1. Introduction

Polymer insulators have been widely used in transmission and distribution line. Various insulators are used in electrical equipment to support and separate electrical conductors without allowing current through itself ⁽¹⁾. Further, in applications of railway traction lines, insulators are also subjected to adverse environmental conditions and mechanical vibrations. Railway insulators can be largely classified into post, stem, and tension insulator.

Proper operation of network railway traction lines is highly dependent upon the proper working of insulators. Traction insulators have an important role as far as a power supply to trains is concerned. They are used to provide rigid support for the overhead catenary wire ⁽²⁾-⁽³⁾. The proper functioning of traction insulators is essential to maintain the reliability of a power supply to electric trains. They may malfunction because of regular exposure to mechanical vibrations, vandalism and environmental effects ⁽³⁾. If an insulator in a cantilever failed under tensile, compression or bending loads, this could lead to damage of pantographs resulting in the tear down of overhead contact lines along the full braking distance of the train. Similar effects could ensue from failures of the tension insulators, stressed by tensile forces ⁽⁴⁾.

In this paper, structural analysis that focuses on cantilever load test and tensile force test is carried out by using COMSOL Multiphysics, an analysis tool using a finite element method (FEM) for post, stem, and tension insulator for railroad manufactured by GUJU Technology Inc.. There are two types of post insulator, NSP-50 and NSP-40, usually intended for high-speed railway. Afterwards, there are three types of stem insulator usually intended for electric railway and high-speed railway, namely T-m, T-ms, and T-mx, respectively. Lastly, there is one type of tension insulator intended for electric railway, namely N-a. The maximum stress value confirmed by structural analysis is compared with yield strength value to verify the robustness of insulators. The stability and reliability of railway traction line insulators are analyzed through mechanical stress analysis.

Fig. 1. Polymeric railway insulator

Fig. 2. 3D Model of 25 kV polymeric railway insulator

2. FEM Analysis

2.3 Structure Analysis Results

The stress calculation results of railway insulators under load and tensile force are calculated and the relationship between stress, safety factor, cantilever load and tensile force according to the type of railway insulators are obtained in Table 3 and Table 4.

(1)

$\sigma_{M=}\sqrt{\dfrac{1}{2}[(\sigma_{x-}\sigma_{y})^{2}+(\sigma_{y-}\sigma_{z})^{2}+(\sigma_{z-}\sigma_{x})^{2}+6(\tau_{xy}+\tau_{yz}+\tau_{zx})]}$

(2)

$\sigma_{M=}\sqrt{\dfrac{1}{2}[(\sigma_{x-}\sigma_{y})^{2}+(\sigma_{y-}\sigma_{z})^{2}+(\sigma_{z-}\sigma_{x})^{2}]}$

(3)

$Safety Factor(SF)=\dfrac{Material Yield Strength}{\max i\mu m von Mises Stress}$

That means the fracture occurs when the estimated results of cantilever load test and tensile force test exceed the yield stress value. The von Mises stress is a kind of failure criterion, that is based on the von Mises-Henckey theory. This theory states that a ductile material start to yield when the von Mises stress becomes equal to the yield strength. In an FEM, von Mises stress is used to find a criteria to assess the safety of products. The von Mises stress is defined as (1) and it can be also expressed as (2) ⁽⁹⁾-⁽¹⁰⁾. $\sigma_{M}$ is maximum von Mises stress that we obtained from structure analysis simulation. The von Mises stress is usually used to present the mechanical safety of elasto-plastic properties such as FRP. The von Mises stress could be simply expressed as (2) if the shear stress are extinguished by adjusting the angular orientation of the stress beam.

According to the von Mises failure criterion, the safety factor is expressed as (3). In (3), yield strength means the maximum amount of stress or elastic deformation ⁽¹⁰⁾.

A. Cantilever Load Test

In cantilever load tests, a load is applied to the free end of a core or beam until failure occurs.

Fig. 3. Boundary conditions: (a) Cantilever load test; (b) Tensile load test

Fig. 4 shows the result of mechanical analysis by cantilever load test and detailed results are summarized in Table 3. As a result, maximum stress is obtained on a FRP part. Maximum stress happens at one end of a core, therefore one end of a core experienced the most severe stress. Fig. 4 shows the mechanical analysis of post insulator and the value of maximum stress is about 959 MPa. As summarized in Table 3, we present the maximum load of each type of railway insulators. It is confirmed that the maximum stress caused by applied maximum load is under the yield strength value, 1200 MPa.

Fig. 4. Cantilever load analysis for an insulator, type

Fig. 5. Tensile force analysis for an insulator, type I

B. Tensile Test

Tensile properties are used to predict the behavior of a material under forms of loading other than uniaxial tension. Therefore, tensile force tests are performed and the results of tensile force test can be used in selecting materials. Fig. 5 shows the result of mechanical analysis for insulator by given tensile force to both ends of an insulator. As a result, it is found that maximum stress is obtained on end fittings, metallic part. In this tensile test simulation, both ends of a core are experienced the most severe stress. The stress values on each end of cores are similar. Fig. 5 shows the mechanical analysis of a post insulator and the value of maximum stresses, 575 MPa. As summarized in Table 4, we present the maximum tensile force of each type of railway insulators. It is confirmed that the maximum stress of all insulators caused by maximum tensile force is still under the yield strength value, 1,200 MPa.

Fig. 6. Distribution of stress for cantilever load analysis

Fig. 7. Distribution of stress for tensile force analysis

Table 3. Mechanical stresses due to external forces (Cantilever load test)

Load Value (N)	Insulator Type	Yield Strength (MPa)	Max. Stress (MPa)	SF	Max. Load (N)
1,500	Type VI	1,200	1,074	1.1	1,650
3,832	Type III		792	1.5	5,748
4,573	Type IV		732	1.6	7,317
6,963	Type I		959	1.2	8,356
7,143	Type V		997	1.2	8,571
9,058	Type II		868	1.4	12,681

Table 4. Mechanical stresses due to external forces (Tensile force test)

Load Value (N)	Insulator Type	Yield Strength (MPa)	Max. Stress (MPa)	SF	Max. Load (N)
39,227	Type I	1,200	575	2.1	82,377
40,000	Type II		298	4.0	160,000
45,000	Type V		140	8.6	387,000
54,917	Type VI		218	5.5	302,044
58,840	Type III		170	7.1	417,764
58,840	Type IV		170	7.1	417,764

3. Discussion

Safety factor of electrical apparatuses is necessary to assess the reliability of design. Designer and customer need a simple factor which can represent robustness of product as an indicator. An enough safety factor enhances the reliability and reduces the risk of failure of product. Therefore, we perform the structure analysis and present a safety factor as results. In conventional papers to design insulators, safety factor has not been considered to verify the reliability of insulators. However, this paper deals with a safety factor for various insulators. The safety margin of insulators manufactured by GUJU Technology Inc. and is presented as results.

Cantilever load and tensile force are applied and the maximum stresses are evaluated for each insulator. The point of maximum stress that obtained in an insulator by cantilever load analysis and tensile force analysis is different. Estimated results can be seen in Fig. 6 and Fig. 7, that show the distribution of stress that experienced by each insulator.

Safety factor can be calculated by defined as ratio between yield strength of material and maximum stress that experienced by an insulator. When the stress in the design remains smaller than the strength of materials, safety factor stays larger than 1 and the design is safe ⁽¹¹⁾. It is revealed that every insulator for 25 kV railway traction lines manufactured by GUJU Technology Inc. are designed with safety factor from 1.1 to 8.6. It is known that safety factor for electric apparatuses is designed over 1.1 considering reliability and economic feasibility. Based on the results, safety factors for 25 kV railway traction lines obtained by tensile force analysis are superior to that by cantilever load analysis. It means that various insulators for 25 kV railway traction lines manufactured by GUJU Technology Inc. are well designed considering cantilever load test and should be improved considering tensile force test.

4. Conclusion

Structural analysis is performed according to cantilever load and tensile force to ensure the reliability and safety of 25 kV railway traction line insulators. Six types of insulators with different FRP rod sizes and mounting distances are used for post, stem, and tension insulator. The maximum stress value and position are confirmed by cantilever load and tensile force analysis. The stress distribution of railway insulators under cantilever load and tensile force are calculated.

The concrete results are as follows: when the load is applied in one end of insulator, the stress is concentrated at one other end of insulator, FRP part, is the most severe and when the tensile is applied to both ends of an insulator, the maximum stress is concentrated at end fittings of an insulator, metallic part. The results for mechanical stress analysis of post, stem, and tension insulator for 25 kV railway traction line applications are presented. Safety factors for each insulator according to cantilever load analysis are calculated as about 1.2, 1.4, 1.5, 1.6, 1.2, and 1.1, respectively. Whereas safety factors with respect to tensile force analysis are estimated as about 2.1, 4.0, 7.1, 7.1, 8.6, and 5.5, respectively. It is found that the tensile force of six types of insulators are superior to that of cantilever load strength when the value of yield strength is 1,200 MPa. It shows that mechanical design of insulators for cantilever load design is appropriate from the view point of engineering and that for tensile force design should be improved.

All types of insulators manufactured by GUJU Technology Inc. are certified by Korea Electrotechnology Research Institute (KERI). In the future, improved design for insulators considering tensile force test would be performed.