Theoretical correlations amongst electrical and mechanical characteristics of polymeric housing materials for outdoor insulators

Theoretical Correlations amongst Electrical and Mechanical Characteristics of Polymeric Housing

Materials for Outdoor Insulators R. Raja Prabu

B.S.A Crescent Engineering College Vandalur, Chennai – 600 048

Tamil Nadu, India

S. Usa, K. Udayakumar High voltage division, College of Engineering, Anna University

Guindy, Chennai – 600 025 Tamil Nadu, India

M. Abdullah Khan and S.S.M. Abdul Majeed

B.S.A Crescent Engineering College Vandalur, Chennai – 600 048

Tamil Nadu, India

ABSTRACT

In this paper, theoretical correlation amongst various electrical characteristics of a housing / weather shed material is attempted. Also, a correlation relating tensile strength (a mechanical property) to insulation characteristics is proposed. The housing material used, is made of polymeric blends (Silicone/EPDM) with and without fillers (silica and alumina trihydrate).The proposed correlation is obtained through Dimensional Analysis technique. An attempt is also made to provide qualitative interpretations for these relationships, based on the fundamental physical quantities. Multivariate regression analysis of experimental values of the dependent and independent variables, that figure in these correlations is carried out. It yielded almost the same values for the exponents as those in the correlations developed using dimensional analysis. This confirmed similar quantitative and qualitative influences of various insulation parameters on tracking resistance and tensile strength, as predicted by the dimensional analysis approach.

Index Terms - Insulators, polymeric housing, weather shed material, silicone rubber, EPDM, insulation characteristics, dimensional analysis, matrix analysis, multivariate regression, tracking resistance, tensile strength, fillers, ATH, silica.

1 INTRODUCTION

POLYMERIC housing materials are being accepted increasingly for use in outdoor insulators. It is difficult to evaluate life expectancy of polymeric insulators. The tremendous growth is due to their advantages over the traditional ceramic and glass insulators [1].

Faulty insulators are difficult to detect and the long reliability is unknown. Usually, more than ten different insulation characteristics are studied by conducting suitable experiments and many of them are tedious and time consuming. It has been noticed that the failure of outdoor insulation structures is mainly due to tracking [2]. The

Manuscript received on 28 August 2007, in final form 12 December 2007.

1070-9878/08/$25.00 © 2008 IEEE

IEEE Transactions on Dielectrics and Electrical Insulation Vol. 15, No. 3; June 2008 771

leakage current that leads to tracking depends on various factors such as volume resistivity, surface resistivity, dielectric strength, arc resistance, and thermal conductivity of the composite [3].

In polymeric insulators, polymers are dependent for enhanced electrical characteristics and fillers are used to improve their mechanical properties.

Extensive experimentation on the housing material, with a combination of silicone and EPDM (ratio on weight basis) polymeric blend is conducted. The blends are tested for their insulation characteristics as per IEC and ASTM standards. Volume and surface resistivity, dielectric strength, dielectric constant, tan δ, tracking resistance, arc resistance, comparative tracking index, tensile strength, and percentage elongation at break of the blends are studied and used [4].

The presence of fillers in the insulator offers defence in helping to prevent tracking of the material. There are few studies to establish the efficiency of surface treated filler (e.g. silane treated silica flour). Improved thermal conductivity of the composite material due to the added fillers is an important factor in deciding tracking silicone insulators [5, 6]. There is a clear correlation established between erosion and thermal conductivity of the composite insulators with added filler [7].Hence, with 50% silicone and 50% EPDM blend, experiments are carried out with various levels of fillers such as alumina trihydrate and silica and the results are used, for this work..

Having determined all the insulation characteristics with various blends of EPDM / Silicone blend with and without fillers, an attempt is made to derive correlation among the various insulation characteristics.

Literature suggests [8] that tracking resistance is an important index of the performance of outdoor insulators. In this work, an empirical correlation is derived between the tracking resistance and other insulation characteristics.

It is found that the Dimensional Analysis (DA) is a powerful tool for simplifying the equations by reducing the number of parameters into a set of essential parameters [9-11]. In this paper, a mathematical analysis is presented based on DA that relates most of the insulation characteristics. The empirical correlations derived based on dimensional analysis not only relate electrical characteristics of the housing material amongst themselves but also relate electrical characteristics of housing / weather shed materials to mechanical property (tensile strength). This assumes importance when inorganic fillers like silica, alumina trihydrate are added to improve its tracking resistance.

The strength of the empirical correlations amongst insulator properties developed in this work is tested by the multivariate regression analysis of the experimental results. This is carried out to find the exponent values of each and every independent parameter in the equation and compare the same with the exponents obtained using dimensional analysis technique. In the multivariate regression, the sum-squared error is the least for the dependencies expressed by the dimensional analysis technique

Comparison is also made between the predictive abilities of the correlations developed using dimensional analysis technique and multivariate regression. These correlations help to identify the dominant characteristics that influence the efficiency of a polymeric housing material in an outdoor insulator. Qualitative interpretations based on fundamental relationships of physical variables are also attempted and it lends credence to the correlations proposed in this work.

2 EXPERIMENTAL SET-UP AND PROCEDURES

Test Samples: Blends containing various percentages of

silicone and EPDM with and without fillers (alumina trihydrate and silica) are blended in a two-roll mill at room temperature. Dicumyl peroxide is used as a vulcanizing agent. Blends prepared are compression moulded into sheets. Test specimens are prepared from compression moulded sheets according to the standards. When the study is carried out with fillers, various levels of alumina trihydrate or silica are added at parts per hundred parts of rubber (PHR) to the best combination (50:50) of silicone and EPDM blend.

The blend preparation procedure is detailed in Appendix-A.

In Appendix-B, the test conditions and procedure for the insulation characteristics are provided.

3 RESULTS The experimental data of various insulator properties for

the silicone/EPDM blend housing material are given in Table 1 and the experimental data for 1:1 silicone: EPDM blend with various levels of silica and alumina trihydrate (in PHR) are given in Tables 2 and 3.

All the tests are carried out as per the IEC/ASTM standards. In general, 5 samples are tested per blend composition per test per property. Occasionally, 7 samples are also tested, to rule out the experimental errors.

Various levels of silica filler are added to the silicone and EPDM composite (in 1:1 weight ratio). The levels of filler added are in parts per hundred parts of rubber (PHR).This is shown along with the measured parameters and results in Table 2.

Various levels of alumina trihydrate (ATH) filler are added to the silicone and EPDM composite (in 1:1 weight ratio). The levels of filler added are in parts per hundred parts of rubber (PHR).This is shown along with the experimentally determined parameters and their results in Table 3.

772 R. R. Prabu et al.: Theoretical Correlations amongst Electrical and Mechanical Characteristics of Polymeric Housing Materials

Table 1. Experimental Data For Silicone:EPDM Blends.

Silicone: EPDM

(weight ratio)

Tracking Res. (TR) (minute)

Vol. Res. (VR) Ohm-

m

Surf. Res. (SR) Ohm

Arc Res. (AR)

(second)

Dielec. Str. (DES) kV/mm

CTI (Volt)

Tens. Str. (TS) N/mm2

0:100 086 8.00 e12 5.65 e13 182 20.00 415 4.257 10:90 095 2.00 e13 1.30 e14 246 24.27 435 2.971 30:70 108 3.00 e13 1.80 e14 308 25.92 452 2.733 50:50 116 4.70 e13 2.60 e14 363 27.56 475 2.332 70:30 123 8.00 e13 5.00 e14 382 31.95 495 1.936 90:10 129 1.30 e14 7.80 e14 427 33.26 505 1.490 100:0 138 6.29 e14 3.10 e15 600 36.08 520 0.500

Table 2. Experimental Data For 50:50 Silicone:EPDM Blend With Silica Filler. Silica filler in

PHR


Vol. Res. (VR) Ohm-

m

Surf. Res. (SR) Ohm

Arc Res. (AR)

(second)


CTI (Volt)

Tens.Str. (TS) N/mm2

0 116 4.70e13 2.60e14 363 27.56 475 2.332 10 127 4.10e13 2.65e14 370 30.60 495 3.700 20 135 3.58e13 2.68e14 376 33.50 501 4.970 30 146 3.18e13 2.73e14 379 35.70 505 6.420

30 (wst) 218 3.20e13 3.40e14 395 35.90 530 6.320 40 163 3.10e13 2.78e14 382 33.30 509 6.100

40 (wst) 235 3.28e13 3.46e14 400 34.10 536 6.050 50 175 3.05e13 2.82e14 386 32.50 512 6.037 60 193 2.99e13 2.86e14 390 32.00 515 5.985 70 205 2.95e13 2.90e14 394 31.50 517 5.865 80 213 2.90e13 2.93e14 397 31.40 518 5.814 90 222 2.87e13 2.95e14 401 31.00 521 5.758 100 228 2.85e13 2.97e14 408 30.50 518 5.650

wst – with silane treatment

Table 3. Experimental Data For 50:50 Silicone:EPDM Blend With ATH Filler.

ATH filler in PHR


Vol. Res. (VR) Ohm-

m

Surf. Res. (SR) Ohm

Arc Res. (AR)

(second)


CTI (Volt)

Tens.Str. (TS) N/mm2

0 116 4.70e13 2.60e14 363 27.56 475 2.332 10 149 3.85e13 2.68e14 384 30.92 482 3.500 20 155 3.45e13 2.71e14 391 34.80 495 5.050 30 164 3.18e13 2.74e14 395 36.90 515 6.350

30 (wst) 220 3.36e13 2.78e14 400 37.20 540 6.200 40 181 3.10e13 2.78e14 400 35.10 527 5.825

40 (wst) 238 3.31e13 3.60e14 412 35.50 546 5.780 50 193 3.05e13 2.82e14 404 33.20 532 5.406 60 211 2.99e13 2.86e14 408 32.50 544 5.387 70 223 2.96e13 2.89e14 412 32.10 556 5.258 80 232 2.90e13 2.94e14 417 31.60 No Failure 5.165 90 240 2.87e13 2.98e14 420 31.30 No Failure 5.080

100 246 2.85e13 3.02e14 424 30.80 No Failure 4.980 wst – with silane treatment


It is interesting to note from Tables 2 and 3, that as the level of silica or alumina trihydrate(ATH) filler added to silicone/EPDM blend increases, the volume resistivity continues to decrease whereas the surface resistivity continues to increase albeit marginally. The dielectric strength and tensile strength increase up to the filler loading of 30 PHR to silicone/EPDM blend and thereafter both the dielectric strength and tensile strength start decreasing. However, the tracking resistance, arc resistance, and comparative tracking index continue to increase with the increase in the level of fillers (silica and ATH). With more than 80 PHR of ATH added to the silicone/EPDM blend insulator, there was no failure observed, while assessing the comparative tracking index.

4 DIMENSIONAL ANALYSIS TECHNIQUE TO PREDICT TRACKING RESISTANCE

Dimensional analysis technique is a very widely used

technique in engineering to explain and/or predict the experimental data. It is rigorous than regression-based correlation or data fitting as it takes into account the relationships amongst the parameters chosen to explain or predict the data.

The electrical parameters that are measured are tracking resistance, arc resistance, dielectric strength, dielectric constant, dissipation factor, volume resistivity, surface resistivity, and comparative tracking index. The mechanical parameters that are of interest are the tensile strength and % elongation at break.

Amongst these parameters, dielectric constant, dissipation factor, and % elongation at break are dimensionless and they are reported as numerical values. Thus, there are seven dimensional parameters that are assessed for housing material of any insulator.

Tracking resistance takes a longer duration to determine. Also, there are no relationships established amongst these various electrical parameters. More importantly, the mechanical properties and electrical properties go in opposite direction when housing materials made with blends such as silicone and EPDM are tested. Hence, a relationship that links up the mechanical property with electrical properties of an insulator is always useful to have a combined assessment of the housing material of an insulator instead of looking at either electrical or mechanical properties.

The objective is to arrive at such useful relationships that connect electrical and mechanical properties and also help in predicting a parameter that is difficult to measure i.e. tracking resistance of an insulator. The aim is not only to develop relationships but also to develop them based on fundamental logic. Thus, it is attempted here to predict tracking resistance based on few other electrical properties

and also to establish a relationship between tensile strength and some of the electrical properties based on dimensional analysis technique.

In the electrical properties listed, tracking resistance (TR), arc resistance (AR), dielectric strength (DES), volume resistivity (VR), surface resistivity (SR), and comparative tracking index (CTI) are dimensional parameters. Amongst the mechanical properties mentioned, only tensile strength (TS) is the dimensional parameter. Thus, these seven insulator parameters alone are considered to develop a relationship between them. These parameters can be expressed with the combination of four fundamental dimensions MLTQ where M, L, T, and Q are the mass, length, time and charge respectively.

There are two alternatives, either to develop expressions for three different characteristics based on a common set of four repeated variables or to develop two equations one for tracking resistance and another one for tensile strength relating all the seven dimensional properties. However, in this case, it is necessary to suitably club the properties to reduce them to four repeated variables for the sake of dimensional analysis. Here, the latter approach is adopted, as one does not know a priori as to which characteristics can be ignored. Hence, as described in the “Dimensional Analysis” (DA) approach, volume resistivity (VR) and arc resistance (AR) are clubbed to reduce them into one variable

The dimensions of the above parameters are: TR -> T AR -> T DES -> M L T-2 Q-1

VR - M L3 T-1 Q-2 SR -> M L2 T-1 Q-2

CTI -> M L2 T-2 Q-1

TS -> M L-1 T-2

The dimensional matrix of the six parameters and the four fundamental dimensions can be written as follows: TR TS VR/AR DES SR CTI M 0 1 1 1 1 1 L 0 -1 3 1 2 2 T 1 -2 -2 -2 -1 -2 Q 0 0 -2 -1 -2 -1

The rank (r) of the above dimensional matrix is 4 and the number of parameter (n) is 6. The solution can be expressed as two (n -r = 2) independent dimensionless products (Π1 and Π2) with the dimension M0 L0 T0 Q0. The

variables considered common and repeated, to arrive at the two expressions are (AR/VR), DES, SR, and CTI.

The two expressions for TR (Tracking Resistance) and TS (Tensile Strength) are given, as under. Π1 = [CTI]a

1 [DES]b1 [SR]c

1 [VR/AR]d1 TR (1)


Π2 = [CTI]a2 [DES]b

2 [SR]c2 [VR/AR]d

2 TS (2)

Here an, bn, cn, and dn are the power indexes of the

repeated variables. The dimensionless expression for Π1 and

Π2 are: Π1 D1 [M L2 T-2 Q-1]a

1 [M L T-2 Q-1]b1 [M L2 T-1 Q-2]c

1 [ M L3 T-2 Q-2]d

1 [T] = [M0 L0 T0 Q0] (3)

Π2 D2 [M L2 T-2 Q-1]a

2 [M L T-2 Q-1]b2 [M L2 T-1 Q-2]c

2 [ M L3 T-2 Q-2]d

2 [M L-1 T-2] = [M0 L0 T0 Q0] (4)

Equating the powers of fundamental units M, L, T, and Q

on both sides of the above two expressions would lead to homogeneous linear algebraic equations. The solutions of those linear algebraic equations would give the values of the power indexes using which one can construct the mathematical relationship for Tracking Resistance (TR) and Tensile Strength (TS) using the repeated variables.

Using equation (1), an expression for Tracking Resistance (TR) can be written as Π1 D1 [M] a1

+b1+c

1+d

1 [ L] 2a1

+b1

+2c1

+3d1 [T] –2a

1-2b

1-c

1-2d

1+1 [Q] –

a1-b

1-2c

1-2d

1 = [M]0 [L]0 [T]0 [Q]0 (5)

a1 + b1 + c1 + d1 = 0 2a1 + b1 + 2c1 + 3d1 = 0 2a1 + 2b1 + c1 + 2d1 = 1 a1 + b1 + 2c1 + 2d1 = 0

The above homogenous linear equations can be solved using the matrix solution of linear systems.

Using the a1, b1, c1, and d1 values i.e. power index values in equation (1), the mathematical relationship with the dimensionless constant (D1) for predicting the Tracking Resistance (TR) of an insulator is arrived. Thus,

TR = D1 [CTI]+1 [DES]-1 [SR]+1 [VR/AR]-1

This can be rewritten as, TR = D1 [CTI]+1 [DES]-1 [SR]+1 [AR/VR]+1

Rearranging the RHS of the above equation, we get TR = D1 . {[CTI] /[DES]} . [SR][AR]/ [VR]} (6)

5 DIMENSIONAL ANALYSIS TECHNIQUE

TO PREDICT TENSILE STRENGTH Using equation (2), an expression for Tensile Strength

(TS) can be written as Π2 D2 [M] a

2+b

2+c

2+d

2+1 [ L] 2a

2+b

2+2c

2+3d

2-1 [T] –2a

2-2b

2-c

2-2d

2-2

[Q] –a2-b

2-2c

2-2d

2 = [M]0 [L]0 [T]0 [Q]0 (7)

a2 + b2 + c2 + d2 = -1 2a2 + b2 + 2c2 + 3d2 = 1 2a2 + 2b2 + c2 + 2d2 = -2 a2 + b2 + 2c2 + 2d2 = 0

As described before, the above homogenous linear equations can be solved using the matrix solution of linear systems and thus a2 = 0, b2 = 2, c2 = 0, and d2 = -1. Using the a2, b2, c2, and d2 values i.e. power index values in equation (2), the mathematical relationship with the dimensionless constant for predicting the Tensile Strength (TS) of an insulator is obtained.

Thus, TS = D2 [CTI]0 [DES]+2 [SR]0 [VR/AR]-1

This can be rewritten as, TS = D2 [DES]+2 [AR/VR]+1 (8)

The units of the above equation are N/m2 = (Volt/m)2 (sec/Ohm.m) i.e., N/m2 = (Volt2/m3) (sec/Ohm)

The dimensionless constants D1 and D2 are determined from the experiment. The predictions of tracking resistance and tensile strength are made using the above mathematical equations (6) and (8). The predictions are very satisfactory and match with the experimental data.

6 MULTIVARIATE REGRESSION ANALYSIS

In order to make sure whether the relationship arrived at using the DA approach is the best possible equation for predicting TR, the multivariate regression is done on the entire set of experimental data obtained with and without fillers and with and without tri ethoxy vinyl silane treatment involving the above mentioned variables. Here, the TR is the dependent variable (Y). CTI, DES, SR, AR and VR are the independent variables (X1, X2, X3, X4, X5) respectively.

While carrying out the dimensional analysis, the exponents of the independent variables in that equation are arrived at purely by adjusting the dimensions on either side of the equation. The multivariate regression gives the exponent values for the independent variables and also the value of the constants. Multivariate regression is trying to correlate or fit the entire set of independent variable data obtained with and without fillers and with tri ethoxy vinyl silane treatment (X1, X2, X3, X4 and X5) to the dependent variable (Y) and this gives rise to the exponent values. Multivariate regression often leaves a residual dimension to the constant. Thus, the constant arrived at using multivariate regression is 'dimensional' in nature whereas


the empirical constant in the DA technique is 'dimensionless'. The errors in predictions are basically minimized in multivariate regression as it adjusts the dimensional constant.

Similarly, the multivariate regression is done on the entire set of experimental data obtained for TS. Here, the TS is the dependent variable (Y) and DES, VR and AR are the independent variables (X1, X2, X3) respectively.

Table 4 shows a comparison of the predictive capabilities of expressions arrived at using dimensional analysis and multivariate regression for tracking resistance (TR) for the silicone-EPDM blend with and without fillers and with tri ethoxy vinyl silane treatment.

Residual Dimensions of the Multivariate Regression constant ‘D1’ used in the correlation to predict tracking resistance of silicone-EPDM blend, with and without fillers and with tri ethoxy vinyl silane treatment is obtained by equating the powers of M, L, T and Q on both sides of the expression arrived by using multivariate regression. Table 4. Comparison of Predictive Capabilities of Dimensional Analysis and Multivariate Regression to Predict Tracking Resistance for an Insulator Housing Material made of Silicone/EPDM Blends with and without Fillers.

Dimensional Analysis

Multivariate Regression

Exponent for CTI (X1)

+1 +0.884

Exponent for DES(X2)

-1 -0.674

Exponent for SR (X3)

+1 +0.978

Exponent for AR (X4)

+1 +0.843

Exponent for VR (X5)

-1 -0.974

Value of Constant (D1)

2,00,000 3344.2

Dimensions of Const. D1

NIL M-0.214 L-0.128 T0.581 Q0.218

Range of Errors -3.033% to 0.793%

-10.17% to 5.2%

The equation based on multivariate regression to predict tracking resistance is: TR = D1 (CTI)0.884 (DES)–0.674 (SR)0.978

(AR)0.843 (VR)-0.974

In terms of the dimensions, the above equation is represented as [T] = D1 [M L2 T-2 Q-1]0.884 [M L T-2 Q-1]–0.674

[M L2 T-1 Q-2]0.978 [T]0.843 [M L3 T-1 Q-2]-0.974

By equating the powers of M, L, T and Q on both sides, the residual dimensions of the constant D1 is obtained as [M]-0.214 [L]-0.128 [T]0.581 [Q]0.218.

Similar procedure is followed for tensile strength. Table 6.2 shows a comparison of the predictive capabilities of the dimensional analysis and multivariate regression for tensile strength (TS) of the silicone-EPDM blend with and without fillers and with tri ethoxy vinyl silane treatment. As described above, by equating the powers of M, L, T and Q on both sides of the multivariate regression equation, the residual dimensions of constant D2 in Table5 is obtained.

Table 5. Comparison of Predictive Capabilities of Dimensional Analysis and Multivariate Regression to Predict Tensile Strength for an Insulator

Housing Material made of Silicone/EPDM Blends with and without Fillers. Dimensional

Analysis Multivariate Regression

Exponent for DES (X1)

+2 +2.017

Exponent for AR (X2)

+1 +0.747

Exponent for VR (X3)

-1 -0.966

Value of Constant (D2)

412 460.37

Dimensions of Const. D2

NIL M-0.051 L-0.119 T0.321 Q0.085

Range of Errors -11.91% to 3.92%

-12.88% to 8.53%

7 PREDICTIONS OF TR AND TS

The comparison between experimental values of

tracking resistance and tensile strength against the values predicted by the empirical relationships equations (6) and (8) for the silicone-EPDM blend housing material are shown in Tables 6 and 7.

As can be seen from Table 6, the empirical correlations based on dimensional analysis and multivariate regression predict the decrease in tensile strength with increasing levels of silicone in the blend.

It is to be mentioned that the tracking resistance (TR) and tensile strength (TS) are given in their typical units i.e. minute and N/mm2 respectively, although the values of the independent variables appearing in the equations are taken in SI units. The experimental values of dielectric strength are given in kV/mm. These are converted to V/m when predicting tracking resistance and tensile strength using equations (6) and (8).

Tables 8 and 9 show the comparisons between experimental values of tracking resistance and tensile strength against the values predicted by the empirical relationships (arrived at using dimensional analysis and multivariate regression) for the housing material made of 50:50 Silicone-EPDM blend in an outdoor insulator with various levels (in phr) of silica added to the blend as filler (Table 8 and Table9).


Table 6. Measured and Predicted Values of Tracking Resistance for 50:50 Silicone:EPDM Blends.

Silicone:EPDM (Weight Ratio)

measured Tracking Resis. (TR in Minute)

Predicted TR based on DA (minute)

Predicted TR based on Multivariate Regression (minute)

0:100 86 88.91 84.48 10:90 95 95.53 92.22 30:70 108 107.42 102.16 50:50 116 115.37 108.85 70:30 123 123.3 120.45 90:10 129 129.67 126.19 100:0 138 142.06 135.56

Table 7. Measured and Predicted Values of Tensile Strength for 50:50 Silicone: EPDM Blends.

Silicone: EPDM (weight ratio)

Measured TS

(N/mm2)

Predicted TS based on

DA (N/mm2)

Predicted TS based on Multivariate Regression (N/mm2)

0:100 4.257 3.75 4.10 10:90 2.971 2.98 3.13 30:70 2.733 2.84 2.86 50:50 2.332 2.42 2.37 70:30 1.936 2.01 1.99 90:10 1.49 1.50 1.46 100:0 0.5 0.512 0.485

Table 8. Measured and Predicted Values of Tracking Resistance for 50:50

Silicone:EPDM Blend with Various Levels (in PHR) of Silica Filler.

Silica filler in

PHR

Measured Tracking Res. (TR) (minute)

Predicted TR based

on DA (minute)

Predicted TR based on


(minute) 0 116 115 108.85

10 127 129 124.42 20 135 140 138.37 30 146 153 153.58

30 (wst) 218 206.53 203.69 40 163 175 170.26

40(wst) 235 221.08 213.77 50 175 187 180.82 60 193 200 191.51 70 205 212 201.2 80 213 221 208.78 90 222 231 217.07 100 228 241 224.55

Table 9. Measured and Predicted Values of Tensile Strength for 50:50 Silicone/EPDM Blend with Various Levels (in PHR) of Silica Filler. Silica

filler in PHR

Measured. Tensile Strength

(TS) (N/mm2)

Predicted TS based on DA

(N/mm2)


Multivariate Regression (N/mm2)

0 2.332 2.42 2.37 10 3.7 3.48 3.39 20 4.97 4.86 4.7 30 6.42 6.26 6.02

30 (wst) 6.32 6.55 6.24 40 6.1 5.63 5.4

40 (wst) 6.05 5.84 5.55 50 6.037 5.51 5.26 60 5.985 5.50 5.24 70 5.865 5.46 5.18 80 5.814 5.56 5.26 90 5.758 5.53 5.22 100 5.65 5.49 5.15

It is interesting to note that the equations predict the

decline in tensile strength as silicone composition is increased in the blend of the insulator while predicting the increase in electrical properties such as tracking resistance and dielectric strength. This adds credence to the approach used in this work and also the prediction capability of the proposed equations.

Similarly, Tables 10 and 11 show the comparisons between experimental values of tracking resistance and tensile strength against the values predicted by the empirical relations (arrived at using dimensional analysis and multivariate regression) for the housing material made of 50:50 Silicone:EPDM blend with various levels (in PHR) of ATH added to the blend, as filler.

Table10. Measured and Predicted Values of Tracking Resistance for 50:50 Silicone:EPDM Blend with Various Levels (in PHR) of Alumina

Trihydrate (ATH) Filler. ATH

filler in PHR

Measured Tracking resistance (TR)

(minute)

Predicted TR based

on DA (minute)

Predicted TR based on


(minute) 0 116 115 108.85

10 149 139 133.84 20 155 146 144.53 30 164 158 158.81

30(wst) 220 201.61 200.45 40 181 180 176.16

40(wst) 238 229.73 223.4 50 193 200 191.61 60 211 218 206.64 70 223 232 218.51 80 232 - - 90 240 - -

100 246 - -


Table 11. Measured and Predicted Values of Tensile Strength for 50:50 Silicone/EPDM Blend with Various Levels (in PHR) of Alumina

Trihydrate (ATH) Filler. ATH

filler in PHR

Measured Tensile Strength

(TS) (N/mm2)

Predicted TS based on DA

(N/mm2)


Multivariate Regression (N/mm2)

0 2.332 2.42 2.37 10 3.5 3.93 3.78 20 5.05 5.65 5.41 30 6.35 6.97 6.64

30(wst) 6.2 6.79 6.46 40 5.825 6.55 6.21

40(wst) 5.78 6.46 6.1 50 5.406 6.02 5.68 60 5.387 5.94 5.59 70 5.258 5.91 5.54 80 5.165 5.92 5.53 90 5.08 5.91 5.51

100 4.98 5.81 5.40

It is clear from Tables 8 and 10 that the increased arc resistance and surface resistivity enhance the tracking resistance of the silicone:EPDM blend with fillers (silica or ATH) added to it.

Tables 9 and 11 show that the empirical correlations based on dimensional analysis and multivariate regression predict the maxima in tensile strength with 30 parts of filler (silica or alumina trihydrate) per hundred parts of rubber in silicone / EPDM blend housing material in an insulator. This clearly establishes the fact that tensile strength, which is a bulk property, is highly dependent on or influences the other bulk properties such as dielectric strength and volume resistivity.

This establishes the qualitative influences of independent variables on dependent variables.

1. It is quite interesting to note that both dimensional

analysis and multivariate regression technique matched with respect to the sign of the exponent values and numerical values for the independent variables (X1 to X5 in Table 4 and X1 to X3 in Table 5)..

2. There are two orders of magnitude difference between the two values of the constant D1 which is used to predict tracking resistance using DA technique and multivariate regression (Table 4) and the values of the constant D2 which is used to predict tensile strength by both the approaches are more or less the same (Table 5).

3. The same values of D1 and D2 are used to predict tracking resistance and tensile strength of the silicone-EPDM blend housing material with and without fillers and with silane treatment, using the equations derived

based on dimensional analysis. This adds to the strength of the equation derived based on dimensional analysis.

4. The ranges of errors in both the approaches are small (given the fact that the data are collected from different set of experiments) and regression equation is obtained using the entire set of experimental data.

5. The constants D1 and D2 arrived at using multivariate regression are dimensional and carry the residual dimensions of the independent variables in order to match with the dimensions of the dependent variable.

Going by the above comparisons, the equations arrived at using the dimensional analysis technique for predicting tracking resistance and tensile strength are quite robust as the constants D1 and D2 are dimensionless. It gains credence as the multivariate regression also gave rise to the equations that are very similar to the ones developed.

8 QUALITATIVE INTERPRETATIONS

The equation (6) can be qualitatively interpreted based on

their units and dimensions as follows: CTI / DES = V/ (V/m) = m i.e. length that withstands tracking; (SR * AR) / VR = (Ohm. Sec) / (Ohm. m) = sec/m i.e. 1/ velocity of tracking

Thus, equation (6) is interpreted as TR (in seconds) = D1 * (Length that withstands tracking) / (Velocity of tracking)

Of course, this is only a qualitative interpretation of the mathematical relationship.

Considering the definition of CTI and DES, it is possible

to understand the qualitative feature of dividing CTI by DES. According to IEC 60112, CTI (comparative tracking index) is the maximum endurable voltage for a certain insulator without causing tracking up to 50 drops of the electrolyte in each of the 5 repeated tests. Dielectric strength (DES) is the voltage at which dielectric failure of the insulating material occurs under specific condition of test. According to IEC 60243-1 (ASTMD149) standard, dielectric breakdown strength (kV/mm) is calculated by the ratio of dielectric breakdown voltage (kV) to the thickness of the specimen (mm). In a way, the physical meaning of dividing CTI divided by DES is nothing but [maximum endurable voltage (against tracking)] / [(dielectric breakdown voltage /thickness of the insulator specimen)]. This is nothing but the thickness of the specimen.

Volume resistance is the resistance to leakage through the body of the material. It takes into account the length/thickness of the material that possess resistance to leakage and that is how the unit for volume resistivity is reported (Ohm. m). Hence, VR/SR must represent length or thickness of insulator that possesses the resistance to


leakage. As per ASTM D495, arc resistance is the time taken for failure when an arc is struck between two electrodes and in practice it is an arc struck on the surface of the insulator.

Thus, the physical interpretation for equation (6) should be:

Tracking Resistance (in seconds) = D1 * (Thickness of insulator that withstands tracking and dielectric failure) / [(Thickness of insulator that possess the resistance to leakage) / (time taken for failure due to an arc)]

Similarly, the equation (8) can be qualitatively interpreted based on the fundamental principle of conservation of energy. The dielectric failure or tracking occurs when the mechanical strength of the insulator housing material is not able to resist the insulation failure. The equation (8) is attempting to relate the electrical properties such as dielectric strength, volume resistivity, and arcing resistance - of an insulator housing material to its mechanical property, which is tensile strength. It gains credence and gets justified when the mechanical energy to the electrical energy of an insulator is compared.

Tensile strength means the stress at the maximum load. It is shown as the load divided by the minimum cross sectional area of the specimen before the initiation of the test (as due to the application of load there would be elongation). Hence, tensile strength is nothing but the stress or pressure that a material can withstand.

According to the law of conservation of energy, (Mechanical Energy)= (Electrical Energy) (A) The time differential of mechanical and electrical energy is Mechanical Power = Electrical power (B) Mechanical Power = (Volumetric flow rate) (pressure difference) (C)

The analogy of ‘pressure difference’ in electrical terms is the product of charge density and electrical potential difference. Pressure difference = (charge density) (electrical potential difference) (D)

Electrical potential difference is denoted as voltage (V) and is given in Volts. Substituting (D) in (C), we get, Mechanical Power = (Volumetric flow rate) (pressure difference) = (Volumetric flow rate) (charge density) (electrical potential difference) (E)

However, (Volumetric flow rate) (charge density) = Current (I) (F)

Thus (E) becomes, Mechanical Power = (Volumetric flow rate) (Pressure

difference) = I x V = Electrical Power In the units and dimensions analysis, the term (Cosineθ) in

the expression for electrical power is ignored. Since tensile strength is nothing but the pressure term, if

we multiply this with volumetric flow rate (Q), we must get the value of mechanical power. This product must be equal to V x I, which is electrical power based on the above analogy. Therefore, TS * Q = V * I ‘I’ can be expressed as (V / R) or alternately ‘I’ is expressed as (V σ ) where ‘σ’ is the electrical conductance (which is 1/R). (TS) (Q) = (V) (V σ) =V2 σ

This same expression for electrical power can be obtained

by an alternate way also. ‘Dissipative power’ or ‘Joule heating’ in an insulator is

given by

P = I2 R = (V/R)2 * R = V2 (1/R) = V2 σ i.e. Power = electrical conductance * V2

Thus, TS* Q = V2 * σ; Divide both sides by volumetric flow rate to get, TS = (V2 * σ) / Q; The units on both sides of above equation are, N/m2 = (Volt)2 * (1/Ohm) * (sec/m3) This can be rearranged as, N/m2 = (Volt/m)2 * (1/Ohm.m) * (sec)

In terms of the electrical properties of an insulator that are considered in this work, it is expressed as, TS = (DES)2*(1/VR)*(AR) = (DES)2 * (AR/VR)

9 SUMMARY 1. Dimensional analysis technique is used to

develop a mathematical relationship between tracking resistance and other electrical characteristics and also between tensile strength


and electrical characteristics of a polymeric housing material used in outdoor insulators.

2. These correlations are valid for the set of electrical and mechanical properties that are taken into account. The constants D1 and D2 are obtained from experimental data.

3. It is found that the equation predicts the decline in tensile strength as silicone composition is increased in the blend while predicting the increase in electrical properties such as tracking resistance and dielectric strength. This adds credit to the approach used in this work and also the prediction capability of the proposed equations.

4. The multivariate regression analysis of the physical variables in the proposed empirical correlations, found to get errors in acceptable limits.

5. The comparison between the predictive abilities of the correlations based on dimensional analysis and the multivariate regression analysis proves that the correlations proposed based on dimensional analysis approach are quite better, as the constant in those correlations are dimensionless whereas, the constants in the correlations from multivariate regression analysis have residual dimensions.

6. These correlations would help in predicting an electrical property (tracking resistance), that is tedious and time consuming, to experimentally determine, based on a few insulation characteristics that are easy to measure and quantify.

7. Also, the relationship derived between tensile strength and electrical characteristics would help in choosing the right type and amount of filler that offers optimal tracking resistance while improving the mechanical strength of the housing material used in an outdoor insulator.

APPENDIX A A.1 PREPARATION OF BLENDS

Passing through the rollers for three minutes softens EPDM rubber initially and then silicone rubber is mixed. The mixing of EPDM and silicone rubber is carried out for twelve minutes. Di cumyl peroxide is mixed at the final stage of mixing. The blends of silicone and EPDM containing various proportions of component polymers are prepared in a laboratory model two roll mixing mill at a temperature of 353 K. Dicumyl Peroxide is mixed during the mill mixing as a curing agent to all the blends at 2.5 parts per hundred parts of rubber (phr).

A.2 VULCANIZATION The vulcanization of the blends is carried out in a

hydraulically operated press at 443 K for 10 minutes. The vulcanized samples are post cured at 423 K for 2 hours in an air circulated oven. Test specimens are punched out from the compression moulded sheets.

A.3 BLEND COMPOSITION Various compositions of silicone rubber and EPDM

blends prepared are given as follows First EPDM rubber is blended with silicone rubber in a

complementary mixture of 0, 10, 30, 50, 70, 90, and 100 percent by weight. 2.5 phr of di-cumyl peroxide is added as the curing agent. With the above set of mixtures, it becomes possible to analyze the performance characteristics of silicone rubber alone, EPDM rubber alone and a mixture of silicone and EPDM in various ratios.

APPENDIX B B.1 CHARACTERIZATION

In this section, the test conditions and procedure for the important electrical and mechanical insulation characteristics of a polymeric insulator are described.

B.2 TRACKING RESISTANCE A partially conducting part of localized deterioration on

the surface of the insulating material is called a 'track’. The process that produces track as a result of action of electrical discharges on or close to insulation surface is called 'tracking'. 'Tracking resistance' is the quantitative expression of the voltage and time required to develop tracking under specified conditions. Tracking resistance was assessed as per IEC-60587 standards. Tracking resistance is determined as per IEC-60587. The distance between the top and bottom electrode is adjusted to be equal to 50 mm and 4.5 kV is applied. Ammonium chloride solution of 0.1 % concentration is used as contaminant at a flow rate of 0.6 ml / min, which is controlled by using a peristaltic pump. The conductivity of the contaminant is 2500 μS/cm. The conductivity is measured using Lutron CD 4302. Time to failure due to tracking is noted.

B.3 VOLUME RESISTIVITY AND SURFACE RESISTIVITY

The volume and surface resistivity of the samples are measured as per ASTM D257 (IEC 60093) Standards. The voltage applied is 500 V (DC) for 60 seconds at room temperature. The diameter and thickness of the specimen are 100 mm and 3 mm respectively. Million meg-Ohm meter is used to measure volume and surface resistivity


B.4 ARC RESISTANCE Arc resistance of the sample is determined as per ASTM

D 495 standard at 250 V and 50 Hz. The applied voltage is 12.5 kV and the distance between the electrodes is 6 mm. The thickness of the specimen used is 3 mm. Two electrodes are kept above the specimen, which is placed on the specimen holder. The voltage is applied intermittently and severity is increased in steps, until the failure occurs. An arc is struck in between the electrodes. After some time, the carbon path developed on the surface of the material led to conduction. The arc resistance is measured in terms of time in seconds for failure to take place.

B.5 COMPARATIVE TRACKING INDEX (CTI)

The comparative tracking index is determined as per IEC 60112. The voltage applied is 500 V. The electrolyte used is 0.1 % of aqueous ammonium chloride. The distance between the electrodes is 4 mm. The thickness of the electrode is 3 mm. Two chisel edged electrode, usually of brass are rested on horizontal test piece 4 mm apart. Drops of specified size of 0.1 % NH4Cl solution are made to fall between the electrodes at 30 seconds interval. The number of drops required to cause failure is found for several voltages and a curve of number of drops to failure against voltage is constructed. The voltage corresponding to 50 drops is noted. The numerical value of this voltage is called C.T.I.

B.6 DIELECTRIC STRENGTH

Dielectric strength of the blended sample is determined as per IEC-60243-1 (ASTM D 149) standard at 250 V and 50 Hz. The diameter and thickness of the samples are 100 mm and 1 mm respectively. Test specimen is placed between two electrodes and the voltage is increased at a fixed rate of 2 kV/s, until the dielectric breakdown occurs. The voltage at which dielectric breakdown occurs is read as dielectric breakdown voltage. Dielectric breakdown strength (kV/mm) is calculated from the ratio of dielectric breakdown voltage (kV) to the thickness of the specimen (mm). The Top electrode size is 25 mm and the Bottom electrode is 75 mm.

B.7 DIELECTRIC CONSTANT AND DISSIPATION

FACTOR (tan δ) The measurement of dielectric constant and dissipation

factor (tan δ) is carried out as per IEC 60250 standard at 50 Hz. The specimens with 50 mm in diameter and 3 mm in thickness are used

B.8 TENSILE STRENGTH AND PERCENTAGE

ELONGATION AT BREAK The tensile Strength and percentage elongation at break

are assessed by ASTM D-412, using universal testing machine. The shape and the size of the test specimen used

are also as per ASTM D-412. The tensile testing machine of constant rate of crosshead movement is used.

ACKNOWLEDGEMENT The authors wish to express their gratitude to the

Management of B.S.A Crescent Engineering College, Mr Abdul Qadir A. Rahman Buhari, Correspondent, Dr.V.M. Periasamy, Principal, Dean(s) and Director, for their support and encouragement.

Special encomiums are due to the faculty, department of High Voltage Engineering, College of Engineering, Guindy, Anna University, Chennai-25.

The authors wish to thank All India Council for Technical Education (AICTE), Government of India, for providing funds to carry out the research work.

REFERENCES

[1] R. Hackam, “Outdoor HV Composite Polymeric Insulators”, IEEE Trans. Dielectr. Electr. Insul., Vol. 6, pp. 557-585 , 1999. [2] N.Yoshimura, S. Kumagai and B. Du, “Research in Japan on the Tracking Phenomenon of Electrical Insulating Materials, IEEE Electr. Insul. Mag., Vol. 13, No.5, pp 8-18, 1997. [3] S.H. Kim and R. Hackam, “Effects of Saline-Water Flow Rate and Air Speed on Leakage Current in RTV Coatings”, IEEE Trans. Power Delivery, Vol. 10, pp. 1956-1964, 1995. [4] R. Raja Prabu, S. Usa, K. Udayakumar,M. Abdullahkhan and S.S.M. Abdulmajeed,”Electrical Insulation Characteristics of Slicone and EPDM Polymeric Blends – Part I”, IEEE Trans. Dielectr. Electr. Insul., Vol. 14, pp.1207-1214, 2007. [5] R.S. Gorur, E.A, Cherney and R. Hackam, "The AC and DC Performance of Polymeric Insulating Materials under Accelerated Aging in a Fog Chamber", IEEE Trans. Power Delivery, Vol. 3, pp..1892-1902, 1988. [6] L.H. Meyer, S.H. Jayaram, and E.A. Cherney, "Thermal Characteristics of RTV and Hot Pressed Silicone rubber filled with ATH and Silica under Laser Heating", IEEE Conf. Elect. Insul. Dielect. Phenomena (CEIDP), Albuquerque, pp.383-386, 2003. [7] L.H. Meyer, E.A. Cherney and S.H. Jayaram, "The Role of Inorganic Fillers in Silicone Rubber for Outdoor Insulation - Alumina Trihydrate or Silica", IEEE Electr. Insul. Mag., Vol. 20, No. 4, pp.13-21, 2004. [8] A. M. Piah and A. Darus, “Modelling Leakage Current and electric field behaviour of wet contaminated insulators”, IEEE Trans. Power Delivery, Vol.19, pp. 432-433, 2004. [9] G.A.Vignaux, Dimensional Analysis in Data Modelling, Kluwer Academic Publishers, 1992. [10] E.Q. Isaacson and M.Q. Isaacson, Dimensional Methods in Engineering and Physics, Edward Arnold, 1975. [11]H.L. Langhaar, Dimensional Analysis and Theory of Models, Wiley, 1951.

Dr. R. Raja Prabu (M’05-SM‘07) was born in 1967. He received the B.E. and M.E. degrees in Electrical Engineering and Power System Engineering, respectively in 1988 and 1990. He received the Ph.D. degree in High Voltage Engineering from Anna University. Currently, he is working as Professor and Head in the department of E.E.E in B.S.A. Crescent Engineering College, Chennai. All India Council for Technical Education, India, sponsored his research work. He

is a member of IEEE, CIGRE, I.E (I) and I.S.T.E. His research interests include Outdoor Insulation, Digital Protection, High Voltage Engineering , Nano- Dielectrics etc.,.


Dr. S. Usa received the B.E, M.E., and Ph.D., degrees in electrical engineering from College of Engineering, Anna University in 1986, 1989 and 1995, respectively. From 1992 to 2000, she worked as Lecturer and since 2000 as Assistant Professor at the College of Engineering, Anna University. Her research interests include electromagnetic field computation and high voltage engineering. She is a member of IEE, UK.

Dr. K. Udayakumar (SM’80) received the B.E., M.E., and Ph.D., degrees from the College of Anna University in 1972, 1974 and 1987, respectively. He started his career as Lecturer in Anna University and subsequently promoted as Assistant Professor and currently he is a Professor, in the Department of Electrical and Electronics Engineering, Anna University. He guided a number of Ph.D. students and has several publications in journals. He served as Director of various centers

of the University. His research interest is in high voltage engineering. Dr. Udayakumar was the Chair of the Madras Chapter of IEEE.

Dr. M. Abdullah Khan (M’78) was born in 1940. He obtained the B.E. degree in electrical engineering, the M.E. degree in high voltage engineering and the Ph.D. degree in power system engineering, respectively in 1961, 1968 and 1974. He guided several Ph.D. and M.E. students. Currently he is working as a Professor in the Dept. of EEE, Crescent Engineering College. He is a member of ISTE (India). He published several papers in journals and conferences. Previously, he

was the Dean and Director of Anna University. He has teaching and research experience of more than 40 years.

Dr. S.S.M. Abdul Majeed received the M.Sc. degree in industrial chemistry from Bharathidasan University, India and the Ph.D. degree in polymer science and technology from Anna University, India, in 2002. He has been with Crescent Engineering College, Chennai, India, since 1988 and currently he is serving as Assistant Professor in the Department of Polymer Technology. His research interest includes the development and characterization of polymeric insulators, polymer

blends, biodegradable plastics and composites.


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Theoretical correlations amongst electrical and mechanical characteristics of polymeric housing materials for outdoor insulators