Defibrator grinding disc based on Fermat spiral and design method of defibrator grinding disc

Abstract

The invention discloses a defibrator grinding disc based on Fermat spiral and a design method thereof, the tooth blade contour of the defibrator grinding disc is the Fermat spiral, the included angle between the polar axis and the x axis at any point of the Fermat spiral is defined as the polar angle t, the Fermat spiral equation of the defibrator grinding disc is # imgabs0 #, a represents the parameter for adjusting the specific shape of the Fermat spiral, a belongs to [921, 2262], and t represents the parameter for adjusting the specific shape of the Fermat spiral. T represents the polar angle of the Fermat spiral and is used for adjusting the length t of the Fermat spiral, t belongs to [t1, t2], t1 is the polar angle of the starting point of the tooth edge curve, and t2 is the polar angle of the ending point of the tooth edge curve. According to the invention, the contour of the tooth blade of the grinding disc of the defibrator is designed, so that the gradually increased sliding cutting angle is matched with the gradually reduced cutting force, and the purposes of reducing the energy consumption, improving the grinding quality and increasing the fitness of raw materials and the process are achieved.

Description

Technical Field

[0001] The invention relates to the technical field of fiberboard manufacturing, and in particular to a thermal mill grinding disc based on Fermat spiral and a design method thereof. Background Art

[0002] As one of the three major types of boards, fiberboard is widely used in the construction, panel furniture, interior decoration and other industries because of its smooth surface, good dimensional stability and good machining performance. Fiber structure design is one of the important links in fiberboard production, and grinding discs are the core executive components in fiber structure design, because the separation of plant fibers is achieved through the grinding action of grinding discs. Therefore, the quality of grinding discs directly affects the quality of structural design fibers, energy consumption and the life of the grinding discs themselves. The tooth structure is an important factor of grinding discs, and the optimization of tooth structure is the key point in the research and development of hot mill grinding discs. The existing technology has very limited breakthroughs in the optimization of grinding disc tooth structure, which makes the manufacturing technology of hot mill grinding discs develop slowly.

[0003] The grinding disc of the hot refiner is an important component in the production of fiberboard raw materials. The design of its grinding teeth has a great influence on the grinding quality. Sliding is an effective means to reduce energy consumption, and the sliding angle is an important parameter of the tooth edge. The appropriate sliding angle can reduce energy consumption and improve the grinding quality. In particular, the gradually increasing sliding angle can adapt to different raw materials and process requirements.

[0004] In the prior art, there are the following deficiencies:

[0005] From the inner circle to the outer circle of the grinding disc, the grinding teeth are mostly straight lines or empirical curves, ignoring the matching of the increasing separation speed and cutting force, and thus ignoring the matching of the sliding angle and cutting force, which ultimately affects the fiber separation quality. When the gradually increasing sliding angle does not match the gradually decreasing cutting force, the fiber separation quality is affected. Summary of the invention

[0006] In view of the above-mentioned shortcomings of the prior art, the present invention provides a Fermat spiral-based hot mill grinding disc and a design method thereof. The profile of the tooth edge of the hot mill grinding disc is designed so that the gradually increasing sliding angle matches the gradually decreasing cutting force, so as to achieve the purpose of reducing energy consumption, improving the quality of refining, and increasing the adaptability of raw materials and processes.

[0007] To achieve the above effects, the technical solution of the present invention is as follows:

[0008] The present invention provides a hot mill grinding disc based on a Fermat spiral, wherein the tooth edge profile of the hot mill grinding disc is a Fermat spiral, and the angle between the polar axis and the x-axis at any point of the Fermat spiral is defined as the polar angle t. The Fermat spiral equation of the hot mill grinding disc is:

[0009]

[0010] Among them, a represents the parameter for adjusting the specific shape of the Fermat spiral, a∈[921,2262]; x and y are the horizontal and vertical coordinates of any point on the Fermat spiral respectively.

[0011] Furthermore, the angle of the starting point of the Fermat spiral is expressed as t 1 The turning angle of the Fermat spiral end point is represented by t 2 Indicates that the rotation angle t satisfies t∈(t 1 , t 2 ); wherein, the t 1 ∈[0.0702, 0.1063], t 2 ∈[0.233,0.42].

[0012] A method for designing a grinding disc for a hot mill based on a Fermat spiral, the method comprising the following steps: Step 1: setting the inner radius of the grinding disc for the hot mill to R 1 , the outer radius is R 2 ; said R 1 The range is [300~600]mm;

[0013] The outer radius R 2 for:

[0014] R 2 =C 1 ·R 1 (1)

[0015] The C 1 Indicates adjustment of the outer circle radius R 2 Size parameters;

[0016] Step 2: Set the point of the Fermat spiral as the center O of the grinding disc of the hot grinding machine;

[0017] Step 3: Definition of any point of Fermat spiral, starting point, starting point gyration radius, ending point gyration radius, slip angle, starting slip angle, ending slip angle, polar angle, starting point polar angle, and ending point polar angle:

[0018] The intersection of the Fermat spiral and the inner diameter of the grinding disc of the hot mill is defined as the starting point of the Fermat spiral, and P is used to represent the intersection of the Fermat spiral and the inner diameter of the hot mill disc. 1 express;

[0019] The radius of gyration of the starting point of the Fermat spiral is defined as ρ 1 ,have

[0020] ρ 1 =R 1 (2);

[0021] The radius of gyration at the end point of the Fermat spiral is defined as ρ 2 ,have

[0022] ρ 2 =R 2 (3);

[0023] The angle between the cutting speed and the cutting force at any point of the Fermat spiral is defined as the slip angle α, and the slip angle at the starting point of the Fermat spiral is expressed as α 1 , set α 1 ∈[8°, 12°]; the slip angle of the Fermat spiral termination point is represented as α 2 , set α 2 ∈[25°, 40°];

[0024] The angle between the polar axis and the x-axis at any point of the Fermat spiral is defined as the polar angle t. The polar angle at the starting point of the Fermat spiral is t. 1 The polar angle of the end point of the Fermat spiral is represented by t 2 express;

[0025] Step 4: Find the equation of the Fermat spiral:

[0026] (1) Assume that the parametric equation of the Fermat spiral is:

[0027]

[0028]

[0029]

[0030] The a represents a parameter for adjusting the specific shape of the Fermat spiral;

[0031] (2) Find the polar angle t of the starting point of the Fermat spiral ρ 1 ;

[0032] Calculate the derivatives of equations (5) and (6) with respect to the polar angle t, and obtain equations (7) and (8);

[0033]

[0034]

[0035] Find the derivative of y with respect to x, where the derivative of y with respect to x is equal to the slope of the tangent corresponding to the polar angle t on the Fermat spiral, as shown in formula (9):

[0036]

[0037] From formula (9), we get:

[0038]

[0039] Simplifying the above formula, we get:

[0040]

[0041] Simplifying the above formula, we get:

[0042]

[0043] Simplifying the above formula, we can get the expression of the slip angle α:

[0044] Simplifying the above formula, we can get the expression of polar angle t:

[0045]

[0046] Then the polar angle t of the starting point of the Fermat spiral is 1 The expression is:

[0047]

[0048] According to formula (13) and the sliding angle α at the starting point of the Fermat spiral 1 ∈[8°, 12°] to obtain the polar angle t of the starting point of the Fermat spiral 1 ∈[4°, 6.1°], expressed in radians as t 1 ∈[0.0702, 0.1063];

[0049] Derivative of the sliding angle α:

[0050]

[0051] From formula (14), it can be seen that the slip angle α increases with the increase of the polar angle t, which means that the slip angle α increases with the rotation of the grinding disc of the hot mill;

[0052] (3) Find the range of parameter a:

[0053] Let the expression of parameter a be:

[0054] a=C 2 ·R 1 (15)

[0055] The C 2 Indicates the parameter for adjusting the size of parameter a;

[0056] Combining equations (1), (2), (4), and (15), we can get the outer radius R of the grinding disc of the hot grinding machine. 2 The expression is:

[0057]

[0058] The parameter C is obtained from formula (16): 2 The expression is:

[0059]

[0060] Substituting equation (13) into equation (17), we get parameter C 2 The expression is transformed into:

[0061] Then the starting point of the Fermat spiral is set to the sliding angle α 1 ∈[8°,12°] is substituted into formula (18) to obtain the parameter C 2 The maximum value of C 2MAX and parameter C 2 The minimum value of C 2MIN :

[0062]

[0063]

[0064] Then we get the parameter C 2 ∈[3.07,3.77], the parameter C 2 Substituting into formula (15), we get the range of parameter a as a∈[921,2262].

[0065] Furthermore, the parameter C of the Fermat spiral equation is 1 Range and outer radius R 2 The value of is obtained through the following process:

[0066] Combining equations (1), (3), (4), and (15) yields the following expression:

[0067]

[0068] From equation (12), we can get the polar angle t 2 The expression is:

[0069]

[0070] Combining equation (19) with equation (20), we get the following expression:

[0071]

[0072] So the parameter C 1 Translates to:

[0073] Substituting equation (18) into equation (21), we get parameter C 1 The expression is:

[0074]

[0075] The sliding angle α 1∈[8°,12°] and the sliding angle α 2 ∈[25°, 40°] is substituted into formula (22) to obtain the parameter C 1 ∈[1.48,2.44];

[0076] C 1 ∈[1.48,2.44]Substitute into formula (1) and we get the outer radius R 2 Values:

[0077] R 2 ∈[444,1464]mm.

[0078] Furthermore, the method further comprises:

[0079] Find the polar angle t of the end point of the Fermat spiral 2 :

[0080] From formula (20) and α 2 ∈[25°, 40°]

[0081] Solve for t 2 ∈[0.233,0.42], that is, t 2 ∈[13.4°, 24.0°]

[0082] So the Fermat spiral equation is:

[0083]

[0084] Among them, a∈[921,2262], t∈[t 1 , t 2 ], t 1 ∈[0.0702, 0.1063], t 2 ∈[0.233,0.42](23).

[0085] Furthermore, the tooth grinding starting point P 1 and the grinding end point P 2 The Fermat spiral segment P 1 P 2 The grinding tooth profile of the grinding disc of the hot grinding machine is shown in Figure 1. 1 P 2 A circular array is formed to obtain a complete hot mill grinding plate structure.

[0086] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0087] (1) The tooth edge profile of the grinding disc of the hot mill is designed to be a Fermat spiral function expression, which is convenient for processing and for analyzing the force condition of any point on the tooth edge of the grinding disc of the hot mill by mathematical methods.

[0088] (2) With the increase of the polar angle of the Fermat spiral, that is, the increase of the rotation radius, the slip angle gradually increases, which matches the increasing dissociation rate and the decreasing dissociation force requirements, improves the refining quality, increases the adaptability of raw materials and processes, and reduces energy consumption. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Figure 1 is the design diagram of the Fermat spiral of the present invention;

[0090] Figure 2 It is the tooth-shaped structure of the thermal grinding machine grinding disc based on the Fermat spiral of the present invention, and the tooth edge profile is the Fermat spiral (a total of 6 pieces, 2 pieces are drawn);

[0091] Figure 3 The invention discloses a thermal grinding machine grinding disc tooth shape structure based on the Fermat spiral, and the tooth edge profile is the Fermat spiral (whole-piece type). DETAILED DESCRIPTION

[0092] The following will describe the embodiments of the present invention with reference to the accompanying drawings and preferred embodiments. Those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be understood that the preferred embodiments are only for illustrating the present invention, not for limiting the scope of protection of the present invention.

[0093] It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and thus the drawings only show components related to the present invention rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout may also be more complicated.

[0094] Example 1

[0095] See also Figure 1 and Figure 2 , Figure 1 Interpretation of the parameters: O——the center of the grinding disc of the hot grinding machine, the origin of the curve; R 1 ——Inner radius of grinding disc of thermal grinding machine; R 2 ——Outer radius of grinding disc of hot grinding machine; P——Any point; ω 1 ——Hot grinding rotation direction; P 1 ——Grinding starting point; P 2 ——Grinding end point; α 1 ——slip angle at the starting point of tooth grinding; α 2 ——slip angle at the grinding end point; t 1 ——Grinding starting point rotation angle; t 2——Grinding end point rotation angle; ω——Refiner grinding disc rotation direction; P 1 P 2 ——Fermat spiral segment, that is, the profile of the grinding tooth edge. Figure 2 It is a thermal mill grinding disc tooth structure based on Fermat spiral, and the tooth edge profile is Fermat spiral; there are 6 Fermat spiral thermal mill grinding discs in total. Figure 2 Draw 2 pieces in the middle.

[0096] This embodiment proposes a thermal grinding machine grinding disc based on Fermat spiral. Figure 1 The tooth edge profile of the hot mill grinding disc is a Fermat spiral, and the angle between the polar axis and the x-axis at any point of the Fermat spiral is defined as the polar angle t. The Fermat spiral equation of the hot mill grinding disc is:

[0097]

[0098]

[0099]

[0100] Among them, a represents the parameter for adjusting the specific shape of the Fermat spiral, a∈[921,2262]; x and y are the horizontal and vertical coordinates of any point on the Fermat spiral respectively.

[0101] As a preferred technical solution, in this embodiment, the angle of the starting point of the Fermat spiral is t 1 The turning angle of the Fermat spiral end point is represented by t 2 Indicates that the rotation angle t satisfies t∈[t 1 , t 2 ]; wherein, the t 1 ∈[0.0702, 0.1063], t 2 ∈[0.233,0.42].

[0102] Example 2

[0103] This embodiment provides 6 specific embodiments of the method for designing a hot mill grinding disc based on Fermat spiral, including specific embodiments a to f. The specific design steps of specific embodiment f are similar to those of specific embodiment a, so the results of specific embodiments b to f are given in table form, please refer to Table 1 for details;

[0104] The specific embodiment a is as follows:

[0105] This embodiment proposes a method for designing a grinding disc for a thermal mill based on Fermat spirals, and the design method comprises the following steps:

[0106] Step 1: Set the inner radius of the grinding disc of the hot mill to R 1 , the outer radius is R2 ; wherein said R 1 The range is [300~600] mm. In this embodiment, the R 1 The value is 350mm;

[0107] The outer radius R 2 for:

[0108] R 2 =C 1 ·R 1 (1)

[0109] The C 1 Indicates adjustment of the outer circle radius R 2 Size parameters;

[0110] Step 2: Set the point of the Fermat spiral as the center O of the grinding disc of the hot grinding machine;

[0111] Step 3: Definition of any point of Fermat spiral, starting point, starting point gyration radius, ending point gyration radius, slip angle, starting slip angle, ending slip angle, polar angle, starting point polar angle, ending point polar angle: (1) Any point of Fermat spiral: The intersection of Fermat spiral and the straight line where the radius of the hot mill grinding disc lies is defined as point P;

[0112] (2) Starting point: The intersection of the Fermat spiral and the inner diameter of the grinding disc of the thermal mill is defined as the starting point of the Fermat spiral, and P is used to represent the starting point of the Fermat spiral. 1 express;

[0113] (3) The radius of gyration of the starting point of the Fermat spiral is defined as ρ 1 ,have

[0114] ρ 1 =R 1 (2);

[0115] (3) The radius of gyration of the end point of the Fermat spiral is defined as ρ 2 ,have

[0116] ρ 2 =R 2 (3);

[0117] (4) Slip angle α at any point on the Fermat spiral: the angle between the cutting speed and the cutting force at that point. Figure 1 It is reflected as the angle between the polar axis at that point and the tangent at that point, represented by α;

[0118] The angle between the cutting speed and the cutting force at any point of the Fermat spiral is defined as the slip angle α, and the slip angle at the starting point of the Fermat spiral is expressed as α 1 , where α 1 ∈[8°, 12°], in this embodiment, α is set1 =8°; the slip angle of the Fermat spiral end point is represented by α 2 , where α 2 ∈[25°, 40°];

[0119] (5) Define the angle between the polar axis and the x-axis at any point on the Fermat spiral as the polar angle t. The polar angle at the starting point of the Fermat spiral is t 1 The polar angle of the end point of the Fermat spiral is represented by t 2 express;

[0120] Step 4: Find the equation of the Fermat spiral:

[0121] (1) Assume that the parametric equation of the Fermat spiral is:

[0122]

[0123]

[0124]

[0125] The a represents a parameter for adjusting the size of the Fermat spiral ρ;

[0126] (2) Find the polar angle t of the starting point of the Fermat spiral ρ 1 ;

[0127] Calculate the derivatives of equations (5) and (6) with respect to the polar angle t, and obtain equations (7) and (8);

[0128]

[0129]

[0130] Find the derivative of y with respect to x, where the derivative of y with respect to x is equal to the slope of the tangent corresponding to the polar angle t on the Fermat spiral, as shown in formula (9)

[0131]

[0132] From formula (9), we get:

[0133]

[0134] Simplifying the above formula, we get:

[0135]

[0136] Simplifying the above formula, we get:

[0137] in

[0138] Simplifying the above formula, we can get the expression of the slip angle α:

[0139] Simplifying the above formula, we can get the expression of polar angle t:

[0140]

[0141] Then the polar angle t of the starting point of the Fermat spiral is 1 The expression is:

[0142]

[0143] According to formula (13) and the sliding angle α at the starting point of the Fermat spiral 1 ∈[8°, 12°] to obtain the polar angle t of the starting point of the Fermat spiral 1 ∈[4°, 6.1°], expressed in radians as t 1 ∈[0.0702, 0.1063]; In this embodiment, the sliding angle α is set 1 =8°, find the polar angle t 1 = 4°, expressed in radians as t 1 =0.0702.

[0144] Derivative of the sliding angle α:

[0145]

[0146] From formula (14), it can be seen that the slip angle α increases with the increase of the polar angle t, which means that the slip angle α increases with the rotation of the grinding disc of the hot mill (that is, the increase of the dissociation radius);

[0147] (3) Find the range of parameter a:

[0148] Let the expression of parameter a be:

[0149] a=C 2 ·R 1 (15)

[0150] The C 2 Indicates the parameter for adjusting the size of parameter a;

[0151] Combining equations (1), (2), (4), and (15), we can get the outer radius R of the grinding disc of the hot grinding machine. 2 The expression is:

[0152]

[0153] The parameter C is obtained from formula (16): 2 The expression is:

[0154]

[0155] Substituting equation (13) into equation (17), we get parameter C 2 The expression is transformed into:

[0156] In this embodiment, the starting point of the Fermat spiral is set to the sliding angle α 1 =8°Substitute into formula (18) and we get the parameter C 2 value:

[0157]

[0158] Set parameter C 2 Substituting into equation (15), we obtain parameter a=1320.

[0159] As a preferred technical solution, in this embodiment, the parameter C of the Fermat spiral equation is 1 Range and outer radius R 2 The value of is obtained through the following process:

[0160] Combining equations (1), (3), (4), and (15) yields the following expression:

[0161]

[0162] From equation (12), we can get the polar angle t 2 The expression is:

[0163]

[0164] Combining equation (19) with equation (20), we get the following expression:

[0165]

[0166] So the parameter C 1 Translates to:

[0167] Substituting equation (18) into equation (21), we get parameter C 1 The expression is:

[0168]

[0169] The sliding angle α 1 =8° and α 2 =29.3°Substitute into formula (22) and obtain the parameter C 1 =2;

[0170] C 1 Substitute into formula (1) and get the outer circle radius R 2 Values:

[0171] R 2 =700mm.

[0172] As a preferred technical solution, in this embodiment, the method further includes:

[0173] Find the polar angle t of the end point of the Fermat spiral 2 :

[0174] From formula (20) and α 2 =29.3°

[0175] Solve for t 2 =0.28, that is, t 2 = = [16.1°]

[0176] So the Fermat spiral equation is:

[0177]

[0178] As a preferred technical solution, in this embodiment, the grinding starting point P 1 and the grinding end point P 2 The Fermat spiral segment P 1 P 2 The grinding tooth profile of the grinding disc of the hot grinding machine is shown in Figure 1. 1 P 2 Circumferential array, to obtain a complete hot mill grinding plate structure (see attached Figure 2 and 3 ).

[0179] As a preferred technical solution, in this embodiment, six specific embodiments of the design method of the thermal mill grinding disc based on Fermat spiral are provided, including specific embodiments a to f. For specific parameters, please refer to Table 1 below.

[0180] Table 1 Parameters and Fermat spiral equation of specific implementation methods

[0181]

[0182]

[0183] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the embodiments here. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A thermal grinding machine grinding disc based on Fermat spiral, characterized in that: The tooth edge profile of the hot mill grinding disc is a Fermat spiral, and the angle between the polar axis and the x-axis at any point of the Fermat spiral is defined as the polar angle t. The Fermat spiral equation of the hot mill grinding disc is: Among them, a represents the parameter for adjusting the specific shape of the Fermat spiral, a∈[921,2262]; x and y are the horizontal and vertical coordinates of any point on the Fermat spiral respectively.

2. The Fermat spiral-based thermal grinding mill grinding disc according to claim 1, characterized in that: The angle of the starting point of the Fermat spiral is represented by t1, and the angle of the ending point of the Fermat spiral is represented by t2, and the angle t satisfies t∈[t1, t2); wherein, t1∈[0.0702, 0.1063], t2∈[0.233, 0.42].

3. A method for designing a grinding disc for a thermal mill based on Fermat spiral, characterized in that: The design method comprises the following steps: Step 1: Set the inner radius of the grinding disc of the hot grinding machine to R1 and the outer radius to R2; the range of R1 is [300~600] mm; The outer radius R2 is: R2=C1·R1 (1) The C1 represents a parameter for adjusting the size of the outer circle radius R2; Step 2: Set the point of the Fermat spiral as the center O of the grinding disc of the hot grinding machine; Step 3: Definition of any point of Fermat spiral, starting point, starting point gyration radius, ending point gyration radius, slip angle, starting slip angle, ending slip angle, polar angle, starting point polar angle, and ending point polar angle: The intersection of the Fermat spiral and the straight line where the radius of the thermal mill grinding disc is located is defined as point P; The intersection of the Fermat spiral and the inner diameter of the grinding disc of the thermal mill is defined as the starting point of the Fermat spiral, denoted by P1; The radius of gyration of the starting point of the Fermat spiral is defined as ρ1, ρ1=R1 (2); The radius of gyration of the end point of the Fermat spiral is defined as ρ2, ρ2=R2 (3); The angle between the cutting speed and the cutting force at any point of the Fermat spiral is defined as the slip angle α. The slip angle at the starting point of the Fermat spiral is represented as α1, and α1∈[8°,12°] is set; the slip angle at the end point of the Fermat spiral is represented as α2, and α2∈[25°,40°] is set; The angle between the polar axis and the x-axis at any point of the Fermat spiral is defined as the polar angle t. The polar angle at the starting point of the Fermat spiral is represented by t1, and the polar angle at the end point of the Fermat spiral is represented by t2. Step 4: Find the equation of the Fermat spiral: (1) Assume that the parametric equation of the Fermat spiral is: The a represents a parameter for adjusting the specific shape of the Fermat spiral; (2) Find the polar angle t1 of the starting point of the Fermat spiral ρ; Calculate the derivatives of equations (5) and (6) with respect to the polar angle t, and obtain equations (7) and (8); Find the derivative of y with respect to x, where the derivative of y with respect to x is equal to the slope of the tangent corresponding to the polar angle t on the Fermat spiral, as shown in formula (9): The following expression is obtained from formula (9): Simplifying the above formula, we get: Simplifying the above formula, we get: in Simplifying the above formula, we can get the expression of the slip angle α: Simplifying the above formula, we can get the expression of polar angle t: Then the expression of the polar angle t1 of the starting point of the Fermat spiral is: The polar angle t1∈[4°,6.1°] of the starting point of the Fermat spiral is obtained from formula (13) and the slip angle α1∈[8°,12°], which is expressed in radians as t1∈[0.0702,0.1063]; Derivative of the sliding angle α: From formula (14), it can be seen that the slip angle α increases with the increase of the polar angle t, which means that the slip angle α increases with the rotation of the grinding disc of the hot mill; (3) Find the range of parameter a: Let the expression of parameter a be: a=C2·R1 (15) The C2 represents a parameter for adjusting the size of parameter a; Combining equations (1), (2), (4) and (15), we can get the expression of the outer radius R2 of the grinding disc of the hot grinding machine: The expression of parameter C2 obtained from formula (16) is: Substituting equation (13) into equation (17), The expression of parameter C2 is converted to: Then, the sliding angle α1∈[8°,12°] at the starting point of the Fermat spiral is substituted into equation (18) to obtain the maximum value C of the parameter C2. 2MAX and the minimum value C of parameter C2 2MIN : Then we obtain the parameter C2∈[3.07,3.77], and substitute the parameter C2 into formula (15) to obtain the parameter a∈[921,2262].

4. The method according to claim 3, characterized in that: The range of the parameter C1 of the Fermat spiral equation and the value of the outer radius R2 are obtained by the following process: Combining equations (1), (3), (4), and (15) yields the following expression: From formula (12), we can get the expression of polar angle t2: Combining equation (19) with equation (20), we get the following expression: Therefore, parameter C1 is transformed into: Substituting equation (18) into equation (21), we get the expression of parameter C1: Substitute the sliding angle α1∈[8°,12°] and the sliding angle α2∈[25°,40°] into formula (22) to obtain the parameter C1∈[1.48,2.44]; Substituting C1∈[1.48,2.44] into formula (1), we can obtain the value of the outer circle radius R2: R2∈[444,1464]mm.

5. The method according to claim 4, characterized in that The method further comprises: Find the polar angle t2 of the end point of the Fermat spiral: From formula (20) and α2∈[25°,40°] The solution is t2∈[0.233,0.42], that is, t2∈[13.4°,24.0°] So the Fermat spiral equation is: Among them, a∈[921,2262],t∈(t1,t2),t1∈[0.0702,0.1063],t2∈[0.233,0.42](23).

6. The method according to claim 5, characterized in that The Fermat spiral line segment P1P2 formed by the tooth grinding starting point P1 and the tooth grinding ending point P2 is the tooth grinding profile of the hot mill grinding plate. The Fermat spiral line segment P1P2 is arranged in a circular array to obtain a complete hot mill grinding plate structure.

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