Mechanical Products, a manufacturer of High Quality Marine Circuit Breakers will be exhibiting at the IBEX - 2014 Marine Trade Show, in Tampa, Florida

September 30 through October 2, 2014

See all our NEW Product Introductions

Series 12 - Series 15 - Series 17 Circuit Breakers

Mechanical Products Company, 1112 N. Garfield Street, Lombard, Illinois 60148

Phone:  630-953-4100 -- Email:  helpme@mechprod.com

Visit our website at www.mechprod.com

NEW 17 SERIES THERMAL

CIRCUIT BREAKERS

Standard designs, New Side-By-Side Surface and Easy Access 90^o Panel Mount

Available in 25 to 200 Amp Ratings

Mechanical Products (MP) announces the release of the Series 17, which is designed for industrial transportation and vehicle accessory manufacturers to include Agricultural, Construction, Marine, Bus, Emergency Vehicles, Automotive Lifts, Battery Chargers, Recreational Vehicles and Trucks.  The Series 17, manufactured in the U.S.A., is a main or branch circuit breaker used in accessory or auxiliary direct circuit (DC) electrical systems operating in harsh environments to provide protection in the event of overload and, or short circuit interruptions.  The Series 17 is offered in 25 to 200 amps and is specifically designed with features including new mounting configurations and termination styles.  The Series 17 is available in the second quarter of 2014 through MP’s authorized distribution partners.

The Series 17 offers end users and designers improved access to wiring and operation, corrosion resistant studs and hardware, superior moisture sealing, a variety of mounting options, higher amperage ratings, and potential use of bus bars while enclosed in a durable, sealed thermoplastic housing.  The Series 17 is compatible to existing mounting profiles while offering new features and mounting styles that allow for next generation designs. 

The MP Series 17 offers NEW Side by Side Surface and Easy Access 90^o Panel Mount designs, in addition to standard mounting profiles.  Surface Mount configurations are available in 1/4” and 3/8” heavy duty stainless steel terminal studs.  Panel Mount units are available with 1/4” brass, nickel plated terminal studs.  All are available in 25 to 200 amp ratings with stainless steel terminal sems nuts as an option.  Priced competitively, these high quality breakers, commonly known as High Amp circuit breakers or Hi Amp circuit breakers, are assembled right here in the USA, with minimal lead time required.

MP has been a leading supplier of thermal circuit protection since 1943.  MP circuit breakers are used in thousands of commercial and industrial applications ranging from medical equipment, appliances, lighting, and communication devices, to recreational and off road vehicles/equipment, and electrical protection devices.  MP has been management owned and operated since 1998, is headquartered in Lombard, Illinois and maintains manufacturing capabilities in the US and overseas.

For additional information on these and other high quality MP thermal circuit protection devices, visit Mechanical Products at www.mechprod.com.

Mechanical Products, a manufacturer of High Quality Circuit Protection Devices will be exhibiting at the CONEXPO/CONAGG SHOW,  in Las Vegas

March 4 -8, 2014

See all of our New Product Introductions

Mechanical Products, 1112 Garfield Street, Lombard, Illinois 60148

Phone:  630-953-4100 -- Email: helpme@mechprod.com

Visit our Website at www.mechprod.com

MECHANICAL PRODUCTS UL1077 SERIES 12 THERMAL CIRCUIT BREAKER

THE SERIES 12 PUSH-TO-RESET 

Available in ratings from 3 to 20 Amps, the Series 12 offers a very economical, compact design in single pole circuit protection.  The Series 12 Thermal Circuit Breakers have a rated voltage of 125/250VAC, 50 VDC with an Interrupt Capacity of 1000 A and a Dielectric Strength of 1500 VAC.  All are ROHS Compliant and UL1077 approved, with many amp ratings having CSA, CCC and VDE approvals as well.

 The MP 12 Series is designed for various applications: Marine, Household Appliances, Power Strips, Audio Visual Equipment, and more.   Various threaded and snap-in bushings, along with multiple Quick Connect terminal styles are available.   The 12 Series thermal circuit breakers are the choice where space and price are vital to the application.    For additional information on these and other high quality MP thermal circuit protection devices, visit Mechanical Products at www.mechprod.com

MP has been a leading supplier of thermal circuit protection since 1943.  MP circuit breakers are used in thousands of commercial and industrial applications ranging from medical equipment, appliances, lighting and communication devices, to recreational and off road vehicles/equipment, and electrical protection devices.  MP has been management owned and operated since 1998, is headquartered in Lombard, Illinois and maintains manufacturing capabilities in the US and overseas. 

We show in Figure 5.15a the complete steady-state DC solution for a flat arc heat flux potential with arc current I = 10i_o.

 In Figure 5.15A we also show a simple one term approximation solution  

Where the mid-plasma space magnitude S_m is given by the exact value (See Equation 5.32)

As is evident, this one term solution is an excellent approximation for the exact solution, given by (5.13) and (5.21) for this relatively high level of current drive.

Now consider the low current drive exact, and approximate solution for I = 0.1i_o given in Figure 5.15b.  Here we see that the one term approximate solution overestimates the plasma region width by a factor of

But when considered as a fraction of the total interwall space this overestimate is only 14%.

Figure 5.16 illustrates a summary comparison of the exact and approximate solutions for the plasma region halfwidth as a function of plasma steady-state current.  The worst case overestimate is seen to occur near the i/i_o = 0.1 drive point.  And here, as stated above, it is only a 14% overestimate.  The approximate solution for the heat flux potential given by Equations 5.33 and 5.34 is thus seen to be a “safe” or conservative estimate for the spatial variation of the heat flux potential of the actual flat arc.  We will use this one term approximation as the basis for a simplified dynamic arc model.

The one term transient solution for a step driven change in the heat-flux potential is taken from (5.30).

where the initial state magnitude S_mo and the final state magnitude S_mf are determined from the initial and final steady-state currents and (5.34).  The single arc thermal time constant τ is given by

The transient value of the plasma region halfwidth x_i is the x_i root of

which, in closed form, is

The transient current electric field relationship is given by

where

Performance Equations 5.35 through 5.40 are ideally suited for numerical analysis since they are based on stepwise change which, in an incremental sense, is the basis for all numerical solution techniques.  For example, assume that a flat arc is driven by a sinusoidal current source.  We approximate the continuous drive current by a stepped, discrete, staircase current, such as that shown in Figure 5.17. 

At the end of each step we solve for the resultant new electric field E(t) and plasma region halfwidth x_i using (5.35), (5.38), (5.39) and (5.40).  We then reassign these values as initial values for the next time step and repeat the solution process.  Typical results are shown in Figures 5.18 through 5.20 for ratios of arc thermal time constant τ to drive frequency period T, τ/T = 1.0, 0.1 and 0.01.

In these current driven results we note particularly the collapse of the arc, as indicated by the halfwidth x_i, as the current goes through a zero crossing.  For a given drive frequency period T, we see that the arc collapse tends to follow the current zero crossing very closely for “fast” time constant arcs (i.e. τ<<T).  But for “slow” time constant arcs (i.e. when τ is comparable to T), the arc collapse is incomplete and lags behind the current zero crossing.

In terms of practical circuit breaker design, we desire fast time constant arcs.  Fast arcs will fully collapse at a current zero crossing and thus not be subject to thermal reignition when the arc contact voltage redevelops.  From the arc thermal time constant expression (5.36), we see that in order to obtain a fast arc we need only confine the arc in narrow arc channels.  The arc time constant is seen to vary as the square of the channel width.  To confirm this theoretical prediction, Frind [5.11] conducted careful measurements of the time constants of flat arcs using the apparatus shown in Figure 5.21. 

The results of Frind’s measurements are shown in Figure 5.22. 

The dotted straight line in Figure 5.22 indicates adependency rather than the theoretical square relationship.  However in view of the inability to hold the channel walls at a constant temperature and the rough approximations that were made in deriving (5.36), the agreement can be considered to be quite satisfactory.  At very small channel widths, near 20 mils, the measured time constant were extremely fast, approximately 0.1 μsec.  This encouraging result alone, not withstanding our theory, suggests the advisability of arc confinement in cool arc channels.  

A contact arc in a circuit breaker is an extremely complex electro-thermo-hydro-dynamic process and that we never fully mathematically describe the detailed physics of an arc.  Our goal, here, is to develop an approximate arc model such that we can treat an arc as a circuit element, and analyze electric circuits containing arcs.

During normal circuit breaker operation, the arc, when present, is in a continual state of change.  It is dynamically lengthened by parting contacts and by electromagnetic forces which push it away from its original trajectory.  It is dynamically heated by its current.  It is dynamically cooled by its environment and, perhaps, by other auxiliary means (forced gas flow, cool containment walls, etc.).  And, dependent on the net rate of energy absorption (heating minus cooling), it dynamically grows in cross-sectional area.

As the arc changes physically and thermally, it also changes electrically.  A change in the electrical characteristics of the arc, in turn, changes the amount of through current that the external electrical circuit can supply.  Therefore, an engineering description (which is all that we seek) of a circuit breaker arc must include a dynamic description of the breaker-electrical network interaction.  Now, we will discuss the components of an electrical arc:  Cathodes, Anodes and Plasma Columns.

The two arc electrodes are referred to as the cathode and the anode.  Electrons are injected into the arc by the cathode at a rate proportional to the arc current.  Arc electrons are collected by the anode at the same rate, since the current must be continuous.  The region between the cathode and the anode is divided into three sub-regions:  the cathode fall region, the plasma column (sometimes referred to as the positive column), and the anode fall region.

A typical voltage profile along the path of a “short” arc is shown in Figure 5.7.

By short, we mean that the voltage drop across the plasma column is small in comparison to the combined voltage drops across the cathode and anode fall regions.  Typically, this will occur when the physical length of the plasma column is small.  The cathode and anode fall regions are the transition regions between the metallic cathode and anode electrodes and the gaseous plasma column.  The magnitudes of the electric fields within the cathode and the anode fall regions are much higher than the magnitudes of the fields within the metallic cathode and anode.  And, much higher than the magnitude of the field within the plasma region.  Higher electric fields are, by definition,  higher voltage drops per unit distance, and thus the use of the term “fall,” as in “voltage fall” in the descriptions of the cathode and anode transition regions.

The voltage drops or “falls” within the cathode and anode fall regions are strong functions of the materials used as cathode and anode electrodes, but relatively weak functions of the current level within the arc.  The energy required to completely remove an electron from the surface of a material body is defined as the “work function” of that material.  Expressed as an equivalent voltage (energy divided by the charge of one electron), the vacuum work functions of most metallic elements are approximately 4 to 5 volts.  The detailed physics of electron emission and collection in cathode and anode regions under arc conditions is of such complexity that only a limited number of low current, simplified cases have been theoretically analyzed by researchers.  For our purposes, it is sufficient to say that the cathode and anode voltage drops are “of the order” of the cathode and anode work functions.

The actual surface area of the cathode electron emission and anode electron collection varies with the total arc current.  The current densities within these active areas, however, are extremely large, particularly so for the cathode.  Current densities exceeding 10⁶ A/cm², and surface temperatures exceeding 4000^oK have been postulated by Lee for cathode “spots”.  At these current densities and temperature electron emission is a combination of thermionic and field emission.  Electrons with enough thermal energy can thermionically escape the surface of the cathode but, due to the large concentration of positive ions in front of the cathode, a high surface electric field is also present.   It enables surface electrons to tunnel through a reduced surface work function energy barrier, and be accelerated away or “emitted” by field emission. 

Even higher surface “spot” temperatures can be present at the anode.  When electrons leave the cathode, they take energy with them.  Therefore, the cathode is actually cooled by their exit (On a net basis, however, the cathode is heated by the I²R heating within the cathode spot and the energy of incoming positive ions).  When electrons arrive at the anode, they dump their energy into the anode surface and heat it up (in addition to the anode I²R heating).

Dependent on the actual surface spot temperatures, anode and cathode evaporated surface material will transfer from hotter to cooler surfaces if the gap is sufficiently small (as in a breaker at initial contact parting).  Some investigators have shown that material transfer can be a function of peak arc current, where the peak surface temperature transfers from cathode to anode as the peak arc current increases beyond a certain threshold.

The plasma column in an arc is composed of a partially ionized gas.  Gas molecules are “ionized” when neutral gas molecules separate into negatively charged free electrons and positively charged ions.  This occurs by a number of different processes:  high electric field electron and positive-ion collisions; absorption of radiation; and thermal ionization, ionization by means of collisions with high temperature (i.e. high energy) electrons, positive ions and neutral molecules.  All of these processes occur in an arc; the relative importance of each is dependent on location within the plasma column and the strength of the arc.  The energy input to the plasma column is the Joule heating due to mobile current carriers.

Since there is a large difference between the mass of an electron and the mass of a positive ion, there is a large difference between the response of an electron and a positive ion to an applied electric field.  By far, the majority of the current within the plasma column of an arc is carried by electrons.  Therefore, the initial energy transfer to the plasma is to the electron gas within the plasma.  But very rapidly, by means of collisions, this energy is shared with the plasma positive ions and the background neutral molecules.  Thus, in time intervals of interest to the circuit breaker design engineer, and to a very good degree of approximation, the plasma is in a state of thermal equilibrium.  That is, all components (electrons, ions and neutral molecules) within a spatial region are at the same temperature.

At thermal equilibrium conditions, the rate of ionization within a particular differential region is balanced by an equal rate of ion-electron recombination.  Also, the net concentrations or densities of electrons and positive ions are approximately equal and monotonically dependent on the plasma temperature.

The conductivity of the plasma region in the arc is a strong function of the plasma temperature.  The higher the temperature, the higher the level of thermal ionization and carrier concentration.  The more carriers, the less the value of electric field needed to support a given level of current density (i.e. the conductivity increases).  This positive feedback effect – more current → higher heating → more carriers → more current for a given level of external excitation – partially accounts for the steady-state negative differential resistance of an arc.

Another contributor to the steady-state negative differential resistance of an arc is the cross-sectional spreading of the plasma column at higher current levels.  As the temperature of the active (ionized) plasma column increases, so too does the temperature of the gas surrounding the plasma column due to thermal conduction (and perhaps convection and radiation).  At high enough temperatures above a threshold temperature, the immediate surrounding gas will also undergo thermal ionization.  There will then be additional carriers present to carry the arc current, increasing further the net arc conductivity.

A typical static or steady-state voltage current characteristic of an arc is given in Figure 5.8.

In general, for a given level of arc current, the arc voltage is proportional to the arc length.  But for a given arc length, higher arc currents result in lower arc voltage drops due to the static negative differential resistance characteristic.

A common arc control scheme used in many circuit breaker designs, (i.e. a method used to increase the total arc voltage across the main contacts), is to force the arc into an arc baffle or splitter structure.  A typical arc baffle structure in a small circuit breaker is shown in Figure 5.9.

Arc baffles act to break a single arc into several shorter arcs connected in series.  The anode and cathode voltage drops of these multiple arcs then add and comprise a major portion of the total device – arc voltage.  The movement of the arc into the baffle is initiated by the magnetic Lorentz force, or J x B force, due to the arc current itself (J is the arc current density and B is the magnetic flux density due to the current).  This magnetic Lorentz force is the same force which tends to repel the contact faces apart due to constriction current flow paths to minute contact points.  The movement of the arc, due to this self magnetic force, is referred to as magnetic blow-out of the arc.

Magnetic blow-out is also used to force arc movement onto arc “runners”, which are attached to the contact structures (see Figure 5.10).

Use of arc runners preserves the more expensive silver alloy contact material by moving the cathode/anode “feet” of the arc off the contacts, and onto the less expensive runner material.  In addition, the arc runners present a longer arc path for the arc to traverse, and can act as the transfer medium between the inter-contact region and any arc baffle or arc chamber region.  Arc runners can be enhanced with the addition of staged electromagnetic drive coils to even further strengthen the magnetic blow-out force along the runner length. (see Figure 5.11).

In circuit breaker design and analysis the static characteristics of the arc are certainly of interest, but, it is the dynamic characteristics of the arc that are of prime concern.  The arc carries the circuit current until an interruption will be successful, that is, whether or not the arc will reignite as the voltage across the breaker contacts rises, is a question that can only be answered by a study of the arc dynamic behavior.

In a typical circuit breaker, upon release of the restraining latch the movable-contact arm will begin to accelerate.  The dynamic behavior of the movable arm is determined by the effective mass of the arm, the strength and preloading of the drive spring, the magnitude of the current through the contacts, frictional forces on the arm hinge and arm travel, and the speed and detailed action of the latch release mechanism.

Since the current flow is constricted and forced to flow in converging paths to contact spots on both bulk contact faces, as shown in Figure 5.1, there will be components of current flow which are anti-parallel to each other within the adjoining contacts. 

These anti-parallel components form single-turn “loop” inductors.  These inductors tend to expand in an effort to minimize their self-inductance, and thus minimize their stored magnetic energy.  The magnetic force which acts to expand the current loop inductors is then a net repulsion force between the two bulk contacts.  Holm [5.1], Snowdon [5.2] and a number of others,

have shown that the repulsion force due to the current constriction in a single contact spot is approximately given by

where i is the magnitude of the instantaneous current through the contact spot, a is the effective radius of the single contact spot, and A is the effective radius of the total bulk contact surface area.  This force of electromagnetic repulsion adds to any mechanical forces which tend to separate the contacts.  By itself, it is generally small in comparison to the movable contact spring force, except under high current conditions.  At high currents the repulsion force (due to the current squared term in Equation 5.3) can become significant, even dominant, in certain structures [5.3].

This repulsion force has even been utilized in the construction of a mechanical AC fault current limiter [5.3].  In this device, movable contact arms, are restrained together by a spring mechanism (see Figure 5.2a).

Under very high fault current levels the electromagnetic repulsion between the contact arms overcomes the restraining springs and forces the contacts apart.  Figure 5.2b illustrates that the resulting arcis longer than that needed in a normal AC breaker.  It thus has a very high arc voltage, which “bucks” the fault current drive voltage, and limits the peak fault current to values less than that which would flow without the arc voltage in series with the faulted circuit.

The mechanical dynamics of the parting of circuit breaker contacts are very similar to the dynamics of the armature of a magnetic circuit breaker.  Barkan [Equations 5.4, 5.5 and 5.6] has presented detailed studies of contact dynamics for large, electric utility type breakers.  The theory of small light duty breakers, however, is very similar. 

Figure 5.3 shows a simplified contact mechanism.

This figure is an adaptation of Barkan’s Figure 2 given in reference [5.4].  Barkan obtained closed form solutions for the system shown in Figure 5.3 for the following situations:  (a) ideal system, lumped concentrated masses, no drag forces, negligible electromagnetic force, and instantaneous latch release;  (b) as in (a) but with a finite latch release time;  (c) as in (a) but with viscous drag proportional to the square of the moving contact velocity; (d) as in (a) but with distributed but rigid contact linkages; and (e) as in (a) but with distributed flexible contact linkages.  We will restrict our interest to only cases (a) and (b).

For an ideal system, case (a), we have for the equation of motion for the movable contact

where m is the equivalent mass of the movable contact (including the contact arm), x is the contact position measured from complete contact closure, k is the drive spring constant, and x_s is an equivalent position which is proportional to the initial force on the contact immediately after latch release.  If the latch releases instantaneously at time = 0, we have for the solutions of (5.4)

where ω is the angular velocity  v(t) is the contact velocity, x_o is the initial contact position ( = 0 at start) and v_o is the initial contact velocity ( = 0 at start).

If the latch does not release the contact instantaneously then the initial forcing term in (5.4) must be modified.  From strain gauge measurements during latch release Barkan [5.4] found that a latch restraining force drops off approximately as a cubic time function.  Thus, the equation of motion becomes

where T is the time required for the latch to completely release the contact arm.  The solutions to (5.7), valid for 0<t<T and zero initial position and velocity are given by

and

For t > T we can use (5.6) and (5.7), with initial conditions given by (5.8) and (5.9) evaluated at t=T, and with time t given by t—T.

We plot the contact position x, normalized to the equivalent initial force position X_s, for both instantaneous and non-instantaneous latch release in Figure5.4.

In this plot we have assumed that the non-instantaneous release is completed in two tenths of the spring-mass cycle time, that is, ωT/2π = 0.2.  The corresponding contact velocity plots for these cases normalized to ωx_s, are given in Figure 5.5 the movable contact “average” velocity v_av

Also normalized to ωx_s.  Typical measured values for average velocities for small circuit breaker structures are 20-300 cm/sec.

If the movable contact is not on a spring loaded arm, but rather on a flexible snapaction bi-metal structure, the simple equation of motion, Equation 5.4, does not apply.  The actual dynamics of a snapping structure are quite complex, but the end result, a co-sinusoidal (in time) like movement is quite similar to that of a simple spring loaded arm.

Figure 5.6 is a plot of the measured displacement of a contact on a snap-action low power toggle switch [5.7].  The solid line is the measured result taken from a high speed film.  The dashed line is an empirical fit of the data to an equation of the form

Where x_ss is the steady state separation (1.1mm), α= 208 sec^-1, n = 1.45 and ω is the radian mechanical frequency.  For this structure the average velocity at x =͂ 1.0 mm is seen to be

The device current in thermal and magnetic circuit breakers passes through both a detection mechanism and a set (or sets) of electrical contacts.  The contacts are generally spring loaded and latch restrained.  When triggered by the overcurrent detection mechanism, the latch will release a movable contact arm.  The arm then withdraws from the fixed contact at a rate determined by spring loading and electromagnetic forces due to the contact current.

When the contacts are closed, or “latched”, current flows between the contacts only at very small physical contact points, or asperities, due to surface roughness on the bulk contact faces.  The actual area of electrical contact is only a small fraction, less than 1%, of the apparent area of the bulk contact surface (see Figure 5.1).

Current flowing in the contact bulk regions is constricted at these contact points, much like fluid flowing through a pipe with an insert containing very small holes.  The extra electrical resistance due to this current restriction is referred to as the spreading or constrictive resistance of the contact.  It can be shown [5.1] that the constriction resistance on each side of an individual contact “spot” is given by

where ϱ_r is the bulk resistivity of the contact material, and a is the effective radius of the asperity or actual contact spot area.  If the contacts are constructed of two different materials, with respective bulk resistivities  ϱ_r1 and ϱ_r2, the total series spreading resistance due to current constriction in both contacts is

Normally, contacts are fabricated with identical materials and, normally, actual contact is made at N number of spots on the contact surfaces.  The net constriction resistance for the contacts is then the parallel combination of all the individual contact values, or

The effective radius of each contact spot, a_i, is dependent on the preparation of the bulk contact surface, the normal forces applied to the contacts, the “hardness” of the contact material (i.e will each contact asperity be under elastic or plastic deformation?), and the temperature at the contact interface.

In addition to constrictive resistance at contact asperities, there may be a resistance due to a thin film or layer of material oxide between contacting asperities.  Electrons either tunnel quantum mechanically through this thin film, or break through the film by a process Holm refers to as “fritting” [5.1].  The film resistance is between the constriction resistances of individual asperities, so the net “contact” resistance would be a modification of Equation (5.1):

where R_fi is the film resistance at asperity i.

In practice there is no attempt to determine contributions to R_contact due to individual contact spots.  The net excess resistance of the contact system, beyond the bulk resistances of the two contacting bodies, is simply referred to as the contact resistance.  The voltage drop across this resistance is commonly referred to as the contact drop.  In most cases this contact drop does not exceed .1-.2 volts.  Contact drops tend to saturate at these levels since, as the magnitude of the current rises, the asperity interface temperature rises softening the asperity material.  The softer material spreads out and increases the actual asperity contact area, thus lowering the contact resistance.

When two bulk metallic contacts which are carrying an electrical current separate, the last point or points of physical and electrical contact will be at one or more (if more than one, a small number) constriction asperity spots.  The current density at these points will be very large, easily enough to melt the asperity material and form molten bridges between the two contacts.  These bridges are then heated and stretched to the point that they vaporize.  The process initiates the arc between the two contacts.  If the contacts are not metallic, such as carbon, the asperity points do not melt, but rather arc immediately upon physical separation.  

In comparison, to the detection time response of thermal circuit breakers, we can classify the detection time response of magnetic circuit breakers as “fast”.  In many cases, magnetic breakers are in fact “too fast”, and are subject to nuisance trips due to transient inrush currents.  Whereas thermal breakers can “ride through” transient inrush currents by means of their relatively long thermal time constants, magnetic breakers tend to respond to the instantaneous magnitudes of inrush currents due to their relatively low trip energy requirements once the threshold current has been exceeded.

Over the years magnetic circuit breaker designers have developed several schemes to delay the detection response to transient inrush currents.  In essence, the goal is to mimic the dual element “slow blow” fuse structure.  The ideal “dual element” magnetic breaker would have two detection mechanisms in series:  one slow, low threshold current mechanism to ride through inrush currents; and one fast, high threshold current mechanism to quickly respond to true, high level fault currents.  The detection time current response characteristic would look much like the dual-element fuse characteristic shown in Figure 3.9.

A true, almost ideal dual-element characteristic can be achieved in a magnetic circuit breaker through use of an inertial core-delay tube.  This clever device is shown in Figure 4.13a.  The drive coil core is a hollow tube which contains a moveable, but spring restrained core ferromagnetic slug.  At low coil currents the slug is spring restrained in a recessed position, x = 0.

At coil currents above a certain operating current threshold, I_th1, the attractive magnetic force (solenoid effect) of the coil is enough to overcome the spring force and to initiate movement of the slug.  The slug moves toward the coil center and begins to fill the hollow coil core with ferromagnetic material.  As the coil core fills with magnetic material the core section reluctance falls to lower values, enabling the total magnetic flux produced by the coil to increase.  When the core slug reaches a certain point in the core section, dependent on the level of drive coil current, the core reluctance is decreased to a value low enough that the magnitude of the armature gap flux is sufficient to cause the armature to breakaway from its stopped position.  The breaker then trips as described previously.

The dynamics of the slug movement can be further slowed by the addition of a viscous fluid within the hollow core section.

If the initial core current is high enough – above a second threshold level I_th2 – the gap flux will be strong enough to trip the armature without the need of flux enhancement by slug movement through the core section.  The dynamics of this high-level trip are then the fast dynamics of a pure, simple magnetic breaker, unaffected by the flow dynamics of the core slug mechanism.

In terms of a magnetic equivalent circuit, the moveable-core dual element magnetic circuit breaker can be described as shown in Figure 4.13b.  The core path reluctance R_c is now a function of the slug displacement from its restrained x = 0 position.  It is a maximum when the slug is at x = 0, and a minimum when the slug has advanced to its core-filled position at x = x_max.

The equation of motion for the slug is given by

where M_s is the mass of the core slug, F_m is the force of the magnetic attraction on the slug, D is the coefficient of friction due to the addition of a viscous fluid environment, ξ is the spring constant of the slug restraint spring, and x_o is an equivalent displacement representing the initial restraining force of the spring.  The force of magnetic attraction F_m will be proportional to the core flux ф squared (just as the armature attractive torque T_m is proportional to the gap flux ф_g squared).  A complete solution to the dynamics of the total device would then require a simultaneous solution of Equations 4.1 and 4.18, and the magnetic circuit of Figure 4.13b.

We will not attempt to solve this system of equations here.  We will only note that the “slow” behavior of the complete system is determined by the slug movement Equation 4.18; the “fast” behavior of the system is determined by the armature movement of Equation 4.1; and coupling between the two is determined by the magnetic circuit, Figure 4.13b.  The resultant combined detection time-device current characteristics are sketched in Figure 4.13c.

Other methods of desensitizing the response of magnetic breakers to inrush currents include the tailoring of the core flux reluctance path as a function of the core slug position and the addition of an inertial device, similar to a flywheel, to the armature structure.

Flux can be “bled-off” from the core-gap-armature path through use of flux shunts (sometimes referred to as flux busters) or through the use of an elongated core path which is not covered by the drive coil.  In either situation a major portion of the core flux produced by the drive coil tends not to flow  through the core-armature gap until a movable internal core slug (similar to the one in Figure 4.13a) has reached its fully advanced position.  Rather, this flux “bleeds” into leakage paths, producing no useful armature torque.  However, when the core slug is at its most advanced position these leakage paths are effectively “shorted” and the major portion of the core flux crosses the core armature gap.  Magnetic breakers with these tailored core flux paths have an enhanced, true, dual-element response characteristic.

Extra inertial mass when added to the armature mechanism increases the total effective armature moment of inertia, or equivalently, the total effective armature characteristic time.  This addition does not change the sensitivity of the detection mechanism; it only slows its response.  It slows it, however, across the board.  It does not create the desired dual-element response; rather it simply burdens the armature with additional inertia, enabling it to ride through the transient inrush currents by means of sheer sluggishness.

The production of magnetic flux is instantaneously proportional to the coil current i.  Strictly speaking, this is only true for magnetic circuits which do not contain any electrically conductive magnetic flux paths.  When the level of magnetic flux changes (i.e. is raised or lowered) in a path/medium which can also conduct electric current, such as iron, there will arise, by Faraday’s Law, circulating eddy currents.

(Faraday’s Law states that the voltage induced in any closed path in space is proportional to the time rate of change of the net magnetic flux which flows through the closed path cross-sectional area.  If the closed path is in an electrically conducting medium, there will then be a circulating current around that closed path proportional to the generated voltage and the electrical conductivity of the medium).

These eddy currents will, in turn, produce reaction magnetic flux which will tend to cancel out a portion of, or all of, the original excitation flux.  The direction of eddy current flow can be deduced by the “ right hand rule” and by the requirement that the reaction magnetic flux produced by the eddy currents must flow in the opposite direction to the flow of excitation flux.  Eddy current production in a simple cylindrical path in iron is illustrated in Figure 4.11.

As a result of eddy currents, flux cannot be instantaneously produced in conducting mediums.  There will always be a time “lag” between the flux flow and the exciting mmf.  A simple magnetic equivalent circuit representation of this time-delay effect can be made by including “inductive” elements in series with reluctance elements which represent electrically conductive paths.  For example, the structure shown in Figure 4.4 has two magnetic paths which are made up of ferromagnetic material: the core path and the armature path.

We include eddy current effects in these two paths by placing inductive elements in series with the reluctive elements which represent these paths.  This modified circuit is shown in Figure 4.12.

The value of the inductive element for each magnetic path in a conducting medium is a function of the cross-sectional geometry of the path, the electrical conductivity of the material, and the effective length of the path.  In the simple cylindrical structure of Figure 4.11, it can be easily shown that the equivalent eddy current inductance L_e is given by

where L is the axial length of the conductor and ϱ_r is the electrical resistivity of the material.  The magnetic reluctance of this path is

where µ_m is the magnetic permeability of the material , A is the cross-sectional area = πr², and r is the cylinder radius.  The magnetic time constant τ_e of this cylindrical path is then

As typical values, let the material be a 1.5mm radius rod of magnetic iron with µ_m=˜ 2000µ_o and ϱ_r = 10^-5Ω-cm.  Thus,

If such a rod is used as a magnetic core in a magnetic circuit breaker, and if we wish to accurately predict the breaker time response over time intervals of this magnitude, we must then necessarily include eddy current effects in our calculations.  We can no longer use the simple results for the gap flux calculated from the static circuit of Figure 4.4.  Rather, we must use the dynamic circuit of Figure 4.12.  Results such as those given in Figures 4.9 and 4.10, calculated using static equivalent magnetic circuits, are optimistic at predicted operating time intervals equal to or less than the eddy current time constants of the structure elements.

For a rectangular cross-section magnetic path with side length ratio k, the equivalent eddy current inductance can be shown to be equal to

The path lengths of eddy currents in a rectangular cross-section magnetic conductor are longer than those in circular cross-section magnetic conductor.  Thus, for equal electrical conductivities, the effective eddy current inductance in a rectangular conductor is lower.

To mitigate eddy current effects in magnetic materials, we see from Equations 4.16 and 4.17, that we should construct magnetic cores with

1)     Magnetic irons (steels) with high resistivity values, (i.e. silicon steels). And

2)     Very thin sheets (i.e. laminations) of magnetic steels stacked in the thin direction, and oriented such that the thin direction is perpendicular to the flow of magnetic flux.

The cost of such construction is only justified for devices which must operate at very high speeds (i.e. operating periods of the order of milliseconds).