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Handbook of railway vehicle dynamics pdf

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Understanding the dynamics of railway vehicles, and indeed of the entire Handbook of Railway Vehicle Dynamics DownloadPDF MB. Request PDF on ResearchGate | A Handbook of Railway Vehicle Dynamics | The principal aim of this handbook is to present a detailed. of the rail-wheel interaction problem and its effect on vehicle dynamics. As Although the subject of railway vehicle dynamics is constantly gaining importance.


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The consent of CRC Press LLC does not extend to copying for general refer to frequently as my Handbook of Medi Men are from Mars, Women are from Venus. soundofheaven.info No-Drama Discipline. Handbook of Railway Vehicle Dynamics sets a new standard of authority and. I. INTRODUCTION. It is clear from the preceding chapters that the subject of railway vehicle dynamics has developed principally as a mechanical engineering .

Therefore, hydraulic dampers are often modelled as a spring and viscous damper in series. Modern Research on Curving The short wheelbase two-axle wagons then in use experienced hunting at low speeds and a high rate of derailment. Crude representations of creep saturation had long been available, but consideration was given to the representation of the graph of rolling radius difference against lateral displacement of the wheelset, which determines the yaw moment of the longitudinal creep forces in the equations of motion, as mentioned above. Recently cartridge-type bearings have been widely used.

A striking validation of the theory came from a series of full-scale experiments with two kinds of standard two-axle vehicles Gilchrist et al. The dynamic response of the vehicles was measured on a full-scale test track that featured a series of track imperfections. In addition, as the linear critical speeds of these vehicles were low, it was possible to measure the fully developed hunting limit cycle. Careful measurement of the vehicle parameters followed by a nonlinear analogue simulation led to a successful replication of the fully developed hunting motion of these vehicles by Hobbs published in Ref.

Quite apart from the highly nonlinear suspension characteristics, which were realistically modelled, two major limitations of linear theory were faced. These were creep saturation and wheel — rail geometry. Crude representations of creep saturation had long been available, but consideration was given to the representation of the graph of rolling radius difference against lateral displacement of the wheelset, which determines the yaw moment of the longitudinal creep forces in the equations of motion, as mentioned above.

For a coned wheelset the equivalent conicity is simply the cone angle of the tread. An example of the comparative results by Gilchrist et al. Inset shows waveforms of H. Predicted results indicated by full lines. From Ref. Some results are shown in Figure 2. The results of Figure 2. Although a larger roller rig was built at Derby, the use of roller rigs there was soon entirely superseded by track tests using random process methods of analysis. Various approaches to the analysis of nonlinear hunting motions have been developed.

Cooperrider et al. They also introduced the limit cycle or bifurcation diagram, an example of which is shown in Figure 2. Gasche, Moelle, and Knothe71,72 who approximated the limit cycle by a Fourier series and used a Galerkin method to solve the equations.

This made it possible to establish much detail about the limit cycle. Developments in nonlinear dynamics revealed that apparently simple dynamical systems with strong nonlinearities can respond to a disturbance in complex ways. In fact, for certain ranges of parameters no periodic solution may exist. Moreover, systems with large nonlinearities may respond to a disturbance in an apparently random way.

In this case, the response is deterministic but is very sensitive to the initial conditions. Such chaotic motions have been studied for railway vehicles by True.

As the wheelsets are constrained by the longitudinal and lateral springs connecting them to the rest of the vehicle, the wheelsets are not able to take up the radial attitude of perfect steering envisaged by Redtenbacher. Instead, a wheelset will balance a yaw couple applied to it by the suspension by moving further in a radial direction so as to generate equal and opposite longitudinal creep forces, and it will balance a lateral force by yawing further.

For the complete vehicle, the attitude of the vehicle in the curve and the set of forces acting on it, are obtained by solving the equations of equilibrium. The bogie vehicle had 14 degrees of freedom representing lateral displacement and yaw of the wheelsets, bogie frames, and car body.

He also included the effects of gravitational stiffness and spin creep. These linear theories are valid only for large radius curves. On most curves, the curving of conventional vehicles involves the same nonlinearities due to creep saturation and wheel —rail geometry that were noted in the case of hunting. At this stage the complication of two-point contact was to be the subject of much future research. As the contact moves across wheel and rail, account is taken of the increasing inclination of the normal force and the lateral creep force generated by spin.

Elkins and Gostling installed this table in their computer program so that values could be read by interpolation as needed. The resulting equations were solved by iterative numerical procedures, of which two alternatives were given. The accuracy of the predictions of Elkins and Gostling was demonstrated by experiments carried out on HSFV-1 and the tilting train research vehicle APT-E, an example of their results being given in Figure 2.

EE LS 0. HSFV-1,75 results are factored to account for two loading conditions. If the wheels and rails are considered to be rigid, as in the case of single-point contact, discontinuities occur in the geometric characteristics such as the rolling radius difference and slope difference graphs.

The mathematical aspects of two-point contact in this case have been considered by Guang. In , Gilchrist et al. Jenkins et al.

Of vehicle pdf railway handbook dynamics

Subsequently, quite complex models of track and vehicle have been used to establish transient stresses resulting from geometric defects in both track and wheels. Similar calculations have been carried out on the response of vehicles to switch and crossing work. The development of the heavy-haul railway with extremely long trains, often with locomotives attached at various points along the train, introduced serious problems arising from the longitudinal response of trains to hills and to braking.

The availability of the digital computer made it possible to develop dynamic models and also to support the development of train-driving simulators.

This, of course, had been a continuing design consideration from the earliest days of the railways but attempts to resolve it often resulted in intuitive schemes of articulation, as discussed in Section VI.

Not only are the parameters that are associated with wheel —rail contact, both geometrical and frictional, not under the control of the designer or operator, but they are not known exactly and can vary over a wide range. It follows that practical designs must be very robust in relation to such parameters. On the other hand, there is enormous scope for the design of the suspension system in terms of the way in which the wheelsets and car bodies in a train are connected. It was shown99 that such a vehicle should possess zero bending stiffness to achieve radial steering, but would be dynamically unstable at low speeds.

The design of a two-axle vehicle with a purely elastic suspension therefore requires a compromise between stability and curving. This limitation is removed if the wheelsets are connected directly by diagonal elastic elements or crossbracing, or interconnections which are structurally equivalent. Such an arrangement is termed a self-steering bogie. In the s the self-steering bogie was successfully developed and put into service, notably by Scheffel.

In Ref. This is so-called forced steering as it can be considered that the vehicle body imposes a radial position on the wheelsets. A considerable body of work by Anderson and Smith and colleagues — covers the analysis of a vehicle with bogies having separately steered wheelsets. Many examples of body steering are in current use. It was shown that for a vehicle with three or more axles it is possible, in principle, to arrange the suspension so that radial steering and dynamic stability are both achieved.

The three-axle vehicle was examined in this context in a series of papers. However, additional forms of instability can occur. A general theory for the stability of unsymmetric vehicles and the derivation of theorems relating the stability characteristics in forward motion with those in reverse motion has been provided.

However, the margin of stability is small. In the case of the three-piece freight truck, calculations taking account of the effects of unsymmetric wear have been described by Tuten et al. Suda, studied bogies with unsymmetric stiffnesses and symmetric conicity, and this development work has led to application in service.

The concept has been extended to include lack of symmetry of the wheelsets by equipping the trailing axle with freely rotating wheels. The lock is switched depending on the direction of motion. Independently rotating wheels have been frequently proposed as they eliminate the classic hunting problem. Some of the possibilities have been surveyed by Frederich. A generic wheelset model including the effect of modest amounts of camber has been studied theoretically and experimentally by Jaschinski and Netter.

A current example of a train which has single-axle running gear is the Copenhagen STog which embodies forced steering of the wheelsets through hydraulic actuators driven by the angle between adjacent car bodies. Extensive design calculations have been carried out on this train and its lateral stability has also been discussed. The dynamics of the derailment process was considered by Matsui and Sweet et al.

The mechanics of derailment remains a topic for research and presents a challenge to the modelling of vehicle dynamics. The analysis of the restrained wheelset, perhaps the most fruitful model with which to understand stability, could be carried out analytically. Once the importance of the suspension stiffnesses was recognised, the solution of the equations of motion of a system with many degrees of freedom presented a problem that, if attempted, was timeconsuming and error-prone even using the calculating machines of the early s.

Dynamics handbook of railway pdf vehicle

As already mentioned, Matsudaira resorted to a graphical method to establish stability boundaries for a twoaxle vehicle. The advent of the digital computer provided the means to calculate the eigenvalues for complete vehicles, while the general purpose electronic analogue computer could be used to compute stability boundaries.

The linear equations of motion of a railway vehicle and the aeroelastic equations of an aircraft wing are formally the same, provided that vehicle speed is interpreted appropriately. The work by Gilchrist et al. Many companies set up groups specialising in bogie and suspension design dependent on dynamics calculations. This motivated the development of complete packages, which covered a range of dynamics calculations, using the same consistent model of the vehicle.

In these programs, the input data consist of basic dimensions, masses, and the type of interconnections, such as massless force elements representing springs and dampers that connect the bodies that make up the vehicle.

The variety and scope of programs available was reviewed in Such software is extensively used in industry where the emphasis is on design.

The second approach to simulation involves the use of general vehicle models in general situations, so-called multibody programs. The theoretical basis of the multibody approach had its origin in work carried out on satellite dynamics in the s when satellites became more complex and could no longer be considered as single rigid bodies. The degree of generality varies: Software has been developed that allows the automatic formulation of the complex equations of motion by the computer.

A further development is that the formulation of the equations of motion may be carried symbolically instead of numerically. Another variation in methods lies in the treatment of constraints associated with the motion of the wheelset rolling along the track.

Some packages work with a set of differential equations involving all the states, i. Alternatively, many packages work with generalised coordinates and a minimal set of differential equations.

The formulation of the equations of motion therefore requires special care and their logical derivation has been considered by de Pater, Guang,90 and Schiehlen. As an example of the sophistication of modelling now considered necessary, the modelling of an articulated vehicle consisting of three car bodies and four single-axle bogie frames and wheelsets involves states to cover these bodies and the suspension details. In railways there are three principal areas of application of active suspensions — car body tilting systems, secondary, and primary suspensions.

Various demonstrations were made of monorail systems which exploited gyroscopic stabilisation, that of Brennan being perhaps the most successful within the limits of contemporary technology.

Bogies with provision for pendular suspension of the car body were put into service in limited numbers in the United States. This has been followed by operation of tilting trains, developed by several manufacturers, in a number of countries. The basic theoretical considerations have been outlined by Hedrick. Magnetic suspension relies on active control for stabilisation. Albertson, Bachelet, and Graeminger all proposed schemes for magnetic levitation in the s, and in Kemper demonstrated a model showing the feasibility of a wheelless train.

There has been considerable cross-fertilisation between the dynamics of rail and magnetically levitated vehicles as a result, both in terms of technique and personnel.

Turning to primary suspensions, feedback control system methods were used in the stability analysis of the wheelset in Bennington used control system techniques to propose an active torque connection between the two wheels of a wheelset, and subsequently, a wheelset with an active torque connection using a magnetic coupling was developed.

Currently, many possibilities are being considered. This chapter has reviewed the development of ideas about the basic problems associated with stability, response to track geometry, and behaviour in curves of the railway vehicle. The extrapolation of conventional railway technology to higher speeds has led in many cases to increased traction forces, increased wheelset mass, and greater track stiffness.

New problems of interaction between vehicle and track have emerged, such as irregular ballast settlement and deterioration, increased levels of rail corrugation, and out-of-round wheels.

The solution of these problems requires the consideration of structural dynamics of both vehicle and track in the frequency range of about 40 to Hz together with the analysis of the long-term behaviour of wheel and track components.

At these frequencies a nonsteady-state analysis of the contact forces is needed. Moreover, for problems such as corrugation and squealing in curves it is necessary to account for the contact forces at large values of the creepages. It has gradually been recognised that the interaction between traction and guidance due to the contact forces at the wheel — rail interface may severely affect overall performance.

Although traction and guidance have usually been considered separately, a systems approach is needed for design in which the control of the drive system is combined with the needs of guidance. Industrial applications demand integration of software tools with design and manufacturing systems.

Wickens, A. Dendy Marshall, C. Vaughan, A. Klingel, W. Winans, R. Adams, W. Redtenbacher, F. Mackenzie, J. Gilchrist, A. Heumann, H. Porter, S. Clark, D. Timoshenko, S. Weiner, L. Liechty, R. Ahrons, E. White, J. Hopkirk, K. Carter, F. Reynolds, O. Bennett, S. Routh, E.

Hurwitz, A. Bryan, G. Hopkinson, B. Whipple, F. Bairstow, L. Frazer, R. Love, A. Rocard, Y. Langer, B. Cain, B. Davies, R. Jaschinski, A. Matsudaira, T. Shima, H. A, 6, — , Doctoral dissertation, Technische Hogeschool Delft, Poritsky, H. ASME, 72, — , ASME, 72, —, Johnson, K. ASME, 80, — , Haines, D. Vermeulen, P. ASME, 86, —, Kalker, J. Amsterdam, B70, — , King, B. Solids Struct.

Fundamental considerations of lateral stability, Proc. Pooley, R. Kochenburger, R. AIEEE, 69, —, Hobbs, A. September, Cooperrider, N.

Handbook of Railway Vehicle Dynamics - CRC Press Book

Moelle, D. H, Ed. Gasch, R. True, H. Boocock, D. Newland, D. Elkins, J. Pocklington, A. Muller, C. Gostling, R. Nefzger, A. Hauschild, W. Duffek, W. Guang, Y. Netter, H. Pascal, J. Jenkins, H. Illingworth, R. Clark, R. September , Wickens, A. Proving trials and three site measurements. Horak, D. Control, , , Kar, A.

Handbook of Railway Vehicle Dynamics

Fujioka, T. JSME, 27 , — , Hedrick, J. Conventional, radial and innovative trucks, U. Scheffel, H. Angewandte Wissenschaft und Technik, 3, 81 — , Schwanck, U. Bell, C. Stability and curving mechanics, Vehicle Syst. Gilmore, D. Fortin, J. Smith, R. Anderson, R. Weeks, R. Keizer, C. ASME J. Tuten, J.

August , Hedrick, J. Suda, Y. Series III, 33 2 , — , Frederich, F. Becker, P. Eickhoff, B. Rose, R. Slivsgaard, E. Nadal, M. Matsui, N. Sweet, L. Control, September, Measurements using dynamically scaled models. Control, 3 , — , Ceruzzi, P.

Kortum, W. Schiehlen, W. Evans, J. Sauvage, G. Gretzscel, M. Mauzin, F. Goodall, R. Implementation status and technological trends, Vehicle Syst. Kemper, H. Zeus, 59, — , Bennington, C. A method for performance improvement, J. Geuenich, W. Le Rail, Juillet-Aout, pp.

Popp, K. Berlin, Springer-Verlag, Periard, F. Mei, T. Ueki, K. Stribersky, A.

Main Functions of the Running Gear and Terminology Elastic Elements Springs Constraints and Bumpstops Horn Guides Cylindrical Guides Beam Links Constraints Using Radius Links Constraints Using Trailing Radial Arms Traction Rods Car Body to Bogie Connection Flat Centre Plate Spherical Centre Bowl Centre Pivot Watts Linkage Pendulum Linkage Connection of Car Body to Bolsterless Bogies Common Passenger Vehicle Bogie Designs Common Freight Wagon Bogie Designs Common Tram Bogie Designs Principles of Selecting Suspension Parameters Selecting Vertical Suspension Characteristics Selecting Suspension Damping Advanced Bogie Designs The surface of the rails not only supports the wheels, but also guides them in a lateral direction.

The rails and the switches change the rolling direction of wheels and thus determine the travelling direction of the railway vehicle. The running gear is the system that provides safe motion of the vehicle along railway track. The running gear includes such components as wheelsets with axleboxes, the elastic suspension, the brakes, the traction drive, and the device to transmit traction and braking forces to the car body.

Its main functions are: In vehicles without bogies the suspension, brakes, and traction equipment are mounted on the car body frame. Conventional two-axle vehicles will generate larger forces in tight curves than the equivalent bogie vehicle; therefore their length is limited.

Running gear mounted on a separate frame that can turn relative to the vehicle body is known as a bogie or truck.

Railway pdf vehicle dynamics of handbook

The most common type is the two-axle bogie, but three- and four-axle bogies are also encountered, often on locomotives. Previously, the bogies simply allowed the running gear to turn in a horizontal plane relative to the car body thus making it possible for the wheelsets to have smaller angles of attack in curves. In modern bogies, the bogie frame transmits all the longitudinal, lateral, and vertical forces between the car body and the wheelsets. The frame also carries braking equipment, traction drive, suspension, and dampers.

It may also house tilting devices, lubrication devices for wheel-rail contact and mechanisms to provide radial positioning of wheelsets in curves. Bogied vehicles are normally heavier than two-axle vehicles. The wheelset is supported on bearings mounted on the axle journals.

The wheelset provides: Despite the variety of designs, all these wheelsets have two common features: In curves, the outer rail will be a larger radius than the inner rail. This means that a cylindrical wheel has to travel further on the outer rail than on the inner rail. As the wheels moving on the inner and outer rails must have the same number of rotations per time unit such motion cannot occur by pure rolling. It can be seen that for each curve radius only one value of conicity exists that eliminates slip.

Figure 3. For understanding the dynamic behaviour of a railway vehicle the conicity of interface is critical. In vicinity of the tape circle the conicity is 1: For high speed rolling stock, the conicity is reduced to around 1: It can be seen from Figure 3.

This is intended to lift the outer side of the wheel off the rail and thus ease the motion on switches. This is the ratio of the rolling radius difference to twice the lateral displacement of the wheelset: Tread wear Figure 3. In extreme conditions, this could increase the risk of switch-splitting derailments.

This can normally be carried out without the necessity to remove the wheelset from the vehicle. This may take the form of single-point, two-point, or conformal contact as shown in Figure 3. Wheels wear quickly towards the local rail shape. AXLEBOXES The axlebox is the device that allows the wheelset to rotate by providing the bearing housing and also the mountings for the primary suspension to attach the wheelset to the bogie or vehicle frame.

The axlebox transmits longitudinal, lateral, and vertical forces from the wheelset on to the other bogie elements. Internal construction of the axlebox is determined by the bearing and its sealing method. Axleboxes with plain bearing Figure 3. Front and rear seals 5 and 6 prevent dirt and foreign bodies entering the axlebox, while the front seal 6 can be removed to monitor the condition of the bearing and add lubricant.

Vertical and longitudinal forces are transmitted through the internal surface of the bearing and lateral forces by its faces. Plain bearing axleboxes are now largely obsolete as they have several serious disadvantages: In recent years, plain bearing axleboxes that do not require lubrication have been reintroduced on certain types of rolling stock though their use is still rare.

Axleboxes with roller type bearings Figure 3. Cylindrical roller bearings have high dynamic capacity in the radial direction, but do not transmit axial forces Figure 3.

Experience in operation of railway rolling stock showed that the faces of rollers can resist lateral forces. However, to do this successfully it is necessary to regulate not only the diameter, but also the length of rollers, and the radial, and axial clearances.

Conical bearings Figure 3. This makes it necessary to keep the tolerances on roller diameters and clearances almost an order of magnitude tighter than for cylindrical bearings. Recently cartridge-type bearings have been widely used. Ball bearings are, however, often combined with cylindrical bearings in railway applications to transmit axial forces. High speed rolling stock often has three bearings in the axlebox: Mechanical failure or exceedance of design dimensions can cause derailment.

Solid wheels Figure 3. Tyred wheels Figure 3. Wheels may have straight, conical, S-shaped, spoked, or corrugated type discs when viewed in cross-section. A straight disc reduces the weight of the construction and can be shaped such that the metal thickness corresponds to the level of local stress. Corrugated discs have better resistance to lateral bending. The desire of reducing wheel-rail interaction forces by reducing the unsprung mass has led to development of resilient wheels Figure 3.

These help to attenuate the higher frequency forces acting at the wheel-rail interface. By decoupling the wheels, the independently rotating wheelset inevitably eliminates the majority of wheelset guidance forces. If the bogie has a rigid frame, the suspension usually consists of two stages: Such bogies are termed double suspended. Elastic elements are used to: Force characteristics can be linear or non-linear. The principal types of elastic elements are shown below in Table 3.

A leaf spring picture A in Table 3.

Depending on their design, leaf springs can be closed picture A in Table 3. They consist of layered leafs 1 and 2 having different length and held together by a buckle 3. The largest leaf 1 is named the master and the other leafs 2 the slaves. Leaf springs also provide damping due to the inter-leaf friction.

A plate spring or washer picture B in Table 3. The stiffness of the plate spring depends on the number of plates and their relative arrangement in series or in parallel. A ring spring picture C in Table 3. Coil springs are the most commonly used elastic elements which can either be cylindrical picture D in Table 3. Usually they are produced of steel spring wire typically of circular cross-section. Coil springs are cheap and robust, but provide very little damping in suspension applications.

Torsion springs picture E in Table 3. The force P causes elastic torsion of rod 1. The most common application of this type of spring in railway vehicles is the roll bar. Rubber-metal springs picture F in Table 3. This type of spring is widely used in passenger rolling stock, particularly on primary suspensions as it allows damping of high frequency vibrations and reduction of maintenance costs due to the elimination of wearing friction components.

Some types of rubber-metal springs are illustrated in Figure 3. Air spring picture G in Table 3. This type of elastic elements is characterised by its small mass, excellent noise and vibration isolation and ability to maintain a constant ride height for different vehicle load conditions.

Such springs are found almost universally in the secondary suspension of modern passenger vehicles. The operation of a typical air suspension with pressure control to maintain constant ride height is shown in schematic form in Figure 3. To reduce the spring stiffness the elastic chamber is connected to the surge reservoir additional volume 2. When the load increases position b the airbag 1 is compressed and moves the valve 5 of control system 4 down.

Reduction of the load position c makes the airbag rise and control valve 5 moves up. The spring height reduces and returns to the equilibrium position again. Increasing the surge reservoir volume leads to decreasing spring stiffness. The lateral stiffness of the pneumatic spring depends on the shape of elastic chamber. Railway vehicles often use devices whose stiffness is derived from gravitational forces, as for example in the swing link arrangement shown in picture H in Table 3.

Rollers on inclined planes and various lever systems have also found applications in vehicle suspension arrangements. The swing link suspension is the most common application of those listed above.

It consists of swing links 1 that are attached to mountings 2 and connected with a beam or spring plank 3. Swing link suspension effectively acts as a pendulum and is often used in secondary suspensions to give constant lateral frequency. Typical force characteristics of elastic elements are shown in Table 3. A piecewise linear characteristic Table 3. Parabolic characteristics picture D are obtained from coil springs with variable step or wire diameter, conical springs, rubber, or pneumatic springs without pressure control system.

An automatically controlled parabolic characteristic may be obtained from airsprings with automatic pressure control that is dependent on the vehicle loading picture F. These may be combined with an elastic bump stop acting in compression. Dry friction results from the relative slip between two rigid bodies in contact. The friction force can be constant or dependent on the mass of the car body, but always acts to resist the relative motion.

Handbook of Railway Vehicle Dynamics

This dependence can be represented by the following formula: The minus sign denotes that the friction force is always in the opposite direction to the velocity. The damping force in viscous case is proportional to velocity: Depending on the construction of the device and the liquid properties the power n can be greater, equal or less than 1.

Intermolecular damping hysteresis originates mainly in rubber and polyurethane elastic elements. In such cases, the damping force is proportional to oscillations velocity and is inverse to the frequency: A damper is the device that controls oscillations in the primary or secondary suspension of the vehicle by energy dissipation.

Friction dampers are the devices that transform the energy of oscillations into the heat energy by dry friction. Friction dampers are mainly used in freight vehicle suspensions due to their low cost and simplicity. Dampers integrated with an elastic element consist of the barrel 1 and friction wedges 2 that are held in contact by a spring. When the elastic element deforms, the friction forces act on the contacting surfaces between the barrel 1 and the wedges 2 transforming the kinetic energy into the heat.

TABLE 3. Dampers integrated in the suspension are mostly used in three-piece bogies and consist of friction wedges 2 that move relative to side frame 6 and bolster 5. Construction of the dampers Table 3. For example, the Russian CNII-H3 bogie has wedges 2 with inclined faces contacting with the bolster 5 and pressed to the side frame 6 by springs underneath. Simultaneous and integrated friction dampers are connected to the springs in the suspension, whereas telescopic dampers are independent devices.

Friction dampers may be arranged to produce either constant or variable friction force and can be designed to act in one linear , two planar , or three spatial directions. Friction dampers integrated in elastic elements have found wide application in freight bogies in Russia, the USA, and many other countries, due to the following advantages: Telescopic dampers have the advantage of being autonomous, protected from the environment which reduces the likelihood of contamination of the friction surfaces , can be installed at angles other than vertically and hence can be used to damp vertical or horizontal vibrations of sprung elements of the vehicle.

They can be inspected and repaired without lifting the car body. One of the reasons that such telescopic dampers are not widely used in freight vehicles using the popular threepiece bogie is that an integrated friction wedge as shown above is required to resist warping in vertical and horizontal planes. In case of the bogies with a solid frame, friction dampers in the primary suspension must resist wheelset displacements.

It is desirable that in primary suspensions the damper has an asymmetric characteristic providing lower damping forces in compression than extension. Hydraulic dampers are superior in this respect. The main advantage of plane and spatial friction dampers is their ability to damp vibrations in several directions and in certain cases provide friction — elastic connections between parts of bogie frames.

They are therefore widely used in freight bogies despite a number of disadvantages including providing unpredictable friction forces, and the fact that repair and adjustment of friction forces may require lifting the car body and disassembling the spring set.

Typical force characteristics for friction dampers are presented in Figure 3. Different designs of friction damper have varying arrangements for transmitting the normal force to the friction surfaces. Depending on the design, the damper may provide constant or variable friction. In the latter case, such damper is usually arranged such that a component of the force in one or more of the suspension springs is transmitted via a linkage or wedge to the friction faces. Force characteristic a describes a constant friction damper, where the friction force does not depend on deformation of the spring set and is the same for compression and tension.

The dashed line shows the characteristic of the same damper, where the friction pairs are elastically coupled. This can occur, for example, as a result of the friction surface having an elastic layer underneath. Characteristic b is common for most friction dampers used on freight bogies. It can be seen that the variety of force characteristics available from friction dampers allows freight vehicle to be designed with suspensions providing satisfactory ride qualities.

Hydraulic dampers are almost universally used in passenger bogies and are sometimes also used in modern freight bogies. The energy dissipated in a hydraulic damper is proportional to velocity, and therefore to the amplitude and frequency of vibration. Thus the hydraulic damper is self-tuning to dynamic excitations and provides reliable and predictable damping of vehicle oscillations. Railway vehicles use the telescopic hydraulic dampers as shown in Figure 3. This produces viscous damping and the kinetic energy of the oscillations is transformed into heat.

Telescopic hydraulic dampers Figure 3. The reliability of hydraulic dampers mostly depends on the sealing between the shaft and the body. The damper characteristic may be either symmetrical, when the resistance forces are the same for extension and compression, or asymmetric.

Dampers with symmetric characteristics are typically used in secondary suspensions. In primary suspensions, asymmetric dampers are often used as the motion of the wheel over a convex irregularity causes larger forces than negotiating a concave one. As a result, dampers may be designed with an asymmetric characteristic providing a smaller force in compression than in extension.

Therefore the railway dampers are less asymmetric than the automobile ones. Common force characteristics of hydraulic dampers are shown in Figure 3. Hydraulic dampers having characteristic B have a resistance force proportional to the velocity and the displacement.

In scheme D, the size of the valve cross-section and the saturation limit for emergency valve are controlled together depending on the relative displacement and velocity of the piston. Attachment of hydraulic dampers to the vehicle is usually done using the elastic mountings or bushes to prevent the transmission of high frequency vibrations.

The internal pressure in the damper often gives it elastic properties. Therefore, hydraulic dampers are often modelled as a spring and viscous damper in series. In some designs, the hydraulic dampers are united with the elastic elements.

The schematic of a hydraulic damper integrated into coaxial rubber-metal spring is shown in Figure 3. Horn Guides A simple primary suspension design uses horn guides to limit the movement of the axlebox Figure 3. This design has several disadvantages, including fast wear of friction surfaces leading to the increases in clearances, lack of elastic longitudinal and lateral characteristics, and increased friction force in vertical direction in traction and braking modes, when the axlebox is pressed against the slides.

The design could be improved by the application of anti-friction materials that do not require lubrication and have high resistance to wear. Cylindrical Guides These comprise two vertical guides and two barrels sliding along them. Typically the vertical guides are attached to the bogie frame and the barrels to the axlebox as shown in Figure 3.

Due to axial symmetry of the rubber bushes, the stiffness in longitudinal and lateral directions is the same, which may limit the provision of optimal suspension characteristics.

Axlebox constraint with cylindrical guides, where the displacement of the axlebox along the guides occurs by shear deformation of multi-layer rubber-metal block is free from disadvantages of classical construction.

In order to obtain the optimum relationship of horizontal and vertical stiffness this block consists of two longitudinally oriented sections Figure 3. Beam Links The desire to avoid wear led to the development of links in the form of thin elastic beams that hold the wheelset in the longitudinal direction Figure 3.

The main disadvantage of such designs is high stress which develops around the joints at either end of the beam. Constraints Using Radius Links The use of rubber-metal bushes avoids surface friction and corresponding wear.

The main problem with a radius link arrangement is obtaining linear motion of axleboxes when the links rotate. By careful choice of size and the material of the rubber elements it is possible to obtain the required stiffness values in different directions. Due to the position of the links, lateral displacements do not cause misalignment of the axlebox therefore providing optimum conditions for the bearings.

Increasing the length of the levers would decrease the vertical stiffness, but it is limited by the space available in the bogie frame. Constraints Using Trailing Radial Arms Trailing arm suspensions allow the design of shorter and lighter bogie frames. Such designs are now widely used in passenger vehicle primary suspensions, such as the Y32 bogie shown in Figure 3. The disadvantages of such designs include the longitudinal displacement of the axleboxes caused by vertical displacement of the suspension and torque applied to bogie frame due to wheelset lateral displacement.

Traction Rods These are normally used to transmit longitudinal traction and braking forces in either the primary or secondary suspension. They may be adjustable length to maintain the necessary linear dimensions as wheels or suspension components wear Figure 3.

If the vehicle is stable up to the design speed, then introduction of additional yaw resistance torque is not necessary. Designs generally aim to make the bogie to car body connection as simple as possible by the use of a small number of elements and reduction of the number of elements with surface friction. The plate transmits the majority of the car body weight and the longitudinal and lateral interaction forces. The pin pivot has large in-plane gaps to the car body and only provides emergency restraint.

The centre plate allows the bogie to rotate in curves and creates a friction torque that resists bogie rotation. Hence the circular centre plate provides a connection between the bogie and the car body in all directions. Such a unit is of simple construction, but has several disadvantages. Firstly, clearances exist in the lateral and longitudinal directions.

In curves, the car body leans on the side bearer creating additional friction torque that resists bogie rotation and increases wheel — rail forces.

When the car body rocks on straight track, the contact surface becomes very small and high contact pressures can lead to cracks in the centre plate.

Spherical Centre Bowl In this case, the car body rests on the spherical centre bowl and elastic side bearers Figure 3. The advantage of this design is the lack of clearance in the horizontal plane and no edge contact during car body roll. Such centre bowls are widely used in UIC freight bogies, electric trains, and underground cars in Russia. Centre Pivot The desire to exclude edge contact and increase the friction torque to resist bogie yaw led to development of bogies with centre pivots as shown in Figure 3.

The majority of the car body mass is in this case transmitted to the side bearers and the car body can only turn relative to the bolster about the vertical axis. This design is widely used in passenger coaches of former USSR. The disadvantages include the clearances in longitudinal and lateral directions. Watts Linkage This arrangement, illustrated in Figure 3. It therefore provides a means of transmitting traction and braking forces.

Pivots in the linkage are provided with rubber bushes to prevent the transmission of high frequency vibrations through the mechanism. Pendulum Linkage The pendulum linkage consists of a vertical rod connected at each end to the body and bogie frame by conical rubber bushes as shown in Figure 3. The mechanism is held in a central position by two precompressed springs.

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Elastic side supports provide lateral stability to the car body. Thus, the pendulum support has a soft nonlinear characteristic. The drawback of such an arrangement is the rigid connection with a gap in the longitudinal direction, complex tuning requirements for the precompressed springs and friction forces in the additional sliding supports.

Transmission of longitudinal forces is done through the centre pivot, Watts linkage, traction rods, or in the case of a Y32 bogie, through the backstay cables. Bolsterless bogie designs typically achieve reductions in bogie mass of around 0. However, in articulated trains, for example the French TGV, two-axle bogies are positioned between the car bodies, whilst the Spanish Talgo trains use single-axle articulated bogies.

The primary suspension transmits forces from the wheelsets to the bogie frame and the secondary suspension transmits forces from the bogie frame to the car body. The principal functions of the primary suspension are guidance of wheelsets on straight track and in curves, and isolation of the bogie frame from dynamic loads produced by track irregularities. The secondary suspension provides the reduction of dynamic accelerations acting on the car body which determines passenger comfort.

An example of a traditional type of secondary suspension used on passenger vehicles for over years is shown in Figure 3. The secondary suspension swing consists of the secondary springs and dampers 2 , spring plank 1 that is attached to the bogie frame 3 by swing links 4. This arrangement provides low lateral stiffness, and the height of the secondary springs remains comparatively small.

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