Analysis and Experimental Study on the Friction Force at the Binding Point of Flexible Cable on Satellite

Ziquan Wang, Jinzhu Li, Xuefeng Gao, Yunqiang Wu,Yingjie Lin, Zhiwen Luo, Donglei Jiang

Abstract: Mainly for the problem that the friction force generated by the existing process of binding, fixing and fastening the flexible cable on the satellite is unknown, the friction force analysis and experimental research on the binding point of the flexible cable are carried out.The equivalent model of the cable bundle bound by nylon cable ties is established, the force on the binding point is analyzed, and the empirical formula for calculating the friction force at the binding point is established.The formula shows that the friction force is related to the cable bundle diameter, the number of winding cycles of silicone rubber tape, the width of nylon cable ties, and the binding force.The friction force tests of the cable diameter of 5.06 mm, 8.02 mm, 24.02 mm, 38.04 mm under different winding turns of tape were carried out, which was compared with the theoretical calculation value.It is concluded that the calculation accuracy of the theoretical model is more than 95%,which can estimate the actual friction force value accurately.This provides a reference and basis for the theoretical and experimental research on the friction force of the flexible cable binding point on satellite.

Keywords: flexible cable; binding point; equivalent model; friction force; experimental study

1 Introduction

The flexible cable network products on satellite include but not limited to low-frequency cables,grounding networks, cable accessories and other flight products, as well as force and thermal sensor cables, electrical test ground cables and other process products.Satellite cable network belongs to flexible body and has special requirements such as binding and fixing.It has practical engineering features such as large numbers of connectors, narrow wiring space, centralized wire distribution, and difficult wiring operation [1-8].As a flexible body, the size, shape and spatial trend of cables are constrained by the structure space of product.The assembly of cable network itself is a technological problem due to the limitation of assembly space, the complexity of cable structure and the flexibility of cables in assembly operation [9-18].According to the statistical analysis report on the quality problems of a batch of products of the national academy of astronautics and astronautics, 20% of all product failures are caused by cables.In the overall internal structure of a spacecraft, the mass of various power supplies, cables, and their accessories accounts for 20%-30% of the total mass of the spacecraft.As the design of satellite cable network tends to be diversified, intensive and lightweight, and special cables such as high voltage and high rigidity are introduced, as well as the development trend of small batch quantification, refinement and short cycle of satellites, the pressure on the consistency of production and assembly quality of satellite cable network increases.At present, in the process of cable binding on satellite, the binding tape specifications, binding force and other process parameters used for cables with different wire diameters have been quantified through physical experimental methods only, and the cable binding operation specifications have been formed.However,the friction force at the binding point caused by the quantified process parameters has not been studied in depth.At the same time, different cable diameters, binding tape specifications, binding force, and the influence of changes in process parameters such as the winding number of insulating protective tape on the friction force are not distinct, and let alone whether the cable is loose or partially tightened in the mechanical test or during rocket launch.Therefore, it is urgent to study the influence of cable binding process parameters on the friction force at the binding point, establish a theoretical model for estimating the friction force at the binding point, and further promote the growth of cable binding reliability.

Due to the nonlinear physical constitutive property of flexible cables, the internal mechanical properties of cable bundles are extremely complex, like the contact among cable elements in the layer, resulting in contact pressure.The relative motion of the cable generates friction,including axial sliding friction and torsional sliding friction [19-25].At the same time, the friction among cables will hinder the relative movement among materials, cause energy dissipation,produce damping effects, etc., which will increase the complexity of cable dynamics model establishment [26-36].Therefore, scholars at home and abroad usually compare flexible cables to slender curved beams, and use the centerline analogy method to solve the large displacement problem of slender curved beams in elastic media [37-48].By assuming that the cable section is homogeneous and isotropic, the constitutive equation of the cable is obtained, which leads to the dynamic model of the cable further, based on the analogy method of elastic thin rod centerline proposed by Kirchhoff in 1859, which transformed the deformation of the elastic thin rod into the rotation of the rod section along the rod centerline, so that the statics of the elastic thin rod has the same mathematical expression as the dynamics of the rigid body [49-58], which provides a reference for the establishment of the equivalent model of the cable bundle bundled with nylon straps.In recent years, there have been many mechanical studies on the winding force exerted on the circular tube shaped structure [59-66].M.Jia [67] based on the theory of large elastic deformation, analyzed the stress at the free end of the optical fiber,deduced the balance equation of the infinitely small optical fiber, and deduced the deformation equation by substituting the end conditions.Under the condition that there is only axial tension, the approximate curve equation in the range of small angle deformation is established.The integral constant is given by comparing the theoretical and approximate tangent ordinate results.The spiral disk winding method is analyzed, and the spiral disk four pole mode winding method is introduced.The analysis results prove the applicability of the winding model.It provides a reference for the analysis and establishment of the mechanical model of friction force.But, at present, there are only a few research results on the theoretical model and test of the friction force at the binding point of the flexible cable on the satellite.

In this paper, the stress state of the flexible cable binding point on the satellite is analyzed,and the equivalent friction force model of the binding point is established.According to the principle of symmetry, the stress and stress state of the circular cross-section of the cable are analyzed, and the theoretical calculation formula of the friction force of the binding point is established.The friction test of silicone rubber selfadhesive tape was carried out for the cables with the measured diameters of 5.06 mm, 8.02 mm,24.02 mm and 38.04 mm under different winding cycles, and the results were compared with the theoretical calculated values.The results showed that the theoretical model could accurately estimate the friction force of the cable at the binding point, which had certain practicability, and solved the problem that the friction force of the satellite flexible cable after binding, fixing and tightening was unknown, and laid a foundation for the subsequent optimization design of process parameters.

2 Mechanical Model of Binding Point Friction

The stress deformation diagram of the cable after binding is shown in Fig.1.It can be seen that the cable is mainly subjected to the binding forceFof nylon tape and silicone rubber tape at the binding point, the friction forcefat the binding point, the root bending momentMs, and the torsional momentMθ.The main tensile force outside the binding point isFσ, the shear force isFτand the torsinoal moment isMo.

Fig.1 Schematic diagram of cable deformation after binding

In this paper, only the friction force at the binding point is considered, so the stress model assumption can be shown as

It can be seen that the torsional moment and root bending moment at the binding point are zero, that is

Referring to the elastic curved beam equivalent analogy modeling method of flexible cables,a wire harness composed of multiple cables can be equivalent to a cylinder, as shown in Fig.2.Winding silicone rubber tape on the wire harness can be equivalent to winding silicone rubber tape on a cylinder.Similarly, the nylon tie used for binding and fixing can be equivalent to a thin-walled cylinder with a certain preload, and the analysis shows that the pre-tightening force of thin-walled cylinder is related to the winding force of silicone rubber tape.

Fig.2 Equivalent model of cable bundle with nylon tie

Fig.3 Stress analysis of binding point

According to the assembly relationship shown in Fig.2 and the principle of symmetry,take the symmetrical sections of nylon cable ties,silicone rubber tapes and cables for stress analysis, as shown in Fig.3.It can be seen that the nylon cable ties are subject to the binding forceFNland the positive pressurepSNof silicone rubber tape on them.The silicone rubber tape is subject to the tape pre-tightening forceFSi, the positive pressurepNSfrom the nylon cable ties and the positive pressurepCSfrom the cable alignment.The cable is subjected to the positive pressurepSCaligned by the silicone rubber tape, and all forces and pressures meet the static equilibrium relationship.

According to the stress analysis diagram, the positive pressure on the cable is the sum of the tightening forceFNlof the cable tie and the preloadFSiof the silicone rubber tape.According to the principle of symmetry, the expression is

The pre-tightening forceFSiof silicone rubber tape is related to the number of silicone rubber winding cycles and the winding force of single-layer tape.FSican be expressed as

whereNis the number of winding cycles of silicone rubber tape (N=1, 2,...),Fsis the winding force of single-layer silicone rubber tape.

The radial stress of the cable under external pressure in the binding area of nylon tape and silicone rubber tape can be obtained, which is represented byσrand circumferential stressσθas

whereDcis the cable diameter,dNlis the width of nylon cable tie, the sign of stress indicates the direction of stress, the negative direction indicates contraction force, and positive direction indicates relaxation force.

Under the condition of online elasticity,according to the generalized Hooke’s law, the relationship between the radial and circumferential stresses and strain of the cable section can be obtained as

whereEis the equivalent elastic modulus of the cable,μis the Poisson’s ratio.

The radial displacement of any point on the cable section can be obtained as

whereρis the distance from any point on the cable section to the section center,Ecis the equivalent elastic modulus of the cable.

Thus, the total radial displacement of the cable after being stressed is

Similarly, the radial stress of silicone rubber tape under external pressure and internal pressure at any point in the binding area of nylon tape can be obtained.The radial stressσSrand circumferential stressσSθcan be expressed as [68]

wheretis the thickness of silicone rubber tape.Therefore, the radial displacement of any point on the section of silicone rubber tape is

whereENis the equivalent elastic modulus of silicone rubber tape.

Thus, the total radial displacement of silicone rubber tape after being stressed is

whereDis the sum of the winding thickness of the cable and silicone rubber tape,Tis the thickness of single-layer silicone rubber tape, 1/Kis the viscosity coefficient,K＞0, and it is related to the surface material of the cable harness.The value range ofKcan be determined according to the test method.

It can be seen from the analysis and calculation that the radial displacement of the cable and silicone rubber tape is very small and negligible under the binding force of tens of kilograms.Therefore, Eq.(12) can be simplified as

It can be seen from the Eq.(12) and Eq.(13) that the friction force is related to the cable bundle diameter, the number of winding cycles of silicone rubber tape, the width of nylon cable ties, and the binding force.In the actual operation process of engineering, these variables can be controlled for research on friction control of cables, thus providing a foundation for the active control of interference forces in flexible cable binding belts.

3 Tie Clamp and Tightening Process of Flexible Cable

Before the cable is bound, the silicone rubber tape shall be wound according to the specification.The number of winding turns of the silicone rubber tape is generally an integer, that is,N=1, 2, ···.At present, the winding number of layers of silicone rubber tape is generally 2, 3 or 4.The cable binding point can be bound, tightened and fixed with a tape clamp in three steps:manual binding, selecting the tension gear of the strap clamp, binding, fixing and fastening with band clamps.

3.1 Manual Binding

As shown in Fig.4, The manual binding process includes winding the binding tape below the target binding point, leading out the tie from the tie buckle with the tail down, and binding the cable to its own direction manually.

Fig.4 Manual binding

3.2 Selecting the Tension Gear of the Strap Clamp

The relationship between the binding force of the binding belt and the band clamp gear is shown in Tab.1 and Fig.5.It can be seen that the tension value corresponding to the band clamp gear changes linearly.Therefore, the tension values of gear 0 - gear 8 can be calculated according to the linear interpolation theory.The linear interpolation formula can be expressed as

Tab.1 Band clamp gear and tension gauge

Fig.5 Band clamp gear and force curve

whereFis the gear force,Fnis the front gear force,Fn+1is the rear gear force,Gnis the front gear of the currently selected gear,Gn+1is the rear gear of the currently selected gear,Gis the currently selected gear.

For commonly used nylon cable ties, 3 mm×65 mm, 6 mm×150 mm, 8 mm×240 mm, the recommended gears are shown in Tab.2.the strap clamp, rotating the dial, selecting the appropriate tension gear according to the required size of the cut strap, adjusting the position of the strap locator according to the width of the cut strap, selecting the appropriate step notch,inserting the strap into the strap clamp head and tension clamp, and pulling the trigger of the strap clamp to tighten the strap slowly, and after the trigger is buckled to the bottom, the strap clamp automatically cuts the strap.

Tab.2 Recommended gear of band clamp

4 Friction Test Research

4.1 Silicone Rubber Tape Winding Cable

As shown in Fig.7, after the cable is wound with silicone rubber tape, it will automatically stick to the cable due to the effect of the winding force.The thickness of a single layer of silicone rubber tape after winding the cable is about 0.64 mm,that is,t=0.64 mm.The winding force of a single layer of silicone rubber tape is about 7.5 N,that is,Fs=7.5 N.

According to the band clamp gear force and gear recommendation shown in Tab.1, Tab.2 and Fig.5, and the linear interpolation calculation formula of Eq.(14), the selected gear and corresponding gear tension of nylon cable ties of different specifications can be obtained.

3.3 Binding, Fixing and Fastening the Band Clamp

As shown in Fig.6, the tightening process of the strap clamp includes adjusting the dial switch of

Fig.6 Bind with clamp

Fig.7 Winding state of silicone rubber tape on the cable

4.2 Specification, Gear and Tightening Force of Binding Tape

According to the survey, the diameter of the cable bundle formed during the laying of low-frequency cable network is about 5 mm-60 mm, and the diameter of the cable bundle is divided into 5 mm-10 mm, 10 mm-30 mm and 30 mm-60 mm during the size selection of the binding tape.In order to tie the cable bundles of different thicknesses with the cable support, the nylon binding tape is classified into three grades: 3 mm×65 mm, 6 mm×150 mm, 8 mm×240 mm.

According to the recommended gear and tension of the tie clamp, the size of the tie tape used for binding is determined for different cable diameter ranges, but the number of winding layers of the silicone rubber tape used for binding is uncertain.Therefore, according to the control variable research method, the cable bundles with different diameters can be tied with 3 mm×65 mm, 3 mm×65 mm, 6 mm×150 mm, 8 mm×240 mm binding, and tensile test of wrapping 2, 3 and 4 layers of silicone rubber tape.

According to the recommended gear and Eq.(14) of the band clamp 3 mm×65 mm nylon cable tie, the gear selected is 0.5, and the tension value is 71 N.According to that of the band clamp 6 mm×150 mm nylon cable tie, the gear selected is 1, and the tension value is 89 N.According to that of the band clamp 8 mm×240 mm nylon cable tie, the gear selected is 2.5,and the tension value is 124.5 N.

Make cable bundles with diameters of 5 mm,8 mm, 24 mm and 38 mm for tensile test.Use vernier caliper to measure the actual test cable diameter (excluding the winding thickness of silicone rubber tape) to be 5.06 mm, 8.02 mm,24.02 mm and 38.04 mm, and the corresponding binding tape specification is 3 mm×65 mm,3 mm×65 mm, 6 mm×150 mm and 8 mm×240 mm.

4.3 Friction Test

Fig.8 Friction test

As shown in Fig.8 , use a self-locking tension meter (accuracy 0.1 N) to pull along the cable axially.When the cable slips, the tension meter automatically displays the process tension value,and automatically locks the maximum tension value in the pulling process, so that the maximum friction value in the cable pulling process can be judged.The friction test value shall be rounded according to the rounding method.

According to the friction test, the friction test values of 5.06 mm diameter cable with silicone rubber tape winding number of 2, 3 and 4 are 30.2 N, 45.1 N and 65.4 N.The friction test values of 8.02 mm diameter cable with silicone rubber tape winding number of 2, 3 and 4 are 64.6 N, 84.8 N and 108.6 N.The friction test values of 24.02 mm diameter cable with silicone rubber tape winding cycles of 2, 3 and 4 are 139.7 N,169.5 N and 199.6 N.The friction test values of 38.04 mm diameter cable with silicone rubber tape with 2, 3 and 4 winding cycles are 240.8 N,275.2 N and 319.6 N, as shown in Fig.9.

Fig.9 Test value of friction

5 Comparative Analysis

5.1 Calculation Accuracy of Theoretical Model

In order to compare and analyze the theoretical friction calculated by the theoretical model with the actual friction error, the calculation accuracy of the theoretical model is defined as

whereFTNis the theoretical calculated friction force when the number of winding turns of silicone rubber tape isNfor cables of the same diameter,FANrefers to the actual friction force when the number of winding turns of silicone rubber tape isNfor cables of the same diameter.

5.2 Comparison Between Theoretical Envelope and Test Value of Friction Force when Cable Diameter is 5.06 mm

The comparison diagram between the theoretical envelope and the test value of the friction force of the cable with a diameter of 5.06 mm is obtained, as shown in Fig.10.It can be seen that whenK=125, the theoretical value of the friction force obtained is consistent with the test value in the change trend.In terms of numerical value, when the silicone rubber is wound for 2 cycles, the theoretical minimum value is 33.6 N.When the silicone rubber is wound for 4 cycles,the theoretical maximum value is 73.2 N.When the silicone rubber is wound for 3 cycles, the theoretical median value is 49.5 N, which is greater than the friction force of 30.2 N, 45.1 N and 65.4 N when the silicone rubber tape is wound for 2, 3 and 4 cycles of 5.06 mm diameter cable obtained in the test.

Fig.10 Comparison between theoretical envelope and test value of friction force of 5.06 mm cable

WhenK=150, the theoretical value of friction force obtained is consistent with the test value in the change trend.In terms of numerical value, when the silicone rubber is wound for 2 cycles, the theoretical minimum value is 28.0 N.When the silicone rubber is wound for 4 cycles,the theoretical maximum value is 61.0 N.When the silicone rubber is wound for 3 cycles, the theoretical median value is 41.3 N, which is smaller than the friction force obtained in the test.Therefore, it can be seen that the minimum theoretical envelope curve of the friction force value obtained through theoretical calculation is lower than the test value, the maximum theoretical envelope curve is higher than the test value, and the test value is within the theoretical envelope range.

WhenK=137.5, the theoretical value of friction force obtained is consistent with the test value in the change trend.In terms of numerical value, when the silicone rubber is wound for 2 cycles, the theoretical minimum value is 30.6 N.When the silicone rubber is wound for 4 cycles,the theoretical maximum value is 66.5 N.When the silicone rubber is wound for 3 cycles, the theoretical median value is 45.0 N, which is basically equal to the friction test value.

Based on the numerical variation law and size obtained from theoretical calculation, it can be seen that the theoretical model has well estimated the friction force, and the theoretical envelope covers the test friction force value.The deviation between the theoretical value of friction force calculated byK=137.5 and the actual value is not more than ±3%.

5.3 Comparison Between Theoretical Envelope and Test Value of Friction Force when Cable Diameter is 8.02 mm

Fig.11 Comparison between theoretical envelope and test value of friction force of 8.02 mm cable

The comparison diagram between the theoretical envelope and the test value of the friction force of the cable with a diameter of 8.02 mm is obtained, as shown in Fig.11.It can be seen that whenK=125, the theoretical value of the friction force obtained is consistent with the test value in the change trend.In numerical value,when the silicone rubber is wound for 2 turns,the theoretical minimum value is 69.7 N.When the silicone rubber is wound for 4 turns, the theoretical maximum value is 123.9 N.When the silicone rubber is wound for 3 turns, the theoretical median value is 92.8 N, which is greater than the friction force of 64.6 N, 84.8 N and 108.6 N when the silicone rubber tape is wound for 2, 3 and 4 turns of 8.02 mm diameter cable obtained in the test.

WhenK=150, the theoretical value of friction force obtained is consistent with the test value in the change trend.In terms of numerical value, when the silicone rubber is wound for 2 cycles, the theoretical minimum value is 58.0 N.When the silicone rubber is wound for 4 cycles,the theoretical maximum value is 103.2 N.When the silicone rubber is wound for 3 cycles, the theoretical median value is 77.3 N, which is smaller than the friction force obtained in the test.Therefore, it can be seen that the minimum theoretical envelope curve of the friction force calculated by theory is lower than the test value, the maximum theoretical envelope curve is higher than the test value, and the test value is within the theoretical envelope range.

WhenK=137.5, the theoretical value of friction force obtained is consistent with the test value in the change trend.In terms of numerical value, when the silicone rubber is wound for 2 cycles, the theoretical minimum value is 63.3 N.When the silicone rubber is wound for 4 cycles,the theoretical maximum value is 112.6 N.When the silicone rubber is wound for 3 cycles, the theoretical median value is 84.3 N, which is basically equal to the friction test value.

Based on the numerical variation law and size obtained from theoretical calculation, it can be seen that the theoretical model has well estimated the friction force, and the theoretical envelope covers the test friction force value.The deviation between the theoretical value of friction force calculated byK=137.5 and the actual value is not more than ±5%.

5.4 Comparison Between Theoretical Envelope and Test Value of Friction Force when Cable Diameter is 24.02 mm

The comparison diagram of theoretical envelope and test value of friction force of 24.02 mm diameter cable is obtained, as shown in Fig.12.It can be seen that whenK=125, the theoretical value of friction force is consistent with the test value in the change trend.In terms of numerical value,when the silicone rubber is wound for 2 cycles,the theoretical minimum value is 151.4 N.When the silicone rubber is wound for 4 cycles, the theoretical maximum value is 209.1 N.When the silicone rubber is wound for 3 cycles, the theoretical median value is 177.5 N, which is greater than the friction force of 139.7 N, 169.5 N and 199.6 N for the 24.02 mm diameter cable, when the silicone rubber tape is wound for 2, 3 and 4 cycles.

Fig.12 Comparison between theoretical envelope and test value of friction force of 24.02 mm cable

WhenK=150, the theoretical value of friction force obtained is consistent with the test value in the change trend.In terms of numerical value, when the silicone rubber is wound for 2 cycles, the theoretical minimum value is 126.1 N.When the silicone rubber is wound for 4 cycles,the theoretical maximum value is 174.3 N.When the silicone rubber is wound for 3 cycles, the theoretical median value is 147.8 N, which is smaller than the friction force obtained in the test.Therefore, it can be seen that the minimum theoretical envelope curve of the friction force value obtained through theoretical calculation is lower than the test value, the maximum theoretical envelope curve is higher than the test value, and the test value is within the theoretical envelope range.

WhenK=137.5, the theoretical value of friction force obtained is consistent with the test value in the change trend.In terms of numerical value, when the silicone rubber is wound for 2 cycles, the theoretical minimum value is 137.6 N.When the silicone rubber is wound for 4 cycles,the theoretical maximum value is 190.1 N.When the silicone rubber is wound for 3 cycles, the theoretical median value is 161.3 N, which is basically equal to the friction test value.

Based on the numerical variation law and size obtained from theoretical calculation, it can be seen that the theoretical model has well estimated the friction force, and the theoretical envelope covers the test friction force value.The deviation between the theoretical value of friction force calculated byK=137.5 and the actual value is not more than ±5%.

5.5 Comparison Between Theoretical Envelope and Test Value of Friction Force when Cable Diameter is 38.04 mm

Fig.13 Comparison between theoretical envelope and test value of friction force of 38.04 mm cable

The comparison diagram between the theoretical envelope and the test value of the friction force of the cable with a diameter of 38.04 mm is obtained, as shown in Fig.13.It can be seen that whenK=125, the theoretical value of the friction force obtained is consistent with the test value in the change trend.In numerical value,when the silicone rubber is wound for 2 turns,the theoretical minimum value is 272.2 N.When the silicone rubber is wound for 4 turns, the theoretical maximum value is 340.9 N.When the silicone rubber is wound for 3 turns, the theoretical median value is 303.9 N, which is greater than the friction force of 240.8 N, 275.2 N and 319.6 N when the silicone rubber tape is wound for 2, 3, and 4 turns of 38.04 mm diameter cable obtained in the test.

WhenK=150, the theoretical value of friction force obtained is consistent with the test value in the change trend.In terms of numerical value, when the silicone rubber is wound for 2 cycles, the theoretical minimum value is 226.8 N.When the silicone rubber is wound for 4 cycles,the theoretical maximum value is 284.1 N.When the silicone rubber is wound for 3 cycles, the theoretical median value is 253.3 N, which is smaller than the friction force obtained in the test.Therefore, it can be seen that the minimum theoretical envelope curve of the friction force calculated by theory is lower than the test value, the maximum theoretical envelope curve is higher than the test value, and the test value is within the theoretical envelope range.

WhenK=137.5, the theoretical value of friction force obtained is consistent with the test value in the change trend.In terms of numerical value, when the silicone rubber is wound for 2 cycles, the theoretical minimum value is 247.4 N.When the silicone rubber is wound for 4 cycles,the theoretical maximum value is 310.0 N.When the silicone rubber is wound for 3 cycles, the theoretical median value is 276.2 N, which is basically equal to the friction test value.

Based on the numerical variation law and size obtained from theoretical calculation, it can be seen that the theoretical model has well estimated the friction force, and the theoretical envelope covers the test friction force value.The deviation between the theoretical value of friction force calculated byK=137.5 and the actual value is not more than ±3.5%.

6 Conclusion

According to the dynamic modeling method of elastic thin rods for flexible cables, the equivalent model of the cable bundle bound by nylon cable ties is established, and the empirical mechanical model of the friction force at the binding point is established.It is concluded that the friction force at the binding point is related to the binding force, the cable diameter, the number of winding cycles of silicone rubber tape,the thickness of single-layer silicone rubber tape,the width of nylon cable ties, the winding force of single-layer silicone rubber tape, and the viscosity coefficient.The friction force test at the binding point was carried out, and the friction force test values of cables with different diameters, different winding coils and different binding forces were obtained.The results were compared with the theoretical calculation envelope, and it was found that the variation law and size of the theoretical calculation values were basically consistent with the test values.WhenK=137.5, the deviation between the theoretical value and the actual value of the friction force is not more than±5%, and the calculation accuracy is more than 95%.The model can effectively estimate the actual friction force, providing support and reference for theoretical and experimental research on the friction force at the binding point.By controlling the variables that affect the friction force of the binding point, the process parameters of the binding point can be optimized, thereby obtaining the minimum binding force corresponding to a larger friction force and the specifications of the nylon binding tape, etc.