Method for avoiding thread defect caused by mandrel-containing rotary swaging forming of super-long pipe fitting
By matching the length of the mold finishing section, the position of the mandrel and the feed motion parameters, the thread defects in the rotary forging of the ultra-long pipe fittings are solved, and high-quality forming effect is achieved.
Patent Information
- Application Number
- CN202411720827.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-28
- Publication Date
- 2025-01-10
AI Technical Summary
In the manufacturing of ultra-long pipe fittings with core rods, defects such as internal threads, external threads or internal threads are prone to occur during the rotary forging process, resulting in poor forming quality.
By collaborating with the mold finishing segment length, mandrel position, circumferential feeding movement, axial feeding movement and mold hammering frequency, we ensure the mold's radial forging frequency, axial feeding speed and finishing segment length in the radial direction, we can ensure the mold's radial forging frequency, axial feeding speed and finishing segment length in the sequential direction. to avoid thread defects during rotary forging.
It effectively avoids the occurrence of internal threads, external threads and internal thread defects during the manufacturing of ultra-long pipe fittings with core rods, and ensures the forming quality of ultra-long pipe fittings.
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Figure CN119282000A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of mechanical engineering, and in particular relates to a method for preventing thread defects from occurring during rotary forging of an overlong pipe including a mandrel. Background Art
[0002] The rotary forging manufacturing method has the advantages of continuous fiber streamline, good forming quality, easy forming of hollow structures with variable cross-section and thickness, high production efficiency and high material utilization rate. It is an advanced high-performance manufacturing technology. Rotary forging manufacturing includes mandrel-containing rotary forging with equal cross-section and equal wall thickness and mandrel-free rotary forging with variable cross-section and variable wall thickness. The mandrel-containing rotary forging blank is supported by the mandrel inside. During the rotary forging process, the inner and outer surfaces are compressed and have good mechanical properties. The geometric quality and shape quality of the forming are high and easy to guarantee. The dimensional accuracy of the mandrel-containing rotary forging can reach 0.02mm, and the surface roughness R a It can reach below 0.4μm, and the size and mechanical properties requirements of the core rod rotary forging blank are relatively low.
[0003] Different from the conventional rotary forging with mandrel, the rotary forging with mandrel forging of super-long pipe fittings has its own unique characteristics: the blank is very long, mainly limited by the manufacturing space, and can be up to 30 meters long; the length of the die finishing section is very short, the shortest is only 5mm; the mandrel is short, and its working section does not exceed the finishing section of the die; the axial feed speed is very high, much higher than the conventional rotary forging with mandrel.
[0004] In the rotary forging of extra-long pipes with mandrels, the rotary forging quality is affected by process parameters such as rotary forging frequency, length of die finishing section, mandrel position, axial feed, circumferential feed, etc. When these parameters are not matched reasonably, defects such as external threads, internal threads, or internal and external threads will occur during the rotary forging process. Summary of the invention
[0005] The present invention is made to solve the above-mentioned problem, and aims to provide a method for avoiding thread defects during rotary forging of an extra-long pipe with a mandrel.
[0006] The present invention provides a method for avoiding thread defects during rotary forging of an extra-long pipe with a mandrel, which is used for matching and controlling process parameters during the use of a rotary forging device containing a mandrel so as to avoid internal threads and / or external threads during the rotary forging of an extra-long pipe. The rotary forging device containing a mandrel comprises a mandrel and a die. The mandrel is used for sleeves of an extra-long pipe to be rotary forged, and provides guidance and support for the part of the extra-long pipe to be rotary forged during the rotary forging process. The area of the mandrel that supports the part along the axial direction is recorded as a working section, the radial outer diameter of the mandrel is recorded as r1, and the radial outer diameter of the extra-long pipe before rotary forging is recorded as r2. The inner diameter is recorded as r2, and the radial inner diameter after rotary forging is recorded as r3, r1=r3<r2. When rotary forging is performed, a number of dies are evenly fixed to the core rod and the part of the super-long pipe to be rotary forged, and the super-long pipe is forged along the radial direction. The dies include a forming section and a finishing section in sequence along the axial feeding direction of the super-long pipe. The forming sections of the dies respectively form a truncated cone channel during the rotary forging process. The radial inner diameter of the truncated cone channel gradually decreases along the axial feeding direction of the super-long pipe. The forming section is used to rotary forge the super-long pipe until the radial inner diameter of the super-long pipe is rotary forged from r2 to r 3. The finishing sections of the plurality of dies form a circular channel during the rotary forging process, which is used to finish the formed super-long pipe fittings. The method for preventing thread defects from occurring during the rotary forging of super-long pipe fittings containing a mandrel provided by the present invention has the following characteristics, including the following steps: S10, matching the frequency of the dies forging the super-long pipe fittings in the radial direction, the axial feeding speed of the super-long pipe fittings, and the axial length of the finishing section, so that the super-long pipe fittings do not have external thread defects during the axial feeding movement; S20, matching the circumferential rotation speed of the super-long pipe fittings, the number of dies, and the axial length of the dies during the radial forging movement; The frequency of punching the over-long pipe fittings is matched, so that the over-long pipe fittings will not be repeatedly forged at the same position by the die during the circumferential feeding movement and will not have external thread defects; S30, the finishing section is controlled not to be misaligned with the working section in the axial direction, and the axial feed of the over-long pipe fitting each time is not greater than the axial length of the overlapping part of the working section and the finishing section, so as to match the axial position of the core rod and the axial feed to avoid internal thread defects in the over-long pipe fittings during the rotary forging process; S40, the parameter settings during the use of the rotary forging device containing the core rod are controlled to simultaneously meet the matching settings in steps S10 to S30.
[0007] The method for avoiding thread defects during rotary forging of an extra-long pipe with a mandrel provided by the present invention may also have the following characteristics: wherein, in step S10, the frequency of radially forging the extra-long pipe with the die is recorded as f, the axial feed speed of the extra-long pipe is recorded as v, the axial length of the finishing section is recorded as B, and v / f≤B.
[0008] The method for avoiding thread defects during rotary forging of extra-long pipes with a mandrel provided by the present invention may also have the following characteristics: wherein, in step S20, the circumferential rotation speed of the extra-long pipe is denoted as ω, the number of dies is denoted as n, and the frequency of the dies forging the extra-long pipes radially is denoted as f, ω / f≠kn / 2π, and k is an arbitrary integer.
[0009] The method for preventing thread defects during rotary forging of an extra-long pipe with a mandrel provided by the present invention may also have the following characteristics: wherein n≥2.
[0010] The method for preventing thread defects from occurring during rotary forging of an extra-long pipe with a mandrel provided by the present invention may also have the following characteristics: wherein, in step S30, the frequency of radial forging of the extra-long pipe by the die is recorded as f, the axial feed speed of the extra-long pipe is recorded as v, the axial length of the finishing section is recorded as B, the axial overlap length of the finishing section and the working section is recorded as C, the axial length of the working section is recorded as L, the axial distance between the center point of the mandrel and the entrance end of the finishing section is recorded as x, It is an empty set, v / f≤C, C>0.
[0011] Functions and Effects of the Invention
[0012] The method for avoiding thread defects during rotary forging of super-long pipe fittings containing a mandrel of the present invention avoids the generation of internal threads, external threads and internal and external thread defects during rotary forging of super-long pipe fittings containing a mandrel by coordinated matching of process parameters such as die finishing section length, mandrel position, circumferential feed motion, axial feed motion and die hammer forging frequency, thereby ensuring the quality of rotary forging of super-long pipe fittings containing a mandrel. BRIEF DESCRIPTION OF THE DRAWINGS
[0013] Figure 1 is an axial side cutaway view of the mandrel-containing rotary forging device in an embodiment of the present invention during use;
[0014] Figure 2 is a radial cross-sectional view of the mandrel-containing rotary forging device in the embodiment of the present invention during use;
[0015] Figure 3 It is a stereoscopic view of an extra-long pipe fitting with external threads that is rotary forged using a rotary forging device containing a mandrel in the prior art;
[0016] Figure 4 It is a stereoscopic view of an extra-long pipe fitting with internal threads that is rotary forged using a rotary forging device containing a mandrel in the prior art;
[0017] Figure 5 It is a stereoscopic view of an extra-long pipe obtained by rotary forging using the method for avoiding thread defects in rotary forging of an extra-long pipe containing a mandrel in the test example of the present invention. DETAILED DESCRIPTION
[0018] In order to make the technical means, creative features, objectives and effects achieved by the present invention easy to understand, the following embodiments and drawings specifically illustrate a method of the present invention for avoiding thread defects in rotary forging of extra-long pipes containing mandrels.
[0019] <Example>
[0020] Figure 1 is an axial side cutaway view of the mandrel-containing rotary forging device in an embodiment of the present invention during use; Figure 2 It is a radial cross-sectional view of the core rod-containing rotary forging device in the embodiment of the present invention during use.
[0021] like Figure 1 and Figure 2 As shown, the mandrel-containing rotary forging device 100 in this embodiment includes a mandrel 10 and a plurality of dies 20 .
[0022] The mandrel 10 is used for the extra-long pipe 30 to be swaged to be sleeved thereon, and provides guidance and support for the part of the extra-long pipe 30 to be swaged during the swaging process.
[0023] The area of the core rod 10 that supports the core rod 10 along the axial direction is recorded as the working section 11, the radial outer diameter of the core rod 10 is recorded as r1, the radial inner diameter of the extra-long pipe 30 before rotary forging is recorded as r2, and the radial inner diameter after rotary forging is recorded as r3, r1=r3<r2.
[0024] When rotary forging is performed, a plurality of dies 20 are evenly fixed around the core rod 10 and the portion of the extra-long pipe 30 to be rotary forged, and the extra-long pipe 30 is forged along the radial direction thereof.
[0025] The die 20 includes a forming section 21 and a finishing section 22 in sequence along the axial feeding direction of the extra-long pipe 30 .
[0026] The forming sections 21 of the respective dies 20 form a truncated cone-shaped channel during the rotary forging process, and the radial inner diameter of the truncated cone-shaped channel gradually decreases along the axial feed direction of the extra-long pipe 30. The forming section 21 is used to rotary forge the extra-long pipe 30 until the radial inner diameter of the extra-long pipe 30 is rotary forged from r2 to r3.
[0027] The finishing sections 22 of the plurality of dies 20 form a circular channel during the rotary forging process, which is used to finish the formed extra-long pipe 30 .
[0028] This embodiment provides a method for avoiding thread defects during the rotary forging of an extra-long pipe with a mandrel, which is used to match and control the process parameters during the use of the rotary forging device 100 with a mandrel to avoid the occurrence of internal and / or external threads during the rotary forging of the extra-long pipe 30.
[0029] First, the conditions for the appearance of internal and / or external threads in the extra-long pipe fitting 30 are analyzed:
[0030] Conditions for the appearance of external threads: (1) The axial feed of the extra-long pipe 30 is too fast. When the axial feed is greater than the length of the external forming channel (i.e., the length of the mold finishing section) during one cycle of hammering of the forming channel (finishing section 22), external threads appear on the extra-long pipe 30. (2) The periodic changes (hammering in the radial direction) of the forming channel (finishing section 22) are synchronized with the circumferential movement of the extra-long pipe 30, and the forging is at the same position, resulting in external threads.
[0031] Conditions for the appearance of internal threads: (1) When the axial feed of the super-long pipe 30 is too fast and each axial feed is greater than the axial overlap length of the working section 11 and the finishing section 22, internal threads appear. (2) When the working section 11 and the finishing section 22 are axially misaligned, that is, when there is no axial overlap between the working section 11 and the finishing section 22, internal threads appear and cannot be eliminated.
[0032] On this basis, a method for avoiding thread defects in the rotary forging of an overlong pipe with a mandrel in this embodiment comprises the following steps:
[0033] S10, matching axial feed motion to avoid external thread defects:
[0034] The frequency f of the die 20 radially forging the extra-long pipe 30, the axial feed speed v of the extra-long pipe 30 and the axial length B of the finishing section 22 are matched so that no external thread defects occur in the extra-long pipe 30 during the axial feed movement.
[0035] The matching method in this step is achieved by the following formula: v / f≤B (Formula 1)
[0036] S20, matching circumferential feed motion to avoid external thread defects:
[0037] The circumferential rotation speed ω of the extra-long pipe 30, the number n of the dies 20 and the frequency f of the dies 20 radially forging the extra-long pipe 30 are matched so that the extra-long pipe 30 will not be repeatedly forged at the same position by the dies 20 during the circumferential feeding movement to cause external thread defects.
[0038] The matching method in this step is implemented by the following formula: ω / f≠kn / 2π (Formula 2), n≥2, and k is an arbitrary integer.
[0039] S30, matching the axial position and axial feed of the mandrel 10 to avoid internal thread defects in rotary forging:
[0040] The finishing section 22 is controlled not to be misaligned with the working section 11 in the axial direction, and the axial feed of the extra-long pipe 30 each time is made not greater than the axial length of the overlapping part of the working section 11 and the finishing section 22, thereby matching the axial position and axial feed of the core rod 10 to avoid internal thread defects of the extra-long pipe 30 during the rotary forging process.
[0041] The matching method in this step is implemented by the following formula:
[0042] Is an empty set.
[0043] v / f≤C (Formula 4).
[0044] C>0(Formula 5).
[0045] In the above formulas 3, 4 and 5, C is the axial overlap length between the finishing section 22 and the working section 11, L is the axial length of the working section 11, and x is the axial distance between the center point of the core rod 10 and the entrance end of the finishing section 21.
[0046] S40, controlling the parameter settings during the use of the mandrel-containing rotary forging device to simultaneously satisfy Formula 1, Formula 2, Formula 3, Formula 4 and Formula 5 in Steps S10 to S30.
[0047] <Test example>
[0048] This test example uses the example in the embodiment Figure 1 and Figure 2 The mandrel-containing rotary forging device 100 shown is used to conduct actual testing on an extra-long pipe 30 using a method provided in an embodiment to avoid thread defects during the mandrel-containing rotary forging of an extra-long pipe.
[0049] In this test example, a 30-meter-long extra-long pipe 30 including a mandrel forging is used as the object, and the material of the extra-long pipe 30 is Q235.
[0050] The extra-long pipe 30 has an outer diameter of 60 mm and a wall thickness of 4.5 mm before rotary forging, and the area before rotary forging is recorded as the blank area 31 ; the outer diameter after rotary forging is 50 mm and the wall thickness is 5 mm, and the area after rotary forging is recorded as the product area 35 .
[0051] During the rotary forging process with a core rod, the rotary forging process from the blank area 31 to the product area 35 is respectively a sinking area 32, a forging area 33, and a finishing area 34, wherein the finishing area 34 forms the product size and precision requirements.
[0052] In this test example, the number of dies 20 is 4, and the 4 dies 20 periodically move radially to forge the blank area 31, and continuously form from the blank area 31 to the product area 35 through the sinking area 32, the forging area 33, and the finishing area 34.
[0053] The extra-long pipe 30 performs radial feeding, circumferential feeding and axial feeding relative to the die 20 and the mandrel 10. The mandrel 10 supports the extra-long pipe 30 during the rotary forging process and guides the radial flow of metal during the rotary forging process. The initial contact point between the extra-long pipe 30 and the mandrel 10 during the rotary forging process is the dividing point between the sinking area 32 and the forging area 33, and the finishing area 34 forms part of the product.
[0054] In this test example, the forging frequency f=60 Hz, the axial feed speed range is 1000 mm / min to 35000 mm / min, and the length B of the finishing section 22 is 5 mm.
[0055] In this test example, when the length of the working section 11 of the mandrel 10 completely overlaps with the length of the finishing section 22 of the die 20, the internal and external threads will appear simultaneously as the axial feed speed increases; when the length of the working section 11 of the mandrel 10 does not completely overlap with the length of the finishing section 22 of the die 20, the formation of the internal thread will be aggravated. Only when the actual working length of the inner channel exceeds 60mm, any axial feed speed within the range of the equipment in this test example will not produce internal threads.
[0056] Figure 3 It is a stereoscopic view of an extra-long pipe fitting with external threads that is rotary forged using a rotary forging device containing a mandrel in the prior art; Figure 4 It is a stereoscopic view of an extra-long pipe fitting with internal threads that is rotary forged using a rotary forging device containing a mandrel in the prior art; Figure 5 It is a stereoscopic view of an extra-long pipe obtained by rotary forging using the method for avoiding thread defects in rotary forging of an extra-long pipe containing a mandrel in the test example of the present invention.
[0057] like Figure 3 to Figure 5 As shown, in this test example, a method for avoiding thread defects in rotary forging of an extra-long pipe including a mandrel is used, and the extra-long pipe obtained by rotary forging effectively avoids the occurrence of internal and external threads in the extra-long pipe.
[0058] Functions and Effects of the Embodiments
[0059] According to a method provided in this embodiment to avoid thread defects during rotary forging of an extra-long pipe with a mandrel, the process parameters of the rotary forging device with a mandrel are matched and controlled during use to avoid internal and / or external threads during rotary forging of the extra-long pipe. The rotary forging device with a mandrel includes a mandrel and a die. The mandrel is used for the extra-long pipe to be rotary forged to be sleeved thereon, and to provide guidance and support for the part of the extra-long pipe to be rotary forged during the rotary forging process. The area of the mandrel that supports the axial direction is recorded as the working section, the radial outer diameter of the mandrel is recorded as r1, and the extra-long pipe is rotary forged. The radial inner diameter before forging is recorded as r2, and the radial inner diameter after forging is recorded as r3, r1=r3<r2. When forging is performed, several dies are evenly fixed to the mandrel and the part of the super-long pipe to be forged, and the super-long pipe is forged along the radial direction. The dies include a forming section and a finishing section in sequence along the axial feeding direction of the super-long pipe. The forming sections of the several dies form a truncated cone channel during the forging process. The radial inner diameter of the truncated cone channel gradually decreases along the axial feeding direction of the super-long pipe. The forming section is used to forge the super-long pipe until the radial inner diameter of the super-long pipe is reduced from r2 to r3. The rotary forging is performed to r3, and the finishing sections of the respective dies form a circular channel during the rotary forging process, which is used to finish the formed super-long pipe fittings. The method provided in this embodiment to avoid thread defects during rotary forging of super-long pipe fittings containing a mandrel comprises the following steps: S10, matching the frequency of radial forging of the super-long pipe fittings by the dies, the axial feeding speed of the super-long pipe fittings, and the axial length of the finishing section, so that the super-long pipe fittings do not have external thread defects during the axial feeding movement; S20, matching the circumferential rotation speed of the super-long pipe fittings, the number of dies, and the radial forging speed of the dies. The frequency of the extra-long pipe is matched, so that the extra-long pipe will not be repeatedly forged at the same position by the die during the circumferential feeding movement, resulting in external thread defects; S30, the finishing section is controlled not to be misaligned with the working section in the axial direction, and the axial feeding of the extra-long pipe each time is not greater than the axial length of the overlapping part of the working section and the finishing section, so as to match the axial position of the mandrel and the axial feeding to avoid internal thread defects of the extra-long pipe during the rotary forging process; S40, the parameter setting of the rotary forging device containing the mandrel is controlled to meet the matching settings in steps S10 to S30 at the same time. Therefore, a method of avoiding thread defects in rotary forging of extra-long pipes containing mandrels in this embodiment avoids the generation of internal threads, external threads, and internal and external thread defects during rotary forging of extra-long pipes containing mandrels, and ensures the quality of rotary forging of extra-long pipes containing mandrels.
[0060] Furthermore, in step S10, the frequency of the die forging the extra-long pipe in the radial direction is recorded as f, the axial feed speed of the extra-long pipe is recorded as v, and the axial length of the finishing section is recorded as B, v / f≤B. This setting matches the axial feed motion of the extra-long pipe, effectively avoiding the occurrence of external thread defects during the rotary forging process of the extra-long pipe.
[0061] Furthermore, in step S20, the circumferential rotation speed of the super-long pipe is recorded as ω, the number of dies is recorded as n, and the frequency of the dies forging the super-long pipe in the radial direction is recorded as f, ω / f≠kn / 2π, k is an arbitrary integer, and n≥2. In this way, the circumferential feed motion of the super-long pipe is matched, and the external thread defects in the process of rotary forging of the super-long pipe are effectively avoided.
[0062] Further, in step S30, the frequency of the die forging the extra-long pipe in the radial direction is recorded as f, the axial feed speed of the extra-long pipe is recorded as v, the axial length of the finishing section is recorded as B, the axial overlap length of the finishing section and the working section is recorded as C, the axial length of the working section is recorded as L, and the axial distance between the center point of the mandrel and the entrance end of the finishing section is recorded as x. It is an empty set, v / f≤C, C>0. With such a setting, the axial position of the mandrel and the axial feed are matched, which effectively avoids the occurrence of internal thread defects during the rotary forging process of the super-long pipe fittings.
[0063] Those skilled in the art should understand that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.
Claims
1. A method for avoiding thread defects during the rotary forging of an extra-long pipe with a mandrel, which is used to match and control the process parameters of the rotary forging device with a mandrel so as to avoid the occurrence of internal and / or external threads during the rotary forging of the extra-long pipe. The mandrel-containing rotary forging device comprises a mandrel and a die. The mandrel is used for the extra-long pipe to be swaged to be sleeved thereon, and provides guidance and support for the part of the extra-long pipe to be swaged during the swaging process. The area of the mandrel that supports the axial direction is recorded as the working section. The radial outer diameter of the mandrel is recorded as r1, the radial inner diameter of the extra-long pipe before swaging is recorded as r2, and the radial inner diameter after swaging is recorded as r3, r1=r3<r2, When rotary forging is performed, a plurality of the dies are evenly fixed around the core rod and the portion of the super-long pipe to be rotary forged, and the super-long pipe is forged along the radial direction. The die includes a forming section and a finishing section in sequence along the axial feeding direction of the super-long pipe. The forming sections of the plurality of dies respectively form a truncated cone-shaped channel during the rotary forging process, and the radial inner diameter of the truncated cone-shaped channel gradually decreases along the axial feeding direction of the extra-long pipe. The forming sections are used to rotary forge the extra-long pipe until the radial inner diameter of the extra-long pipe is rotary forged from r2 to r3. The finishing sections of the plurality of dies respectively form a circular channel during the rotary forging process, which is used to finish the formed extra-long pipe. It is characterized in that The following steps are involved: S10, matching the frequency of the die forging the extra-long pipe in the radial direction, the axial feeding speed of the extra-long pipe, and the axial length of the finishing section, so that no external thread defect occurs on the extra-long pipe during the axial feeding movement; S20, matching the circumferential rotation speed of the extra-long pipe, the number of the dies, and the frequency at which the dies radially forge the extra-long pipe, so that the extra-long pipe will not be repeatedly forged at the same position by the dies during the circumferential feeding movement to cause external thread defects; S30, controlling the finishing section to prevent misalignment with the working section in the axial direction, and ensuring that each axial feed of the super-long pipe is not greater than the axial length of the overlapping portion of the working section and the finishing section, thereby matching the axial position and axial feed of the mandrel to avoid internal thread defects of the super-long pipe during the rotary forging process. S40, controlling the parameter settings during use of the mandrel-containing rotary forging device to simultaneously satisfy the matching settings in steps S10 to S30.
2. The method for preventing thread defects during rotary forging of an extra-long pipe with a mandrel according to claim 1, characterized in that: in, In step S10, the frequency of the die forging the extra-long pipe in the radial direction is recorded as f, the axial feeding speed of the extra-long pipe is recorded as v, and the axial length of the finishing section is recorded as B. v / f≤B.
3. The method for preventing thread defects during rotary forging of an extra-long pipe with a mandrel according to claim 1, characterized in that: in, In step S20, the circumferential rotation speed of the extra-long pipe is recorded as ω, the number of the dies is recorded as n, and the frequency of the dies forging the extra-long pipe in the radial direction is recorded as f. ω / f≠kn / 2π, where k is an arbitrary integer.
4. The method for preventing thread defects during rotary forging of an extra-long pipe with a mandrel according to claim 3 is characterized in that: in, n≥2。 5. The method for preventing thread defects during rotary forging of an extra-long pipe with a mandrel according to claim 1, characterized in that: in, In step S30, the frequency of the die forging the extra-long pipe in the radial direction is recorded as f, the axial feeding speed of the extra-long pipe is recorded as v, the axial length of the finishing section is recorded as B, the axial overlap length of the finishing section and the working section is recorded as C, the axial length of the working section is recorded as L, and the axial distance between the center point of the mandrel and the inlet end of the finishing section is recorded as x. is an empty set, v / f≤C, C>0。
Citation Information
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