Electrodynamic Contact Bounce Induced by Fault Current in Low-Voltage Relays

energies

Article Electrodynamic Contact Bounce Induced by Fault Current in Low-Voltage Relays

Andrzej Ksiazkiewicz, Grzegorz Dombek * , Karol Nowak and Jerzy Janiszewski Institute of Electric Power Engineering, Poznan University of Technology, Piotrowo 3A, 60-965 Poznan, Poland; [email protected] (A.K.); [email protected] (K.N.); [email protected] (J.J.) * Correspondence: [email protected]; Tel.: +48-61-665-2192

Received: 13 August 2019; Accepted: 16 October 2019; Published: 16 October 2019

Abstract: Due to fault currents occurring in electrical installations, high electromagnetic force values may be induced in current paths of low-voltage electromagnetic relays. This force may lead to an electromagnetic bounce that will further result in an electric arc ignition between contacts, and under some circumstances, it will result in contact welding. For the proper exploitation of relays, the threshold value of the maximum current, and thus the electrodynamic force, should be known. This force depends on several factors, including: contact materials, dimensions of relay current paths, relay electromagnetic coil, etc. This paper presents the results of calculations and an experiment on electromagnetic forces, which cover these factors. A static closing force, acting on the contacts, and the fault current were measured. As a result, values of the force and current threshold were obtained, which inform when an electrodynamic bounce may occur. The obtained result may be used in designing contact rivets and relay current paths together with the selection of adequate fault protection devices.

Keywords: relays; contact materials; contact bounce; electric arc; contact welding

1. Introduction The flow of electric current in apparatus current paths, electric arc, or conductors located in a foreign magnetic field leads to the appearance of electrodynamic forces. These forces affect the flow of electrical charges, and consequently also on current paths, electric arc, or wires. In electromagnetic relays, the flow of current of a considerable value can lead to the emergence of an electrodynamic force, affecting the contact system, and it can be large enough to cause a dynamic opening of the contacts. As a result, an electric arc will occur between the contacts, which may be welded [1–4] when the contacts close again. Welded contact will make the relay inoperable, which will necessitate its replacement or an exchange of the entire device within which it is incorporated. The electric arc will lead to the degradation of contact surface and may reduce the expected operating time of the relay [5–7]. Welding will depend on the type of contact material [8,9], arc burning time, arc energy [10–12] and the type of load [13,14]. It is important from the point of view of the design and exploitation of relays to determine the value of the current which may lead to the occurrence of an electrodynamic bounce. The knowledge of these values would allow the selection of the correct relay model for a given electric circuit, taking into account the peak current value of short-circuit. This is why the authors have decided to test the static contact force of an electromagnetic relay and test it with a fault current to determine the electrodynamic response. It has been proven that there is a correlation between the current value, static contact force, and electrodynamic bounce, and that it can be calculated with an acceptable level of accuracy.

Energies 2019, 12, 3926; doi:10.3390/en12203926 www.mdpi.com/journal/energies Energies 2019, 12, 3926 2 of 13

Studies of electrodynamic forces that can act on electrical contacts have provided insight as to how these phenomena work. Both theoretical and experimental results are available that can, in some manner, describe these phenomena [15]. They describe the electrodynamic force generated by current flowing between contacts, but they do not link all force components. There are studies that utilize the contact force to describe the working principles of electrical equipment [16]. Many studies combine electrodynamic bounce of contacts with contact welding [1–3]. As shown in these studies there is a relation between contact bounce, contact welding, and electrodynamic force, however they do not focus on that subject. There is research concerning contact pressure, contact displacement, and contact bounces allowing the measurement of the dynamic characteristics of contactors [17]. Other ongoing research focuses on controlling the contact closing process by means of electromagnetic coil energy control [18,19]. Another approach is to use FEM methods for non-linear dynamic analysis of electrical machines in the time domain [20]. These studies are focused on controlling the electromagnetic coil and electrical contacts at make and do not address the topic of effects of electrodynamic bounce of contacts. The experimental results presented in this paper provide information regarding the electrodynamic contact bounce related to the static contact force of the electromagnetic coil installed in a relay. These results can be useful in determining the electrodynamic bounce threshold solely on the dimensions of the relay current path and its rivet contact material. A theoretical analysis was conducted, taking into account three force components mentioned above, together with an experimental confirmation, which provided satisfactory consistency between theory and practice. Research into the issue of electrodynamic bounce and electrodynamics in electrical contacts, focuses mainly on a single component of this force. It is focused mostly on the repulsion force between contacts [15] or force generated by electric arc [21]. Other studies attempt to describe these phenomena but only for very high currents, with a magnitude of kiloamperes [1,2,16]. Therefore, in this paper, the authors present results attempting to combine all force components induced during a fault current flow. The peak value of the current barely exceeds one kiloampere, as can be observed in typical, low voltage electrical installations. The spectrum of research presented in this paper is not covered by other studies. The paper has been organized in the following way. The second chapter describes the main electrodynamic force components that have an impact on the electrodynamic bounce of contacts. In the third chapter the experimental setups and electromagnetic relays used in the research are presented and described. The results of the study were analyzed in the fourth chapter. The last and fifth chapter contains a summary and the final conclusions.

2. Analysis of Electrodynamic Contact Forces In electric devices, the magnetic field is usually caused by the flow of electric current through the current paths of the same or another electrical circuit. The mutual forces of any pair of wires are proportional to the product of the values of currents flowing through these circuits and to the magnetic permeability of the environment in which these circuits are located. Electrodynamic forces and moments acting on conductive elements (rectilinear in particular) are calculated on the basis of Biot–Savart and Lorentz laws. The forces of dynamic interactions in electric circuits are distributed continuously. Assuming that the current path can be treated as a rigid body, elementary forces can be replaced by one cumulative force. In operating conditions, the continuous current flow should not lead to the appearance of significant forces and stresses in the current paths. However, such considerations should be taken into account in the case of flow of short-circuit currents through current paths. When two wires L1 and L2 (Figure1) are parallel and distant from each other by y, then there would be only one component of the electrodynamic force. When considering current paths with the same and finite length L placed opposite to each other and with a distance between them equal to a, the electrodynamic force can be calculated from the formula:  r  2 µ0 L a a  Fp = i1i2  1 +  [N], (1) 2π a  L2 − L EnergiesEnergies 20192019, 12, 12, x, 3926FOR PEER REVIEW 3 of3 of13 13 Energies 2019, 12, x FOR PEER REVIEW 3 of 13 92 where: i1, i2—current flowing through the first and second current path (A), L—length of the current where: i , i —current flowing through the first and second current path (A), L—length of the current 9392 pathwhere: (m), i 1a, —distancei22—current between flowing thethrough current the paths first (m).and second current path (A), L—length of the current 9493 pathTaking (m), a —distanceinto account between between the construction the the current current paths pathsof the (m). (m).tested relays (presented in Chapter 3), it can be 9594 concludedTaking that into such account assumptions the construction are justified dueof the to the tested simple relays construction (presented of thein Chaptercurrent path 3), it system. can be 9695 concludedDue to that the step such change assumptions of the arecontact justified justified surface, due anto to the theadditional simple simple construction constructionelectrodynamic of of the the force current current is created path path system. system.in the 9796 contact,Due which to to the the repels step step thechange change contacts of of the thefrom contact contact each surface, other. surface, Th anis an additional force additional is caused electrodynamic electrodynamic by a change force in force the is createdshape is created of in the the in 9897 currentcontact,the contact, path, which whichand repels thus repels the a change contacts the contacts in from the fromdirectioneach eachother. and other. Th densityis force This forceofis causedcurrent is caused by streams a change by a(Figure change in the 2). inshape For the shapenon-of the 9998 detachablecurrentof the current path, contacts and path, thusand and fora change thusconducting a changein the operating direction in the directioncurr andents, density this and forceof density current does of not streams current pose any(Figure streams hazards 2). (Figure For for non-the2). 10099 contacts.detachableFor non-detachable In the contacts case of and contactsmovable for conducting contacts, and for conductingwhenoperating a curre curr operatingntents, of considerable this currents, force does value this not flows forcepose (faultany does hazards current), not pose for this anythe 101100 forcecontacts.hazards may forcauseIn the the contactcase contacts. of movableopening, In the contacts, appearance case of movable when of thea curre contacts, electricnt of arc, whenconsiderable and a consequential current value of considerable flows contact (fault damage current), value flows[22]. this 102101 Theoretical(faultforce may current), causeconsiderations this contact force opening, may assume cause appearance that contact all contac opening, of thet elgeometryectric appearance arc, is and symmetrical, of consequential the electric and arc, contact andthen consequential damagethe current [22]. 103102 conductionTheoreticalcontact damage area considerations on [22 the]. Theoreticalcontact assume surf considerationsace that is circular. all contac assumeIn tthe geometry case that of all axis contactisymmetric symmetrical, geometry contacts, and is symmetrical,then repulsive the current force and 104103 Fconductionthens is possible the current areato be conductionon determined the contact area for surf any onace the cu isrrent contact circular. density surface In theat isthe case circular. contact of axisymmetric Inpoint the case[22]. of contacts, axisymmetric repulsive contacts, force repulsive force Fs is possible to be determined for any current density at the contact point [22]. 104 Fs is possible to be determined for any current density at the contact point [22].

105 106105 Figure 1. Determination of the electrodynamic interaction of one-dimensional wires of finite length Figure 1. Determination of the electrodynamic interaction of one-dimensional wires of ﬁnite length 107106 withFigure the 1.currents Determination i1 and i2, oflying the on electrodynamic the OXY plane, interaction with one of theone-dimensional wires lying on wires the X of axis finite [23]. length with the currents i1 and i2, lying on the OXY plane, with one of the wires lying on the X axis [23]. 107 with the currents i1 and i2, lying on the OXY plane, with one of the wires lying on the X axis [23].

(a) (b) 108 FigureFigure 2. 2.SketchesSketches for for(thea) thecalculation calculation of el ofectrodynamic electrodynamic forces forces caused caused by: (a) by: the(b) (change a) the changein the cross- in the 109108 sectionFigurecross-section of 2. the Sketches conductor of the for conductor the and, calculation (b and,) in the (b ) ofpoint in el theectrodynamic contact point contact [24]. forces [24]. caused by: (a) the change in the cross- 109 section of the conductor and, (b) in the point contact [24]. 110 For a point contact, this force can be determined from the following dependence [23]: 110 For a point contact, this force can be determined from the following dependence [23]:

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For a point contact, this force can be determined from the following dependence [23]:

µ0 2 r1 FS = i ln [N], (2) 4π r2 where: r1—the radius of the apparent contact surface (m), r2—the radius of the real contact surface (m). In the real contact arrangement of the tested low voltage electromagnetic relays, there are forces coming from two parallel paths (current paths supplying electricity to the contact rivets), as well as from the narrowing of the contact area in the electrical contact. In order to analyze electrodynamic interactions in the case considered, the following assumptions were made:

- dynamic impacts are distributed continuously, - the current path can be treated as a rigid body, - the forces are parallel to each other.

The system of forces acting in the contact model under consideration and aﬀecting the contact can be presented as sliding vectors and moved along the lines of their operation so that they are all hooked at one point, forming a convergent system of forces. Based on the above premises, it was assumed that the resultant force acting repulsively on the contactors can be determined as the sum of forces coming from two parallel wires FP and narrowing in the contact area FS:

F1 = FP + FS. (3)

During the ﬂow of short-circuit current, in the extreme case, the forces generated may lead to the opening of the contacts. When the contacts are open, an electric arc is formed between them. This arc causes the occurrence of additional electrodynamic forces in the system of current paths. According to Reference [21], the value of this force was estimated at 22 10 5 (NA 1). It is directed towards the × − − current paths, which leads to their further mutual repulsion. Ultimately, the resultant force acting repulsively on the contactors is determined as the sum of the individual components, taking into account that FA only occurs when the electric arc is present:

F1 = FP + FS + FA. (4)

3. Results and Discussion

3.1. Used Materials The following models of miniature relays were used to carry out the research experiments:

- RM85–2011–35–1012 (Relpol S.A., Poland) with contact material AgNi (Figure3a), - RM83–1011–25–1012 (Relpol S.A., Poland) with contact material AgCdO (Figure3b).

The models used have a rated operating current of 16 A a.c., working voltage 250 V a.c., and coil operating voltage of 12 V d.c. The dimensions of contact springs, for two relay models, are shown in Figure4. The dimensions of contact rivets and current paths are deliberately di fferent in order to show the influence of relay construction on the resulting repulsion force. The typical values of switching on and off times for RM85 and RM83 models are 7 ms and 3 ms, respectively. According to the manufacturer’s data, the resistance of the contacts in each of the selected models is less than 100 mΩ. Similar models of relays are manufactured by many companies worldwide, for example: Relpol (RELPOL S.A., Poland), Finder (Finder S.p.A. con unico socio, Italy), and Hongfa (Xiamen Hongfa Electroacoustic Co., Ltd., China). These relays have all utilized similar contact materials, both AgNi and AgCdO, and have almost identical dimensions. This can lead to the conclusion that the presented results can be applied to other types of relays, which are similar in design. Energies 2019, 12, 3926 5 of 13

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(a()a ) (b()b )

(c()c ) (d()d )

148148 FigureFigure 3. 3.View 3. ViewView of of selected selected of selected electromagnetic electromagnetic electromagnetic relays: relays: relays:(a ()a external) external (a) view external view of of RM85–2011–35–1012 RM85–2011–35–1012 view of RM85–2011–35–1012 relay, relay, (b ()b ) 149149 internalinternalrelay, (viewb view) internal of of RM85–2011–35–1012 RM85–2011–35–1012 view of RM85–2011–35–1012 with with its its contact contact with positions, positions, its contact (c ()c external) external positions, view view (ofc )of RM83–1011–25– external RM83–1011–25– view of 150150 10121012RM83–1011–25–1012 relay, relay, (d ()d internal) internal relay,view view of (d of )RM83–1011–25–1012 internalRM83–1011–25–1012 view of RM83–1011–25–1012 with with its its contact contact positions. withpositions. its contact positions.

(b) (a()a ) (b) 151 Figure 4. Dimensions (in millimeters) of moving contact springs for individual relay models: (a) 151 Figure 4. DimensionsDimensions (in (in millimeters) millimeters) of ofmoving moving contact contact springs springs for forindividual individual relay relay models: models: (a) 152 RM85–2011–35–1012, (b) RM83–1011–25–1012. 152 RM85–2011–35–1012,(a) RM85–2011–35–1012, (b) (RM83–1011–25–1012.b) RM83–1011–25–1012.

153153 3.2.3.2. Circuit Circuit Circuit Diagram Diagram 154154 TheThe circuit circuit diagram diagram for for for a a atesting testing circuit circuit circuit is is ispresented presented presented in in inFigure Figure Figure 5 55and andand the thethe test testtest bench benchbench in in Figure Figure 6.6 6. . 155155 TheThe circuit circuit is issupplied supplied directly directly from from the the public public power power network network of ofof a alow low voltage voltage of of 230 230 V Va.c. a.c. The The peak peak 156156 currentcurrent value value is isset set by by the the value value of ofof limiting limitinglimiting resistor resistorresistor R RlimRlimlim. Voltage.. Voltage Voltage between between between contact contact contact relays relays relays and and current current 157157 flowingflowingﬂowing through through them them are are recorded recorded using using an an an osci osci oscilloscopelloscopelloscope GW GW GW Instek Instek Instek GDS-3154 GDS-3154 GDS-3154 (GW (GW (GW Instek, Instek, Instek, Taiwan). Taiwan). Taiwan). 158158 TheThe voltage voltage was was used used to to determine determine if ifthe the contacts contacts ar ar aree eopened opened or or closed closed and and is is not not shown shown directly directly in in 159159 anyany figure figure ﬁgure in in this this paper. paper. The circuit is protected against short circuits and overloads with an installation switch of rated operating current 16 A and characteristics B. The static contact force was measured using an FH–S (SAUTER GmbH, Germany) universal digital force gauge mounted on a dedicated TVL manual

Energies 2019, 12, 3926 6 of 13

test bench for highly accurate tensile and compressive force measurement, equipped with length Energies 2019, 12, x FOR PEER REVIEW 6 of 13 measurement. A single test was performed for each relay; at the beginning of the test, the contacts were in closed position. This situation simulates the occurrence of an unintentional short circuit during its normal exploitation. Calculations of the electrodynamic force were based on theoretical principles presented in Chapter 2 and experimental results presented in Chapter 4, with the use of Scilab software (ESI Group, France) Energies 2019, 12, x FOR PEER REVIEW 6 of 13 for numerical computation.

160

161 160Figure 5. Testing circuit diagram: R—tested relay, P—protection of the circuit (installation switch), Figure 5. Testing circuit diagram: R—tested relay, P—protection of the circuit (installation switch), 162 Rlim—limiting resistor, CP—current probe,— VP—voltage— probe, CH1, CH2—oscilloscope channels. 161 RFigurelim—limiting 5. Testing resistor, circuitCP diagram:—current R probe,testedVP relay,—voltage P protection probe, CH 1,ofCH the2—oscilloscope circuit (installation channels. switch), 162 Rlim—limiting resistor, CP—current probe, VP—voltage probe, CH1, CH2—oscilloscope channels.

163 163 164 Figure 6. Photograph of the test bench used in the study.

164 165 The circuit is protectedFigureFigure 6. against Photograph 6. Photograph short circuits of of the the test testand bench benchoverloads used used in with thein the study.an installationstudy. switch of rated 166 operating current 16 A and characteristics B. The static contact force was measured using an FH–S 3.3. Algorithm 165 167The (SAUTERcircuit is GmbH, protected Germany) against universal short digital circuits force and gauge overloads mounted withon a dedicated an installation TVL manual switch test of rated 168 benchTo for determine highly theaccurate values tensile of individual and compress componentsive force of the measurement, resultant electrodynamic equipped force,with i.e.,lengthFS, 166 operating current 16 A and characteristics B. The static contact force was measured using an FH–S 169 Fmeasurement.P, and FA, a calculation A single test script was forperformed the Scilab for program each relay; was at created. the beginning This script of the algorithmized test, the contacts the 167 (SAUTER170 mathematicalwere GmbH, in closed Germany) equations position. presenteduniversal This situation in digital Chapter simulates force 2. The thegauge algorithm occurrence mounted used of is an presentedon unintentional a dedicated in Figure short TVL7. circuit manual test 168 bench171 forduring highly its normal accurate exploitation. tensile and compressive force measurement, equipped with length 169 measurement.172 Calculations A single oftest the was electrodynamic performed forcefor eachwere relay;based onat thetheoretical beginning principles of the presented test, the in contacts 170 were173 in Chapterclosed position.2 and experimental This situation results presentedsimulates in theChapter occurrence 4, with the of use an ofunintentional Scilab software short (ESI circuit 174 Group, France) for numerical computation. 171 during its normal exploitation. 172 175Calculations 3.3. Algorithm of the electrodynamic force were based on theoretical principles presented in 173 Chapter 2 and experimental results presented in Chapter 4, with the use of Scilab software (ESI 176 To determine the values of individual components of the resultant electrodynamic force, i.e. FS, 174 Group,177 France)FP, and FforA, a numerical calculation computation.script for the Scilab program was created. This script algorithmized the 178 mathematical equations presented in Chapter 2. The algorithm used is presented in Figure 7. 175 3.3. Algorithm

176 To determine the values of individual components of the resultant electrodynamic force, i.e. FS, 177 FP, and F A, a calculation script for the Scilab program was created. This script algorithmized the 178 mathematical equations presented in Chapter 2. The algorithm used is presented in Figure 7.

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179

180 Figure 7. Algorithm of repulsion forces calculation.

4. Results and Discussion 181 4. Results and Discussion Two cases of short-circuit fault current ﬂow through relay contacts for which electrodynamic 182 Two cases of short-circuit fault current flow through relay contacts for which electrodynamic contact bounces were observed and analyzed. Two groups of previously presented relay models 183 contact bounces were observed and analyzed. Two groups of previously presented relay models have have been tested. Figures8 and9 show the time courses of the instantaneous current value and the 184 been tested. Figures 8 and 9 show the time courses of the instantaneous current value and the calculated repulsive force F1. 185 calculated repulsive force F1.

186

Figure 8. Dependence of repulsive force on the short-circuit current value; also marked is the moment 187 Figure 8. Dependence of repulsive force on the short-circuit current value; also marked is the moment of relay contact opening RM85–2011–35–1012: F1—calculated repulsion force, i—current value, contact 188 of relay contact opening RM85–2011–35–1012: F1—calculated repulsion force, i—current value, position—determines whether contacts were open or closed (high state—open contacts). 189 contact position—determines whether contacts were open or closed (high state—open contacts).

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Figure 9. Dependence of repulsive force on the short-circuit current value; also marked is the moment

of relay contact opening RM83–1011–25–1012: F1—calculated repulsion force, i—current value, contact position—determines whether contacts were open or closed (high state—open contacts).

At the same time, time interval was marked during which the contacts remained open as a result of the electromagnetic bounce. Based on the analysis of the presented time series, the following conclusions can be made:

- the current is in phase with the source voltage,

- in the time when the contacts remain closed, force F1 is proportional to the instantaneous current value,

- after the moment when the contacts are opened, there is a signiﬁcant increase in force F1 caused by the appearance of an additional component derived from the electrodynamic interaction of the FA electric arc, - at one point in time the circuit breaker starts to open its contacts, which results in a signiﬁcant decrease of current value (which can be seen at time t = 3.7 ms in Figure8), - the resulting contact force is proportional to current value.

Figure 10 shows the electromagnetic blow-open process, during the fault current flow, for a single test of RM85–2011–35–1012 relay, with a visible eruption of molten contact material. Figure 10 shows four phases of the blow-open process: the ignition of electric arc between contacts, burning of electric arc phase, closing of electrical contacts with an eruption of heated, molten contact material, and welding of contacts phase. For a full view of the phenomena occurring during the current flow, it is necessary to know the dynamics of the relay drive in order to try to determine the force that should arise in the current path with a greater value than that generated by the relay electromagnetic coil. Figures 11 and 12 show the dependence of the contact force of the movable contact versus the path of this contact in relation to the starting position. At the same time, the initial position should be understood as the closing state of the contacts when there is no electrical load and energy consumption by the relay coil is nominal. During the test, the values of coil current and supply voltage were measured. These values did not change with the increase of the force acting on the contacts (an increase of the displacement path). Additionally, one should take into account the force which is caused by the fixed contact, which in its closed position moves slightly in the direction of the drive. This force is for the RM83–1011–25–1012 19 cN model and for the RM85–2011–35–1012 22 cN. During the measurements of the closing force, the relay contacts were opened by the dynamometer until the contact current path was interrupted. With Energies 2019, 12, 3926 9 of 13

an increasing displacement, the force grew until the contacts opened, then rapidly diminished. It has been assumed that a force determined in this way will have to be achieved during the current flow in order for the contacts to be opened electrodynamically. The maximum contact force of the movable contact in the RM83–1011–25–1012 model is 45 cN, and in RM85–2011–35–1012 it is 145.6 cN. The resultant value of the closing force which must be overcome to open the contacts due to the electrodynamic action is therefore 64 cN and 167.6 cN respectively. During the flow of nominal current, the calculated repulsion force is less than 0.03 cN. The contact blow-open process is a complex one, dependent on the pre-open phenomena [25] and on electrodynamic forces [15,22,26,27]. The current thrusts of research are the effects of blow-open contact bounce on contact welding and the phenomena behind it [4,5,13,26]. Studies regarding the influence of electrodynamic forces [15,28] and high current [29,30] do not cover the electrodynamic action of the operating relay coil. Presented research shows the relationship between the electrodynamic blow-open of contacts under high fault currents and the static contact force trying to prevent the Energiescontacts 2019 from, 12, x opening. FOR PEER REVIEW The knowledge of how this process works can lead to both theoretical9 of and 13 experimental contamination of the peak current value which will not result in blow-open phenomena, 223 diminished.thus lowering It has the chancebeen assumed of dynamic that contacta force determin weldinged and in increasing this way will the relayhave to life be expectancy. achieved during 224 the current flow in order for the contacts to be opened electrodynamically.

(a)

(b)

(c)

(d)

225 FigureFigure 10. Photographs ofof thethe electromagneticelectromagnetic blow-open blow-open process process for for RM85–2011–35–1012 RM85–2011–35–1012 relay: relay: (a) ( arca) 226 arcignition ignition during during contact contact opening, opening, (b) electric (b) electric arc burning arc burning between between the contacts, the contacts, (c) closing (c) ofclosing contacts of 227 contactswith eruption with eruption of molten of contact molten material, contact material, (d) closed (d (welded)) closed (welded) contacts withoutcontacts currentwithout ﬂow. current flow.

228 The maximum contact force of the movable contact in the RM83–1011–25–1012 model is 45 cN, 229 and in RM85–2011–35–1012 it is 145.6 cN. The resultant value of the closing force which must be 230 overcome to open the contacts due to the electrodynamic action is therefore 64 cN and 167.6 cN 231 respectively. During the flow of nominal current, the calculated repulsion force is less than 0.03 cN. 232 The contact blow-open process is a complex one, dependent on the pre-open phenomena [25] 233 and on electrodynamic forces [15,22,26,27]. The current thrusts of research are the effects of blow- 234 open contact bounce on contact welding and the phenomena behind it [4,5,13,26]. Studies regarding 235 the influence of electrodynamic forces [15,28] and high current [29,30] do not cover the 236 electrodynamic action of the operating relay coil. Presented research shows the relationship between 237 the electrodynamic blow-open of contacts under high fault currents and the static contact force trying 238 to prevent the contacts from opening. The knowledge of how this process works can lead to both 239 theoretical and experimental contamination of the peak current value which will not result in blow- 240 open phenomena, thus lowering the chance of dynamic contact welding and increasing the relay life 241 expectancy.

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Figure 11. Dependence of the contact force of the movable contact on the path of this contact with respect to the starting position—relay RM85–2011–35–1012.

Figure 12. Dependence of the contact force of the movable contact on the path of this contact with respect to the starting position—relay RM83–1011–25–1012.

5. Conclusions On the basis of the calculations carried out, the following theoretical values of the electrodynamic force were determined, with the corresponding moment of the relay contact opening time. These values are:

- 85.1 cN for the RM83–1011–25–1012 relay, which is 133% of the previously determined closing force, - 122.1 cN for the RM85–2011–35–1012 relay, which is 72.9% of the previously determined closing force. Energies 2019, 12, 3926 11 of 13

The relative error related to the closing force value is plus 33% for the model RM83–1011–25–1012, and minus 27.1% for RM85–2011–35–1012. On the basis of the results obtained, the following factors should be taken into account:

- relays are characterized by different construction of the drive coil, - the force transmitting component of the drive is located at different heights of the current path; in the RM83–1011–25–1012 relay, it is below the contact, and in RM85–2011–35–1012 it is at the top, - current paths have different lengths, widths, and densities, which affects their mechanical parameters, and in particular their elasticity, - the formulas used to calculate the forces are simplified.

Despite the above-mentioned restrictions, it can be assumed that an error of 30% is acceptable with this type of estimated calculation. Thus, it can be considered that it is possible to determine approximately the value of the force and thus the instantaneous value of the current at which an electrodynamic contact bounce may occur. The opening of contacts in the real system occurred at current value of 1000 A in the RM83–1011–25–1012 model and at 1080 A in RM85–2011–35–1012. These values are similar, but due to the significant differences in the geometry of the contact system, they occur at different values of the electrodynamic force. The presented results may be used by relay manufacturers to determine the peak current value which a specified relay model can conduct uninterruptedly under fault conditions. This may result in prolonging relay life expectancy by proposing a protection device (e.g., a fuse) that can limit the maximum value of fault current. Further studies may focus on other types of relays, with particular emphasis on different contact materials, and with a more accurate modeling of contact current paths. However, the new results should lead to a simplification of calculations that will allow engineers to use these studies in their work.

Author Contributions: Section1 was prepared by A.K. and G.D. Section2 was prepared by A.K., G.D., and K.N. Section3 was prepared by A.K. and G.D. Section4 was prepared by A.K., G.D., and J.J. Section5 was prepared by A.K. and G.D. Conclusions were prepared jointly by all the authors. Funding: This research was funded by the Ministry of Science and Higher Education, grant number 04/41/SBAD/4408. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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