High-speed train pneumatic braking system with wheel-slide protection device : A modelling application from system design to HIL testing

Abstract

Train pneumatic brakes are part of a train safety system, and are thus critical components. This paper illustrates how modeling can be applied to efficiently design such system, from requirement definition to HIL testing. The valves modeling is discussed along with the system level model. Moreover, in order to study the wheel-slide protection device, a model of the wheel-rail interface has been developed. The contact model, written in Modelica, has been validated against measurement for different condi-tions of contact (dry, wet…). The model is fully pa-rametric and allows testing of various adherences. Finally, the resulting system composed of pneu-matic valves, wheel-rail interface and rolling-stock is exported through c-code for integration into a HIL system, providing an efficient test platform for the electronic Brake Control Unit.

Full text

High-speed train pneumatic braking system
with wheel-slide protection device :
A modelling application from system design to HIL testing
Lionel Belmon, Chen Liu
Global Crown Technology
Lanchoumingzuo Plaza, Chaoyangmenwai Avenue, Beijing, China
lionel.belmon@globalcrown.com.cn, chenl@globalcrown,com.cn
Abstract
Train pneumatic brakes are part of a train safety
system, and are thus critical components. This paper
illustrates how modeling can be applied to efficiently
design such system, from requirement definition to
HIL testing. The valves modeling is discussed along
with the system level model. Moreover, in order to
study the wheel-slide protection device, a model of
the wheel-rail interface has been developed.
The contact model, written in Modelica, has been
validated against measurement for different condi-
tions of contact (dry, wet…). The model is fully pa-
rametric and allows testing of various adherences.
Finally, the resulting system composed of pneu-
matic valves, wheel-rail interface and rolling-stock is
exported through c-code for integration into a HIL
system, providing an efficient test platform for the
electronic Brake Control Unit.
High speed train; braking ; adherence; pneumatic
1 Introduction
High speed train is under major development in
China and a lot of interest is put on the design of
subsystems. In particular the pneumatic braking sys-
tem, which is used for instance in emergency braking,
is a critical safety system. Much attention and efforts
are dedicated to the robustness and reliability of this
system, especially regarding its performance for
braking distance.
We introduce the main components of the brak-
ing system in Figure 1. The compressor system and
the emergency circuit have been omitted of the fig-
ure.
Figure 1 : Simplified schematic of pneumatic brakes [3]
The pressure is supplied by a large air tank. An
electro-pneumatic valve (EPV) adjusts the control
pressure for the flow amplifier. The flow amplifier
valves will work in such a way that the downstream
pressure is maintained at the input control pressure.
The EPV output pressure is directly controlled by the
Brake Control Unit (BCU) and depends on the brak-
ing level request.
The Wheel Slide Protection Device (WSP) con-
sists of a set of antiskid valves. These valves are con-
trolled by the BCU in such a way that, when wheel
speed is decreasing too fast, the valves modulate
brake pressure and prevent wheel blocking.
Besides this basic working principle, an emergen-
cy circuit is also available for emergency braking.
This circuit has different components and functions
but we will focus in this paper on the main braking
circuit.
We will now introduce how modeling and simu-
lation supports the design process. We choose the
Modelica platform SimulationX® for its convenient

pneumatic and mechanical libraries. We should also
mention the SimulationX® TypeDesigner tool in
which has been quite useful in developing new mod-
els in Modelica.
2 Sizing and target pressure
The first step in the design process is to size the sys-
tem and define subsystems requirements. The EP
brake designer will receive as input requirement a
target deceleration at a given speed, as shown in Fig-
ure 2.
Figure 2 : target train deceleration as a function of
speed
The braking force in the train comes partly from the
electrodynamic braking but needs to be comple-
mented in certain case by the pneumatic braking sys-
tem.
Simulation is used at this stage in order to determine
the target pressure that the pneumatic brake system
should apply to brake cylinders. The model created
is a simple model of the rolling-stock, taking into
account mass of the cars, rotary inertia of the wheel-
sets, frictions (aerodynamic…) and electrodynamic
brake torque. The brakes model are also simplified
but take into account some specific friction effects
described later in section 3.4.
The model applies inverse computation in Simula-
tionX® in order to determine a target pressure to
reach the requested deceleration as a function of
speed.
The process is illustrated in the Figure 3 and some
example of results are provided in Figure 4. The ef-
fect of the speed-dependent brake friction coefficient
can be clearly seen between in the range [0-100]
km/h.
Figure 3 : Target pressure computation
Figure 4 : Computed target brake pressure
The possibility to do inverse computation makes this
sizing step smoother and easier to handle.
3 Components & Valves modeling
Once a target pressure is defined as a function of
speed and deceleration, detailed design can start. We
introduce in this part models that are used by valves
designers.
3.1 Pneumatic model - generalities
The gas properties for air are considered as ideal gas,
this model holds since the system works at pressure
below 10 bar, around room temperature.
Volumes are lumped volumes using mass and energy
balance to compute the pressure and temperature
derivatives in a pretty much conventional fashion.
Flow models for orifices are based on geometrical
flow area and a flow coefficient. Sonic flow is ac-
counted for when a given critical pressure ratio is
reached.
3.2 Valve models
We will only detail the Electro-Pneumatic Valve
(EPV) model, other models being similar. We intro-

duce the basic working principle of the EPV in Fig-
ure 5.
Figure 5 : EPV working principle
The solenoid current is used to adjust the control
pressure applied in the brake calipers. The modeling
of the solenoid is discussed in the next part.
The model considers 2 moving bodies inside the
valve. For each moving body the forces of springs
and of pressure areas are taken into account. Sealing
friction can also be accounted for but can be usually
neglected.
The relative position of each bodies determines the
opening of the flow areas of the valve, connecting
the inlet pressure to the control pressure or control
pressure to exhaust. The variable flow area is defined
by an expression for the orifice area as a function of
the bodies position. This is achieved through an ori-
fice with time dependent parameter for its area. The
time dependent parameters in SimulationX® is quite a
convenient feature because of the great flexibility it
gives to any component. For a flapper nozzle valve,
as found in the EPV, the flow area can be written as :
 ,
where D is the seat diameter.
The resulting model structure is provided in Figure
6. The solenoid model is discussed in the next sec-
tion.
Figure 6 : EVP model structure
For pneumatic valves, it is also common to find de-
signs with membranes. Membranes are modeled as
pistons with variable effective area for the pressure
force. The effective area is computed from the mem-
brane volume variation by the equation :

  ,
Where V(x) is the membrane volume and Aeff is the
effective area of the piston.
We illustrate, in Figure 7, a key output for the EPV
model : the curve giving the control pressure as a
function of the current. The curve is computed with a
current ramp starting at 0 and going down to 0, we
can notice that the hysteresis of the output pressure is
predicted.
Figure 7 : EPV characteristic curve (Current/Pressure)
The detailed valve model presented helps designers
define flow areas, geometries, springs properties,
assess valve stability, and assess flow performance
along with pressure regulation performance. These
models are a key tool to achieve successful designs
of such valves.

3.3 Solenoid model
The Solenoid is modeled by the use of a 2D table
giving the force as a function of airgap and current:
  
The table is directly implemented into the model de-
scribed in Figure 8. The data to feed the table can be
obtained from experiments or from FEA analysis. A
more detailed model, for design purpose of the sole-
noid, can be done using 1D lumped magenetic ele-
ment and FEM analysis for the reluctance of airgaps,
as shown in Figure 9. It is also possible to include
thermal simulation in this part and verify that the
solenoid temperature remains in acceptable ranges.
Figure 8 : EPV Solenoid model in SimulationX
Figure 9 : Detail of a FEM analysis for a solenoid airgap, flux
density and flux lines
Figure 10 : Solenoid force, as a function of airgap [mm]
and current [N]
3.4 Calipers and brake model
The calipers mechanical system consists of brake
cylinder connected to the brake pads through a lever
system, as shown in Figure 12. The corresponding
model is shown in Figure 12.
Figure 11 : Schematic of brake caliper
Figure 12 : brake cylinder – brake caliper mechanism
For the brake pad contact and brake torque, we use
the following equation:
 [N],
where T is the brake torque, R the mean application
radius,  the friction coefficient between the
brake pad and the disk, as a function of the relative
speed and  the normal applied on the brake
pad and disk. The variable friction coefficient as a
function of speed needs also to be taken into account
in the initial sizing step (part 2 of this paper) of the
braking system, since it will modify the required tar-
get pressure.
4 Wheel-rail interface
The wheel-rail interface is an important part for
simulating the Wheel Slide Protection device (WSP).
The role of the WSP is to prevent wheel slide under
all conditions. The properties of the rail contact have
a major impact on the wheel adherence and on the
WSP behavior. For this reason, we need to create a
model of the wheel-rail interface.
An important output of the wheel-rail contact model
is the creep relationship with creep force. Creep is
defined as the relative slip between the wheel and the
rail, creep force is the resulting force opposed to the

direction of motion. Typical curves are provided in
Figure 15.
4.1 Summary of the contact theory
We introduce in Figure 13 the overall geometry
of the rail-wheel contact problem. The Hertz theory
is applied and provides a solution for the contact
patch between rail and wheel. The contact patch is an
ellipse of semi-axes a and b, as shown in Figure 14.
Figure 13 : Wheel-rail geometry
Figure 14 : contact patch geometry
The Hertz theory gives also a formula giving a rela-
tion for the semi-axes a and b :
  ,
where  [N] is the normal force, [Pa] the Young
modulus of each body,  the Poisson ratios and 
the curvature radius at the contact point. The tangen-
tial force  is computed according to the model
proposed in [9] which applies Kalker’s linear theory
and provides :



  
 ,
where is a variable friction coefficient computed
as :    ,
with , A, B,  being parameters of the model
and  being the total creep velocity between rail and
wheel.
The proposed creep force model has only 5 parame-
ters that need to be identified on measurement. This
model have the advantage of being able to cover ac-
curately small creep and large creep conditions,
while being able to account for train velocity and
different rail-wheel interface conditions (ice, rain,
leaves, dry…).
The main output of interest of the model is the
creep force curve, as shown in Figure 15.
Figure 15 : Classical creep force / creep curves
4.2 Model implementation in Modelica
The model proposed described in 4.1 is implemented
into Modelica through the help of the TypeDesigner
in SimulationX®. The model extends a rotary inertia
element and represents a wheelset accounting for the
wheel-rail interface. We introduce the resulting icon
with 1 rotary mechanical connection in Figure 16.
Figure 16 : Wheelset model in SimulationX®.
4.3 Validation of rail-wheel contact model
Implementation validation and parameters identifica-
tion of the wheel-rail contact are done using mea-
surements from [9] , [10], [12], [13], [14].

Figure 17 : Comparison of results from [9] with the modelica
implementation, Siemens locomotive S252 (dry, v=30km/h)
Figure 18 : Comparison of results from [9] with the
modelica implementation, Bombardier locomotive 12X
(wet, V=20 and 60 km/h)
We provide also an example of creep curves for 2
different cars under heavy rain. The front car has a
reduced adherence coefficient compared to car in the
middle of the train. We illustrate this effect in Figure
19.
Figure 19 : adherence coefficient at 300km/h under
heavy rain, comparison of front car and car 4.
The maximum adherence coefficients provided in
Figure 19 are consistent with the measurement on a
Japanese Shinkansen from [10], which gives values
around 0.02 for the front car and 0.05 for the car 4.
Overall, parameters for the following conditions
were identified :
 Dry – high adherence
 Dry – medium adherence
 Dry – contaminated surface
 Water/rain (multiple cars)
 Oil film
 Fallen leaves residues
The model being parametric, the user can also pro-
vide his values for the 5 relevant parameters.
Integrating the wheel-rail contact inside our pneu-
matic and mechanical model has several advantages
over using a full-blown 3D multi-body specialized
rail dynamics simulation package. The first advan-
tage is that there is no need for tool couplings or
model import/export. The other advantage is that we
obtain a very high performance in terms of simula-
tion time, with the possibility to easily integrate our
complete model into a HIL simulator.
5 Wheel Skid Protection device
With the availability of a predictive wheel-rail con-
tact model, it is possible to perform design and anal-
ysis of the Wheel Skid Protection (WSP) device. The
device consists of a set of valves piloted by an elec-
tronic controller. These valves modulates pressure in
order to maintain brake torque but without wheel
blocking. Each wheelset is equipped with a WSP,
requiring 2 valves by wheelset. One valve is used to
close pressure input port, the second valve is used for
venting the cylinder to exhaust if necessary. The
valves are controlled by the BCU control logic. We
show the WSP valve block model in Figure 20.
Figure 20 : WSP valve block model structure
We introduce some example of WSP action under
heavy rain in Figure 21.

Figure 21 : WSP in action at 300km/h under heavy rain,
modulation of brake pressure
The pneumatic model coupled with the wheelset
model is used to assess the robustness of the WSP
device and optimize the control algorithm, balancing
wheel-slide protection and braking distance. The
models introduced in this section provide mechanical
and control designers with a valuable simulation tool
for achieving robust and reliable performance.
6 Rolling-stock
The rolling-stock is considered as one mass, or
several masses linked together through non-linear
spring-dampers. Rolling-stock models needs to ac-
count for aerodynamic friction, rolling friction and
dry friction. These are implemented as additional
forces depending on train velocity.
The system we consider in this article does not
use an air-spring load sensing system. If this was the
case, a simplified 3D mechanical model of the roll-
ing-stock could be created in order to assess the air-
spring pressure during braking.
7 System modeling and HIL simula-
tion
7.1 System model on the laptop
The models developed previously are integrated into
a system model :
 Compressors and feed lines
 pneumatic tanks, main valves, pipes
 WSP valves
 brakes model
 wheelset with wheel rail contact
 rolling-stock (car)
The system model on the laptop can be used for a
MIL (Model In the Loop) step to design the control
strategy. It can be used to assess the performance of
the Wheel Slide Protection (WSP) device before an
actual hardware implementation. The WSP device
should insure that the wheel cannot be blocked dur-
ing braking by modulating the caliper pressure but
also maintaining a short braking distance as stipu-
lated by safety regulations (<3000m at 250 km/h for
instance).
Multiple configurations can be evaluated and tested
very efficiently, including fault and failure simula-
tions on a complete train composed of 8 to 16 cars.
7.2 Real time model
Besides the need for laptop simulation, it is also
possible to use the models to test the controller
hardware in a HIL simulator. To achieve this, we
need real-time capable models, which will be differ-
ent than the detailed design models.
The real-time models for components and valves are
developed and integrated into a real-time system lev-
el model. The model is tested off-line with a fixed
step solver and its accuracy is compared with the
detailed model developed previously. Numerical sta-
bility of the solution is achieved around 1e-3 [s] time
step, while maintaining a safe margin for CPU time
compared to real-time.
7.3 C-code export and HIL simulator
The model can then be exported for the HIL simula-
tor that is used to develop and test the Brake Control
Unit. SimulationX c-code export is used. The c-code
can be either integrated into a s-function for Simu-
link and used then for exporting with RTW, but it is
also possible to directly export the model for a given
real-time target such as a dSpace system, a NI Veris-
tand system or a Cosateq Scale-RT based system.
Depending on the cases and requirements, it is poss-
ible to interface the input/output cards of the HIL
simulator directly inside the SimulationX model, us-
ing a I/O boards library.
8 Conclusions
A methodology for developing and testing high-
speed train pneumatic braking system has been dem-
onstrated. The existing modelica tools have been

extended with a wheel-rail contact model in order to
simulate the wheel-slide protection device.
The proposed tool can then cover needs from siz-
ing and requirements definition, detailed component
design down to HIL simulation for control validation
and testing.
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