Experimental Study of Contact Resistance Variation for Pantograph-Contact Line Contact

Constantin-Florin OCOLEANU*, Gheorghe MANOLEA**, Grigore CIVIDJIAN*

Electrical Apparatus and Technologies*, Electromechanical**

University of Craiova, Faculty of Electrical Engineering*, Faculty of Electromechanical, Industrial Information, Environment Engineering**

Bd. Decebal, no. 107, 200440, Craiova ROMANIA

focoleanu@elth.ucv.ro, ghmanolea@gmail.com, gcividjian@elth.ucv.ro

Abstract: - In this paper we performed an experimental study of electrical contact resistance dependence of the pressing force for pantograph-contact line contact. The parameters of the well-known formula for the constriction resistance were determined. The pantograph is asymmetric EPC type and the contact line wire is TF 100 type, both used in Romanian Electric Railways. The variation of contact resistance with contact force and calculated values of material parameters for graphite plates with different degree of wear are pointed out. Keywords: Electric railway, contact resistance, graphite, statistical distribution. 1. Introduction The contact between pantograph and AC electric railway system supply contact line is studied in literature and represents an important problem concerning the exploitation of rails vehicles. The pantograph - catenary system is still today the most reliable form of collecting electric energy for the train, when high speed operational conditions are considered. This system should ideally operate with relatively low contact forces and no contact loss should be observed, so that the power rests constant.

The estimation of contact wire wear must take into account the variation of electrical contact resistance with radius of contact spots and contact force. The effects of friction and electrical phenomena govern the wear rate in the sliding contact between pantograph collector strip and contact wire [1].

As well known, when two surfaces are in contact, the real contact area is much smaller than the nominal one. The contact occurs in a finite number of asperities that are subjected to an elastic, plastic or combined elastic–plastic deformation depending on the normal pressure value, on the superficial roughness and on the material properties [3].

Fig.1 Contact between rough surfaces modeled as contact between a rough surface and a hard

smooth surface.

At increasing walking speed, due to the dynamic forces, the separation of the wire from pantograph occurs more frequently, increasing the contact resistance.

The values of electrical contact resistance are very dispersed and difficult to predict, in spite of very simple theoretical formulas [2]. In this paper, direct measurements of surface parameters were made and the theoretical explanation of the measured contact resistance variation with contact force is tried.

The proper balance between the dynamic characteristics of the pantograph and the contact line depends on the quality of current collectors and on the longevity of the contact wire and inserts. The pantograph must support them with sufficient force to remain in permanent contact with the wire, but not unduly raise, which would lose contact after the points of attachment.

Real contact area, the total area of microcontacs, is a small fraction of the nominal area, usually a few percent. Macro contact area [6] (area where microcontacs are distributed) is formed as a result of surface curvature of the bodies in contact (fig.2).

Fig.2 Rough surfaces in contact

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ISSN: 1790-2769 101 ISBN: 978-960-474-182-3

To decrease the electrical resistance of the line, the contact wire and cable are placed in parallel, at regular intervals using a copper shunt.

2. Theoretical model of the contact

between two flat surfaces Theoretically the contact resistance is given by

formula [10]:

=c mcR

F(1)

Where:

cR is contact resistance; ,c m are material coefficients; F is contact force.

In formula (1) theoretically the exponent m is equal to 0.33 for elastic deformation and 0.5 for plastic deformation [10]. In case of sphere-plane contact the exponent m has a small dependency on the granulation level and is independent on the surface irregularities and material resistivity, while in the case of flats contacts there is a small dependency on the mean irregularities height and on the resistivity [2].

Considered the normal distribution of the random unevenness height and a spherical shape for asperity, we can write the density distribution function of the asperity height deviation z from average asperity height:

2

med2

(z h )1f (z) exp( )22

− −= ⋅⋅ σσ ⋅ ⋅ π

(2)

Where:

σ is standard deviation of asperity height; medh is medium height of asperity.

The elastic force, P, at the compression x (fig.4) has the expression [2]:

max

max

3h 2max

m mh x

z h xP(x) N E D f(z) dz1.04

−

− + = ⋅ ⋅ ⋅ ⋅ ⋅ ∫ (3)

Where:

N is the number of irregularities on each cm2; Em is Young elastic modulus; Dm is diameter of spherical irregularity.

Fig.3 Contact between two elements

The number of contact spots per cm2 and the radius of the constriction zone at the level z will be [2]:

max med medh h z hn(z) N ( ) ( )− − = ⋅ ϕ −ϕ σ σ

(4)

11r (z)

2 n(z)=

⋅(5)

The radius of mechanical contact spots of a Dm

diameter spherical segment, having the height z, when the deformation is x, will be [2]:

( ) ( )max maxa(z,x) z x h D z x h= + − ⋅ − − + (6)

The constriction resistance of a singular contact spot

with radius a, when the constriction area radius is r1, will have the expression [2]:

( )1R(z,x) A B2ρ= ⋅ −⋅π

(7)

( ) ( )( )

2 21

21

r z a z,xB

r z

−= (8)

( )( ) ( )

( )

2 21r z a z,x1A a tan

a z,x a z,x

− = ⋅

(9)

The conductance and the resistance of multi-spot

contact per cm2 of flat contact surface, for the deformation x is given by equation [2]:

Proceedings of the International Conference on RISK MANAGEMENT, ASSESSMENT and MITIGATION

ISSN: 1790-2769 102 ISBN: 978-960-474-182-3

max

max

h

h x

f (z)G(x) N dzR(z, x)−

= ⋅ ⋅∫ (10)

11R (x)

G(x)= (11)

The variation of multi-spots contact resistance versus

pressing force can be presented as [10]:

c mcR

P= (12)

The exponent m is independent on the density contact

spots but depends on the unevenness shape and their height distribution.

For uniform distribution of the unevenness height the exponent m = 0.6 [2].

For normal distribution of the unevenness height this exponent can be evaluated for elastic domain as in [2], using the eq. (2)…(11) and considering the asperities having the spherical shape. For considered graphite m is given in figure 4 for various coefficient values of heights variations, as function of maximum deformation reported to the average asperity height.

Fig.4 Exponent m versus ratio maximum contact displacement over the average irregularities height

3. Experimental results Using the roughness values obtained from the

diagrams of three pantograph graphite plates with different degree of wear (fig.7) and considering the case of uniform distribution of asperity height, we can determine contact resistance parameters for graphite plates (table 1).

In the figure 5 can be seen the variation of contact pressure with the contact approach x, for the same N=10000 spherical unevenness per square mm of flat graphite and hmax = 22 mµ , but for two different unevenness height statistical distribution: uniform and

normal with σ = 5.38 mµ . The influence of the distribution is evident.

Prober

2

N

1 cmmDmµ

maxhmµ

medhmµ m

σµ

Exponent m

1 9000 20 27 7.69 5.38 0.0942 6400 20 17 4.1 3.73 0.0753 1600 20 12 5.42 2.1 0.196

Table.1 Graphite plates parameters values

Fig. 5 Contact pressure versus displacement

Using formula (2) and roughness diagram for three graphite plates (fig.7), in figure 6 is presented density distribution function considering the cases for normal and uniform distribution of asperity height.

Fig.6 Density distribution function of the asperity height deviation from average asperity height

In figure 7 the following notation of the roughness

parameters are used: Ra is the arithmetic mean of the absolute values

of the profile variations from the mean line; Rz is the ten point height of irregularities; Rq is root-mean-square deviation of the profile.

Proceedings of the International Conference on RISK MANAGEMENT, ASSESSMENT and MITIGATION

ISSN: 1790-2769 103 ISBN: 978-960-474-182-3

Fig.7 A sample of roughness diagram for graphite

The contact resistance variations with contact force for graphite plates are presented in figure 8 and table 2.

Rc1 (mΩ) Rc2 (mΩ) Rc3 (mΩ) Fc (kg)18.8 36 20.8 2.5 18.5 35.7 20.3 3 18.2 35.3 19.8 3.5 18 34.9 19.1 4 17.9 34.5 18.8 4.5 17.8 34.2 18.5 5 17.7 33.9 18.2 5.5 17.6 33.8 17.9 6 17.6 33.6 17.7 6.5 17.6 33.4 17.4 7 17.6 33.4 17.2 7.5

Table.2 Experimental results

Parameter m can be calculating using formula:

1

2

2

1

FF

ln

RR

lnm c

c

= (13)

Fig.8 Contact resistance variation with contact force for graphite plates

4. Conclusion

Using a graphite plate for pantograph with small value of electrical resistivity the electrical contact resistance and the contact temperature can be reduced.

The smaller electrical contact resistance is, the lower are the level of pantograph and contact wire wear.

The increasing contact pressure reduces the contact resistance, but increases the plate and wire wear rate.

The variation of contact pressure with the displacement, apart from the density, shape and dimensions of the asperities, depends essentially on statistical distribution of irregularities heights (fig.5).

The exponent m in case of elastic deformation and normal distribution of the height of Dm = diameter spherical asperities, can be in the range 0.5 – 1, for variation coefficient xmax/hmed between 0.13 and 0.5, (fig.4). For very small deformation the common value, for all the relative standard deviations is m = 0.6.

The experimental values of parameter m for studies three samples show that the real values are smaller than 0.6 (0.094…0.196). Exponent m values are 3 to 6 times lower than corresponding values for model of surface plane.In this case may be these explanations: the contact surface is cylindrical and not flat and it falls under plastic deformation.

With increasing wear the graphite plates becomes smoothing rough and the exponent m increases from 2 times if the surface is less worn.

With increasing wear occurs polishing surface and the contact resistance decreases.

Proceedings of the International Conference on RISK MANAGEMENT, ASSESSMENT and MITIGATION

ISSN: 1790-2769 104 ISBN: 978-960-474-182-3

References: [1] Bucca G, Collina A., A procedure for the wear

prediction of collector strip and contact wire in pantograph–catenary system, Wear 266, pp. 46–59, 2009.

[2] Cividjian G.A., Pascu I., Bunescu A., Matei D.,M., Dolan A., Experimental study of the resistance of flat Cu-W contacts, XII-th International Symposium on Electrical Apparatus and Technologies, SIELA, Procedingss, Vol.1, 31 May-1 june, Plovdiv,, Bulgaria, pp.58-65, 2001.

[3] Greenwood J .A., Williamson J. B. P., Contact of nominally flat surfaces, Proceedings of the Royal Society Series A295, pp. 300–319, 1966.

[4] He D.H., Manory R., Grady N., Wear of railway contact wires against current collector materials,Wear 215, pp. 146–155, 1998.

[5] J. A. Greenwood, K. L. Johnson, and M. Matsubara, “A surface roughness parameter in hertz contact,” Wear, vol. 100, pp. 47—57, 1984.

[6] Majid Bahrami, Modeling of Thermal Joint Resistance for Sphere-Flat Contacts in a Vacuum, Thesis, Waterloo, Ontario, Canada, 2004.

[7] Ocoleanu C.F., Popa I., Manolea Ghe., Study of the Skin Effect Influence on Electric Railway System Supply Line Heating, Environmental problems and development, Proceeding of the 1st WSEAS International Conference on Urban Rehabilitation And Sustainability - URES 2008, pp. 142-146, Bucharest, Romania, November 7-9, 2008.

[8] Ocoleanu C.F., Popa I., Manolea Ghe., Dolan A.I., Temperature measurement in contact pantograph-AC contact line, Proceedings of 11th WSEAS International Conference on Automatic, Control, Modeling and Simulation, Istanbul, Turkey, Published by WSEAS Press (ISBN 978-960-474-082-6), pp. 184 – 188, May 30-June 1, 2009.

[9] Rauter F.G, Pombo J., Ambrosio J., Chalansonnet J., Bobillot Adrien, Contact model for the pantograph-catenary interaction, Journal of System Design and Dynamics, Vol. 1, no. 3, 2007.

[10] Ragnar Holm, Electric Contacts, 4-th ed., Springer – Verlag, Berlin/Heidelberg/New York, 1967.

Proceedings of the International Conference on RISK MANAGEMENT, ASSESSMENT and MITIGATION

ISSN: 1790-2769 105 ISBN: 978-960-474-182-3