A cycloidal-based hot mill blade and method of designing the same

Abstract

The application discloses a cycloid-based hot mill grinding piece and a design method thereof, and belongs to the technical field of hot mill grinding pieces. The design method of the cycloid-based hot mill grinding piece comprises the following steps: S1, determining the inner circle radius R1 and the outer circle radius R2 of the hot mill grinding piece; S2, determining the origin of the cycloid as the center O of the hot mill grinding piece; S3, defining the X-axis as a horizontal axis passing through the origin, and the positive direction of the X-axis is to the right; S4, defining a moving circle generating the cycloid as a circle rolling along the X-axis, and the radius of the moving circle is a; S5, defining the rolling angle of the moving circle as the angle rolled by the moving circle along the positive direction of the X-axis, and the rolling angle is represented by t; S6, defining an arbitrary point P on the cycloid, a grinding tooth starting point P1, a grinding tooth ending point P2, a rotation radius p1 of the grinding tooth starting point, a sliding angle a of the arbitrary point on the cycloid, and a polar angle theta of the arbitrary point on the cycloid; and S7, obtaining the cycloid equation of the hot mill grinding piece. The hot mill grinding piece can improve the fiber separation quality, reduce energy consumption, and prolong the tool life.

Description

TECHNICAL FIELD

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

[0002] Fiberboard is one of the three major board types and is widely used in the construction, panel furniture and interior decoration industries. Fiber preparation is an important link in the production of fiberboard, and the grinding plate is the core executive component in fiber preparation, because the separation of wood fibers is achieved through the grinding action of the grinding plate. Therefore, the quality of the hot mill grinding plate directly affects the quality of the prepared fiber, energy consumption and the service life of the grinding plate itself. The tooth edge structure is an important factor in the grinding plate, and its design method is worth studying. Generally, the grinding plate is divided into a crushing zone, a coarse grinding zone and a fine grinding zone from the inner circle to the outer circle, and correspondingly, the grinding rate and cutting force gradually change with the increase of the radius, and the sliding angle should be gradually changed more reasonably.

[0003] Currently, most of the patents related to the tooth edge of the hot mill grinding plate are straight teeth, such as the Chinese invention patent "Design method of circular ring partition large diameter level hot mill grinding plate tooth shape structure" with the application number CN201210437023.X and the Chinese invention patent "Design method of hot mill grinding plate tooth shape structure" with the application number CN201910891957.2, the sliding angle of which does not change with the increase of the rotating radius, and during grinding, the following problems exist:

[0004] 1. From the inner circle of the grinding plate to the outer circle of the grinding plate, the cutting angle is constant, and the cutting force on the wood is constant. The constant cutting force does not match the force required to separate the gradually reduced wood;

[0005] 2. Due to the mismatch between the actual cutting force and the required cutting force, the fiber separation quality is affected, the energy consumption is increased, and the service life of the grinding plate is reduced. SUMMARY

[0006] To improve the fiber separation quality, reduce energy consumption and prolong the service life of the tool, the present application provides a hot mill grinding plate based on cycloid and a design method thereof.

[0007] To solve the above technical problems, the technical solution of the present application is as follows:

[0008] The present application provides a hot mill grinding plate based on cycloid, the tooth edge profile of the hot mill grinding plate is a cycloid,

[0009] The cycloid equation of the hot mill grinding plate is:

[0010]

[0011] Wherein, p represents the polar radius; a is the radius of the generating circle of the cycloid; t is the angle of the rolling of the generating circle along the positive direction of the X axis;

[0012] The horizontal coordinate and the vertical coordinate of the point on the cycloid composed of the tooth edge profile of the hot mill grinding blade are:

[0013] x=a·(t-sin t)

[0014] y=a·(1-cos t)

[0015] In the formula, x and y are respectively the horizontal coordinate and the vertical coordinate of the point on the cycloid, a is the radius of the generating circle of the cycloid, and t is the angle of the rolling of the generating circle along the positive direction of the X axis;

[0016] Wherein, the radius of the generating circle ranges from 342 mm to 1230 mm.

[0017] Further, the angle t of the rolling of the generating circle along the positive direction of the X axis satisfies t∈(t1, t2), t1 is the rolling angle of the starting point of the cycloid, and t2 is the rolling angle of the terminal point of the cycloid; wherein, the rolling angle t1 of the starting point of the cycloid ranges from 57.8° to 85.5°.

[0018] The hot mill grinding blade based on the cycloid is matched with the gradually increasing slide-cutting angle and the gradually increasing cutting rate from the inner circle to the outer circle, and the gradually increasing slide-cutting angle is matched with the gradually decreasing cutting force; the quality of fiber separation can be improved, the energy consumption can be reduced, and the tool life can be prolonged.

[0019] The application further provides a design method of the hot mill grinding blade based on the cycloid, and the design method comprises the following steps:

[0020] S1, determining the inner circle radius R1 and the outer circle radius R2 of the hot mill grinding blade;

[0021] The inner circle radius R1 ranges from 360 mm to 600 mm, and the outer circle radius R2 is expressed as:

[0022] R2=C1·R1 (1)

[0023] Wherein, C1 is a constant, and the range of C1 is from 1.8 to 2.5;

[0024] S2, determining that the origin of the cycloid is the center O of the hot mill grinding blade;

[0025] S3, defining that the X axis is a horizontal axis passing through the origin, and the positive direction of the X axis is to the right;

[0026] S4, defining that the generating circle of the cycloid is a circle rolling along the X axis, and the radius of the generating circle is a;

[0027] S5, defining that the rolling angle of the generating circle is the angle of the rolling of the generating circle along the positive direction of the X axis, and the rolling angle is represented by t.

[0028] S6, define an arbitrary point P on the cycloid, a grinding starting point P1, a grinding termination point P2, a rotation radius ρ1 of the grinding starting point, a sliding angle α of an arbitrary point on the cycloid, a polar angle θ of an arbitrary point on the cycloid;

[0029] The arbitrary point P on the cycloid is the intersection of the cycloid and the straight line where the radius direction of the hot mill grinding piece is located;

[0030] The grinding starting point P1 is the intersection of the cycloid and the inner diameter of the hot mill grinding piece;

[0031] The grinding termination point P2 is the intersection of the cycloid and the outer diameter of the hot mill grinding piece;

[0032] The expression of the rotation radius ρ1 of the grinding starting point is:

[0033] ρ1=R1 (2)

[0034] The sliding angle α of an arbitrary point on the cycloid is the included angle between the polar axis at the point and the tangent at the point, the sliding angle of the cycloid starting point is represented by α1, and the sliding angle of the cycloid termination point is represented by α2, the sliding angle α1 of the cycloid starting point ranges from 9.6° to 14.5°;

[0035] The polar angle θ of an arbitrary point on the cycloid is the included angle between the polar axis at the point and the x-axis, the polar angle of the cycloid starting point is represented by θ1, and the polar angle of the cycloid termination point is represented by θ2;

[0036] S7, obtain the cycloid equation of the hot mill grinding piece;

[0037] The cycloid equation of the hot mill grinding piece is

[0038] In the formula, t∈(t1, t2);

[0039] Wherein, ρ represents the polar radius; a is the radius of the generating cycloid; t is the angle of the moving circle rolling along the positive direction of the X-axis; t1 is the rolling angle of the cycloid starting point, and t2 is the rolling angle of the cycloid termination point.

[0040] Further, step S7 specifically comprises:

[0041] S71, set the parametric equation of the cycloid;

[0042] The parametric equation of the cycloid is:

[0043] x=a·(t-sin t) (3)

[0044] y=a·(1-cos t) (4)

[0045]

[0046] S72, calculate the rolling angle t1 of the cycloid starting point;

[0047] Derivate the formula (3) and formula (4) with the polar angle t respectively, and formula (6) and formula (7) are obtained:

[0048]

[0049]

[0050] Derivate y with respect to x, and the derivative of y with respect to x is equal to the tangent slope corresponding to the polar angle θ on the cycloid, as shown in formula (8):

[0051]

[0052] According to formula (8), when t∈(0, π), k>0, and formula (8) can be obtained:

[0053]

[0054] Also:

[0055]

[0056] From formula (10):

[0057]

[0058] By combining formula (9) and formula (11), we get:

[0059]

[0060] From formula (12), it can be seen that the sliding angle of the present application increases with the increase of the rolling angle and the polar angle, which matches the gradually increasing cutting speed and the gradually decreasing cutting force;

[0061] According to formula (12) and the range of the sliding angle α1 of the cycloid starting point being 9.6° to 14.5°, the rolling angle t1 of the cycloid starting point is calculated to be in the range of 57.8° to 85.5°;

[0062] S73, get a value;

[0063] Let:

[0064] a=C2·R1 (13)

[0065] By combining formula (1), (2), (5), (13), we get:

[0066]

[0067] Simplify to get:

[0068]

[0069] According to the rolling angle t1 of the cycloid starting point, the range of C is 57.8° to 85.5°, and C 2MIN and C 2MAX :

[0070] C 2MIN = 0.95

[0071] C 2MAX = 2.05

[0072] Therefore, the range of C2 is 0.95 to 2.05, and the range of a value is 342-1230mm by bringing it into equation (13);

[0073] The cycloid equation of the hot mill grinding piece is obtained as follows:

[0074]

[0075] In the formula, t ∈ (t1, t2);

[0076] Wherein, ρ represents the polar radius; a is the radius of the generating circle of the cycloid; t is the angle of the generating circle rolling along the positive direction of the X axis; t1 is the rolling angle of the cycloid starting point, and t2 is the rolling angle of the cycloid ending point.

[0077] Further, the step S7 further comprises:

[0078] S74, the sliding angle α2 of the cycloid ending point is obtained;

[0079] The numerical value of t2 is brought into equation (12) to obtain the sliding angle α2 of the cycloid ending point;

[0080] S75, the polar angle θ1 of the cycloid starting point and the polar angle θ2 of the ending point are obtained;

[0081] The numerical values of t1 and t2 are brought into equation (10) to obtain the polar angle θ1 of the cycloid starting point and the polar angle θ2 of the ending point.

[0082] Further, the cycloid line segment P1P2 formed by the gear grinding starting point P1 and the gear grinding ending point P2 is the gear profile of the hot mill grinding piece, and the cycloid line segment P1P2 is arranged in a circle to obtain a complete hot mill grinding piece.

[0083] Compared with the prior art, the technical scheme of the present application has the beneficial effects that:

[0084] The application provides a cycloid-based hot mill grinding piece and a design method thereof. BRIEF DESCRIPTION OF DRAWINGS

[0085] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description only some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0086] Figure 1 Figure 1 is a cycloid diagram of the cycloid-based hot mill grinding piece of the present application; wherein, point O is the center of the hot mill grinding piece, which is also the center of the moving circle; R1 is the inner circle radius of the hot mill grinding piece; R2 is the outer circle radius of the hot mill grinding piece; P is an arbitrary point on the grinding tooth; ω0 is the rotation direction of the grinding piece; ω1 is the rotation direction of the moving circle; P1 is the starting point of the grinding tooth; P2 is the end point of the grinding tooth; α1 is the sliding angle of the starting point of the grinding tooth; α2 is the sliding angle of the end point of the grinding tooth; t1 is the rolling angle of the starting point of the cycloid; t2 is the rolling angle of the end point of the cycloid; θ1 is the polar angle of the starting point of the grinding tooth; θ2 is the polar angle of the end point of the grinding tooth; the cycloid segment P1P2 is the tooth edge of the grinding tooth;

[0087] Figure 2 Figure 2 is a tooth profile structure diagram of the cycloid-based hot mill grinding piece of the present application, the tooth edge profile of which is a cycloid, and the cycloid-based hot mill grinding piece comprises 6 pieces, and only 2 pieces are shown in the figure;

[0088] Figure 3 Figure 3 is a flow chart of the design method of the cycloid-based hot mill grinding piece of the present application. DETAILED DESCRIPTION

[0089] In order to better understand the purpose, structure and function of the present application, the technical solutions of the present application will be further described in detail below in combination with the drawings and specific preferred embodiments.

[0090] In the description of the present application, it should be understood that the terms "left side", "right side", "upper part", "lower part" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and "first", "second" and the like do not represent the importance of the parts and therefore cannot be understood as a limitation on the present application. The specific dimensions used in the examples are only for the purpose of illustrating the technical solutions and do not limit the protection scope of the present application. It is understandable that some well-known structures in the drawings and their descriptions may be omitted for those skilled in the art.

[0091] Unless otherwise explicitly specified and limited, the terms "mounting", "setting", "connecting", "fixing" and the like should be broadly understood, for example, it can be fixedly connected, or it can be detachably connected, or it can be integrated; it can be mechanically connected, or it can be electrically connected; it can be directly connected, or it can be indirectly connected through an intermediate medium; it can be the internal communication of two elements or the interaction relationship between two elements. For those skilled in the art, the specific meaning of the above terms in this application can be understood according to the specific circumstances.

[0092] Embodiment 1:

[0093] As Figures 1-2 shown, the present application provides a technical solution: a cycloid-based hot mill grinding piece, the tooth edge profile of the hot mill grinding piece is a cycloid,

[0094] The cycloid equation of the hot mill grinding piece is:

[0095]

[0096] Wherein, p represents the polar radius; a is the radius of the generating circle of the cycloid; t is the angle of the generating circle rolling along the positive direction of the X axis;

[0097] The horizontal coordinate and the vertical coordinate of the point on the cycloid composed of the tooth edge profile of the hot mill grinding piece are:

[0098] x=a·(t-sin t)

[0099] y=a·(1-cos t)

[0100] In the formula, x and y are respectively the horizontal coordinate and the vertical coordinate of the point on the cycloid, a is the radius of the generating circle of the cycloid, and t is the angle of the generating circle rolling along the positive direction of the X axis;

[0101] Wherein, the radius of the generating circle ranges from 342mm to 1230mm.

[0102] Further, the angle t that the moving circle rolls along the positive direction of the X axis satisfies t∈(t1, t2), t1 is the rolling angle of the cycloid starting point, and t2 is the rolling angle of the cycloid ending point; wherein the rolling angle t1 of the cycloid starting point ranges from 57.8° to 85.5°.

[0103] The embodiment provides a cycloid-based hot mill grinding piece, which is matched with gradually increasing slide cutting angles and gradually increasing cutting rates from the inner circle to the outer circle, and the gradually increasing slide cutting angles are matched with gradually decreasing cutting forces; the fiber separation quality can be improved, the energy consumption can be reduced, and the tool life can be prolonged.

[0104] Embodiment 2

[0105] As shown in Figure 3 The application also provides a design method of the cycloid-based hot mill grinding piece, and the design method comprises the following steps:

[0106] S1, determining the inner circle radius R1 and the outer circle radius R2 of the hot mill grinding piece;

[0107] The inner circle radius R1 ranges from 360 mm to 600 mm, and the outer circle radius R2 is expressed as:

[0108] R2=C1*R1 (1)

[0109] wherein C1 is a constant, and the range of C1 is 1.8-2.5;

[0110] S2, determining that the origin of the cycloid is the center O of the hot mill grinding piece;

[0111] S3, defining the X axis as a horizontal axis passing through the origin, and the positive direction of the X axis is to the right, and the X axis is the axis along which the moving circle rolls;

[0112] S4, defining the moving circle generating the cycloid as a circle rolling along the X axis, and the radius of the moving circle is a;

[0113] S5, defining the rolling angle of the moving circle as the angle t that the moving circle rolls along the positive direction of the X axis;

[0114] S6, defining an arbitrary point P on the cycloid, a grinding tooth starting point P1, a grinding tooth ending point P2, a rotation radius p1 of the grinding tooth starting point, a slide cutting angle a of the arbitrary point P on the cycloid, and a polar angle of the arbitrary point P on the cycloid;

[0115] The arbitrary point P on the cycloid is the intersection of the cycloid and the straight line in the radius direction of the hot mill grinding piece;

[0116] The grinding tooth starting point P1 is the intersection of the cycloid and the inner diameter of the hot mill grinding piece;

[0117] The tooth grinding end point P2 is the intersection point of the cycloid and the outer diameter of the hot mill grinding plate;

[0118] The expression of the rotary radius p1 where the tooth grinding start point is located is:

[0119] p1=R1 (2)

[0120] The sliding angle a of any point on the cycloid is the included angle between the cutting speed and the cutting force at the point, the sliding angle a of any point on the cycloid is embodied in the drawing as the included angle between the polar axis at the point and the tangent at the point, the sliding angle of the cycloid start point is represented by a1, the sliding angle of the cycloid end point is represented by a2, and the sliding angle a1 of the cycloid start point ranges from 9.6° to 14.5°;

[0121] The polar angle θ of any point on the cycloid is the included angle between the polar axis at the point and the x-axis, the polar angle of the cycloid start point is represented by θ1, and the polar angle of the cycloid end point is represented by θ2;

[0122] S7, obtaining the cycloid equation of the hot mill grinding plate;

[0123] The cycloid equation of the hot mill grinding plate is

[0124] In the formula, t∈(t1, t2);

[0125] Wherein, p represents the polar radius; a is the radius of the generating circle of the cycloid; t is the angle of the rolling of the generating circle along the positive direction of the X-axis; t1 is the rolling angle of the cycloid start point, and t2 is the rolling angle of the cycloid end point.

[0126] Further, step S7 specifically comprises:

[0127] S71, setting the parametric equation of the cycloid;

[0128] The parametric equation of the cycloid is:

[0129] x=a·(t-sin t) (3)

[0130] y=a·(1-cos t) (4)

[0131]

[0132] S72, calculating the rolling angle t1 of the cycloid start point;

[0133] Derivatives of formula (3) and formula (4) are obtained by taking the polar angle t as the variable, and formula (6) and formula (7) are obtained:

[0134]

[0135]

[0136] The derivative of y with respect to x is equal to the tangent slope of the polar angle θ on the cycloid, as shown in equation (8):

[0137]

[0138] According to equation (8), when t∈(0, π), k>0, and equation (8) can be obtained as:

[0139]

[0140] It can also be known from equation (9) that when t is as large as 180°, the sliding angle is 32.5°, which is within the allowable range;

[0141] Therefore, the rolling angle t2 of the cycloid end point does not need to be analytically obtained. The cycloid end point is formed by the intersection of the cycloid and the outer diameter of the grinding piece, and the rolling angle t2 can be obtained by a geometric method.

[0142] Also:

[0143]

[0144] From equation (10):

[0145]

[0146] By combining equation (9) and equation (11), we get:

[0147]

[0148] According to equation (12) and the range of the sliding angle α1 of the cycloid starting point being 9.6° to 14.5°, the rolling angle t1 of the cycloid starting point is calculated to be in the range of 57.8° to 85.5°;

[0149] S73, the value of a is obtained;

[0150] Let:

[0151] a=C2·R1 (13)

[0152] By combining equations (1), (2), (5), and (13), we get:

[0153]

[0154] Simplify to get:

[0155]

[0156] According to the range of the rolling angle t1 of the cycloid starting point being 57.8° to 85.5°, C 2MIN and C 2MAX are obtained:

[0157] C 2MIN = 0.95

[0158] C 2MAX = 2.05

[0159] Then the range of C2 is 0.95 to 2.05, which is brought into equation (13) to obtain the range of a value 342-1230mm;

[0160] The cycloid equation of the hot mill grinding piece is obtained as follows:

[0161]

[0162] In the formula, t is in (t1, t2);

[0163] Wherein, p represents the polar radius; a is the radius of the generating cycloid moving circle; t is the angle of the moving circle rolling along the positive direction of the X axis; t1 is the rolling angle of the starting point of the cycloid, and t2 is the rolling angle of the ending point of the cycloid.

[0164] Further, the step S7 further comprises:

[0165] S74, the sliding angle a2 of the ending point of the cycloid is obtained;

[0166] The numerical value of t2 is brought into equation (12) to obtain the sliding angle a2 of the ending point of the cycloid;

[0167] S75, the polar angle θ1 of the starting point and the polar angle θ2 of the ending point of the cycloid are obtained;

[0168] The numerical values of t1 and t2 are brought into equation (10) to obtain the polar angle θ1 of the starting point and the polar angle θ2 of the ending point of the cycloid.

[0169] Further, the cycloid segment P1P2 formed by the gear grinding starting point P1 and the gear grinding ending point P2 is the gear profile of the hot mill grinding piece, and the cycloid segment P1P2 is arranged in a circle to obtain a complete hot mill grinding piece.

[0170] In the prior art, cutting impact can increase energy consumption and reduce tool life, and a sliding cutting mode is often used in the tool to reduce cutting impact. Figure 1 And in equation (12), it can be known that the sliding angle of the present application increases with the increase of the rolling angle and the polar angle, which matches the gradually increasing cutting speed and the gradually decreasing cutting force. Therefore, the beneficial effects are reflected in improving the fiber separation quality, reducing energy consumption and prolonging the tool life.

[0171] Example 3:

[0172] On the basis of example 2, the present example provides three specific examples of design methods of the hot mill grinding piece based on the cycloid, including specific example a, specific example b and specific examplec Embodiment a illustrates the specific design steps, Embodiment b and Embodiment c The specific design steps of Embodiment b are similar to those of Embodiment a, and thus Embodiment b and Embodiment c The results are given in the form of a table, please refer to Table 1 for details.

[0173] Embodiment a is specifically as follows:

[0174] Step 1:

[0175] Determine the inner radius and outer radius of the hot mill grinding plate;

[0176] The inner radius is R1 and the outer radius is R2;

[0177] The R1 is 400 mm;

[0178] The outer diameter is:

[0179] R2 = C1 R1 (1)

[0180] The C1 is 2.25, i.e. R2 is 900 mm;

[0181] Step 2: Determine the coordinate origin:

[0182] The coordinate of the cycloid is the center of the grinding plate O;

[0183] Step 3: Determine the X-axis, i.e. the axis along which the moving circle rolls;

[0184] Define the horizontal axis to the right of the origin as the X-axis;

[0185] Step 4: Determine the moving circle that generates the cycloid;

[0186] Define the circle that rolls along the X-axis as the moving circle, with its center at O and radius a;

[0187] Step 5: Definition of the rolling angle of the moving circle:

[0188] The angle rolled by the moving circle along the X-axis is denoted by t;

[0189] Step 6: Definition of an arbitrary point, the starting point, the radius of curvature at the starting point, the angle of sliding, and the polar angle of the cycloid;

[0190] (1) Arbitrary point of the cycloid: the intersection of the cycloid and the straight line on which the radius of the hot mill grinding plate lies, denoted by point P;

[0191] (2) Starting point: the intersection of the cycloid and the inner diameter of the hot mill grinding plate, denoted by P1;

[0192] (3) End point: the intersection of the cycloid and the outer diameter of the hot mill grinding plate, denoted by P2;

[0193] (4) The rotation radius where the starting point is located is defined as p1, and p1 = R1.

[0194] p1 = R1 (2);

[0195] (5) The sliding angle of any point of the cycloid: the angle between the cutting speed and the cutting force at the point, which is embodied in the figure as the angle between the polar axis at the point and the tangent at the point, denoted by a, the sliding angle of the starting point of the cycloid is denoted by a1, and the range is 9.6°-14.5°, the sliding angle of the terminal point of the cycloid is denoted by a2;

[0196] (6) The polar angle of any point of the cycloid: the angle between the polar axis at the point and the x-axis, denoted by θ, the polar angle of the starting point of the cycloid is denoted by θ1, and the polar angle of the terminal point of the cycloid is denoted by θ2;

[0197] Step 7: Obtain the cycloid equation;

[0198] (1) Let the cycloid parameter equation be:

[0199] x = a · (t - sin t) (3)

[0200] y = a · (1 - cos t) (4)

[0201]

[0202] (2) Obtain the rolling angle t1 of the starting point of the cycloid;

[0203] Take the derivative of formula (3) and formula (4) with respect to the polar angle t respectively, and obtain formula (6) and formula (7);

[0204]

[0205]

[0206] Take the derivative of y with respect to x, and the derivative of y with respect to x is equal to the tangent slope corresponding to the polar angle θ on the cycloid, as formula (8):

[0207]

[0208] From formula (8), when t ∈ (0, π), k > 0, and from formula (8), we have:

[0209]

[0210] Also:

[0211]

[0212] From formula (10), we have:

[0213]

[0214] From equation (9) and equation (11), we have:

[0215]

[0216] From equation (12) and the sliding angle α1 of the cycloid starting point being 11.4°, the solution of the rolling angle t1 of the cycloid starting point is 67.5°.

[0217] (3) Obtain a value

[0218] Let a = C2·R1 (13)

[0219] From equation (1), (2), (5), (13), we have:

[0220]

[0221] Simplify to obtain:

[0222]

[0223] From the value of the rolling angle t1 of the cycloid starting point being 67.5°, we have C2 = 1.5

[0224] Then, the value of a is 600 by substituting the value of C2 into equation (13).

[0225] From equation (9), when t is as large as 180°, the sliding angle is 32.5°, which is also within the allowable range. Therefore, the rolling angle t2 of the cycloid ending point does not need to be solved, and the cycloid ending point is obtained by the intersection of the cycloid and the outer diameter of the grinding piece. The rolling angle t2 can be obtained by geometric method, which is 103.9°.

[0226] Therefore, the cycloid equation for gear grinding is:

[0227]

[0228] (4) Obtain the sliding angle α2 of the cycloid grinding ending point:

[0229] Substitute the value of t2 into equation (12) to obtain α2 = 17.8°.

[0230] (5) Obtain the polar angle θ1 of the cycloid starting point and the polar angle θ2 of the ending point

[0231] Substitute the values of t1 and t2 into equation (10) to obtain θ1 = 67.7° and θ2 = 55.9°.

[0232] The cycloid segment P1P2 is the gear grinding profile of the grinding piece, and its circumferential array obtains a complete grinding piece. For details, please refer to Figure 2 .

[0233] The embodiment provides three specific embodiments of design methods of the cycloid-based hot mill grinding piece, including specific embodiment a, specific embodiment b and specific embodiment c, and specific parameters can be referred to Table 1.

[0234] Table 1, parameters of specific embodiment a, specific embodiment b and specific embodiment c and cycloid equation

[0235]

[0236] Obviously, the above embodiment of the present application is only an example for clearly illustrating the present application, and is not intended to limit the implementation manner of the present application. Based on the above description, other different forms of changes or variations can be made by those skilled in the art. Here, it is not necessary and also impossible to enumerate all the implementation manners. Any modification, equivalent replacement and improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the claims of the present application.

Claims

1. A method of designing a hot mill plate based on a cycloid, characterized in that, The design method comprises the following steps: S1, determining the inner radius R1 and the outer radius R2 of the hot mill grinding piece; The inner radius R1 ranges from 360 to 600 mm, and the outer radius R2 is expressed as: R2=C1·R1 (1) Wherein, C1 is a constant, and the range of C1 is 1.8-2.5; S2, determining the origin of the cycloid as the center O of the hot mill grinding piece; S3, defining the X axis as the horizontal axis passing through the origin, and the positive direction thereof is to the right; S4, defining the generating circle of the cycloid as a circle rolling along the X axis, and the radius thereof is a; S5, defining the rolling angle of the generating circle as the angle of the generating circle rolling along the positive direction of the X axis, and denoted by t; S6, defining an arbitrary point P on the cycloid, a gear grinding starting point P1, a gear grinding termination point P2, a rotation radius ρ1 of the gear grinding starting point, a sliding angle α of the arbitrary point on the cycloid, and a polar angle θ of the arbitrary point on the cycloid; The arbitrary point P on the cycloid is the intersection point of the cycloid and the straight line in the radius direction of the hot mill grinding piece; The gear grinding starting point P1 is the intersection point of the cycloid and the inner diameter of the hot mill grinding piece; The gear grinding termination point P2 is the intersection point of the cycloid and the outer diameter of the hot mill grinding piece; The rotation radius ρ1 of the gear grinding starting point is expressed as: ρ1=R1 (2) The sliding angle α of the arbitrary point on the cycloid is the included angle between the polar axis at the point and the tangent at the point, the sliding angle of the cycloid starting point is denoted by α1, and the sliding angle of the cycloid termination point is denoted by α2, and the sliding angle α1 of the cycloid starting point ranges from 9.6° to 14.5°; The polar angle θ of the arbitrary point on the cycloid is the included angle between the polar axis at the point and the x axis, the polar angle of the cycloid starting point is denoted by θ1, and the polar angle of the cycloid termination point is denoted by θ2; S7, obtaining the cycloid equation of the hot mill grinding piece; The tooth edge profile of the hot mill grinding blade is a cycloid, and the cycloid equation of the hot mill grinding blade is Wherein, the angle t of the generating circle rolling along the positive direction of the X axis satisfies t∈(t1, t2); Wherein, ρ represents the polar radius; a is the radius of the generating circle of the cycloid; t is the angle of the generating circle rolling along the positive direction of the X axis; t1 is the rolling angle of the cycloid starting point, and t2 is the rolling angle of the cycloid termination point; The rolling angle t1 of the cycloid starting point ranges from 57.8° to 85.5°; The horizontal coordinate and the vertical coordinate of the point on the cycloid composed of the tooth edge profile of the hot mill grinding piece are: x=a·(t-sint) y=a·(1-cost) Wherein, x and y are respectively the horizontal coordinate and the vertical coordinate of the point on the cycloid; The radius of the generating circle ranges from 342 mm to 1230 mm.

2. The method of designing a trochoidal based hot mill slice according to claim 1, wherein, Step S7 specifically comprises: S71, setting the parametric equation of the cycloid; The parametric equation of the cycloid is: x=a·(t-sint) (3) y=a·(1-cost) (4) S72, calculating the rolling angle t1 of the cycloid starting point; Deriving the derivatives of formula (3) and formula (4) with respect to the polar angle t respectively, formula (6) and formula (7) are obtained: Deriving the derivative of y with respect to x, the derivative of y with respect to x is equal to the tangent slope corresponding to the polar angle θ on the cycloid, as shown in formula (8): According to formula (8), when t∈(0, π), k>0, formula (9) can be obtained from formula (8): Also: From formula (10), we have: By combining formula (9) and formula (11), we have: According to formula (12) and the range of the sliding angle a1 of the cycloid starting point being 9.6° to 14.5°, the range of the rolling angle t1 of the cycloid starting point is calculated to be 57.8° to 85.5°; S73, obtaining the value of a; Let: a = C2·R1 (13) By combining formula (1), (2), (5), (13), the following is obtained: Simplifying the above formula, the following is obtained: According to the range of the rolling angle t1 of the cycloid starting point is 57.8° to 85.5°, C 2MIN and C 2MAX : C 2MIN ＝0.95 C 2MAX ＝2.05 The range of C2 is 0.95 to 2.05, and the range of the value of a obtained by bringing C2 into formula (13) is 342-1230mm; The cycloid equation of the hot mill grinding plate is obtained as follows: In the formula, t ∈ (t1, t2); Wherein, ρ represents the polar radius; a is the radius of the generating circle of the cycloid; t is the angle of the generating circle rolling along the positive direction of the X axis; t1 is the rolling angle of the cycloid starting point, and t2 is the rolling angle of the cycloid ending point.

3. The method of designing a trochoidal based hot mill slice according to claim 2, wherein, Step S7 further includes: S74, obtaining the sliding angle a2 of the cycloid ending point; The value of t2 is brought into formula (12) to obtain the sliding angle a2 of the cycloid ending point. S75, obtaining the polar angle θ1 of the cycloid starting point and the polar angle θ2 of the cycloid ending point; The values of t1 and t2 are brought into formula (10) to obtain the polar angle θ1 of the cycloid starting point and the polar angle θ2 of the cycloid ending point.

4. The method of designing a trochoidal based hot mill slice according to claim 1, wherein, The cycloid line segment P1P2 formed by the gear grinding starting point P1 and the gear grinding ending point P2 is the gear grinding profile of the hot mill grinding plate, and the cycloid line segment P1P2 is arranged in a circular array to obtain a complete hot mill grinding plate.

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