1. Numerical Simulation of Railway Vehicle Derailments
Vladislav Yazykov, Dmitry Pogorelov, Vitaly Simonov, Gennady Mikheev, Roman Kovalev, Dmitry Agapov, Nikolay Lysikov
Laboratory of Computational Mechanics,
Bryansk State Technical University
I would like to talk about simulation of train derailment processes and the identification of causes of derailments by using Universal mechanism software.

2. Railway derailments
A derailment is an accident on a railway in which wheels of a vehicle run off the rails. Of course, derailment is an emergency and should be avoided as much as possible for safety and economical reasons. Derailments have always been a big problem since the first days of railways to this day. Though railway technologies have significantly advanced, unfortunately, derailments occur rather often.

3. Railway vehicle derailment
Railway derailments
The leading train accident causes*:
Rail, joint bar, and anchoring
Track geometry defect
General switching rules
Wheels
Axles and journal bearings
Switches
Frog, switches and track appliances
Bogie components
Train handling/train make up
Highway rail grading
* by Federal Railroad Administration (USA)
Railway vehicle derailment
There are many main reasons of derailment: obstructions on the track, failures of running gear, railway track defects, train handling errors and others. Derailment can also be a secondary effect after a collision between two trains. Here you can see the leading train accident causes by Federal Railroad Administration (USA). The reasons could be very different but finally the result is that a train leaves the rails.
In some derailment cases, the causes of derailments are obvious, for example – obstructions on the tracks. In other cases especially for freight trains, derailments can occur due to loss of the lateral guidance at the wheel and rail interface. For this case, it is more difficult to understand the reason. In this report I will consider only this type of derailments.

4. Railway derailment mechanisms
Railway vehicle derailment mechanisms:
1. Wheel flange climb (L/V criterions)
Nadal limit criterion
Weinstock limit criterion
Time duration criteria
2. Gauge widening
3. Rail rollover
Lateral rail-to-wheel forces
Lateral rail displacements
4. Track panel shift
Lateral axle force
The derailments due to loss of the lateral guidance at the wheel and rail interface can be divided into 4 cases: wheel flange climbing, gauge widening, rail rollover, and track panel shifting. Railway engineers use various criteria for these cases to estimate the probability of derailment. Some of them are shown in this slide. For wheel flange climbing, they are Nadal limit criterion, Weinstock limit criterion, time duration criteria; for gauge widening and rail rollover – lateral rail-to-wheel forces and lateral rail displacements; for track panel shift –lateral axle forces.
* Pictures from Handbook of railway vehicle dynamics / Simon Iwnicki, CRC Press, 2006.

5. Process of wheel flange climbing
Let’s consider wheel flange climb process more detailed.
Wheel flange climb derailments are caused by wheels climbing onto the top of the railhead then further running over the rail Wheel climb derailments generally occur in situations where the wheel experiences a high lateral force combined with circumstances where the vertical force is reduced on the flanging wheel The high lateral force is usually induced by a large wheelset angle-of-attack The vertical force on the flanging wheel can be reduced significantly on bogies having poor vertical wheel load equalization, such as when negotiating rough track, large track twist, or when the car is experiencing roll resonances The forces between the wheel and the rail are explained in more detail in Chapter 4
Range climb derailments generally occur on curves. The wheels on the outer rail usually experience a base level of lateral force to vertical force ratio (L/V) that is mainly related to
Curve radius
Wheel-rail profiles
Bogie suspension characteristics
Vehicle speed
These factors combine to generate a base wheelset angle of attack, which in turn generates the base level of lateral curving force
A significantly misaligned bogie is likely to induce higher wheelset angle of attack. Furthermore, any track irregulanties and dynamic discontinuities may lead to an additional increase of the wheel LA' ratio When this ratio exceeds the limit that the wheel can sustain, flange climb occurs
Wheel climb derailments can also occur on tangent track when track irregularities and vehicle lateral dynamic motion are severe, such as during vehicle hunting and aggressive braking.
Process of wheel flange climbing

6. Safety criterion Nadal criterion Wheel flange climb
Fy is lateral force,
Fz is vertical force,
Fcy is tangential contact force,
N is normal contact force.
Safety criterion
Nadal criterion
The most-widely-used relationship for understanding wheel climb was presented in 1896 by Nadal. The Nadal equation for flange-climb derailment was derived based on the equilibrium of forces on the inclined plane of contact between wheel and rail. These formulas give us the condition when wheel climb occurs. The accurate formula looks like here. Due to the problems of measurement of μy in field tests, Nadal proposed to use the value of friction coefficient instead.
μ is friction coefficient

7. Vehicle lateral instability
And several words about vehicle lateral instability. Stability of the railway vehicle is the one of the most important criteria of dynamical properties of the vehicle. Especially big importance this parameter has for high-speed trains. The high lateral forces induced from hunting may cause the derailment of all four types shown before. For example in this slide you can see the derailment of an instable vehicle caused by wheel climb.
Single wheelset with conical profiles
Example of derailment

8. UM Safety Expert
UM Safety Expert has been intended for the simulation of train derailment processes and the identification of causes of derailments to the order of Russian Railways
UM Safety Expert is based on the mathematical core of Universal Mechanism (UM)
The numerical simulation of railway vehicle dynamics by using multibody system approach can help to analyze such kinds of derailments and find its real causes. In the Laboratory of Computational Mechanics, to the order of Russian railways, the program for the simulation of train derailment processes and the identification of causes of derailments has been developed. This program was named UM Safety Expert. It is based on the mathematical core of Universal Mechanism software. Now it is used in Diagnostic Center of Moscow Railways for analyzing the causes of train derailments.
The program allows users to simulate the dynamics of different kinds of railway vehicles with various initial conditions and analyze obtained results.
As a result of dynamics simulations, the output parameters such as safety factors for the determination of risk of wheel climbing, lateral forces in wheel-rail contact and forces between wheelset and bogie frame which show the probability of gauge widening and track panel shifting, longitudinal in-train forces which high values can be the cause of intercar coupling failure and other parameters are available for the posterior analysis.
UM Safety Expert is used in Diagnostic Center of Moscow Railways for analyzing the causes of train derailments

9. MBS models for derailment analysis
Single vehicle
Tractive connection
At first a vehicle or train model according to the real object parameters should be chosen. An expert can analyze dynamics of single railway vehicles, tractive connections of several vehicles and train with simplified vehicle models or with detailed 3D vehicle models.
3D tractive connection
One-dimensional train
1D train with 3D vehicle models

10. Railway vehicle database
The program includes a database of vehicle models which are multibody systems. This database contains most of operating Russian locomotives and cars. All models are parameterized, so it is possible to take into account the real parameters of the investigated railway vehicle.
VL65
VL60

11. Database of MBS models of Russian locomotives
ChS4
ChS2
ChME3
2ChS8
2VL85
In this slide you can see some examples of UM models of locomotives.
2ChS6
2ChS7

12. Models of freight car with three-piece bogies
Freight car models
From the point of view of derailment risk, freight cars are the most dangerous vehicles, so freight car models should be very detailed and accurate. Models of freight cars with two types of bogie: three-piece bogie and Y25 bogie can be used for derailment simulation in the program.
Models of freight car with three-piece bogies

13. Friction system of freight car
Friction wedges
For adequate simulation of the three-piece bogie it is necessary to introduce in the model a number of contact force elements which lead to stiff equations of motion. Such contact force elements are introduced in the bogie model between wheelsets and side frames, between wedges in the friction system, between the bolster and side frames, and in the pivot unit between the bolster and the car body. Real contact parameters are so high that it leads to a sharp decrease of a step-size and an increase of time efforts. In order to accelerate the simulation process analytical solutions for elements of Jacobian matrices of force elements were obtained and implemented in UM. It made the simulation of freight wagons several times faster.
Bringing 6-d.o.f. wedges with contact force elements in the multibody model significantly increases adequacy and accuracy of the model. Numerical and field experiments showed that using simplified analytical functions (without 6-d.o.f. wedges) for the simulation of the contact interaction with friction in the mathematical model of the three-piece bogie had low accuracy.
Contact points for the wedge

14. Railway vehicle models: three-piece bogie by AmstedRail
Here you can see the model of three-piece bogie of the biggest producer in the world – AmstedRail company.
Three-piece bogie by AmstedRail, USA, 2008

15. Railway vehicle models: Y25 bogie
Real model
Y25 bogie and its analogues are widely used in Europe. This bogie has only primary suspension which connects side frame and wheelsets.
More than 40 force elements are applied for the description of the bogie suspension, different structural components and contact interactions. In particular, springs of the suspension are modeled by viscoelastic force elements with bilinear stiffness.
UM model

16. Railway vehicle models: Y25 bogie
Special force elements are used for modeling Lenoir links, the center pivot, side bearings, interactions of the pusher with the spring holder and the axle-box, and the axle-box with friction surfaces of the bogie frame that allows taking into account dynamical properties of these elements in details.

17. 3D tractive connection of three hoppers
Tractive connections
3D tractive connection of three hoppers
The second type of models applying for the derailment simulation is tractive connections. It should be used when it is necessary to take into account longitudinal force acting in a train, and longitudinal forces are known, for example calculated in other program or an expert wants to vary [veari] them to find some danger combinations of factors.
3D tractive connection of locomotive and 2 hoppers

18. Models of auto-couplers and cushioning devicesс а b
Couplers
Cushioning device
Thrust plate
UM includes visual components for fast adding traction coupling systems to 3D vehicle models. Standard components correspond to automatic couplers and buffers. An expert may develop his own components of coupling systems.

19. Train model creation Train creation wizard
For the estimation of in-train longitudinal forces at various train operation modes, simplified train models in which vertical and lateral dynamics are neglected are used. All vehicles of such train model have one translational degree of freedom. The motion of a train model in a curve is modeled by introduction of an additional resistance force which depends on vehicle mass, curve radius and in some models on vehicle speed. In transient curves, the resistance force increases from zero value to the value for a curve of constant radius and decreases to zero again. When traveling on a tangent track with a grade, the additional longitudinal component of gravity force is introduced. Separate vehicles of a train are connected by force elements which simulate intercar couplings.
A train model is created by using the special tool which picture is presented in this slide.
Train creation wizard

20. Railway vehicle database
Locomotives
TE116
ChS7
EP10
EP200
ChS4
VL80

21. Railway vehicle database
Cars
Tank-car
Passenger car
Hopper
Flat car
Open wagon

22. Macro-geometry creation window
The special tool is developed for the creation of complex railway track profile
Macro-geometry creation window

23. Setting the traction mode:
Traction modes
Setting the traction mode:
Run-out mode
Throttle position setting mode
Speed setting mode
Tractive force setting mode
Quasi-static mode
There are several ways to set traction mode for a train model in UM Train module: by using the graph of the throttle position history, by using the speed history graph, by using the traction force history graph and quasi-static mode with constant forces applied to locomotives
Speed graph

24. Braking force: Braking force setting Speed of braking wave, m/s
Friction coefficient “wheel – brake pad”
Pressure in brake cylinder
When forming a train braking system, user should set the speed of braking and release waves, models of loading forces, release and friction coefficients for every vehicle.

25. 1D train with 3D vehicle models
3D tractive connection of three cars in train
And about the last type of models– 1D train with 3D vehicle models. It has advantages of both: 1D train models – since it can simulate the train handling modes, so it calculates in-train forces; and 3D vehicle models – since it simulate spatial dynamics of vehicles, so all derailment safety factors are calculated. For such kinds of models, 1D train models include several 3D vehicle models which dynamics is most interesting.
Numerical experiments show that as a rule connections of 3-5 3D models of vehicles are enough for the advanced analysis of rail vehicle dynamics.
3D tractive connection of locomotive and tank-cars in train

26. + - Model type Derailment safety factors In-train forces
Types of MBS models
Model type
Derailment
safety factors
In-train forces
Single vehicle + -
Tractive connection
predefined only
1D train
1D train with 3D vehicles
In this slide the table of comparison of all types is presented. So you can see that for 1D train derailment safety factors are not calculated, for others – calculated; while only train models can simulate the process of train handling.
After, when the model is ready and all parameters are assigned, the simulation process starts.

27. + Main performances: Any other kinematical and dynamical performances:
Output parameters
Main performances:
Safety factors (wheel flange climbing),
Lateral and vertical forces in wheel-rail contact,
Normal forces on wheel tread and flange,
Forces between wheelset and bogie frame (frame forces),
In-train forces (for train models), +
Any other kinematical and dynamical performances:
forces ,
accelerations,
velocities.
The simulation results are represented as a report in table and graph forms which contains the main performances:
safety factors,
lateral and vertical forces in wheel-rail contact,
normal forces on wheel tread and flange,
forces between wheelset and bogie frame,
in-train forces (for train models) and so on.
and other kinematical and dynamical performances such as forces, accelerations and others.

28. Example: simulation of derailment
The derailment of train which consists of two coupled trains with common brake system
Curve R = 487 m
Gradient = 7,5 ‰
2VL cars + 2VL cars
And one example of derailment simulation, I would like to show to you. The derailed train consists of two coupled trains with common brake system. The first train consists of a two-section electric locomotive VL80 and sixty six loaded freight cars, the second one contains a locomotive of the same type and sixty five loaded freight cars. The derailment took place during emergency braking of the coupled train in a curve of 475 m radius. Because of a technical failure of the train control system the first train started to brake in the emergency mode while the second one in the service mode. This led to the derailment of several cars of the first train.
To analyze this situation, two UM models of the derailed train were created. The first model consists only of simplified vehicles. This simplified train model was intended for the evaluation of longitudinal forces in intercar couplings. The second model included the tractive connection of three 3D models of freight car. The connection was placed at the end of the first train where the derailed cars were situated. This 3D train model gave an opportunity to estimate the derailment safety factors for wheels of the cars.
First train:
emergency braking mode
Second train:
service braking mode

29. Example: simulation of derailment
F, N
On the first step the forces in couplings were analyzed. In this slide, these forces are presented.
t, s
Forces in couplings

30. Example: simulation of derailment
F, N
The forces acting in the rear coupling of the sixty fifth car of the first train, which is one of the derailed cars with the maximal forces in couplings, are presented in this slide. It is obvious that the breakage of couplings when acting such high longitudinal forces is highly probable.
t, s
Forces in coupling of 66th car

31. Example: simulation of derailment
3D simulation of tractive connection in train
On the next stage, the possibility of the derailment caused by wheel climb or rail rollover was estimated. For this purpose the train model included 3D tractive connection was used. The first one is the train model with tractive connection of two-section locomotive and 2 freight cars.
2. Tractive connection of two-section locomotive VL80 and 2 freight cars

32. Example: simulation of derailment
1. 3D simulation of tractive connection of VL80 and two freight cars
Lateral forces:
Gauge widening
Rail rollover
Safety factors:
Wheel climb
Here are the graphs of lateral forces by using which we can estimate the probability of derailment by gauge widening and rail rollover. The limit value of this force is 100 kN. We can see that the maximal values are higher than the limit ones but not very much and the duration is not long, so it must not lead to derailment. The safety factor for wheel climb even does not reach the limit values.

33. Example: simulation of derailment
3D simulation of tractive connection in train
The second analyzing model was the train model with tractive connection of thee open wagons at the trail end of the first train.
1. Tractive connection of thee open wagons at the trail end of the first train

34. Example: simulation of derailment
1. 3D simulation of tractive connection of three freight cars
Lateral forces:
Gauge widening
Rail rollover
Safety factors:
Wheel climb
Here we can see that the maximal lateral forces do not exceed the limit level which. The derailment safety factor reaches the critical value as well but the duration of it is very small.
The simulation results showed that the most probable cause of the derailment was the breakage of couplings due to nonsynchronous braking of the coupled train.

35. Thank you for your kind attention!