Device and method for improving verticality of large-diameter bored piles

Abstract

The present invention provides a device and method for improving the verticality of large-diameter bored piles, comprising: a clamping ring 1, comprising two clamping arc plates 1, the inner diameter of which matches the diameter of the drill rod, and the two clamping arc plates 1 being connected by bolts; a clamping ring 2, comprising two clamping arc plates 2, the inner diameter of which matches the diameter of the annular groove of the drill rod, and the two clamping arc plates 2 being connected by bolts; and a plurality of support rods, the two ends of which are connected to the side walls of the clamping ring 1 through adjustment assemblies. The present invention has the following beneficial effects: when the device is pushed downward along with the drill rod, the outer support rods contact the hole wall formed by the drill bit. If the drill rod deviates from the vertical direction due to various stress conditions, the reaction force formed between the support rods and the hole wall can ensure that the drilling direction of the drill rod returns to the predetermined vertical direction, thereby playing a guiding role and ensuring the verticality of large-diameter boreholes.

Description

Technical Field

[0001] The invention belongs to the technical field of drilling, and in particular relates to a device and a method for improving the verticality of large-diameter bored piles. Background Art

[0002] During the construction process, various high-rise buildings and large bridges often use bored cast-in-place piles as their foundation, especially large-diameter bored cast-in-place piles. Unlike oil drilling, large-diameter bored cast-in-place piles require a drill assembly with a larger annular gap, and the drill string in the hole is in a complex stress state; therefore, during the drilling process of the drill bit, large-diameter drill holes often fail to meet the verticality requirements. Currently, the solution to the problem of non-compliant verticality is mostly to start with process parameters such as light pressure, slow rotation, and hanging driving, but these measures inevitably lead to low drilling efficiency. Summary of the Invention

[0003] In view of this, the present invention aims to provide a device and method for improving the verticality of large-diameter bored piles, in order to solve at least one of the above-mentioned technical problems.

[0004] To achieve the above object, the technical solution of the present invention is achieved as follows:

[0005] In one aspect, the present invention provides a device for improving the verticality of large-diameter bored piles, comprising:

[0006] Clamping ring 1: The clamping ring 1 includes two clamping arc plates 1, the inner diameter of the clamping arc plates 1 matches the diameter of the drill rod, and the two clamping arc plates 1 are connected by bolts to clamp the drill rod;

[0007] Clamping ring 2: The clamping ring 2 includes two clamping arc plates 2, the inner diameter of which matches the diameter of the annular groove of the drill rod. The two clamping arc plates 2 are connected by bolts, and the two clamping arc plates 1 clamp the annular groove of the drill rod;

[0008] Multiple support rods, both ends of the support rods are connected to the side wall of the clamp ring 1 through an adjustment component, the adjustment component is used to adjust the distance between the support rods and the drill rod, and the clamp ring 2 is connected to the support rods through a telescopic component.

[0009] Furthermore, the inner side of the first clamping arc plate is provided with anti-slip grooves, and the inner side of the second clamping arc plate is provided with anti-slip grooves.

[0010] Furthermore, the second clamping ring is provided with a gasket ring, and the gasket ring includes two limiting arc plates, the inner diameter of the limiting arc plates matches the diameter of the annular groove of the drill rod, and the two limiting arc plates are connected by bolts, and the two limiting arc plates clamp the annular groove of the drill rod;

[0011] The backing ring is installed between the second clamp ring and the side wall of the annular groove;

[0012] There are many types of limit arc plates, and different types of limit arc plates have different heights, which are used to adjust the distance between the clamping ring 2 and the drill bit;

[0013] The inner side of the limiting arc plate is provided with anti-slip grooves.

[0014] Furthermore, a mounting tube 1 is provided on the side wall of the clamping arc plate 2, and a mounting tube 2 matching the mounting tube 1 is fixed on the limiting arc plate. An insertion rod is fixed on the inner side of one end of the mounting tube 2, and the diameter of the insertion rod matches the inner diameter of the mounting tube 1.

[0015] Furthermore, both ends of the support rod are bent toward the axis direction of the clamping ring 1 to form guide plates.

[0016] Furthermore, the support rod is a structural member made of wear-resistant steel.

[0017] Furthermore, the adjustment assembly includes a receiving tube and a plug rod matching the receiving tube, the plug rod is installed on the inner side of the receiving tube, the receiving tube is fixedly connected to the clamp ring, the plug rod is fixedly connected to the support rod, a strip hole is opened on one side wall of the receiving tube and arranged along the length direction of the receiving tube, a plurality of limiting holes are opened on the receiving tube, and the plurality of limiting holes are arranged perpendicular to the strip holes and arranged along the length direction of the receiving tube;

[0018] A limit block is provided on the plug rod 1, one end of the limit block is rotatably connected to the plug rod 1, and the other end is fixedly provided with a limit pin matching the limit hole, and the limit pin is installed on the inner side of the limit hole. A spring sheet is provided corresponding to the end surface of the limit block away from the limit hole, one end of the spring sheet is fixedly connected to the plug rod 1, and the other end presses against the end surface of the limit block away from the limit hole.

[0019] Furthermore, there are two clamp rings one, and there is one clamp ring two. The two ends of the support rod are respectively connected to the two clamp rings one through an adjustment component. The clamp ring two is installed between the two clamp rings one. The telescopic component includes a receiving tube two and a plug-in rod two. The receiving tube two is fixed on the side wall of the clamp ring two, and the support rod is fixed with a plug-in rod two matching the receiving tube two. The plug-in rod two is installed on the inner side of the receiving tube two.

[0020] Another aspect of the present invention provides a method for applying the device for improving the verticality of large-diameter bored piles described in the first aspect above, wherein the distance between the device and the drill bit is adjusted according to the angular velocity of the drill rod, the axial pressure of the drill rod, and the linear weight.

[0021] Furthermore, the distance between the device and the drill bit satisfies the following formula:

[0022] 0.319qw 2 L 4 -qL 3 +2PL 2 -80.06EI=0;

[0023] in:

[0024] L is the distance between the device and the drill bit;

[0025] q is the line weight;

[0026] w is the angular velocity of the drill pipe;

[0027] P is the axial pressure of the drill pipe;

[0028] E is Young's elastic modulus;

[0029] I is the moment of inertia of the drill pipe cross section.

[0030] Compared with the prior art, the device for improving the verticality of large-diameter bored piles described in the present invention has the following beneficial effects:

[0031] (1) The present invention relates to a device for improving the verticality of large-diameter bored piles. When the device is pushed downward along with the drill rod, the outer support rod contacts the hole wall formed by the drill bit. If the drill rod deviates from the vertical direction due to various stress conditions, the reaction force formed between the support rod and the hole wall can ensure that the drilling direction of the drill rod returns to the predetermined vertical direction, thereby playing a guiding role and ensuring the verticality of the large-diameter drill hole.

[0032] (2) The device for improving the verticality of large-diameter bored piles described in the present invention can adjust the distance between the support rod and the drill rod according to the diameter of the drill bit, so that the distance between the outer side of the support rod and the drill rod matches the radius of the drill bit. It is suitable for working conditions of drilling holes of different diameters, thereby improving the scope of application of the device. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The accompanying drawings, which constitute part of the present invention, are provided to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an undue limitation of the present invention. In the accompanying drawings:

[0034] Figure 1 This is a schematic diagram of the three-dimensional structure of the device in use according to an embodiment of the present invention;

[0035] Figure 2 A schematic diagram of the three-dimensional structure of the device according to an embodiment of the present invention;

[0036] Figure 3 This is a schematic diagram of the three-dimensional structure of the upper clamping ring according to an embodiment of the present invention;

[0037] Figure 4 This is a schematic diagram of the three-dimensional structure of the lower clamping ring according to an embodiment of the present invention;

[0038] Figure 5 This is a schematic diagram of the three-dimensional structure of the gasket ring according to an embodiment of the present invention;

[0039] Figure 6 A schematic cross-sectional view of the device according to an embodiment of the present invention;

[0040] Figure 7 The embodiment of the present invention Figure 6 Schematic diagram of the structure at A in the middle;

[0041] Figure 8 This is a schematic diagram of the three-dimensional structure of the adjustment component according to an embodiment of the present invention;

[0042] Figure 9 This is a schematic diagram of a three-dimensional structure of a connecting rod according to an embodiment of the present invention;

[0043] Figure 10 This is a schematic diagram of the cross-sectional structure of the adjustment component according to an embodiment of the present invention.

[0044] Description of reference numerals:

[0045] 1. Drill bit; 2. Drill rod; 3. Clamping ring 1; 4. Clamping ring 2; 5. Support rod; 6. Adjustment assembly; 7. Gasket; 8. Telescopic assembly; 301. Clamping arc plate 1; 401. Clamping arc plate 2; 402. Mounting tube 1; 501. Guide plate; 701. Limiting arc plate; 702. Mounting tube 2; 703. Insert rod; 601. Receiver tube 1; 602. Connecting rod 1; 603. Limit block; 604. Spring sheet; 60201. Limit hole; 60202. Strip hole; 60301. Limit pin. DETAILED DESCRIPTION

[0046] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0047] The present invention will be described in detail below with reference to the accompanying drawings and in conjunction with embodiments.

[0048] Example 1:

[0049] like Figures 1-10 As shown, a device for improving the verticality of large-diameter bored piles,

[0050] The device comprises: a clamping ring 1 (3), which includes two curved clamping plates 1 (301), whose inner diameter matches the diameter of the drill rod 2. These plates are bolted together to clamp the drill rod 2. A clamping ring 2 (4), which includes two curved clamping plates 2 (401), whose inner diameter matches the diameter of the annular groove of the drill rod 2. These plates are bolted together to clamp the annular groove of the drill rod 2. A plurality of support rods 5 are connected at both ends to the sidewalls of the clamping ring 1 (3) via adjustment assemblies 6, which are used to adjust the distance between the support rods 5 and the drill rod 2. The clamping ring 2 (4) is connected to the support rods 5 via telescoping assemblies 8. There are four support rods 5, evenly spaced circumferentially along the axis of the drill rod 2.

[0051] The inner side of the clamping arc plate 1 301 is provided with anti-skid lines, and the inner side of the clamping arc plate 2 401 is provided with anti-skid lines. The anti-skid lines improve the friction.

[0052] A corresponding gasket ring 7 is provided to the clamping ring 2 4, and the gasket ring 7 includes two limiting arc plates 701. The inner diameter of the limiting arc plates 701 matches the diameter of the annular groove of the drill rod 2. The two limiting arc plates 701 are connected by bolts, and the two limiting arc plates 701 clamp the annular groove of the drill rod 2; the gasket ring 7 is installed between the clamping ring 2 4 and the side wall of the annular groove; there are various models of limiting arc plates 701, and different models of limiting arc plates 701 have different heights, which are used to adjust the distance between the clamping ring 2 4 and the drill bit 1; the inner side of the limiting arc plate 701 is provided with anti-slip grooves.

[0053] A mounting tube 1 402 is provided on the side wall of the clamping arc plate 2 401 , and a mounting tube 2 702 matching the mounting tube 1 402 is fixed on the limiting arc plate 701 , and an insertion rod 703 is fixed on the inner side of one end of the mounting tube 2 702 , and the diameter of the insertion rod 703 matches the inner diameter of the mounting tube 1 402 .

[0054] Both ends of the support rod 5 are bent toward the axis direction of the upward clamping ring to form a guide plate 501. The guide plates 501501 play a guiding role in the process of the support rod 5 moving up and down.

[0055] The support rod 5 is a structural member made of wear-resistant steel, and the support rod 5 made of wear-resistant steel prolongs the service life of the device.

[0056] The adjustment component 6 includes a receiving tube 601, a plug-in rod 602 matching the receiving tube 601, the plug-in rod 602 is installed on the inner side of the receiving tube 601, the receiving tube 601 is fixedly connected to the clamp ring 3, the plug-in rod 602 is fixedly connected to the support rod 5, and a strip hole 60202 arranged along the length direction of the receiving tube 601 is opened on the side wall of the receiving tube 601, and a plurality of limiting holes 60201 are opened on the receiving tube 601, and the plurality of limiting holes 60201 are arranged perpendicular to the strip hole 60202 and along the receiving tube. A 601 is arranged in the length direction; a limit block 603 is provided on the connecting rod 1 602, one end of the limit block 603 is rotatably connected to the connecting rod 1 602, and the other end is fixed with a limit pin 60301 matching the limit hole 60201, and the limit pin 60301 is installed on the inner side of the limit hole 60201, and a spring piece 604 is provided corresponding to the end surface of the limit block 603 away from the limit hole 60201, and one end of the spring piece 604 is fixedly connected to the connecting rod 1 602, and the other end is pressed against the end surface of the limit block 603 away from the limit hole 60201. When it is necessary to adjust the distance between the support rod 5 and the drill rod 2, move the limit pin 60301 into the strip hole 60202 (the spring sheet 604 is deformed during this process). At this time, the connecting rod 602 can slide inside the receiving tube 601. When it slides to the specified position, under the action of the elastic force of the spring sheet 604, the limit pin 60301 is inserted into the limit hole 60201 to complete the distance adjustment between the support rod 5 and the drill rod 2. The distance between the support rod 5 and the drill rod 2 can be adjusted according to the diameter of the drill bit 1, so that the distance between the outer side of the support rod 5 and the drill rod 2 matches the radius of the drill bit 1, which is suitable for working conditions of drilling holes of different diameters, thereby improving the applicability of the device.

[0057] There are two clamping rings 1 (3) and one clamping ring 2 (4). The two ends of the support rod 5 are connected to the two clamping rings 1 (3) via an adjustment assembly 6. Clamping ring 2 (4) is installed between the two clamping rings 1 (3). The telescopic assembly 8 includes a second receiving tube and a second plug-in rod. The second receiving tube is fixed to the side wall of the second receiving tube, and the second plug-in rod is fixed to the support rod 5. The plug-in rod is installed inside the second receiving tube. The second receiving tube is a square tube, and the plug-in rod is a square rod. The telescopic assembly 8 withstands forces along the axis of the drill rod 2, while the adjustment assembly 6 withstands forces perpendicular to the axis of the drill rod 2 and does not withstand forces along the axis of the drill rod 2, thus extending the service life of the device.

[0058] Working process:

[0059] When this solution is implemented, the distance between the device and the drill bit 1 is adjusted according to the rotational angular velocity of the drill rod 2, the axial pressure of the drill rod 2, and the linear weight. Then, a spacer ring 7 of corresponding length is selected, and the insertion rod 703 of the limiting arc plate 701 is inserted into the mounting tube 1 402. (If the height of one limiting arc plate 701 is insufficient, an additional limiting arc plate 701 can be added, and the insertion rod 703 of the additional limiting arc plate 701 is inserted into the mounting hole 2 of the adjacent limiting arc plate 701). Then connect the two clamping arc plates 301 with bolts, clamp the drill rod 2 with the two clamping arc plates 301, and then connect the two clamping arc plates 401 and the limiting arc plates 701 in turn. The two clamping arc plates 401 clamp the annular grooves of the drill rod 2, and the two limiting arc plates 701 clamp the annular grooves of the drill rod 2. At this time, the limiting arc plates 701 play an axial limiting role for the lower clamping ring 4, and the connecting rod 703 plays a radial limiting role for the lower clamping ring 4.

[0060] When the device is pushed downward along with the drill rod 2, the outer support rod 5 contacts the hole wall formed by the drill bit 1. If the drill rod 2 deviates from the vertical direction due to various stress conditions, the reaction force formed between the support rod 5 and the hole wall can ensure that the drilling direction of the drill rod 2 returns to the predetermined vertical direction, playing a guiding role and ensuring the verticality of large-diameter drilling holes.

[0061] Example 2:

[0062] A method for improving the verticality of large-diameter bored piles using the device described in the first embodiment above, wherein the distance between the device and the drill bit 1 is adjusted according to the rotational angular velocity of the drill rod 2, the axial pressure of the drill rod 2, and the linear weight.

[0063] The distance between the device and the drill bit 1 satisfies the following formula:

[0064] 0.319qw 2 L 4 -qL 3 +2PL 2 -80.06EI=0;

[0065] in:

[0066] L is the distance between the device and the drill bit;

[0067] q is the line weight;

[0068] w is the angular velocity of the drill pipe;

[0069] P is the axial pressure of the drill pipe;

[0070] E is Young's elastic modulus;

[0071] I is the moment of inertia of the drill pipe cross section.

[0072] Buckling curve equation: y = a(x 2 +bx+c)sin(πx / L),

[0073] x is the circumferential coordinate parallel to the drill pipe axis, y is the radial coordinate perpendicular to the drill pipe axis,

[0074] Substituting x = 0, y = 0, the derivative of y is 0 and x = L, y = 0, the derivative of y is 0 into the buckling shape curve equation, we get b = -L, c = 0;

[0075] Buckling curve equation: y = a(x 2 -Lx)sin(πx / L);

[0076] Elastic potential energy of drill pipe

[0077] Bending of drill pipe

[0078] The weight of the drill pipe

[0079] Centrifugal force of the device Here g is taken as 9.8.

[0080] Also V=W, calculated as: 0.319qw 2 L 4 -qL 3 +2PL 2 -80.06EI=0.

[0081] When the linear weight, the rotational angular velocity of the drill rod, and the axial pressure of the drill rod change, the distance between the adjustment device and the drill bit can ensure the verticality of the drill hole.

[0082] From the above formula, it can be seen that when the angular velocity of rotation increases, the distance between the device and the drill bit should decrease; when the axial pressure of the drill rod increases, the distance between the device and the drill bit should increase; when the linear weight increases, the distance between the device and the drill bit should decrease.

[0083] Those skilled in the art will appreciate that the units and method steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the above description has generally described the components and steps of each example according to their functions. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0084] In the several embodiments provided in this application, it should be understood that the disclosed methods and systems can be implemented in other ways. For example, the division of the units described above is only a logical function division, and there may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. The above-mentioned units may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the embodiment of the present invention.

[0085] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or make equivalent replacements for some or all of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present invention, and they should all be included in the scope of the claims and description of the present invention.

[0086] The above description is only a preferred embodiment of the present invention and is not intended to limit 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 device for improving the verticality of large-diameter bored piles, characterized in that: include: Clamping ring 1 (3): the clamping ring 1 (3) comprises two clamping arc plates 1 (301), the inner diameter of the clamping arc plates 1 (301) matches the diameter of the drill rod (2), the two clamping arc plates 1 (301) are connected by bolts, and the two clamping arc plates 1 (301) clamp the drill rod (2); Clamping ring 2 (4): the clamping ring 2 (4) comprises two clamping arc plates 2 (401), the inner diameter of the clamping arc plates 2 (401) matches the diameter of the annular groove of the drill rod (2), the two clamping arc plates 2 (401) are connected by bolts, and the two clamping arc plates 1 (301) clamp the annular groove of the drill rod (2); A plurality of support rods (5), both ends of the support rods (5) are connected to the side walls of the clamping ring (3) via an adjustment assembly (6), the adjustment assembly (6) is used to adjust the distance between the support rods (5) and the drill rod (2), and the clamping ring (4) is connected to the support rods (5) via a telescopic assembly (8); The clamping ring 2 (4) is provided with a gasket (7) correspondingly, and the gasket (7) comprises two limiting arc plates (701), the inner diameter of the limiting arc plates (701) matches the diameter of the annular groove of the drill rod (2), and the two limiting arc plates (701) are connected by bolts, and the two limiting arc plates (701) clamp the annular groove of the drill rod (2); The backing ring (7) is installed between the clamp ring 2 (4) and the side wall of the annular groove; There are various models of the limiting arc plate (701), and different models of the limiting arc plate (701) have different heights, and are used to adjust the distance between the clamp ring 2 (4) and the drill bit (1); The inner side of the limiting arc plate (701) is provided with anti-slip lines; The adjustment component (6) includes a receiving tube (601) and a plug-in rod (602) matched with the receiving tube (601), the plug-in rod (602) is installed on the inner side of the receiving tube (601), the receiving tube (601) is fixedly connected to the clamp ring (3), the plug-in rod (602) is fixedly connected to the support rod (5), the side wall of the receiving tube (601) is provided with a strip hole (60202) arranged along the length direction of the receiving tube (601), the receiving tube (601) is provided with a plurality of limiting holes (60201), the plurality of limiting holes (60201) are arranged perpendicular to the strip hole (60202) and arranged along the length direction of the receiving tube (601); A limit block (603) is provided on the plug rod (602), one end of the limit block (603) is rotatably connected to the plug rod (602), and the other end is fixedly provided with a limit pin (60301) that matches the limit hole (60201), and the limit pin (60301) is installed on the inner side of the limit hole (60201). A spring sheet (604) is provided corresponding to the end surface of the limit block (603) away from the limit hole (60201), one end of the spring sheet (604) is fixedly connected to the plug rod (602), and the other end is pressed against the end surface of the limit block (603) away from the limit hole (60201).

2. The device for improving the verticality of large-diameter bored piles according to claim 1, characterized in that: The inner side of the first clamping arc plate (301) is provided with anti-skid lines, and the inner side of the second clamping arc plate (401) is provided with anti-skid lines.

3. The device for improving the verticality of large-diameter bored piles according to claim 1, characterized in that: A mounting tube 1 (402) is fixedly provided on the side wall of the clamping arc plate 2 (401), a mounting tube 2 (702) matching the mounting tube 1 (402) is fixedly provided on the limiting arc plate (701), an insert rod (703) is fixedly provided on the inner side of one end of the mounting tube 2 (702), and the diameter of the insert rod (703) matches the inner diameter of the mounting tube 1 (402).

4. The device for improving the verticality of large-diameter bored piles according to claim 1, characterized in that: Both ends of the support rod (5) are bent toward the axis direction of the clamp ring (3) to form a guide plate (501).

5. The device for improving the verticality of large-diameter bored piles according to claim 1, characterized in that: The support rod (5) is a structural member made of wear-resistant steel.

6. The device for improving the verticality of large-diameter bored piles according to claim 1, characterized in that: There are two clamp rings (3) and one clamp ring (4). The two ends of the support rod (5) are respectively connected to the two clamp rings (3) through an adjustment component (6). The clamp ring (4) is installed between the two clamp rings (3). The telescopic component (8) includes a receiving tube (2) and a plug-in rod (2). The side wall of the clamp ring (4) is fixed with a receiving tube (2). The support rod (5) is fixed with a plug-in rod (2) that matches the receiving tube (2). The plug-in rod (2) is installed on the inner side of the receiving tube (2).

7. A method for improving the verticality of large-diameter bored piles using the device according to any one of claims 1 to 6, characterized in that: The distance between the device and the drill bit (1) is adjusted according to the rotational angular velocity of the drill rod (2), the axial pressure of the drill rod (2), and the linear weight.

8. The method according to claim 7, wherein: The distance between the device and the drill bit (1) satisfies the following formula: <h2 style=";text-align:left;direction:ltr">0.319qw<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> L<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> -qL<h2 style=";text-align:left;direction:ltr"> 3 <h2 style=";text-align:left;direction:ltr"> +2PL<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> -80.06EI=0; in: L is the distance between the device and the drill bit; q is the line weight; w is the angular velocity of the drill pipe; P is the axial pressure of the drill pipe; E is Young's elastic modulus; I is the moment of inertia of the drill pipe cross section.

Images