A high-flexibility cable with bending resistance and fatigue resistance for robots and a preparation method thereof

CN122739008BActive Publication Date: 2026-10-23SICHUAN XINDIAN CABLE CO LTD
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Patent Information

Application Number
CN202611193750.4
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2026-08-07
Publication Date
2026-10-23
Estimated Expiration
2046-08-07

AI Technical Summary

Technical Problem

[0003]然而,这些材料在应用于高动态场合时存在诸多不足

Benefits of technology

1.本发明通过在绝缘层母料中引入光反应性环糊精基聚轮烷,提高了绝缘材料的柔韧性和抗疲劳寿命。

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Abstract

The present application relates to the technical field of insulated cable and cable manufacturing, in particular to a kind of robot high flexibility cable resistant to bending and fatigue and its preparation method;For current insulation material is difficult to meet high flexibility, fatigue life and environmental adaptability problem simultaneously;The present application is prepared by preparing photo-reactive cyclodextrin-based polyrotaxan, disulfide crosslinking agent;Then mixed with thermoplastic polyurethane, ultra-low density polyethylene and other materials melt extrusion granulation, and the insulation layer masterbatch is prepared;After the insulation layer masterbatch is extruded and coated on the outer layer of the conductor, the radial gradient distribution of outer layer high crosslinking and inner layer low crosslinking is formed by using ultraviolet gradient crosslinking process and the penetration attenuation of ultraviolet light in the thickness direction of insulation layer;Subsequently, the cable is stranded, the shielding layer is wrapped, the sheath layer is extruded and the heat treatment is carried out, and the cable is obtained, so that the cable has excellent flexibility, fatigue life and environmental adaptability, and can be applied to industrial robots, automated production lines and other high dynamic occasions.
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Description

Technical Field

[0001] This invention relates to the field of insulated cables and cable manufacturing technology, specifically to a high-flexibility, bend-resistant, fatigue-resistant cable for robots and its preparation method. Background Technology

[0002] With the rapid development of industrial automation and intelligent manufacturing, the performance requirements for cables in equipment such as industrial robots, automated production lines, and cable chain systems are becoming increasingly stringent. These cables need to withstand frequent dynamic stresses such as bending, torsion, and tension during operation, therefore they must possess excellent flexibility, fatigue life, and environmental adaptability. High-flexibility cables typically use multi-strand fine copper wire stranded conductors combined with soft and wear-resistant insulation materials to ensure good flexibility and mechanical properties during long-term use.

[0003] However, these materials have several shortcomings when applied to highly dynamic applications. First, there is a trade-off between flexibility and mechanical strength in traditional insulation materials: increasing flexibility often comes at the expense of mechanical strength, while increasing the degree of crosslinking, although enhancing strength, leads to a decrease in flexibility. Second, traditional crosslinking methods generate gases such as methane during cable manufacturing, which degrade electrical insulation performance. Third, existing insulation materials have limited fatigue life under long-term repeated bending, making it difficult to meet the requirement of millions of bending cycles for robot cables. Fourth, when cables are used in harsh environments, the insulation material is prone to aging and cracking, severely affecting the cable's service life and reliability.

[0004] Existing patent CN204130209U discloses a highly flexible torsion-resistant robot cable, which employs a Category VI tinned copper conductor, a TPE rubber insulation layer, an elastic anti-torsion reinforcing core, a waterproof wrapping tape, a tinned copper wire braided layer, and a flexible PVC outer sheath. This design primarily improves bending and torsion performance through the conductor, reinforcing core, and cable structure, but does not address stress dissipation, dynamic bond rearrangement, or crosslinking distribution within the insulation material.

[0005] In summary, there is an urgent need for a robot cable that can simultaneously meet the requirements of high flexibility, fatigue life, and environmental adaptability, as well as its manufacturing method. Summary of the Invention

[0006] This invention provides a high-flexibility cable for robots that is resistant to bending and fatigue and its preparation method. It aims to achieve a comprehensive improvement in the flexibility, fatigue life and environmental adaptability of the insulation layer through the synergistic effect of photoreactive cyclodextrin-based polyrotaxane, dynamic covalent crosslinking network and ultraviolet gradient crosslinking technology.

[0007] The specific technical solution is as follows: A method for preparing a highly flexible, bend-resistant, and fatigue-resistant cable for robots is as follows: S1: Raw material preparation.

[0008] S11: Add α-cyclodextrin and terminally amino-terminated polyethylene glycol to deionized water, stir, filter, wash, and dry to obtain quasi-polyrotaxane.

[0009] S12: The quasi-polyrotaxane prepared in S11 was added to a mixed solvent of N,N-dimethylformamide and water in a volume ratio of 1:3. Then, 1-adamantanecarboxylic acid and 4-(4,6-dimethoxy-1,3,5-triazin-2-yl)-4-methylmorpholine chloride were added, the pH was adjusted to 8.0-8.5, the mixture was stirred, dialyzed, and dried. The resulting end-capped polyrotaxane was added to anhydrous N,N-dimethylformamide, and 2-ethyl isocyanate methacrylate and bismuth neodecanoate catalysts were added under nitrogen protection. The mixture was heated and reacted. The reaction solution was then poured into excess ethanol to precipitate the product. The product was filtered, washed, and dried to obtain photoreactive cyclodextrin-based polyrotaxane.

[0010] S13: Add 4,4'-dithiodiphenylamine and maleic anhydride to N,N-dimethylformamide, stir, precipitate, filter, wash, and dry to obtain bismaleamic acid.

[0011] S14: Add the bismaleamic acid prepared in S13 to acetic anhydride, add anhydrous sodium acetate and stir, cool to room temperature, pour into ice water, filter, wash and dry to obtain disulfide crosslinking agent.

[0012] S2: Preparation of insulating layer masterbatch: Thermoplastic polyurethane and ultra-low density polyethylene are dried separately, and then mixed with photoreactive cyclodextrin-based polyrotaxane prepared in S12, maleic anhydride-grafted polyethylene, disulfide crosslinking agent prepared in S14, silane-modified nano-SiO2, UV photoinitiator, antioxidant, and lubricant. The mixture is then melt-extruded, cooled, granulated, dried, and sieved to obtain insulating layer masterbatch.

[0013] S3: Extrusion and crosslinking. The insulating masterbatch prepared in S2 is extruded and coated onto the outer layer of the copper wire stranded conductor. Gradual crosslinking and cooling are performed to obtain the wire core with the insulating layer.

[0014] S4: Cable preparation.

[0015] S41: The wire cores with insulation prepared in S3 are stranded into a cable, and then a shielding layer is wrapped around the outside of the cable cores to obtain wire cores with a shielding layer.

[0016] S42: The dried thermoplastic polyurethane prepared in S2 is melt-extruded onto the wire core with shielding layer prepared in S41, cooled and shaped, heat-treated, and cooled to room temperature to obtain a highly flexible cable that is resistant to bending and fatigue.

[0017] Furthermore, the stirring described in S11 has the following parameter settings: temperature 30-50℃, rotation speed 200-500rpm, and duration 12-36h.

[0018] The drying process described in S11 has the following parameters: temperature 40–60°C, duration 12–24 hours.

[0019] The stirring described in S12 has the following parameters: temperature 20-40℃, speed 200-500rpm, and duration 12-36h.

[0020] The photoreactive cyclodextrin-based polyrotaxane described in S12 has a axial molecule that is a diamino-terminated PEG with a number average molecular weight of 4000-8000 and a cyclic molecule that is α-cyclodextrin. The end-capping rate of the cyclic molecule is not less than 95%. The composition of each raw material, by mass, is as follows: α-cyclodextrin 60.01 parts, amino-terminated polyethylene glycol 29.91 parts, 1-adamantanecarboxylic acid 2.75 parts, 4-(4,6-dimethoxy-1,3,5-triazin-2-yl)-4-methylmorpholine chloride 5.07 parts, 2-ethyl isocyanate methacrylate 2.20 parts, and bismuth neodecanoate catalyst 0.06 parts.

[0021] The 4,4'-dithiodiphenylamine described in S13 has a molar ratio of 1:2 to 1:2.2 with maleic anhydride.

[0022] The stirring described in S13 has the following parameters: temperature 20-40℃, speed 300-600rpm, and duration 4-12h.

[0023] The drying process described in S13 has the following parameters: temperature 50-60℃, duration 12-24h.

[0024] The stirring described in S14 has the following parameters: temperature 70-90℃, speed 200-400rpm, and duration 2-6h.

[0025] The disulfide crosslinking agent described in S14 has a maleimide equivalent of 190–220 g / eq.

[0026] Furthermore, the mixing parameters described in S2 are set as follows: temperature ≤ 50℃, rotation speed 500~1500rpm, and duration 5~15min.

[0027] The melt extrusion described in S2 has the following parameter settings: feeding section temperature 150-170℃, melting section temperature 170-190℃, homogenization section temperature 180-200℃, die head temperature 185-195℃, and screw speed 100-300rpm.

[0028] The UV photoinitiator described in S2 is one or more of benzophenone, dimethyl benzoate, and 2-hydroxy-2-methyl-1-phenylpropanone.

[0029] The antioxidant mentioned in S2 is antioxidant 1010 or antioxidant 168.

[0030] The lubricant described in S2 is one or more of zinc stearate, calcium stearate, and polyethylene wax.

[0031] The insulating layer masterbatch described in S2 is composed of a matrix resin and additives. The matrix resin contains 55-75 parts by weight of thermoplastic polyurethane and 25-45 parts by weight of ultra-low density polyethylene, with the sum of the contents of thermoplastic polyurethane and ultra-low density polyethylene being 100 parts by weight. Relative to 100 parts by weight of the matrix resin, the additives include: 2-8 parts by weight of maleic anhydride-grafted polyethylene, 3-10 parts by weight of photoreactive cyclodextrin-based polyrotaxane, 1-4 parts by weight of disulfide crosslinking agent, 2-6 parts by weight of silane-modified nano-SiO2, 0.5-1.5 parts by weight of UV photoinitiator, 0.3-1.2 parts by weight of antioxidant, and 0.2-0.8 parts by weight of lubricant.

[0032] Furthermore, the gradient crosslinking described in S3 has the following parameter settings: 8 groups of UV-LEDs are evenly distributed in a ring, and the cumulative light dose on the surface is 1.5–6.0 J / cm². 2 .

[0033] The cable with the insulation layer described in S3 has an insulation thickness of 0.4 to 1.2 mm.

[0034] Furthermore, the cable stranding described in S41 has a cable pitch ratio of 12, and the filler rope is made of polypropylene.

[0035] The shielding layer described in S41 is an aluminum-plastic composite tape, which is wrapped longitudinally with the aluminum foil side facing the cable core, and the wrapping overlap rate is ≥25%.

[0036] The melt extrusion described in S42 has the following parameter settings: feeding section temperature 155~175℃, compression section temperature 170~185℃, homogenization section temperature 170~190℃, and die head temperature 195~205℃.

[0037] The cooling and shaping parameters described in S42 are: first stage water temperature 40-60℃, second stage water temperature 20-30℃.

[0038] The heat treatment described in S42 has the following parameters: temperature 70-90℃, duration 12-36h.

[0039] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention improves the flexibility and fatigue life of insulating materials by introducing photoreactive cyclodextrin-based polyrotaxane into the masterbatch of the insulating layer.

[0040] 2. This invention introduces a crosslinking agent containing disulfide bonds to achieve a synergistic effect with photoreactive cyclodextrin-based polyrotaxane, enabling the insulating layer to maintain a high degree of crosslinking while also possessing excellent flexibility. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the cross-sectional structure of a cable, where conductor 1, insulation layer 2, filler 3, shielding layer 4, and sheath layer 5 are shown.

[0042] Figure 2 These are Raman and conversion diagrams of the wire cores with insulation layers prepared in Example 1 and Comparative Example 4, where H represents Example 1 and C represents Comparative Example 4.

[0043] Figure 3 The diagram shows the reaction torque of the bend-resistant and fatigue-resistant high-flexibility cable finally prepared in Example 1 and Comparative Example 4, where H represents Example 1 and C represents Comparative Example 4. Detailed Implementation

[0044] The following embodiments further explain and illustrate the technical solutions of the present invention. It should be specifically noted that each specific embodiment is a concretization and explanation of the technical solution and should not be considered as a limitation on the scope of protection of the present invention. Those skilled in the art still have the right to modify the technical solutions of these embodiments and make equivalent substitutions for some or all of the technical features, and these modifications or substitutions do not change the essence of the corresponding technical solutions, nor do they cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions described in the present invention.

[0045] This invention proposes a highly flexible cable for robots that is resistant to bending and fatigue, and its preparation method. The detailed technical solution is as follows: 1. Raw material preparation α-Cyclodextrin and terminally amino-terminated polyethylene glycol were added to deionized water, stirred, filtered, washed, and dried to obtain quasi-polyrotaxane. The quasi-polyrotaxane was added to a mixed solvent of N,N-dimethylformamide and water in a volume ratio of 1:3, and then 1-adamantanecarboxylic acid and 4-(4,6-dimethoxy-1,3,5-triazin-2-yl)-4-methylmorpholine chloride were added to adjust the pH to 8.0-8.5. The mixture was stirred, dialyzed, and dried. The resulting end-capped polyrotaxane was added to anhydrous N,N-dimethylformamide, and under nitrogen protection, 2-ethyl isocyanate-based methacrylate and bismuth neodecanoate catalysts were added. The mixture was heated to react, and then the reaction solution was poured into excess ethanol to precipitate. The precipitate was filtered, washed, and dried to obtain photoreactive cyclodextrin-based polyrotaxane.

[0046] 4,4'-Dithiodiphenylamine and maleic anhydride were added to N,N-dimethylformamide, stirred, precipitated, filtered, washed, and dried to obtain bismaleamic acid; bismaleamic acid was added to acetic anhydride, and anhydrous sodium acetate was added and stirred, cooled to room temperature, poured into ice water, filtered, washed, and dried to obtain a disulfide crosslinking agent.

[0047] Alpha-cyclodextrin molecules possess a hydrophilic outer surface and a hydrophobic inner cavity. The size of the polyethylene glycol (PEG) chain matches the cavity of the α-cyclodextrin molecule. In aqueous solution, the PEG chain, acting as a "guest molecule," penetrates into the cavity of multiple α-cyclodextrin molecules, forming quasi-polyrotaxanes. The driving force primarily comes from hydrophobic interactions and hydrogen bonding. Although α-cyclodextrin molecules are attached to the PEG chain in quasi-polyrotaxanes, they can still "escape" from the chain ends due to open ends. To prevent α-cyclodextrin from detaching from the PEG chain, large-volume end-capping groups need to be introduced at both ends of the PEG chain. Using adamantyl groups for end-capping effectively prevents α-cyclodextrin molecules from slipping from the PEG chain ends, thus transforming them into stable polyrotaxanes. Ethyl 2-isocyanate methacrylate undergoes nucleophilic addition with the active hydrogen on the side chain or end group of the polyrotaxane, forming a carbamate bond. Bismuth neodecanoate, as an organometallic catalyst, preferentially catalyzes the reaction between -NCO and hydroxyl groups, avoiding side reactions. The methacrylate double bonds introduced in this step impart UV reactivity to polyrotaxane. APDS molecules have an aromatic primary amino group at each end. Maleic anhydride is a cyclic anhydride with high reactivity. Under appropriate conditions, the amino groups of APDS act as nucleophiles, attacking the carbonyl carbon of maleic anhydride, causing the anhydride to open its ring and form an amide bond and a carboxylic acid group. In the presence of acetic anhydride and sodium acetate, heating promotes intramolecular dehydration condensation of adjacent ammonic acid groups in the product, closing the ring to form a more thermally stable five-membered ring structure of maleimide. This bismaleimide contains a reactive C=C double bond at each end, becoming the core functional unit for subsequent thermal / photocrosslinking, while retaining the dynamic disulfide bond at the center.

[0048] 2. Preparation of insulating layer masterbatch Thermoplastic polyurethane (polyether type TPU) and ultra-low density polyethylene (VLDPE) are dried separately, and then mixed with photoreactive cyclodextrin-based polyrotaxane, maleic anhydride-grafted polyethylene, disulfide bond crosslinking agent, silane-modified nano-SiO2, UV photoinitiator, antioxidant, and lubricant. The mixture is then melt-extruded, cooled, granulated, dried, and sieved to obtain the insulation layer masterbatch.

[0049] This invention employs a dual-matrix resin system of TPU and VLDPE as the insulating layer. It provides excellent elasticity, abrasion resistance, and oil resistance, as well as excellent flexibility, crack resistance, and dielectric properties. The blending of the two resins achieves complementary properties: the elasticity of TPU combined with the flexibility of VLDPE ensures the insulating layer exhibits good resilience during repeated bending while being less prone to stress cracking. TPU and PE are incompatible systems; direct blending results in high interfacial tension and uneven dispersion. This invention introduces photoreactive cyclodextrin-based polyrotaxane as a "molecular pulley" and interfacial compatibilizer into the system. By grafting maleic anhydride onto polyethylene and cyclodextrin molecules, effective compatibilization of the two-phase interface is achieved, avoiding the negative impact of adding additional small-molecule compatibilizers on insulation performance. In the photoreactive cyclodextrin-based polyrotaxane molecule, α-cyclodextrin cyclic molecules are interwoven with polyethylene glycol chains and can slide freely along the PEG chains. When the insulating layer is subjected to external bending stress, these sliding cyclic molecules can slide along the PEG chain like "pulleys," dispersing the concentrated stress over a larger area, thereby dissipating strain energy and delaying fatigue damage. The disulfide bond crosslinking agent participates in the crosslinking reaction under UV light initiation, constructing a dynamic covalent crosslinking network in the insulating layer. Disulfide bonds exhibit rapid exchange reaction kinetics, enabling them to break and recombine rapidly under stress, dissipating energy. The silane-modified nano-SiO2 surface changes from hydrophilic to hydrophobic, exhibiting good compatibility with the organic matrix. After uniform dispersion in the matrix, the silane-modified nano-SiO2 effectively enhances the tensile strength, wear resistance, and heat resistance of the insulating layer.

[0050] 3. Extrusion and crosslinking The insulation masterbatch is extruded and coated onto the outer layer of a copper wire stranded conductor, then crosslinked in a gradient and cooled to set, resulting in a cable with an insulation layer.

[0051] UV photoinitiator molecules absorb ultraviolet photon energy of a specific wavelength, transitioning from the ground state to an excited state. The excited-state photoinitiator molecules generate active free radicals through α-cleavage or hydrogen abstraction reactions. These free radicals attack the CH bonds on the polymer molecular chain, forming macromolecular free radicals on the polymer backbone. These macromolecular free radicals combine with each other or react with multifunctional crosslinking agents to form a three-dimensional network crosslinked structure. No small molecule byproducts are generated during the entire crosslinking process, so it does not degrade electrical insulation performance like traditional peroxide chemical crosslinking.

[0052] Ultraviolet light exhibits exponential decay when penetrating an insulating layer: the light intensity gradually decreases with increasing penetration depth. The absorption of ultraviolet light by the photoinitiator is mainly concentrated on the surface of the insulating layer. When the outer layer receives a sufficient dose of ultraviolet light, the photoinitiator is fully activated, and the cross-linking reaction proceeds fully and completely, forming a highly cross-linked structure. When the ultraviolet light penetrates to the inner layer, its intensity has significantly decreased, the photoinitiator activation is low, and the cross-linking reaction is incomplete, forming a low-cross-linked structure. This radial gradient distribution of decreasing cross-linking degree from the outside to the inside endows the insulating layer with unique performance advantages: the high cross-linking of the outer layer provides excellent heat resistance, oil resistance, and mechanical strength; the low cross-linking of the inner layer maintains good flexibility and avoids stress concentration. The insulating layer coating thickness of this invention is 0.4–1.2 mm. Within this thickness range, ultraviolet light can effectively penetrate the entire insulating layer while ensuring a significant gradient cross-linking effect. For thicker insulating layers, sufficient cross-linking degree can be ensured by adjusting the traction speed, extending the illumination time, or increasing the number of electrodeless lamp module units.

[0053] Cable preparation and post-processing The insulating cores are stranded together, and then a shielding layer is wrapped around the cores to obtain a core with a shielding layer. The dried thermoplastic polyurethane is melt-extruded onto the core with the shielding layer, cooled and shaped, heat-treated, and cooled to room temperature to obtain a highly flexible cable that is resistant to bending and fatigue.

[0054] Cable cabling is the process of twisting multiple insulated wire cores into a cable core according to certain rules. Its purpose is to meet the requirements of multi-core cables, maintain cable structural stability, increase cable flexibility, and reduce line loss. The main function of the shielding layer is to reduce external electromagnetic interference and prevent internal cable signals from interfering with the outside world. Aluminum-plastic composite tape is wrapped around the cable core; the aluminum foil layer provides metallic shielding, while the plastic layer provides insulation and mechanical protection.

[0055] During extrusion, TPU melt generates internal stress upon cooling and solidification. Heat treatment allows the TPU molecular chains to gain sufficient energy for segmental movement and conformational rearrangement, thereby releasing internal stress and preventing stress cracking of the sheath layer during use. This process makes the cross-linked network more uniform and complete, improving the overall performance of the insulation layer. Furthermore, at the heat treatment temperature, reversible disulfide bond exchange reactions can occur in the insulation layer, achieving dynamic adjustment of the cross-linked network and stress relaxation. In addition, heat treatment helps improve the interfacial bonding between the sheath layer and the shielding layer, and between the shielding layer and the insulation layer, resulting in tighter bonding between the cable layers and improving the cable's overall integrity and anti-delamination capability.

[0056] Example 1

[0057] A method for preparing a highly flexible, bend-resistant, and fatigue-resistant cable for robots is as follows: Table 1 Main Raw Materials

[0058] S1: Raw material preparation.

[0059] S11: Add 20.06g of α-cyclodextrin and 10g of terminally amino-terminated polyethylene glycol to 300mL of deionized water, stir (temperature 40℃, speed 350rpm, time 24h), filter, wash, and dry at 50℃ for 18h to obtain quasi-polyrotaxane.

[0060] S12: The quasi-polyrotaxane prepared in S11 was added to a mixed solvent of 150 mL water and 50 mL N,N-dimethylformamide, followed by the addition of 0.92 g of 1-adamantanecarboxylic acid and 1.694 g of 4-(4,6-dimethoxy-1,3,5-triazin-2-yl)-4-methylmorpholine chloride. The pH was adjusted to 8.4, and the mixture was stirred (25 °C, 300 rpm, 24 h). After dialyzing and drying, the resulting end-capped polyrotaxane was added to anhydrous N,N-dimethylformamide. Under nitrogen protection, 0.735 g of 2-ethyl isocyanate methacrylate and 0.02 g of bismuth neodecanoate catalyst were added, and the mixture was heated to react. The reaction solution was then poured into excess ethanol to precipitate the precipitate. After filtration, washing, and drying, the photoreactive cyclodextrin-based polyrotaxane was obtained.

[0061] S13: 5.121 g (20.0 mmol) of 4,4'-dithiodiphenylamine and 4.16 g (42 mmol) of maleic anhydride were added to 100 mL of N,N-dimethylformamide. The mixture was stirred at 450 rpm for 8 h at 30 °C, cooled to room temperature, precipitated with ethanol, filtered, washed 5 times with ethanol, and dried at 55 °C for 18 h to obtain bismaleamic acid.

[0062] S14: Add 5g of the bismaleamic acid prepared by S13 to acetic anhydride, stir (temperature 80℃, speed 300rpm, time 4h), cool to room temperature, add excess ethanol to precipitate, filter, wash 5 times with ethanol, and dry at 55℃ for 18h to obtain disulfide crosslinking agent (maleimide equivalent is 190~220g / eq).

[0063] S2: Preparation of insulating layer masterbatch: 70g of thermoplastic polyurethane and 40g of ultra-low density polyethylene were dried separately. Then, 65g of thermoplastic polyurethane, 5g of maleic anhydride-grafted polyethylene, 35g of ultra-low density polyethylene, 5.5g of photoreactive cyclodextrin-based polyrotaxane prepared in S12, 2.5g of disulfide crosslinking agent prepared in S14, 4g of silane-modified nano-SiO2, 1g of UV photoinitiator (benzophenone), 0.7g of antioxidant (antioxidant 1010), and 0.5g of lubricant (zinc stearate) were mixed (temperature 30℃, speed 1000rpm, duration 10min), melt extruded (feeding section temperature 160℃, melting section temperature 180℃, homogenization section temperature 190℃, die head temperature 190℃, screw speed 200rpm), cooled, granulated, dried, and sieved to obtain the insulating layer masterbatch.

[0064] S3: Extrusion and cross-linking. The insulating masterbatch prepared in S2 is extruded and coated onto the outer layer of a copper wire stranded conductor (150 tin-plated soft copper wires with a diameter of 0.08 mm stranded together to form a nominal cross-sectional area of ​​approximately 0.75 mm²). 2 (Conductor), gradient cross-linking (8 groups of UV-LEDs evenly distributed in a ring, ultraviolet light wavelength 365nm, intensity 1000mW / cm²) 2 The wire core is pulled at a speed of 10 m / min and exposed to light for 5 seconds. After cooling and shaping, an insulation layer is obtained (insulation thickness is 0.80 ± 0.05 mm).

[0065] S4: Cable preparation.

[0066] S41: The wire cores with insulation prepared in S3 are stranded into cables (the cable pitch ratio is 12 times, and the filler rope is polypropylene). Then, a shielding layer is wrapped around the outside of the cable core (the shielding layer is an aluminum-plastic composite tape, with the aluminum foil facing the direction of the cable core, wrapped in a longitudinal manner, with a wrapping overlap rate of 45%), to obtain a wire core with a shielding layer.

[0067] S42: The dried thermoplastic polyurethane prepared in S2 is melt-extruded (feeding section temperature 165℃, compression section temperature 177℃, homogenization section temperature 180℃, die head temperature 200℃) and then coated onto the shielded core prepared in S41 (sheath nominal thickness 1.20mm). Cooling and shaping (first stage water temperature 50℃, second stage water temperature 25℃), heat treatment (temperature 80℃, duration 24h), and cooling to room temperature yields a highly flexible cable with bending resistance and fatigue resistance. Figure 1 This is a schematic diagram of the cable cross-section, where conductor 1, insulation layer 2, filler 3, shielding layer 4, and sheath layer 5 are shown.

[0068] Example 2

[0069] The composition and preparation process are the same as in Example 1, except that: In step S11 of the preparation process, the stirring parameters are set as follows: temperature 30℃, rotation speed 200rpm, and time 12h. The drying parameters are set as follows: temperature 40℃ and time 12h. Other steps are the same.

[0070] The stirring parameters in step S12 of the preparation process are set as follows: temperature 20℃, rotation speed 200rpm, duration 12h, and other steps are the same.

[0071] In the S2 step of the preparation process, the mixing parameters are set as follows: temperature 25℃, rotation speed 500rpm, duration 5min. The melt extrusion parameters are set as follows: feeding section temperature 150℃, melting section temperature 170℃, homogenization section temperature 180℃, die head temperature 185℃, screw rotation speed 100rpm. Other steps are the same.

[0072] In the preparation process S2, the UV photoinitiator is benzoin dimethyl ether, the antioxidant is antioxidant 168, the lubricant is calcium stearate, and the other components are the same.

[0073] In the S3 step of the preparation process, the gradient crosslinking parameters were set as follows: 8 groups of UV-LEDs were evenly distributed in a ring, with a cumulative surface light dose of 1.5 J / cm². 2 The other steps are the same.

[0074] In process S3, the thickness of the cable covered with insulation is 0.4 mm, and the other components are the same.

[0075] Example 3

[0076] The composition and preparation process are the same as in Example 1, except that: In step S11 of the preparation process, the stirring parameters are set as follows: temperature 50℃, rotation speed 500rpm, and time 36h. The drying parameters are set as follows: temperature 60℃ and time 24h. Other steps are the same.

[0077] The stirring parameters in step S12 of the preparation process are set as follows: temperature 40℃, rotation speed 500rpm, duration 36h, and other steps are the same.

[0078] In the S2 step of the preparation process, the mixing parameters are set as follows: temperature 40℃, rotation speed 1500rpm, duration 15min. The melt extrusion parameters are set as follows: feeding section temperature 170℃, melting section temperature 190℃, homogenization section temperature 200℃, die head temperature 195℃, screw speed 300rpm. Other steps are the same.

[0079] In the preparation process S2, the UV photoinitiator is 2-hydroxy-2-methyl-1-phenylpropanone, the lubricant is polyethylene wax, and the other components are the same.

[0080] In step S3 of the preparation process, the gradient crosslinking parameters were set as follows: 8 groups of UV-LEDs were evenly distributed in a ring, with a cumulative surface light dose of 6.0 J / cm². 2The other steps are the same.

[0081] In process S3, the thickness of the cable covered with insulation is 1.2 mm, and the other components are the same.

[0082] Example 4

[0083] The composition and preparation process are the same as in Example 1, except that: In the preparation process, the molar ratio of 4,4'-dithiodiphenylamine to maleic anhydride in S13 is 1:2, and the other components are the same.

[0084] In the preparation process S13, the stirring parameters were set as follows: temperature 20℃, speed 300rpm, duration 4h. For drying, the parameters were set as follows: temperature 50℃, duration 12h. Other steps were the same.

[0085] The stirring parameters in step S14 of the preparation process are set as follows: temperature 70℃, rotation speed 200rpm, duration 2h, and other steps are the same.

[0086] In process S2, the UV photoinitiator is benzoin dimethyl ether, the antioxidant is antioxidant 168, the lubricant is calcium stearate, and the insulating layer masterbatch, based on a total mass of thermoplastic polyurethane and ultra-low density polyethylene of 100 parts by weight, comprises: 55 parts thermoplastic polyurethane, 45 parts ultra-low density polyethylene, 2 parts maleic anhydride-grafted polyethylene, 3 parts photoreactive cyclodextrin-based polyrotaxane, 1 part disulfide crosslinking agent, 2 parts silane coupling agent-modified nano-silica, 0.5 parts UV photoinitiator, 0.3 parts antioxidant, and 0.2 parts lubricant, with other components being the same.

[0087] In the S42 process of preparation, the parameters for melt extrusion are set as follows: feeding section temperature 155℃, compression section temperature 170℃, homogenization section temperature 170℃, die head temperature 195℃. The cooling and shaping parameters are set as follows: first stage water temperature 40℃, second stage water temperature 20℃. The heat treatment parameters are set as follows: temperature 70℃, duration 12h. Other steps are the same.

[0088] Example 5

[0089] The composition and preparation process are the same as in Example 1, except that: In the preparation process, the molar ratio of 4,4'-dithiodiphenylamine to maleic anhydride in S13 is 1:2.2, and the other components are the same.

[0090] In step S13 of the preparation process, the stirring parameters are set as follows: temperature 40℃, rotation speed 600rpm, and duration 12h. For drying, the parameters are set as follows: temperature 60℃ and duration 24h. Other steps are the same.

[0091] The stirring parameters in step S14 of the preparation process are set as follows: temperature 90℃, rotation speed 400rpm, duration 6h, and other steps are the same.

[0092] In the S2 step of the preparation process, the UV photoinitiator is benzoin dimethyl ether. The insulating layer masterbatch, based on a total mass of thermoplastic polyurethane and ultra-low density polyethylene of 100 parts by weight, comprises: 75 parts thermoplastic polyurethane, 25 parts ultra-low density polyethylene, 8 parts maleic anhydride-grafted polyethylene, 10 parts photoreactive cyclodextrin-based polyrotaxane, 4 parts disulfide crosslinking agent, 6 parts silane coupling agent-modified nano-silica, 1.5 parts UV photoinitiator, 1.2 parts antioxidant, and 0.8 parts lubricant. The other components are the same.

[0093] In the S42 process of preparation, the parameters for melt extrusion are set as follows: feeding section temperature 175℃, compression section temperature 185℃, homogenization section temperature 190℃, die head temperature 205℃. The cooling and shaping parameters are set as follows: first stage water temperature 60℃, second stage water temperature 30℃. The heat treatment parameters are set as follows: temperature 90℃, duration 36h. Other steps are the same.

[0094] Comparative Example 1 The composition and preparation process are the same as in Example 1, except that: In step S2 of the preparation process, no photoreactive cyclodextrin-based polyrotaxane is added, but 3.58g of TPU and 1.93g of VLDPE are added, and the other steps are the same.

[0095] Comparative Example 2 The composition and preparation process are the same as in Example 1, except that: In step S2 of the preparation process, no disulfide crosslinking agent is added, but 1.63g of TPU and 0.88g of VLDPE are added, and the other steps are the same.

[0096] Comparative Example 3 The composition and preparation process are the same as in Example 1, except that: In step S2 of the preparation process, no photoreactive cyclodextrin-based polyrotaxane and disulfide crosslinking agent are added; instead, 5.20 g of TPU and 2.80 g of VLDPE are added, and the other steps are the same.

[0097] Comparative Example 4 The composition and preparation process are the same as in Example 1, except that: In the S3 step of the preparation process, the ultraviolet light crosslinking process adopts a uniform light irradiation method. By extending the light irradiation time, the insulation layer as a whole achieves the same degree of crosslinking. The other steps are the same.

[0098] Samples of the wire cores with insulation layers prepared in Example 1 and Comparative Example 4 (S3) were taken and placed in an environment of 23°C and 50% relative humidity for 24 hours. They were then coarsely cut and low-temperature leveled (temperature -50°C). The equivalent radius of the conductor and the outer radius of the insulation were measured along the 0°, 45°, 90°, and 135° directions. A wire core that had not undergone UV irradiation was taken as the X=0 reference and Raman testing was performed (laser 785nm, spectral range 700~1800cm⁻¹, step size 25μm). Figure 2 As shown, H represents Example 1, and C represents Comparative Example 4. The overall average conversion rate of H is 73.43%, with an outer layer average of 86.43% and an inner layer average of 56.99%, resulting in an outer-inner difference of approximately 29.44%, forming a continuous and essentially uniform radial gradient in the circumferential direction. This morphology directly corresponds to higher network constraint and wear / heat resistance in the outer layer, and higher segment mobility and flexibility in the inner layer. The overall average conversion rate of C is 74.28%, close to that of H, but the difference between the outer and inner layers is only about 0.47%.

[0099] Samples (800 mm long, 600 mm effective movement length between clamps) of the high-flexibility, bend-resistant, and fatigue-resistant cables finally prepared in Example 1 and Comparative Example 4 were taken and placed in an environment of 23°C and 50% relative humidity for 24 hours. Crimping terminals were preferred for conductor termination, and flexible strain release was implemented. The current and voltage terminals for four-wire resistance measurement were led out separately, with the voltage terminal close to the effective test section. The shielding layer and insulation monitoring terminals were led out separately (bending radius R = 4D, acceleration group R = 2.5D, bending waveform ±90° sine, torsional waveform ±180° sine, axial tension 7.4 N, four-wire 100 mA, 2 kHz sampling, torque ±1 N·m). The initial state was measured before fatigue, and the post-fatigue state was measured at 4.0 × 10⁻⁶. 5 After that, restore the temperature to 23±2℃, and measure again after 2 hours. Figure 3 As shown, H represents Example 1 and C represents Comparative Example 4. The initial peak value of H is approximately 0.112 N·m, and after fatigue it is approximately 0.128 N·m, an increase of approximately 13.9%. C increases from approximately 0.265 N·m to 0.359 N·m, an increase of approximately 35.3%. Therefore, under the same motion trajectory, H applies a significantly lower peak reaction load to the robot joint, and the stiffness drift after fatigue is also smaller. C increases from 0.321 J to 0.493 J. The smaller hysteresis area means that the additional energy consumption generated by internal friction and viscoelastic dissipation in each motion cycle of the cable is lower. The smaller increase in area after fatigue indicates that the structure and material state are more stable.

[0100] Based on Examples 1-5 and Comparative Examples 1-4, samples of the finally prepared bending-resistant and fatigue-resistant high-flexibility cable were taken and subjected to a minimum bending radius test: a cable sample (5m in length) was cut from the sample and placed at room temperature for 24 hours. The midpoint of the cable sample was tightly wrapped around the mandrel, and the cable was bent along the mandrel to 180° (held for 2 minutes). The cable was then removed and inspected. If no cracks, splits, conductor breaks, or other damage were found, the bending radius corresponding to this mandrel diameter was recorded as qualified. If damage was found, it was recorded as unqualified. The above operation was repeated with mandrels of different diameters until the minimum mandrel diameter that would not cause damage was found.

[0101] Based on Examples 1-5 and Comparative Examples 1-4, samples of the finally prepared high-flexibility cable with bending resistance and fatigue resistance were taken for fatigue life testing: a cable sample (600 mm in length) was cut from the specimen and placed at room temperature for 24 hours. The cable sample was then mounted on a testing machine (R = 2.5D, where D is the cable outer diameter), and a load (m = 1.0 kg / mm²) was applied. 2 × total conductor cross-sectional area), reciprocating bending (angle ±90°, 30±5 cycles / min, stroke 1m), stop the machine every 50,000 cycles to check the sheath, shield and insulation. When the conductor conducts a break in conductivity, or when visible cracks are found in the insulation layer during visual inspection, the sample fails. At this time, record the total number of cycles on the equipment, test 5 groups, and take the average value.

[0102] Based on Examples 1-5 and Comparative Examples 1-4, samples of the insulation material of the finally prepared bending-resistant and fatigue-resistant high-flexibility cable were taken for tensile strength retention rate testing: dumbbell-shaped specimens were prepared and placed in an environment of 23°C and 50% relative humidity for 24 hours. They were divided into experimental and blank groups. The blank group was not treated in any way, while the experimental group underwent aging treatment (temperature 85°C, relative humidity 85%, duration 168 hours). After being taken out, they were restored in an environment of 23°C and 50% relative humidity for 4 hours. The experimental and blank groups were subjected to tensile tests (250 mm / min) using a universal testing machine. The maximum tensile force at the time of specimen fracture was recorded, and the tensile strength retention rate was calculated.

[0103] Based on Examples 1-5 and Comparative Examples 1-4, samples of the finally prepared high flexibility cable with bending resistance and fatigue resistance were taken and insulation resistance tests were performed: cable samples (10m in length) were cut from the sample and placed in an environment of 23°C and 50% relative humidity for 24 hours. The insulation resistance between each core and the other cores and the metal layer (connected together) was measured (voltage range 300V). After waiting for 1 minute, the insulation resistance value after stabilization was recorded. The values ​​were calculated, and the average value was taken after 5 measurements.

[0104] The specific test results are shown in Table 2. Figure 2 , Figure 3 As shown: Table 2 Comparison of core performance of Examples 1-5 and Comparative Examples 1-4

[0105] The comparison results above show that Example 1 exhibits the best overall performance. The photoreactive cyclodextrin-based polyrotaxane ensures uniform stress dispersion, while the disulfide crosslinking agent provides dynamic and reversible crosslinking points, allowing for molecular chain rearrangement. During bending, the chain continuously breaks and reassembles, consuming fatigue energy and delaying crack propagation. This demonstrates that Example 1 successfully solves the current problem of insulating materials simultaneously achieving high flexibility, fatigue life, and environmental adaptability. Examples 2 to 5 show slightly lower overall performance than Example 1 but still maintain a high level, indicating that excellent performance balance was achieved even with a wide range of parameter variations. Comparative Example 1, lacking the addition of photoreactive cyclodextrin-based polyrotaxane, suffers from stress concentration leading to poor flexibility, short fatigue life, and reduced resistance to damp heat aging due to the absence of physical shielding properties from cyclodextrin. Comparative Example 2, without the addition of a disulfide crosslinking agent, cannot allow the molecular chains to rearrange during deformation, resulting in insufficient flexibility and fatigue resistance. Its fixed crosslinking structure prevents the release of internal stress during damp heat aging. Comparative Example 3, lacking both photoreactive cyclodextrin-based polyrotaxane and a disulfide crosslinking agent, exhibits comprehensive performance degradation. Comparative Example 4, using uniform illumination, achieves consistent crosslinking levels inside and outside the insulation layer, but the surface layer becomes over-crosslinked and brittle, while the inner layer is under-crosslinked and lacks sufficient strength.

[0106] In summary, it is clear from the above embodiments and comparative examples that the high flexibility cable for robots provided by the present invention is significantly superior to traditional solutions in terms of minimum bending radius, fatigue life, tensile strength retention rate, and insulation resistance. This is attributed to the synergistic effect of photoreactive cyclodextrin-based polyrotaxane and disulfide crosslinking agent components, combined with a gradient ultraviolet crosslinking process, which achieves a balance between flexibility, fatigue life, and environmental adaptability.

Claims

1. A high-flexibility cable for robots, resistant to bending and fatigue, comprising at least one insulated core, a shielding layer disposed outside the insulated core, and a sheathing layer disposed outside the shielding layer, each insulated core comprising a stranded conductor and an insulation layer extruded outside the stranded conductor, characterized in that: The insulating layer is formed by melt extrusion and circumferential ultraviolet irradiation of an insulating layer composition; the insulating layer composition includes thermoplastic polyurethane, ultra-low density polyethylene, maleic anhydride-grafted polyethylene, photoreactive cyclodextrin-based polyrotaxane, disulfide-bonded bismaleimide, silane coupling agent-modified nano-silica, photoinitiator, antioxidant, and lubricant; the photoreactive cyclodextrin-based polyrotaxane includes a polyethylene glycol axial molecule, a plurality of α-cyclodextrin rings sleeved on the polyethylene glycol axial molecule, and end-capping groups disposed at both ends of the polyethylene glycol axial molecule, wherein the α-cyclodextrin rings have acrylate groups that can be polymerized by free radicals; the insulating layer has a crosslinking density that decreases from the outside to the inside along its radial direction.

2. The high-flexibility, bend-resistant, and fatigue-resistant cable for robots according to claim 1, characterized in that: The insulating layer composition comprises a matrix resin and additives; the matrix resin comprises thermoplastic polyurethane and ultra-low density polyethylene, wherein the content of thermoplastic polyurethane is 55-75 parts by weight, the content of ultra-low density polyethylene is 25-45 parts by weight, and the sum of the contents of thermoplastic polyurethane and ultra-low density polyethylene is 100 parts by weight; relative to 100 parts by weight of the matrix resin, the additives comprise: 2-8 parts by weight of maleic anhydride-grafted polyethylene, 3-10 parts by weight of photoreactive cyclodextrin-based polyrotaxane, 1-4 parts by weight of disulfide-containing bismaleimide, 2-6 parts by weight of silane coupling agent-modified nano-silica, 0.5-1.5 parts by weight of UV photoinitiator, 0.3-1.2 parts by weight of antioxidant, and 0.2-0.8 parts by weight of lubricant.

3. The high-flexibility, bend-resistant, and fatigue-resistant cable for robots according to claim 1, characterized in that: The photoreactive cyclodextrin-based polyrotaxane has a axial molecule that is bi-terminated PEG with a number average molecular weight of 4000-8000 and a cyclic molecule that is α-cyclodextrin. The end-capping rate of the photoreactive cyclodextrin-based polyrotaxane is not less than 95%. The composition of each raw material, by mass, is as follows: α-cyclodextrin 60.01 parts, end-amino-terminated polyethylene glycol 29.91 parts, 1-adamantanecarboxylic acid 2.75 parts, 4-(4,6-dimethoxy-1,3,5-triazin-2-yl)-4-methylmorpholine chloride 5.07 parts, 2-ethyl isocyanate methacrylate 2.20 parts, and bismuth neodecanoate catalyst 0.06 parts.

4. The high-flexibility, bend-resistant, and fatigue-resistant cable for robots according to claim 1, characterized in that: The disulfide-containing bismaleimide has a maleimide equivalent of 190–220 g / eq.

5. A method for preparing a high-flexibility, bend-resistant, and fatigue-resistant cable for robots according to any one of claims 1-4, characterized in that, Includes the following steps: S1: Raw material preparation; S11: Add α-cyclodextrin and terminally amino-terminated polyethylene glycol to deionized water, stir, filter, wash, and dry to obtain quasi-polyrotaxane; S12: The quasi-polyrotaxane prepared in S11 was added to a mixed solvent of N,N-dimethylformamide and water in a volume ratio of 1:

3. Then, 1-adamantane carboxylic acid and 4-(4,6-dimethoxy-1,3,5-triazin-2-yl)-4-methylmorpholine chloride were added, the pH was adjusted to 8.0-8.5, the mixture was stirred, dialyzed, and dried. The resulting end-capped polyrotaxane was added to anhydrous N,N-dimethylformamide, and 2-ethyl isocyanate methacrylate and bismuth neodecanoate catalysts were added under nitrogen protection. The mixture was heated and reacted. The reaction solution was then poured into excess ethanol to precipitate the precipitate. The precipitate was filtered, washed, and dried to obtain photoreactive cyclodextrin-based polyrotaxane. S13: Add 4,4'-dithiodiphenylamine and maleic anhydride to N,N-dimethylformamide, stir, precipitate, filter, wash, and dry to obtain bismaleamic acid; S14: Add the bismaleamic acid prepared in S13 to acetic anhydride, add anhydrous sodium acetate and stir, cool to room temperature, pour into ice water, filter, wash and dry to obtain disulfide bond crosslinking agent; S2: Preparation of insulating layer masterbatch: Thermoplastic polyurethane and ultra-low density polyethylene are dried separately, and then mixed with photoreactive cyclodextrin-based polyrotaxane prepared in S12, maleic anhydride-grafted polyethylene, disulfide crosslinking agent prepared in S14, silane-modified nano-SiO2, UV photoinitiator, antioxidant, and lubricant. The mixture is melt-extruded, cooled, granulated, dried, and sieved to obtain insulating layer masterbatch. S3: Extrusion and crosslinking. The insulating masterbatch prepared in S2 is coated onto the outer layer of the copper wire stranded conductor through an extruder, and then crosslinked in a gradient. After cooling and shaping, the wire core with the insulating layer is obtained. S4: Cable preparation; S41: The wire cores with insulation prepared in S3 are stranded into cables, and then a shielding layer is wrapped around the outside of the cable cores to obtain wire cores with shielding layers. S42: The dried thermoplastic polyurethane prepared in S2 is melt-extruded onto the wire core with shielding layer prepared in S41, cooled and shaped, heat-treated, and cooled to room temperature to obtain a highly flexible cable that is resistant to bending and fatigue.

6. The method for preparing a high-flexibility, bend-resistant, and fatigue-resistant cable for robots according to claim 5, characterized in that: The stirring described in S11 has the following parameters: temperature 30-50℃, speed 200-500rpm, and duration 12-36h. The drying described in S11 has the following parameters: temperature 40-60℃, duration 12-24h. The stirring described in S12 has the following parameters: temperature 20-40℃, speed 200-500rpm, and duration 12-36h.

7. The method for preparing a high-flexibility, bend-resistant, and fatigue-resistant cable for robots according to claim 5, characterized in that: The 4,4'-dithiodiphenylamine described in S13 has a molar ratio of 1:2 to 1:2.2 with maleic anhydride. The stirring described in S13 has the following parameters: temperature 20-40℃, speed 300-600rpm, and duration 4-12h. The drying process described in S13 has the following parameters: temperature 50-60℃, duration 12-24h. The stirring described in S14 has the following parameters: temperature 70-90℃, speed 200-400rpm, and duration 2-6h.

8. The method for preparing a high-flexibility, bend-resistant, and fatigue-resistant cable for robots according to claim 5, characterized in that: The mixing parameters described in S2 are: temperature ≤ 50℃, rotation speed 500~1500rpm, and duration 5~15min; The melt extrusion described in S2 has the following parameter settings: feeding section temperature 150-170℃, melting section temperature 170-190℃, homogenization section temperature 180-200℃, die head temperature 185-195℃, and screw speed 100-300 rpm. The UV photoinitiator described in S2 is one or more of benzophenone, dimethyl benzoate, and 2-hydroxy-2-methyl-1-phenylpropanone; The antioxidant mentioned in S2 is antioxidant 1010 or antioxidant 168; The lubricant described in S2 is one or more of zinc stearate, calcium stearate, and polyethylene wax.

9. A method for preparing a high-flexibility, bend-resistant, and fatigue-resistant cable for robots according to claim 5, characterized in that: The gradient crosslinking described in S3 has the following parameter settings: 8 groups of UV-LEDs are evenly distributed in a ring, and the cumulative light dose on the surface is 1.5–6.0 J / cm². 2 ; The insulation layer of the wire core described in S3 has an insulation thickness of 0.4 to 1.2 mm.

10. A method for preparing a high-flexibility, bend-resistant, and fatigue-resistant cable for robots according to claim 5, characterized in that: The cable stranding described in S41 has a cable pitch ratio of 12, and the filler rope is made of polypropylene. The wrapping shielding layer described in S41 is an aluminum-plastic composite tape, which is wrapped longitudinally with the aluminum foil side facing the cable core direction, and the wrapping overlap rate is ≥25%. The melt extrusion described in S42 has the following parameter settings: feeding section temperature 155~175℃, compression section temperature 170~185℃, homogenization section temperature 170~190℃, and die head temperature 195~205℃. The cooling and shaping described in S42 has the following parameter settings: first stage water temperature 40-60℃, second stage water temperature 20-30℃; The heat treatment described in S42 has the following parameters: temperature 70-90℃, duration 12-36h.

Citation Information

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