# Module 6: Train-Track Dynamics

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Module 6: Train-Track Dynamics

Module Objectives Understanding the Rail/Wheel Interface
Identifying Force Generators Understanding Force Effects This module is entitled Train-Track Dynamics. The other area of concern deals with how we keep a moving relatively skinny wheel on an even skinnier rail. wheel lift and/or wheel climb also is not desirable. It shortens wheel and rail life, requires more fuel and eventually can result in derailment. Failure to adhere to recognized practices can create unstable systems. As track engineers, we have little control over wheel and truck configurations, etc. It's our job to make sure that whatever car comes our way, makes it safely over our railroad so long as it meets federal standards, regardless of condition. Anything else is a failure on our part. That's what they are paying us to do. We'd better understand the wheel-rail relationship so that we keep critical parameters within acceptable limits.

Train-Track Dynamics Definition
Interaction of forces occurring as train moves over the track structure Lateral Forces Vertical Forces Vehicle Dynamics Rail & Wheel Profile Many factors affect these forces Train Speed & Handling Train Consist & Placement of Cars, etc. What is Track Train Dynamics? Track Train Dynamics (TTD) is a term that refers to the interaction of many forces that occur when a train moves over a track structure. There are many factors that affect the forces that occur between the train and the track. These include: Train speed and handling. Vehicle condition. Type, weight and distribution of load. Line-up of different cars types of varying weights within each consist. Car body motion. Track design. Deviations in track geometry. Wheel / rail profile. The interaction of forces at the wheel / rail interface will determine the tendency for a wheel to derail. The wheel / rail interface sees a combination of lateral or sideward forces and vertical or downward forces, coupled with vehicle dynamics (rock and roll, pitch and truck hunting) and the wheel / rail profile which determines point(s) of contact and the resultant vector comprised of the cumulative lateral and vertical forces.

L/V Ratio L/V Definition Effect on Stability Lateral Forces
Vertical Forces Wheel/Rail Profile Three inputs affect the interaction between the wheel and rail: vertical forces lateral forces Angle of attack Lateral / Vertical (L/V) ratio The lateral to vertical ratio (L/V) is the lateral force pushing outward against the rail compared to the vertical force pushing downward on the top of the rail. The proportion of lateral to vertical force determines the angle at which the resulting vector force will act. The term commonly used to identify this reaction is Lateral/Vertical (L/V) ratio. A new contour wheel will overclimb rail more readily than typical worn wheel. Worn rail is more susceptible to overclimb than new rail. These conditions lower the threshold L/V ratio for wheel climb. Let's examine the role played by both lateral and vertical forces.

Lateral Forces Flanging Force Centrifugal Force

Frictional Curving Force
Difference in Distance Outside Vs. Inside Wheel Rolls in Curve Effect of Conical Wheel Tread Generation of Creep Forces Cause Truck to Steer to Curve Outside Magnitude of Forces Vs. Wide Gage, Corrugations & Geometry Problems Importance of Lubrication The profile of new wheel treads for standard railroad service is conical rather than cylindrical to accommodate the different distances the wheels on an axle must travel in a curve. On curves of up to 20, depending on wheel and rail wear, the wheelset adjusts to curves by moving laterally toward the outer rail. This shifts the contact area of the low rail to a slightly smaller diameter. Therefore with each turn, the low rail wheel travels less distance than the high rail, thus allowing the wheel to steer through the curve without slipping. Typical wheel and rail head profile is never perfect and for curves greater than 20 the wheel cannot shift over far enough to compensate for pure rolling. One of the wheels will slip on its rail; which is termed wheel creep. In a curve, either the inner wheel creeps forward and outward or the outer wheel creeps backward and inward. Wheel creep produces a frictional force between the wheel and the rail on either side of the wheelset. This additional lateral force is additive to other lateral forces at the wheel / rail interface. These frictional side forces increase the truck assembly's tendency to steer towards the outside of the curve. The magnitude of the lateral force, which has the effect of spreading the rail, (dynamic gage widening), promoting corrugations, wheel climb and rail rollover, depends on the ease with which the wheel can slip, that is the presence or lack of lubrication at the contact patch of the wheel / rail interface and the weight on the axle.

Coupler Forces Position of Coupler Faces in Curves
Of concern is the relative position of coupler faces at the extreme ends of cars. As a car traverses a curve, the center of the car between the trucks translates to the inside of the curve, while the extreme ends of the car and the couplers translate to the outside of the curve. If two cars coupled together are of the same design, the limiting factor can be the inside corners of the ends of the cars may meet, or the coupler is twisted to the point of failure. A greater problem is a longer car coupled to a shorter car. The coupler face of the longer car translates farther off the centerline of track than the shorter one, and under the right situations can physically pull the shorter car off the track. The shorter car is usually the one that derails first due to the mechanical advantage of the longer distance from the end of the longer car to the truck center. Longitudinal coupler forces (draft or buff) produce lateral forces in curves due to the triangle of forces developed from non-linearity of the couplers. Such forces can be accentuated by differences in end swing of the coupled cars as they encounter changes in curvature, and by coupler misalignments resulting from the coupling of long and short cars. Angularity at the couplers produces a lateral force that is carried down through the vehicle body and the trucks to the wheel/rail interface. The magnitude and direction of the lateral force depend on the magnitude and direction of the longitudinal force and the degree of angularity. Position of Coupler Faces in Curves Long Car Coupled to Short Car Longitudinal Force Effect Angularity of Couplers Torque Applied at Wheel-Rail Interface

Buff & Draft Forces Longitudinal Train Forces Result of Changes in Gradient, Curvature & Speed Buff - Run-in = Train in Compression - Produces Outward Force on Curve, Increases Vertical Load on Outside Draft - Run-Out = Train in Tension Produces Inward Force on Curve, Increases Vertical Load on Inside Train in Simultaneous Buff & Draft -Torque Produced - Force Applied at Coupler Resisted at the Rail Trains will always have longitudinal forces acting along their length as the train speeds up or down, as well as reacting to changes in grade and curvature. It is not unusual for a train to be in compression over part of its length (negative longitudinal force) and in tension (positive) on another portion. Trains are connected together with couplers. The mechanical connections of most couplers in North America have several inches (up to six or eight in some cases) of play between pulling and pushing. This is termed slack. If one considers that a long train of 100 cars may be 6000' long, and that each car might account for six inches of slack, it becomes mathematically possible for a locomotive and the front end of a train to move fifty feet before the rear end moves at all. As a result, the dynamic portion of the buff and draft forces can become quite large if the operation of the train or the geometry of the alignment contribute significantly to the longitudinal forces. A longitudinal tension force (draft) will produce an inward force on the curve. A longitudinal compression force (buff) will produce an outward force. Because the lateral load from the couplers is imposed at coupler height, but must be resisted by forces from the rail at rail head height, a torque results that will increase wheel load on one side of the car and decrease it on the other. Draft force increases vertical load on the inside rail of a curve and decreases it on the outside. Buff force decreases vertical load on the inside of a curve and increases it on the outside. Slack 6"/Car 50' Slack/6000' Train

Hunting Caused by: Empty or lightly loaded cars (though heavy cars can also hunt). Train speeds above 45 mph. Dry rail. Three piece freight car truck. Roller side bearings. Tangent track or curvature of 1 degree. Roller bearing wheelsets. Worn wheel treads having a hollow appearance over good quality track. Poor vertical snubbing. s v Truck hunting is associated with the high speed lateral oscillation or shimmy of the vehicle trucks. Hunting increases lateral forces at the rail, causing spread gauge if the unit is heavy (locomotive hunting) which may lead to wheel climb and in extreme cases will cause wheel lift. It generally involves: Empty or lightly loaded cars (though heavy cars can also hunt). Train speeds above 45 mph. Dry rail. Three piece freight car truck. Roller side bearings. Tangent track or curvature of 1 degree. Roller bearing wheelsets. Worn wheel treads having a hollow appearance over good quality track. Poor vertical snubbing. The swing motion suspension truck provides significant control of hunting over the the conventional 3-piece truck however at the expense of guidance. Through the side-to-side motion of the wheel tread taper along a track, a truck negotiates curves. As pairs of wheels come around a bend, they move away from a curve’s center. Just how much they move depends on the radius of the curve. Each wheel rolls without slipping along a corresponding shortened or lengthened track sector. Wheels riding along parallel rails have to balance diameters by hunting. Hunting wears down both wheels and rails because a wheel must move sideways to find balance. The wheels chase the ideal curvature but they can never reach. The sinusoidal motion of the wheels rock the car body, exciting a resonance that can damage cargo on board. Demonstrate with styrofoam coffee cups.

Track Geometry Forces Lateral Force Result of Changes in Alignment & Gage Wide Gage > Truck Hunting at High Speeds Tight Gage > Truck Hunting at Low Speeds Vertical Force Result of Changes in Cross-level/Superelevation & Profile Vehicle Rocks About CG Produces Horizontal Component at Rail because of Shift in CG Track geometry produces lateral forces primarily by changes in alignment and width of gauge. For example, because of increased flange clearance, wide gage will increase the forces generated by truck hunting at higher speeds. Tight gage reduces truck forces generated by truck hunting, but will cause hunting at lower speeds.However, vertical changes in track geometry such as crosslevel / superelevation and rail profile can produce lateral forces at the wheel by causing the vehicle to try to rock around its center of gravity. The fixed position of the track forces a shift in the position of the vehicle’s center of gravity (CG) which will produce a lateral force reaction at the rail. Likewise, vertical bounce will affect the vertical component of the L/V ratio.

Vertical Forces Vehicle Weight Unbalanced Elevation in Curves

Effects of Centrifugal Force
UNDERBALANCE Superelevation Centrifugal Force Gravity Resultant Center of EQUILIBRIUM OVERBALANCE D E V a 0007 . 3 max + = = Maximum allowable operating speed (mph). = Average elevation of the outside rail (inches). = Degree of curvature (degrees). Amount of Underbalance As a car traverses a curve, the car transmits a centrifugal force to the rail at the point of wheel contact. This force is a function of the degree of the curve, speed of the car, and the weight of the car. This force acts at the center of gravity of the rail car. This force is resisted by the track. If the car is traveling fast enough, it may derail due to rail rollover, the car rolling over, or simply derailing from the combined transverse force exceeding the limit allowed by rail-flange contact. This centrifugal force can be counteracted by the application of superelevation (or banking), which raises the outside rail in the curve above the inside rail. The point, at which this elevation of the outer rail relative to the inner rail is such that the weight is again equally distributed on both rails, is considered the equilibrium elevation. Track is rarely superelevated to the equilibrium elevation because the same track may serve trains operating at widely varying speeds. The difference between the equilibrium elevation and the actual superelevation is termed underbalance or overbalance. Curves may be safely underbalanced 3-inches for the higher train speeds in order to prevent excessive weight loading the inner or low rail in a curve for slower operated trains. The maximum speed that a train may be operated around a curve with a given amount of superelevation and a given degree of curvature is expressed by the equation in the slide. If the desired underbalance is less than 3”, substitute the amount for the + 3. Conversely, the required elevation can be calculated to operate at a given speed on a curve with a given degree of curvature.

Car & Locomotive Dynamics
Bounce Increase & Decrease Vertical Loading Speeds > 40 MPH Change in Track Modulus Pitch Varying Vertical Load Transfers End to End Square Joints Wheel Climb & Short Flange Marks Pitch and bounce is the rocking of the vehicle due to surface variations. With bounce, the entire vehicle moves up and down increasing and decreasing the vertical loading simultaneously. Pitch occurs when one end of the car goes down while the other end goes up. The result is a varying transfer of vertical forces between the truck assemblies resulting in repeated high vertical loads. Pitch will cause a vertical weight transfer from one end of the car to the other which may result in wheel climb and short flange marks. Pitch is most commonly found in jointed track laid with square joints (opposite each other). Bounce usually occurs at speeds above 40 mph, particularly at places where vertical track stiffness changes such as bridge abutments or road crossings. As previously stated, if surface variations on both rails are opposite each other (symmetric), and the wheelbase (WB) = wavelength () of the variation, they may produce pitch or bounce. Bounce: WB =  Pitch: WB = 1 ½  Bounce & Pitch Result of Surface Variations

Track Geometry Deviations in Geometry Accentuate Pitch & Bounce
Deviation in Uniform Profile Mismatched, Bent or Battered Joints Worn Points/Battered Frogs & Crossing Diamonds Poor Cross-level Rock & Roll Spirals Warp Forces Suspension Diagonally to Limits Bind Side Bearings - Trucks Can't Turn Track geometry influences vertical forces by causing pitching or rocking of the vehicle which will cause transfer of the static vertical weight of the vehicle from wheel to wheel or bounce which causes the load of the entire vehicle on the track to vary with time. Poor surface can promote bounce or pitch because of a change in the uniform profile. Mismatched, bent or battered joints and worn points or frogs at rail crossings can also contribute to pitch and roll. Poor cross-level can initiate roll. But the most dangerous form of roll is harmonic or resonant roll, known as "Rock and Roll". On long cars, the warp and twist on spirals and in curves can force the suspension of diagonally opposing truck assemblies to their limit. The differential loading results in diagonal unloading and possible wheel lift on opposite corners of the car. The problem is compounded by the transfer of much of the load to the diagonal side bearings, which prevents the trucks from turning to follow the spiral or the curve.. Under excessive warp when leaving a curve, the leading truck assembly is most likely to derail. When two cars move over excessive run-off at the end of a track raise, the rapid change in uniform surface profile in a short distance causes pitch or bounce at high speeds and may uncouple cars at low speeds.

Harmonic Oscillation Rock & Roll
High Center of Gravity Cars & Low Joints at Truck Spacing Rocking Magnifies Alternate Rocking on Other Rail Wheel Lift on Successive Joints Especially Dangerous on Curves Resonance Occurs at Critical Speed Critical Speeds Occurs at Multiples of Frequency & Wavelength Harmonic roll, commonly referred to as rock and roll, is associated with the side to side rocking action of a car. Rock and Roll occurs when a car with a high center of gravity travelling on soft track at a certain speed moves over a successive series of low spots or joints spaced at a distance similar to the spacing between the center of trucks. The rocking magnifies the alternate rocking on each rail causing wheel unloading and possibly wheel lift. If this occurs on a curve, the wheel may come down with the flange on top of the rail. Rock and roll or harmonic oscillation type derailments occur at speeds of between 15 and 23 mph which causes the car suspension to reach its natural frequency, thus putting the entire system into resonance. . However, rock and roll derailments are also possible at other speeds, depending on the spacing of the low joints. The longer the distance between the joints the higher the critical speed for oscillation. For example, a high center of gravity car that rocks at 15 mph at 39 feet, will rock at 30 mph at 78 feet, or at 60 mph at 156 feet. Usually, rock and roll is a low frequency phenomenon occurring at low speeds, but given the right conditions it can occur at high speeds, as well. It can occur on CWR in areas where wavelength and frequency combine with speed to produce the harmonic rock action.

Center of Gravity & Oscillation
Energy is input to the car as it rolls. The resulting forces act through the car's Center of Gravity (CG). The higher the vertical CG, the greater the tendency for the resultant forces to tip the car to the side. Harmonic roll derailments often involve heavy, high CG freight cars with insufficiently damped spring systems and with truck center spacing close to the 39 foot rail length that are traveling in the critical speed range of 14 to 21 mph over several consecutive staggered low joints. The higher the CG, the higher the amplitude of sway in the vehicle. When the resultant force is great enough, springs will be compressed solid and opposite wheels will tend to lift from the rail. Wheel lift has been observed on conventional 39 foot rail at speeds as low as 10 mph and as high as 25 mph, depending on the truck suspension and height of CG. Heavily loaded cars with high CG's will suffer greater roll angles than empty cars with low CG's on the same track. Often, but in not all cases, such derailments occur on curves. Research has shown the above condition to be rare in conventional equipment outside the speed range of 15 to 23 mph. Tests indicate that lift can occur as early as the third joint when the cross-level deviation is ¾ of an inch when measured under load. Derailments from this cause may occur on welded rail where the track surface has assumed a jointed rail geometry from poor ballast drainage at the former joint locations. They may also occur when vehicles having similar rock and roll characteristics all operate at the same speed, regardless of joint locations. Most high speed rock-offs have this contributory cause. However, with CWR, harmonic roll derailments are also showing up at higher speeds: 78 foot wavelengths at 30 mph, 160 foot wavelengths at 60 mph.

Longitudinal Coupler Forces
Loaded car coupled to empty car (difference in compression of springs). Differences in wheel wear, especially with multi-wear wheels. Inequality of track surface, or sharp vertical curvature. Vehicle bounce or pitch. Effects of slack run-in or run-out. As previously discussed, coupler forces are a significant factor influencing the lateral and vertical force reactions that characterize TTD related derailments and L/V ratio. Coupler forces occur as a result of the rolling resistance of the weight of the train and the dynamic input of force to the couplers as the locomotives exert forces or the train is retarded by the brakes or changes in track grade. The following general areas must be reviewed to determine the net influence of coupler forces on the derailment. Longitudinal forces at couplers also produce vertical forces from vertical coupler misalignment. Some possible sources of vertical misalignment are the above. Because the center of gravity of the car is above the center line of couplers, a slack run-in causes an inertial effect that transfers some of the weight of the car from the rear trucks to the front trucks. The trailing end of the first car goes down, and the leading end of the second car comes up, producing a non-linearity. A slack run-out has the opposite effect. The trailing end of the first car goes down, and the leading end of the second car comes up. Forces from coupler non-linearity during sudden acceleration or deceleration are additive to those resulting from load transfer resulting from the “g” forces of the acceleration/deceleration itself. Assessment of load transfer resulting from slack run-out or run-in requires knowledge of the rate of acceleration or deceleration (respectively), the distance between trucks of each car, and the height of combined center of gravity. Where extremely high coupler forces are present, as in collisions and overspeed impacts when switching, sufficient inertial weight transfer may occur to lift the trailing ends of vehicles off their trucks. This effect is not to be confused with the common observation that in collisions the impacting vehicles often buckle upward. The upward buckling in the latter case is simply the effect of putting too much compression on what effectively is a long horizontal column. It cannot buckle downwards or sideways, because it is restrained by the track, so it buckles upwards.

Coupler Forces & Derailments
Time duration of coupler forces Train consist and makeup Train handling by crew Terrain Geometry of coupled cars Time duration of coupler forces: Coupler forces can be steady state or dynamic. For example, the coupler force that exists as a train moves up a heavy grade is more or less steady state. A dynamic coupler force occurs during slack action or impact couplings. The usual criteria is that the high L/V ratio must exist for about 50 milliseconds in order to be significant. The train consist and makeup determines the distribution of forces in the couplers over a given terrain. Train handling (by crew): The method of train handling will determine the magnitude of coupler forces that will occur over and above those that exist as a result of the train consist. Terrain :The terrain over which the train consist moves will influence the magnitude of the coupler forces from the standpoint of rolling resistance of the consist and the type of train handling that is used to negotiate the terrain. The geometry of coupled cars will determine the coupler angles that can develop as the train negotiates a track arrangement. The force reactions at the wheels will be determined by the location of the trucks with respect to these coupler angles.

Rail-Wheel Profile New Wheel & Worn Rail New Wheel & New Rail

Critical L/V Ratio L/V = 1.29 wheel may climb new rail.
L/V = .82 wheel lift impending. L/V = .75 wheel may climb worn rail. L/V = .64 rail overturn force starts (unrestrained rail may overturn: rail rollover). The importance of the L/V ratio is that although lateral forces try to tip the rail over, the appropriate amount of vertical force holds the rail in place. The greater this ratio becomes, the greater the likelihood of wheel climb and eventual derailment. These values may differ widely depending on the wheel / rail contour and point of application of the lateral and vertical forces.

QUESTIONS? Author: Joseph E. Riley, P.E.
Federal Railroad Administration (202) Contributors: Robert Kimicata, P.E. Kimicata Rail Consulting (847) Acknowledgements

REVISION HISTORY

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