Anti-loose method for anchor device of suspension bridge sling
Patent Information
- Application Number
- CN202611299608.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-08-26
- Publication Date
- 2026-10-27
AI Technical Summary
[0008]本发明的目的在于克服现有悬索桥吊索锚具螺纹连接在振动、冲击、交变荷载等多因素耦合作用下易发生微动磨损和渐进松动的技术缺陷,提供一种防松型悬索桥吊索锚具的防松方法
[0029]本发明提供了一种防松型悬索桥吊索锚具的防松方法,是一种通过多重锥面锁紧机制实现长效防松的吊索锚具的防松方法,具备以下具体优点:
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Figure CN122980331A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of suspension bridge engineering technology, and in particular to a method for preventing loosening of anti-loosening suspension bridge cable anchorages. Background Technology
[0002] The suspender cable is a key load-bearing component in a suspension bridge, connecting the main cable and the stiffening girder. Its reliable anchorage directly affects the overall safety and service life of the bridge. Therefore, the design of the suspender cable anchorage structure has always been a core technical issue in suspension bridge engineering. The suspender cable itself consists of multiple parallel steel wire bundles, and its ends are anchored to achieve the transmission of cable force and reliable anchorage.
[0003] A typical sling anchoring structure consists of three core parts: the anchor cup, the anchoring material, and the wire bundle. The anchor cup is a cylindrical or conical steel sleeve, with one end threaded to the sling lug or connecting plate, and the other end open to accommodate the anchoring material. The anchoring material is typically a high-strength zinc-copper alloy or epoxy iron sand, forming an anchoring cone within the anchor cup cavity. The wire bundle, after its ends unfurl, is wrapped by the anchoring medium. The sling force is transferred through the gripping force and mechanical interlocking force between the anchoring medium and the wire bundle. The sling force is transmitted via the following path: twisted wire bundle → anchoring material → anchor cup conical cavity → anchor cup external thread → nut or lug → main cable clamp or stiffening beam.
[0004] The fit between the anchor cup's external thread and the nut or lug is crucial for transferring cable force from the anchor cup to the lug. Threaded connections generally possess self-locking properties, ensuring safety and reliability under static loads. Because the helix angle of the thread is smaller than the equivalent friction angle of the threaded pair, the threaded connection is structurally self-locking under non-alternating load conditions. Furthermore, the friction on the supporting surfaces such as the nut after tightening also prevents the threads from loosening.
[0005] However, during the service life of suspension bridges, the cables are subjected to the combined effects of multiple factors, including vibrations caused by vehicle traffic, wind-induced vibrations, and temperature changes. Studies have shown that lateral loads (tangential loads) are more likely to cause thread loosening than axial loads. The core mechanism is that lateral loads cause radial relative displacement between the thread engagement area and the bearing surface, significantly increasing the probability of rotational loosening. Under specific load conditions, the main cable suspenders of long-span suspension bridges exhibit significant lateral displacement and longitudinal oscillation, and the threaded pairs are highly susceptible to fretting wear and gradual loosening under alternating forces.
[0006] In existing technologies, anti-loosening measures for suspension cables mainly include: traditional anti-loosening methods such as spring washers and locking washers; friction-based anti-loosening methods such as nylon insert locking nuts; or mechanical anti-loosening methods such as double-nut locking. In recent years, some bridges have adopted conical clamping self-locking anti-loosening nuts or separable elastic self-tightening anti-loosening nuts. However, the above-mentioned anti-loosening measures are mainly aimed at general threaded fasteners and are not specifically designed for the special stress characteristics and service environment of suspension bridge cable anchorages. The threaded connection of the anchorage bears hundreds of tons of alternating cable force, and the anchorage is exposed to the atmosphere for a long time. Ordinary anti-loosening measures are difficult to meet the long-term anti-loosening requirements of suspension cable anchorages during their decades of service.
[0007] Therefore, there is an urgent need for a special anti-loosening method for suspension bridge cable anchorages that can maintain the reliability of threaded connections under the coupled effects of multiple factors such as vibration, impact, and alternating loads, and ensure the long-term service safety of the cables. Summary of the Invention
[0008] The purpose of this invention is to overcome the technical defects of existing suspension bridge cable anchorage threaded connections that are prone to fretting wear and gradual loosening under the coupled effects of multiple factors such as vibration, impact, and alternating loads, and to provide a method for preventing loosening of suspension bridge cable anchorage.
[0009] The objective of this invention is achieved as follows:
[0010] A method for preventing loosening of a suspension bridge cable anchor is based on a type of anti-loosening suspension bridge cable anchor, which includes an upper ear plate for the cable, an upper anti-loosening nut, an upper cable anchor cup, a cable body, a lower cable anchor cup, a nut with an eccentric cone, and a lower anti-loosening nut.
[0011] The bottom of the upper ear plate of the sling is provided with an outer conical surface, and the upper anti-loosening nut is provided with an inner conical hole and a cylindrical hole. The inner conical hole of the upper anti-loosening nut is fitted outside the outer conical surface of the upper ear plate of the sling, and the cylindrical hole of the upper anti-loosening nut is threadedly connected to the upper sling anchor cup. The half-cone angle β of the outer conical surface of the upper ear plate of the sling is greater than the half-cone angle α of the inner conical hole of the upper anti-loosening nut.
[0012] The eccentric truncated cone nut has an outer truncated cone and an eccentric internal threaded hole. The lower anti-loosening nut has an internal conical hole and a cylindrical hole. The internal conical hole of the lower anti-loosening nut is fitted onto the outside of the outer truncated cone of the eccentric truncated cone nut. The eccentric internal threaded hole of the eccentric truncated cone nut is threadedly connected to the lower sling anchor cup. The cylindrical hole of the lower anti-loosening nut is threadedly connected to the lower sling anchor cup.
[0013] There is an eccentricity e between the rotation axis of the outer frustum with the eccentric frustum nut and the central axis of the body of the eccentric frustum nut.
[0014] The anti-loosening method includes the following steps:
[0015] Step 1: Insert the sling body into the upper and lower sling anchor cups. The steel wires spread out in the conical cavity of the anchor cups. Cast the anchoring material to form a conical casting, thus completing the sling anchoring.
[0016] Step 2: Connect the upper sling anchor cup to the upper ear plate of the sling with threads. Screw the upper anti-loosening nut into the upper sling anchor cup along the external thread, so that the inner conical hole of the upper anti-loosening nut and the outer conical surface of the upper ear plate of the sling form a conical contact. The wedge effect is formed by the angle difference generated by the half-cone angle α of the inner conical hole being smaller than the half-cone angle β of the outer conical surface, thus achieving the first anti-loosening locking.
[0017] Step 3: Insert the lower sling anchor cup into the eccentric cone nut and the lower anti-loosening nut. Screw the eccentric cone nut into the lower sling anchor cup along the external thread, so that the outer cone of the eccentric cone nut and the inner cone hole of the lower anti-loosening nut form a conical surface fit.
[0018] Step 4: Continue to rotate the eccentric cone nut. Utilize the eccentricity e between the center of rotation of the outer cone and the central axis of the nut body to make the contact pressure between the outer cone surface and the inner cone hole asymmetrically distributed along the circumference, thereby achieving progressive self-locking of the eccentric cone surface and forming the second anti-loosening locking mechanism.
[0019] Furthermore, the upper ear plate of the sling is a fork-shaped ear plate structure, including two ear plates and a connecting platform. The connecting platform is shaped like a frustum of a cone. The two ear plates are arranged opposite each other above the connecting platform. A pin hole is opened in the middle of the ear plate. An anchor cup hole is provided on the bottom surface of the connecting platform. The inner wall of the anchor cup hole is provided with internal threads, which are threaded to the top of the upper sling anchor cup.
[0020] Furthermore, the semi-cone angle β of the outer conical surface of the upper ear plate of the sling and the semi-cone angle α of the inner conical hole of the upper anti-loosening nut satisfy α < β, and the angle difference is... The value range is 1° to 5°.
[0021] Furthermore, the eccentric truncated cone nut includes a truncated cone nut body, an outer truncated cone, and an eccentric hole. The upper part of the truncated cone nut body is cylindrical, and the lower part is an outer truncated cone. The outer truncated cone is in the shape of an inverted truncated cone. The eccentric hole penetrates the truncated cone nut body and has internal threads on its inner wall. The eccentricity e exists between the central axis of the eccentric hole and the central axis of the truncated cone nut body.
[0022] Furthermore, the semi-cone angle of the outer frustum of the eccentric frustum nut is equal to the semi-cone angle of the inner conical hole of the lower anti-loosening nut, forming a full conical surface contact fit.
[0023] Furthermore, the ratio of the eccentricity e of the eccentric truncated cone nut to the nominal radius R of the outer truncated cone, e / R, ranges from 0.02 to 0.10.
[0024] Furthermore, the number of threaded engagements between the upper sling anchor cup and the upper sling ear plate is 10-15 turns, and the number of threaded engagements between the upper anti-loosening nut and the upper sling anchor cup is 5-6 turns; the number of threaded engagements between the lower sling anchor cup and the eccentric cone nut is 10-12 turns, and the number of threaded engagements between the lower anti-loosening nut and the lower sling anchor cup is 5-6 turns.
[0025] Furthermore, in step two, the radial wedging amount generated by the angular difference wedging effect... ,in This refers to the axial advance displacement of the upper lock nut. Total preload , This is the initial preload.
[0026] Furthermore, the ratio of the conical surface length to the conical surface radius of the upper and lower locking nuts... It is in the range of 0.3 to 0.5.
[0027] Furthermore, in step four, the condition for the progressive self-locking of the eccentric conical surface is: the semi-cone angle α of the outer frustum with the eccentric frustum nut. c The semi-cone angle α between the inner conical hole of the lower anti-loosening nut and c The semi-cone angle β of the lower inner conical hole of the anti-loosening nut s They are equal, and the eccentricity e satisfies ,in The nominal radius of the cone surface, The equivalent friction angle is taken into account for the eccentric effect.
[0028] Compared with the prior art, the beneficial effects of the present invention are:
[0029] This invention provides a method for preventing loosening of suspension bridge cable anchorages. This method utilizes a multi-conical locking mechanism to achieve long-term anti-loosening of the cable anchorage, and has the following specific advantages:
[0030] (1) The dual anti-loosening mechanism works synergistically: the upper end adopts the angle difference cone surface wedge anti-loosening, and the lower end adopts the eccentric cone progressive self-locking anti-loosening. The two systems complement each other in function and cooperate in mechanics, jointly undertaking the transmission of cable force and anti-loosening guarantee, so that the anti-loosening life of the anchor under alternating load is much higher than that of the single anti-loosening system.
[0031] (2) Continuous preload amplification through angle difference wedging: By designing the angle difference (α < β) between the inner cone angle of the upper anti-loosening nut and the outer cone angle of the ear plate, a continuous wedging effect is generated when the nut is screwed in. Each axial displacement generates a radial wedging amount, causing the anti-loosening nut to elastically expand, which is equivalent to applying an interference fit to the nut, and adding a preload amplification factor. The thread tooth side remains in a compressed state at all times.
[0032] (3) Asymmetrical contact pressure distribution caused by eccentric conical surface: The outer conical surface of the lower bearing nut adopts an eccentric design. When it is fitted with the inner conical hole of the anti-loosening nut, the contact pressure is distributed cosinely along the circumference, and the compression side , stretching side The frictional resistance on the biased side is much greater than that on the opposite side. The loosening and rotating motion must first overcome the high frictional resistance on the compression side, which effectively improves the critical torque for preventing loosening.
[0033] (4) The progressive wedging effect eliminates the saturation limitation of "tightening to the end": When the load-bearing nut is rotated and tightened in the support cone hole, the geometric center of the eccentric cone surface rotates with the nut, and the cone surface is continuously "wedged" in the support cone hole, generating an additional axial displacement with each rotation. The preload increases continuously with the rotation angle instead of saturating, which solves the limitation of traditional conical surfaces that "saturate when screwed to the bottom".
[0034] (5) Optimization design of tapered surface length and number of thread engagement turns: The tapered surface length range is determined according to the contact stress criterion, self-locking reliability criterion and uniform contact criterion; the number of thread engagement turns is designed differently according to the functional requirements of different parts, taking into account load-bearing capacity, anti-loosening accuracy and freedom of movement. Attached Figure Description
[0035] Figure 1 This is a schematic diagram of the overall structure of a non-loosening suspension bridge cable anchorage according to the present invention.
[0036] Figure 2 This is a front view of the upper lug plate of the sling of the present invention.
[0037] Figure 3 This is a side view of the upper lug plate of the sling of the present invention.
[0038] Figure 4 This is a front view of the upper anti-loosening nut of the present invention.
[0039] Figure 5 This is a front view of the upper sling anchor cup of the present invention.
[0040] Figure 6 This is a front view of the eccentric frustum nut of the present invention.
[0041] Figure 7 This is a front view of the lower anti-loosening nut of the present invention.
[0042] in:
[0043] 1. Upper ear plate of sling, 1.1. Pin hole, 1.2. Connecting platform, 1.3. Anchor cup hole, 1.4. Upper anti-loosening nut, 2. Upper nut body, 2.1. Upper inner conical hole, 2.2. Upper cylindrical hole, 2.3. Upper sling anchor cup, 3. Sling body, 4. Beam end pad, 5. Nut with eccentric cone, 6. Conical nut body, 6.1. Outer cone, 6.2. Eccentric hole, 6.3. Lower anti-loosening nut, 7. Lower nut body, 7.1. Lower inner conical hole, 7.2. Lower cylindrical hole, 7.3. Lower sling anchor cup, 8. Detailed Implementation
[0044] To better understand the technical solution of the present invention, a detailed description will be provided below in conjunction with relevant illustrations. It should be understood that the specific embodiments described below are not intended to limit the specific implementation of the technical solution of the present invention, but are merely possible implementations of the technical solution of the present invention. It should be noted that the descriptions of the positional relationships of the components herein, such as component A being located above component B, are based on the relative positions of the components in the illustrations and are not intended to limit the actual positional relationships of the components.
[0045] Example 1:
[0046] See Figure 1-7 , Figure 1 A schematic diagram of the overall structure of an anti-loosening suspension bridge cable anchorage according to the present invention is shown. As shown in the figure, the anti-loosening method of the anti-loosening suspension bridge cable anchorage involved in this embodiment 1 is based on an anti-loosening suspension bridge cable anchorage. The upper end of the cable anchorage is connected to the main cable clamp, and the lower end is connected to the steel box girder. From top to bottom, it includes: an upper cable ear plate 1, an upper anti-loosening nut 2, an upper cable anchor cup 3, a cable body 4, a beam end pad 5, a nut with an eccentric cone 6, a lower anti-loosening nut 7, and a lower cable anchor cup 8. The bottom of the upper cable ear plate 1 is inserted into the upper cable anchor cup 3, and the upper anti-loosening nut 2 is sleeved on the outside of the connection between the two. The upper cable anchor cup 3 is connected to the lower cable anchor cup 8 below through the cable body 4. The lower cable anchor cup 8 is sleeved on the outside from top to bottom with a beam end pad 5, a nut with an eccentric cone 6, and a lower anti-loosening nut 7. The specific structure is as follows:
[0047] (a) Upper anchoring structure
[0048] like Figure 2 As shown, the upper ear plate 1 of the sling is a forked ear plate structure with a truncated cone shape at the bottom. The upper ear plate 1 of the sling includes two ear plates 1.1 and a connecting platform 1.3. The connecting platform 1.3 is truncated cone-shaped, with an ear plate 1.1 vertically arranged on each of its upper left and right sides. The two ear plates 1.1 are arranged opposite each other, and a pin hole 1.2 is opened in the middle of the ear plate 1.2. The upper ear plate 1 of the sling is hinged to the ear plate of the main cable clamp through the pin hole 1.2 and a pin, and is the upper output end of the cable force of the entire sling anchoring system.
[0049] The bottom surface of the connecting platform 1.3 is provided with an anchor cup hole 1.4, which is located inside the lower part of the connecting platform 1.3. The inner wall of the anchor cup hole 1.4 is provided with internal threads, and its shape and size match the top of the upper sling anchor cup 3. The top of the upper sling anchor cup 3 is threadedly connected to the anchor cup hole 1.4 of the upper ear plate 1 of the sling. The cone angle of the outer conical surface of the connecting platform 1.3 is β.
[0050] like Figure 4 As shown, the upper anti-loosening nut 2 includes an upper nut body 2.1, which is cylindrical and has an upper inner conical hole 2.2 and an upper cylindrical hole 2.3 that are arranged vertically and communicate with each other. The upper inner conical hole 2.2 is shaped like an inverted frustum of a cone, and the angle of the inner conical surface of the upper inner conical hole 2.2 is α. The lower part of the connecting platform 1.3 of the upper ear plate 1 of the sling is inserted into the upper inner conical hole 2.2, and the inner conical surface of the upper inner conical hole 2.2 and the outer conical surface of the connecting platform 1.3 form a conical surface contact with an angle difference, thus forming the first anti-loosening mechanism of the upper ear plate of the sling.
[0051] The upper cylindrical hole 2.3 is used for the passage of the upper sling anchor cup 3, and the inner wall of the upper cylindrical hole 2.3 is provided with an internal thread that matches the external thread of the upper sling anchor cup 3.
[0052] like Figure 5 As shown, the outer wall of the upper sling anchor cup 3 is provided with external threads, which are threaded to the upper ear plate 1 and the upper anti-loosening nut 2 of the sling respectively. It has a conical cavity inside for inserting the sling body 4. The steel wires of the sling body 4 are spread out in the conical cavity. Zinc-copper alloy or epoxy iron sand is cast to form a conical casting to achieve sling body anchoring.
[0053] (II) Central cable structure
[0054] The sling body 4 is composed of multiple parallel steel wire bundles. The upper end is inserted into the upper sling anchor cup 3, and the lower end is inserted into the lower sling anchor cup 8. The steel wires at both ends are spread out in the conical cavity of the anchor cup and then anchored by the grouting material.
[0055] (III) Lower end anchoring structure
[0056] The lower sling anchor cup 8 has the same structure as the upper sling anchor cup 3, and is a cylindrical anchor cup with external threads. It is screwed into the eccentric cone nut 6 and the lower anti-loosening nut 7 through the external threads. The top of the lower sling anchor cup 8 is fitted with a beam end pad 5, which is a steel structure pad.
[0057] like Figure 6As shown, the eccentric frustum nut 6 is sleeved on the outside of the lower sling anchor cup 8 and positioned below the beam end pad 5. It includes a frustum nut body 6.1, an outer frustum 6.2, and an eccentric hole 6.3. The upper part of the frustum nut body 6.1 is cylindrical, and the lower part is an outer frustum 6.2. The outer frustum 6.2 is an inverted frustum, and its outer diameter is not greater than the outer diameter of the upper cylindrical part.
[0058] The frustum nut body 6.1 has a through eccentric hole 6.3 inside. The inner wall of the eccentric hole 6.3 has an internal thread for the passage of the lower sling anchor cup 8. The internal thread of the eccentric hole 6.3 is matched and screwed into the external thread of the lower sling anchor cup 8. The outer frustum 6.2 of the eccentric frustum nut 6 is eccentrically designed. The central axis of the outer frustum 6.2 does not coincide with the central axis of the upper cylindrical part of the eccentric frustum nut 6, resulting in an eccentricity e.
[0059] like Figure 7 As shown, the lower anti-loosening nut 7 includes a lower nut body 7.1, which is cylindrical and has an inner conical hole 7.2 and a lower cylindrical hole 7.3 that are arranged vertically and communicate with each other. The lower inner conical hole 7.2 is shaped like an inverted frustum of a cone and is fitted onto the outside of the outer frustum of a cone 6.2 of the eccentric frustum nut 6. The inner conical surface of the lower inner conical hole 7.2 mates with the outer frustum of a cone 6.2, forming a double locking mechanism of eccentricity and conical surface, constituting the second anti-loosening mechanism. The lower cylindrical hole 7.3 is used for the passage of the lower sling anchor cup 8, and the inner wall of the lower cylindrical hole 7.3 has an internal thread that matches the external thread of the lower sling anchor cup 8.
[0060] This embodiment 1 relates to a method for preventing loosening of a suspension bridge cable anchorage, which uses the aforementioned anti-loosening suspension bridge cable anchorage and includes the following steps:
[0061] Step 1: Insert the sling body into the upper and lower sling anchor cups. The steel wires spread out in the conical cavity of the anchor cups. Cast zinc-copper alloy or epoxy iron sand to form a conical casting, thus completing the sling anchoring.
[0062] Step 2: Connect the upper sling anchor cup to the anchor cup hole of the upper ear plate of the sling with threads. Screw the upper anti-loosening nut into the external thread of the upper sling anchor cup so that the upper inner conical hole of the upper anti-loosening nut forms a conical contact with the outer conical surface of the upper ear plate connecting platform. Utilize the angle difference generated by the inner conical surface angle α of the upper inner conical hole being smaller than the outer conical surface angle β of the connecting platform to form a wedge effect, thus achieving the first anti-loosening locking.
[0063] Step 3: Insert the lower sling anchor cup into the beam end pad, the eccentric cone nut, and the lower anti-loosening nut in sequence. Screw the eccentric cone nut into the external thread of the lower sling anchor cup so that the outer cone of the eccentric cone nut and the lower inner cone hole of the lower anti-loosening nut form a conical surface fit.
[0064] Step 4: Continue to rotate the eccentric cone nut. Utilize the eccentricity e between the rotation center of the outer cone and the central axis of the nut body to make the contact pressure between the outer cone surface and the lower inner cone hole asymmetrically distributed along the circumference. The bias side generates higher frictional resistance, thus achieving progressive self-locking of the eccentric cone surface.
[0065] In the aforementioned anti-loosening method, the condition for achieving the angle difference wedge effect in step two is that the half-cone angle α of the upper inner conical hole of the upper anti-loosening nut is less than the half-cone angle β of the outer conical surface of the upper ear plate connecting platform of the sling, and the angle difference... Each axial displacement of the nut causes it to be screwed in one direction. This generates radial wedging amount .
[0066] In the aforementioned anti-loosening method, the condition for achieving the progressive self-locking of the eccentric conical surface in step four is: the semi-cone angle α of the outer frustum with the eccentric frustum nut. c The semi-cone angle β of the lower inner conical hole of the anti-loosening nut s They are equal, and the eccentricity e between the center of rotation of the outer cone and the central axis of the nut body satisfies... ,in The nominal radius of the cone surface, The equivalent friction angle is taken into account for the eccentric effect.
[0067] The method further includes: when the end of the sling beam is a lug connection structure, the lower end of the lug is designed as an eccentric truncated cone, and the eccentricity is designed in the same way as the eccentricity design method with the eccentric truncated cone nut, and the eccentric geometry of the outer cone surface of the lug is used to generate a progressive wedging effect.
[0068] Example 2:
[0069] Based on Example 1, Example 2 relates to a method for preventing loosening of a suspension bridge cable anchorage, and provides a detailed description of the key design parameters of the upper angle difference anti-loosening structure in Example 1.
[0070] (1) Design of cone angle difference
[0071] The semi-cone angle of the upper inner conical hole 2.2 of the upper anti-loosening nut 2 is α, and the semi-cone angle of the outer conical surface of the connecting platform 1.3 of the upper ear plate 1 of the sling is β. The design condition is α < β. (Angle difference) The value ranges from 1° to 5°. The wedging effect caused by the angle difference is as follows:
[0072] When the anti-loosening nut 2 is screwed into and tightened along the external thread of the upper sling anchor cup 3, the nut is pushed forward along the axial direction of the lug plate. Since α < β, the inner conical surface of the nut and the outer conical surface of the lug plate are not in full conical contact in the initial state, but rather form a non-uniform contact state where the smaller diameter end contacts first and a gap remains at the larger diameter end. As the nut continues to tighten, the inner conical surface "wedges" into the outer conical surface, and the gap gradually closes towards the larger diameter end.
[0073] Each axial displacement of the nut The resulting radial wedging depth is:
[0074] ;
[0075] Since Δα > 0, Δr is always positive, meaning the outer conical surface of the lug is always compressed radially. The inner conical surface of the lock nut is "spread out" by the outer conical surface of the lug. The calculation process for amplifying the preload force caused by the angle difference is as follows:
[0076] When the lock nut with an inner conical hole is screwed in, the effective wedging angle at which the inner conical surface of the lock nut at the upper end of the sling slides on the outer conical surface of the lug at the upper end of the sling is [value missing]. For each turn the nut is screwed in, the axial displacement is equal to the pitch p, and the resulting radial wedging amount is:
[0077] ;
[0078] This radial wedging causes the locknut to expand elastically, effectively applying an interference fit. The axial component of the radial contact pressure P generated by the interference fit is an additional preload.
[0079] ;
[0080] in This represents the actual contact area of the cone surface. The equivalent coefficient is used to account for the friction of the conical surface.
[0081] When the lock nut is tightened, since β > α, the force exerted by the outer cone surface of the lug on the inner cone surface of the lock nut is along the β direction, that is, along the normal direction of the outer cone surface of the lug. The radial component Fr of this force "opens up" the inner cone surface of the lock nut, generating circumferential tensile stress within the nut body. :
[0082] ;
[0083] in The effective bearing area of the cone-shaped section of the nut. The applied bolt preload.
[0084] The circumferential tensile stress causes the lock nut to expand elastically, and the reaction force of the elastic expansion is converted into an additional axial preload through the difference in the cone angle. :
[0085] ;
[0086] Therefore, the total preload is:
[0087] ;
[0088] Magnification factor .
[0089] (2) Determination of the length of the cone surface
[0090] The design of the cone length must meet three basic principles:
[0091] Criterion 1: Contact Stress Criterion.
[0092] The maximum contact stress shall not exceed the allowable contact stress of the material. :
[0093] ;
[0094] Where N is the normal force of the cone surface. This represents the effective contact area of the conical surface. For a conical surface with a semi-cone angle of α:
[0095] ;
[0096] in Let be the average radius of the cone. From this, we obtain the lower limit of the cone length:
[0097] .
[0098] Criterion 2: Self-locking reliability criterion.
[0099] The length of the conical surface must ensure sufficient frictional torque to resist the loosening torque. The frictional torque is:
[0100] ;
[0101] The torque for loosening rotation is:
[0102] ;
[0103] Self-locking condition ≥ Simplified to The friction angle condition is not directly related to the length of the conical surface. However, when machining errors exist on a long conical surface, the actual cone angle of each section may deviate from the design value, causing some sections to fail to meet the self-locking condition. Therefore, the length of the conical surface should not be too long to ensure the self-locking reliability within the machining accuracy range.
[0104] Criterion 3: Uniform Contact Criterion.
[0105] The length of the conical surface must be sufficient to ensure uniform contact within the machining error range. Let the straightness tolerance of the conical surface be δ, then the cone angle deviation over the entire length of the conical surface is... To ensure full conical surface contact, it is necessary to (Allowable cone angle deviation, typically 0.5°~1°). This gives the upper limit of the cone surface length:
[0106] ;
[0107] With δ=0.02mm, For example, 0.5° = 0.0087 rad:
[0108] ;
[0109] Recommended engineering value for cone length: the ratio of cone length to cone radius. The contact area should ideally be controlled within the range of 0.3 to 0.5 mm to ensure sufficient contact area while keeping machining errors and tightening torque within a reasonable range. The recommended range for the cone surface length in engineering applications is:
[0110] Small diameter anchors ( <50mm): =12~18mm;
[0111] Medium diameter anchorage ( =50~100mm): =18~25mm;
[0112] Large diameter anchorage ( >100mm): =25~40mm.
[0113] Example 3:
[0114] Based on Example 1, Example 3 provides a detailed explanation of the key design parameters of the lower eccentric frustum self-locking structure in Example 1.
[0115] (1) Geometric design of eccentric cone surface
[0116] The outer half-cone angle of the outer frustum 6.2 of the eccentric frustum nut 6 is α. c The semi-cone angle of the lower inner conical hole 7.2 of the lower anti-loosening nut 7 is β. s In this scheme, α c =β s This forms a full conical surface contact fit. There is an eccentricity e between the rotation axis O' of the outer conical frustum 6.2 and the central axis O of the body of the eccentric conical nut 6. The ratio of the eccentricity e to the nominal radius R of the outer conical frustum, e / R, ranges from 0.02 to 0.10.
[0117] In any inscribed angle Location (with the eccentric direction as) =0), the radial clearance between the outer conical surface and the supporting conical hole is:
[0118] ;
[0119] in Let be the nominal gap when there is no eccentricity. This formula shows that when e is large enough such that g(0) < 0, contact interference occurs on the eccentric side; when g(π) > 0, there is a gap on the opposite side. This is the geometric root of the asymmetric contact pressure generated by the eccentric conical surface.
[0120] (2) Contact pressure distribution
[0121] For small eccentricities (e << R), the contact pressure is cosine distributed along the circumference:
[0122] ;
[0123] in For average contact pressure, This represents the relative eccentricity. The physical meaning of this distribution is:
[0124] =0 side (compression side): As contact pressure increases, frictional resistance increases;
[0125] =π side (tension side): As the contact pressure decreases, it approaches zero when e / R→1 (disengagement from contact).
[0126] At point =±π / 2: p= This is to nominally relieve pressure;
[0127] The total normal force N is obtained by integrating the contact pressure:
[0128] ;
[0129] Since the cosine integral is zero, the total normal force is the same as when there is no eccentricity. However, the distribution of the normal force has undergone a fundamental change—from a uniform distribution to an asymmetric distribution, and it is this asymmetry that produces the anti-loosening effect.
[0130] Calculation of frictional torque and self-locking condition: The frictional resistance torque of the support tapered hole on the bearing nut is:
[0131] ;
[0132] Since the cosine integral is zero, the average frictional torque is the same as when there is no eccentricity. However, the key point is that the effectiveness of the frictional torque in resisting loosening depends on its distribution characteristics. When the nut is subjected to a reverse loosening torque... During the loosening motion, the nut slides along the surface of the support cone hole. Due to the asymmetrical distribution of contact pressure, the frictional resistance on the compression side is much greater than that on the tension side. The loosening motion must first overcome the high frictional resistance on the compression side. The critical torque required for loosening is:
[0133] ;
[0134] in The equivalent friction angle is calculated to account for the eccentricity effect. Due to the presence of asymmetric contact, The friction angle is greater than that of symmetrical contact. :
[0135] ;
[0136] Where k is a correction factor related to the geometry and material of the cone surface, typically k = 1.0~2.0.
[0137] The self-locking condition is modified as follows:
[0138] ;
[0139] by =15° Taking 0.15 (steel-to-steel dry state), e / R=0.05, and k=1.5 as an example:
[0140] =0.15×(1+1.5×0.05)=0.15×1.075=0.161;
[0141] = =9.15°.
[0142] The self-locking condition is: This condition is not currently met. This indicates that even with an eccentricity effect, under the condition of μ=0.15, Even at 15°, it still cannot self-lock. The coefficient of friction needs to be increased or the cone angle decreased. .
[0143] For example, knurling on a conical surface can increase μ to over 0.30 to increase the coefficient of friction.
[0144] If μ = 0.30:
[0145] =0.30 × 1.075 = 0.3225, =17.9°;
[0146] At this point, 15° < 17.9°, satisfying the self-locking condition.
[0147] (4) Gradual wedging effect
[0148] When the load-bearing nut is tightened by rotating it in the support cone hole, the geometric center of the eccentric cone surface rotates along with the nut. If the nut rotates through an angle θ, then the peak position of the contact pressure distribution also rotates synchronously by an angle θ. Due to the inclination of the cone surface, the eccentric cone surface continuously "wedges" into the support cone hole during rotation, generating a continuous axial displacement. For each revolution (2π radians), the additional axial displacement generated by the eccentric cone surface is:
[0149] ;
[0150] This axial displacement causes the nut to tighten further, and the preload continues to increase. This is the source of the "can't be fully tightened" effect—the eccentric conical surface makes the nut tend to wedge axially during rotation, and the preload will not saturate after being "fully tightened" like a normal conical surface.
[0151] The relationship between preload and angle change is as follows:
[0152] ;
[0153] in Let θ be the preload force when the nut has rotated through an angle of θ. E is the initial preload, E is the elastic modulus of the anti-loosening nut material, A is the effective cross-sectional area of the conical section, and L is the length of the conical section;
[0154] This formula shows that the preload increases linearly with the rotation angle θ until it reaches the material's yield limit or the upper limit of the cone surface contact stress.
[0155] Example 4:
[0156] Based on Example 1, Example 4 provides a detailed explanation of the design principles for the number of thread engagement turns in different locations.
[0157] When the effective engagement length of the thread is less than 0.8 times the nominal thread diameter or the effective number of engagement turns is less than 10 turns, the following defects will occur: the number of bearing teeth is too small, the total friction area is insufficient, and under vibration and alternating impact, the small slippage on the thread flank accumulates, and the self-locking friction resistance instantly exceeds the critical value; all the load is concentrated in the first 2 turns of the thread, the shear stress at the root of the thread exceeds the standard, and repeated vibration causes plastic deformation of the thread; under alternating load conditions, the short engagement thread has stress concentration, and microcracks quickly develop at the root of the thread.
[0158] When the effective engagement length is greater than 1.5 times the nominal diameter, further increasing the number of engagement turns results in a small improvement in anti-loosening performance. At the same time, the cumulative pitch error is amplified, the internal and external thread sides are not evenly fitted, and gaps appear in some areas.
[0159] The number of thread engagement turns in different parts of this scheme is designed as follows:
[0160] The connection thread between the anchor cup and the ear plate (upper sling anchor cup 3 and upper sling ear plate 1): 10-15 turns, taking into account both load-bearing capacity and anti-loosening design.
[0161] Upper anti-loosening nut (upper anti-loosening nut 2 and upper sling anchor cup 3): 5-6 turns. The wedging function accuracy requirement is no more than 6 turns to avoid cumulative errors affecting the angle difference wedging accuracy.
[0162] Lower eccentric load-bearing nut (with eccentric cone nut 6 and lower sling anchor cup 8): 10-12 turns, taking into account both load-bearing capacity and anti-loosening design. Eccentric movement requires a certain axial guide length, but not more than 12 turns to avoid restricting the eccentric degree of freedom.
[0163] Lower anti-loosening nut (lower anti-loosening nut 7 and lower sling anchor cup 8): 5-6 turns. It needs to be coordinated with the eccentric movement of the eccentric bearing nut. Too many turns will restrict the eccentric degree of freedom.
[0164] Working principle:
[0165] The present invention relates to a suspension bridge cable anchorage with anti-loosening features. The upper end of the cable anchorage is connected to the main cable clamp, and the lower end is connected to the steel box girder. From top to bottom, it includes: upper ear plate of the cable, upper anti-loosening nut, upper cable anchor cup, cable body, beam end pad, nut with eccentric cone, lower anti-loosening nut and lower cable anchor cup.
[0166] The upper ear plate of the sling is a forked ear plate structure with a truncated cone shape at the bottom, including two ear plates and a connecting platform. The connecting platform is truncated cone-shaped, with an ear plate vertically installed on each of its upper left and right sides. The two ear plates are positioned opposite each other, and a pin hole is opened in the middle of the ear plate. The upper ear plate of the sling is hinged to the ear plate of the main cable clamp through the pin hole and the pin, and is the upper output end of the cable force of the entire sling anchoring system. The bottom surface of the connecting platform has an anchor cup hole, which is located in the lower part of the connecting platform. The inner wall of the anchor cup hole has internal threads, and its shape and size match the top of the upper sling anchor cup. The top of the upper sling anchor cup is threadedly connected to the anchor cup hole of the upper ear plate of the sling. The cone angle of the outer conical surface of the connecting platform is β.
[0167] The upper anti-loosening nut includes an upper nut body, which is cylindrical and has an upper inner conical hole and an upper cylindrical hole that are arranged vertically and communicate with each other. The upper inner conical hole is shaped like an inverted frustum of a cone, with an inner conical surface angle of α. The lower part of the connecting platform of the upper ear plate of the sling is inserted into the upper inner conical hole, and the inner conical surface of the upper inner conical hole and the outer conical surface of the connecting platform form a conical surface contact with an angle difference, forming the first anti-loosening mechanism. The angle difference is β-α, and α < β. The upper cylindrical hole is used for the passage of the upper sling anchor cup. The inner wall of the upper cylindrical hole has an internal thread that matches the external thread of the upper sling anchor cup, which is an internal thread hole of the same diameter that engages with the external thread of the upper sling anchor cup.
[0168] The outer wall of the upper sling anchor cup is provided with external threads, which are threaded to the upper ear plate of the sling and the upper anti-loosening nut respectively. The inside is provided with a conical cavity for inserting the sling body. The steel wires of the sling body are spread out in the conical cavity. Zinc-copper alloy or epoxy iron sand is cast to form a conical casting to achieve sling body anchoring.
[0169] The lower sling anchor cup has the same structure as the upper sling anchor cup, and is a cylindrical anchor cup with external threads. It is screwed into the eccentric cone nut and the lower anti-loosening nut through the external threads. A beam end pad is fitted on the top of the lower sling anchor cup, and the beam end pad is a steel structure pad.
[0170] The eccentric truncated cone nut is fitted onto the outside of the lower sling anchor cup and positioned below the beam end plate. It includes a truncated cone nut body, an outer truncated cone, and an eccentric hole. The upper part of the truncated cone nut body is cylindrical, and the lower part is an outer truncated cone. The outer truncated cone is an inverted truncated cone, and its outer diameter is no larger than the outer diameter of the upper cylindrical part. The truncated cone nut body has a through-hole with internal threads on its inner wall for the passage of the lower sling anchor cup. The internal threads of the eccentric hole engage with the external threads of the lower sling anchor cup. The outer truncated cone of the eccentric truncated cone nut is eccentrically designed; the central axis of the outer truncated cone does not coincide with the central axis of the upper cylindrical part of the eccentric truncated cone nut, resulting in an eccentricity e.
[0171] The lower anti-loosening nut includes a lower nut body, which is cylindrical and has an inner conical hole and a lower cylindrical hole that are arranged vertically and communicate with each other. The lower inner conical hole is shaped like an inverted frustum of a cone and fits over the outer frustum of the eccentric frustum nut. The inner conical surface of the lower inner conical hole mates with the outer frustum, forming a double locking mechanism of eccentricity and conical surface, constituting the second anti-loosening mechanism. The lower cylindrical hole is used for the passage of the lower sling anchor cup, and the inner wall of the lower cylindrical hole has an internal thread that matches the external thread of the lower sling anchor cup.
[0172] The semi-cone angle β of the outer conical surface of the connecting platform and the semi-cone angle α of the upper inner conical hole of the upper anti-loosening nut satisfy α < β, and the angle difference is... The value range is 1°-5°.
[0173] The half-cone angle of the outer cone of the eccentric truncated cone nut is equal to the half-cone angle of the lower inner cone hole of the lower anti-loosening nut, forming a full cone surface contact fit.
[0174] The ratio of the eccentricity e of the eccentric truncated cone nut to the nominal radius R of the outer truncated cone, e / R, ranges from 0.02 to 0.10.
[0175] The number of threaded engagements between the upper sling anchor cup and the upper ear plate of the sling is 10-15 turns, and the number of threaded engagements between the upper anti-loosening nut and the upper sling anchor cup is 5-6 turns; the number of threaded engagements between the lower sling anchor cup and the nut with the eccentric cone is 10-12 turns, and the number of threaded engagements between the lower anti-loosening nut and the lower sling anchor cup is 5-6 turns.
[0176] This invention relates to a method for preventing loosening of suspension bridge cable anchorages. The anti-loosening suspension bridge cable anchorages employ a dual anti-loosening mechanism of "upper end angle difference conical surface wedge locking" and "lower end eccentric conical progressive self-locking," the working principle of which is as follows:
[0177] (a) Upper end angle difference wedged anti-loosening principle
[0178] The outer conical surface of the upper ear plate 1 of the sling forms a conical contact with the inner conical surface of the upper anti-loosening nut 2. The half-cone angle of the inner conical hole of the anti-loosening nut 2 is α, and the half-cone angle of the outer conical surface of the ear plate is β. The design condition is α < β, and there is an angle difference between the two. .
[0179] When the anti-loosening nut 2 is screwed into and tightened along the external thread of the anchor cup, the nut is pushed axially toward the ear plate. Since α < β, the inner conical surface of the nut and the outer conical surface of the ear plate are not in full conical contact in the initial state, but rather form a non-uniform contact state where the smaller diameter end contacts first and the larger diameter end leaves a gap. As the nut continues to tighten, the inner conical surface "wedges" into the outer conical surface, and the gap gradually closes toward the larger diameter end.
[0180] The mechanical essence of this wedging process is: for every axial displacement the nut screws in... The inner cone surface produces a radial wedging amount on the outer cone surface. The radial wedging caused by the angular difference causes the lock nut to expand elastically, which is equivalent to applying an interference fit to the nut, introducing additional axial preload into the threaded joint. Total preload Magnification factor .
[0181] When the sling is subjected to alternating loads such as wind vibration and vehicle vibration, the upper angle difference system maintains the clamping force of the threaded pair through the wedging effect, minimizing the fretting wear between the threaded surfaces.
[0182] (II) Self-locking principle of the lower eccentric cone
[0183] The outer cone 6.2 of the eccentric frustum nut 6 mates with the lower inner cone hole 7.2 of the lower anti-loosening nut 7. There is an eccentricity e between the rotation axis O' of the outer cone 6.2 and the central axis O of the nut body, and the semi-cone angle α of the outer cone 6.2 is... c Equal to the half cone angle β of the lower inner cone hole s .
[0184] Due to the eccentricity, the contact pressure between the outer conical surface and the lower inner conical hole exhibits a cosine distribution along the circumference: compression side , stretching side This asymmetrical contact results in significantly greater frictional resistance on the compression side than on the tension side. The loosening motion must first overcome the high frictional resistance on the compression side. The critical torque required for loosening is... ,in To account for the equivalent friction angle due to eccentricity, the self-locking condition is: .
[0185] When the load-bearing nut is rotated and tightened in the support cone hole, the geometric center of the eccentric cone surface rotates along with the nut, and the cone surface continuously "weaves" into the support cone hole. Each rotation generates an additional axial displacement. The preload increases continuously with the rotation angle rather than saturating.
[0186] The lower eccentric cone system maintains the preload on the cone surface through a progressive wedging effect, ensuring that the cone surface does not separate or loosen under alternating loads.
[0187] (III) Coordinated Response of the Two Systems
[0188] The upper angle difference system maintains the threaded pair clamping force through continuous wedging; the lower eccentric cone system maintains the cone surface preload through progressive wedging. The synergistic response of the two systems makes the anchorage's anti-loosening life under vibration conditions much longer than that of a single system. The transmission path of the suspending cable tension from the lower end to the upper end is as follows: suspending cable body 4 → inner cavity of lower suspending cable anchor cup 8 → external thread of lower suspending cable anchor cup 8 → lower anti-loosening nut 7 (conical surface locking) → nut 6 with eccentric cone (eccentric cone self-locking) → beam end pad 5 → steel box girder connection structure. At the same time, the upper tension transmission path is as follows: suspending cable body 4 → conical casting of upper suspending cable anchor cup 3 → external thread of upper suspending cable anchor cup 3 → upper anti-loosening nut 2 (angle difference wedging) → upper ear plate 1 of suspending cable → pin shaft → main cable clamp.
[0189] The above are merely specific application examples of the present invention and do not constitute any limitation on the scope of protection of the present invention. All technical solutions formed by equivalent transformations or substitutions fall within the scope of protection of the present invention.
Claims
1. A method for preventing loosening of anti-loosening suspension bridge cable anchorages, characterized in that: This is achieved based on a type of anti-loosening suspension bridge cable anchor, which includes an upper cable lug plate, an upper anti-loosening nut, an upper cable anchor cup, a cable body, a lower cable anchor cup, a nut with an eccentric cone, and a lower anti-loosening nut. The bottom of the upper ear plate of the sling is provided with an outer conical surface, and the upper anti-loosening nut is provided with an inner conical hole and a cylindrical hole. The inner conical hole of the upper anti-loosening nut is fitted outside the outer conical surface of the upper ear plate of the sling, and the cylindrical hole of the upper anti-loosening nut is threadedly connected to the upper sling anchor cup. The half-cone angle β of the outer conical surface of the upper ear plate of the sling is greater than the half-cone angle α of the inner conical hole of the upper anti-loosening nut. The eccentric truncated cone nut has an outer truncated cone and an eccentric internal threaded hole. The lower anti-loosening nut has an internal conical hole and a cylindrical hole. The internal conical hole of the lower anti-loosening nut is fitted onto the outside of the outer truncated cone of the eccentric truncated cone nut. The eccentric internal threaded hole of the eccentric truncated cone nut is threadedly connected to the lower sling anchor cup. The cylindrical hole of the lower anti-loosening nut is threadedly connected to the lower sling anchor cup. There is an eccentricity e between the rotation axis of the outer frustum with the eccentric frustum nut and the central axis of the body of the eccentric frustum nut. The anti-loosening method includes the following steps: Step 1: Insert the sling body into the upper and lower sling anchor cups. The steel wires spread out in the conical cavity of the anchor cups. Cast the anchoring material to form a conical casting, thus completing the sling anchoring. Step 2: Connect the upper sling anchor cup to the upper ear plate of the sling with threads. Screw the upper anti-loosening nut into the upper sling anchor cup along the external thread, so that the inner conical hole of the upper anti-loosening nut and the outer conical surface of the upper ear plate of the sling form a conical contact. The wedge effect is formed by the angle difference generated by the half-cone angle α of the inner conical hole being smaller than the half-cone angle β of the outer conical surface, thus achieving the first anti-loosening locking. Step 3: Insert the lower sling anchor cup into the eccentric cone nut and the lower anti-loosening nut. Screw the eccentric cone nut into the lower sling anchor cup along the external thread, so that the outer cone of the eccentric cone nut and the inner cone hole of the lower anti-loosening nut form a conical surface fit. Step 4: Continue to rotate the eccentric cone nut. Utilize the eccentricity e between the center of rotation of the outer cone and the central axis of the nut body to make the contact pressure between the outer cone surface and the inner cone hole asymmetrically distributed along the circumference, thereby achieving progressive self-locking of the eccentric cone surface and forming the second anti-loosening locking mechanism.
2. The method for preventing loosening of a suspension bridge cable anchorage according to claim 1, characterized in that: The upper ear plate of the sling is a fork-shaped ear plate structure, including two ear plates and a connecting platform. The connecting platform is shaped like a frustum of a cone. The two ear plates are arranged opposite each other above the connecting platform. A pin hole is opened in the middle of the ear plate. An anchor cup hole is provided on the bottom surface of the connecting platform. The inner wall of the anchor cup hole is provided with internal thread, which is threaded to the top of the upper sling anchor cup.
3. The method for preventing loosening of a suspension bridge cable anchorage according to claim 1, characterized in that: The semi-cone angle β of the outer conical surface of the upper ear plate of the sling and the semi-cone angle α of the inner conical hole of the upper anti-loosening nut satisfy α < β, and the angle difference is... The value range is 1° to 5°.
4. The method for preventing loosening of a suspension bridge cable anchorage according to claim 1, characterized in that: The eccentric truncated cone nut includes a truncated cone nut body, an outer truncated cone, and an eccentric hole. The upper part of the truncated cone nut body is cylindrical, and the lower part is an outer truncated cone. The outer truncated cone is an inverted truncated cone. The eccentric hole penetrates the truncated cone nut body and has internal threads on its inner wall. There is an eccentricity e between the central axis of the eccentric hole and the central axis of the truncated cone nut body.
5. The method for preventing loosening of a suspension bridge cable anchorage according to claim 1, characterized in that: The half-cone angle of the outer frustum of the eccentric frustum nut is equal to the half-cone angle of the inner conical hole of the lower anti-loosening nut, forming a full conical surface contact fit.
6. The method for preventing loosening of a suspension bridge cable anchorage according to claim 1, characterized in that: The ratio of the eccentricity e of the eccentric truncated cone nut to the nominal radius R of the outer truncated cone, e / R, ranges from 0.02 to 0.
10.
7. The method for preventing loosening of a suspension bridge cable anchorage according to claim 1, characterized in that: The number of threaded engagements between the upper sling anchor cup and the upper sling ear plate is 10-15 turns, and the number of threaded engagements between the upper anti-loosening nut and the upper sling anchor cup is 5-6 turns; the number of threaded engagements between the lower sling anchor cup and the eccentric cone nut is 10-12 turns, and the number of threaded engagements between the lower anti-loosening nut and the lower sling anchor cup is 5-6 turns.
8. The method for preventing loosening of a suspension bridge cable anchorage according to claim 1, characterized in that: In step two, the radial wedging amount generated by the angle difference wedging effect ,in This refers to the axial advance displacement of the upper lock nut. Total preload , This is the initial preload.
9. The method for preventing loosening of a suspension bridge cable anchorage according to claim 1, characterized in that: The ratio of the cone length to the cone radius of the upper and lower lock nuts. It is in the range of 0.3 to 0.
5.
10. The method for preventing loosening of a suspension bridge cable anchorage according to claim 1, characterized in that: In step four, the condition for the progressive self-locking of the eccentric conical surface is: the semi-cone angle α of the outer frustum with the eccentric frustum nut. c The semi-cone angle α between the inner conical hole of the lower anti-loosening nut and c The semi-cone angle β of the lower inner conical hole of the anti-loosening nut s They are equal, and the eccentricity e satisfies Where R is the nominal radius of the cone. The equivalent friction angle is taken into account for the eccentric effect.