PDC (Polycrystalline Diamond Compact) drill bit tooth arrangement method

Abstract

The invention discloses a PDC drill bit tooth arrangement method, and relates to the technical field of drilling tools. According to the expected drill bit mechanical drilling speed and the drill bit rotating speed; the drilling footage of a drill bit in each rotation of a circle, the total volume of rock cut off in each rotation of the drill bit, the average cutting volume and the average cutting area of each cutting tooth in each rotation of the drill bit, the maximum cutting area of a single cutting tooth, and the minimum rotation radius of each cutting tooth for realizing equal cutting volume are calculated in sequence; the average cutting area is larger than the average cutting volume of each cutting tooth and the average cutting area of each cutting tooth with the minimum rotation radius for achieving the equal cutting volume, and then the cutting section of each cutting tooth is equivalent to a quadrangle, so that the relation between the radial coordinates of the left and right boundaries of the section of each cutting tooth and the average cutting volume of each cutting tooth is obtained; the radial coordinate of the section centroid of the cutting tooth is calculated; and finally, the positioning radius and height of the cutting teeth are calculated by combining the crown profile curve equation of the drill bit and the radius of the cutting teeth, so that the service life of the arranged drill bit is long.

Description

Technical Field

[0001] The invention relates to the technical field of drilling tools, and in particular to a PDC drill bit tooth arrangement method. Background Art

[0002] PDC (polycrystalline diamond compact, made of diamond powder and cemented carbide substrate sintered under ultra-high pressure and high temperature conditions) drill bits rely on high hardness, wear resistance, and self-sharpening properties as cutting elements to shear and crush rocks. At the same time, PDC drill bits have high mechanical drilling speed, long service life, and low drilling costs in soft to medium-hard formations, so they are widely used in the drilling of oil and gas wells. In oil and gas drilling projects, the geological conditions of the formations are often very complex. Under the pressure of the overlying formations and high-density drilling fluids, the density and hardness of the mud shale and mud sandstone in the deep formations not only increase, but also the brittle rock under normal pressure transforms into plastic brittle rock or plastic rock. In addition, the hydraulic energy in the deep well section is seriously insufficient, and the hydraulic-assisted rock breaking function cannot be effectively exerted, and the rock breaking efficiency of the drill bit is quite low.

[0003] It should be noted that: Assume that there is a cutting plane on the drill bit that passes through the drill bit axis and a certain point on the drill bit (called the axis plane or axial plane passing through the point). When the drill bit rotates around its own axis under the condition of zero drilling speed, the contour line of the cutting element intersects with the cutting plane or axial plane to form an intersection line. The intersection line is the axial surface contour line of the cutting element. The axial surface contour lines of all cutting elements are brought together to form the bottom hole coverage map of the drill bit. In the bottom hole coverage map, an envelope curve tangent to the axial surface contour lines of all cutting units can be made, which is called the drill bit cutting contour line. The drill bit cutting contour line reflects the basic shape characteristics of the bottom hole drilled by the drill bit. The drill bit body contour line is a position curve reflecting the drill bit body in the bottom hole coverage map, and is an important characteristic curve of the diamond drill bit. It is worth pointing out that the drill blade body contour line and the blade cutting contour line should not include the drill gauge part. This is obtained from the definition of the blade cutting contour line and the body contour line. The main cutting teeth in the drill generally refer to the cutting elements with longitudinal cutting ability, while the gauge teeth of the gauge part do not have longitudinal cutting ability, so the main cutting does not include the gauge teeth. In this way, the blade cutting contour line and the body contour line should start from the drill center and end at the gauge teeth. The drill tooth surface refers to the surface formed by the intersection of the drill body with the drill axis as the rotation center and the drill body contour line as the rotation radius after one rotation.

[0004] Therefore, a reasonable tooth arrangement calculation method is the key to ensure the excellent performance of the drill bit and is also the premise for improving the efficiency of PDC drill bit tooth arrangement. Achieving full coverage of the bottom of the well by the drill bit, ensuring that the drill bit can completely remove the rock after one rotation, forming a smoother bottom of the well, and making sure that there are no excessively protruding rock ridges at the bottom of the well are the basic requirements for PDC drill bit design, especially the radial tooth arrangement design of PDC drill bits. At present, there are weaknesses in the tooth arrangement design method of PDC drill bits, such as large arbitrariness and unclear drill bit performance targets, which lead to the early failure of individual teeth during the use of the drill bit, resulting in the rapid failure of the entire drill bit and a short drill bit life. Summary of the invention

[0005] The present invention provides a PDC drill bit tooth arrangement method, which can meet the requirement of full coverage of the well bottom by the drill bit, and each cutting tooth has a similar workload, so that the cutting teeth on the drill bit are evenly worn, and the premature failure of individual cutting teeth is avoided, thereby extending the service life of the drill bit.

[0006] The present invention is achieved through the following technical solutions:

[0007] The present invention provides a PDC drill bit tooth arrangement method, comprising the following steps:

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

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

[0011] S40, calculating the average cutting area of ​​the i-th cutting tooth located at the set positioning radius according to the average cutting volume of each cutting tooth per rotation of the drill bit;

[0012] S50, calculating the maximum cutting area of ​​a single cutting tooth when there is no interference from other cutting teeth;

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

[0014] S70, given the cutting teeth that cannot achieve equal cutting volume within the minimum rotation radius, and combined with the maximum cutting area of ​​a single cutting tooth, calculate the average cutting area of ​​the cutting teeth that are larger than the minimum rotation radius for each cutting tooth to achieve equal cutting volume and the average cutting volume of each cutting tooth;

[0015] S80, the cutting cross section of each cutting tooth is equivalent to a quadrilateral, so as to obtain the relationship between the radial coordinates of the left and right boundaries of the j-th quadrilateral cutting tooth cross section which is arbitrarily larger than the minimum rotation radius for each cutting tooth to realize equal cutting volume and the average cutting volume of each cutting tooth, and calculate the radial coordinates of the centroid of the j-th quadrilateral cutting tooth cross section which is arbitrarily larger than the minimum rotation radius for each cutting tooth to realize equal cutting volume;

[0016] S90, combining the drill crown profile curve equation and the radius of the cutting teeth, calculating the positioning radius of the jth cutting tooth that is larger than the minimum rotation radius of each cutting tooth for achieving equal cutting volume, and equidistantly arranging the cutting teeth with radii smaller than the minimum rotation radius of each cutting tooth for achieving equal cutting volume on the inner side of the minimum rotation radius of each cutting tooth for achieving equal cutting volume;

[0017] S100, calculating the positioning height of the cutting teeth by combining the drill crown profile curve equation and the positioning radius of the cutting teeth, and arranging the teeth on the drill bit according to the positioning radius and the positioning height.

[0018] The PDC drill bit tooth arrangement method provided by the present invention first calculates the footage per revolution of the drill bit, the total volume of rock cut 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 a set positioning radius according to the expected mechanical drilling speed of the drill bit 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 to achieve equal cutting volume based on the maximum cutting area, calculates the average cutting area of ​​cutting teeth greater than the minimum rotation radius for each cutting tooth to achieve equal cutting volume and the average cutting volume of each cutting tooth, and then equates the cutting section of each cutting tooth 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, thereby calculating the radial coordinates of the centroid of the cutting tooth section; finally, combining the drill crown profile curve equation and the radius of the cutting tooth, calculates the positioning radius and positioning height of the cutting tooth.

[0019] Therefore, the positioning radius and positioning height of the PDC drill bit cutting teeth that can be obtained by the present invention can ensure that the rock volume cut by each cutting tooth during operation is the same based on these parameters, and there is no phenomenon that some cutting teeth have heavy workloads and some cutting teeth have light workloads, thus avoiding the situation that some teeth fail early and cause the adjacent cutting teeth to fail quickly, and finally achieving the purpose of extending the service life of the drill bit. At the same time, it overcomes the shortcomings of the traditional PDC drill bit tooth arrangement design method, which is very random and has unclear drill bit performance targets.

[0020] Specifically, in S10, the calculation model for the drilling footage per revolution of the drill bit is:

[0021] Where:

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

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

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

[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] Where:

[0027] V is the total volume of rock cut 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 rotation of the drill bit is v = V / N = π*R 2 *δ / N;

[0030] Where:

[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 the set positioning radius is Si=R 2 δ / 2Nx i ;

[0034] Where:

[0035] S i is the average cutting area of ​​the i-th cutting tooth with a 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 when there is no interference from other cutting teeth is:

[0038] Where:

[0039] S max The maximum cutting area of ​​a single cutting tooth when there is no interference from other cutting teeth;

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

[0041] Specifically, in S60, the calculation model of the minimum rotation radius of each cutting tooth to achieve equal cutting volume is: In the formula, x min Minimum radius of rotation to achieve equal cutting volume for each cutting tooth.

[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] Where:

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

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

[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 j-th quadrilateral cutting tooth cross section that is larger than the minimum rotation radius for each cutting tooth to achieve equal cutting volume is:

[0048] Where:

[0049] R' j is the radial coordinate of the centroid of the jth tooth quadrilateral cutting section that is larger than the minimum rotation radius;

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

[0051] Specifically, greater than the minimum rotation radius x min The calculation model of the positioning radius of the jth cutting tooth is R j =f(R' j , r), where R j is greater than the minimum rotation radius x min The positioning radius of the jth cutting tooth;

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

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

[0054] The PDC drill bit tooth arrangement method provided by the present invention first calculates the footage per revolution of the drill bit, the total volume of rock cut 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 a set positioning radius according to the expected mechanical drilling speed of the drill bit and the rotation speed of the drill bit, and then calculates the maximum cutting area of ​​a single cutting tooth when there is no interference from other cutting teeth, and then calculates the minimum rotation radius of each cutting tooth to achieve equal cutting volume based on the maximum cutting area, calculates the average cutting area of ​​the cutting teeth greater than the minimum rotation radius of each cutting tooth to achieve equal cutting volume, and the average cutting volume of each cutting tooth The cutting cross 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 cross section and the average cutting volume of each cutting tooth, thereby calculating the radial coordinates of the centroid of the cutting tooth cross section; finally, the positioning radius and positioning height of the cutting tooth are calculated by combining the drill crown profile curve equation and the radius of the cutting tooth. The drill bit arranged in this way can ensure that the rock volume cut by each cutting tooth during work is the same, and there is no phenomenon that the workload of individual cutting teeth is heavy and the workload of individual cutting teeth is light, so as to avoid the situation that the failure of individual teeth in advance leads to the rapid failure of adjacent cutting teeth, and finally achieve the purpose of extending the service life of the drill bit. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0056] In the attached picture:

[0057] Figure 1 Schematic diagram of the process of the PDC drill bit tooth arrangement method according to an embodiment of the present invention;

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

[0059] Figure 3 Schematic diagram of the quadrilateral representation method for cutting cross-sectional 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 by the centroid of the cutting section;

[0062] Figure 6 This is a schematic diagram showing the cutting teeth arranged in a clockwise direction in the circumferential direction of the drill bit. DETAILED DESCRIPTION

[0063] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments.

[0064] Example

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

[0066] The present invention provides a PDC drill bit tooth arrangement method, comprising the following steps:

[0067] S10. Calculate the drilling footage per revolution of the drill bit according to the expected mechanical drilling speed of the drill bit and the rotation speed of the drill bit.

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

[0069] Where:

[0070] ROP is the expected mechanical penetration rate of the drill bit, in m / h;

[0071] RPM is the rotation speed of the drill bit, in revolutions per minute;

[0072] δ is the penetration of the drill bit per revolution, in mm / revolution.

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

[0074] 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;

[0075] Where:

[0076] V is the total volume of rock cut off per revolution of the drill bit, in mm 3 ;

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

[0078] 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 rock cut per revolution of the drill bit.

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

[0080] Where:

[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, that is, the total number of teeth on the drill bit.

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

[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] Where:

[0086] S i is the average cutting area of ​​the i-th cutting tooth with a 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 can be known that the closer the cutting tooth is to the center of the drill bit, the larger the cutting area is needed to achieve equal cutting, but this maximum cutting area has a certain limit. Therefore, there is a minimum rotation radius, and only cutting teeth larger than the minimum rotation radius can achieve equal cutting.

[0089] S50, calculating the maximum cutting area of ​​a single cutting tooth when there is no interference from other cutting teeth.

[0090] Combination Figure 2 Specifically, in S50, the calculation model of the maximum cutting area of ​​a single cutting tooth when there is no interference from other cutting teeth is:

[0091] Where:

[0092] S max The maximum cutting area of ​​a single cutting tooth when there is no interference from other cutting teeth;

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

[0094] S60. Calculate the minimum rotation radius of each cutting tooth for achieving equal cutting volume based on 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 equal cutting volume is: In the formula, x min Minimum radius of rotation to achieve equal cutting volume for each cutting tooth.

[0096] S70. Given the cutting teeth that cannot achieve equal cutting volume within the minimum rotation radius, and combined with the maximum cutting area of ​​a single cutting tooth, calculate the average cutting area of ​​the cutting teeth that are larger than the minimum rotation radius for each cutting tooth to achieve equal cutting volume and the average cutting volume of each cutting tooth.

[0097] Specifically, in S70, the minimum rotation radius x is given min The number of teeth that cannot achieve equal cutting volume within the set positioning radius can be combined with the calculation model of the average cutting area of ​​the i-th cutting tooth located at the set positioning radius. The calculation model of the average cutting area of ​​the cutting teeth and the average cutting volume of each cutting tooth can be obtained as follows: ;

[0098] Where:

[0099] S i is the average cutting area of ​​the cutting teeth,

[0100] n is the given minimum rotation radius x min The number of cutting teeth that cannot achieve equal cutting volume is

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

[0102] S80. Equivalently transform the cutting cross section of each cutting tooth into a quadrilateral to obtain the relationship between the radial coordinates of the left and right boundaries of the j-th quadrilateral cutting tooth cross section that is arbitrarily larger than the minimum rotation radius for each cutting tooth to achieve equal cutting volume and the average cutting volume of each cutting tooth, and calculate the radial coordinates of the centroid of the j-th quadrilateral cutting tooth cross section that is arbitrarily larger than the minimum rotation radius for each cutting tooth to achieve equal cutting volume.

[0103] Combination Figure 3 It should be noted that in this embodiment, the cutting section of each tooth is equivalent to a quadrilateral shape, and δ is set as the length of one side of the quadrilateral. The radial coordinates of the left and right boundaries of the cutting section of the quadrilateral of any tooth greater than the minimum rotation radius and the average cutting volume can be obtained. The relationship between.

[0104] Combination Figure 4 , the cutting section position relationship model of each cutting tooth is: where r'j is the radial coordinate of the right boundary of the quadrilateral cross-section of the jth tooth, r'0 is equal to the minimum rotation radius x min .

[0105] Among them, the calculation model of the radial coordinates of the centroid of the j-th quadrilateral cutting tooth section that is larger than the minimum rotation radius of each cutting tooth to achieve equal cutting volume is:

[0106] Where:

[0107] R' j is the radial coordinate of the centroid of the jth tooth quadrilateral cutting section that is larger than the minimum rotation radius;

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

[0109] S90. Combine the drill crown profile curve equation and the radius of the cutting tooth to calculate the positioning radius of the jth cutting tooth that is larger than the minimum rotation radius of each cutting tooth for achieving equal cutting volume, and arrange the cutting teeth with radii smaller than the minimum rotation radius of each cutting tooth for achieving equal cutting volume equidistantly on the inner side of the minimum rotation radius of each cutting tooth for achieving equal cutting volume.

[0110] Combination Figure 5 Specifically, combining the given crown profile equation f and cutting tooth radius r, the radius greater than the minimum rotation radius x can be obtained. min The positioning radius R of the jth cutting tooth j . Among them, greater than the minimum rotation radius x min The calculation model of the positioning radius of the jth cutting tooth is R j =f(R' j , r), where R j is greater than the minimum rotation radius x min The positioning radius of the j-th cutting tooth.

[0111] It can be understood that the minimum rotation radius x min The cutting teeth, i.e. the cutting teeth with tooth numbers 1 to j-1, are arranged at equal intervals within this interval, wherein the positioning radius of the first cutting tooth is equal to the radius of the cutting tooth, i.e. r1 = r. In other words, the cutting teeth with a radius smaller than the minimum rotation radius for each cutting tooth to achieve equal cutting volume are arranged at equal intervals on the inner side of the minimum rotation radius for each cutting tooth to achieve equal cutting volume.

[0112] S100, calculating the positioning height of the cutting teeth by combining the drill crown profile curve equation and the positioning radius of the cutting teeth, and arranging the teeth on the drill bit according to the positioning radius and the positioning height.

[0113] Specifically, the positioning height of any cutting tooth can be obtained by combining 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 ), where H j is the positioning height of the cutting tooth, γ j is the normal angle.

[0114] Combination Figure 6 Specifically, the PDC teeth are arranged on the drill bit in a sequential or reverse order in the circumferential direction. Figure 6 The cutting teeth are arranged on the drill bit in a clockwise and sequential arrangement in the circumferential direction. The sequential arrangement here means that the arrangement order 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 opposite is reverse arrangement.

[0115] In summary, the PDC drill bit tooth arrangement method provided by the present invention first calculates the footage per revolution of the drill bit, the total volume of rock cut 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 mechanical drilling speed of the drill bit and the rotation speed of the drill bit, and 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 to achieve equal cutting volume based on the maximum cutting area, calculates the average cutting area of ​​the cutting teeth greater than the minimum rotation radius for each cutting tooth to achieve equal cutting volume and the average cutting volume of each cutting tooth, and then equates the cutting section of each cutting tooth 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, thereby calculating the radial coordinates of the centroid of the cutting tooth section; finally, combining the drill crown profile curve equation and the radius of the cutting tooth, the positioning radius and positioning height of the cutting tooth are calculated.

[0116] Therefore, the positioning radius and positioning height of the PDC drill bit cutting teeth that can be obtained in this embodiment can ensure that the rock volume cut by each cutting tooth during operation is the same based on this parameter arrangement, and there is no phenomenon that some cutting teeth have heavy workloads and some cutting teeth have light workloads, thus avoiding the situation where some teeth fail early and cause the adjacent cutting teeth to fail quickly, and ultimately achieving the purpose of extending the service life of the drill bit. At the same time, it overcomes the shortcomings of the traditional PDC drill bit tooth arrangement design method, which is very random and has unclear drill bit performance targets.

[0117] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A PDC drill bit tooth arrangement method, characterized in that: The following steps are involved: S10, calculating the drilling footage per revolution of the drill bit according to the expected mechanical drilling speed of the drill bit and the rotation speed of the drill bit; S20, calculating the total volume of rock cut per revolution of the drill bit according to the footage per revolution of the drill bit; 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 rock cut per revolution of the drill bit; S40, calculating the average cutting area of ​​the i-th cutting tooth located at the set positioning radius according to the average cutting volume of each cutting tooth per rotation of the drill bit; S50, calculating the maximum cutting area of ​​a single cutting tooth when there is no interference from other cutting teeth; S60, calculating the minimum rotation radius of each cutting tooth to achieve equal cutting volume according to the maximum cutting area of ​​a single cutting tooth; S70, given the cutting teeth that cannot achieve equal cutting volume within the minimum rotation radius, and combined with the maximum cutting area of ​​a single cutting tooth, calculate the average cutting area of ​​the cutting teeth that are larger than the minimum rotation radius for each cutting tooth to achieve equal cutting volume and the average cutting volume of each cutting tooth; S80, the cutting cross section of each cutting tooth is equivalent to a quadrilateral, so as to obtain the relationship between the radial coordinates of the left and right boundaries of the j-th quadrilateral cutting tooth cross section which is arbitrarily larger than the minimum rotation radius for each cutting tooth to realize equal cutting volume and the average cutting volume of each cutting tooth, and calculate the radial coordinates of the centroid of the j-th quadrilateral cutting tooth cross section which is arbitrarily larger than the minimum rotation radius for each cutting tooth to realize equal cutting volume; S90, combining the drill crown profile curve equation and the radius of the cutting teeth, calculating the positioning radius of the jth cutting tooth that is larger than the minimum rotation radius of each cutting tooth for achieving equal cutting volume, and equidistantly arranging the cutting teeth with radii smaller than the minimum rotation radius of each cutting tooth for achieving equal cutting volume on the inner side of the minimum rotation radius of each cutting tooth for achieving equal cutting volume; S100, calculating the positioning height of the cutting teeth by combining the drill crown profile curve equation and the positioning radius of the cutting teeth, and arranging the teeth on the drill bit according to the positioning radius and the positioning height.

2. The PDC drill bit tooth arrangement method according to claim 1, characterized in that: In S10, the calculation model of the drilling footage per revolution of the drill bit is: Where: ROP is the expected mechanical penetration rate of the drill bit, RPM is the speed of the drill bit, δ is the penetration 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 of the total volume of rock cut off per revolution of the drill bit is V = π*R 2 *δ; Where: V is the total volume of rock cut 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 of the average cutting volume of each cutting tooth per rotation of the drill bit is v=v / N=π * R 2 δ / N; Where: v is 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 calculation model of the average cutting area of ​​the i-th cutting tooth located at the set positioning radius is S i =R 2 δ / 2Nx i ; Where: S i is the average cutting area of ​​the i-th cutting tooth with a set radius; x i is the positioning radius of the i-th cutting tooth.

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

7. The PDC drill bit tooth arrangement method according to claim 6, characterized in that: In S60, the calculation model of the minimum rotation radius of each cutting tooth to achieve equal cutting volume is: In the formula, x min Minimum radius of rotation 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 model of the average cutting area of ​​the cutting teeth and the average cutting volume of each cutting tooth is: ; Where: S i is the average cutting area of ​​the cutting teeth, n is the given minimum rotation radius x min The number of cutting teeth that cannot achieve equal cutting volume is is the average cutting volume of each cutting tooth.

9. The PDC drill bit tooth arrangement method according to claim 8, characterized in that: In S80, the calculation model of the radial coordinate of the centroid of the j-th quadrilateral cutting tooth cross section, which is larger than the minimum rotation radius for each cutting tooth to achieve equal cutting volume, is: Where: R' j is the radial coordinate of the centroid of the jth tooth quadrilateral cutting section that is larger than the minimum rotation radius; r' j is the radial coordinate of the right boundary of the quadrilateral cross-section of the jth tooth.

10. The PDC drill bit tooth arrangement method according to claim 9, characterized in that: In S90, greater than the minimum rotation radius x min The calculation model of the positioning radius of the jth cutting tooth is R j =f(R' j , r), where R j is greater than the minimum rotation radius x min The positioning radius of the jth cutting tooth; In S100, the calculation model of the positioning height of the cutting tooth is (H j , γ j )=f(R j ), where H j is the positioning height of the cutting tooth, γ j is the normal angle.

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