equation (10), we can obtain the value of a as 2370.

[0188] (4) Obtain the polar angle θ2 of the termination point of the cardioid;

[0189] From equation

[0190] R2 = a·(1-cosθ2) (13)

[0191] We have:

[0192]

[0193] Therefore, the equation of the ground tooth cardioid is:

[0194] p = 2370 · (1 - cos θ), θ ∈ (32°, 48.5°) (15)

[0195] The heart line segment P1P2 is the tooth profile of the grinding plate; the circumferential array thereof obtains a complete grinding plate, and details are shown in Figure 2 .

[0196] The embodiment provides three specific embodiments of the design method of the hot grinder grinding plate based on the heart line, including a specific embodiment a, a specific embodiment b and a specific embodiment c, and specific parameters are shown in Table 1.

[0197] Table 1, parameters of the specific embodiment a, the specific embodiment b and the specific embodiment c and heart line equation

[0198]

[0199] Obviously, the above embodiments of the present application are merely examples for clearly illustrating the present application, and are not intended to limit the implementation modes of the present application. Based on the above description, other different forms of changes or variations can be made by those skilled in the art. Here, all the implementation modes are not required or can not be exhausted. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the claims of the present application.

Claims

1. A method of designing a hot mill strip based on a heart line, characterized by, The method comprises the following steps: S1, determining the inner radius R1 and the outer radius R2 of the hot mill grinding piece; The outer radius R2 is 400-2000 mm, and the expression of the inner radius R1 is: （1） wherein is a constant, ranges from 0.4 to 0.6; S2, determining the origin of the cardioid as the center O of the hot mill grinding piece; S3, define any point P on the heart line, the grinding starting point P1, the grinding termination point P2, the grinding starting point is in the radius of gyration , the slide angle of any point on the heart line α, the polar angle of any point on the heart line θ; Any point P on the cardioid is the intersection of the cardioid and the straight line where the radius of the hot mill grinding piece is located; The grinding starting point P1 is the intersection of the cardioid and the inner diameter of the hot mill grinding piece; The grinding termination point P2 is the intersection of the cardioid and the outer diameter of the hot mill grinding piece; The revolution radius where the gear tooth starting point is located The expression is: = （2） The sliding angle α of any point on the cardioid is the included angle between the polar axis at the point and the tangent at the point, the sliding angle of the starting point of the cardioid is represented by α1, the sliding angle of the termination point of the cardioid is represented by α2, and the sliding angle α1 of the starting point of the cardioid is 14°-30°; The polar angle θ of any point on the cardioid is the included angle between the polar axis at the point and the x-axis, the polar angle of the starting point of the cardioid is represented by θ1, and the polar angle of the termination point of the cardioid is represented by θ2; S4, obtaining the cardioid equation of the hot mill grinding piece, and the specific steps comprise: S41, setting the parametric equation of the cardioid; The parametric equation of the cardioid is: （3） （4） （5） S42, calculating the polar angle of the starting point of the heart line ; Take the derivative of equation (4) and equation (5) with respect to polar angle respectively, to obtain equation (6) and equation (7). （6） （7） The derivative of y with respect to x is equal to the polar angle on the cardioid The corresponding tangent slope, as in equation (8): （8） From equation (8), we have: （9） According to equation (9) and the range of the sliding angle α1 of the starting point of the cardioid being 14°-30°, the range of the polar angle θ1 of the starting point of the cardioid is 28°-60°; S43, obtain value; Let （10） By combining equations (1), (2), (3) and (10), we have: （11） We have: = （12） By 0.4 to 0.6 and polar angle θ1 ranging from 28° to 60°, we obtain and : =5.0 =0.8， then ranging from 0.8 to 5.0, into equation (10) gives values; S44, finding the polar angle of the end point of the heart line ; From the following equation （13） We have: （14） The cardioid equation of the hot mill grinding piece is obtained, and the cardioid equation of the hot mill grinding piece is: ， （15） wherein, is the distance from any point on the cardioid to the origin of the cardioid, i.e. the polar radius; is the parameter of the cardioid, representing the shape of the cardioid; is the polar angle of any point on the cardioid, i.e. the angle between the polar axis and the x-axis at that point; θ1is the polar angle of the starting point of the cardioid; θ2is the polar angle of the ending point of the cardioid.

2. The design method of a hot mill based on the heart line of the mill according to claim 1, characterized in that, The cardioid segment P1P2 formed by the grinding starting point P1 and the grinding termination point P2 is the grinding profile of the hot mill grinding piece.

3. The design method of a hot mill based on the heart line of the mill according to claim 2, characterized in that, The cardioid segment P1P2 is arranged in a circumferential array to obtain a complete hot mill grinding piece.

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