Method for calculating drilling direction of torsion surface excavation face in engineering

Abstract

The present invention discloses a method for calculating the drilling direction of the excavation surface of a twisted surface in engineering, which specifically includes the following steps: Mark the four vertices of the construction twisted surface in the measurement coordinate system; Define points N, M, F, E, P1, and P2 in the measurement coordinate system; Solve the vector coordinates of points N, M, F, E, P1, and P2 according to the formula for dividing a line segment in a given ratio; Perform adjustment calculations on the obtained coordinates of P1 and P2 to obtain the spatial coordinates of the drill bit P; Define the actually measured point of the drill tail as T, and the designed coordinate of the drill tail on the twisted surface as T′. From the coordinates of points T, P, and E, obtain #imgabs0#, #imgabs1#, and obtain #imgabs2#; Obtain the coordinate of the drill tail T′ according to the formula for dividing a line segment in a given ratio; Obtain the angle θ of the drill rod relative to the drill bit and the position T′ of the drill tail when excavating the twisted surface, and determine the drill rod direction line as PT′. The method for calculating the drilling direction of the excavation surface of a twisted surface in engineering according to the present invention solves the problem of inaccurate drilling direction of the excavation surface in the construction of a twisted surface in the prior art.

Description

Technical Field

[0001] The present invention belongs to the technical field of engineering surveying, and relates to a method for calculating the drilling direction of a torsional surface excavation surface in a project. Background Art

[0002] In the construction of hydropower station projects, a torsional surface is a connecting section that transitions from a rectangular cross-section to a trapezoidal cross-section. During the construction of the torsional surface, it often occurs that due to the lack of theoretical guidance and relying solely on on-site practical experience, the excavation of the torsional surface is inaccurate, resulting in a large amount of over-excavation or under-excavation, and ultimately causing economic losses to the construction unit / construction company.

[0003] The traditional method for the construction of the torsional surface excavation surface is that after the on-site surveying technicians loft the side lines of the torsional surface, the on-site construction workers rely on experience to carry out drilling orientation. In this case, the accuracy of the torsional surface excavation mainly depends on experience. Without determining the direction line of the drill pipe or relevant theoretical guidance, it is very easy to have engineering quality problems, low efficiency, and great economic waste. Especially in places where the construction conditions are difficult or there is a lack of theoretical guidance and on-site practical experience, it is even more important to ensure the accuracy of the torsional surface excavation surface.

[0004] In summary, there is an urgent need to find a method for calculating the drilling direction line of the torsional surface excavation surface in the project to solve the problems existing in the above-mentioned technologies. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for calculating the drilling direction of the torsional surface excavation surface in a project, which solves the problem of inaccurate drilling direction of the excavation surface during the construction of the torsional surface in the prior art.

[0006] The technical solution adopted by the present invention is a method for calculating the drilling direction of the torsional surface excavation surface in a project, which specifically includes the following steps:

[0007] Step 1: Mark the four vertices of the construction torsional surface in the measurement coordinate system;

[0008] Step 2: Define points N, M, F, E, P1, and P2 in the measurement coordinate system;

[0009] Step 3: Solve the vector coordinates of points N, M, F, E, P1, and P2 according to the fixed-point ratio formula;

[0010] Step 4: Perform adjustment calculation on the obtained coordinates of P1 and P2 to obtain the spatial coordinates of the drill bit P point;

[0011] Step 5: Define the actually measured point of the drill tail as T, and the designed coordinate of the drill tail on the torsional surface as T'. From the coordinates of points T, P, and E, obtain 、 , and obtain ; Obtain the coordinate of the drill tail T' according to the fixed-point ratio formula;

[0012] Step 6: Obtain the angle θ of the drill pipe relative to the drill bit and the position T' of the drill tail when excavating the twisted surface, and finally determine the drill pipe direction line as PT'.

[0013] The features of the present invention also lie in:

[0014] The specific process of Step 1 is as follows:

[0015] The four vertices of the construction twisted surface are respectively marked as A(X A , Y A , H A )、B(X B , Y B , H B )、C(X C , Y C , H C )、D(X D , Y D , H D ) in the measurement coordinate system in a clockwise or counterclockwise direction.

[0016] The specific process of Step 2 is as follows:

[0017] Take a point on the AB line as point N, and take a point on the CD line as point M. Points M and N are respectively the definite ratio division points of the CD line and the AB line, and the definite ratio coefficient is λ, λ ∈ R and λ ≠ -1;

[0018] Take a point on the AD line as point F, and take a point on the BC line as point F. Points E and F are respectively the definite ratio division points of the BC line and the AD line, and the definite ratio coefficient is K, K ∈ R and K ≠ -1;

[0019] Take points P1(X P1 , Y P1 , H P1 ), P2(X P2 , Y P2 , H P2 ) and P(X P , Y P , H P ). The points P1, P2 and P are all the same point of the drill bit on the twisted surface. Point P2 is the upper definite ratio division point of the MN connection line, and P1 is the upper definite ratio division point of the EF connection line.

[0020] The specific process of Step 3 is as follows:

[0021] According to the space vector calculation formula: , , let , ( ), substitute specific numerical values to get:

[0022] (1),

[0023] The coordinates of point N are thus obtained as (2),

[0024] Similarly, the coordinates of point M are (3),

[0025] Then (4),

[0026] When points N and M are the midpoints of line segments AB and DC respectively; when points N and M are the internal division points of line segments AB and DC respectively; when points N and M are the internal division points of line segments AB and DC respectively; when points N and M are points A and D respectively;

[0027] Similarly, let , , then there is:

[0028] The coordinates of point F are (5),

[0029] The coordinates of point E are (6),

[0030] Then (7).

[0031] Step 3 further includes:

[0032] Furthermore, since P1 is a point on line segment FE and , then there is:

[0033] The coordinates of are (8);

[0034] Furthermore, since is a point on line segment NM and , then:

[0035] The coordinates of are; (9).

[0036] The specific process of Step 4 is as follows:

[0037] Since P1, P2, and P are the same point of the drill bit on the torsional surface, combining formulas (8) and (9), the coordinates of the drill bit at point P can be obtained as:

[0038] (10),

[0039] Furthermore, from formulas (2), (3), (5), (6), (8), (9) and formula (10), the coordinate equation of point P on the twist surface of the drill bit can be obtained:

[0040] (11).

[0041] The specific process of step 5 is as follows:

[0042] Take the actual measured point of the drill tail as T(X T , Y T , H T ), and take the designed coordinates of the drill tail on the twist surface as T'(X T′ , Y T′ , H T′ ); Define the drill pipe length ; ; Point P is the intersection of MN and EF, T' is on the generatrix EF, is the cosine value of the angle ;

[0043] Then , , then there is:

[0044] (12),

[0045] When at this time , at this time ; When at this time , at this time ;

[0046] Furthermore, let , , we get:

[0047] (13),

[0048] Furthermore, , the coordinates of point can be solved as:

[0049] (14).

[0050] The specific process of step 6 is as follows:

[0051] From the angle between the actual measured drill pipe obtained in step 5 and and the coordinates of the drill tail point T on , with the drill bit point P unchanged, by adjusting the rotation angle of the drill tail, make the drill tail T coincide with the point on the generatrix FE ​ Coincide That is the drilling direction of the drill pipe.

[0052] The beneficial effects of the present invention are as follows:

[0053] The method for calculating the drilling direction of the torsional surface excavation face in the project of the present invention solves the torsional surface through vector space operation, calculates the vector coordinates of the drill bit and the drill tail of the drill pipe, and then calculates the angle between the drill pipe and the generatrix. By swinging the drill tail to make the drill pipe coincide with the generatrix on the torsional surface, the drilling direction line can be accurately determined during the excavation of the torsional surface. While ensuring the accuracy of the calculation results, the present invention simplifies the calculation process, improves efficiency and saves project costs. Description of the Drawings

[0054] Figure 1 is the flow chart of the method for calculating the drilling direction of the torsional surface excavation face in the project of the present invention;

[0055] Figure 2 is the schematic diagram of the coordinate system of the method for calculating the drilling direction of the torsional surface excavation face in the project of the present invention. Detailed Embodiment

[0056] The present invention will be described in detail below in conjunction with the drawings and specific embodiments.

[0057] As Figure 1 shown, the technical solution adopted by the present invention is a method for calculating the drilling direction of the torsional surface excavation face in the project, which specifically includes the following steps:

[0058] Step 1: The four vertices of the torsional surface are A, B, C, and D, and point P is any point on the torsional surface of the drill bit of the drill pipe;

[0059] Step 2: On the torsional surface, pass through point P and intersect with vectors AB and DC at N and M respectively. NM is the first generatrix on the torsional surface, and N and M are the definite ratio points on vectors AB and DC, and the definite ratio coefficient is (λ ∈ R, λ ≠ -1); on the torsional surface, pass through point P and intersect with vectors AD and BC at F and E respectively. FE is the second generatrix on the torsional surface, and F and E are the definite ratio points on vectors AD and BC, and the definite ratio coefficient is (K ∈ R, K ≠ -1);

[0060] Step 3: Solve the vector coordinates of the equal ratio points N, M, F, E, P1, and P2 by the definite ratio point formula;

[0061] Step 4: Perform adjustment calculation on the obtained coordinates of P1 and P2, and finally obtain the spatial coordinates of the drill bit P point;

[0062] Step 5: From the coordinates of points T, P, and E, it is easy to obtain 、 , and then obtain ; Obtain the coordinates of the drill tail T' by the definite ratio point formula;

[0063] Step 6: Obtain the angle θ of the drill pipe relative to the drill bit rotation and the position T' of the drill tail when excavating the twisted surface, and finally determine the drill pipe direction line as PT';

[0064] Furthermore, step 1: As Figure 2 shown, the spatial coordinates of the four intersection points on the twisted surface are: A(X A , Y A , H A ), B(X B , Y B , H B ), C(X C , Y C , H C ), D(X D , Y D , H D ), and the coordinates of the drill pipe bit on the twisted surface are P1(X P1 , Y P1 , H P1 ), P2(X P2 , Y P2 , H P2 ), P(X P , Y P , H P ).

[0065] Furthermore, step 2: As Figure 2 shown, on the twisted surface, it passes through point P and intersects vectors AB and DC at N and M respectively. NM is a generatrix on the twisted surface, and N and M are the definite ratio points on vectors AB and DC, with the definite ratio coefficient being (λ ∈ R, λ ≠ -1); on the twisted surface, it passes through point P and intersects vectors AD and BC at F and E respectively. FE is a generatrix on the twisted surface, and F and E are the definite ratio points on vectors AD and BC, with the definite ratio coefficient being (K ∈ R, K ≠ -1).

[0066] Furthermore, step 3: As Figure 2 shown, from the spatial vector calculation formula, we get: , , N and M are points on line segments AB and DC. Let , ( ),

[0067] (1),

[0068] That is, the coordinates of point N (2),

[0069] Similarly, the coordinates of point M can be obtained (3),

[0070] (4),

[0071] Discussion: Particularly appropriate are that points N and M are the midpoints of line segments AB and DC respectively; when points N and M are the internal division points of line segments AB and DC respectively; when points N and M are the internal division points of line segments AB and DC respectively; when points N and M are points A and D respectively.

[0072] Similarly, let , , then there is

[0073] Coordinates of point F (5),

[0074] Coordinates of point E (6),

[0075] (7),

[0076] Also, since P1 is a point on line segment FE and , then there is

[0077] The coordinates of (8),

[0078] Also because is a point on line segment NM and , then there is

[0079] The coordinates of (9).

[0080] Further, Step 4: As Figure 2 shown, since are all the same point of the drill bit on the torsion surface, combining formulas (8) and (9), the coordinates of point P of the drill bit are: (10),

[0081] From formulas (2), (3), (5), (6), (8), (9) and formula (10), the coordinate equation of point P of the drill bit on the torsion surface can be obtained:

[0082] (11).

[0083] Further, Step 5: As Figure 2 shown, it is easy to obtain , , then there is:

[0084] (12),

[0085] Discuss when time , at this time ; when time , at this time .

[0086] Furthermore, let , , then it can be obtained that

[0087] (13),

[0088] Furthermore, , the coordinates of point can be solved as:

[0089] (14).

[0090] Furthermore, step 6: As Figure 2 shown, there is the included angle between the measured drill pipe obtained in step E and and the coordinates of the drill tail point T on . The drill bit point P remains stationary, and by adjusting the rotation angle of the drill tail, the drill tail T is made to coincide with on the generatrix FE, which is the drill pipe drilling direction.

[0091] The main principle of the present invention is: from the four corner points A(X A , Y A , H A ), B(X B , Y B , H B ), C(X C , Y C , H C ), D(X D , Y D , H D ) coordinates and the fixed ratio division point coefficients and , the fixed ratio division points M(X M , Y M , H M ), N(X N , Y N , H N ), E(X E , Y E , H E ), F(X F , Y F , HF ) coordinates, and then obtain the coordinates P(X P , Y P , H P ) of the drill pipe bit on the torsional surface; there are also the coordinates (X T , Y T , H T ) of the actual measurement point T of the drill tail. The coordinates T'(X T′ , Y T′ , H T′ ) of the drill pipe drill tail on the torsional surface can be obtained, and the included angle between the actual drill pipe direction and can be obtained. Using the equal ratio point formula, the coordinates (X ) of the point on the drill tail can be obtained. Finally, the drill pipe direction line is determined as (X T′ , Y T′ , H T′ ), and finally the drill pipe direction line is determined as .

[0092] While ensuring the accuracy of the calculation results, the present invention simplifies the calculation process, improves efficiency, and saves project costs.

[0093] Embodiment 1

[0094] As shown in Figure 1 and Figure 2 , the method for calculating the drilling direction of the excavation surface of the torsional surface in the present embodiment of the project specifically includes the following steps:

[0095] Step 1: Mark the four vertices of the construction torsional surface in the measurement coordinate system;

[0096] Step 2: Define points N, M, F, E, P1, and P2 in the measurement coordinate system;

[0097] Step 3: Solve the vector coordinates of points N, M, F, E, P1, and P2 according to the fixed ratio point formula;

[0098] Step 4: Perform adjustment calculations on the obtained coordinates of P1 and P2 to obtain the spatial coordinates of the drill bit P point;

[0099] Step 5: Define the actual measurement point of the drill tail as T, and the designed coordinate of the drill tail on the torsional surface as T'. From the coordinates of points T, P, and E, obtain , , and obtain ; obtain the coordinates of the drill tail T' according to the fixed ratio point formula;

[0100] Step 6: Obtain the angle θ of the drill pipe relative to the drill bit when excavating the torsional surface and the position T' of the drill tail, and finally determine the drill pipe direction line as PT'.

[0101] Embodiment 2

[0102] As Figure 1 and Figure 2 shown, the method for calculating the drilling direction of the torsional surface excavation surface in the project proposed in this embodiment specifically includes the following steps:

[0103] Step 1: Mark the four vertices of the construction torsional surface in the measurement coordinate system;

[0104] The four vertices of the construction torsional surface are respectively marked as A(X A , Y A , H A )、B(X B , Y B , H B )、C(X C , Y C , H C )、D(X D , Y D , H D ) in the measurement coordinate system in a clockwise or counterclockwise direction.

[0105] Step 2: Define points N, M, F, E, P1, and P2 in the measurement coordinate system;

[0106] Step 3: Solve the vector coordinates of points N, M, F, E, P1, and P2 according to the fixed-point ratio formula;

[0107] Step 4: Perform adjustment calculation on the obtained coordinates of P1 and P2 to obtain the spatial coordinates of the drill bit P point;

[0108] Step 5: Define the actual measured point of the drill tail as T, and the designed coordinate of the drill tail on the torsional surface as T′. From the coordinates of points T, P, and E, obtain , , and obtain ; Obtain the coordinate of the drill tail T′ according to the fixed-point ratio formula;

[0109] Step 6: Obtain the angle θ of the drill pipe relative to the drill bit and the position T′ of the drill tail when excavating the torsional surface, and finally determine the drill pipe direction line as PT′.

[0110] Embodiment 3

[0111] As Figure 1 and Figure 2 shown, the method for calculating the drilling direction of the torsional surface excavation surface in the project proposed in this embodiment specifically includes the following steps:

[0112] Step 1: Mark the four vertices of the construction torsional surface in the measurement coordinate system;

[0113] The four vertices of the construction torsional surface are respectively marked as A(X A , YA , H A ), B(X B , Y B , H B ), C(X C , Y C , H C ), D(X D , Y D , H D ).

[0114] Step 2: Define points N, M, F, E, P1, and P2 in the measurement coordinate system;

[0115] Take a point on line AB as point N, and a point on line CD as point M. Points M and N are the definite ratio division points of lines CD and AB respectively, and the definite ratio coefficient is λ, where λ ∈ R and λ ≠ -1;

[0116] Take a point on line AD as point F, and a point on line BC as point F. Points E and F are the definite ratio division points of lines BC and AD respectively, and the definite ratio coefficient is K, where K ∈ R and K ≠ -1;

[0117] Take points P1(X P1 , Y P1 , H P1 ), P2(X P2 , Y P2 , H P2 ), and P(X P , Y P , H P ). The points P1, P2, and P are the same point of the drill bit on the torsional surface. Point P2 is the upper definite ratio division point of the MN connection line, and P1 is the upper definite ratio division point of the EF connection line.

[0118] Step 3: Solve the vector coordinates of points N, M, F, E, P1, and P2 according to the definite ratio division point formula;

[0119] Step 4: Perform adjustment calculations on the obtained coordinates of P1 and P2 to obtain the spatial coordinates of the drill bit P point;

[0120] Step 5: Define the measured point of the drill tail as T, and the designed coordinate of the drill tail on the torsional surface as T'. From the coordinates of points T, P, and E, obtain , , and obtain ; Obtain the coordinate of the drill tail T' according to the definite ratio division point formula;

[0121] Step 6: Obtain the angle θ of the drill pipe relative to the drill bit during the excavation of the torsional surface and the position T' of the drill tail, and finally determine the drill pipe direction line as PT'.

[0122] Example 4

[0123] AsFigure 1 and Figure 2 As shown, the method for drilling direction of the twisted surface excavation surface in the calculation project proposed in this embodiment specifically includes the following steps:

[0124] Step 1: Mark the four vertices of the construction twisted surface in the measurement coordinate system;

[0125] The four vertices of the construction twisted surface are respectively labeled as A(X A , Y A , H A )), B(X B , Y B , H B )), C(X C , Y C , H C )), D(X D , Y D , H D ) in the measurement coordinate system in a clockwise or counterclockwise direction.

[0126] Step 2: Define points N, M, F, E, P1, and P2 in the measurement coordinate system;

[0127] Take a point on line AB as point N, and take a point on line CD as point M. Points M and N are respectively the definite ratio division points of line CD and line AB, and the definite ratio coefficient is λ, where λ ∈ R and λ ≠ -1;

[0128] Take a point on line AD as point F, and take a point on line BC as point F. Points E and F are respectively the definite ratio division points of line BC and line AD, and the definite ratio coefficient is K, where K ∈ R and K ≠ -1;

[0129] Take points P1(X P1 , Y P1 , H P1 ), P2(X P2 , Y P2 , H P2 ) and P(X P , Y P , H P ). The points P1, P2, and P are all the same point of the drill bit on the twisted surface. Point P2 is the upper definite ratio division point of the MN connection line, and P1 is the upper definite ratio division point of the EF connection line.

[0130] Step 3: Solve the vector coordinates of points N, M, F, E, P1, and P2 according to the definite ratio division point formula;

[0131] According to the spatial vector calculation formula: , , let , ([] ), substituting specific numerical values gives:

[0132] (1),

[0133] That is, the coordinates of point N are (2),

[0134] Similarly, the coordinates of point M are (3),

[0135] Then (4),

[0136] When Points N and M are the midpoints of line segments AB and DC respectively; when Points N and M are the internal division points of line segments AB and DC respectively; when Points N and M are the internal division points of line segments AB and DC respectively; when Points N and M are points A and D respectively;

[0137] Similarly, let , , then there is:

[0138] The coordinates of point F are (5),

[0139] The coordinates of point E are (6),

[0140] Then (7).

[0141] Step 3 further includes:

[0142] Furthermore, since P1 is a point on line segment FE and , then there is:

[0143] The coordinates of (8);

[0144] Furthermore, since is a point on line segment NM and , then:

[0145] The coordinates of ; (9).

[0146] Step 4: Perform adjustment calculations on the obtained coordinates of P1 and P2 to obtain the spatial coordinates of the drill bit P;

[0147] Step 5: Define the actual measured point of the drill tail as T, and the designed coordinates of the drill tail on the torsion surface as T′. From the coordinates of points T, P, and E, obtain , , and obtain ; Obtain the coordinates of the drill tail T' by the fixed-point ratio formula;

[0148] Step 6: Obtain the angle θ of the drill pipe relative to the drill bit during the excavation of the twisted surface and the position T' of the drill tail, and finally determine the drill pipe direction line as PT'.

[0149] Example 5

[0150] As Figure 1 and Figure 2 shown, the method for calculating the drilling direction of the excavation surface of the twisted surface proposed in this example specifically includes the following steps:

[0151] Step 1: Mark the four vertices of the construction twisted surface in the measurement coordinate system;

[0152] The four vertices of the construction twisted surface are respectively marked as A(X A , Y A , H A )), B(X B , Y B , H B ), C(X C , Y C , H C ), D(X D , Y D , H D ) in the measurement coordinate system in a clockwise or counterclockwise order.

[0153] Step 2: Define points N, M, F, E, P1, P2 in the measurement coordinate system;

[0154] Take a point on the AB line as point N, and take a point on the CD line as point M. Points M and N are respectively the fixed-point ratio points of the CD line and the AB line, and the fixed-point ratio coefficient is λ, λ ∈ R and λ ≠ -1;

[0155] Take a point on the AD line as point F, and take a point on the BC line as point F. Points E and F are respectively the fixed-point ratio points of the BC line and the AD line, and the fixed-point ratio coefficient is K, K ∈ R and K ≠ -1;

[0156] Take points P1(X P1 , Y P1 , H P1 ), P2(X P2 , Y P2 , H P2 ) and P(X P , Y P , H P ). The points P1, P2 and P are all the same point of the drill bit on the twisted surface. Point P2 is the upper fixed-point ratio point of the MN connection line, and P1 is the upper fixed-point ratio point of the EF connection line.

[0157] Step 3: Solve the vector coordinates of points N, M, F, E, P1, and P2 according to the fixed-point ratio formula;

[0158] According to the spatial vector calculation formula: , , let , ( ), substitute specific numerical values to get:

[0159] (1),

[0160] That is, the coordinates of point N are (2),

[0161] Similarly, the coordinates of point M are (3),

[0162] Then (4),

[0163] When points N and M are the midpoints of line segments AB and DC respectively; when points N and M are the internal division points of line segments AB and DC respectively; when points N and M are the internal division points of line segments AB and DC respectively; when points N and M are points A and D respectively;

[0164] Similarly, let , , then there is:

[0165] The coordinates of point F are (5),

[0166] The coordinates of point E are (6),

[0167] Then (7).

[0168] Step 3 also includes:

[0169] Furthermore, since P1 is a point on line segment FE and , then there is:

[0170] The coordinates of (8);

[0171] Furthermore, since is a point on line segment NM and , then:

[0172] The coordinates of ; (9).

[0173] Step 4: Conduct adjustment calculation on the obtained coordinates of P1 and P2 to obtain the spatial coordinates of the P point of the drill bit;

[0174] Since P1, P2, and P are the same point of the drill bit on the torsional surface, combining formulas (8) and (9), the coordinates of the P point of the drill bit can be obtained as:

[0175] (10),

[0176] Furthermore, from formulas (2), (3), (5), (6), (8), (9), and formula (10), the coordinate equation of the P point of the drill bit on the torsional surface can be obtained:

[0177] (11).

[0178] Step 5: Define the actual measured point of the drill tail as T, and the designed coordinate of the drill tail on the torsional surface as T'. From the coordinates of points T, P, and E, we get and , and obtain ; Obtain the coordinate of the drill tail T' by the definite ratio point formula;

[0179] Step 6: Obtain the angle θ of the drill pipe relative to the drill bit during the excavation of the torsional surface and the position T' of the drill tail, and finally determine the drill pipe direction line as PT'.

[0180] Example 6

[0181] See Figure 2 , the calculation method of the drilling direction line of the torsional surface excavation in the project. This example is used to calculate the coordinates of the drill bit and drill tail of the drill pipe on the torsional surface and the included angle between the drill pipe and the generatrix.

[0182] This example uses a certain hydropower project. The intake slope is a torsional surface. The coordinates of the four endpoints A, B, C, and D of the torsional surface are shown in Table 1, and the coordinates of the definite ratio points N, M, F, and E on the four sides of the torsional surface are shown in Table 2. The drill pipe length S is 5.0 meters to excavate the torsional surface. The point P on the torsional surface is the position of the drill bit, the actual measured position of the drill tail is T, and the designed coordinate of the drill tail on the torsional surface is T'. From the coordinates of points T, P, and E, we get and , and obtain ; Obtain the coordinate of the drill tail T' by the definite ratio point formula, thereby determining the angle θ of the drill pipe relative to the drill bit and the position T' of the drill tail during the excavation of the torsional surface, and finally determining the drill pipe direction line as PT'. Combining Figure 2 and formulas (1) to (14), the calculation results are shown in Table 1-6 below.

[0183] Table 1: Coordinates of known points

[0184]

[0185] Table 2: Coordinates of the equal ratio points on the four sides of the torsional surface

[0186]

[0187] Table 3: Drill Bit Coordinates

[0188]

[0189] Table 4: Vector Coordinates

[0190]

[0191] Table 5: Drill Pipe Direction and included angle

[0192]

[0193] Table 6: Coordinates of the Drill Tail on the Element Line FE

[0194]

[0195] It can be seen from the data analysis results in the tables of the above embodiments that with the theoretical guidance of the calculation method of the drilling direction line of the torsional surface excavation surface during the process, the coordinates of the drill pipe and drill bit on the torsional surface and the included angle between the drill pipe and the element line can be calculated, thereby determining the rotation angle of the drill pipe. At the same time, the coordinates of the drill tail can also be calculated to determine the drilling direction of the drill pipe , and finally control the accuracy of the torsional surface excavation surface. While ensuring the accuracy of the calculation results, the present invention simplifies the calculation process, improves efficiency and saves project costs.

Claims

1. A method for calculating the drilling direction of the torsion surface excavation face in engineering, characterized in that Specifically, it includes the following steps: Step 1: Mark the four vertices of the construction torsional surface in the measurement coordinate system; Step 2: Define points N, M, F, E, P1, and P2 in the measurement coordinate system; Step 3: Solve the vector coordinates of points N, M, F, E, P1, and P2 according to the fixed-point ratio formula; Step 4: Perform adjustment calculations on the obtained coordinates of P1 and P2 to obtain the spatial coordinates of the drill bit point P; Step 5: Define the actual measurement point of the self-drilling screw as T, and the designed coordinate of the self-drilling screw on the torsion surface as T'. From the coordinates of points T, P, and E, obtain , , and calculate ; Obtain the coordinates of the drill tail T′ by the fixed-point ratio formula; Step 6: Obtain the angle θ of the drill rod relative to the drill bit and the position of the drill tail T′ when excavating the torsional surface, and finally determine that the drill rod direction line is PT′; The specific process of the said Step 1 is: The four vertices of the constructed twisted surface are marked as A(X A , Y A , H A ), B(X B , Y B , H B ), C(X C , Y C , H C ), D(X D , Y D , H D ) in the measurement coordinate system in a clockwise or counterclockwise direction; The specific process of the said Step 2 is: Take a point on line AB as point N, and take a point on line CD as point M. Points M and N are the fixed-point ratio points of lines CD and AB respectively, and the fixed-point ratio coefficient is λ, where λ ∈ R and λ ≠ -1; Take a point on line AD as point F, and take a point on line BC as point F. Points E and F are the fixed-point ratio points of lines BC and AD respectively, and the fixed-point ratio coefficient is K, where K ∈ R and K ≠ -1; Take points P1(X P1 , Y P1 , H P1 ), P2(X P2 , Y P2 , H P2 ), and P(X P , Y P , H P ). The points P1, P2, and P are the same point of the drill bit on the torsional surface. The point P2 is the upper definite ratio dividing point of the line segment MN, and the point P1 is the upper definite ratio dividing point of the line segment EF.

2. The method for calculating the drilling direction of the twisted surface excavation face in the calculation project according to claim 1, characterized in that, The specific process of the said Step 3 is: Obtained from the spatial vector calculation formula: , , let , ( ), substituting specific numerical values gives: （1）， That is, the coordinates of point N are (2), Similarly, the coordinates of point M are (3), Then (4), When Points N and M are the midpoints of line segments AB and DC respectively; when Points N and M are the internal division points of line segments AB and DC respectively; when Points N and M are the internal division points of line segments AB and DC respectively; when Points N and M are points A and D respectively; Similarly, let , , then we have: The coordinates of point F are (5), The coordinates of point E are (6), Then (7).

3. The method for calculating the drilling direction of the torsional surface excavation face in the calculation project according to claim 2, characterized in that, The said Step 3 also includes: Furthermore, since P1 is a point on the line segment FE, and , then we have: The coordinates of are (8); Further, since is a point on line segment NM, and , then: coordinates ; (9).

4. The method for drilling direction of the twisted surface excavation face in the calculation project according to claim 3, characterized in that, The specific process of the said Step 4 is: Since P1, P2, and P are all the same point of the drill bit on the torsional surface, combining formulas (8) and (9), the coordinates of the drill bit point P can be obtained as: （10）， Furthermore, from formulas (2), (3), (5), (6), (8), (9), and formula (10), the coordinate equation of the drill bit point P on the torsional surface can be obtained: （11）。 5. The method for calculating the drilling direction of the twisted surface excavation face in the calculation project according to claim 4, characterized in that, The specific process of the said Step 5 is: Take the actual measurement point of the drill tail as T(X T 、Y T 、H T ), and take the design coordinates of the drill tail on the torsion surface as T'(X T′ 、Y T′ 、H T′ ); Define the drill pipe length ; ; Point P is the intersection of MN and EF, T' is on the generatrix EF, is the cosine value of the angle ; Then , , then there is: （12）， When time At this time ; When time At this time ; Furthermore, let , , and we get: （13）， Further, , the solvable point coordinates are: （14）。 6. The method for drilling direction of the twisted surface excavation face in the calculation project according to claim 5, characterized in that, The specific process of the said Step 6 is: The measured drill pipe obtained in step 5 and the included angle and the coordinates of the drill tail point T on are used. With the drill bit point P fixed, by adjusting the rotation angle of the drill tail so that the drill tail T coincides with the point on the generatrix FE, which is the drilling direction of the drill pipe.

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