MODELING THE BUFFERS HYSTERETIC BEHAVIOR FOR EVALUATION OF LONGITUDINAL DYNAMIC IN-TRAIN FORCES

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SISOM 2012 and Session of the Commission of Acoustics, Bucharest 30-31 May
MODELING THE BUFFERS HYSTERETIC BEHAVIOR FOR EVALUATION OF
LONGITUDINAL DYNAMIC IN-TRAIN FORCES
Camil CRACIUN
1
, Ana-Maria MITU
2
, Cătălin CRUCEANU
1
, Tudor SIRETEANU
2
1
POLITEHNICA University of Bucharest, Rolling Stock Engineering Departament, 313 Splaiul Independentei, sect. 6 Bucharest
2
Institute of Solid Mechanics of Romanian Academy, 15 C.Mille Street, sect. 1, Bucharest
In this paper the authors develop a simulation program for analyzing the dynamic behavior of friction
ring buffers that equip railway vehicles, based on their hysteretic characteristics. This characteristics
and the longitudinal response to various types of actions have an important role on the maximum
values and the evolution of longitudinal dynamic response of railway vehicles. The reduction of
longitudinal dynamic loads is a necessity due to traffic safety reasons, passenger comfort and
protection of goods transported. The simulation was performed for typical situations found in railway
operations. To assess the evolution of forces between the vehicles of any train and vehicle overall
response, the case of only one vehicle was considered, tapping a fixed system with an imposed an
initial velocity. The paper presents three case studies: (a) the vehicle equipped with buffers is
launched with an initial velocity limit to a fixed system, such as the buffer deformation be less than
the maximum allowed value; (b) the vehicle is fitted with a traction device on this system and an
initial velocity under the same conditions is applied; (c) the buffer characteristic is remodeled by
inserting a stroke limiter that allows the launch of the vehicle at higher initial speeds, than in the
previous cases.
Key words: railway vehicles, buffer; hysteretic model, longitudinal dynamics forces.
1. INTRODUCTION
Train braking is a very complex process, specific to rail vehicles and of great importance by the
essential contribution on the safety of the traffic. This complexity results from the fact that during braking
occur numerous phenomena of different kinds - mechanical, thermal, pneumatic, electrical, etc. The actions
of these processes take place in various points of the vehicles and act on different parts of the train, with
varying intensities. The major problem is that all must favorably interact for the intended scope, to provide
efficient, correct and safe braking actions.
In the case of classical UIC brake system, due to the air compressibility and to the length of the train,
there will always be a time lapse between the reaction of the leading vehicle and the reaction of the rear one.
Corresponding to the propagation rate of air pressure signal, the air distributors will come into action
successively and the braking of vehicles begins at different times along the train so that, while some cars are
slowing down, others are trying to push, still unbraked, from the rear. This creates the conditions that during
transitional braking stages, immediately following the command of pressure variation in the brake air pipe, to
develop important longitudinal in-train reactions causing stress to the couplers and affecting passenger
comfort and, sometimes, even the traffic safety.
A classical approach for theoretical studies of the dynamic longitudinal forces developed during the
braking actions along trains equipped with automated compressed-air brakes is a mechanical
cascade-mass-
point
model in which vertical and lateral dynamics are usually neglected [1], [2], [3].

Railway vehicles are linked to each other by different kinds of couplers that must have certain elastic
and damping characteristics, according to their remarkable contribution not only for the protection of the
vehicle’s structure and loading’s integrity, but also for the passengers comfort. Generally, traditional
couplers wide used in Europe consist of a pair of lateral buffers, a traction gear and a coupling apparatus at
each extremity of the vehicle. Their characteristics have significant influences for the longitudinal dynamics
Camil CRACIUN, Ana-Maria MITU, Cătălin CRUCEANU, Tudor SIRETEANU
 
 
106
of the train, with running stability implications. There are specific types of buffers for railway vehicles with
characteristics according to the requirements determined by mass, potential collision shocks and passengers
comfort, etc. Therefore, there are different constructive solutions, using metallic, rubber, silicon type
elastomers, hydraulic, pneumatic or hydro-pneumatic elastic elements.

According to the particular constructive and operational characteristics, behavior of buffer and draw-
gear devices is quite complex due to several non linear phenomena like variable stiffness-damping, hysteretic
properties, preloads of elastic elements, draw-gear compliance, clearance between the buffers discs, etc.
Buffers and draw-gears, still widely equipping railway vehicles, are based on metallic elastic rings
(RINGFEDER
®
type) [4], using friction elements to fulfill the required damping effects
.
For freight wagons there are in use buffers with 75 mm elastic stroke, high capacity buffers with 105
mm stroke and high energy absorption capacity buffers with 130 and 150 mm stroke, while for coaches there
are in use buffers with 110 mm stroke (prescriptions in UIC leaflets no. 526-1, 2, 3 and 528) [5, 6, 7, 8].



Fig. 1 Buffer used for passenger coach type ICPVA –
Romania, in conformity with UIC 528
Fig. 2 Buffer used for freight cars in conformity with UIC
526-2

Studies regarding the longitudinal dynamics of trains during braking actions are mainly focused on
long, heavy freight trains, due to the more obvious effects determined by the length of the brake pipe and
numerous large masses interconnected [9, 10, 11, 12, 13, 1, 2, etc]. Comparatively, issues regarding the
longitudinal dynamic reactions in passenger train body seem to be less important. In fact, these are generally
short, having a constant and much uniform composition than freight trains and there are sufficient arguments
to support these assertions, e.g. passenger railcars are typically two axles bogies vehicles and have almost the
same length, the mass difference between an empty and fully charged coach is significantly lower.
Still, prove not only the complex evolution of dynamic in-train reactions during braking actions, but
also possible circumstances conducting to significant forces levels [8].
2. ANALYTICAL MODEL OF BUFFER HYSTERETIC CHARACTERISTIC.
According to the importance of buffers behavior for the dynamic in-train forces during braking actions,
the accuracy of an appropriate mechanical and mathematical model is relevant for correct simulation results.
Such a model has to fulfill the particular constructive and operational characteristics of these devices.
In simulation of individual shock and traction apparatus equipping railway vehicles one must take into
account the nonlinear phenomena like variable stiffness-damping, hysteretic properties, preloads of elastic
elements. In the case of a train, the draw-gear compliance or clearance between the buffers discs are also
relevant, while longitudinal forces between successive vehicles may be applied with shock.
The model for the shock and traction devices developed considered the energy dissipation capacity [14,
15, 16]. Generally, about 75% of accumulated potential energy has to be dissipated, in order to protect for
shocks the vehicles structure and load during the wagon gravity shunting.
The classical RINGFEDER
®
type buffer characteristics reveal the action of friction forces between the
elastic rings. Accordingly, the forces within the buffer may be valued assuming an algebraic sum of elastic
and friction forces [17].
Modelling the buffers hysteretic behaviour for evaluation of longitudinal dynamic in-train forces
 
107
The elastic and friction forces depend on the relative displacement between the vehicles, while for the
second one, considering a constant friction coefficient according to Coulomb model, it is relevant the sense
of displacement given by the sign of the relative velocity. In our case, assuming the interaction between a
railway vehicle and a rigid fixed system equipped with identical features as the vehicle, the relative
displacements and velocities are in fact the displacements x and the wagon velocities.
x

Considering a constant depending on the elasticity of the device and a constant depending on the
inner friction process, the forces within the buffer are:
e
k
f
k
b e f
1
(,) (1 sgn ) ( sgn )
2
F x x x k x k x x= ⋅ + ⋅ ⋅ + ⋅ ⋅ 

(1)
Case study 1. It was considered the situation of a vehicle having a mass M, equipped with above
presented type pair of buffers, launched against a rigid fixed referencial (see fig. 3 and 4) with an initial
velocity, adopted in respect to the constructive maximum strike of the shock devices [8].
0
x





Fig.3 Schematics of the wagon and fixed system Fig.4 Schematics of buffer (A) and coupling devices (B)
Considering R the resistences the railway vehicle is generally submitted to, including in that case the
braking forces, and the acceleration, the equation of motion for this case is:
..
x
e f
(1 sgn ) ( sgn ) sgn 0M x x k x k x x R x⋅ + + ⋅ ⋅ + ⋅ ⋅ + ⋅ =  

(2)
Case study 2. It was considered the situation of a vehicle having a mass M, equipped both with
buffers and a traction device fixed by a rigid central coupler to the rigid fixed referencial (see fig. 4 and 5),
submitted to the same actions. Considering a constant depending on the elasticity of the traction device
and a constant depending on the inner friction process, the forces within the traction apparatus are:
et
k
ft
k
  
et ft
1
(,) (1 sgn ) ( sgn )
2
t
F x x x k x k x x= ⋅ + ⋅ ⋅ + ⋅ ⋅
 
          (3)                         

Fig.5 Schematic wagon connections
In this case, the equation of motion is:
      
0sgn),(),(2 =⋅
+
+

+

xRxxFxxFxM
tb

                 (4)
Case study 3. The buffers were remodeled
considering a stroke limiter to permit lounching simulations
with higher initial velocities without exceeding the
constructive maximum strike of the shock devices.
Consequently, the buffer force model adopted is:
       

),(
lim
xxF

),(),(
lim
xxFxxF
bb

+
=
(5)

Camil CRACIUN, Ana-Maria MITU, Cătălin CRUCEANU, Tudor SIRETEANU
 
 
108

with
)]sgn(1[
2
1
),(
max
5
limlim
xxxkxxF −+⋅⋅⋅=

(6)
Considering that the forces developed in the traction device are given by relation (3), the equation of
motion is:
     
0sgn),(),(2
lim
=

+
+
⋅+⋅ xRxxFxxFxM
tb


(7)
3. NUMERICAL SIMULATION RESULTS
For the simulations performed, the main parameters used for buffers are ,
, ,
e
2800 kN/mk
=
f
1400 kN/mk
=
7
lim
8 10 kN/mk
= ⋅
10 kNR
=
,
40000 kgm
=
. For draw-gears, there were considered
identical characteristics as for buffers:
k
et
2800 kN/m
=
,
ft
1400k kN/m
=
. According to these numerical
data and imposing that buffers stroke do not exceed the maximum 110 mm value, the vehicle velocity for the
first and second cases was determined to be
0
x 1.55 m/s
=


while for the last case it was assumed in the
domain , according to real collision velocities due to gravity shunting. The positive
values correspond to compression process, while the negative one to the traction.

0
1.55x

2.5m/s
= ÷
Some of the representative results are presented in figs. 6 ... 17.
0.0 0.2 0.4 0.6 0.8 1.0
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
Displacement [m]
Time [s]
 
0.0 0.2 0.4 0.6 0.8 1.0
-1.0
-0.5
0.0
0.5
1.0
1.5
Velocity [m/s]
Time [s]
 
Fig.6 Vehicle displacement time history in case study 1 Fig.7
 
Vehicle velocity time history in case study 1
 

Modelling the buffers hysteretic behaviour for evaluation of longitudinal dynamic in-train forces
 
109
0.0 0.2 0.4 0.6 0.8 1.0
0
1x10
5
2x10
5
3x10
5
4x10
5
5x10
5
Buffer forces [N]
Time [s]
 
0.00 0.02 0.04 0.06 0.08 0.10 0.12
0
100
200
300
400
500
Force [kN]
Displacement [m]
Fig.8 Buffer forces time history in case study 1 Fig.9 Characteristic buffer force-displacement, case study 1

0.0 0.5 1.0 1.5 2.0
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
0.12
Displacement [m]
Time [s]
 
0.0 0.5 1.0 1.5 2.0
-1.0
-0.5
0.0
0.5
1.0
1.5
Velocity [m/s]
Time [s]
 
Fig. 10 Vehicle displacement time history in case study 2 Fig.11 Vehicle velocity time history in case study 2
0.0 0.5 1.0 1.5 2.0
0
1x10
5
2x10
5
3x10
5
4x10
5
5x10
5
Buffer Forces [N]
Ti me [s]
 
0.0 0.5 1.0 1.5 2.0
-3x10
5
-2x10
5
-1x10
5
0
Draw-gear Forces [N]
Time [s]
 
Fig.12 Buffer force time history in case study 2 Fig.13 Draw-gear force time history in case study 2
Camil CRACIUN, Ana-Maria MITU, Cătălin CRUCEANU, Tudor SIRETEANU
 
 
110
0.0 0.5 1.0 1.5 2.0
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
Displacement [m]
Time [s]
 
0.0 0.5 1.0 1.5 2.0
- 1.5
- 1.0
- 0.5
0.0
0.5
1.0
1.5
2.0
2.5
Velocity [m/s]
T im e [ s ]
 
Fig. 14 Vehicle displacement time history in case study 3
 
Fig.15 Vehicle velocity time history in case study 3
0.0 0.5 1.0 1.5 2.0
0.0
5.0x10
5
1.0x10
6
1.5x10
6
Buffer Forces [N]
Time [s]
0.0 0.5 1.0 1.5 2.0
-1.0x10
6
-8.0x10
5
-6.0x10
5
-4.0x10
5
-2.0x10
5
0.0
Draw- gear Force [N]
Time [s]
 
Fig.16 Buffer forces in case study 3
 
Fig.17 Draw-gear force in case study 3
 

4. CONCLUSIONS

Analyzing the results of simulations, it is first to notice the concordance to the real mechanical
expected evolution of studied responses.

The moments of null relative displacements correspond to the end of buffers, respectively draw-gear
action, and the relative velocity is zero at the maximum stroke of these devices.
It is whorth noting the succesive actions of these devices, according to the results presented in fig. 16
and 17 for the third case study.
We consider an useful feature of the simulation program the fact that the displacement of the vehicle
remains constant while the inner friction forces in buffers are exceeded by the external forces while the sense
of displacements changes. This aspect is more obvious in the first case, fig. 6 and 8 in the vicinity of 0.1 s.
The same thing can be said about the evolution of relative velocities in case study 3, observing that these
remain constant while the inner friction forces in buffers and draw-gear forces are exceeded by the external
forces. The realistic description of the phenomena is obvious by analyzing comparatively figs. 14-17.
Such models are useful and can be developed for a train assembly in order to study the longitudinal
dynamics and to establish specific conditions in terms of braking features and train composition, as well as
constructive and operational, to diminish the in-train dynamic reactions in such a manner to avoid disturbing
or dangerous levels. It is worth mentioning that the presented models permit also studies regarding collision
forces levels on railway vehicles.

Modelling the buffers hysteretic behaviour for evaluation of longitudinal dynamic in-train forces
 
111
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