An innovative numerical modeling approach for train noise sources simulation

Transcription

1 An innovative numerical modeling approach for train noise sources simulation P. Napolitano 1, M. Viscardi 1, D. Siano 2 1 Department of Industrial Engineering, University of Naples Federico II Via Claudio, Naples ITALY massimo.viscardi@unina.it 2 CNR (National Research Council of Italy) - Istituto Motori Viale Marconi, Naples ITALY d.siano@im.cnr.it Abstract: - The recent growth in the railway sector has involved a fast increment in technologies and requirements. The first trains were slow, noisy and polluting, the modern ones are more comfortable and the electrical engine can guarantee a safe-life for nature. The recent improvement in technology has been pulled by the more strictly requirements imposed by the law and by the customers, especially in terms of safety and comfort criteria. One of the more hard-to-satisfy criteria is the acoustical one. The European Union has recently approved a new technical regulation that must be satisfied for trains: the value of allowable SPL inside the cabin is fixed to 65 db. This requirements is than generally lowered by the customer requirements that imposes a technical minimum requirement more strictly than legislative one. Before the train is available for experimental tests just a numerical approach can be used to forecast the acoustic performance of the system. Many numerical approaches are available in this sense, as those based on Fem, BEM, SEA or Ray Tracing formulations; the availability of new computers and technologies has increased the computational capabilities and increased the accuracy of these tools. In any case, all these approaches can be used only to predict the distribution of noise field (in terms of SPL for example) and/or to identify the relative spectral characteristics; they cannot exactly replicate the subjective response to noise exposure. To reproduce this sensation of sound or noise, during this work, an hybrid approach based upon standard numerical technique and novel mathematical approaches have been used. Two train noise sources have been chosen (wheel and engine) and mathematical models have be developed to calculate the SPL vs time relationship. The model, implemented in a Simulink environment, has been used for a real-time simulation of the source noise emission and relative interaction with the physical environment. The computed noise can be heard using a speaker system. Key-Words: - noise source characterization, train, wheel-rail interaction, electrical engine, numerical modeling 1 Introduction In recent years the acoustical problem on train has became more and more important. The changes in the European law about the allowable noise level has pushed the manufacturer to characterize the acoustical performances of their vehicles. The principal reason to keep the eye on the maximum acoustic level is due to a comfort factor for passengers and to a security factor for conductors. A lot of studies have been done to investigate the relationship between acoustic sound pressure level and human performances and they have shown a concentration lack and the higher attitude to do errors if the work environment is noising. Today the method used to investigate the acoustic response of a system under acoustic or vibrational inputs is based on the FEM, BEM, SEA or Ray Tracing methods. Even if well assessed algorithms, the conceptual complexity and the high computational cost often get a physical limit to the number, or the accuracy, of performed analysis. Expecially if referred to multi-domain physical systems. 2 Problem Formulation Everyone has travelled on a train, metropolitan or high speed long distances, everyone has appreciated the noise level inside the compartment. Perhaps just a little of us has noticed the changes in the noise spectrum and source. For very low speed the noise is due to the wheel-rail interaction. Growing up with the velocity we have a middle zone in which the engine noise dominate. At very high velocity the ISBN:

2 aerodynamic noise become the dominant component and the pantograph is the dominant source. The task of presented analysis is to create e model simple and fast to process a certain number of samples for a real-time auralization. This task will be performed in a Simulink environment. The choice of this approach is supported by the facilities available in Simulink. In particular the FIR filter approach will be used in this case to ensure an analysis only in the time domain. For the real-time auralization it is important to work in the time domain. The classics methods are based on a frequency response so, to continue to use this approach, a double passage time-frequency, frequency-time back is necessary. This double step is very expansive from a computational point o f view and is impossible to perform it in a fast simulation or in a real-time auralization. The mathematical models for wheelrail, engine. Pantograph, will be developed in the following with the respective Simulink schemes. wheel. To develop a model for which the analytical solution can be calculated some hypotheses must be done. The first is the elasticity of the elements and, in general, the absence of plasticity during the rolling motion. Considering Fig. 1 the model is based on three fundamental equations. Fig. 1: linearized model Eulerian-Bernoulli for beam 3 Wheel-rail interaction The wheel-rail noise is due to the forces they exchange each other during the relative motion. In particular the relative motion, supposed to be like a rolling body motion on a rigid surface, in influenced by the roughness of the surfaces. If the wheel and the rail were perfectly smooth they have no exchange of forces and the noise in void. The perfectly smooth surfaces are condition necessary and sufficient to make the suspensions not necessary. In the real world, although, the roughness of wheel and rail require a suspension system for reciprocal coupling and to guarantee the comfort of passengers to generated noise. The process of noise generation has been studied in the European project CALM. The CALM project has shown a differentiation between the frequency range in which every element is more noise. The wheel in the Hz band and the rail in the Hz band. 3.1 Mathematical model The mathematical model shown in the following is originally due to Thompson which developed the original version. The Thompson work has been rearranged by Steenbergen[1] in its final formulation. The model developed by Thompson and Steenbergen give an information about the interaction force between wheel and rail. This force will be introduced in a FEM/BEM model to numerically calculate the noise induced by the Harmonic oscillator Contact force (1) (2) (3) To solve the differential system is necessary to apply an appropriate boundary condition set. The conditions the have been applied are: Boundary conditions: no perturbations at an infinite distance; Starting conditions: for t=0 all function are null except the train speed; Coupling the differential equations with the explicit boundary conditions in the Laplace domain the equation of the problem can be written as (4) The force in the Laplace domain can be so written as: ISBN:

3 (5) the Laplace domain solving equation (5); the second solve the equation (6) to translate the equation from Laplace to time domain. the same equation can be returned in the time domain applying the following integral (6) 3.2 Simulink model Simulink is a physical simulation environment used to solve a lot of different problems governed by differential equations. The approach that has been used for the specific problem is based on a discretetization of the problem. The solution at the time is calculated from the solution at time increasing the time. The variable time step will be used to maximize the efficiency of the solving algorithm. The first step is to implement the data that will be used as input; with reference to (5) the first parameter is the equivalent roughness of the wheel-rail interaction. The roughness function is given in [1] and the function shown in Fig. 2. The function is periodic to perform a periodic analysis for a real time simulation. Fig. 3: Simulink model The principal parameter is the function that depend from roughness and is shown in Fig. 4 Fig. 2: in function of complex number omega. Fig. 4 imaginary part (up) and real part (down) of The model shown in Fig. 3 is the complete Simulink model. In this model there are two main blocks; the first to calculate the force in The first block of Fig. 3 is divided in a numerator and denominator in which the basic operations (sum, subtraction, root, power, division, product) are combined to obtain the ISBN:

4 final result. In this two blocks the constants and the parameters are read from a database in which all train parameters are defined. This choice is a simply way to perform the same analysis for different train simply changing the input parameters. In Fig. 7 is shown the total force computed by the Simulink model for two different velocity, respectively 10 m/s an 20 m/s. From the comparison of two curves is self-evident the system is not liner; double speed implies not a double maximum force value. 3.3 BEM model The BEM (boundary elements model) is based on definition of an appropriate set of conditions to solve a differential problem. The basic approach is based on the resolution in time and frequency domain of the wave propagation equations in a deined volume. The advantages offered by a BE Model is that a good result can be obtained for a small volume if the right set if boundary conditions in imposed. Fig. 5: numerator (up) and denominator (down) The second block, illustrated in Fig. 3, is used to change domain. A step-by-step integration is performed for the values of calculated force. The manual integration is done with the Cavalieri-Simpson method. Fig. 7: Contact force, time domain for different speeds; 10 m/s (blue) and 20 m/s (green) CAD and mesh In Fig. 8 is shown the geometry of the wheel used for the simulation. Also for a BE Model the wheel must be meshed. The geometry is realized with a CAD software; the mesh using another software. Fig. 6: Inverse of Fourier Transformat In Fig. 9 and Tab. 1 the result of the mesh and the mesh parameters are than, respectively showed. ISBN:

5 Tet elements Minimum element quality Average element quantity Volume ratio 1.705E-9 Mesh volume 1.133E10 mm 3 Fig. 8: Wheel geometry Mazimum mesh grow rate Average mesh grow rate Tab. 1: Mesh parameters As a first analysis, wheel s normal modes have been extracted as these reported in the next figure 10. Fig. 9: wheel mesh (up) and a zoom (down) Fig. 10: an example of wheel s normal modes at 622 and 1970 Hz ISBN:

6 3.3.2 Frequency response The FEM/BEM model has been solved in a multyphisic environment. This approach is necessary to perform a correct acoustic-structure coupling. The task of the model is to transform the applied force in an audible noise measured by a microphone at a distance of 10cm from the wheel surface. Fig. 11 show a sketch of the microphones positioned in the acoustic domain Fig. 14: SPL (db) for a 1N force Fig. 12: Vibro-acoustic domain The coupled system is governed by the following equation (7) The analysis has been performed in the Hz frequency range with a step of 1 Hz. Next picture show an example of acoustic response both in the time and in the acoustic domain The force applied is a constant force of 1N in all the investigation range. It is evident, from the time based diagram, the time delay of the acoustic response with reference to the input force; after this transitory condition, the level remain constant. Main peaks in the frequency domain response, mainly coincide with the wheel s normal frequencies. 4 Electrical engine The engine of modern train is an electrical engine. The old diesel engine, since from the last century, have been substituted with modern engine that use the electricity to generate a rotating electromagnetic field capable of start the train. In general an electrical machine is maiden up of two elements. The rotor, which rotate at high speed (about 2000 rpm), and the stator that enclose the rotor and give a solid support to the structure. The standard engine used on commercial train is a three-phase engine supported by an AC correct. The alimentation line is, perhaps, a DC so an inverter must be used as interface between the two systems. 4.1 Mathematical model The electric engine is governed by the electromagnetic laws. The current inside the rotor is Fig. 13: SPL (db) for a 1N force ISBN:

7 (8) the rpm of the engine by the relationship of Fig. 15. the stator current is (9) and the flux inside is (10) where (11) (12) Fig. 15: Couple vs. rotor speed relationship The mathematical model is solved in the time domain solving a differential equations system. The time step used is a variable step limited to the maximum value of 1E-3 seconds. 4.2 Simulink model The Simulink model of the engine is maiden up by two elements. The first is asynchronous machine that convert the input voltage in a current, than in a rotating electromagnetic field to move the wheels. The second is an inverter which is an interface between the engine and the outer electrical elements. Amore detailed description is available in [2] and reported briefly in Fig. 16. The model has been composed of two elements, the inverter the first, the engine itself the second. The inverter is powered by a 480 V AC current and a switching system transform it in a DC current for the engine. The engine has three poles so the current is a sum of three sinusoidal functions. The fourth input in the mechanical required couple. The couple is the input given by the conductor and is related to Fig. 16: Simulink electrical engine The engine give in output the parameters about its running condition. The parameter, we are looking for, is the rotational speed of the rotor. Other electrical parameters are available for further uses. 4.3 Analytical noise The analytical equation is given by [3] and shown in the following: ISBN:

8 (13) where is the first resonance frequency calculated by (14) And the others members of (13) are the amplification factor (AF), showed in (15) and the testing frequency ( ) reported in (16) (15) (16) Equation (13) is implemented in Simulink environment. The created block requires in input the rotor speed and give the noise in the frequency domain. Instead to obtain the noise in the time domain an inverse of a FTT operation is required. The calculation block is shown in Fig. 17. As said below some input parameters are function of the engine and they are loaded from a database in which the engine is defined. Changing the parameter change the engine so the simulation can be very easy to apply to other engines. The equation, when solved, give a graph is the time response over a certain position for a rotor speed (rpm). In Fig. 18 is shown the analytical results of the simulation, that s seems to be according to the experimental results and tests. Fig. 17: Electromagnetic noise Fig. 18:SPL over the time 5 Conclusion In conclusion the noise generated by a train has been divided into two contributes one arriving from the wheel-rail system; the second one arrive from the motor. The results obtained during the numerical simulation seems to be consistent with the physic of the system. No experimental data are availed to validate the numerical model. The coupling between the two sources can be done using an ulterior BE model to perform a successive analysis including the cabin geometry and a microphone inside the cabin at the head of the conductor. The response of the full structure is the last step to complete the BE model. The characterization of the sources has been done according the hypothesis of punctual source without diffraction. In real application, for no source is valid the approximation of punctual source. In this case the source characterization was based only on the frequency response of the object. References: [1] X1. Steenbergen Micheal J. J. M., The applicability of lumped wheel models in the analysis of dynamic wheel-rail contact for short-length rail irregularities., Zaltbommel, [2] X3. Meenakshi Mataray, Vinay Kakkar, Asynchronous machine modelling using Simulink fed by a PWM inverter, International Journal of Advances in Engineering & Technology, May [3] X4. Radu S. Curiac, Sumit Singhal, Magnetic noise in induction motor, Dearborn : NoiseCon2008-ASME NCAD, NCAD [4] Viscardi M., Marino N., Isernia G., Setola R. HERMES: A new stand-alone platform for active noise control and damage detection, Proceedings of the 1999 International Congress on Noise Control Engineering, ISBN: