A hot mill grinding disc based on Cartesian blade line and its design method

Abstract

The invention discloses a hot mill grinding disc based on Cartesian blade line and a design method thereof, belonging to the technical field of hot mill grinding discs; wherein, the design method of the hot mill grinding disc based on Cartesian blade line comprises the following steps: S1, determining the inner circle radius R1 and the outer circle radius R2 of the hot mill grinding disc; S2, determining the origin of the Cartesian blade line as the center O of the hot mill grinding disc; S3, defining any point P on the Cartesian blade line, the tooth grinding starting point P1, the tooth grinding ending point P2, the starting point rotation radius r1, the ending point rotation radius r2, the slip angle α of any point on the Cartesian blade line and the polar angle θ of any point on the Cartesian blade line; S4, obtaining the Cartesian blade line equation of the hot mill grinding disc. The invention provides a hot mill grinding disc based on Cartesian blade line and a design method thereof, provides a theoretical and highly generalized hot mill grinding disc design, and a hot mill grinding disc that can improve the dissociation quality, reduce energy consumption, and extend the tool life.

Description

Technical Field

[0001] The present invention relates to the technical field of grinding discs for hot mills, and more specifically to a grinding disc for hot mills based on Cartesian blade lines and a design method thereof. Background Art

[0002] Fiberboard is widely used in furniture, packaging and other industries due to its homogeneous materials, small vertical and horizontal strength difference, and not easy to crack. Fiberboard is made of wood fiber through a series of processes such as gluing and hot pressing, and wood fiber is obtained by hot grinding machine to dissociate and cook wood chips. When the cooked wood chips are continuously subjected to shear force on the grinding disc, they will dissociate into wood fibers. The grinding disc structure directly affects the fiber dissociation quality, energy consumption, and grinding disc life.

[0003] In order to improve the quality of dissociation, some scholars have proposed several patents related to hot mill grinding discs, represented by the Chinese invention patent "A design method for the tooth structure of a large-diameter hot mill grinding disc with circular partition" with application number CN201210437023.X and the Chinese invention patent "A design method for the tooth structure of a hot mill grinding disc" with application number CN201910891957.2. The grinding disc is divided into crushing zone, coarse grinding zone, fine grinding zone and other areas, and the parameters of each zone are set according to the hot grinding raw materials, which improves the separation quality to a certain extent and reduces energy consumption.

[0004] On the one hand, each area of ​​these patents has independent structural parameters, which are relatively cumbersome to express and lack generalization and theoreticality; on the other hand, the sliding angles of the crushing area, coarse grinding area, fine grinding area, etc. are assumed to be the same, ignoring the requirement that in the actual dissociation process, the dissociation force of each area should gradually change due to the increase of the dissociation radius and dissociation rate. Therefore, it is necessary to provide a thermal mill grinding disc design that is both theoretical and highly generalized, and can improve the dissociation quality, reduce energy consumption, and extend the tool life. Summary of the invention

[0005] In order to solve the above problems in the prior art, the present invention provides a hot mill grinding plate based on Cartesian blade lines and a design method thereof.

[0006] In order to solve the above technical problems, the technical solution of the present invention is as follows:

[0007] The present invention provides a hot mill grinding disc based on a Cartesian blade line, wherein the tooth edge profile of the hot mill grinding disc is a Cartesian blade line.

[0008] The Cartesian blade line equation of the hot refiner grinding plate is:

[0009]

[0010] Where θ is the polar angle of any point on the Cartesian lobate, a is a constant, and θ 1 is the polar angle of the starting point of the Cartesian lobate, θ 2 is the polar angle of the Cartesian lobate end point.

[0011] Furthermore, the polar angle θ of the starting point of the Cartesian lobate line 1 The range is 10.8° to 20.3°; the polar angle θ of the termination point of the Cartesian lobe line 2 The range is 22.0° to 37.5°.

[0012] The present invention also provides a design method for a hot mill grinding disc based on Cartesian blade lines, the design method comprising the following steps:

[0013] S1. Determine the inner radius R of the grinding disc of the hot grinding machine 1 and the outer radius R 2 ;

[0014] The outer radius R 2 The range is 720-1200mm, the inner radius R 1 The expression is:

[0015] R 1 =C 1 ·R 2 (1)

[0016] Among them, C 1 is a constant, C 1 The range is 0.47-0.56;

[0017] S2, determine the origin of the Cartesian blade line as the center O of the grinding disc of the hot mill;

[0018] S3. Define any point P on the Cartesian blade line and the starting point P of the gear grinding 1 , Grinding end point P 2 , starting point rotation radius r 1 , the radius of gyration of the end point r 2 , the shear angle α of any point on the Cartesian lobe and the polar angle θ of any point on the Cartesian lobe;

[0019] Any point P on the Cartesian lobe line is the intersection of the Cartesian lobe line and the straight line where the radius of the hot mill grinding disc is located;

[0020] The grinding starting point P 1 It is the intersection of the Cartesian blade line and the inner diameter of the grinding disc of the hot mill;

[0021] The grinding end point P 2 It is the intersection of the Cartesian blade line and the outer diameter of the grinding disc of the hot mill;

[0022] The starting point rotation radius r 1 Equal to the inner radius R of the grinding disc of the hot grinding machine 1 , the starting point rotation radius r 1 The expression is:

[0023] r 1 =R 1 (2)

[0024] The end point radius of gyration r 2 Equal to the outer radius R of the grinding disc of the hot grinding machine 2 , the radius of gyration of the end point r 2 The expression is:

[0025] r 2 =R 2 (3)

[0026] The slip angle α of any point on the Cartesian lobe is the angle between the polar axis at that point and the tangent at that point. The slip angle of the starting point of the Cartesian lobe is α 1 The sliding angle of the Cartesian leaf line end point is represented by α 2 It indicates that the sliding angle α of the end point of the Cartesian lobe line 2 The range is 20° to 48°;

[0027] The polar angle θ of any point on the Cartesian lobate is the angle between the polar axis at that point and the x-axis. The polar angle of the starting point of the Cartesian lobate is θ 1 The polar angle of the Cartesian lobate end point is represented by θ 2 express;

[0028] S4, obtaining the Cartesian blade line equation of the hot refiner grinding disc;

[0029] The Cartesian blade line equation of the hot refiner grinding plate is:

[0030]

[0031] Where θ is the polar angle of any point on the Cartesian lobate, a is a constant, and θ 1 is the polar angle of the starting point of the Cartesian lobate, θ 2 is the polar angle of the Cartesian lobate end point.

[0032] 4. The method for designing a grinding disc for a hot mill based on Cartesian blade profiles according to claim 3, wherein step S4 specifically comprises:

[0033] S41. Assume the rectangular coordinate equation of the Cartesian leaf shape line;

[0034] The rectangular coordinate equation of the Cartesian leaf shape is:

[0035] x 3 +y 3 =3axy (4)

[0036] Where a is a constant and a>0;

[0037] The polar coordinate equation of the Cartesian leaf shape is:

[0038]

[0039] make

[0040] y=t·x (6)

[0041] Where t is the slope at any point on the Cartesian leaf line;

[0042] t=tanθ,t∈(0,1) (7)

[0043] Substituting equation (6) into equation (4), we get the parametric equation of the Cartesian leaf shape line:

[0044]

[0045] Also because

[0046]

[0047] Combining equation (8) and equation (9), we get:

[0048]

[0049] S42. Find the polar angle θ of the end point of the Cartesian leaf line 2 and its slope t 2 ;

[0050] Calculate the derivative of equation (8) with respect to slope t, and we get equations (11) and (12);

[0051]

[0052] Find the derivative of y with respect to x. The derivative of y with respect to x is equal to the slope of the tangent corresponding to the polar angle θ on the Cartesian leaf line, as shown in the following formula (13):

[0053]

[0054] Formula (13) is simplified to:

[0055]

[0056] Substituting formula (7) into formula (14) and further simplifying it, we get:

[0057]

[0058] Simplified:

[0059]

[0060] According to equations (7), (16) and the sliding angle α at the end point of the Cartesian leaf line 2 The range is 20.0° to 48.0°, which can be solved to obtain the polar angle θ of the end point of the Cartesian leaf line 2 The range is from 22.0° to 37.5°, and its slope t 2 The range is 0.404 to 0.768;

[0061] S43, obtaining the value of a;

[0062] Let a be expressed as:

[0063] a=C 2 ·R 2 (17)

[0064] Combining equations (1), (3), (10), and (17), we get:

[0065]

[0066] have to:

[0067]

[0068] According to the slope t of the end point of the Cartesian leaf line 2 The range is 0.404 to 0.768, and C 2MIN and C 2MAX :

[0069] C 2MIN =0.498

[0070] C 2MAX =0.815

[0071] Then C 2 The range of is 0.498 to 0.815, which is substituted into formula (17) to obtain the value of a;

[0072] S44. Verify the polar angle θ of the starting point of the Cartesian leaf line 1 and its slope t 1 ;

[0073] From equation (1), equation (17) and equation (18), we can get:

[0074]

[0075] have to:

[0076]

[0077] According to equation (7) and equation (21) and C 1 The range is 0.47 to 0.56, C 2 The range is 0.498 to 0.815, and the polar angle θ of the starting point of the Cartesian leaf line is obtained. 1 The range is from 10.8° to 20.3°, and its slope t 1 The range is from 0.190 to 0.370, which are all within the reasonable range;

[0078] Therefore, the Cartesian blade line equation of the hot refiner grinding disc is

[0079]

[0080] Where θ is the polar angle of any point on the Cartesian lobate, a is a constant, and θ 1 is the polar angle of the starting point of the Cartesian lobate, θ 2 is the polar angle of the Cartesian lobate end point.

[0081] Further, step S4 also includes:

[0082] S45, verify the sliding angle α of the starting point of the Cartesian leaf line 1 ;

[0083] The slope t 1 Substitute the value of into formula (16), and we get α 1 The range is 10.2° to 18.4°, which is within a reasonable range.

[0084] Furthermore, the grinding starting point P 1 and the grinding end point P 2 The Cartesian leaf segment P 1 P 2 The grinding tooth profile of the grinding disc of the hot grinder is represented by the Cartesian blade segment P 1 P 2 Circular array to obtain a complete hot mill grinding plate.

[0085] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0086] The present invention provides a hot mill grinding disc based on Cartesian blade lines and a design method thereof, wherein the grinding tooth profile of the hot mill grinding disc is designed as a Cartesian blade line function, which is convenient for design expression and practical processing; the hot mill grinding disc based on Cartesian blade lines provided by the present invention has a gradually increasing sliding angle from the inner circle to the outer circle that matches the gradually increasing cutting rate, and the gradually increasing sliding angle matches the gradually decreasing cutting force, thereby improving the fiber separation quality, reducing energy consumption, and extending the tool life. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0088] Figure 1 Schematic diagram of the Cartesian blade line of the heat refiner grinding plate based on the Cartesian blade line of the present invention,

[0089] Among them, point O is the center of the grinding disc of the thermal grinding machine; R 1 R is the inner radius of the grinding disc of the hot grinding machine; 2 is the outer radius of the grinding disc of the hot mill; P is an arbitrary point; ω is the rotation direction of the grinding disc of the hot mill; P 1 is the starting point of tooth grinding; P 2 is the grinding end point; α 1 is the sliding angle at the starting point of gear grinding; α 2 is the sliding angle at the grinding end point; θ 1 is the polar angle of the starting point of gear grinding; θ 2 is the polar angle of the grinding end point; Cartesian leaf segment P 1 P 2 For grinding tooth edges;

[0090] Figure 2 The figure is a schematic diagram of the tooth structure of the grinding disc of the hot mill based on the Cartesian blade line of the present invention, and the tooth edge profile thereof is the Cartesian blade line;

[0091] Figure 3 The present invention is a flow chart of the method for designing a grinding disc for a hot mill based on Cartesian blade lines. DETAILED DESCRIPTION

[0092] In order to better understand the purpose, structure and function of the present invention, the technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings and specific preferred embodiments.

[0093] In the description of the present 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 drawings, which is only for the convenience of describing the present invention and simplifying the description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. "First", "second", etc. do not indicate the importance of the parts, and therefore cannot be understood as a limitation on the present invention. The specific dimensions used in the embodiments are only for illustrating the technical solution and do not limit the scope of protection of the present invention. It is understandable to those skilled in the art that some well-known structures and their descriptions in the drawings may be omitted.

[0094] Unless otherwise clearly specified and limited, the terms "install", "set", "connect", "fix" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements. For ordinary technicians in this field, the specific meanings of the above terms in this application can be understood according to specific circumstances.

[0095] Embodiment 1:

[0096] like Figure 1-2 As shown, the present invention provides a technical solution: a hot mill grinding disc based on Cartesian blade line, wherein the tooth edge profile of the hot mill grinding disc is a Cartesian blade line,

[0097] The Cartesian blade line equation of the hot refiner grinding plate is:

[0098]

[0099] Where θ is the polar angle of any point on the Cartesian lobate, a is a constant, and θ 1 is the polar angle of the starting point of the Cartesian lobate, θ 2 is the polar angle of the Cartesian lobate end point.

[0100] Furthermore, the polar angle θ of the starting point of the Cartesian lobate line 1 The range is 10.8° to 20.3°; the polar angle θ of the Cartesian lobe end point 2 The range is 22.0° to 37.5°.

[0101] In this embodiment, the grinding tooth profile of the hot mill grinding disc is designed as a Cartesian blade line function, which is convenient for design expression and actual processing; the hot mill grinding disc based on the Cartesian blade line provided by the present invention has a gradually increasing sliding angle from the inner circle to the outer circle that matches the gradually increasing cutting rate, and the gradually increasing sliding angle matches the gradually decreasing cutting force, thereby improving the fiber separation quality, reducing energy consumption, and extending the tool life.

[0102] Embodiment 2:

[0103] like Figure 3 As shown, the present invention provides a technical solution: a design method for a hot mill grinding disc based on Cartesian blade lines, the design method comprising the following steps:

[0104] S1. Determine the inner radius R of the grinding disc of the hot grinding machine 1 and the outer radius R 2 ;

[0105] The outer radius R 2 The range is 720-1200mm, the inner radius R 1 The expression is:

[0106] R 1 =C 1 *R 2 (1)

[0107] Among them, C 1 is a constant, C 1 The range is 0.47-0.56;

[0108] S2, determine the origin of the Cartesian blade line as the center O of the grinding disc of the hot mill;

[0109] S3. Define any point P on the Cartesian blade line and the starting point P of the tooth grinding 1 , Grinding end point P 2 , starting point rotation radius r 1 , the radius of gyration of the end point r 2 , the shear angle α of any point on the Cartesian lobe and the polar angle θ of any point on the Cartesian lobe;

[0110] Any point P on the Cartesian lobe line is the intersection of the Cartesian lobe line and the straight line where the radius of the hot mill grinding disc is located;

[0111] The grinding starting point P 1 It is the intersection of the Cartesian blade line and the inner diameter of the grinding disc of the hot mill;

[0112] The grinding end point P 2 It is the intersection of the Cartesian blade line and the outer diameter of the grinding disc of the hot mill;

[0113] The starting point rotation radius r 1 Equal to the inner radius R of the grinding disc of the hot grinding machine 1 , the starting point rotation radius r 1 The expression is:

[0114] r 1 =R 1 (2)

[0115] The end point radius of gyration r 2 Equal to the outer radius R of the grinding disc of the hot grinding machine 2 , the radius of gyration of the end point r 2 The expression is:

[0116] r 2 =R 2 (3)

[0117] The slip angle α of any point on the Cartesian lobe is the angle between the polar axis at that point and the tangent at that point. The slip angle of the starting point of the Cartesian lobe is α 1 The sliding angle of the Cartesian leaf line end point is represented by α 2 It indicates that the sliding angle α of the end point of the Cartesian lobe line 2 The range is 20° to 48°;

[0118] The polar angle θ of any point on the Cartesian lobate is the angle between the polar axis at that point and the x-axis. The polar angle of the starting point of the Cartesian lobate is θ 1 The polar angle of the Cartesian lobate end point is represented by θ 2 express;

[0119] S4, obtaining the Cartesian blade line equation of the hot refiner grinding disc;

[0120] The Cartesian blade line equation of the hot refiner grinding plate is:

[0121]

[0122] Where θ is the polar angle of any point on the Cartesian lobate, a is a constant, and θ 1 is the polar angle of the starting point of the Cartesian lobate, θ 2 is the polar angle of the Cartesian lobate end point.

[0123] The problems in the prior art are:

[0124] 1. The expression is rather cumbersome and lacks generalization and theoreticality, which will lead to complicated design and cumbersome manufacturing.

[0125] 2. In the actual fiber dissociation process, the dissociation rate increases with the increase of the dissociation radius, and the dissociation force decreases with the increase of the dissociation radius. Therefore, if the grinding tooth sliding angle does not change with the dissociation radius, the provided dissociation force does not match the required dissociation force, which will have an adverse effect on the fiber quality, energy consumption, and grinding disc life.

[0126] In view of the problems existing in the prior art, this embodiment provides a design method for a hot mill grinding disc based on Cartesian blade lines to achieve the following objectives:

[0127] 1. The grinding tooth profile of the grinding disc of the hot grinding machine is designed as a Cartesian blade line function, which is convenient for design expression and actual processing.

[0128] 2. From the inner circle to the outer circle, the gradually increasing sliding angle matches the gradually increasing cutting rate, and the gradually increasing sliding angle matches the gradually decreasing cutting force, thereby improving the fiber separation quality, reducing energy consumption, and extending the tool life.

[0129] Embodiment 3:

[0130] Based on Example 2, step S4 specifically includes:

[0131] S41. Assume the rectangular coordinate equation of the Cartesian leaf shape line;

[0132] The rectangular coordinate equation of the Cartesian leaf shape is:

[0133] x 3 +y 3 =3axy (4)

[0134] Where a is a constant and a>0;

[0135] The polar coordinate equation of the Cartesian leaf shape is:

[0136]

[0137] make

[0138] y=t·x (6)

[0139] Where t is the slope at any point on the Cartesian leaf line;

[0140] t=tanθ,t∈(0,1) (7)

[0141] Substituting equation (6) into equation (4), we get the parametric equation of the Cartesian leaf shape line:

[0142]

[0143] Also because

[0144]

[0145] Combining equation (8) and equation (9), we get:

[0146]

[0147] S42. Find the polar angle θ of the end point of the Cartesian leaf line 2 and its slope t 2 ;

[0148] Calculate the derivative of equation (8) with respect to slope t, and we get equations (11) and (12);

[0149]

[0150] Find the derivative of y with respect to x. The derivative of y with respect to x is equal to the slope of the tangent corresponding to the polar angle θ on the Cartesian leaf line, as shown in the following formula (13):

[0151]

[0152] Formula (13) is simplified to:

[0153]

[0154] Substituting formula (7) into formula (14) and further simplifying it, we get:

[0155]

[0156] Simplified:

[0157]

[0158] According to equations (7), (16) and the sliding angle α at the end point of the Cartesian leaf line 2 The range is 20.0° to 48.0°, which can be solved to obtain the polar angle θ of the end point of the Cartesian leaf line 2 The range is from 22.0° to 37.5°, and its slope t 2 The range is 0.404 to 0.768;

[0159] S43, obtaining the value of a;

[0160] Let a be expressed as:

[0161] a=C 2 ·R 2 (17)

[0162] Combining equations (1), (3), (10), and (17), we get:

[0163]

[0164] have to:

[0165]

[0166] According to the slope t of the end point of the Cartesian leaf line 2 The range is 0.404 to 0.768, and C 2MIN and C 2MAX :

[0167] C 2MIN =0.498

[0168] C 2MAX =0.815

[0169] Then C 2 The range of is 0.498 to 0.815, which is substituted into formula (17) to obtain the value of a;

[0170] S44. Verify the polar angle θ of the starting point of the Cartesian leaf line 1 and its slope t 1 ;

[0171] From equation (1), equation (17) and equation (18), we can get:

[0172]

[0173] have to:

[0174]

[0175] According to equation (7) and equation (21) and C 1 The range is 0.47 to 0.56, C 2 The range is 0.498 to 0.815, and the polar angle θ of the starting point of the Cartesian leaf line is obtained. 1 The range is from 10.8° to 20.3°, and its slope t 1 The range is from 0.190 to 0.370, which are all within the reasonable range;

[0176] Therefore, the Cartesian blade line equation of the hot refiner grinding disc is

[0177]

[0178] Where θ is the polar angle of any point on the Cartesian lobate, a is a constant, and θ 1 is the polar angle of the starting point of the Cartesian lobate, θ 2 is the polar angle of the Cartesian lobate end point.

[0179] Further, step S4 also includes:

[0180] S45, verify the sliding angle α of the starting point of the Cartesian leaf line 1 ;

[0181] The slope t 1 Substitute the value of into formula (16), and we get α 1 The range is 10.2° to 18.4°, which is within a reasonable range.

[0182] Furthermore, the grinding starting point P 1 and the grinding end point P 2 The Cartesian leaf segment P 1 P 2 The grinding tooth profile of the grinding disc of the hot grinder is represented by the Cartesian blade segment P 1 P 2 Circular array to obtain a complete hot mill grinding plate.

[0183] Embodiment 4:

[0184] This embodiment provides three specific embodiments of the design method of the hot mill grinding plate based on Cartesian blade line, including specific embodiment a, specific embodiment b, and specific embodiment c; specific embodiment a describes the specific design steps, and the specific design steps of specific embodiments b and specific embodiments c are similar to those of specific embodiment a, so the results of specific embodiments b and specific embodiments c are given in table form, please refer to Table 1 for details;

[0185] The specific embodiment a is as follows:

[0186] first step:

[0187] Determine the inner radius and outer radius of the grinding disc of the thermal grinding machine;

[0188] The inner radius is R 1 , the outer radius is R 2 ;

[0189] The R 2 The value of is 1200mm;

[0190] The inner diameter is:

[0191] R 1 =C 1 ·R 2 (1)

[0192] The C 1 The value of is 0.5.

[0193] Step 2:

[0194] Determine the Cartesian leaf origin:

[0195] The point of the Cartesian blade line is defined as the center O of the grinding disc;

[0196] Step 3:

[0197] Definitions of any point on the Cartesian leaf line, starting point, starting point gyration radius, ending point gyration radius, slip angle, and polar angle:

[0198] (1) Any point on the Cartesian blade line: The intersection of the Cartesian blade line and the straight line where the radius of the thermal refiner blade is located is represented by point P;

[0199] (2) Starting point: The intersection of the Cartesian blade line and the inner diameter of the grinding mill, expressed as P 1 express;

[0200] (3) The radius of gyration of the starting point is defined as r,

[0201] r 1 =R 1 (2)

[0202] (4) The radius of gyration at the end point is defined as r 2 ,have

[0203] r 2 =R 2 (3)

[0204] (5) The slip angle at any point of the Cartesian lobe is the angle between the polar axis at that point and the tangent at that point, represented by α. The slip angle at the starting point of the Cartesian lobe is represented by α 1 The sliding angle of the Cartesian leaf line end point is represented by α 2 Indicates that its value is 48°.

[0205] (6) Polar angle of any point on the Cartesian lobate: The angle between the polar axis and the x-axis at that point is denoted by θ. The polar angle of the starting point of the Cartesian lobate is denoted by θ. 1 The polar angle of the Cartesian lobate end point is represented by θ 2 express.

[0206] Step 4: Obtain the Cartesian leaf line equation:

[0207] (1) Assume the Cartesian leaf line rectangular coordinate equation;

[0208] x 3 +y 3 =3axy,a>0 (4)

[0209] Its polar coordinate equation is:

[0210]

[0211] make:

[0212] y=t*x (6)

[0213] Where t is the slope at any point on the leaf line,

[0214] t=tanθ,t∈(0,1) (7)

[0215] Substituting equation (6) into equation (4), we get the parametric equation of the Cartesian leaf shape line:

[0216]

[0217] Also because

[0218]

[0219] Combining equation (8) and equation (9), we get:

[0220]

[0221] (2) Find the polar angle θ of the Cartesian leaf line end point 2 and its slope t 2 ;

[0222] Calculate the derivative of equation (8) with respect to slope t, and we get equations (11) and (12);

[0223]

[0224] Find the derivative of y with respect to x. The derivative of y with respect to x is equal to the slope of the tangent line corresponding to the polar angle θ on the Cartesian leaf line (such as Figure 1 As shown in formula (13)

[0225]

[0226] Formula (13) is simplified to:

[0227]

[0228] Substituting formula (7) into formula (14) and further simplifying it, we get:

[0229]

[0230] Simplified:

[0231]

[0232] According to equations (7), (16) and the sliding angle α at the end point of the Cartesian leaf line 2 The value of is 48.0°, which can be solved to obtain the polar angle θ of the end point of the Cartesian leaf line. 2 The value is 37.5°, and its slope t 2 The value of is 0.767.

[0233] (3) Obtain the value of a

[0234] set up

[0235] a=C 2 ·R 2 (17)

[0236] Combining equations (1), (3), (10), and (17), we get

[0237]

[0238] have to

[0239]

[0240] have to:

[0241] C 2 =0.498

[0242] Then C 2 The value of is 0.498. Substituting it into formula (17) yields the value of a, a = 0.498 × 1200 = 598;

[0243] (4) Find the polar angle θ of the starting point of the Cartesian leaf line 1 and its slope t 1 ;

[0244] From equation (1), equation (17) and equation (18)

[0245]

[0246] have to

[0247]

[0248] By C 1 The value of C is 0.50. 2 The value of is 0.498, equation (7) and equation (21), and the polar angle θ is obtained 1 The value is 18.2° and its slope t 1 The value of is 0.329, which is within the reasonable range.

[0249] Therefore, the grinding gear Cartesian blade line equation is:

[0250]

[0251] (5) Verify the sliding angle α at the starting point of the Cartesian leaf line 1 :

[0252] t 1 Substituting the value of into formula (16), we can get α 1 The value is 16.6°, which is also within a reasonable range.

[0253] Cartesian leaf segment P 1 P 2This is the grinding tooth profile of the grinding disc. Array its circumference to obtain the following Figure 2 Complete grinding disc shown.

[0254] This embodiment provides three specific embodiments of the design method of the hot mill grinding plate based on the Cartesian blade line, including specific embodiment a, specific embodiment b, and specific embodiment c. For specific parameters, please refer to the following Table 1;

[0255] Table 1. Parameters and Cartesian leaf line equations of specific embodiment a, specific embodiment b, and specific embodiment c

[0256]

[0257] 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 design method for a hot mill grinding disc based on Cartesian blade lines, characterized in that: The design method comprises the following steps: S1, determine the inner radius R1 and outer radius R2 of the grinding disc of the hot grinding machine; The range of the outer circle radius R2 is 720-1200 mm, and the expression of the inner circle radius R1 is: R1=C1·R2 (1) Among them, C1 is a constant, and the range of C1 is 0.47-0.56; S2, determine the origin of the Cartesian blade line as the center O of the grinding disc of the hot mill; S3, define any point P on the Cartesian lobe line, the grinding starting point P1, the grinding ending point P2, the starting point gyration radius r1, the ending point gyration radius r2, the slip angle α of any point on the Cartesian lobe line, and the polar angle θ of any point on the Cartesian lobe line; Any point P on the Cartesian lobe line is the intersection of the Cartesian lobe line and the straight line where the radius of the hot mill grinding disc is located; The grinding tooth starting point P1 is the intersection of the Cartesian blade line and the inner diameter of the grinding disc of the hot mill; The grinding tooth termination point P2 is the intersection of the Cartesian blade line and the outer diameter of the grinding disc of the hot mill; The starting point rotation radius r1 is equal to the inner radius R1 of the grinding disc of the hot grinding machine. The expression of the starting point rotation radius r1 is: r1＝R1 (2) The end point gyration radius r2 is equal to the outer circle radius R2 of the grinding disc of the hot grinding machine. The expression of the end point gyration radius r2 is: r2＝R2 (3) The slip angle α of any point on the Cartesian lobe line is the angle between the polar axis at the point and the tangent at the point. The slip angle at the starting point of the Cartesian lobe line is represented by α1, and the slip angle at the ending point of the Cartesian lobe line is represented by α2. The slip angle α2 at the ending point of the Cartesian lobe line ranges from 20° to 48°. The polar angle θ of any point on the Cartesian lobe is the angle between the polar axis at that point and the x-axis. The polar angle of the starting point of the Cartesian lobe is represented by θ1, and the polar angle of the ending point of the Cartesian lobe is represented by θ2. S4, obtaining the Cartesian blade line equation of the hot refiner grinding disc; The Cartesian blade line equation of the hot refiner grinding plate is: Where θ is the polar angle of any point on the Cartesian lobe, a is a constant, θ1 is the polar angle of the starting point of the Cartesian lobe, and θ2 is the polar angle of the ending point of the Cartesian lobe.

2. The method for designing a grinding disc for a hot mill based on Cartesian blade lines according to claim 1, characterized in that: Step S4 specifically includes: S41. Assume the rectangular coordinate equation of the Cartesian leaf shape line; The rectangular coordinate equation of the Cartesian leaf shape is: x 3 +y 3 =3axy (4) Where a is a constant and a>0; The polar coordinate equation of the Cartesian leaf shape is: make y=t·x (6) Where t is the slope at any point on the Cartesian leaf line; t=tanθ,t∈(0,1) (7) Substituting equation (6) into equation (4), we get the parametric equation of the Cartesian leaf shape line: Also because Combining equation (8) and equation (9), we get: S42, finding the polar angle θ2 and the slope t2 of the Cartesian leaf line end point; Calculate the derivative of equation (8) with respect to slope t, and we get equations (11) and (12); Find the derivative of y with respect to x. The derivative of y with respect to x is equal to the slope of the tangent corresponding to the polar angle θ on the Cartesian leaf line, as shown in the following formula (13): Formula (13) is simplified to: Substituting formula (7) into formula (14) and further simplifying it, we get: Simplified: According to equations (7) and (16) and the range of the slip angle α2 at the end point of the Cartesian lobe line is 20.0° to 48.0°, it can be solved that the polar angle θ2 at the end point of the Cartesian lobe line ranges from 22.0° to 37.5°, and its slope t2 ranges from 0.404 to 0.768; S43, obtaining the value of a; Let a be expressed as: a=C2·R2 (17) Combining equations (1), (3), (10), and (17), we get: have to: According to the slope t2 of the Cartesian leaf line termination point ranging from 0.404 to 0.768, we get C 2MIN and C 2MAX : C 2MIN ＝0.498 C 2MAX ＝0.815 Then the range of C2 is 0.498 to 0.815, which is substituted into formula (17) to obtain the value of a; S44, verifying the polar angle θ1 and the slope t1 of the starting point of the Cartesian leaf line; From equation (1), equation (17) and equation (18), we can get: have to: According to equations (7) and (21), and the range of C1 is 0.47 to 0.56, and the range of C2 is 0.498 to 0.815, the polar angle θ1 of the starting point of the Cartesian leaf line is in the range of 10.8° to 20.3°, and the range of its slope t1 is in the range of 0.190 to 0.370, both of which are within the reasonable range; Therefore, the Cartesian blade line equation of the hot refiner grinding disc is Where θ is the polar angle of any point on the Cartesian lobe, a is a constant, θ1 is the polar angle of the starting point of the Cartesian lobe, and θ2 is the polar angle of the ending point of the Cartesian lobe.

3. The method for designing a grinding disc for a hot mill based on Cartesian blade lines according to claim 2, characterized in that: Step S4 also includes: S45, verifying the sliding angle α1 of the starting point of the Cartesian leaf line; Substituting the value of slope t1 into equation (16), we get that the range of α1 is 10.2° to 18.4°, which is within a reasonable range.

4. The method for designing a grinding disc for a hot mill based on Cartesian blade lines according to claim 1, characterized in that: The Cartesian blade 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 Cartesian blade line segment P1P2 is arranged in a circular array to obtain a complete hot mill grinding plate.

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