DEMİRYOLU TAŞITI TEKERLEK TAKIMI SİNÜS HAREKETİNİNANALİTİK VE HESAPLAMALI YÖNTEMLERLE İNCELENMESİ
ANALYTICAL AND COMPUTATIONAL INVESTIGATION OF HUNTINGINSTABILITY FOR A RAILWAY VEHICLE WHEELSET
Yazar: RIDVAN AKÇAY
Danışman: DR. ÖĞR. ÜYESİ OSMAN TAHA ŞEN
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Raylı Sistemler Mühendisliği Ana Bilim Dalı / Raylı Sistemler Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2019
Konu: Makine Mühendisliği = Mechanical Engineering

Özet:
Raylı taşıt dinamiği raylı sistemler mühendisliğinin temel konularından biridir. Farklı
fiziksel koşullar altında aracın davranışı yapılan dinamik analizler sonucu belirlenir.
Aracın dinamiğini etkileyen temel parametreler taşıtın boyutları, kütle ve atalet
değerleridir. Ayrıca süspansiyon elemanlarının yay ve sönüm katsayıları ve bu
elemanların bağlantı noktalarının konumları da taşıt dinamiğini etkilemektedir.
Farklı çalışmalarda taşıtın davranışını belirleyen parametler için farklı modeller
tavsiye edilmiş ve bu tavsiyeler ışığında ray-tekerlek ilişkisi açıklanmaya
çalışılmıştır.
Örneğin Prof. Dr. J.J. KALKER ray tekerlek ilişkisini 1960'larda hazırladığı doktora
tezinde açıklamak için kendi adıyla anılan modelini önermiş; daha sonraki yıllarda
aynı konuda çalışma yapan Prof. Dr. Olridch POLACH çoklu gövde
simülasyonlarında daha hızlı sonuçlar verecek farklı bir model önermiştir.
Raylarla tekerlek takımları arasındaki kinematik ilişkiler, geometrik formlarından
dolayı demiryolu taşıtlarının ilginç bir dinamik salınımlı davranış sergilemelerine
neden olmaktadır. Bu kendi kendine tahrikli titreşim hareketi aynı zamanda sinüs
salınımı olarak da bilinir ve ilk olarak "tekerlek takımının raylar üzerinde salınımlı
fakat kolay bir hareketi" olarak tanımlanmıştır. Bu harekete neden olan ana faktörler
tekerleklerin konikliği, ray-tekerlek temas arayüzündeki koruyucu olmayan sürünme
kuvvetleri ve tekerlek takımı ve boji üzerindeki süspansiyon sistemi arasındaki
kuvvet etkileşimleridir. Daha yüksek hızlarda sinüs salınımları kararsız hale gelebilir
ve bu nedenle demiryolu araçları belirlenen kritik hızların üzerinde çalışamaz. Bu
nedenle, operasyonel hız aralığını arttırmak için aracın kritik hızı yüksek olmalıdır.
Stabilite analizlerine dayanarak, tekerlek takımının ataletini azaltmak, süspansiyon
sisteminin sertliğini arttırmak, tekerlek yarıçapını büyütmek gibi kritik hızları
arttırmanın birkaç yolu önerilir.
Bu tez kapsamında demiryolu taşıtının dinamik davranışlarının incelenmesinde
gerçeğe en yakın sonuçları veren hesaplamalı model, bazı kabuller yapılarak kurulan
analitik model ve analitik modelin daha da basitleştirilmesiyle kurulan
basitleştirilmiş modeller için çözüm yapılarak kritik hız bulunmuş, sistem
parametrelerinin tekerlek takımının dinamik stabilitesi üzerindeki etkileri araştırılmış
ve karşılaştırmalar yapılmıştır.
Çalışmada demiryolu araç dinamiğinde önemli bir etkiye sahip olan, "hunting"
salınımı" da denilen raylı taşıt sinüs hareketi üzerinde durulmuş; 3 serbestlik
derecesine sahip tekerlek takımı ile kurulan matematik model üzerinde derayman
analizi yapılmıştır. Daha sonra karayolu taşıt dinamiğine benzer bir model baz
alınarak matematik model basitleştirilmiş bir modele dönüştürülmüş ve aynı
parametrelerle çözüm yapılmıştır. Son olarak hesaplamalı model için matematik
modele benzer olarak tek dingilli boji sistemi kurulmuş ve her 3 modelde elde edilen
sonuçlar parametreler bazında karşılaştırılmıştır.

Abstract:
Rail vehicle dynamics is one of the main subjects of rail systems engineering. The
behavior of the vehicle under different physical conditions is determined by the
results of dynamic analysis. The main parameters affecting the dynamics of the
vehicle are the dimensions of the vehicle, mass and inertia values. In addition, the
spring and damping coefficients of the suspension elements and the locations of the
connecting points of these elements also affect the vehicle dynamics.
Different models have been recommended for the parameters that determine the
behavior of the vehicle in different studies and the rail-wheel relation has been
explained in the light of these recommendations.
For example, Prof. Dr. J.J. KALKER In order to explain the relationship between rail
and wheel in the 1960s, proposed the model referred to by his name. who worked in
the same subject in later years. Dr. Olridch POLACH has proposed a different model
which will give faster results in multi-body simulations.
The kinematic relationships between rails and wheel sets cause railway vehicles to
exhibit an interesting dynamic oscillating behavior due to their geometric form. This
self-propelled oscillatory motion is also known as sine oscillation and was first
described as oscillating but easy movement of the wheel assembly on rails ". The
main factors that cause this movement are the taper of the wheels, the non-protective
creep forces at the rail-wheel contact interface and the force interactions between the
suspension system on the wheel assembly and the bogie. At higher speeds, sine
oscillations may become unstable, and thus railway vehicles cannot operate at
specified critical speeds. Therefore, in order to increase the operational speed range,
the vehicle's critical speed must be high. Based on stability analyzes, several ways to
increase critical speeds, such as reducing inertia of the wheel assembly, increasing
the rigidity of the suspension system, and increasing the wheel radius, are
recommended.
Within the scope of this thesis, the computational model which gives the closest
results to the realistic results of the dynamic behavior of the railway vehicle, the
analytical model established by making some assumptions and the simplified models
established by further simplification of the analytical model were found to be critical
speed, the effects of the system parameters on the dynamic stability of the wheel set
were investigated and the results weere compared.
The study focuses on the sine movement of the rail vehicle, also called "hunting"
oscillation, which has a significant impact on the dynamics of railway vehicles;
Derayman analysis was carried out on the mathematical model established with the
wheel set having 3 degrees of freedom. Then, based on a model similar to road
vehicle dynamics, the mathematical model was transformed into a simplified model
and the solution was made with the same parameters. Finally, for the computational
model, a single axle bogie system was established similar to the mathematical model
and the results obtained in all 3 models were compared on the basis of parameters.
With the strengthening of computer programs and processors, it has become possible
to model and analyze complex mechanical systems. It is very easy to see the effect of
the change of the parameters on the program with the mathematical model of the rail
system tool installed on the computer. The model outputs provide information about
the vehicle's dynamic behavior and vehicle-road interaction. The suspension or other
components can be optimized. The necessary changes can be made through
mathematical models in order to create the conditions studied for safe operating
conditions.
Simpack, which we used in this thesis, is a general purpose Multibody Simulation
(MBS) software for dynamic analysis of any mechanical or mechatronic system.
Enables engineers to create and solve virtual 3D models to predict and visualize
motion, coupling forces, and stresses.
Topology determines the degree of freedom, constraints and connection properties of
each component of the model. Before the model is created, the topology is created by
considering the operation of the system. Firstly, the joint '7 için is used for wheel-rail
contact and the restriction' 78 için is used for rail wheel. The axles are connected to
the wheels in a tight fit. Primary suspension elements are modeled between the wheel
set and the bogie. The bogie and the axle are connected to each other by a spring
number 4 and 1 degree of freedom. The bogie can only travel in the rail direction.
The wheel set is connected to the traverse with 6 degrees of freedom using the joint
'07 olup and the joint' 91 arasında is used between the traverse and ballast.
Simpack 2018.1 version was created dynamic model of the vehicle. First, the wheel
assembly was placed in the appropriate position on the 60E1 type rail. Then bogie
and suspension elements were added on the wheel model. The model installation
phase was completed by assigning variables such as wheel-rail profile, contact
model, road input, speed value.
In the Simpack model, the input of the path was made by creating a 1000-meter track
that does not include any curves, gradients and slopes to be in harmony with the
MATLAB model. Wheel profile is one of the important parameters affecting the
dynamic behavior of the rail vehicle. While determining the wheel profile according
to the standards in high speed trains and conventional line operations, the line profile,
radius etc. can be determined by looking at the line and operation status. It is
selected. S1002 profiled wheel is selected in the Simpack model
The design of railway vehicles and the characteristics of the equipment used are
effective on the maximum speed the vehicle can make without derailing. Knowing
which component will affect the speed of the vehicle and how much it will help to
achieve the intended goal in design. In this thesis, analytical and computational
models were established in order to investigate the effect of components of a railway
vehicle on derayman, and the response of the vehicle was measured and the results
were compared. The main parameters determining the character of the railway
vehicle were determined and their effects on critical speed were tried to be observed.
The solution of the analytical equations was examined with the change of the
parameters and the effects of the parameters on the system behavior were
determined. It is tried to understand how different parameters affect the system in
solving the equations and what can be more effective while optimization. While
determining the critical speed, the critical speed was determined by changing the
speed according to the increase or decrease of accepted amplitudes starting from a
certain speed.
In the simplified model, critical velocity determination was made by finding roots
with solved eigenvalue problem.
In order to determine the effect of the springs on the stability of the model, the lateral
and longitudinal spring coefficients were changed to determine the critical velocity.
It was observed that the critical speed of the established model increased with the
increase of longitudinal and lateral spring coefficients from 105 to 106 for the
mathematical and computational models.
For mathematical models and computational models, critical speed determination
was performed with different wheel radii. As a result of the analyzes made with the
values ​​of the wheel radius between 0.46 m and 1 m, it was observed that the increase
of the wheel radius had a critical speed increasing effect for all three models.
In order to understand the effect of the load on the railway vehicle on the critical
speed, critical speed analysis was performed for all three models at different loads.
As a result of the analyzes carried out for loads between 40 kN and 100 kN, it was
observed that the transported load had no significant effect on stability.
Analyzes were performed with springs placed at different distances in order to
understand how the stability changes when the springs connecting the bogie and the
wheel in the rail direction approach each other. The most unexpected results were
observed when compared with other parameters. In the analysis made with analytical
and simplified models, the increase in the distance between the springs significantly
increased the critical speed and a slight increase in the computational model was
observed.
The analytical and computational models are based on the Kalker linear model and
the models are solved by computer. Firstly, according to the model designed on the
basis of real values, it was observed that there was very little difference in terms of
critical speed between the analytical model simplified model and all three models.
In the computational model, the critical speed was lower than the other models. The
response of the rail vehicle to the variation of the coefficients of the longitudinal and
lateral springs is similar for all 3 models.
An increase in the critical velocity was observed with the increase of spring
coefficient; however, the response of the analytical models to the change in spring
stiffness was found to be more obvious.
The increase in the wheel radius increases the critical speed on all 3 models,
paralleling the use of wheels with a higher radius on high speed trains. It is
noteworthy that the computational model shows a steep rise from a certain wheel
radius.
For all three models, it was observed that the wheel load or the weight of the wagon,
railway vehicle had almost no effect on the critical speed. Finally, the effect of the
distance of the longitudinal springs to the center of the rail on the critical velocity
was examined, but for analytical and simplified models the critical velocity increased
as this distance increased, while the computational model did not have a significant
effect on critical velocity.
In this study, the wheels used in the analytical model are in the form of a full cone
and can make large oscillations horizontally on the rail. In the computational model,
the S1002 railway wheel has a different geometry than the analytical model, but also
has a flanged boden. It is considered that the impact loads resulting from the impact
of the basin on the rail in horizontal movement is a factor affecting the stability of
the system and it is emphasized that the critical speed of the computational model
may be the reason of lower than the analytical models. Therefore, analytical,
simplified and computational models can be used to observe the effect of parameters
on the critical speed of the vehicle; however, the computational model should be
used to calculate the critical speed of the railway vehicle.