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Increasing the trains’ speed has always been one of the goals of any railway industry and train manufacturers. Also, the influence of the train speed on bogie’s dynamics has an immense importance. Therefore, it is important to analyze the effect of train speed on the stress distribution in different parts of train structure. In this study the result of the increasing speed on the applied stresses of a biaxial bogie frame has been examined. For this purpose, a biaxial bogie frame has been modeled using finite element analysis. Static and dynamic forces applied on the bogie with biaxial frame have been obtained for different speeds and rail roughness. The Von Mises stresses are adopted as equivalent stresses in the strength calculation. The results show that maximum stress always has been induced in the bogie bowl also the increase in bogie’s speed has remarkable effect on the increment of applied stresses in the bogie frame.

Nowadays, modern technology and its new features bring higher speeds with reliable safety and better ride comfort in rail transportation industries. Lately, railway industry has encountered newer stages of progress such as high speeds, traffic services, load traffics, magnetic trains and etc. In the past, railway progress was influenced by industrial revolution, discovery of steam engines and extensive extractions of coal and iron mines. The first rail way lines started to work in European countries in about 1830s and railway networks reached high congeries in the early 20^{th} century. The rapid advances in train-related industries have introduced high speed trains that resulted in faster transportations. Steam power motors showed wonderful operation during test stages. The maximum speed of these trains was 100 km/h in 1835 in England, 144 km/h in 1890 in France, 213 km/h in 1930 in Germany. Nowadays modern trains can easily travel at the speed of about 250 km/h [

Since 1960, developing of finite element method made scientists use this method to improve their calculation in many engineering fields. In this way and by developing these methods, a broad range of related software’s having been introduced and developed [

Generally, the simulation of rail based-vehicles is calculated in two distinct ways, called longitudinal dynamic and lateral dynamic. In longitudinal dynamics, some collection of wagons that are connected to each other by a hook, are the scope of analysis. For example, the strikes imported from collision of wagons, were analyzed by Yi M.Y. [

One of the wagon’s components is bogie that is called upon wagon’s movement system and it consists of the frame (longitudinal and lateral beam), spring system (suspension), wheel and axis system and brakes and related instrument system. In addition to the homogenous distribution of frame’s weight, bogie makes the wagon to perform smoothly on turns. It also provides track’s safety, the convenience of frame movement on railways with different lateral lines and it increases the wagon’s loading capacity. Therefore, one can conclude that bogie is one of the most important components in wagon frame. There are several standards for strength evaluation of the conventional bogie frame such as JIS E 4207 [

All previous studies mentioned above do not quantify the change in stress distribution in bogie frame caused by the increase in train velocity Therefore, in this research, bi-axis bogie frame (I79) has been modeled to investigated the effect of train’s velocity on the induced stresses in the bogie. For this purpose the velocity of the train has been changed from 20 m/s to 40 m/s at different loads. The analysis method is shown in

A solution method has also been used to analyze the dynamic behaviour of the system. It has been assumed that the train is passing through the ruggedness of the rail-way with a big pockets shape wave. Bogie suspension system is simulated with three degrees of freedom

and the forces and reactions of the initial and secondary suspension systems have been calculated. The out put of this stage has been used in the finite element (FE) based stress analysis. For this purpose, firstly, a FE model has been developed and is verified using modal analysis. Then, the stress analysis of the bogie frame has been carried out and the effect of train speed on this stresses has been investigated.

The bogie as shown in

Bogie is formed of several parts: two wheel and axis (1), two side beams (2), cradle (3), cushions (8), suspension system (4) and levering of brake (5).

Primary suspension system is positioned between the wheel and the side beam that is formed of two cap springs on the arm of each roller bearing. There are eight cap-springs for each primary suspension system. This system should absorb shocks and sudden vibrations. So it has a considerable elasticity and damping coefficient. In this model, each cap-spring has been simulated using a couple of parallel spring-dampers in which they have an equal spring and damping coefficients due to the same kind of the plastic that is used. The whole bogie has also been modeled using a spring and damper with coefficients that are eight times bigger than the coefficients of

the cap-springs.

Second suspension system consists of fourteen sets of internal and external helical springs and four friction dampers that ten sets of these springs are used straightly between side beam and the cradle and four sets are between side beam and friction damper. Springs are modeled in an equal manner in the dynamic model. Introduction of the friction dampers make the treatment of the model non-linear. The performance of these dampers can be influenced by the environmental conditions (like humidity, etc.). Also, their damping effect depends on the magnitude and rate of the applied load.

In this study, viscose dampers have been used instead of friction dampers. In order to obtain equal viscose dampers, the dissipated energy of each cycle should be computed, however for this bogie-design, it is theoretically impossible because of the variation of the normal forces. But if we experimentally find the diagram of the force-displacement for a damper, the area of this diagram will give the wasted energy and using this quantity, the damping coefficient can be found.

The dynamic model has also two masses, one of them is total mass of side beams and is between two suspension systems and the other includes mass of wagon, load and horizontal beam (the Cradle) that is on the second hang. The bogie and the suspension system are shown in

• Rail’s profile is symmetric in both sides.

• Springs and Dampers are completely ideal.

• Sliding and tolerances haven’t been considered.

• The effect of longitudinal vibrations has been ignored, because it is insignificant in comparison with the effect of body’s vertical movements.

• For reducing the degrees of freedom and having a simple model, system is considered as a single input model.

Once an appropriate physical model has been developed,

dynamic equations used in the model can be obtained. Differential equations of the bogie’s model in vertical directions are proposed as:

After simplification:

After simplifying:

After simplifying:

The parameters that are used in the above equations are:

• m_{1}: Total mass of side beams.

• m_{2}: Total mass of the wagon, the load and the cradle.

• x_{1}: Displacement of m_{1}.

• x_{2}: Displacement of m_{2}.

• x_{3}: Displacement of the connection point of damper and spring at secondary suspension.

• k_{1}: The equal elasticity coefficient at first suspension.

• k_{2}: The equal elasticity coefficient of springs that that are lied directly between of linear beam and cradle.

• k_{3}: The equal elasticity coefficient of springs which stand between the longitudinal beam and frictional damping.

• c_{1}: The equal damping coefficient at first suspension.

• c_{2}: The equal damping coefficient of viscous for frictional dampers.

And finally, matrixes of mass, stiffness, damping and forces for the model, may be obtained as below:

The matrixes above define a system of equations as:

A sinusoidal wave for unevenness of the railroad has been considered in this study which provides an exciting force that is used to carry out the harmonic analysis of the system of Equation (6). So, the particular answer for Equation (6) can be considered as:

Generally, “X_{j}” is a complex number that depends on (natural frequency) and parameters of the system. By superseding the particular answer in Equation (6), we will have (8).

Now, the main task is the solution of Equation (8) which can be solved using an appropriate computer program. The applied forces to the parts of the bogie frame can be calculated by obtaining x_{1}, x_{2} and x_{3} as follows:

• : Applied force from the equal spring of each cap spring to the side beam

• : Applied force from the equal damper of each cap spring to the side beam

• : Applied force from secondary suspension system to the side beam

• : Applied force from secondary suspension helical springs to the cradle The parameters used above are:

• : The equal elasticity coefficient of each capspring

• : The equal elasticity coefficient of each set from secondary helical suspension springs (the sum of the elasticity coefficient of an internal spring and an external spring)

• : The equal damping coefficient of each cap spring

• : The equal viscous damping coefficient of each frictional damper in the secondary suspension

To carry out the necessary dynamic analysis, it is necessary to have a model of the vehicle for calculating the values of the induced forces and displacements which are applied to the vehicle tires and carried through the suspension system in to the upper hand systems like chassis and its attaching links. The input of this analysis, is the displacement due to the road surface roughness and the response of the suspension system as spring and damper reaction forces will be produced because of their stiffness and resilience. These forces will be transferred to the upper hand systems. Because of the alternative and repetitive nature of these forces, they may cause fatigue in the vehicle parts and in their joints.

To develop a dynamic model and to find the reaction forces, different models such as 1/4, 1/2 or even a full model of the vehicle can be used and the latter one is the most sophisticated model and takes into account the effect of pitch, roll and bounces caused by passing the vehicle over a road with random roughness profile.

To carry out the dynamic analysis using numerical simulations, because of the large volume of data required for the real and accurate body models, usually simplified models can been used. However, to obtain accurate solutions, the major parameters, such as mass properties and inertia should be defined in the model in a correct way. Also, due to the large number of mechanical parts in the real vehicle body, their equivalent mass and inertia has been obtained using Solid Works software and has been introduced in the simple model shown in