High-Speed Train Running Characteristics Assessments Using Multibody Dynamics Simulation

The development of railway transportation in Indonesia in recent years has increased the number of new vehicles with various types and specifications. These new vehicles should pass a series of running characteristics assessments against standards to ensure safety and comfort in operation. Before the field testing, the assessments using numerical simulation in the design stage need to be done. This study aims to assess the high-speed train running characteristics through modeling and testing using multibody dynamics simulation software. The standards used for the assessments refer to EN 14363 – Testing and Simulation for The Acceptance of Running Characteristics of Railway Vehicles. The high-speed train model was built and validated through four methods with comparative values calculated analytically. The validated model was then run in the simulation to get the parameters for assessment. The parameters include the coefficient of flexibility, critical speed, safety against derailment with various methods, ride comfort, and vibration mode. The parameters obtained from the simulation are compared to the acceptance criteria specified in the standard. The results show that the vehicle performance fulfills the requirement prescribed by EN 14363 standard. After the vehicle and the track infrastructure are ready, they need to be confirmed by a series of testing performed on the main line. This study supports the development of high-speed trains in Indonesia and is expected to give more insight into the usefulness of numerical simulation to predict the characteristic of dynamic performances of railway vehicles in actual operating conditions.


Introduction
The development of railway transportation in Indonesia in recent years has increased the number of new vehicles with various types and specifications.These vehicles should pass a series of design, manufacturing, and testing stages before they are ready for operation on the rail.The testing stage is done on all aspects of the vehicle, one of which is assessing the running characteristics.It is performed to ensure the safety and comfort of the vehicle during operation.
The testing stage is usually done after the prototype of a product has been made.However, it takes a lot of time and cost.The alternative solution to this problem is to use numerical simulation for testing during the design stage.It can be advantageous before conducting field tests, especially for a new vehicle that has never been made before, such as a high-speed train.A computer simulation can easily define the vehicle and the track parameters [1].Optimization of the vehicle can also be done concurrently with the simulation being run.
In European countries, vehicle acceptance tests can be performed by simulations according to EN 14363 -Testing and Simulation for The Acceptance of Running Characteristics of Railway Vehicles [2].Polach [3] previously did a simulation of a rail vehicle based on EN 14363.Meanwhile, the standards governing rail vehicle testing procedures in Indonesia are insufficient, especially for new types of vehicles.The study to develop the standard for new vehicle testing procedures in Indonesia has been initiated in the last few years including the utilization of the computer simulation.Wikaranadhi [4] performed a dynamic simulation for testing the Jabodebek LRT model regarding EN 14363 standard.Then, the study continued for a test case of the high-speed train early design developed in Indonesia supported by National Research and Innovation Agency and Indonesian rolling stock manufacturer PT Industri Kereta Api (Persero).This paper reports the assessment of the highspeed train running characteristics through modeling and testing using multibody dynamics simulation software.The assessment carried out refers to EN 14363 standard.

High-Speed Train Model and Validation
In this research, the high-speed train was modeled as a multibody system consisting of four wheelsets, two bogie systems (including suspension systems), and a carbody.Figure 1 shows a schematic diagram of the model.All bodies were modeled as rigid bodies and the suspensions as massless interconnections.The model built using Universal Mechanism software was a single vehicle, see Figure 2.
The model validation procedure referred to the method that Putra [5] did on the tilting train model, which was performed by considering the vertical wheel force in static, tangent track, and curving conditions and the system natural frequencies.Only static and curving validations are explained in this paper.Theoretically, the weight of the entire rail vehicle is equally distributed on each wheel in a static condition.Curving validation was done by running the model on an ideal curving condition.The outer and inner wheels have the same vertical forces while curving ideally at balance speed.Therefore, they can be calculated analytically using the equations in Handoko [6].Table 1 shows the difference of the vertical wheel forces in the static condition obtained from the simulation and the analytical calculation is about 0.06 -0.07%.While in the curving condition, the vertical wheel forces obtained from the simulation have a difference of 0.33 -4.30% against the analytical calculation, as shown in Table 2.According to the results of the entire validation steps, the high-speed train model was considered valid and ready to use for running characteristics assessment simulation.

Running Characteristics Assessments
The running characteristics assessment was carried out for the validated high-speed train model by dynamic multibody simulation.The simulations referred to a commonly used standard for rail vehicles, i.e., EN 14363.Moreover, the coefficient of flexibility, critical speed, ride comfort according to the Sperling index, and vibration mode were also analyzed.The parameters obtained from the simulation were then compared to the acceptance criteria specified in the standard.The irregularities applied on the track for several simulations were defined by UIC Good and UIC Bad tracks; see Figure 3.

Coefficient of Flexibility Analysis
Rail vehicle coefficient of flexibility is defined by the ratio of an angle  formed by the carbody perpendicular to the rail level to the cant angle of the track  in a static condition [7].The coefficient of flexibility of the high-speed train was determined by analytic calculation and simulation.Equation (1) defined by Zhang [8], was used to calculate the coefficient of flexibility analytically.
The coefficient of flexibility should not exceed 0.4 [7,9].Table 3 shows the coefficient of flexibility of the high-speed train model for each simulation scenario that meets the requirement.However, the analytical value exceeds the maximum value and the simulation results.It could be caused by small angle approximation and linearization of the suspension parameters.

Critical Speed Analysis
In designing a rail vehicle, the critical speed must be analyzed to ensure the value exceeds the operational speed.In addition, it helps to prevent hunting motion when the vehicle is running on a tangent track.The analysis was carried out by running the model on a tangent track with a high initial speed of 400 km/h for this case.Then, the model was given a constant braking force of 12.5 kN to reduce the speed.On the other hand, an initial lateral displacement was given to the model so that the hunting motion could occur.The vehicle speed when there are no longer oscillations due to hunting is the critical speed, see Figure 4.The result shows that 304 km/h was the critical speed of the highspeed train.

Safety Against Derailment on Twisted Track
Three methods are prescribed in EN 14363 that can be selected according to the vehicle conditions and availability of the infrastructures for testing the safety against derailment on twisted tracks.The methods consist of a test on the twisted track, a twist test rig and flat test track, and a twist test rig and yaw test rig.All methods were simulated and showed that the high-speed train can safely go through the twisted track.However, only one method was explained in this paper, i.e., the first method.The method was done by running the model on a curve with a radius of 150 m and a speed of 10 km/h.Superelevation of the test track on the curve section twisted with the slope of 2‰.The parameters of simulation consist of derailment coefficient (Y/Q), wheel lift (Δz), and angle of attack (α) of a leading wheelset.The value of Y/Q and Δz was used for the assessment, while α was only documented.The results of the simulation are shown in Figure 5.The value of Y/Q of the outer wheel was higher and fluctuated more than the inner one.It might be caused by contact between the flange of the outer wheels and the rail.The angle of attack of the outer wheel also caused the wheel to be more sensitive to derailment.Overall, the value of the derailment coefficient Y/Q of the model can be accepted for this method and no wheel lift was detected during the model running on the curve.

Dynamic Performance Assessment
As the second assessment in EN 14363, dynamic performance assessment tests could show the rail vehicle characteristics that only appear at high speed.The characteristics consist of running safety, track loading, and ride characteristics.The test simulations were performed by running the model with the speed of 330 km/h on a tangent track of 500 m and 90 km/h on a curve with a radius of 400 m.The parameters observed for assessment and the limit value are shown in Table 4 and Table 5.Table 4 shows the model had good results in all parameters when running on the UIC Good track.Besides, the results on the UIC Bad track show the sum of lateral wheel forces beyond the limit value that affects the value of the derailment coefficient Y/Q.However, in a high-speed train operational, the rails always keep good quality to avoid UIC Bad track irregularities.Furthermore, as shown in Table 5, all parameters were satisfied on the curving simulation.Thus, the simulation results show that the model had a good dynamic performance.

Analysis of Ride Comfort
Ride comfort represents the comfort level perceived by passengers in the carbody.This research used the Sperling index (Wz) to evaluate ride comfort [10,11].The Sperling index is formulated by Equation ( 2) for lateral direction and Equation (3) for vertical direction [12].
, = 10√∫  3   3  30 0,5 with a is acceleration in the frequency domain (cm/s 2 ), f is the frequency (Hz), B w is the weighting factor for lateral acceleration, and Bs is the weighting factor for vertical acceleration.Simulations were performed by running the model with the speed of 250 km/h, 275 km/h, and 300 km/h on the tangent tracks with UIC Good and UIC Bad irregularities.The acceptance value for the Sperling index in this research was Wz ≤ 2.50 for more pronounced but not unpleasant vibration sensitivity.The acceleration measurement points were located in the center of the carbody floor, above the front bogie, and above the rear bogie.The Sperling indices were checked for lateral and vertical directions to see the vibrations that influence the passengers in the carbody.
The Sperling index of the high-speed train model while running on UIC Good and UIC Bad tracks are shown in Table 6.The indices increased with the increase of speed.It could be caused by the increase of vibration at a higher speed.The results show that all Sperling indices for UIC Good track were in the acceptance region, while on UIC Bad track, the index exceeds 2.5 at the speed of 275 and 300 km/h.From the results, we can also see that the lateral index is always more significant than the vertical one.Those indicated that vertical suspensions better comfort the passengers than lateral suspensions.Therefore, most of the Sperling indices fulfilled the requirements.However, the UIC Bad track condition should be avoided for high-speed train operations.

Vibration Mode Analysis
Vibration mode analysis compared the acceleration power spectral density (PSD) of the simulation results with the system natural frequencies.The natural frequencies of the carbody rigid body mode are listed in Table 7.The high-speed train model was run at 300 km/h on tangent tracks with UIC Good and UIC Bad irregularities.The carbody acceleration PSDs on the UIC Bad track are shown in Figure 6.The peak of each acceleration PSD occurred at around the natural frequencies of the carbody rigid body mode.Those were probably correlated with the carbody vibration mode.For example, the peak of vertical acceleration PSD occurred at around 0.88 Hz, likely correlated with the bounce vibration mode.

Conclusion
Modeling and simulation of the high-speed train running characteristics assessment based on EN 14363 standard have been performed using Universal Mechanism multibody dynamics software.The simulation results show that the vehicle performances fulfill the requirements prescribed by the standard.However, an optimization of the design is needed to obtain more optimum results.On the other hand, the results must be confirmed by a series of testing performed on the main line after the vehicle and the track infrastructure are ready.This study is done to support the development of highspeed trains in Indonesia.It is also expected to give more insight into the usefulness of numerical simulation to predict the characteristics of the dynamic performances of railway vehicles in the actual operating condition.

Figure 1 .
Figure 1.Schematic diagram of the high-speed train multibody model

Figure 4 .
Figure 4. Lateral oscillations of the wheelset vs speed

Table 1 .
Vertical wheel forces in static condition

Table 2 .
Vertical wheel forces in curving condition

Table 3 .
Coefficient of flexibility of the high-speed train

Table 4 .
The dynamic simulation results on a tangent track

Table 5 .
The simulation results on the R400 curve with superelevation of 89 mm

Table 6 .
Sperling index on UIC Good and UIC Bad tracks