A parameter calculation method for a highway slope compensation tensioning equipment slip clamp

Abstract

The application discloses a highway side slope compensation tensioning equipment slip clamp parameter calculation method, equivalent slip teeth are regarded as contact bodies acting on a working anchor; the contact between the slip teeth and the working anchor is equivalent to plane strain, and then a slip tooth-working anchor friction contact model is constructed; when the deformation energy of a metal material reaches the deformation energy required by metal material yielding, the metal material will yield or brittlely break; a slip tooth-yield strength model is constructed in this way; and the slip clamp with parameters meeting stress requirements is selected in combination with the need of an engineering safety factor. The method combines geotechnical engineering theory, Hertz contact mechanics theory, tribology and elastic-plastic mechanics theory to first provide a calculation method of a clamp of a highway side slope engineering prestressed anchor cable compensation tensioning equipment; the clamp material of the anchor cable compensation tensioning equipment is improved through calculation, the equipment range is improved, the anchor cable with a larger tonnage in the original design is applicable, the fatigue life of the slip clamp is increased, and the design parameters are optimized.

Description

Technical Field

[0001] This invention relates to the field of highway slope engineering, specifically to a method for calculating the parameters of the clamping device for highway slope compensation tensioning equipment. Background Technology

[0002] In recent years, prestressed anchor cable support has been widely used in slope and tunnel support in highway and railway transportation, water conservancy and hydropower, industrial and civil construction, and mining engineering. However, due to the different functional requirements of different projects, the design service life requirements for prestressed anchor cables also vary across industries. In foundation pit engineering in the industrial and civil construction sector, prestressed anchor cables are mostly temporary support measures with relatively short operating cycles and low prestress loss, thus receiving less attention. In contrast, in railway and highway construction, the slopes of the railway lines typically need to meet an operating cycle of more than fifty years. During this period, the anchoring force of the anchor cables will significantly decrease, and the safety risks will increase significantly with the extension of operating time, thus receiving more attention and concern.

[0003] Studies have shown that the prestressed anchor cable holding capacity loss rate in highways operating for more than ten years in hot and humid regions is around 30%-60%. The main reasons for this holding capacity loss, besides construction quality and system defects, are corrosion of the anchor cable reinforcement leading to reduced mechanical properties and rheological changes in the surrounding rock causing stress relaxation in the free section of the anchor cable. To extend the service life of highway slope engineering projects, it is necessary to compensate for the holding capacity loss in the anchor cables with tension loss. However, traditional equipment has limitations. Traditional equipment cannot solve the problem of excessively short prestressed anchor cable strands after anchor sealing; in this situation, it cannot effectively clamp the prestressed strands after the anchor caps are removed for compensatory tensioning.

[0004] For prestressed anchor cables on highway slopes during the operational phase, where the reserved length is insufficient to employ traditional compensating tensioning techniques, it is necessary to use clamping anchors to pull up the anchor cables in order to perform compensating tensioning. This places high demands on the performance of the clamping slips. However, the application time of this type of compensating tensioning equipment is still relatively short, and currently, the selection of clamping slip materials and related parameters relies heavily on experience, resulting in a situation where theory lags behind practice. Summary of the Invention

[0005] To address the aforementioned problems, this invention aims to provide a method for calculating the parameters of the clamping device for highway slope compensation tensioning equipment.

[0006] To achieve this technical objective, the present invention provides a method for calculating the parameters of a clamping device for highway slope compensation tensioning equipment, with the following specific steps: S1, constructing a basic parameter library for the clamping device and the working anchor;

[0007] S2. Divide the protruding structure on the slip into several slip teeth, and treat the slip teeth as an infinitely long contact body acting on the working anchor.

[0008] S3. Under the assumption of small deformation, the axial deformation effect caused by Poisson's ratio is ignored, and the contact between the slip tooth and the working anchor is equivalent to plane strain, and then a frictional contact model of slip tooth-working anchor is constructed.

[0009] S4. According to the von Mises strength criterion, when the deformation energy of a metallic material reaches the deformation energy required for the material to yield, the metallic material will yield or undergo brittle fracture. That is, when the equivalent stress is greater than or equal to the yield strength of the metallic material, the material will yield or undergo brittle fracture. Based on this, the material yields or undergoes brittle fracture. The ... Based on this, the material yields or undergoes brittle fracture.

[0010] S5. Based on the engineering safety factor requirements, select a clamp with parameters that meet the stress requirements for use in the prestressed anchor cable compensation tensioning project of the high-speed slope engineering.

[0011] Preferably, in step S3, it is assumed that the load acting on the slip tooth is uniformly distributed, and the frictional resistance T of a single slip tooth satisfies:

[0012] ;

[0013] When the slip contacts the working anchor, multiple slip teeth of the same size usually come into contact with the working anchor. Ignoring the mutual influence of the slip tooth forces, the total frictional resistance between the slip and the working anchor can be obtained by the superposition principle, thus yielding the pull-out force T. t :

[0014] ;

[0015] Where W and P are the line loads, and u is the static friction coefficient. For the contact half-width, r m denoted as , where is the outer diameter of the slip tooth; is the distance from a point on the contact plane between the slip tooth and the working anchor to the contact center; n is the number of slip teeth on the slip; when the spacing between the slip teeth decreases, or the strength of the slip material increases, the slip frictional resistance increases, i.e., the required pull-out force T increases. t Increase.

[0016] Preferably, the yield stress of a single locking tooth is calculated in step S4. ; Obtain the yield strength of metallic materials According to the engineering safety factor F s The design selects suitable clamps, and the calculation method for the engineering safety factor to ensure the strength of the material under load is as follows:

[0017] ;

[0018] Under a certain safety factor, the yield strength meets the allowable stress requirements generated under the parameters selected for the maximum axial force range of the tensioning equipment.

[0019] As a preferred option, metal materials with design dimensions and tensioning equipment range that meet the engineering requirements are selected from the basic parameter library in step S1, and corresponding slips with tooth pitch and contact length are manufactured.

[0020] Preferably, in step S4, a fatigue correction coefficient is introduced or the cyclic yield strength is used to correct or replace the yield strength of the chuck material under each fatigue condition, so as to obtain a safety factor under fatigue conditions.

[0021] Preferably, in step S4, the stress expression for the contact between a circular or arc-shaped surface and a plane can be obtained from the Johnson solution:

[0022] ;

[0023] In the formula, x and z represent the coordinates of any point in the xz plane of the working anchor on the contact plane between the working anchor and the slip clamp; The distributed contact pressure on the contact surface between the jaws of the slip clamp and the working anchor. The tangential force distributed on the contact surface between the jaw clamp teeth and the working anchor; This represents the normal stress acting on a cross section perpendicular to the x-axis, with its direction along the x-axis. This represents the normal stress acting on a cross section perpendicular to the z-axis, with its direction along the z-axis. This represents the shear stress acting on a cross section perpendicular to the x-axis, in a direction along the z-axis.

[0024] The method for calculating the parameters of the clamps in highway slope compensation tensioning equipment is applied to the prestressed anchor cable compensation tensioning project of an operating highway slope engineering project.

[0025] Beneficial effects: This method, combining geotechnical engineering theory, Hertz contact mechanics theory, tribology, and elastoplastic mechanics theory, provides for the first time a calculation method for the clamps of prestressed anchor cable compensation tensioning equipment in highway slope engineering; this method can improve the material of the anchor cable compensation tensioning equipment clamps through calculation, increase the equipment range, be applicable to anchor cables with larger tonnage in the original design, increase the fatigue life of the clamps, and optimize design parameters; this method provides a more rigorous calculation method, breaking through the current "empiricism" status quo of anchor cable compensation tensioning equipment clamp design. Attached Figure Description

[0026] Figure 1 This invention ensures that the slip teeth of the device are in normal contact with the working anchor plane;

[0027] Figure 2The present invention provides a frictional sliding contact between the slip teeth and the working anchor plane;

[0028] Figure 3 This is a schematic diagram showing the locations of stress feature points A, B, and C in Embodiment 1 of the present invention;

[0029] Figure 4 These are the stress values ​​at points A, B, and C in Embodiment 1 of the present invention;

[0030] Figure 5 This is the trend of point B changing with tensile force in Embodiment 1 of the present invention;

[0031] Figure 6 The effect of the center distance of the cavitation teeth in Embodiment 1 of the present invention;

[0032] Figure 7 The effect of contact length in Embodiment 1 of the present invention;

[0033] Figure 8 The radius of curvature of the contact protrusion of the tooth in Embodiment 1 of the present invention is shown. Detailed Implementation

[0034] The following is in conjunction with the appendix Figure 1-8 The present invention will be further described in detail with reference to specific embodiments.

[0035] The specific embodiment of this invention is a method for calculating the parameters of the clamping device for highway slope compensation tensioning equipment. The specific steps are as follows:

[0036] S1. Construct a basic parameter library for slips and working anchors;

[0037] S2. Divide the protruding structure on the slip into several slip teeth, and treat the slip teeth as an infinitely long contact body acting on the working anchor.

[0038] S3. Under the assumption of small deformation, neglecting the axial deformation effect caused by Poisson's ratio, the contact between the slip tooth and the working anchor is equivalent to plane strain, and a frictional contact model of the slip tooth and the working anchor is constructed. It is assumed that the load acting on the slip tooth is uniformly distributed, and the frictional resistance T of a single slip tooth satisfies:

[0039] ;

[0040] When the slip contacts the working anchor, multiple slip teeth of the same size usually come into contact with the working anchor. Ignoring the mutual influence of the slip tooth forces, the total frictional resistance between the slip and the working anchor can be obtained by the superposition principle, thus yielding the pull-out force T. t :

[0041] ;

[0042] Where W and P are line loads, u is the static friction coefficient, a is the contact half-width, and r m denoted as , where is the outer diameter of the slip tooth; is the distance from a point on the contact plane between the slip tooth and the working anchor to the contact center; n is the number of slip teeth on the slip; when the spacing between the slip teeth decreases, or the strength of the slip material increases, the slip frictional resistance increases, i.e., the required pull-out force T increases. t Increase.

[0043] S4. According to the von Mises strength criterion, when the deformation energy of a metallic material reaches the deformation energy required for the material to yield, the material will yield or undergo brittle fracture. That is, when the equivalent stress is greater than or equal to the yield strength of the metallic material, the chuck will yield or undergo brittle fracture. Based on this, a chuck-yield strength model is constructed. The yield stress of a single chuck is calculated using step S4. ; Obtain the yield strength of metallic materials According to the engineering safety factor F s The design selects suitable clamps, and the calculation method for the engineering safety factor to ensure the strength of the material under load is as follows: ;

[0044] Under a certain safety factor, the yield strength meets the allowable stress requirements generated under the parameters selected for the maximum axial force range of the tensioning equipment. In step S4, a fatigue correction factor is introduced or the cyclic yield strength is used to correct or replace the yield strength of the chuck material under each fatigue condition to obtain the safety factor under fatigue conditions.

[0045] S5. Based on the safety factor requirements of the project, select clamps with parameters that meet the stress requirements for the prestressed anchor cable compensation tensioning project of the operational highway slope engineering. According to the basic parameter library in step S1, select metal materials with design dimensions and tensioning equipment range that meet the project requirements, and manufacture clamps with corresponding clamp tooth pitch and contact length.

[0046] (1) Calculation method for static friction contact of the Kawa

[0047] Under the assumption of small deformation and neglecting the axial deformation effect caused by Poisson's ratio, the contact between the slip and the working anchor can be equivalent to a plane strain problem. When an infinitely long slip "convexity" acts on the working anchor, its calculation model is as follows: Figure 1 As shown.

[0048] Figure 1 In the middle, the elastic modulus and Poisson's ratio of the chuck and the working anchor are respectively , , and The working anchor is subjected to a downward external load W. This is the distance from a point on the contact plane between the chuck and the working anchor to the center of the contact.

[0049] Assuming the load acting on the slipper is uniformly distributed, the line load generated by the slipper is:

[0050] ;

[0051] In the formula, L is the axial length of the locking tooth, which is the circumference of the inner diameter of the locking tooth, 2πr. m It is also the outer diameter length of the circular working anchor; r m The radius of the end of the chuck tooth.

[0052] Therefore, the formula It can be rewritten as: ;

[0053] The normal line load P can be expressed by the following formula: ;

[0054] In the formula, It is the equivalent elastic modulus; Represents the radius of curvature of the contact body. For contact half-width.

[0055] The equivalent elastic modulus is: ;

[0056] In the formula: E1 is the elastic modulus of the slip; v1 is the Poisson's ratio of the slip; E2 is the elastic modulus of the working anchor; v2 is the Poisson's ratio of the working anchor.

[0057] From the formula It can be seen that the contact half-width 'a' between the slip tooth and the working anchor is:

[0058] ;

[0059] Based on Hertz theory, the distribution function of the contact pressure at the contact surface is:

[0060] ;

[0061] From the formula The contact pressure distribution function shows that it is zero at the contact edge, and the contact pressure at the center (s=0) is: ;

[0062] Combined Japanese style It can be known that: ;

[0063] To prevent engineering accidents during operation, the slip teeth and working anchor must be in static friction mode when the tensioning equipment is in operation. When the slip teeth and working anchor are in static friction mode, the shear stress distribution on the contact surface is as follows:

[0064] ;

[0065] In the formula, is the static friction coefficient, which is usually 0.15 between steels. is the distributed contact pressure on the contact surface between the jaw clamp teeth and the working anchor.

[0066] Combined Japanese style The expression for the shear stress distribution on the contact surface of the Dekawa is:

[0067] ;

[0068] The formula Integral equations can be used to obtain the expression for the frictional resistance provided by a single valve tooth:

[0069] ;

[0070] Combined Japanese style The formula for calculating the frictional resistance T of a single chuck is as follows:

[0071] ;

[0072] When the slip contacts the working anchor, there are usually multiple slip teeth of the same size in contact with the working anchor. Ignoring the mutual influence of the slip tooth forces, we can obtain the following by the superposition principle:

[0073] ;

[0074] Assuming the tooth spacing of the card is The contact length between the slip and the working anchor is Q. Therefore, the number of slip teeth in contact with the working anchor is:

[0075] ;

[0076] Combined Japanese style The total frictional resistance of the slip and the working anchor can be obtained, and thus the pull-out force M can be calculated.

[0077] ;

[0078] From the formula As mentioned above, the key to increasing the range of tensioning equipment lies in increasing the frictional resistance of the slips. This can be achieved by reducing the spacing between the slip teeth and increasing the strength of the slip material (to withstand greater anchor reaction forces, thus providing greater frictional resistance).

[0079] (2) Calculation process for selecting alloy steel material for the slip

[0080] From Johnson's solution, the stress component expressions for circular and arc-shaped surface problems in contact with a plane are:

[0081] ;

[0082] In the formula, x and z represent the coordinates of any point in the xz plane of the working anchor on the contact plane between the working anchor and the slip clamp; The distributed contact pressure on the contact surface between the jaws of the slip clamp and the working anchor. The tangential force distributed on the contact surface between the jaw clamp teeth and the working anchor; This represents the normal stress acting on a cross section perpendicular to the x-axis, with its direction along the x-axis. This represents the normal stress acting on a cross section perpendicular to the z-axis, with its direction along the z-axis. This represents the shear stress acting on a cross section perpendicular to the x-axis, in a direction along the z-axis.

[0083] Combined ,Mode Japanese style The expression for the stress components under the contact state of the kava can be obtained:

[0084]

[0085] ;

[0086] The coefficients and coordinate system in the formula are:

[0087] ;

[0088] In equations (1.17) and (1.18), and like Figure 2 In this context, the coordinates of any point in planar space are determined by dividing by the contact half-width. Dimensionlessize it and form and Two dimensionless parameters; and When s=0 and . This represents the normal stress acting on a cross section perpendicular to the x-axis, with its direction along the x-axis. This represents the normal stress acting on a cross section perpendicular to the z-axis, with its direction along the z-axis. This represents the shear stress acting on a cross section perpendicular to the x-axis, in a direction along the z-axis.

[0089] Metallic materials obey the maximum strain energy strength criterion (von Mises strength criterion). This criterion states that when the strain energy of a metallic material reaches the strain energy required for it to yield, the material will yield or undergo brittle fracture. Its equivalent stress form is as follows:

[0090] ;

[0091] Under plane strain conditions, the stress in the axial direction (y direction) has the following relationship:

[0092] ;

[0093] Combined Japanese style The expression for the equivalent stress of the deformation energy of the Kawa can be obtained as follows:

[0094] ;

[0095] In equations (1.19), (1.20), and (1.21) This represents the normal stress acting on a cross section perpendicular to the z-axis, with its direction along the z-axis. This represents the normal stress acting on a cross section perpendicular to the y-axis, with its direction along the y-axis. This represents the shear stress acting on a section perpendicular to the x-axis along the z-axis; v1 is Kava's Poisson's ratio.

[0096] When the equivalent stress is greater than or equal to the yield strength of the metallic material, the material undergoes yielding and brittle fracture. (Combined type) Japanese style The expression for the yield stress of a single slip tooth can be obtained as follows:

[0097]

[0098] ;

[0099] In the formula, v1 is Kava's Poisson's ratio. and The two dimensionless parameters are shown in equations (1.17) and (1.18). and When s=0 and When s=0, the contact pressure and shear stress have their maximum values. Therefore, the point at the vertex of the contact surface is a relatively concentrated stress point. This can be determined by substituting the dimensionless coordinates of that point into the equation. This allows us to determine whether the metallic material will yield. Based on the design dimensions and the range of the tensioning equipment, the metallic material that meets the engineering requirements can be determined. Here, an engineering safety factor is defined to ensure the material's strength under load.

[0100] ;

[0101] In the formula, The yield strength of metallic materials. The yield stress of the slip material can be used. A fatigue correction factor or cyclic yield strength can be introduced to correct or replace the yield strength of the slip material under fatigue conditions to obtain a safety factor under fatigue conditions.

[0102] When the slip material is selected, and the yield strength meets the allowable stress requirements generated under the parameters such as the slip tooth pitch and contact length selected under a certain safety factor, it can be used for prestressed anchor cable compensation tensioning projects in high-speed slope engineering.

[0103] In practical applications, the design and calculation of the clamping device and the clamping device for overall tensioning compensation will be carried out.

[0104] This method addresses the current "empirical" approach to the design of clamps for prestressed anchor cable compensation tensioning equipment. Combining geotechnical engineering theory, Hertz contact mechanics, tribology, and elastoplastic mechanics, this method provides, for the first time, a calculation method for clamps in prestressed anchor cable compensation tensioning equipment for highway slope engineering. This method can improve the material of the clamps through calculation, increase the equipment's range, make it suitable for anchor cables with larger tonnages in the original design, increase the fatigue life of the clamps, and optimize design parameters.

[0105] Example 1

[0106] After the original anchor cable construction and tensioning were completed, most of the cable at the borehole opening was cut off. Due to construction errors, the elongated section of the cut anchor cable at the borehole opening was insufficient. After the anchoring was opened during the slope operation period, it was found that traditional tensioning equipment could not compensate for the prestress. To solve this problem, tensioning can only be performed by tightening the anchorage, thereby lifting the anchorage to achieve the effect of compensating for the prestress.

[0107] This shows the stress distribution characteristics around the contact body. The stress concentration location is around the contact surface. In order to analyze the stress distribution characteristics near the contact surface, we take the commonly used design parameters of the Kawa for analysis and study the general mechanical laws. The relevant parameters are shown in Table 1 below.

[0108] Table 1: Common Design Parameters for Kava

[0109] Parameter name unit value Kava (body 1) elastic modulus GPa 200 body 2 elastic modulus GPa 200 Kava (body 1) Poisson's ratio / 0.25 Poisson's ratio / 0.25 Radius of curvature of the contact protrusion of the card tooth mm 1.5 Contact length of the chuck anchor mm 100 static friction coefficient / 0.2 Kava inner diameter (outer diameter of the contacted body) mm 100 Cavalier distance (center distance) mm 5

[0110] A program was developed to calculate the stress components and von Mises stress at the contact surface boundary. Characteristic points A, B, and C (three points) were then analyzed. (See...) Figure 3 These three points are special points on the boundary where stress distribution will reach its maximum value. Point A is in the direction of frictional force on the working anchor, and point B is in the opposite direction.

[0111] In the current coordinate system, the coordinates of A, B, and C are (-1, 0), (0, g / a), and (1, 0), respectively. Substituting these values ​​into the expression above, and considering a frictional force (tension) of 400 kN, the distribution diagrams of each stress component are plotted as follows. Figure 4 As shown. By Figure 4 From (a)-(g), we can see that compressive stress concentrations exist at points A (in the same direction as the frictional force) and B (the center point of the slip tooth), while tensile stress concentrations exist at point C (in the opposite direction of the frictional force). The stress in the x-direction manifests as compressive stress at points A and B, with the same distribution pattern at point B. The von Mises stress, on the other hand, shows the highest surface stress concentration at point B (the center point of the slip tooth), with the von Mises stress at points A and C being approximately equal. Von Mises stress is the stress criterion for judging the yield strength of metallic materials. When using metal slips, the casting material should meet the ultimate stress requirements under working conditions.

[0112] To investigate the stress variation at the center point of the collet under different frictional (tension) forces and to provide a reference for engineering design, stress variation curves at point B with frictional (tension) forces were plotted. Figure 5 .

[0113] Depend on Figure 5 It can be seen that within a certain range, the stresses increase nearly linearly with the increase of the tensile force. When the tension reaches 400 kN, the von Mises stress on the contact surface reaches 366.88 MPa, and the working anchor made of 45 carbon steel has already shown local yielding, because the yield strength of the 45 carbon steel working anchor is 330 MPa. When the tension reaches 800 kN, the von Mises stress on the contact surface reaches 519.48 MPa. The failure stress of 45 carbon steel is typically around 600 MPa. Therefore, in the design, the upper limit of the tension that the working anchor can withstand can be calculated from the failure stress to determine the range of the equipment.

[0114] In addition, the tension and stress at the points of the equipment are also affected by the center distance of the slip teeth and the contact length. Figure 5 , Figure 6 .

[0115] Depend on Figure 6 It can be seen that, with other parameters remaining constant, the tension force that the equipment can provide decreases almost linearly as the center distance of the slips increases, but the magnitude of the von Neumann stress at the maximum stress point of a single slip remains unchanged. Therefore, when conditions permit, the spacing between the slip teeth should be minimized to ensure the tension range of the equipment.

[0116] Depend on Figure 7 It can be seen that, with other parameters constant, the tension force provided by the equipment is positively correlated with the contact length, exhibiting a linear increasing relationship. It is worth noting that the contact length has virtually no impact on the von Neumann stress at the point of maximum stress on a single slip. Therefore, when conditions permit, the contact length should be increased as much as possible to ensure the tension range of the equipment.

[0117] In addition, the radius of curvature of the contact protrusion of the KAV tooth affects the degree of von Mises stress concentration. The stress at point B changes significantly due to the radius of curvature of the contact protrusion. Figure 8 .

[0118] Depend on Figure 8 It can be seen that the von Mises stress at point B exhibits an exponential decreasing trend with the increase of the contact body half-width. At this point, the von Mises stress at point B corresponding to a total tensile force of 50 kN is 226.15 MPa, which is quite close to the yield strength of 45 carbon steel (330 MPa). Increasing the jack pressure to increase the tensile force could easily cause buckling and fracture of the contact body. Therefore, in this situation, the tension range of the equipment is relatively short. To meet the actual engineering requirements, it is necessary to select appropriate center distances and half-width dimensions of the locking jaws during the engineering design.

[0119] The design of the new equipment primarily determines the dimensions of equipment components based on actual needs, clarifying the materials, dimensional parameters, and operating conditions of key components. Since this equipment is designed for tensioning anchor cables and working anchorages, it mainly consists of hydraulic jacks, high-pressure oil pumps, slip clamps, connecting cylinders (clamps), and extension rods. The slip clamps are the core component; by clamping the working anchorage, they generate frictional force, indirectly pulling the steel strand. This causes relative displacement between the steel strand and the anchor body, achieving a tension compensation effect. The slip clamps have internal teeth; through the interaction of forces between the teeth and the working anchorage, the half-width of the teeth, the center-to-center distance, and the slip material are crucial parameters affecting the equipment's tensioning effect, tensioning range, and applicable scope. In addition, the tensioning effect is also influenced by the dimensions and physical and mechanical conditions of the working anchorage itself.

[0120] Four-strand prestressed anchor cables are commonly used on the road cutting slopes of expressways in Guangdong Province. The working anchor has a diameter of 9.5cm and a thickness of 4.5cm. This is a design scheme for a new type of tensioning equipment for four-strand anchor cables.

[0121] The parameters of the slip clamp and the casting material of the slip clamp are calculated by using the required range of the equipment. To meet the compensation tension requirements, over-tensioning of 1.1-1.2 times the design value is necessary. Therefore, the equipment range cannot be lower than 1.2 times the design anchoring force of 400kN for the four anchor cables, which is 480kN. Here, the upper limit of the range is taken as twice the target range, i.e., 960kN. The expression for the upper limit of the force on a single steel strand corresponding to the upper limit of the range is as follows.

[0122] ;

[0123] In the formula, This represents the tension corresponding to a single bundle of steel strands. This is the force corresponding to the upper limit of the range.

[0124] The normal stress in small-section steel strands can usually be considered to be uniformly distributed, and its relationship with the force on the steel strand is as follows:

[0125] ;

[0126] In the formula, The diameter of the single-strand anchor cable steel strand is 15.2mm in this case. This represents the yield stress of a single strand of steel wire, which is 1860 MPa in this case. The cross-sectional stress of the steel wire strand must not exceed this value.

[0127] Combining the above two equations and substituting the relevant parameters, it can be calculated that when the upper limit of the equipment range is 600kN, the cross-sectional normal stress of a single anchor cable strand is 826.63MPa, which is less than the yield stress of 1860MPa, and will not cause the steel strand to yield and fail.

[0128] Under the requirement of the upper limit of the range, the strength of the two contacting bodies is also required. Based on the upper limit of the range, after determining the size and spacing of the slip teeth, the slip teeth will not experience localized yielding due to excessive stress concentration, and the working anchor will not break. On this basis, the design parameters of the working anchors of commonly used four-cable anchors in Guangdong expressways were investigated, and the design parameters were input into the corresponding expressions above to obtain the equipment tension force and the yield stress values ​​of the contact surface (see Tables 2 and 3).

[0129] Table 2: Design Parameters

[0130] Parameter name unit value Kava elastic modulus GPa 200 Working anchorage (four bundles) elastic modulus GPa 200 Kava clamp Poisson's ratio / 0.25 Working anchorage (four bundles) Poisson's ratio / 0.25 Radius of curvature of the contact body of the kava tooth mm 4 Contact length of the chuck anchor mm 100 static friction coefficient / 0.2 Working anchorage (four bundles) outer diameter mm 95 Cavalier distance (center distance) mm 5 Ultimate strength of working anchorage MPa 600 Kavaya yield strength MPa /

[0131] Table 3: Calculation Results

[0132] Parameter name unit value Contact surface von Neumann stress MPa 587.64 Tensioning force upper limit kN 1000

[0133] The results that meet the requirements can be calculated based on the parameters in Table 2. These results ensure that the working anchor will not experience localized damage or buckling, guaranteeing stability during the loading process. Furthermore, the protrusion of the slip tooth used to contact the working anchor must meet the requirement of sufficient contact. Substituting the parameters from Table 2, the half-width of the contact protrusion is 0.0314 mm. For ease of machining, the height of the slip tooth is 2 mm, and the bottom width is 1.8 mm. Based on the above and Table 2, and considering the von Mises stress value of 542.03 MPa on the contact surface, a commonly used alloy material is selected for casting. 45CrNi has a yield strength of 835 MPa, is commonly used in the manufacture of mechanical bearings, has strong fatigue resistance, meets the conditions of repeated loading and unloading of equipment, and has a safety factor of approximately 1.54.

[0134] After selecting materials and determining key parameters, a prototype was fabricated in the factory. Utilizing the slope to be widened during the Guangshao Expressway expansion project, a four-strand anchor cable with a pre-existing short steel strand was selected for tensioning. The device has been successfully tested in the field, capable of loading up to 600kN. After unloading and disassembly, the working anchor left "teeth marks" with a width of 3cm, indicating significant plastic deformation, but not reaching its limit. Substituting the 3cm contact length into the formula above, the upper limit of the tensioning device's range was calculated to be 716kN. This demonstrates that the preceding theoretical calculations are quite close to the actual working conditions, providing a solid theoretical basis for the equipment's development and application.

[0135] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any minor modifications, equivalent substitutions, and improvements made to the above embodiments based on the technical essence of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating the parameters of a highway slope compensation tensioning equipment slip clamp, characterized in that, The specific steps are as follows: S1, constructing a basic parameter library of the slip-on and the working anchor; S2, splitting the convex structure on the slip-on into a plurality of slip-on teeth, and equivalent the slip-on teeth to an infinite long contact body acting on the working anchor; S3, under the small deformation assumption, ignoring the axial deformation effect caused by Poisson's ratio, equivalent the contact between the slip-on teeth and the working anchor to plane strain, and further constructing a slip-on tooth-working anchor friction contact model; in step S3, it is assumed that the load acting on the slip-on tooth is uniformly distributed, and the friction resistance T of a single slip-on tooth satisfies: ； When the slips are in contact with the working anchor, there are usually several same size slip teeth in contact with the working anchor. Ignoring the mutual influence of slip teeth force, the total frictional force of the slip and the working anchor can be obtained by superposition principle, so as to obtain the pulling force T t : ； where W, P are the line load, u is the static friction coefficient, a is the contact half-width, r m is the outer diameter of the slip teeth; s is the distance from the point of contact of the slip teeth with the contact plane of the working anchor to the contact center; wherein n is the number of slip teeth on the slip; When the distance between the jaws is reduced, or the strength of the jaw material is increased, the jaw drag increases, i.e. the pulling force T required t increases. S4, according to the von Mises intensity criterion, when the metal material deformation energy reaches the deformation energy required for the metal material to yield, the metal material will yield or brittlely break, that is, the equivalent stress is greater than or equal to the yield strength of the metal material, the slip ring tooth yields and brittlely breaks; a slip ring tooth-yield strength model is constructed; the yield stress of a single slip ring tooth is calculated through step S4 ; the yield strength of the metal material is obtained , and a slip ring meeting the requirements is designed and selected according to the engineering safety factor F s . The engineering safety factor calculation method for ensuring the strength of the material under load is as follows: ； Under a certain safety factor, the yield strength meets the allowable stress demand generated by the selected parameters under the maximum axial force range of the tensioning equipment; S5, in combination with the need for engineering safety factor, selecting the slip-on with parameters meeting the stress demand for operation of high-speed slope engineering prestressed anchor cable compensation tensioning engineering.

2. The method according to claim 1, wherein the method is characterized by: According to the basic parameter library of step S1, the metal material meeting the engineering needs is selected in terms of design size and tensioning equipment range, and the corresponding slip-on with slip-on tooth distance and contact length is made.

3. The method according to claim 1, wherein: The fatigue correction factor is introduced in step S4 or the cyclic yield strength is used to correct the yield strength of the slip ring material under fatigue conditions The correction or replacement is made to obtain a safety factor under fatigue conditions.

4. The method according to claim 1, wherein the method is characterized by: In step S4, it is known from Johnson solution that the stress expression of the circular and arc surface problem is the same as that of the plane contact: ； In the formula, x and z represent the coordinates of an arbitrary point in the xz plane of the working anchor at the contact plane between the slip clamp and the working anchor; is the distribution contact pressure on the contact surface between the slip clamp teeth and the working anchor, is the distribution tangential force on the contact surface between the slip clamp teeth and the working anchor; represents the normal stress acting on the section perpendicular to the x axis and in the direction along the x axis; represents the normal stress acting on the section perpendicular to the z axis and in the direction along the z axis; represents the shear stress acting on the section perpendicular to the x axis and in the direction along the z axis.

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