Defibrator grinding disc with constant sliding cutting angle and design method thereof

Abstract

The invention discloses a defibrator grinding disc with a constant sliding cutting angle and a design method thereof, the tooth blade profile of the defibrator grinding disc is a tooth blade curve, the included angle between the polar axis and the x axis at any point of the tooth blade curve is defined as a polar angle theta, the tooth blade curve equation of the defibrator grinding disc is rho = a * eb * theta, theta belongs to [theta 1, theta 2], in the formula, a and b are constants, and a is a positive integer. The shape of the tooth blade curve is controlled; theta1 is the polar angle of the starting point of the tooth blade curve, and theta2 is the polar angle of the ending point of the tooth blade curve. According to the grinding disc of the defibrator, the tooth blade outline of the grinding disc of the defibrator is designed to be the tooth blade curve, the sliding cutting angle of the designed grinding disc of the defibrator does not change along with the radius change, the stability of a mechanical structure is improved, abrasion of the grinding disc of the defibrator is reduced, and the service life of the grinding disc of the defibrator is prolonged.

Description

Technical Field

[0001] The invention relates to the technical field of fiberboard manufacturing, and in particular to a hot grinder grinding plate with a constant sliding cutting angle and a design method thereof. Background Art

[0002] The refiner disc is a component that directly separates fibers. The key to its performance and potential lies in its design and manufacturing quality. The sliding angle of the refiner disc is one of its important geometric parameters, which directly affects the fiber separation effect and the wear of the refiner disc.

[0003] At present, the documents related to the slip angle disclosed include patent application numbers CN202410120981.7, CN202410053749.6, CN202311750390.X, CN202410326683.3, and CN202410204016.8, which respectively apply the methods of Cartesian blade curve, Archimedean spiral, cycloid, custom tooth edge curve, heart line tooth edge curve and other functions to design the tooth edge profile. The innovation of these documents is that the slip angle increases with the increase of hot grinding radius, and the slip angle increases with the increase of dissociation speed, so as to achieve the purpose of matching the gradually increasing slip angle with the gradually increasing cutting rate and the gradually increasing slip angle with the gradually decreasing cutting force. These documents can undoubtedly improve the quality of fiber separation and reduce energy consumption, but they are not involved in terms of fiber separation consistency.

[0004] However, in the manufacture of medium density fiberboard, to ensure the uniformity and quality of medium density fiberboard, it is necessary to ensure the consistency of fiber separation. This consistency is guaranteed by a constant sliding angle. In addition, the constant sliding angle also improves the stability of the mechanical structure, which can also help reduce the wear of the grinding disc and extend its service life. In addition, due to the change of the sliding angle, the above-mentioned file needs to calculate the initial cutting angle and the final sliding angle separately during design, which increases the design difficulty to a certain extent. Based on the discussion of the above background, it is necessary to design a hot mill grinding disc with a constant sliding angle. Summary of the invention

[0005] In view of the above-mentioned shortcomings of the prior art, the present invention provides a hot grinder grinding plate with a constant sliding angle and a design method thereof.

[0006] To achieve the above effects, the technical solution of the present invention is as follows:

[0007] The present invention provides a hot mill grinding disc with a constant sliding angle, wherein the tooth edge profile of the hot mill grinding disc is a tooth edge curve, and the angle between the polar axis and the x-axis at any point of the tooth edge curve is defined as the polar angle θ. The tooth edge curve equation of the hot mill grinding disc is:

[0008] ρ=a·eb·θ , θ∈[θ1,θ2]

[0009] Where a and b are constants used to control the shape of the tooth edge curve; θ1 is the polar angle of the starting point of the tooth edge curve, θ2 is the polar angle of the ending point of the tooth edge curve, a∈[380,580], b∈[1.732,5.76].

[0010] Furthermore, the slip angle α∈[10°, 30°].

[0011] A method for designing a hot grinder grinding disc based on a constant sliding angle, the method comprising the following steps:

[0012] Step 1: Define the inner radius of the grinding disc of the hot grinding machine as R1 and the outer radius as R2;

[0013] The outer radius is:

[0014] R2=C1·R1 (1)

[0015] The range of C1 is 1.8 to 2.6, and the range of R1 is 380 to 580 mm;

[0016] Step 2: Define the tooth edge curve parameters (refer to the attached Figure 1 and attached Figure 2 ):

[0017] 1) Define the origin of the tooth edge curve as the center O of the grinding disc of the hot grinding machine;

[0018] 2) Define the intersection point of the tooth edge curve and the straight line where the radius of the hot grinder grinding disc is located as P;

[0019] 3) Define the angle between the polar axis and the x-axis at any point on the tooth edge curve as θ, the polar angle at the starting point of the tooth edge curve is represented by θ1, and the polar angle at the end point of the tooth edge curve is represented by θ2;

[0020] 4) The angle between the cutting speed and the cutting force at any point on the tooth edge curve is defined as the sliding angle α. At any point on the tooth edge curve, the sliding angle is equal, and the sliding angle α is defined to be in the range of 10° to 30°;

[0021] 5) Define the complementary angle of the sliding angle as β;

[0022] 6) Define the reverse angle between the tangent line of the tooth edge curve at any point and the x-axis as

[0023] 7) Define the intersection of the tooth edge curve and the inner diameter of the grinding disc of the hot grinder as the starting point, represented by user 1;

[0024] 8) Define the radius of gyration where the starting point P1 is located as ρ1,

[0025] ρ1=R1(2);

[0026] Step 3: Derivation of the initial expression of the tooth edge curve with constant sliding angle:

[0027] Let the sliding angle α = C1, C1 is a constant;

[0028] Then β=C2, C2 is a constant;

[0029] but but

[0030] Assume the parametric equation of the tooth edge curve is:

[0031] ρ=ρ(θ), (θ>0)

[0032] Then x = ρ(θ)·cosθ

[0033] y=ρ(θ)·sinθ

[0034] but Other

[0035] Substituting equations (4) and (5) into equation (3), we get Simplified

[0036] Right now C3 is a constant, b is a constant;

[0037] Then (lnρ)′=b

[0038] Then lnρ=b·θ+C4, C4 is a constant;

[0039] but

[0040] In the formula, C4 is a constant, so is a constant;

[0041] make

[0042] Then ρ = a·e b·θ (7)

[0043] Step 4: Define the value of a and the starting polar angle θ1 in equation (7):

[0044] For equation (7), let θ = 0, then

[0045] So ρ=a

[0046] We can set a=ρ1=R1(8)

[0047] That is, the starting point of the tooth edge curve is the starting point of the actual tooth edge, that is

[0048] θ1=0(9)

[0049] Step 5: Find the relationship between the sliding angle α and the constant b in the tooth edge curve expression (7):

[0050] From formula (7), we can get x = a·e b·θ ·cosθ (10)

[0051] y=ae b·θ .sinθ (11)

[0052] but

[0053]

[0054] but

[0055] set up

[0056] Combining (14) and (15),

[0057] get have to have to

[0058] Simplified to 1-b(tanθ) 2 tanα=btanα-(tanθ) 2

[0059] Simplifying, we get 1+(tanθ) 2 = btanα(1+(tanθ) 2 )

[0060] Simplifying, we get b tanα=i (17)

[0061] The expression of the slip angle α is obtained from formula (17):

[0062]

[0063] In formula (18), b is a constant, so formula (18) verifies that the sliding angle of the tooth edge curve is a constant value and does not change with the change of the polar angle θ;

[0064] Or from formula (17) we can also get

[0065] Furthermore, in step 5, equation (19) obtains the parameter b of the tooth edge curve equation by the specified slip angle α. According to the slip angle α∈[10°, 30°] defined in step 2, the parameter b∈[1.732, 5.76] is obtained.

[0066] Further, step 6: determining the polar angle θ2 of the end point of the tooth edge curve:

[0067] By

[0068]

[0069] We get θ2 = tanα·ln C1 (21) which can be converted into angle to obtain

[0070] At this point, the design of the heat mill tooth edge curve (including the tooth edge curve expression, the definition domain of the expression parameters, and the constant values ​​in the expression) is completed, and the tooth edge curve segment P1P2 is the grinding tooth profile of the heat mill grinding disc. Array its circumference to obtain a complete heat mill grinding disc (see Appendix Figure 3 and 4 ).

[0071] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0072] The present invention designs the tooth edge profile of the hot mill grinding disc as a curve with a constant sliding angle, and the sliding angle of the designed hot mill grinding disc does not change with the radius, which simplifies the design and ensures the consistency of fiber separation. It can improve the stability of the mechanical structure, help reduce the wear of the hot mill grinding disc, and extend the service life of the hot mill grinding disc. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 This is a schematic diagram of the preliminary derivation of the tooth edge curve of the present invention;

[0074] Figure 2 It is a schematic diagram of the tooth edge curve design of the hot grinder grinding disc of the present invention;

[0075] Figure 3 It is the tooth shape structure of the grinding disc of the hot grinder based on the self-defined tooth edge curve of the present invention (a total of 9 pieces, 4 pieces are drawn in this embodiment);

[0076] Figure 4 The invention discloses a grinding disc tooth structure (whole disc) for a hot grinding machine with a constant sliding cutting angle. DETAILED DESCRIPTION

[0077] 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.

[0078] It should be noted that the illustrations provided in the following embodiments are only used to schematically illustrate the basic concept of the present invention. Therefore, 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 are subject to arbitrary changes, and the component layout type may also be more complicated.

[0079] Before introducing the embodiments of the present invention, the relevant parameters involved in the embodiments of the present invention are explained as follows:

[0080] O——The origin of the tooth edge curve coordinates, also the center of the grinding disc of the thermal grinding machine; ω ——Hot grinding rotation direction; L——tooth edge curve; P——any point on the tooth edge curve; L2——tangent line of the tooth edge curve at any point, its slope is K2; L1——line connecting the tooth edge curve and the coordinate origin at any point, its slope is K1; α——slip angle at any point on the tooth edge curve; β——slip angle supplementary angle at any point on the tooth edge curve; θ——polar angle at any point on the tooth edge curve ——The reverse angle between the tangent line of the tooth edge curve at any point and the x-axis; O——The center of the circle of the grinding disc of the hot mill, the origin of the tooth edge curve; ω——The rotation direction of the hot mill; R1——The inner radius of the grinding disc of the hot mill; R2——The outer radius of the grinding disc of the hot mill; P——The intersection of the tooth edge curve and the straight line where the radius of the hot mill grinding disc is located; P1——The starting point of the grinding tooth edge of the hot mill grinding disc; P2——The end point of the grinding tooth edge of the hot mill grinding disc; α——The sliding angle of the grinding tooth edge of the hot mill grinding disc, at any point on the grinding tooth edge, the sliding angle is constant. θ1——The polar angle of the starting point of the grinding tooth, here is 0°, which cannot be marked in the figure; θ2——The polar angle of the end point of the grinding tooth; P1P2——The tooth edge curve segment, that is, the grinding tooth edge profile.

[0081] Example 1

[0082] This embodiment provides a constant sliding angle hot grinder grinding disc, including a tooth edge profile curve of the hot grinder grinding disc. Figure 1 and Figure 2 The tooth edge profile of the hot mill grinding disc is a tooth edge curve, and the angle between the polar axis and the x-axis at any point on the tooth edge curve is defined as the polar angle θ. The tooth edge curve equation of the hot mill grinding disc is:

[0083] ρ=a·e b·θ , θ∈[θ1,θ2]

[0084] Where a and b are constants used to control the shape of the tooth edge curve; θ1 is the polar angle of the starting point of the tooth edge curve, θ2 is the polar angle of the ending point of the tooth edge curve, a∈[380,580], b∈[1.732,5.76].

[0085] As a preferred technical solution, in this embodiment, the sliding angle α∈[10°, 30°].

[0086] Example 2

[0087] The present invention provides a technical solution: a method for designing a hot grinder grinding disc based on a constant sliding angle, the design method comprising the following steps (see Figures 1 to 4 ):

[0088] Step 1: Define the inner radius of the grinding disc of the hot grinding machine as R1 and the outer radius as R2;

[0089] The outer radius is:

[0090] R2=C1·R1 (1)

[0091] The range of C1 is 1.8 to 2.6, and the range of R1 is 380 to 580 mm;

[0092] Step 2: Define the tooth edge curve parameters (refer to the attached Figure 1 and attached Figure 2 ):

[0093] 1) Define the origin of the tooth edge curve as the center O of the grinding disc of the hot grinding machine;

[0094] 2) Define the intersection point of the tooth edge curve and the straight line where the radius of the hot grinder grinding disc is located as P;

[0095] 3) Define the angle between the polar axis and the x-axis at any point on the tooth edge curve as θ, the polar angle at the starting point of the tooth edge curve is represented by θ1, and the polar angle at the end point of the tooth edge curve is represented by θ2;

[0096] 4) The angle between the cutting speed and the cutting force at any point on the tooth edge curve is defined as the sliding angle α. At any point on the tooth edge curve, the sliding angle is equal, and the sliding angle α is defined to be in the range of 10° to 30°;

[0097] 5) Define the complementary angle of the sliding angle as β;

[0098] 6) Define the reverse angle between the tangent line of the tooth edge curve at any point and the x-axis as

[0099] 7) Define the intersection of the tooth edge curve and the inner diameter of the grinding disc of the hot mill as the starting point, user, indicating;

[0100] 8) Define the radius of gyration where the starting point P1 is located as ρ1,

[0101] ρ1=R1(2);

[0102] Step 3: Derivation of the initial expression of the tooth edge curve with constant sliding angle:

[0103] Let the sliding angle α = C1, C1 is a constant;

[0104] Then β=C2, C2 is a constant;

[0105] but but

[0106] Assume the parametric equation of the tooth edge curve is:

[0107] ρ=ρ(θ), (θ>0)

[0108] Then x = ρ(θ)·cosθ

[0109] y=ρ(θ)·sinθ

[0110] but Other

[0111] Substituting equations (4) and (5) into equation (3), we get Simplified

[0112] Right now C3 is a constant, b is a constant;

[0113] Then (lnρ)′=b

[0114] Then lnρ=b·θ+C4, C4 is a constant;

[0115] but

[0116] In the formula, C4 is a constant, so is a constant;

[0117] make

[0118] Then ρ = a·e b·θ (7)

[0119] Step 4: Define the value of a and the starting polar angle θ1 in equation (7):

[0120] For equation (7), let θ = 0, then

[0121] So ρ=a

[0122] We can set a=ρ1=R1(8) That is, the starting point of the tooth edge curve is the starting point of the actual tooth edge, that is

[0123] θ1=0(9)

[0124] Step 5: Find the relationship between the sliding angle α and the constant b in the tooth edge curve expression (7):

[0125] From formula (7), we can get x = a·e b·θ ·cosθ (10)

[0126] y=ae b·θ ·sinθ (11)

[0127] but

[0128]

[0129] but

[0130] set up

[0131] Combining (14) and (15),

[0132] get have to have to

[0133] Simplified to 1-b(tanθ) 2 tanα=btanα-(tanθ) 2

[0134] Simplifying, we get 1+(tanθ) 2 = btanα(1+(tanθ) 2 )

[0135] Simplifying, we get b tanα=1 (17)

[0136] The expression of the slip angle α is obtained from formula (17):

[0137]

[0138] In formula (18), b is a constant, so formula (18) verifies that the sliding angle of the tooth edge curve is a constant value and does not change with the change of the polar angle θ;

[0139] Or from formula (17) we can also get

[0140] Furthermore, in step 5, equation (19) obtains the parameter b of the tooth edge curve equation by the specified slip angle α. According to the slip angle α∈[10°, 30°] defined in step 2, the parameter b∈[1.732, 5.76] is obtained.

[0141] Step 6: Further, the polar angle θ2 of the end point of the tooth edge curve is determined:

[0142] By

[0143]

[0144] We get θ2 = tanα·ln C1 (21)

[0145] Convert to angle

[0146] At this point, the design of the heat mill tooth edge curve (including the tooth edge curve expression, the definition domain of the expression parameters, and the constant values ​​in the expression) is completed, and the tooth edge curve segment P1P2 is the grinding tooth profile of the heat mill grinding disc. Array its circumference to obtain a complete heat mill grinding disc (see Appendix Figure 3 and 4 ).

[0147] In the prior art, there are the following problems:

[0148] (1) Ignoring the uniformity and consistency of fiber separation is not conducive to the manufacturing quality of medium density fiberboard.

[0149] (2) Ignoring the mechanical stability of the grinding disc

[0150] In summary, the method for designing a hot mill grinding disc with a constant sliding angle provided in this embodiment improves the existing technology. The constant sliding angle can ensure the consistency of fiber separation, improve the stability of the mechanical structure, and help reduce the wear of the hot mill grinding disc and extend the service life of the hot mill grinding disc.

[0151] Example 3

[0152] On the basis of Example 2, this embodiment provides 8 specific embodiments of the design method of the hot grinding machine grinding disc with a constant sliding angle, including specific embodiments a to h; Specific embodiment a describes the specific design steps, and the specific design steps of specific embodiments b to h are similar to those of specific embodiment a, so the results of specific embodiments b to h are given in a tabular form, please refer to Table 1 for details;

[0153] The specific embodiment a is as follows:

[0154] This embodiment proposes a method for designing a hot grinder grinding disc based on a constant sliding angle, and the design method comprises the following steps:

[0155] Step 1: Define the inner radius and outer radius of the grinding disc of the hot mill;

[0156] The inner circle radius is R1, and the outer circle radius is R2;

[0157] The range of R1 is 380-580 mm, and the value of R1 is set to 380 mm in this embodiment;

[0158] The outer radius is:

[0159] R2=C1·R1(1)

[0160] The range of C1 is 1.8 to 2.6. In this embodiment, the value of C1 is set to 1.8, so the value of R2 is 684 mm.

[0161] Step 2: Define the origin of the tooth edge curve, any point, polar angle, sliding angle and its related angles, starting point, and starting point rotation radius: (1) The origin of the tooth edge curve is defined as the center O of the grinding disc of the hot mill;

[0162] (2) Any point on the tooth edge curve: The intersection of the tooth edge curve and the straight line where the radius of the grinding disc of the thermal grinder is located is represented by point P (combined with the attached Figure 1 and 2 );

[0163] (3) Polar angle at any point on the tooth edge curve: The angle between the polar axis and the x-axis at that point is represented by θ (combined with the attached Figure 1 ), the polar angle of the starting point of the tooth edge curve is represented by θ1, and the polar angle of the ending point of the tooth edge curve is represented by θ2 (combined with the attached Figure 2 );

[0164] (4) Slip angle at any point on the tooth edge curve: the angle between the cutting speed and the cutting force at that point. Figure 1 and 2 It is reflected as the angle between the polar axis at that point and the tangent at that point, represented by α. At any point on the tooth edge curve, the sliding angle is equal, and its value is 10°;

[0165] (5) β: The complementary angle of the sliding angle (combined with the attached Figure 1 );

[0166] (6) The reverse angle between the tangent line of the tooth edge curve at any point and the x-axis (combined with the attached Figure 1 );

[0167] (7) Starting point: The intersection of the tooth edge curve and the inner diameter of the grinding disc of the hot mill, user, indicates (combined with the attached Figure 2 );

[0168] (8) The radius of gyration of the starting point is defined as ρ1 (combined with the attached Figure 2 ),have

[0169] ρ1=R1(2); Step 3: Define the preliminary expression of the tooth edge curve of the grinding wheel (refer to the attached Figure 1 )

[0170] Let the sliding angle α = C1, C1 is a constant;

[0171] Then β=C2, C2 is a constant;

[0172] but but

[0173] If the parameter equation of the tooth edge curve is:

[0174] ρ=ρ(θ), (θ>0)

[0175] Then x = ρ(θ)·cosθ

[0176] y=ρ(θ)·sinθ

[0177] but Other

[0178] Substituting equations (4) and (5) into equation (3), we get Simplified

[0179] Right now C3 is a constant, b is a constant

[0180] Then (lnρ)′=b

[0181] Then lnρ=b·θ+C4, C4 is a constant

[0182] but In the formula, C4 is a constant, so is a constant,

[0183] make

[0184] Then ρ = a·e b·θ (7)

[0185] Formula (7) is the preliminary expression of the tooth edge curve of the hot grinder grinding wheel.

[0186] Step 4: Define the value a and the starting polar angle θ1 in equation (7) (i.e., the tooth edge curve expression) (refer to the attached Figure 2 ):

[0187] For equation (7), let θ = 0, then

[0188] So ρ=a

[0189] We can set a=ρ1=R1=380(8) that is, the starting point of the tooth edge curve is the starting point of the actual tooth edge.

[0190] That is, θ1=0 (9)

[0191] Step 5: Find the relationship between the sliding angle α and the constant b in equation (7) (i.e., the tooth edge curve expression) (see Appendix Figure 1 and 2 ):

[0192] From formula (7), we get

[0193] x=a·e b·θ ·cosθ (10)

[0194] y=a·e b·θ ·sinθ (11)

[0195] but

[0196]

[0197] but At the same time,

[0198] Combining (14) and (15),

[0199] have have to have to

[0200] Simplified to 1-b(tanθ) 2 tanα=btanα-(tanθ) 2

[0201] Simplifying, we get 1+(tanθ) 2 = btanα(1+(tanθ) 2 )

[0202] Simplifying, we get b tanα=1 (17)

[0203] From formula (17), we can finally get

[0204] In formula (18), b is a constant, so this formula verifies that the sliding angle of the tooth edge curve is a constant value and does not change with the change of the polar angle θ.

[0205] Or from formula (17) Formula (19) can be used to obtain the parameters of the tooth edge curve equation by specifying the sliding angle (α = 10°):

[0206] b=5.67

[0207] Step 6: Find the polar angle θ2 of the end point of the tooth edge curve:

[0208] By

[0209]

[0210] Obtain θ2=tanα·ln C1=tan 10°·ln 1.8=0.104 (21)

[0211] Convert to angle

[0212] At this point, the design of the heat mill tooth edge curve (including the tooth edge curve expression, the definition domain of the expression parameters, and the constant values ​​in the expression) is completed, and the tooth edge curve segment P1P2 is the grinding tooth profile of the heat mill grinding disc. Array its circumference to obtain a complete heat mill grinding disc (see Appendix Figure 3 and 4 ).

[0213] As a preferred technical solution, in this embodiment, Figure 3 and Figure 4 It is a tooth-shaped structure of a hot mill grinding disc with a constant sliding angle, and the tooth edge profile is a designed tooth edge curve. This embodiment provides 8 specific embodiments of the design method of a hot mill grinding disc based on the tooth edge curve, and obtains the tooth edge curve equation under different parameters and constants, namely, specific implementation methods 1 to 8. For specific parameters, please refer to Table 1 below;

[0214] Table 1 Parameters and corresponding tooth edge curve equations in different specific implementations

[0215]

[0216]

[0217] 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 hot grinding mill grinding disc with a constant sliding angle, characterized in that: The tooth edge profile of the hot mill grinding disc is a tooth edge curve, and the angle between the polar axis and the x-axis at any point on the tooth edge curve is defined as the polar angle θ. The tooth edge curve equation of the hot mill grinding disc is: p=a·e b·θ ,θ∈[θ1,θ2] Where a and b are constants, a∈[380,580], b∈[1.732,5.76], which are used to control the shape of the tooth edge curve; θ1 is the polar angle of the starting point of the tooth edge curve, and θ2 is the polar angle of the ending point of the tooth edge curve.

2. The constant sliding angle hot grinder grinding disc according to claim 1, characterized in that: The slip angle α∈[10°,30°].

3. A method for designing a hot grinder grinding disc based on a constant sliding angle, characterized in that: The design method comprises the following steps: Step 1: Define the inner radius of the grinding disc of the hot grinding machine as R1 and the outer radius as R2; The outer radius is: R2=C1·R1 (1) The range of C1 is 1.8 to 2.6, and the range of R1 is 380 to 580 mm; Step 2: Define the tooth edge curve parameters: 1) Define the origin of the tooth edge curve as the center O of the grinding disc of the hot grinding machine; 2) Define the intersection point of the tooth edge curve and the straight line where the radius of the hot grinder grinding disc is located as P; 3) Define the angle between the polar axis and the x-axis at any point on the tooth edge curve as θ, the polar angle at the starting point of the tooth edge curve is represented by θ1, and the polar angle at the end point of the tooth edge curve is represented by θ2; 4) The angle between the cutting speed and the cutting force at any point on the tooth edge curve is defined as the sliding angle α. At any point on the tooth edge curve, the sliding angle is equal, and the sliding angle α is defined to be in the range of 10° to 30°; 5) Define the complementary angle of the sliding angle as β; 6) Define the reverse angle between the tangent line of the tooth edge curve at any point and the x-axis as 7) Define the intersection of the tooth edge curve and the inner diameter of the grinding disc of the hot grinder as the starting point, denoted by P1; 8) Define the radius of gyration where the starting point P1 is located as ρ1, ρ1=R1 (2); Step 3: Derivation of the initial expression of the tooth edge curve with constant sliding angle: Let the sliding angle α = C1, C1 is a constant; Then β=C2, C2 is a constant; but but Assume the parametric equation of the tooth edge curve is: ρ=ρ(θ), (θ>0) Then x = ρ(θ)·cosθ y=ρ(θ)·sinθ but Other Substituting equations (4) and (5) into equation (3), have to Simplified Right now C3 is a constant, b is a constant; Then (lnρ)′=b Then lnρ=b·θ+C4, C4 is a constant; but In the formula, C4 is a constant, so is a constant; make Then the preliminary expression of the tooth edge curve is ρ = a·e b·θ (7) Step 4: Define the value of a and the starting polar angle θ1 in equation (7): For equation (7), let θ = 0, then So ρ=a We can set a=ρ1=R1 (8) That is, the starting point of the tooth edge curve is the starting point of the actual tooth edge, that is θ1=0 (9).

4. The method according to claim 3, characterized in that The method further comprises: Step 5: Find the relationship between the sliding angle α and the constant b in the tooth edge curve expression (7): From formula (7), we can get x = a·e b·θ ·cosθ (10) y=a·e b·θ ·sinθ (11) but but set up Combining (14) and (15), get have to have to Converting to 1-b(tanθ) 2 tan α=b tan α-(tan θ) 2 Simplifying, we get 1+(tanθ) 2 = btanα(1+(tanθ) 2 ) Simplified, btanα=1 (17) The expression of the slip angle α is obtained from formula (17): In formula (18), b is a constant, so formula (18) verifies that the sliding angle of the tooth edge curve is a constant value and does not change with the change of the polar angle θ; Or from formula (17) we can also get 5. The method according to claim 4, characterized in that In step 5, equation (19) obtains the parameter b of the tooth edge curve equation through the specified slip angle α. According to the slip angle α∈[10°,30°] defined in step 2, the parameter b∈[1.732,5.76] is obtained.

6. The method according to claim 3, characterized in that: The method further comprises: Step 6: Determination of the polar angle θ2 of the end point of the tooth edge curve: By We get θ2 = tanα·lnC1 (21) Convert to angle

Images