Cutting Structure for Casing Drilling Underreamer

Abstract

An underreamer earth-boring tool is connected to a bottom hole assembly for casing drilling applications. The underreamer has a tubular body with a longitudinal axis. Arms are pivotally mounted to the body and movable between retracted and extended positions. An array of cutting elements is mounted to each of the arms. Each of the arrays is swept back so that the cutting elements farther from the axis than others rotationally lag the others.

Description

FIELD OF THE INVENTION

This invention relates in general to earth-boring operations using the casing as a drill string, and in particular to a cutting structure of an underreamer.

BACKGROUND OF THE INVENTION

Conventional drilling of wells involves using a drill bit with cutting elements, either fixed or roller cone, connected to a drill pipe. The drill pipe is rotated either by a top drive or a hex Kelly drive. The well bore is drilled to target depth, whereby the drill string and bit are removed and replaced with thin-walled casing, which is then cemented in place.

Casing drilling completes these two steps in one operation by simultaneously drilling and casing a well. A bottom hole assembly mounted to the casing protrudes from the lower end of the casing. The bottom hole assembly has a pilot bit on its lower end and an underreamer located above. The pilot bit drills the primary hole, which is enlarged by the underreamer to a larger diameter than the casing. The underreamer has arms that pivot between a retracted and extended position, enabling the underreamer to be retrieved along with the pilot bit and other portions of the bottom hole assembly. The arms may be pivoted out by hydraulic pressure from drilling fluid being pumped from the surface. The arms are equipped with a fixed cutting structure.

Many versions of underreamer tools have been designed, tested and utilized. The criteria for the success of the tool is most dependent on its ability to reliably enlarge the primary well bore by 40-50% at an acceptable rate of penetration (ROP) similar to that obtained by a bit drilled conventionally with drill pipe. Furthermore, the underreamer has to be able to retract and be successfully tripped to the surface after drilling potentially thousands of feet of formation. Current designs are proven and work well, however a demand exists for drilling harder formations with improved ROP's.

Most underreamers have three arms, each equipped with cutting elements arranged in a wedge orientation. Cutting elements typically have a tungsten carbide base with a polycrystalline diamond “PCD” face or layer on its end. The cutting elements are normally arranged so that a line extending from the axis of rotation through the centerline is straight and is about a 20-30 angle when viewing the cutting arm in a front elevational view. Initially, all of the cutting elements are loaded equally, however non-uniform loading may quickly develop because the outer cutting elements cut more formation and move faster than the inner cutting elements. The outer cutting elements may wear to a greater degree and are more prone to lateral impact damage before the inner or more slowly moving cutting elements. In some cases, this can result in the secondary hole being drilled by the underreamer becoming under-gauge. This wear requires the underreamer to be tripped to the surface and a new assembly dressed and sent back downhole.

SUMMARY OF THE INVENTION

The underreamer of this invention has a tubular body with a longitudinal axis. Arms are pivotally mounted to the body and move relative to the body between a retracted and an extended position. An array of cutting elements is mounted to each of the arms. Each of the arrays is swept back so that the cutting elements farther from the axis than others rotationally lag the others.

Preferably, when viewed in a bottom view, each of the arrays defines a curved line from the inner cutting elements to the outer cutting elements. When viewed in a front view, each array preferably defines a curved line that extends outward and upward. To avoid tracking, preferably each of the cutting elements is located a different distance from the underreamer axis than all the other cutting elements. Preferably, at least the outermost cutting element is partially overlapped by the cutting element adjacent to it so as to reduce the load on the outermost cutting element.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a vertical sectional view of an underreamer constructed in accordance with this invention, and showing one of the arms in a retracted position.

FIG. 2 is an enlarged sectional view of a portion of the underreamer of FIG. 1, showing the arm in an extended position.

FIG. 3 is a sectional view of the underreamer of FIG. 1, taken along the line 3-3 of FIG. 2.

FIG. 4 is a bottom view of the underreamer of FIG. 1 with the arms in the extended position.

FIG. 5 is a schematic view illustrating the negative rake of one of the cutting elements of the underreamer of FIG. 1.

FIG. 6 is a front elevational view of one of the arms of the underreamer of FIG. 1.

FIG. 7 is a bottom view of the arm of FIG. 6.

FIG. 8 is a front elevational view of another one of the arms of the underreamer of FIG. 1.

FIG. 9 is a bottom view of the arm of FIG. 8.

FIG. 10 is a front elevational view of the third arm of the underreamer of FIG. 1.

FIG. 11 is a bottom view of the arm of FIG. 10.

FIG. 12 is a perspective view of an alternate embodiment of an underreamer.

FIG. 13 is a sectional view of the underreamer of FIG. 12.

FIG. 14 is a sectional view of the underreamer of FIG. 12, taken along the line 14-14 of FIG. 13.

DETAILED DESCRIPTION OF THE INVENTION

Referring to FIG. 1, underreamer 11 has a multi-piece body 13. Body 13 is tubular and has an upper end 15 that is threaded for connection into an upper portion of a bottom hole assembly (“BHA”). The BHA normally includes a drill lock assembly that releasably locks the BHA to a string of casing. The BHA might also include well survey tools, a directional steering tool, and a mud motor. Normally, the BHA can be lowered from the surface through the casing into latching engagement with a profile nipple located near the bottom of the casing string. Furthermore, typically the BHA can be retrieved while leaving the casing string in the well bore. The particular underreamer 11 shown is likely to protrude below the lower end or casing shoe of the casing some distance, which might be 50-100 ft., for example. The casing shoe may have cutting elements mounted to it. This invention is also applicable to an underreamer that locates directly at the lower end of the string of casing and interfaces with the casing shoe.

Underreamer 11 also has a lower threaded connector 17 for connection with a pilot bit (not shown). The pilot bit may be a conventional earth-boring bit of the fixed cutter type or of the rolling cone type. Body 13 has a longitudinal axis 19 through which a passage 21 extends. An orifice 20 may be located toward the lower end of passage 21 for creating a back pressure.

An actuator tube 23 is movably carried in passage 21 between an upper position shown in FIG. 1 and a lower position shown in FIG. 2. Actuator tube 23 has an enlarged head 25 on its upper end. Head 25 sealingly engages a larger diameter portion of axial passage 21. The lower end of actuator tube 23 sealingly engages a smaller diameter portion of axial passage 21. Actuator tube 23 has a passage 26 extending through it. When drilling fluid is pumped down the string of casing and into passage 21, the pressure will force head 25 and actuator tube 23 downward. The downward movement is due to the pressure differential between the drilling fluid pressure above actuator tube head 25 and the pressure below orifice 20.

Cutting arms 27, pivotally mounted to body 13, typically comprise three arms 27a, 27b, and 27c as shown in FIG. 4. The arm 27 in FIG. 1 is shown retracted and shown extended in FIG. 2. Each arm 27 has a plurality of gear teeth 29 formed in a semi-circular pattern on its inner side. Gear teeth 29 engage a rack of gear teeth 31 on actuator tube 23. Each arm 27 has a hole 34 that rotatably receives a pivot pin 33. Downward movement of gear teeth 31 act against gear teeth 33 to cause each arm 27 to pivot outward from the retracted position. While in the retracted position, each arm 27 locates within a slot 35 formed within body 13. While in the retracted position, arms 27 are substantially flush with the outer diameter of body 13. Each arm 27 has a cutting element array 37 made up of a plurality of cutting elements. In this embodiment, a cap screw 39, shown in FIG. 3, retains each pivot pin 33.

Referring to FIG. 4, in the preferred embodiment, each of the cutting elements of array 37 comprises a cutting element body 41, typically formed of tungsten carbide. Body 41 is secured to one of the arms 27, normally by brazing. A disc or face 43 is mounted to each body 41. Face 43 is preferably polycrystalline diamond (“PCD”). Face 43 is circular and flat although it could have other geometries. Referring to FIG. 5, cutting element body 41 is oriented relative to axis 19 so that its face 43 is at a negative rake angle relative to borehole bottom 44. FIG. 5 is a schematic view not to scale. Each face 43 has a center point 45 that is coaxial with its cutting element body 41. Referring again to FIG. 4, cutting element array 37 is swept back when viewed in a bottom view. A line 47 that intersects center point 45 of each cutting element in array 37 is a curved line when viewed in a bottom view as in FIG. 4.

In this embodiment, each arm 27 has three cutting elements, but the number could differ. The array 37 includes an inner cutting element 49, an intermediate cutting element 51 and an outer cutting element 53. Inner cutting element 49 of each arm 27 is the one closest to axis 19. Outer cutting element 53 is the one farthest from axis 19. Because of swept back line 47, a radial line 55 extending from axis 19 to center point 45 of outer cutting element 53 does not pass through center points 45 of the other cutting elements 49, 51. Rather, radial line 55 for outer cutting element 53 lags radial line 55 extending through center point 45 of intermediate cutting element 51. Similarly, radial line 55 extending through center point 45 of intermediate cutting element 51 lags radial line 55 extending through center point 45 of inner cutting element 49. Radial line 55 of inner cutting element 49 leads radial line 55 for intermediate cutting element 51 by an acute angle 57. Radial line 55 for intermediate cutting element 51 leads radial line 55 for outer cutting element 53 by an acute angle 59. Acute angles 57, 59 can vary and need not be of the same degree.

In addition to array 37 being swept back along curve 47, in this example face 43 of each cutting element 49, 51, 53 points at a different angle into the direction of rotation. FIGS. 4 and 7 show normal lines 61 emanating from center point 45 of face 43 of each cutting element 49, 51, 53. A series of dotted lines indicate circumferential lines 63 concentric with axis 19 and passing through the center points 45 of cutting elements 49, 51, 53. Normal lines 61 illustrate that each cutting element 49, 51, 53 does not point directly into the direction of rotation, which would be coinciding with the circumferential line 63 passing through it. Rather each is at a side rake angle 65 relative to its circumferential line 63 Preferably, the side rake angle 65 of inner cutting element 49 is less than the side rake angle 65 of intermediate cutting element 51, thus it will be loaded more. The side rake angle 65 of intermediate cutting element 51 is slightly less than the side rake angle 65 of outer cutting element 53, thus it is loaded more. Normal line 61 of inner cutting element 49 thus points more inward than normal line 61 of face 43 of intermediate cutting 51. Similarly, normal line 61 normal to outer cutting element 53 points further outward relative to normal line 61 of intermediate cutting element 51. Normal lines 61 and side rake angles 65 may differ slightly from their counterparts of the other cutting arms 27b and 27c, but preferably, side rake angle 65 increases from inner cutting element 49 to outer cutting element 53 for each of the arms 27. Stated in another manner, as they emanate from the cutting elements 49, 51 and 53, normal lines 61 diverge from each other.

Referring to FIG. 6, cutting arm 27a is shown detached from body 13 (FIG. 1). For the purpose of illustration, the axis of rotation 19 is schematically shown in FIG. 6. Actually, axis 19 would be farther to the left. Inner cutting element 49 is located a radius r1 from axis 19 to its center point 45. Intermediate cutting element 51 is located a radius r2 from axis 19 to its center point 45, radius r2 being greater than radius r1. Outer cutting element 53 is located a radius r3 from its center point 45 to axis 19, radius r3 being greater than radius r2. The differences in radii r1, r2 and r3 are not linear; that is a line 69 extending through center points 45 of cutting elements 49, 51 and 53, when viewed in the elevational view of FIG. 6, curves outward and upward. If linear, cutting element 53 would be farther outward so that line 69 would be straight and at a single angle relative to axis 19. The difference between radius r1 and radius r2 is greater than the difference between radius r2 and radius r3. The same arrangement occurs for arm 27b (FIG. 8) and arm 27c (FIG. 10), although the differences in radii to the cutting elements 49, 51 and 53 differ in each arm 27.

Also, in the preferred embodiment, the radius from axis 19 to the center point 45 of each cutting element 49, 51, 53 is unique. Radius r1 in FIG. 6 differs from the comparable radii of inner cutting elements 49 of arm 27b and arm 27c. More specifically, radius r1 from axis 19 to center point 45 of inner cutting element 49 of arm 27c is greater than the radius r1 for arm 27b, which in turn is greater than radius r1 for arm 27a. Radius r2 from axis 19 to center point 45 of intermediate cutting element 51 of arm 27c is greater than radius r2 for arm 27b, which in turn is greater than radius r2 for arm 27a. Radius r3 from axis 19 to center point 45 of outer cutting element 53 of arm 27c is greater than the radius r3 for arm 27b, which in turn is greater than radius r3 for arm 27a. Because each center point 45 of each cutting element 49, 51, 53 is at a unique radius from axis 19, the paths of the cutting elements will not track each other. Each will be in a slightly different groove as underreamer 11 rotates.

In this example, intermediate cutting element 51 and outer cutting element 53 for each arm 27a, 27b and 27c overlap each other. That is, outer cutting element 53 is slightly behind intermediate cutting element 51 of the same arm. Referring to FIG. 8, the distance di represents the distance from one of the cutting elements 49, 51 or 53 from axis 19 to an innermost point or edge of the cutting element. The distance do represents the distance from axis 19 to an outermost point or edge of one of the cutting elements 49, 51 and 53. With arm 27b, shown in FIG. 8, the distance do for intermediate cutting element 51 is greater than the distance di for outer cutting element 53 of the same arm, creating an overlap. Similarly, an overlap will exist between intermediate cutting element 51 and outer cutting element 53 of arms 27a and 27c. In this example, there are no overlaps between the inner cutting element 49 and intermediate cutting element 51 of arms 27a and 27b. However, there is an overlap between inner cutting element 49 and intermediate cutting element 51 of arm 27c, as can be seen in FIG. 10.

Also, although different, the path of inner cutting element 49 on arm 27a overlaps with the path of inner cutting element 49 of arm 27b, which in turn overlaps with the path of inner cutting element 49 of arm 27c. The same overlap exists for intermediate cutting elements 51 of the different arms 27a, 27b and 27c, and outer cutting elements 53 of the different arms 27a, 27b and 27c.

Another difference between arrays 37 of arms 27a, 27b and 27c concerns the axial placement of the various cutting elements 49, 51 and 53 along lines parallel to axis 19. Referring to FIG. 10 as an example, each hole 34, which receives pivot pin 33 (FIG. 2), is located at the same point along axis 19. A plane 71 perpendicular to axis 19 passes through the center point of hole 34. Inner cutting element 49 is located a distance y1 below plane 71. Intermediate cutting element 51 of arm 27c is located a distance y2 below plane 71, distance y2 being less than distance y1. The distance y3 to center point 45 of outer cutting element 53 is located above plane 71. Preferably, the distances y1, y2 and y3 are unique for each cutting elements 45, 51 and 53. That is, distance y1 for arm 27c differs from distance y1 for arm 27b, which in turn, differs from distance y1 for arm 27a. Distance y2 for arm 27c differs from distance y2 for arm 27b, which in turn, differs from distance y2 for arm 27a. Distance y3 for arm 27c differs from distance y3 for arm 27b, which in turn, differs from distance y3 for arm 27a. In this example, the outer cutting element 53 is located above plane 71 for each arm 27a, 27b and 27c and cutting elements 49, 51 are located below. Each cutting element 49, 51, 53 thus engages borehole bottom 44 (FIG. 5) at a slightly different depth than the others.

In operation, the BHA (not shown) will be assembled with underreamer 11 as shown in FIG. 1. The cutter arms 27 will be retracted. A pilot bit will be connected to lower threaded connection 17. The bottom hole assembly will either be lowered into a drill string of casing (not shown) that is already positioned in the well being drilled, or it will be secured to the drill string of casing and lowered with the casing. When the pilot bit is at the bottom, the operator pumps drilling fluid through passage 21, which causes arms 27 to move to the extended position shown in FIGS. 2, 3 and 4 as a result of actuator tube 23 moving downward. The operator causes underreamer 11 to rotate either by rotating the string of casing or by driving a mud motor, which causes the BHA to rotate relative to the casing. The pilot bit will engage the lower portion of the bore to drill the earth formation. Cutting arrays 37 will engage the borehole bottom 44 (FIG. 5) at a point above the pilot bit, enlarging the well bore. The swept back curve 47, FIGS. 4, 9 and 11, creates a non-uniform load distribution across cutting arrays 37. Essentially, less area of cutter faces 43 is exposed as the radius from axis 19 to the center point 45 of each cutting element increases. Inner cutting elements 49 and intermediate cutting elements 51 of arms 27a, 27b and 27c are loaded to a greater extent than outer cutting elements 53, which are required to cut more at the bottom due to the farther distance from the axis. Cutting element loading will decrease in a smooth manner from the inner cutting element 49 to the outer cutting element 53 as the velocity of the cutting elements increases due to the greater distance from the axis 19. The non-tracking structure due to the unique distances and placement of each cutting element 49, 51, 53 promotes progressive cutter wear to minimize the problem of lateral impact damage at outer cutting elements 53 as the drilling continues. The front view curve 69 shows that each subsequent outer cutting element 53 will be located slightly behind an adjacent intermediate cutting element 51. This overlap reduces the inherent drag that outer cutting elements 53 are exposed to as well as reducing the level of included side rake.

A second embodiment, shown in FIGS. 12-14, also includes an underreamer 73 with a tubular body 75. A plurality of arms 77 are pivotally mounted to body 75, each arm 77 having a cutting element array 79 that may be the same as in the first embodiment. As shown in FIG. 12, an outlet port 81 extends through the side wall of body 75 adjacent each arm 77. Referring to FIG. 13, arms 77 are pivoted out in the same manner as in the first embodiment. An actuator tube 83 is reciprocally carried in an axial passage 84 extending through body 75. When actuator tube 83 is moved downward due to drilling fluid being pumped through passage 84, it pivots arms 77 outward.

Inlet ports 85 extend through the sidewall of actuator tube 83 for registering with the outlet ports 81 when actuator tube 83 is in the lower position. As illustrated in FIG. 14, a nozzle 87 of a hard, wear resistant material such as tungsten carbide is secured to each inlet port 85. Also, in this embodiment, a sleeve 89 is fixed inside the inner diameter of actuator tube 83. Sleeve 89 preferably has at least a coating on its inner diameter of hard, wear resistant material to reduce erosion of actuator tube 83 due to the fluid-turning action caused by the jetting of drilling fluid through nozzles 87. In this embodiment, sleeve 89 is formed of tungsten carbide. Sleeve 89 has holes that register with inlet ports 85 in actuator tube 83.

When drilling fluid is first pumped down the string, it causes actuator tube 83 to move downward, and inlet ports 85 and nozzles 87 move downward in unison. When actuator tube 83 is in the lower position, nozzles 87 will align with outlet ports 81. A portion of the drilling fluid will flow through inlet ports 85, nozzles 87 and outlet ports 81 across the cutting element arrays 79 for cleaning and cooling.

While the invention has been shown in only two of its forms, it should be apparent to those skilled in the art that it is not so limited but it is susceptible to various changes without departing from the scope of the invention. For example, a different number than three arms could be utilized. Other arrangements for moving the arms between the retracted and extended positions may be employed.

Claims

1. An underreamer earth boring tool, comprising:

a tubular body having a longitudinal axis;

a plurality of arms pivotally mounted to the body and movable relative to the body between a retracted position and an extended position;

an array of cutting elements mounted to each of the arms; and

each of the arrays being swept back so that cutting elements farther from the axis than others rotationally lag the others.

2. The tool according to claim 1 wherein when viewed in a bottom view, each of the arrays defines a curved line from the cutting elements closest to the axis to those farthest from the axis.

3. The tool according to claim 1, wherein when viewed in a front view, each array defines a curved line from the cutting elements closest to the axis to those farthest from the axis.

4. The tool according to claim 1, wherein each of the cutting elements is located a different radial distance from the axis than all of the other cutting elements in all of the arms.

5. The tool according to claim 1, wherein a path of the outermost cutting element on each of the arms is overlapped by a path of an adjacent cutting element on the same arm.

6. The tool according to claim 1, wherein each cutting element is located a different axial distance from a plane perpendicular to the axis than all of the other cutting elements in all of the arms.

7. The tool according to claim 1, further comprising:

a passage extending through the body for the delivery of drilling fluid; and

a plurality of nozzles in the body, each of the nozzles being in fluid communication with the passage and oriented to discharge a portion of the drilling fluid across one of the arrays.

8. An underreamer earth boring tool, comprising:

a tubular body having a longitudinal axis;

a plurality of arms pivotally mounted to the body and movable relative to the body between a retracted position and an extended position;

an inner and an outer cutting element mounted to each of the arms, each of the cutting elements having a face facing into a direction of rotation of the body, the face of the inner cutting element being closer to the axis than the face of the outer cutting element; and

the face of the inner cutting element on each of the arms rotationally leading the face of the outer cutting element on the same arm.

9. The tool according to claim 8, further comprising:

an intermediate cutting element mounted to each of the arms and having a face facing into a direction of rotation of the body, the face of the intermediate cutting element being closer to the axis than the face of the outer cutting element and farther from the axis than the face of the inner cutting element; and

the face of the intermediate cutting element on each of the arms rotationally leading the face of the outer cutting element and rotationally lagging the face of the inner cutting element on the same arm.

10. The tool according to claim 8, wherein each of the cutting elements is oriented at a side rake angle, and wherein the side rake angle of the outer cutting element is greater than the side rake angle of the inner cutting element on the same arm.

11. The tool according to claim 8, wherein:

the face of each inner cutting element is at a different distance from the axis than the inner cutting elements on the other arms.

12. The tool according to claim 8, wherein:

each cutting element is located a different axial distance from a plane perpendicular to the axis than all of the other cutting elements on all of the arms.

13. The tool according to claim 8, further comprising:

an intermediate cutting element mounted to each of the arms and having a face facing into a direction of rotation of the body, the face of the intermediate cutting element being closer to the axis than the face of the outer cutting element and farther from the axis than the face of the inner cutting element; and

wherein a path of the outer cutting element on each of the arms is overlapped by a path of the intermediate cutting element on the same arm.

14. The tool according to claim 8, further comprising:

an intermediate cutting element mounted between the inner and the outer cutting elements on each of the arms, each intermediate cutting element having a face facing into a direction of rotation of the body; and

a line extending through a center point of each of the faces on each of the arms curves upward when viewed in a front view.

15. The tool according to claim 8, further comprising:

an intermediate cutting element mounted between the inner and the outer cutting elements on each of the arms, each intermediate cutting element having a face facing into a direction of rotation of the body; and

a line extending through a center point of each of the faces on each of the arms curves away from the direction of rotation when viewed in a bottom view.

16. The tool according to claim 8, further comprising:

a passage extending through the body for the delivery of drilling fluid;

an actuator tube carried in the passage for movement from an upper position to a lower position in response to drilling fluid pressure applied to the passage, the actuator tube being cooperatively coupled to the arms so as to place the arms in the retracted position while the actuator tube is in the upper position, and to place the arms in the extended position while the actuator tube is in the lower position;

a plurality of outlet ports formed in the body adjacent the arms; and

a plurality of nozzles mounted to the actuator tube for movement therewith and in fluid communication with the passage, the nozzles aligning with the outlet ports while the actuator tube is in the lower position to discharge a portion of the drilling fluid across the cutting elements.

17. The tool according to claim 16, further comprising:

a sleeve having a wear-resistant inner diameter mounted in the actuator tube, the sleeve having an inlet port for each of the nozzles.

18. An underreamer earth boring tool, comprising:

a tubular body having a longitudinal axis;

a plurality of arms pivotally mounted to the body and movable relative to the body between a retracted position and an extended position;

inner, intermediate and outer cutting elements mounted to each of the arms, each of the cutting elements having a circular flat face with a center point;

on each of the arms, the center point of the intermediate cutting element being farther from the axis than the center point of the inner cutting element and less than the center point of the outer cutting element;

on each of the arms, a first radial line extending radially from the axis and passing through the center point of the inner cutting element is at an acute angle relative to a second radial line extending radially from the axis and passing through the center point of the intermediate cutting element; and

on each of the arms, the second radial line is at an acute angle relative to a third radial line extending radially from the axis and passing through the center point of the outer cutting element.

19. The tool according to claim 18, wherein each of the cutting elements is oriented at a side rake angle, and wherein the side rake angle of the outer cutting element is greater than the side rake angle of the inner cutting element on the same arm.

20. The tool according to claim 18, wherein:

the center point of each inner cutting element is at a different distance from the axis than the inner cutting elements on the other arms; and

the center point of each intermediate cutting element is at a different distances from the axis than the intermediate cutting elements on the other arms.

21. The tool according to claim 18, wherein:

when each arm is viewed in a front view, a line drawn through the center point each of the cutting elements on that arm curves upward.

22. The tool according to claim 18, wherein:

when each arm is viewed in a bottom view, a line drawn through the center point of each of the cutting elements on that arm curves away from a direction of rotation of the tool.

23. The tool according to claim 18, wherein a path of the outer cutting element on each of the arms is overlapped by a path of the intermediate cutting element on the same arm.