Education teaching test method based on deep hole machining deviation prevention
By introducing the principle of hydrodynamic lubrication and an anti-deviation device into deep hole machining equipment, the lack of experimental teaching equipment for deep hole machining has been solved, students' understanding and innovation abilities have been enhanced, and machining accuracy and stability have been improved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-02-13
- Publication Date
- 2026-04-10
AI Technical Summary
The lack of experimental teaching equipment for deep hole machining courses makes it difficult for students to understand and practice deep hole machining technology.
An anti-deviation device based on the principle of hydrodynamic lubrication is adopted, including built-in and external anti-deviation devices. Through the centering device and self-correcting guide sleeve, combined with the support of the liquid film and pressure difference, the tool system can achieve self-centering, self-correction and self-guiding, and prevent deviation during deep hole machining.
It improved students' understanding and innovation in deep hole machining, enhanced their interest in learning, improved the stress state of the tool system, and improved machining accuracy and stability.
Smart Images
Figure CN121838567A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of mechanical deep hole machining, in particular to an education and teaching test method based on deep hole machining deviation prevention. BACKGROUND
[0002] Deep Hole Machining Technology is a professional course of mechanical or near mechanical majors in some colleges and universities. Modern Deep Hole Machining Technology published by Wang Jun is the main teaching material of the course. Deep Hole Machining Technology is also a postgraduate course of mechanical or near mechanical majors in some colleges and universities. Deep Hole Machining and Detection Technology written by Yu Dakuo and other researchers of Zhongbei University is a postgraduate teaching material. Deep Hole Machining and Detection Technology Innovation written by Yu Dakuo is a guide book for some college students' innovation projects. However, so far, there is still a lack of experimental teaching equipment for deep hole machining courses. SUMMARY
[0003] In view of the shortcomings of the prior art, the present application provides an education and teaching test method based on deep hole machining deviation prevention, which prevents deep hole machining deviation by using liquid dynamic pressure lubrication principle and machining guide mechanism, and provides deep hole machining equipment and test method for cultivating undergraduates and postgraduates and training deep hole machining trainees.
[0004] To achieve the above object, the present application provides the following technical scheme: An education and teaching test method based on deep hole machining deviation prevention, which adopts the following equipment for experiment: The equipment comprises a machine tool main body, a deep hole tool bar and a deep hole tool, characterized in that a feeding box is installed on the machine tool main body, a support frame is fixedly installed on the machine tool main body, a deep hole tool bar is fixedly installed at the output end of the feeding box, an oiler base is fixedly installed on the machine tool main body, an oiler main body is fixedly installed on the oiler base, the deep hole tool bar is in sliding connection with the support frame and the oiler main body, a deep hole tool is fixedly installed on the deep hole tool bar, an end cover is fixedly installed on the oiler main body, a bearing is installed on the oiler main body, a guide sleeve main body is installed on the bearing, a deviation prevention device is installed on the machine tool main body, the deviation prevention device comprises an internal deviation prevention device and / or an external deviation prevention device, the internal deviation prevention device is installed on the deep hole tool bar, the internal deviation prevention device comprises a centering device and / or a self-correction guide sleeve, the centering device is installed on the deep hole tool bar, the self-correction guide sleeve is installed on the deep hole tool bar, the external deviation prevention device comprises a center frame fixedly installed on the machine tool main body, an adjustment support sleeve is installed on the center frame, a main shaft box is installed on the machine tool main body, a motor is fixedly installed on the main shaft box, a chuck is fixedly installed at the output end of the main shaft box, and a deep hole workpiece is installed on the chuck. The experimental steps comprise: Step one: when using the built-in anti-deviation device, the deep hole tool bar is extended from the oiler, and one or more self-correcting guide sleeves are fixed on the deep hole tool bar; Step two: the centering device is fixed on the deep hole tool bar, and the deep hole tool is fixedly connected with the centering device; Step three: the tool system is fed, and the tool and the built-in anti-deviation device enter the deep hole in turn. In the deep hole, the built-in anti-deviation device provides support for the tool system. After the tool system is fed by more than one meter, it can continue to be fed or stop, so that the workpiece is separated from the oiler. The split self-correcting guide sleeve is installed on the tool bar between the workpiece and the oiler, and then the feeding is continued so that the split self-correcting guide sleeve enters the machined deep hole; Step four: when using the external anti-deviation device, start the equipment for normal machining, and observe the vibration of the machine tool. If there is an abnormality, stop immediately; Step five: measure the wall thickness difference of the machined deep hole. Four or more positions are selected near the tool using an ultrasonic thickness gauge. The positions are uniformly distributed along the circumference. The wall thickness of the deep hole is measured and the wall thickness difference of the machined deep hole is calculated; Step six: according to the wall thickness difference of the machined deep hole and the roundness error of the workpiece, adjust the screws on the support sleeve to eliminate the bending deformation of the workpiece or offset part of the bending deformation of the workpiece, and continue to machine the deep hole until the machining is completed; Step seven: when the built-in anti-deviation device and the external anti-deviation device are used at the same time, the above steps are comprehensively processed.
[0005] Preferably, in step two, the centering device is located between the cutting part of the deep hole tool and the deep hole tool bar, and the centering device has three or more protrusions with flow grooves between the protrusions.
[0006] Preferably, in step two, the self-correcting guide sleeve has protrusions and flow grooves around the circumference, and the self-correcting guide sleeve is fixed on the deep hole tool bar through threads, elastic structure or interference fit.
[0007] Preferably, in step one, the centering frame has three rollers inside, and the rollers support the adjustment support sleeve. The adjustment support sleeve is sleeved on the outside of the deep hole workpiece, and there is a gap between the inner hole of the adjustment support sleeve and the outer surface of the deep hole workpiece.
[0008] Preferably, in step six, the adjustment support sleeve is uniformly provided with adjustment screws at both ends along the circumference, and all the adjustment screws pass through the adjustment support sleeve. One end of the adjustment screw is located inside the adjustment support sleeve and contacts the outer circular surface of the deep hole workpiece, and the other end of the adjustment screw is located outside the adjustment support sleeve.
[0009] Preferably, in step two, the surface of the centering device is consistent with the overall material, or the surface has a coating or a covering layer.
[0010] Preferably, in step one, the self-correcting guide sleeve surface is consistent with the overall material, or it has a coating or a covering layer on its surface.
[0011] Preferably, in step two, the deep hole cutter includes a boring tool body, the deep hole cutter is a drill bit or a boring tool, and the deep hole cutter rod is a drill rod or a boring rod.
[0012] Preferably, the boring tool tip on the boring tool body is close to the outer surface of the workpiece, and the contact point of the boring tool tip on the boring tool body with the workpiece expands from the outside to the inside, that is, the cutting edge first cuts the material away from the bottom hole position, and then cuts the material at the bottom hole position.
[0013] Compared with the prior art, the present application has the following beneficial effects: 1. The present application can stimulate students' interest in learning, cultivate students' innovative spirit, and help deepen the understanding of the deep hole machining process for undergraduates and postgraduates by expanding the application range of dynamic pressure lubrication principle. The present application is based on the principle of liquid dynamic pressure lubrication, which is beneficial to better understanding of dynamic pressure lubrication theory for undergraduates.
[0014] 2. The present application improves the stress state of the cutter rod through the centering device and the guide sleeve, and the external correction device corrects the deep hole deflection by cleverly applying force, which is helpful for improving students' analysis ability and problem-solving ability. The improvement of the boring tool structure of the present application not only has practical engineering significance, but also can guide students to carry out technical innovation. BRIEF DESCRIPTION OF DRAWINGS
[0015] The drawings described herein are used to provide further understanding of the present application, and form a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application, and do not constitute an improper limitation on the present application. In the drawings: Figure 1 It is a schematic diagram of the machine tool of the present application; Figure 2 It is a diagram of the self-correcting drilling principle of the present application; Figure 3 It is a schematic diagram of the slot centering device of the present application; Figure 4 It is a schematic diagram of the slot centering device of the present application; Figure 5 It is a schematic diagram of the adjusting support frame of the present application; Figure 6 It is a schematic diagram of the self-correcting guide sleeve with coating of the present application; Figure 7 It is a schematic diagram of the boring tool body modification of the present application.
[0016] In the figure: 1, machine tool main body; 11, feed box; 12, support frame; 13, deep hole cutter bar; 14, oiler base; 15, oiler main body; 16, deep hole cutter; 17, end cover; 18, guide sleeve main body; 19, bearing; 21, centering device; 22, self-correcting guide sleeve; 31, centering frame; 32, adjustment support sleeve; 4, main shaft box; 41, motor; 42, chuck; 43, deep hole workpiece. DETAILED DESCRIPTION
[0017] The embodiments of the present application will be described in detail hereinafter with reference to the drawings and examples, so that the implementation process of how the present application applies technical means to solve technical problems and achieve technical effects can be fully understood and implemented.
[0018] Reference Figures 1-7 The present embodiment proposes an educational teaching test method based on deep hole machining anti-deviation, which uses the following teaching equipment for experiments: The equipment comprises a machine tool body 1, a deep hole tool bar 13 and a deep hole tool 16, characterized in that a feeding box 11 is installed on the machine tool body 1, a support frame 12 is fixedly installed on the machine tool body 1, the output end of the feeding box 11 is fixedly installed with the deep hole tool bar 13, an oiler base 14 is fixedly installed on the machine tool body 1, an oiler main body 15 is fixedly installed on the oiler base 14, and the deep hole tool bar 13 is in sliding connection with the support frame 12 and the oiler main body 15, the deep hole tool bar 13 is fixedly installed with the deep hole tool 16, an end cover 17 is fixedly installed on the oiler main body 15, a bearing 19 is installed on the oiler main body 15, a guide sleeve main body 18 is installed on the bearing 19, a deviation preventing device is installed on the machine tool body 1, the deviation preventing device comprises an internal deviation preventing device and / or an external deviation preventing device, the internal deviation preventing device is installed on the deep hole tool bar 13, the gap between the outer surface of the internal deviation preventing device and the inner wall of the machined deep hole is not greater than 1 mm after the internal deviation preventing device enters the machined deep hole, the cutting fluid is injected from the oiler main body 15 and is transported to the machined deep hole along the outer surface of the deep hole tool bar 13, when the outer diameter of the internal deviation preventing device is smaller than the diameter of the deep hole of the machined deep hole workpiece 43, the cutting fluid forms a liquid film between the wedge-shaped protruding surface of the centering device 21 and the inner wall of the deep hole of the machined deep hole workpiece 43, the thickness of the liquid film is less than 1 mm, after the self-correcting guide sleeve 22 enters the deep hole of the machined deep hole workpiece 43, for the case that the outer diameter of the self-correcting guide sleeve 22 is smaller than the diameter of the deep hole of the machined deep hole workpiece 43, a liquid film is formed between the outer surface of the self-correcting guide sleeve 22 and the inner wall of the deep hole of the machined deep hole workpiece 43, the deep hole tool bar 13 is supported by the above-mentioned liquid film, the internal deviation preventing device comprises the centering device 21 and / or the self-correcting guide sleeve 22, the centering device 21 is installed on the deep hole tool bar 13, the self-correcting guide sleeve 22 is installed on the deep hole tool bar 13, the self-correcting guide sleeve 22 can also be in a half-open style, the machined deep hole workpiece 43 can be clamped in the middle by two groups of half-open self-correcting guide sleeves 22, the external deviation preventing device comprises a center frame 31 fixedly installed on the machine tool body 1, an adjusting support sleeve 32 is installed on the center frame 31, a main shaft box 4 is installed on the machine tool body 1, a motor 41 is fixedly installed on the main shaft box 4, a chuck 42 is fixedly installed on the output end of the main shaft box 4, a deep hole workpiece 43 is installed on the chuck 42, the deep hole workpiece 43 is limited on the chuck 42 by the chuck 42, the output end of the motor 41 is connected with the main shaft box 4, the motor 41 is started to drive the linkage mechanism in the main shaft box 4 to rotate, thereby driving the deep hole workpiece 43 on the chuck 42 to rotate.
[0019] The centering device 21 is located between the cutting part of the deep hole cutter 16 and the deep hole cutter bar 13, and has three or more than three protrusions with flow channels between the protrusions, and the cutting fluid flows through the flow channels, which are straight channels or spiral channels. When the distances from the boundary points c and d of the protrusions to the center of the centering device 21 are equal, the outer surfaces of the protrusions corresponding to the boundary points c and d are circular arcs, and there is a gap between the circular arcs and the machined inner surface of the deep hole. When the cutting fluid flows into the gap, a liquid film is formed. When the cutter bar vibrates, the centering device is offset, the size of the flow channel changes, and pressure is generated, thereby correcting the deep hole cutter bar 13.
[0020] One of the outer surface structures of the protrusions of the centering device 21 is a circular arc, and the other structure has a wedge-shaped feature. When the distances from the boundary points c and d of the protrusions to the center of the centering device 21 are not equal, the outer surfaces of the protrusions corresponding to the boundary points c and d are wedge-shaped. Liquid flows into the wedge-shaped space formed by the protrusions and the machined deep hole, so that the pressure of the liquid in the wedge-shaped space increases, and the oil film with high pressure supports the deep hole cutter bar 13, thereby correcting the deep hole cutter bar 13.
[0021] The self-correcting guide sleeve 22 has protrusions and flow channels in the circumferential direction. The self-correcting guide sleeve 22 is fixed to the deep hole cutter bar 13 by threads, elastic structure or interference fit. The protrusion part of the centering device 21 or the self-correcting guide sleeve 22 is a variable cross-section structure or an equal cross-section structure. When it is a variable cross-section structure, it is a conical shape, and the distance from the large end of the conical surface to the cutter is less than the distance from the small end of the conical surface to the cutter. When the material of the outer surface of the protrusion part is different from the overall material, the connection between the outer surface material and the overall material is screw connection or bonding. When the material of the outer surface of the protrusion is a non-metallic material, the optional part of the material includes reinforced polytetrafluoroethylene, nylon, polyformaldehyde, wood, bakelite. When the outer surface of the protrusion part is a metal material, it is treated by carburizing and nitriding, and a groove can be opened on the outer surface of the protrusion part, and a metal or non-metal material can be fixed in the groove.
[0022] The center frame 31 is internally provided with three rollers, and the rollers support an adjusting support sleeve 32, the adjusting support sleeve 32 is sleeved outside the deep hole workpiece 43, there is a gap between the inner hole of the adjusting support sleeve 32 and the outer surface of the deep hole workpiece 43, the two ends of the adjusting support sleeve 32 are uniformly provided with adjusting screws in the circumferential direction, and all the adjusting screws pass through the adjusting support sleeve 32, one end of the adjusting screw is located in the interior of the adjusting support sleeve 32 and contacts the outer circular surface of the deep hole workpiece 43, and the other end of the adjusting screw is located outside the adjusting support sleeve 32, when the adjusting screw is rotated, the acting point of one end thereof is located on the outer circular surface of the deep hole workpiece 43, and the acting force changes the relative position of the deep hole workpiece 43 and the center frame 31, the angle of rotation of the adjusting screw is determined by the wall thickness of the deep hole of the machined deep hole workpiece 43, the center frame 31 and the adjusting support sleeve 32 can be one set or multiple sets, the surface of the centering device 21 is consistent with the overall material, or the surface has a coating or a covering layer, the surface of the self-correcting guide sleeve 22 is consistent with the overall material, or the surface has a coating or a covering layer.
[0023] The deep hole cutter 16 comprises a boring tool body, for deep hole boring, the boring tool tip is currently used on the right side, and the irregular groove caused by the boring tool tip during deep hole machining can cause large vibration of the deep hole cutter bar 13, in the application, the boring tool tip of the boring tool body is close to the outer surface of the workpiece, in the initial stage of boring, the contact point of the boring tool blade and the workpiece expands from the outside to the inside, and the blade tip first cuts the part of the workpiece end surface far away from the hole wall in the initial stage of boring, the workpiece end surface is previously turned flat, when the deep hole boring starts, the cutting force is uniform, so that the deep hole cutter bar 13 will not be vibrated, the deep hole cutter 16 is a drill bit or a boring tool, the deep hole cutter bar 13 is a drill rod or a boring rod, the deep hole cutter 16 is a drill bit or a boring tool, and the deep hole cutter bar 13 is a drill rod or a boring rod.
[0024] Working Principle: First, the self-aligning guide sleeve 22 is assembled at the rightmost end of the oil supply body 15. Then, the deep hole tool 16, centerer 21, and deep hole tool holder 13 are assembled together. After assembly, the tightness of the connections of each component needs to be checked. Finally, the workpiece is calibrated to lay the foundation for subsequent precise machining. After starting the machining equipment, in the initial stage, the self-aligning guide sleeve 22 and centerer 21 provide dual guidance and alignment. The centerer 21 has four protruding structures evenly arranged around its circumference. These protruding structures can be wedge-shaped or cylindrical. When the cutting fluid is injected from the oil supply body 15 and transported to the hole along the deep hole tool holder 13, the cutting fluid forms a stable wedge-shaped oil film on the wedge-shaped protrusion surface of the centerer 21. This wedge-shaped oil film not only provides lubrication and cooling but also utilizes the oil film pressure difference to achieve the self-centering, self-aligning, and self-guiding functions of the tool system, effectively suppressing tool runout and hole position deviation in the initial drilling stage. When machining reaches a certain stage... When the depth is fixed, the self-correcting guide sleeve 22 enters the hole along with the deep hole tool holder 13. The self-correcting guide sleeve 22 also has four protrusions (wedge-shaped or cylindrical) around its circumference. At this time, the centering device 21 continues to play a stabilizing role at the end of the drill bit, ensuring the machining stability of the cutting edge. The self-correcting guide sleeve 22 forms an intermediate support in the middle area of the deep hole tool holder 13. Through its protruding structure and the oil film formed by the cutting fluid, it further enhances the guiding accuracy and correction capability of the entire tool system, ensuring the straightness and coaxiality requirements of the entire deep hole machining process. When the machined deep hole is long, the equipment is stopped and the oil supply body 15 is moved while keeping the position of the deep hole tool 16 unchanged, thereby exposing the deep hole tool holder 13. The two sets of semi-open self-correcting guide sleeves 22 are locked on the deep hole tool holder 13. After resetting the oil supply body 15, the machine is started, and the self-correcting guide sleeve 22 continues to enter the deep hole to support the deep hole tool holder 13. This operation can be repeated when the machined deep hole is long.
[0025] It should be noted that, in this document, the terms “comprising,” “including,” or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.
[0026] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.
Claims
1. A teaching test method based on deep hole machining deviation prevention, characterized in that, The experiment is carried out by using the following equipment: The equipment comprises a machine tool main body (1), a deep hole tool bar (13) and a deep hole tool (16), characterized in that the machine tool main body (1) is provided with a feeding box (11), the machine tool main body (1) is fixedly provided with a support frame (12), the output end of the feeding box (11) is fixedly provided with the deep hole tool bar (13), the machine tool main body (1) is fixedly provided with an oiler base (14), the oiler base (14) is fixedly provided with an oiler main body (15), and the deep hole tool bar (13) is in sliding connection with the support frame (12) and the oiler main body (15), the deep hole tool bar (13) is fixedly provided with the deep hole tool (16), the oiler main body (15) is fixedly provided with an end cover (17), the oiler main body (15) is provided with a bearing (19), the bearing (19) is provided with a guide sleeve main body (18), the machine tool main body (1) is provided with a deviation prevention device, the deviation prevention device comprises an internal deviation prevention device and / or an external deviation prevention device, the deep hole tool bar (13) is provided with the internal deviation prevention device, the internal deviation prevention device comprises a centering device (21) and / or a self-correcting deviation guide sleeve (22), the deep hole tool bar (13) is provided with the centering device (21), the deep hole tool bar (13) is provided with the self-correcting deviation guide sleeve (22), the external deviation prevention device comprises a center frame (31) fixedly arranged on the machine tool main body (1), the center frame (31) is provided with an adjusting support sleeve (32), the machine tool main body (1) is provided with a main shaft box (4), the main shaft box (4) is fixedly provided with a motor (41), the output end of the main shaft box (4) is fixedly provided with a chuck (42), the chuck (42) is provided with a deep hole workpiece (43); The experimental steps comprise: Step one: when the internal deviation prevention device is used, the deep hole tool bar (13) is extended from the oiler, and one or more self-correcting deviation guide sleeves (22) are fixed to the deep hole tool bar (13); Step two: the centering device (21) is fixed to the deep hole tool bar (13), and the deep hole tool (16) is fixedly connected with the centering device (21); Step three: the tool system is fed, and the tool and the internal deviation prevention device enter the deep hole in sequence, the internal deviation prevention device provides support for the tool system in the deep hole, and after the tool system is fed by more than 1 meter, the feeding can be continued or the machine is stopped to separate the workpiece from the oiler, the split self-correcting deviation guide sleeve (22) is arranged on the tool bar between the workpiece and the oiler, and then the feeding is continued to make the split self-correcting deviation guide sleeve (22) enter the machined deep hole; Step four: when the external deviation prevention device is used, the equipment is started to normally process, the vibration of the machine tool is observed, and the machine is immediately stopped if an abnormality occurs; Step five: the wall thickness difference of the machined deep hole is measured, four or more positions are selected by using an ultrasonic thickness gauge near the tool, the positions are uniformly distributed along the circumference, the wall thickness of the deep hole wall is measured, and the wall thickness difference of the machined deep hole is calculated; Step six: according to the wall thickness difference of the deep hole being processed and the roundness error of the workpiece, adjust the screws on the support sleeve (32) to eliminate the bending deformation of the workpiece or offset part of the bending deformation of the workpiece, and continue to process the deep hole until the processing is completed. Step seven: when the built-in anti-deviation device and the external anti-deviation device are used at the same time, the above steps are comprehensively processed.
2. The education and teaching test method based on deep hole machining deviation prevention according to claim 1, characterized in that, In step two, the centering device (21) is located between the cutting part of the deep hole cutter (16) and the deep hole cutter bar (13), and the centering device (21) has three or more than three protrusions, and the protrusions are flow grooves.
3. The education and teaching test method based on deep hole machining deviation prevention according to claim 1, characterized in that, In step two, the self-correction guide sleeve (22) has protrusions and flow grooves in the circumferential direction, and the self-correction guide sleeve (22) is fixed on the deep hole cutter bar (13) through threads, elastic structure or interference fit.
4. The education and teaching test method based on deep hole machining deviation prevention according to claim 1, characterized in that, In step one, the center frame (31) has three rollers inside, and the rollers support and adjust the support sleeve (32), the support sleeve (32) is sleeved outside the deep hole workpiece (43), and there is a gap between the inner hole of the support sleeve (32) and the outer surface of the deep hole workpiece (43).
5. The education and teaching test method based on deep hole machining deviation prevention according to claim 1, characterized in that, In step six, the two ends of the adjustment support sleeve (32) are uniformly provided with adjusting screws in the circumferential direction, and all the adjusting screws pass through the adjustment support sleeve (32), one end of the adjusting screw is located inside the adjustment support sleeve (32) and contacts the outer circular surface of the deep hole workpiece (43), and the other end of the adjusting screw is outside the adjustment support sleeve (32).
6. The education and teaching test method based on deep hole machining deviation prevention according to claim 1, characterized in that, In step two, the surface of the centering device (21) is consistent with the overall material, or the surface has a coating or a covering layer.
7. The education and teaching test method based on deep hole machining deviation prevention according to claim 1, characterized in that, In step one, the surface of the self-correction guide sleeve (22) is consistent with the overall material, or the surface has a coating or a covering layer.
8. The education and teaching test method based on deep hole machining deviation prevention according to claim 1, characterized in that, In step two, the deep hole cutter (16) includes a boring cutter body (5), and the deep hole cutter (16) is a drill bit or a boring cutter, and the deep hole cutter bar (13) is a drill rod or a boring rod.
9. The education and teaching test method based on deep hole machining deviation prevention according to claim 8, characterized in that, The boring cutter tip on the boring cutter body (5) is close to the outer surface of the workpiece, and the contact point of the boring cutter tip on the boring cutter body (5) with the workpiece expands from the outside to the inside, that is, the cutting edge first cuts off the material away from the bottom hole position, and then cuts off the material at the bottom hole position.