A method of gaging a PDC bit

Abstract

The application discloses a PDC bit tooth distribution method and relates to the technical field of drilling tools. According to the expected bit mechanical drilling speed and the bit rotating speed, the following are calculated in sequence: the footage of the bit per revolution, the total volume of rock cut by the bit per revolution, the average cutting volume of each cutting tooth per revolution, the average cutting area, the maximum cutting area of a single cutting tooth, the minimum rotating radius of each cutting tooth for realizing the equal cutting volume, the average cutting area of the cutting tooth larger than the minimum rotating radius of each cutting tooth for realizing the equal cutting volume, the average cutting volume of each cutting tooth, the relationship between the cutting section of each cutting tooth and the average cutting volume, the radial coordinate of the cutting tooth section center, the bit crown profile curve equation and the radius of the cutting tooth, the positioning radius and height of the cutting tooth, and the bit service life.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of drilling tools, in particular to a PDC bit tooth distribution method. BACKGROUND

[0002] PDC (polycrystalline diamond compact, sintered from diamond powder and hard alloy substrate under ultra-high pressure and high temperature) bit relies on high hardness, wear resistance and self-sharpening characteristics as a cutting element to shear and crush rock. At the same time, PDC bit has high mechanical drilling speed, long service life and low drilling cost in soft to medium-hard formations, so it is widely used in oil and gas well drilling. In oil and gas drilling engineering, the geological conditions of the formation are often very complex. The mud shale and argillaceous sandstone in the deep formation under the overlying strata pressure and high-density drilling fluid conditions not only increase the density and hardness, but also the brittle rock under normal pressure is transformed into plastic-brittle rock or plastic rock. In addition, the hydraulic energy of the deep well section is severely insufficient, and cannot effectively play the role of hydraulic auxiliary rock breaking, so the rock breaking efficiency of the bit is very low.

[0003] It should be noted that: assuming that there is a cross-sectional plane (referred to as the axial plane or axial surface passing through the point) of the bit axis and a certain point on the bit. When the bit rotates around its own axis under the condition that the drilling speed is zero, the profile line of the cutting element intersects with the cross-sectional plane or axial surface to form an intersection line, which is the axial surface profile line of the cutting element. All the axial surface profile lines of the cutting elements are collected together to form a bottom hole coverage diagram of the bit. In the bottom hole coverage diagram, an envelope curve can be drawn which is tangent to all the axial surface profile lines of the cutting elements, which is referred to as the bit cutting profile line. The bit cutting profile line reflects the basic shape characteristics of the bottom hole drilled by the bit. The bit body profile line is the position curve of the bit body in the bottom hole coverage diagram, which is an important characteristic curve of the diamond bit. It is worth noting that the bit blade body profile line and the blade cutting profile line should not include the gauge protection part of the bit. This is obtained from the definition of the blade cutting profile line and the body profile line. The main cutting teeth of the bit generally refer to cutting elements with longitudinal cutting ability, while the gauge protection teeth of the gauge protection part do not have longitudinal cutting ability. Therefore, the main cutting does not include the gauge protection teeth, so the cutting profile line and the body profile line of the blade should start from the center of the bit and end at the gauge protection teeth.

[0004] Therefore, a reasonable tooth arrangement calculation method is the key to ensure the excellent performance of the drill bit and the premise of improving the tooth arrangement efficiency of the PDC drill bit. In order to achieve the full coverage of the drill bit on the well bottom, ensure that the rock can be completely removed by one rotation of the drill bit, form a relatively smooth well bottom, and make the well bottom not have a protruding rock ridge, it is a basic requirement for the design of the PDC drill bit, especially the radial tooth arrangement design of the PDC drill bit. At present, the design method for the tooth arrangement of the PDC drill bit has the weaknesses of randomness and unclear performance target of the drill bit, which leads to the early failure of individual teeth in the use process of the drill bit, the rapid failure of the whole drill bit, and the short service life of the drill bit. SUMMARY

[0005] The present application provides a PDC drill bit tooth arrangement method, which can meet the requirement of full coverage of the drill bit on the well bottom, and the working burden of each cutting tooth is equivalent, so that the wear of each cutting tooth on the drill bit is balanced, the early failure of individual cutting tooth is avoided, and the service life of the drill bit is prolonged.

[0006] The present application is realized by the following technical scheme:

[0007] The present application provides a PDC drill bit tooth arrangement method, which comprises the following steps:

[0008] S10, calculating the footage per revolution of the drill bit according to the expected rate of penetration and the rotation speed of the drill bit;

[0009] S20, calculating the total volume of the rock cut off per revolution of the drill bit according to the footage per revolution of the drill bit;

[0010] S30, calculating the average cutting volume of each cutting tooth per revolution of the drill bit according to the total number of cutting teeth and the total volume of the rock cut off per revolution of the drill bit;

[0011] S40, calculating the average cutting area of the ith cutting tooth located at the set positioning radius according to the average cutting volume of each cutting tooth per revolution of the drill bit;

[0012] S50, calculating the maximum cutting area of a single cutting tooth without interference of other cutting teeth;

[0013] S60, calculating the minimum rotation radius of each cutting tooth for realizing the equal cutting volume according to the maximum cutting area of a single cutting tooth;

[0014] S70, calculating the average cutting area and the average cutting volume of each cutting tooth which are greater than the minimum rotation radius of each cutting tooth for realizing the equal cutting volume according to the maximum cutting area of a single cutting tooth and the cutting teeth which cannot realize the equal cutting volume within the minimum rotation radius;

[0015] S80, equivalent each cutting tooth cutting section to quadrilateral, to obtain the relationship between the radial coordinates of the left and right boundary of the jth quadrilateral cutting tooth section and the average cutting volume of each cutting tooth, which is greater than the minimum rotating radius of each cutting tooth to achieve equal cutting volume, and calculate the radial coordinates of the centroid of the jth quadrilateral cutting tooth section, which is greater than the minimum rotating radius of each cutting tooth to achieve equal cutting volume;

[0016] S90, combined with the bit crown profile curve equation and the radius of the cutting tooth, calculate the positioning radius of the jth cutting tooth, which is greater than the minimum rotating radius of each cutting tooth to achieve equal cutting volume, and arrange the cutting tooth with a radius less than the minimum rotating radius of each cutting tooth to achieve equal cutting volume inside the minimum rotating radius of each cutting tooth to achieve equal cutting volume.

[0017] S100, combined with the bit crown profile curve equation and the positioning radius of the cutting tooth, calculate the positioning height of the cutting tooth, and arrange the cutting tooth on the bit according to the positioning radius and the positioning height.

[0018] The PDC bit tooth arrangement method provided by the application first calculates the footage per revolution of the bit, the total volume of rock cut by the bit per revolution, the average cutting volume of each cutting tooth per revolution of the bit, and the average cutting area of the ith cutting tooth located at the set positioning radius according to the expected bit rate of penetration and the rotation speed of the bit, then calculates the maximum cutting area of a single cutting tooth without interference from other cutting teeth, calculates the minimum rotating radius of each cutting tooth to achieve equal cutting volume based on the maximum cutting area, calculates the average cutting area of the cutting tooth greater than the minimum rotating radius of each cutting tooth to achieve equal cutting volume and the average cutting volume of each cutting tooth, then equivalent each cutting tooth cutting section to quadrilateral to obtain the relationship between the radial coordinates of the left and right boundary of the cutting tooth section and the average cutting volume of each cutting tooth, and finally calculate the radial coordinates of the centroid of the cutting tooth section combined with the bit crown profile curve equation and the radius of the cutting tooth.

[0019] Therefore, the positioning radius and the positioning height of the PDC bit cutting tooth can be obtained based on the parameters, which can ensure that each cutting tooth cuts the same volume of rock during operation, avoid the phenomenon that some cutting teeth have heavy workload and some cutting teeth have light workload, avoid the situation that some teeth fail early and cause rapid failure of adjacent cutting teeth, and ultimately achieve the purpose of prolonging the service life of the bit. At the same time, the randomness of the traditional PDC bit tooth arrangement design method and the unclear performance target of the bit are overcome.

[0020] Specifically, in S10, the footage per revolution of the bit is calculated by the following model:

[0021] In the formula:

[0022] ROP is the expected rate of penetration of the drill bit,

[0023] RPM is the rotational speed of the drill bit,

[0024] δ is the footage per revolution of the drill bit.

[0025] Specifically, in S20, the calculation model of the total volume of rock cut off per revolution of the drill bit is V = π * R 2 * δ;

[0026] In the formula:

[0027] V is the total volume of rock cut off per revolution of the drill bit,

[0028] R is the radius of the drill bit.

[0029] Specifically, in S30, the calculation model of the average cutting volume of each cutting tooth per revolution of the drill bit is v = V / N = π * R 2 * δ / N;

[0030] In the formula:

[0031] v is the average cutting volume of each cutting tooth per revolution of the drill bit,

[0032] N is the number of cutting teeth.

[0033] Specifically, in S40, the calculation model of the average cutting area of the i-th cutting tooth located at a set positioning radius is Si = R 2 δ / 2Nx i ;

[0034] In the formula:

[0035] S i is the average cutting area of the i-th cutting tooth at the set radius;

[0036] x i is the positioning radius of the i-th cutting tooth.

[0037] Specifically, in S50, the calculation model of the maximum cutting area of a single cutting tooth without interference from other cutting teeth is

[0038] In the formula:

[0039] S max is the maximum cutting area of a single cutting tooth without interference from other cutting teeth;

[0040] r is the radius of the cutting tooth.

[0041] Specifically, in S60, the calculation model of the minimum rotational radius of each cutting tooth to achieve equal cutting volume is wherein x min is the minimum rotating radius for each cutting tooth to achieve equal cutting volume.

[0042] Specifically, in S70, the calculation model of the average cutting area of the cutting teeth and the average cutting volume of each cutting tooth is

[0043] wherein:

[0044] S i is the average cutting area of the cutting teeth,

[0045] n is the number of cutting teeth that cannot achieve equal cutting volume within the given minimum rotating radius x min ,

[0046] is the average cutting volume of each cutting tooth.

[0047] Specifically, in S80, the calculation model of the radial coordinate of the centroid of the jth quadrilateral cutting tooth cross section that is greater than the minimum rotating radius for each cutting tooth to achieve equal cutting volume is

[0048] wherein:

[0049] R‘ j is the radial coordinate of the centroid of the jth tooth quadrilateral cutting cross section that is greater than the minimum rotating radius;

[0050] r j is the right side boundary radial coordinate of the jth tooth quadrilateral cross section shape.

[0051] Specifically, the positioning radius calculation model of the jth cutting tooth that is greater than the minimum rotating radius x min is R j = f(R‘ j , r), wherein R j is the positioning radius of the jth cutting tooth that is greater than the minimum rotating radius x min ;

[0052] The calculation model of the positioning height of the cutting tooth is (H j , γ j ) = f(R j ), wherein H j is the positioning height of the cutting tooth, and γ j is the normal angle.

[0053] Compared with the prior art, the present application has the following advantages and beneficial effects:

[0054] The PDC bit distribution method provided by the application comprises the following steps: according to the expected mechanical drilling speed of the bit and the rotation speed of the bit, the footage per revolution of the bit, the total volume of rock cut by the bit per revolution, the average cutting volume of each cutting tooth per revolution of the bit, the average cutting area of the ith cutting tooth located at the set positioning radius are calculated in sequence, then the maximum cutting area of a single cutting tooth without interference from other cutting teeth is calculated, the minimum rotation radius of each cutting tooth for realizing equal cutting volume is calculated based on the maximum cutting area, the average cutting area of the cutting tooth greater than the minimum rotation radius of each cutting tooth for realizing equal cutting volume and the average cutting volume of each cutting tooth are calculated, then the cutting section of each cutting tooth is equivalent to a quadrilateral to obtain the relationship between the radial coordinates of the left and right boundaries of the cutting tooth section and the average cutting volume of each cutting tooth, so that the radial coordinates of the cutting tooth section centroid are calculated; finally, the positioning radius and the positioning height of the cutting tooth are calculated in combination with the bit crown profile curve equation and the radius of the cutting tooth, so that the bit arranged in this way can ensure that the rock volume cut by each cutting tooth during the working process is the same, and the phenomenon that some cutting teeth have heavy working burden and some cutting teeth have light working burden does not exist, the situation that some teeth fail early and cause rapid failure of adjacent cutting teeth is avoided, and the service life of the bit is ultimately prolonged. BRIEF DESCRIPTION OF DRAWINGS

[0055] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiments. It should be understood that the following drawings only show some embodiments of the present application, and therefore should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can also be obtained without creative labor.

[0056] In the drawings:

[0057] Figure 1 It is a flowchart of the PDC bit distribution method of the embodiments of the present application.

[0058] Figure 2 It is a schematic diagram of the maximum cutting area of the cutting tooth without interference from other teeth under the condition of footage.

[0059] Figure 3 It is a schematic diagram of the quadrilateral representation method of the cutting section area.

[0060] Figure 4 It is a schematic diagram of the position relationship of the cutting section of each cutting tooth.

[0061] Figure 5 It is a schematic diagram of determining the positioning radius of the cutting tooth from the cutting section centroid.

[0062] Figure 6 It is a schematic diagram of the cutting tooth arranged in the clockwise direction in the circumferential direction of the bit. Detailed Implementation

[0063] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of this application, but not all embodiments.

[0064] Example

[0065] Combination Figure 1 This embodiment provides a PDC drill bit tooth placement method, including the following steps:

[0066] This invention provides a method for tooth placement in a PDC drill bit, comprising the following steps:

[0067] S10. Based on the expected mechanical drilling speed and the rotational speed of the drill bit, calculate the footage per revolution of the drill bit.

[0068] Specifically, in S10, the calculation model for the footage per revolution of the drill bit is as follows:

[0069] In the formula:

[0070] ROP is the expected mechanical drilling speed of the drill bit, measured in m / h.

[0071] RPM is the rotational speed of the drill bit, measured in revolutions per minute (rpm).

[0072] δ represents the depth of the drill bit per revolution, measured in mm / revolution.

[0073] S20. Calculate the total volume of rock cut off per revolution of the drill bit based on the advance per revolution.

[0074] Specifically, in S20, the calculation model for the total volume of rock cut off per revolution of the drill bit is V = π * R. 2 *δ;

[0075] In the formula:

[0076] V represents the total volume of rock cut away per revolution of the drill bit, in mm. 3 ;

[0077] R is the radius of the drill bit, in mm (known and directly measurable).

[0078] S30. Based on the total number of cutting teeth and the total volume of rock cut off per revolution of the drill bit, calculate the average cutting volume of each cutting tooth per revolution of the drill bit.

[0079] Specifically, in S30, the calculation model of the average cutting volume of each cutting tooth per revolution of the drill bit is c = V / N = π * R 2 * δ / N;

[0080] In the formula:

[0081] v is the average cutting volume of each cutting tooth per revolution of the drill bit, in mm 3 ;

[0082] N is the number of cutting teeth, in pieces, i.e., the total number of teeth on the drill bit.

[0083] S40, according to the average cutting volume of each cutting tooth per revolution of the drill bit, the average cutting area of the i-th cutting tooth located at the set positioning radius is calculated.

[0084] Specifically, in S40, the calculation model of the average cutting area of the i-th cutting tooth located at the set positioning radius is Si = R 2 δ / 2Nx i ;

[0085] In the formula:

[0086] S i is the average cutting area of the i-th cutting tooth at the set radius, in mm 2 ;

[0087] x i is the positioning radius of the i-th cutting tooth, in mm.

[0088] According to the calculation model of the average cutting area of the i-th cutting tooth located at the set positioning radius, it is known that the closer the cutting tooth to the center of the drill bit, the greater the cutting area required to achieve equal cutting, but this maximum cutting area has a certain limit. Therefore, there is a minimum rotation radius, only the cutting tooth greater than the minimum rotation radius can achieve equal cutting.

[0089] S50, the maximum cutting area of a single cutting tooth without interference from other cutting teeth is calculated.

[0090] In combination Figure 2 , specifically, in S50, the calculation model of the maximum cutting area of a single cutting tooth without interference from other cutting teeth is

[0091] In the formula:

[0092] S max is the maximum cutting area of a single cutting tooth without interference from other cutting teeth;

[0093] r is the radius of the cutting tooth.

[0094] S60, calculating the minimum rotation radius of each cutting tooth to achieve the same cutting volume according to the maximum cutting area of a single cutting tooth.

[0095] Specifically, in S60, the calculation model of the minimum rotation radius of each cutting tooth to achieve the same cutting volume is wherein x min is the minimum rotation radius of each cutting tooth to achieve the same cutting volume.

[0096] S70, calculating the average cutting area of each cutting tooth and the average cutting volume of each cutting tooth greater than the minimum rotation radius of each cutting tooth to achieve the same cutting volume according to the maximum cutting area of a single cutting tooth and the number of cutting teeth that cannot achieve the same cutting volume within the minimum rotation radius.

[0097] Specifically, in S70, the number of cutting teeth that cannot achieve the same cutting volume within the minimum rotation radius x min is given, and the calculation model of the average cutting area of each cutting tooth and the average cutting volume of each cutting tooth can be obtained according to the calculation model of the average cutting area of the ith cutting tooth located at the set positioning radius, which is

[0098] wherein:

[0099] S i is the average cutting area of each cutting tooth,

[0100] n is the number of cutting teeth that cannot achieve the same cutting volume within the minimum rotation radius x min ,

[0101] is the average cutting volume of each cutting tooth.

[0102] S80, equivalently taking the cutting section of each cutting tooth as a quadrilateral to obtain the relationship between the radial coordinate of the left and right boundary of the jth quadrilateral cutting tooth section greater than the minimum rotation radius of each cutting tooth to achieve the same cutting volume and the average cutting volume of each cutting tooth, and calculating the radial coordinate of the centroid of the jth quadrilateral cutting tooth section greater than the minimum rotation radius of each cutting tooth to achieve the same cutting volume.

[0103] in combination with Figure 3 It should be noted that in this embodiment, the cutting section of each tooth is equivalently taken as a quadrilateral shape, and δ is set as the length of one side of the quadrilateral, and the relationship between the radial coordinate of the left and right boundary of the jth tooth quadrilateral cutting section greater than the minimum rotation radius and the average cutting volume can be obtained.

[0104] in combination with Figure 4 The position relationship model of the cutting section of each cutting tooth is wherein r'j r'0 is the right boundary radial coordinate of the jth tooth quadrilateral cross-sectional shape, and r'0 is equal to the minimum rotary radius x min .

[0105] wherein the calculation model of the radial coordinate of the jth quadrilateral cutting tooth cross-sectional centroid greater than the minimum rotary radius of each cutting tooth to achieve equal cutting volume is

[0106] In the formula:

[0107] R' j is the radial coordinate of the jth tooth quadrilateral cutting cross-sectional centroid greater than the minimum rotary radius;

[0108] r' j is the right boundary radial coordinate of the jth tooth quadrilateral cross-sectional shape.

[0109] S90, in combination with the bit crown profile curve equation, the radius of the cutting tooth, the positioning radius of the jth cutting tooth greater than the minimum rotary radius of each cutting tooth to achieve equal cutting volume is calculated, and the cutting tooth with a radius less than the minimum rotary radius of each cutting tooth to achieve equal cutting volume is arranged equidistantly inside the minimum rotary radius of each cutting tooth to achieve equal cutting volume.

[0110] In combination with Figure 5 Specifically, in combination with the given crown profile curve equation f and the cutting tooth radius r, the positioning radius R min of the jth cutting tooth greater than the minimum rotary radius x j can be obtained. The calculation model of the positioning radius of the jth cutting tooth greater than the minimum rotary radius x min is R j =f(R' j , r), wherein R j is the positioning radius of the jth cutting tooth greater than the minimum rotary radius x min .

[0111] It can be understood that the cutting tooth less than the minimum rotary radius x min , i.e. the cutting tooth with tooth number 1~j-1 is arranged equidistantly in this interval, wherein the positioning radius of the first cutting tooth is equal to the radius of the cutting tooth, i.e. r1=r. That is, the cutting tooth with a radius less than the minimum rotary radius of each cutting tooth to achieve equal cutting volume is arranged equidistantly inside the minimum rotary radius of each cutting tooth to achieve equal cutting volume.

[0112] S100, in combination with the bit crown profile curve equation and the positioning radius of the cutting tooth, the positioning height of the cutting tooth is calculated, and the cutting tooth is arranged on the bit according to the positioning radius and the positioning height.

[0113] Specifically, the positioning height of any cutting tooth can be obtained in combination with the given crown profile curve equation f and the positioning radius of the cutting tooth. The calculation model of the positioning height of the cutting tooth is (H j , γ j ) = f(R j ), wherein H j is the positioning height of the cutting tooth, and γ j is the normal angle.

[0114] Further, the PDC teeth are arranged on the drill bit in a sequential or reverse sequential manner in the circumferential direction. Figure 6 Further, the PDC teeth are arranged on the drill bit in a sequential or reverse sequential manner in the circumferential direction. Figure 6 The PDC teeth are arranged on the drill bit in a clockwise direction in the circumferential direction in a sequential manner. The sequential arrangement herein refers to that the arrangement sequence of the cutting teeth in the circumferential direction is consistent with the rotation direction of the drill bit from the center of the drill bit to the outside of the drill bit, and the reverse arrangement refers to the opposite.

[0115] In summary, the PDC drill bit tooth arrangement method provided by the present application first calculates the footage per revolution of the drill bit, the total volume of rock cut off per revolution of the drill bit, the average cutting volume of each cutting tooth per revolution of the drill bit, and the average cutting area of the i-th cutting tooth located at the set positioning radius according to the expected ROP and the rotation speed of the drill bit, then calculates the maximum cutting area of a single cutting tooth without interference from other cutting teeth, and then calculates the minimum rotation radius of each cutting tooth for achieving equal cutting volume based on the maximum cutting area, calculates the average cutting area of the cutting tooth greater than the minimum rotation radius of each cutting tooth for achieving equal cutting volume and the average cutting volume of each cutting tooth, and then equivalently takes the cutting section of each cutting tooth as a quadrilateral to obtain the relationship between the radial coordinates of the left and right boundaries of the cutting tooth section and the average cutting volume of each cutting tooth, thereby calculating the radial coordinates of the centroid of the cutting tooth section. Finally, the positioning radius and the positioning height of the cutting tooth are calculated in combination with the crown profile curve equation of the drill bit and the radius of the cutting tooth.

[0116] Therefore, the positioning radius and the positioning height of the PDC drill bit cutting tooth obtained by the present embodiment can ensure that each cutting tooth cuts the same volume of rock during operation based on the arrangement of the parameters, and there is no phenomenon of heavy workload of individual cutting teeth and light workload of individual cutting teeth, thereby avoiding the situation that the rapid failure of adjacent cutting teeth occurs due to the early failure of individual teeth, and ultimately achieving the purpose of prolonging the service life of the drill bit. At the same time, the randomness of the conventional PDC drill bit tooth arrangement design method and the unclear performance target of the drill bit are overcome.

[0117] The above detailed description of the specific embodiments of the present application has been given to understand the purpose, technical solutions and beneficial effects of the present application. It should be understood that the above description is only a specific embodiment of the present application and is not used to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for tooth placement in a PDC drill bit, characterized in that, Includes the following steps: S10. Based on the expected mechanical drilling speed and the rotational speed of the drill bit, calculate the footage per revolution of the drill bit. S20. Based on the feed per revolution of the drill bit, calculate the total volume of rock cut off per revolution of the drill bit. S30. Based on the total number of cutting teeth and the total volume of rock cut off per revolution of the drill bit, calculate the average cutting volume of each cutting tooth per revolution of the drill bit. S40. Based on the average cutting volume of each cutting tooth per revolution of the drill bit, calculate the number of teeth located at the set positioning radius. The average cutting area of ​​each cutting tooth; S50. Calculate the maximum cutting area of ​​a single cutting tooth when there is no interference from other cutting teeth; S60. Based on the maximum cutting area of ​​a single cutting tooth, calculate the minimum rotation radius for each cutting tooth to achieve the same cutting volume. S70. Given the cutting teeth that cannot achieve equal cutting volume within the minimum rotation radius, and in combination with the maximum cutting area of ​​a single cutting tooth, calculate the average cutting area of ​​the cutting teeth that are greater than the minimum rotation radius for achieving equal cutting volume and the average cutting volume of each cutting tooth. S80. The cutting section of each cutting tooth is equivalent to a quadrilateral to obtain the minimum rotation radius that is arbitrarily larger than that of each cutting tooth to achieve equal cutting volume. The relationship between the radial coordinates of the left and right boundaries of the cross-section of a quadrilateral cutting tooth and the average cutting volume of each cutting tooth, and the model of the positional relationship of the cutting cross-sections of each cutting tooth are as follows: ,in For the first The radial coordinates of the right boundary of the granular quadrilateral cross-section shape equal to minimum rotation radius , The footage per revolution of the drill bit Let the average cutting volume of each cutting tooth be denoted, and calculate the minimum rotation radius that is any value greater than the minimum cutting volume of each cutting tooth to achieve equal cutting volume. The radial coordinates of the centroid of the quadrilateral cutting tooth section; the first radii greater than the minimum rotational radius for achieving uniform cutting volume for each cutting tooth. The calculation model for the radial coordinates of the centroid of the quadrilateral cutting tooth section is as follows: In the formula: For the first one that is greater than the minimum rotation radius Radial coordinates of the centroid of the quadrilateral cutting section of the tooth. For the first The radial coordinates of the right boundary of the granular quadrilateral cross-section shape ; S90. Combining the drill bit crown profile curve equation and the radius of the cutting teeth, calculate the minimum rotation radius greater than that of each cutting tooth to achieve equal cutting volume. The positioning radius of each cutting tooth is determined, and cutting teeth with radii smaller than the minimum rotation radius required for achieving equal cutting volume are equidistantly arranged inside the minimum rotation radius required for achieving equal cutting volume; those with radii larger than the minimum rotation radius are positioned inside the minimum rotation radius required for achieving equal cutting volume. The The calculation model for the positioning radius of each cutting tooth is as follows: In the formula For a radius greater than the minimum rotation radius The The positioning radius of each cutting tooth The radius of the cutting teeth; S100. Combining the drill bit crown profile curve equation and the positioning radius of the cutting teeth, calculate the positioning height of the cutting teeth, and arrange the teeth on the drill bit according to the positioning radius and the positioning height; the calculation model for the positioning height of the cutting teeth is as follows: In the formula Positioning height of the cutting teeth, It is the normal angle.

2. The PDC drill bit tooth arrangement method according to claim 1, characterized in that, In S10, the calculation model for the footage per revolution of the drill bit is as follows: ; In the formula: The expected mechanical drilling speed of the drill bit. The rotational speed of the drill bit. This refers to the depth of the drill bit per revolution.

3. The PDC drill bit tooth arrangement method according to claim 2, characterized in that, In S20, the calculation model for the total volume of rock cut off per revolution of the drill bit is as follows: ; In the formula: V represents the total volume of rock cut off per revolution of the drill bit. R is the radius of the drill bit.

4. The PDC drill bit tooth arrangement method according to claim 3, characterized in that, In S30, the calculation model for the average cutting volume of each cutting tooth per revolution of the drill bit is as follows: ; In the formula: v represents the average cutting volume of each cutting tooth per revolution of the drill bit. N is the number of cutting teeth.

5. The PDC drill bit tooth arrangement method according to claim 4, characterized in that, In S40, the position located at the set positioning radius is... The calculation model for the average cutting area of ​​each cutting tooth is as follows: ; In the formula: For the set radius of the first The average cutting area of ​​each cutting tooth; For the first The positioning radius of each cutting tooth.

6. The PDC drill bit tooth arrangement method according to claim 5, characterized in that, In S50, the calculation model for the maximum cutting area of ​​a single cutting tooth when there is no interference from other cutting teeth is as follows: ; In the formula: This represents the maximum cutting area of ​​a single cutting tooth when there is no interference from other cutting teeth. The radius of the cutting teeth.

7. The PDC drill bit tooth arrangement method according to claim 6, characterized in that, In S60, the calculation model for the minimum rotation radius of each cutting tooth to achieve a constant cutting volume is as follows: In the formula, The minimum rotation radius to achieve equal cutting volume for each cutting tooth.

8. The PDC drill bit tooth arrangement method according to claim 7, characterized in that, In S70, the calculation models for the average cutting area of ​​the cutting teeth and the average cutting volume of each cutting tooth are as follows: ; In the formula: This represents the average cutting area of ​​the cutting teeth. Given a minimum rotation radius The number of cutting teeth that cannot achieve a constant cutting volume. This represents the average cutting volume of each cutting tooth.

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