Week 2 Railwheel and Track
Objective: To simulate the rotational movement of a rail wheel on a track and to analyse the stress and strain developed in the system for varying bearing loads.
Modelling of the rail wheel track:
The modelling and setup in ANSYS is carried out assuming the axle doesn't rotate but the wheel does and a bearing is present between the wheel and the axle which felicitates the rotation of the wheel over the axle. The actuation for the movement of the wheel setup is provided by a translational motion in the X direction of the axle translational joint coordinate system provided to the axle which then transmits this translation to the wheel and makes it rotate.
Setup:
Mesh Settings:
Element type: Tetrahedrals
Global element size = 50mm
Face sizing element size = 35mm
Face sizing is applied to the contact regions in the model i.e. the wheel and tarck surfaces in contact and the wheel hub inner surface and the axle surface in contact.
Number of nodes = 12425
Number of elements = 6254
Contact settings:
Contact between wheel and axle: Frictionless contact.
Here, the frictionless contact is provided between the axle and the wheel in order to mirror a bearing which fecilitates the rotational movement of the wheel and the non-rotation of the axle.
Here, the axle transfers all the loads into the wheel and that is why the wheel is kept as the target body and the axle is kept as the contact body.
Contact between wheel and track: Frictional contact (coefficient of friction = 0.3). Here, the load from the wheel is transferred into the tracks through their frictional contact and thus, the track is the target body and the wheel is the contact body.
All other contact settings are default
Joints:
Since the track is supposed to be fixed to the earth, a fixed joint is applied to the track with the ground body as the reference.
The forward motion of the wheel is modelled as follows:
The axle is assumed to be non-rotational and a translational joint (allowing only one translational DOF) between the axle and the ground is defined. Since the axle doesn’t rotate and the wheel has to rotate, a frictionless contact is used between the two to felicitate the sliding of the rotating wheel over the axle body. Since the wheel has to rotate and translate simultaneously, a planar joint is defined between the wheel and the ground allowing translation in the X and Y axis of the joint coordinate system and rotation about the Z axis of the joint coordinate system.
Joint Loads:
A translational motion is introduced in a gradual manner to the translational joint of the axle by introducing it in 5 loadsteps and the total distance to be covered by the motion is 500 mm (100 mm in each loadstep). Basically, due to the contact between the axle and the wheel, the translational motion is transferred to the wheel and since its DOF is restricted to the X-Y plane defined by the planar joint, it starts rotating and translating forward over the track by the virtue of its frictional contact with the track.
Bearing Loads:
The axle is responsible for transfering loads to the wheel. The loads transfered to the wheel may include the weight of the axle, the weight of the carriage, payload and people in the carriage above the wheel set and other loads. To provide a general representation of these loads, a vertical bearing load is intoduced which acts on the inner contact surface of the wheel and has a magnitude of 100kN.
Analysis Settings:
Automatic time stepping is applied for all the loadsteps except the first one. Carry over time step is activated which means there is no pre-defined initial time step value, instead the initial time-step for any loadstep is the same as the timestep for the last substep in the previous loadstep.
Minimum time step = 0.001 seconds
Maximum time step = 0.1 seconds
Large deflection is activated to account for geometric non-linearities. The solver type is set to direct, which uses a sparse matrix-based solver.
Analysis solution information:
The analysis takes 360 cumulative iterations to fully converge on all the substeps and loadsteps. For the second to fifth loadsteps, the time step (load increment) is constant and equal to the maximum allowable timestep (0.1 seconds). Since the first loadstep doesn’t have auto time stepping, the predefined time step limits don’t apply and has 4 substeps with time steps of 0.2 and 0.3 seconds two times.
The animation of the simulation can be seen below:
Animation of wheel on track
Results:
1). Entire system:
Von-Mises Stress
The maximum VM stress occurs on the track surface in contact with the wheel. This signifies the load transfer that occurs from the wheel to the tracks. It is equal to 163.04 MPa and occurs at the time stamp (substep) of t = 4.3 seconds.
Stress distribution in the wheel:
Stress in the wheel is majorly concentrated towards the wheel track contact, with little concentrations occuring at the wheel surface below the wheel hub. The maximum wheel stress generated is 137.26 MPa at a substep time of 3 seconds.
Fatigue Life:
The fatigue life for the entire assembly is 10^6 cycles. Since the all the components are made out of structural steel, this implies that the equivalent fully reversed stress amplitudes in the wheel track contact surfaces are below the endurance strength of structural steel components, as the life of structural steel at its endurance strength is usually 10^6 which means that there will be no failure due to fatigue.
Total Deformation:
Parametrization:
To compare different scenarios with different bearing loads on the wheel, a parametric study can be carried out with the maximum VM stress, maximum elastic strain, minimum fatigue life and the average total deformation (at the end of the final loadstep) being the output parameters and the bearing load value being the input parameter.
Thus, we have the following design points:
DP0: Bearing load = 100kN
DP1: Bearing load = 500kN
|
Bearing Load (kN) |
Max. VM Stress in system (MPa) |
Max. VM Stress in wheel (MPa) |
Minimum Fatigue Life |
Average total deformation (mm) |
|
100 |
163.04 |
137.26 |
1000000 |
358.7747397 |
|
500 |
702.67 |
503.08 |
4359 |
358.8213616 |
VM stress in the entire assmebly for bearing load 500kN
VM stress in the wheel for bearing load 500kN
Minimum fatigue life:
Due to the increased bearing load, the equivalent fully reversed stress amplitude produced in the wheel track contact surpasses the endurance strength of the structural steel component and thus the track will have a finite fatigue life. Since the most of the stress is concentrated at the track surface in contact with the wheel, that region will be the most suceptible for fatigue failure and as seem in the above picture, the mimimum fatigue life is 4358.8 (~4359 cycles) at the surface of the track in contact with the wheel.
Total deformation:
User defined result for calculating total deformation
The total deformation is a scalar measure (i.e. magnitude) of the total displacement of the nodes in the meshed FE model. This total displacement of any node is a vector sum of its displacements in X,Y and Z of the global coordinate system and the magnitude of the vector just gives the total deformation of the particular node. Thus, to find the total displacment on the basis of user defined results, we have to define some expression which represents the vector magnitude of all node displacment components.
Since, the total deformation consists of the directional deformations in each axis, we can find the directional deformation of the entire system in X,Y and Z directions and give them identifier names so that their values can be used in the expressions.
Identifier for X Directional deformation:
dux
Identifier for Y directional deformation:
duy
Identifier for Z directional deformation:
duz
Now that we have the vector components, we can find the magnitude by the expression:
dutot = sqrt((dux)^2 + (duy)^2 + (duz)^2)
where dutot is the identifier for the user defined result calculating the total deformation.
As can be seen from the above results, the user defined result gives the exact same result as given by the total deformation result output for a 100kN bearing load.
ALTERNATE MODELLING TECHNIQUES:
Several alternate modelling techniques can be thought of to simulate the rotation and translation of the wheel assembly. In these alternate models, it is assumed that the wheel has an interference fit with the axle i.e. it s fixed to the axle and thus, when the wheel rotates, the axle will rotate too. The two alternate models which are discussed vary on the basis of method of actuation of motion and the joints used. Because the axle rotates in these models, it is expected that for a same amount of bearing load, the stress generated in the wheel and the tracks will increase slightly.
Alternate Model 1
Mesh Settings:
Global element size = 50mm
Face sizing element size = 20mm
Nodes = 20304
Elements = 10712
Analysis settings:
Automatic time stepping activated for all loadsteps
Minimum time step = 0.005 seconds
Maximum time step = 0.05 seconds
Joints:
Planar joint between the wheel and the ground body
Fixed joint between the track and the ground body
Contacts:
Frictional contact between the wheel and the track with a coefficient of friction = 0.3
Bonded contact between the wheel and the axle
Joint Loads: Translational motion in the X direction of the joint coordinate system given to the wheel. The wheel moves a distance of 500 mm in 5 loadsteps of 100 mm each.
Results:
The motion of the wheel on the track is obtained as desired. Most of the stress is concentrated in the wheel track interface and some stress concentration is present around the hub of the wheel. This may arise due to the rotation of the axle with the wheel.
Equivalent VM stress in the entire assembly
The maximum stress produced is 286.01 MPa at the time instant of t = 3.9737 seconds.
Equivalent VM stress in the wheel
The animation of the simulation can be seen here:
Alternate Model 2:
Mesh Settings:
Global element size = 50mm
Face sizing element size = 30mm
Nodes = 15339
Elements = 7851
Analysis settings:
Automatic time stepping activated for all loadsteps
Minimum time step = 0.005 seconds
Maximum time step = 0.05 seconds
Joints:
Planar joint between the wheel and the ground body
Planar joint between the axle and the ground body
Fixed joint between the track and the ground body
Contacts:
Frictional contact between the wheel and the track with a coefficient of friction = 0.3
Bonded contact between the wheel and the axle
Joint Loads:
Rotational motion given to the axle in which the axle rotates 150 degrees in 5 loadsteps of 30 degree each. The diameter of the wheel is roughly 950mm, and for a 150 degree rotation, a total circumference of 1243.547 mm is covered, which means the wheel should translate that much distance.
Translational motion in the X direction of the joint coordinate system given to the axle. The wheel moves a distance of 1243.547 mm in 5 loadsteps of 248.71 mm each.
Results:
The motion of the wheel on the track is obtained as desired. The maximum stress produced is 233.07 MPa at the wheel track interface at the time instant t = 4.4594 seconds.
Equivalent VM stress in the entire assembly
Equivalent VM stress in the wheel
The animation of the simulation can be seen below: