Fundamental Principle of Dynamics Applied to Rail

7/29/2019 Fundamental Principle of Dynamics Applied to Rail

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Fundamental principle of dynamics applied

to rail

(Assuming a rigid convoy reduced to its center of gravity)

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The fundamental principle of dynamics applied to the center of gravity ofa rigid convoyTake a convoy of a motor vehicle called "locomotive" and a series of towed vehicle.Tosimplify the situation, we consider that the entire convoy is rigid and can be likened to a

point in the center of gravity of the same mass. The latter is obliged to follow thetrajectory imposed by the sloping tread and change of direction.Each vehicle has its own masses.The convoy is largely made up of rotatingmasses such as axles, and a lesser portion of engines and transmissions, thetotal mass of the train is not the same as the convoy is stopped, moving or

halted.The resulting forces applied in sets in the center of gravity are two in number(Figure 1):- The tensile strengthFt, developed by the "engine" of the convoy.It isdirected in the direction of travel of the train and also required to thedevelopment of the tread.- The restraining forceFr, developed by the "towed" the convoy.It restrictedby the tread, and directed in the opposite direction to the convoy.
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We can apply the center of gravity of the convoy global mass m, the fundamental

principle of dynamics as an "axis trajectory"

is the acceleration of the train, speed derivative, itself derived from theposition of the train on a given route.(This is why we talk about the behaviorof second order)

There are two ways the convoy: Accelerateand DecelerateTo accelerate the convoy must 0 is Ft> Fr.The motor has to work at least greater than the resistance force to theadvancement of the trailer.To decelerate the train must > 0, let Ft - Fr


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The previous equation, we deduce:

This view epitomizes the role of "locomotive": Establishing, at all times a balancebetween traction force Ft and the resultant force Fr, Fr sum and quantity .Theacceleration induces resistance to the advancement of the convoy.Finally, the dynamic railway is divided into two main entities:- The forces generated by the progress of the convoy and opposing it in most

situations,- The force generated by the driving section of the convoy.

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This information should in no way be used as a teaching and / or industrial, inthis case please consult the relevant literature on the topic.THANKS please ask my permission if you want to use the sketch of this pagefor your website.Copyright belph80001 / 2005 / All Rights Reserved / Reproduction andduplication of prohibited commercial support.


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Running resistance of the train

Back to overviewBack to previous pageWe can divide by 4, the forces due to towing:- The effort acceleration orinertial- The force gradient,- Efforts to takeoff (when the convoy leaves immobility)- Efforts during walking.Inertial forceThe amount represents the largest share in the effort generated by theconvoy.Plus a driving force is provided, plus the train accelerates, but thisincrease in speed is directly influenced by .The effort inertial precludes the cause that creates:It is opposed to the tensile force Ft, when the latter is able to increase thespeed.On the contrary, ifFt is allowed to be less than Fr, or a braking force isapplied Ft = 0, oppose and tend to keep the convoy at its own speed:We have indeed


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Fd = Mg sin with track gradient and g = 9.8 m.s -In level = 0 it has no action.Ramp, > 0 it opposes the tensile strength Ft.Sloping


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speed lines can afford profile by mountain and valleyswith slopes of about 30mm / m.Efforts takeoff (when the convoy leaves immobility)The rail is made of a spring steel.Wheels mounted on the axles have a more rigidsteel.Setting wheel - rail contact involves a deformation of the rail.The wheel 's crashes in railsteel resulting in a contact surface of the elliptical type, said surface HERTZ.(Fig.4).The dimensions of the ellipse are much larger than the diameter employee and axleloadare important.In some cases, it is possible shear rail.

The wheels face off all dents to be set in motion. It is therefore an effort to overcome offthe convoy.The vehicle's parking rail leads to increase the surface area over time HERTZ.Moreparking time is longer, the resistive effort will be important: The critical parameters of effort off are those couplings and slope.This bringsus to momentarily forget the hypothesis convoy "rigid" for one (fig. 5), realistic,a set of each vehicle with their freedom of movement offered by the team andtamponade.


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In the ideal situation, the locomotive is brought off the train in a progressive manner,

trailer after trailer.The effort off contact wheel / rail remains constant over the life of thisone.It is not the same if the convoy starts in the presence of a gradient. When the convoystarts sloping couplers are more tense.

The locomotive must fly a larger number of

trailers at the same time.Efforts during walkingEfforts during operation can be divided into three distinct groups:- Efforts "static" zero degree, expressed as F = X,- Efforts "sticky" first degree, expressed as F = XV- Efforts "aerodynamic" the second level, expressed as F = X.V .Static forcesStatic forces are of various kinds:Force due to the wheel / rail contact and friction in the bearingsHERTZ surface is always present and creates a resistant force on the wheel in

motion.(Fig. 6) For the trailing, this movement results locally around the contact bydeformation in compression and in tension on the rail and the wheel located upstream

thereof.


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Let us add to this effort, the friction in the bearings and bearings in the axle

boxes.An empirical approximation was made by Davis, it is for two parameters x andy and a load axle to consider the holding force as:

Fp = with axle load and m (x, y) constantNote that as the axle load increases, this force is less important.Moreover, the application of shoe on wheels during braking is likely to increase frictionin the bearings.Effort cornering

A convoy enters a curve sees its resistance to increase promotion.This will beparticularly important that the curve will be a small radius.This is a directconsequence of lateral friction of the flanges on the rail heads and evensliding bogies, axles consisting of two parallel compelled to stay.This force isapplied to the entire convoy, and is expressed as:

Fc = with mean radius of curvature and K factorThe coefficient K is a function of the geometrical factors of the track, in particular

spacing and its coefficient of friction.


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Stress due to easementsThe calculation of the static force can be refined in the presence of passengercars.Some of them take advantage of the progress to power easements suchas lighting through a dynamo.Systems of forced ventilation can be used also

the movement of an axle.Efforts viscousThe viscous efforts are of three types:- Efforts friction of the side faces of the flanges of the rail,- Efforts resulting oscillatory movements of each of the bogies on the running surface,- Braking effort due to the use of shoe or brake disc. Its magnitude is likely to bedominant over other efforts.The role of these parameters in the dynamics is that of the first order, they are

expressed in the form F = XV. V is the speed of the convoy.On the energy front, thereis no question here but continuous leakage dissipation in the form of Joule loss.Note that the viscous stress has no effect at zero speed and whatever happens it

opposes the direction of movement.Aerodynamic forcesIt is the resistance of the air which is expressed F = Cx.V .Cd is the drag coefficient.The first vehicle of the convoy movement sees subjected to air flows which oppose thedirection of motion, rub against the side surfaces and generate turbulence in areas suchas spaces between hyphens trailers and space lower between the track and the chassis

boxes.A large number of parameters come into play in determining the Cx (Fig. 7):- Areas and perimeters of air penetration- Length of vehicles,- Hyphens between boxes,- Surface roughness,- Presence of elements such as pantographs.


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Configuration and the nature of the convoy importance in this type of effort acting on

second degree.As speed increases, the aerodynamic resistance increasessignificantly.The presence of the wind tunnel or strongly influences these parameters.The standard equation of the running resistanceIn conclusion, resistance to progress is an equation of the form:

X0, X1, X2 and M, the characteristic parameters towed convoy (Fig. 8).

AndKnowledge of the Y = X0 + + X1.V X2.V is obtained by measuring andcalculating aerodynamic.

Administration has thus a "catalog" of all rail vehicles circulated on thenetwork.Each vehicle by its configuration, its type, its equation will load thatcharacterizes it.Note that the locomotive is a full vehicle is no exception tothis rule: it also provides a resistive effort!


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This information should in no way be used as a teaching and / or industrial, inthis case please consult the relevant literature on the topic.
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Behavior and performance of the tractionmotor


We remain in the event of a convoy reduced to its center of gravity G.The locomotive of G generates a tensile forcedetermined by the traction ofthe drive part of the convoy.The latter two functions:- Converting potential energy(either thermal shape, or electrical form)into mechanical energy useful for the rim.- Adjust to demand, the importance ofuseful mechanical energy to the rim.Like any system transforming potential energy into mechanical energy, thetraction generates losses as heat and friction.

Also often asked to support the locomotive auxiliary purposesto ensure itsown operation and that of the convoy (ventilation, heating line), which is also aloss of useful energy.The driving ideal "to balance power"The ideal drive train has a power adjustable hope that remains invariant underspeed and time.This has three advantages:
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- The power setting is easy and action rustic perspective equipment,- The link between the traction force and speed of the convoy by Pu =FV allows for low speeds, a very important starting effort.This is a crucialrequirement for driving rail- This link makes the same force inversely proportional to the speed: This' swell suited to the conditions of adhesion railway (which will be discussedlater).Establish the energy balance of the drivetrain ideal (fig. 9):

withPu: mechanical power output, speaking: Pu = Ft.V, Ft is the tensileforce. V the speed of the train.Pa: auxiliary power,Pt: power loss transformations (mainly losses joules)Pe is the potential energy available, it is modulated by a coefficient k which isavailable at the one that controls the locomotive.

All at time t.

We Pu = Ft.V


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Where

The tensile force Ft is inversely proportional to the speed of the train.Atstartup, it is theoretically infinite.It strongly decreases according to theincrease of speed in the form of a hyperbola.(Fig. 10)

Note that the transformations and losses due to food easements have all their

importance in the generation of this force.In general, a locomotive mustwithstand whatever happens losses which it is subjected.Chart speed effortsTo understand the behavior of a locomotive, we face each of thesehyperbolas operating in the plan FV associated with a value ofk.This graph iscalled a diagram effort - speed.We noted a towed vehicle is characterized by its equation and therefore itsoperating curve, it is the same for each series of engine equipment which wecan associate a force-velocity diagram.In the ideal case, the diagram effort - speed corresponds to the intensitycontours powers.The real driving


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Unfortunately, a real motor can not simplify our model driving perfect. Here are thereasons:Dissociation diagram effort - speed and intensity contours - powersThe curves of engine speeds efforts can be hyperbolas "equilateral"having the law Pu= FV.The engine used has its own way to change depending on the speed:

An electric motor torque DC sees drop dramatically when a force against

electromotiveappears at its terminals.By heating, the internal resistancedrift and altersthe current flow itself limited by the effect ofmagnetic saturationof the windings.

An internal combustion engine connected to a gearbox heats and alters

the thermodynamic cycleas the speed increases.Engine performanceis found not inuniform.In both cases the characteristics FV overlap hyperbole balance power, ie the power

output obtained by the traction is not constant.(Fig. 11)

Fragility of the tractionThe drivetrain is fragile: Any solicitation led to alter its operation and


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irreversibly if it is too excessive.More power is required, the greater the heat will be great.If it becomes too large, the system is damaged.For electrical machinery, measuring the current flowing in the windings is

paramount.Assuming a traction motor current exceeds a limit of1500 A, hefinds himself in a critical situation where ventilation (natural or forced) nolonger provides cooling parts.Result, the engine has a limited lifespan toseveral minutes or even seconds.The setting of the first values ofk where thepower developed may become important should be limited in time.For thermal machines, the transmission includes a hydraulic part oftenproviding a speed reduction between inlet and outlet box.If the shiftbetweeninput and output is excessive warming worse parts.The same excessive speed driving parts leads to their deterioration.Therefore the actual drive usage limits both speed that provides stress.Design quality and robustness of the powertrain largely determines theselimits.In terms of tensile strength:- The effectiveness of the ventilation organs traction and conversion

- The resistance of materials to the heating due to current flow, fluid, orelectromagnetic radiation,- Reactivity steering the pulling force on the wheel / rail contact.(For adhesionproblems that we will discuss later).In terms of speed:- The ability of the traction to operate at a high speed without deterioratingmechanical or electromechanical- The stability of the suspension of the body,

- The holding of bogies on the track.Inertia of the establishment of the useful mechanical powerBetween the moment when we increase the parameter step (k) and when itgets the mechanical power output desired is a delay is not negligible.


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In the case of electrical machines, this period is relatively short.But for heatengines, this delay can reach half a minute or more depending on the capacityof the engine.This requires driving with anticipation for the desired power atthe right time.Some vehicle diesel engine does not have enough power at the moment ofdeparture of the convoy to provide both heating and vehicle travelers to setspeed.Therefore, momentarily, the heating line is cut.The traction rid of Pa,has a better performance in traction.

And a traction unit shall be sized in relation to the efforts and speed that isrequired to develop.The performance of the motorQuantifying the performance of the engine is essential to establish a servicewith a given type of train.(Fig. 12)Systems operations and powers associatedPosition at time t:The situation of the motor at time t is defined by the tensile force Ft (t) and thespeed V (t).Point [Ft (t), V (t)] being, close to the inertia, located on one ofthe curves associated with the notch gears efforts k.

We define the instantaneous poweras the useful power to the rimat theinstant t: Pu (t) = Ft (t). V (t)Under overload or uni scheduleThe motor is said to be overloadedwhen it reaches a temperature rise could lead to the

end of a specified period the deterioration of tensile members.The driver can keep this diet but it should not exceed the time of use to which it

corresponds.We define as overload powervalue Pu (t) attained when an overload.The higher thevalue, the greater the implementation period is short.The term united scheduleis traditionally used to describe a system where the maximum

operating temperature of the motor is reached after an hour of use.SteadyBelow the overload, the motor can run indefinitely.The heating temperature is


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stable and not likely to cause bored.This operation corresponds to the steadystate.We define poweras the steadymaximum power output developable inan infinite time.This power is measured at a particular point called "the steady state" whichpresents most often as the intersection of the power curve at steady state and

that of the operating curve the last stop.Power at steady state is the one that is read in the technical gear motors.It isalso called nominal UIC.It is sometimes accompanied Fc and Vc valuescorresponding to its definition.Some electric locomotives due to the settings of the traction system, arecaused to have two continuous points regimes.Areas of continuous systemson the chart speed efforts are made to change as appropriate.(Steady Steadyopen fields and fields reduced).

Stress level diagram speedThe stress diagram speed characterizes the locomotive itself (fig. 13).Each of


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the curves for each operating notches steering available to the driver isplotted.Otherwise, only the envelope limits is shown.The speed limit is valid regardless of the pulling force, it cuts the verticalnetwork.Limitation of Ft is often represented by a straight line delimiting thearea of use "steady."Beyond this line, the engine is considered overloaded.

Certain electrical machines, due to the deformation of the zone of adjustable steady(open fields reduces fields) are characterized by a core extension of the diagram by an

additional contour points between different definitions.This aspect will be discussedlater in the pages dealing specifically with electric traction.

Adhesion of the wheel / rail contact


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Principle of adhesionAdhesion is the ability of two solids in contact to provide a mechanicalconnection without slipping franc, ie without disconnecting total movements.If rail, a wheel loaded on a rail and is biased by traction or braking, creates awheel / rail contact whose existence limit is fixed by adhesion.Physical originsThis is subject to two assumptions empirical- The area between two solids is not perfectly flat on a microscopic scale, ithas geometric deviations in the form of ripples, grooves and cracks.- The two solids, the nature of the materials of inter atomic operate themwhose strength is limited.Mechanical stress, deformation of these parts at the contact and theintervention of a foreign body is producing two kinds of situations distinct (Fig.14):- Location adhesionwherein the surfaces are bonded ways macroscopic andrub them for transmitting a mechanical action.- Situation in which the slidingsurfaces are not related and are not able totransmit mechanical action.
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Laws COULOMB assuming a point contactConsider two solid S1 and S2 contacted at a single point.Vg is, the sliding speed between the two solids.This one, if it is zero, thisimplies that S1 and S2 are still them.

The mechanical action of the R point contact between the two solid having thefollowing properties (Fig. 15):- Its direction is inclined at an angle relative to the axis common to bothnormal solid- The normalcomponent N is oriented towards the inside ofsolid S 1,- The tangentialcomponent T is located in the tangent plane coinciding withthe contact surfaces and in the same direction as the velocity vectorVgslip,- The angle between the direction of the mechanical action of thenormal N depends on the nature of the contact.N is likely to S1 and S2 crush against each other.T has the effect of preventing S1 to slide relative to S2.


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2 Coulomb friction laws tell us when:- IfS1 and S2 are adhered (Vg = 0) then the direction of the force of contact

forms an angle with its normal at an angle lessthan N Said frictionwhich depends on the nature of the contact,- IfS1 and S2 are then sliding angle is equal to the angle of friction .Conversely, if


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Mechanical consequences of these lawsAdhesion is a steady state depending on the characteristics of the contact, butalso mechanical vector, resulting brought other mechanical forces to be

modified.If we increase the tangential force T, the resulting progressively deviate fromits normal, but as long as it remains in the cone of friction, contact maintains astable equilibrium.When the result is found on the surface of the friction cone ( is equal tothe angle of friction ) There bond failure.The balance has shifted in anunstable state that generates the sliding of the two solids.The slip speed has become non-zero, there is movement between the twosolids.If the tangential force T is oriented in the direction of the slidingvelocity Vg, this tends to increase in modulus due to inertia.If the tangential force T is oriented in the opposite direction to the slidingvelocity Vg, the latter tend to decrease in modulus due to inertia.Simple consequence of these laws on the wheel / rail contact


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Consider that the wheel / rail contact point is.The laws of Coulomb as we have outlined allows us to establish the followingtheorem which can be determined experimentally (Fig. 17):P is the load applied to the wheel / rail contact according to its normal.(Axleload)F is the tangential force applied to the contact in the plane and orientedaccording to the use (in traction or braking)Wheel rail contact is a member if:With , Coefficient of adhesionsuch that, and halfapex angle of the cone friction.

Whenever there is bond failure:If we pull the vectorF is found to be the same direction as the velocity


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slip.The wheel is independent of the rail in the direction tangential acceleratesits rotation on the rail, there is skating.If we are braking, the vectorF is found to be opposite to the velocity slip.Thewheel is independent of the rail in the tangential direction, decreases its

sliding on the rail to be blocked, there isskidding.Case of rail adhesionExtension of the laws of Coulomb surface contact HERTZThe wheel / rail contact is not limited to a point but a surface area whoseshape and dimensions are known as approaching ellipse HERTZ (fig. 18).Coulomb laws can be extended to the ellipse by considering the latter as asum of continuous basic point contacts whose mechanical action is anelemental force dR.The angle of friction is considered elementary dphi the same at all points ofthe contact area.


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If the solid adheres to solid S1 S2 (Vg = 0), we have no information on thebasic directions of each of the resulting dR i.Some of them may be includedwithin the friction cone, others are on the surface.That being said, there willalways be at least one inside the cone to justify adherence.For the solid S1 switch can slip on the solid S2, all the elementalforces dRi must be understood on their friction cones.Mechanical action can not be limited to a single force vector (Fig. 19).Thewheel into surface contact on the rail, has degrees of freedom: Swivelling andcrushing along the normal to the plane of contact, rub opportunities laterallyand transversely in the plane of contact.The notion of vector must be extended to that ofthe torque, which gatherstogether a resultant force F and a moment M resulting mechanical.Fullydescribes the torsor total mechanical action exerted on the surface (S) of thewheel / rail contact according to three spatial axes.(Pivot, rubbing and


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crushing)

In conclusion, the equilibrium stable or unstable adhesion sliding is entirelydictated by:- The evolution ofthe torque applied to the mechanical wheel / rail contact,modeled as a sum of a set of point contacts infinitesimal- The behavior of adhesion contacts at the microscopic level that decides toslip or grip.

Nickname sliding wheel / rail contactIf stopped the convoy, HERTZ surface can be considered completeintersection of the contact surfaces, it is not the same movement as it occurslocally on the wheel and the rail movements of traction and compression ofthe material.The wheel / rail contact is no longer homogenous and it is two distinct areas ofequilibrium in terms of Coulomb law on the intersection of the contactsurfaces:- A portion where the wheel / rail contact can still be considered adherent- A portion where the wheel / rail contact is slippery.


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As the intensity of the force of traction or braking increases, the adherentportion decreases and is replaced by the sliding portion.Within the slipping zone, the circumferential speed of the wheel tend to behigher or lower with respect to the translational speed of the hub:- If we are in tension.The tangential part of the mechanical action is in thedirection of velocity slip, so it is engine: zone patinamatter accelerates locallyin the area.- If we are braking.The tangential part of the mechanical action is in theopposite direction to the velocity vector of sliding, and is therefore resistant:The areajams, material tend to lock in the local area.Once the adhesive surface has completely left up slip rupture is adhesive.Theseparation of the contact causes slippageor complete stoppageof the wheelas appropriate.This intermediate state between grip and slip the wheel on the rail is calledthe pseudo slip.Characteristic of the force transmitted on the basis of the slip speedThe force which can be provided on the contact rail wheel is measured as afunction of the slip speed, which is created locally.(Fig. 21)


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As the adherent surface is present, the wheel is in a position of slidingnickname.It can transmit the force to the rail via the contact.The mechanicalequilibrium stabilizes around a sliding velocity proportional to the effort (whichmay be cut friction losses, tension and compression of the material).From a threshold, associable coarsely than the coefficient of adhesion, there

is switching of the steady unstable.The force exerted on the contact is sharplyincreasing sliding speed.Contact surfaces dissociated considerably reducedthe force transmitted, and the wheel is found independently of the rail.Underthe action of the force exerted on the wheel, the latter slips (in the case oftensile strength) or tend to block (in the case of braking).Characteristic of the adhesion as a function of the speed of the train

As the train speed increases, it is verified experimentally that the frictioncoefficient decreases.

An empirical law has been established:


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With V in km / h parameter approximating the coefficient of adhesionto V = 0 km / hThe maximum value of the traction force or braking transmitted via a contact

rail wheel is P is the load applied to the wheel / rail contact inNewton.Characteristics Effort - speed gear motor must register within the area, andtherefore necessarily decreasing and hyperbolic.(Fig.22) a traction ideal"power balance" solves part of the problem, but features even morepronounced strain rate can be obtained with suitable tensile members:- DC motor with series excitation,

- Coupler type hydraulic torque converter.

Factors influencing the friction coefficientEnvironmental factors


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On the ground, the adhesion is subject to various factors such as:- Quality of surface adherent- Climatic conditions,- Presence of organic matter.Realize this particularly complex apprehension of a phenomenon neverthelessessential operating railway.Technological factorsMany criteria influence the mechanical adhesion, and are at the origin of thevarious technological configurations encountered in railway vehicles (we havean opportunity to discuss later):- Keeping the suspension,- Disposition of the traction on the bogies,- Distribution of axle load,- E mpattement(spacing) between axles- Transmission of tractive effort between bogie and body.- Phenomena ofrotationorgrazing(inequalities between heights of contactpoints of one wheel to the other, from one bogie to another) The traction motor is a device by its conduct, to some extent mitigate the risk

of tipping over-candid-wheel drive

- A single-phase high voltage equipment, due to its inductivenature andlow ohmic resistanceis opposed to the instability of the electro-dynamicbehavior of the DC motors.- A diesel-electric adjusting its hyper adhesion, namely the change of voltage-current characteristics of the alternator, stabilizes the operating point of the dcmotors- A traction active semiconductor is reactive able to maintain stableequilibrium point.Control devices embedded adhesion (anti-slipand anti-skid) in railwayvehicles tend to improve adhesion convincingly.The latest technologicaldevelopments can hold the wheel on a normally unstable equilibrium point inorder to ensure the cleaning of rolling contact surfaces.However, the


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understanding of the balance point of the wheel / rail contact is estimatedindirectly on the measurement of acceleration factor and derivative of theacceleration (jerk).Also when the wheel / rail contact is slippery, it is no longerpossible to carry out direct reading of the speed of the wheel.It is still hardlypossible so far to concretely measure the localized slip of a wheel, much less

implement a model of the wheel / rail contact, which would however directcontrol.Sanding, and has always been since the beginning of the railway, the lastresort to maintain a grip on the wheel rail.

Documents

Fundamental Principle of Dynamics Applied to Rail