Hybrid NVH Simulation for Electrical Vehicles III – Acoustic Model

Johannes Klein, Gottfried Behler, Michael VorlanderInstitute of Technical Acoustics, RWTH Aachen University, 52056 Aachen, Germany,

Email: johannes.klein@akustik.rwth-aachen.de

Introduction

The creation of a fast simulation tool for the NVH in-cabin auralization of electrical drive vehicles demandsshort calculation times throughout the whole simulationchain. As part of the FVA research project No. 682,the Institute of Electrical Machines (IEM) and the Insti-tute for Machine Elements and Machine Design (IME)of the RWTH Aachen University have implemented fastsimulation methods for the force excitation of the electri-cal machine ([1]) and its subsequent structural dynamictransmission ([2]) for frequencies up to 5kHz. These twosimulation stages calculate the resulting velocities andforces on the surface of the drive train and at its couplingpoints with the car structure based on the electrical inputof the machine. It is the task of the acoustical model togenerate a fast binaural in-cabin auralization from thosecalculated values. Fig. 4 depicts the structure of theresearch project, starting with the force excitation simu-lation and ending with a binaural auralization.

Figure 1: Structure of the FVA research project No. 682.

The forces and surface velocities are transformed into ra-diated sound pressure and structural velocities and fedinto binaural transfer paths to generate the in cabin sig-nals. While conventional methods such as BEM simu-lations deliver accurate results for the calculation of theradiated sound pressure from the surface velocity of abody, they usually require long computational times andthus are not suitable for a fast simulation chain. As asolution to this problem, the extension of an analyticalapproach for the radiation calculation ([3]) is developed.

The complete and accurate numerical simulation of alltransfer paths in a vehicle is also a slow and error-proneprocedure. Since the focus of the project is on the vari-ability of the drive train simulation and not of the ad-jacent vehicle structure, measuring the required air andstructure borne transfer paths between the engine com-partment and the passenger cabin is the preferable alter-native. The resulting binaural signals offer the full possi-bilities of objective and subjective audio signal analysis.The simulation methods, measurements and examples forthe analysis are presented in this paper.

Interfaces

The preceding stages of the simulation chain yield theforces and velocities on the surfaces of the vibrating bod-ies of the drive train and at their coupling points with thevehicle structure. The data is forwarded to the acousticalmodel through two separate interfaces: one for airborneand one for structure borne sound. The interfaces aredescribed in the following.

Airborne Sound

The maximum regarded frequency of the simulationchain is 5kHz. On cylindrical bodies, only velocity modesof the same or larger wave length contribute to the ra-diated sound pressure [4]. Therefore the regarded struc-tural wave length can also be limited. Two samplingpoints or more per wave length are required for the cor-rect description of the velocity modes, resulting in 216radial and axial surface velocity sampling points on theexemplary electrical drive train, as depicted in Fig. 4.

Figure 2: Electrical drive train model (top) with samplingpoint distribution (bottom).

Structure Borne Sound

The drive train has 3 coupling points with the vehiclestructure. Considering a coupled mechanical system asshown in Fig. 3, the source velocity can be described as

vf = Ys · Fb (1)

using the source admittance Ys and the blocked force Fbexercised by the source. The velocity in the adjacentstructure can be described as

vr = Yr · Fr (2)

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Figure 3: Coupled mechanical system.

with the admittance of the structure Yr and the force Fracting on it. The force Fc of the coupled system is thendescribed by ([7])

Fc = (Ys + Yr)−1 · vf = (Ys + Yr)

−1 ·Ys · Fb (3)

where the blocked force Fb is the result of the structuraldynamics simulation and Fc is the input for the subse-quent structure borne transfer paths. As a consequence,the admittances Ys and Yr have to be measured. Giventhe fact that the elastomer dampeners between the drivetrain and the vehicle structure could not be characterizedin the course of the project, Ys →∞ assumed, resultingin Fb = Fc. Thus, the simulated forces are directly fedinto the structure borne transfer paths.

Airborne Radiation

To connect the simulated velocity values with the air-borne transfer paths the radiated sound pressure causedby the surface vibration of the drive train needs to becalculated. As can be seen in Fig. 4 the surface of thedrive train mostly consists of two surface classes: cylin-drical surfaces and piston-like surfaces. As a means tobypass BEM simulations analytical radiation models forcylinder elements and piston-like plates are implemented.The resulting sound pressure values of both models aresuperposed to calculate the resulting total sound pres-sure.

Cylinder Model

Based on the solution of the wave equation in cylindri-cal coordinates the radiated complex sound pressure ofa cylindrical body at a given point in cylindrical coordi-nates

p(r, ϕ, z) =

1

2π

∞∑n=−∞

ejnϕ∫ ∞−∞

V n(r0, kz)Hn(krr)

H ′n(krr0)ejkzzdkz (4)

can be calculated ([4]). Herein,

V n(r0, kz) =

∫ ∞−∞

v(r0, z)e−jkzzdz. (5)

is the surface velocity spectrum ([4]), which is atwo-dimensional transformation of the normal velocityv(r0, z) on the cylindrical surface at the surface radiusr0. Using the stationary phase approximation ([5] the

integral in Eq. 4 can be approximated in cylindrical co-ordinates. The result is the complex sound pressure

p(R, θ, α) ≈

ρ0c

π

ejkR

R

∞∑n=−∞

(−j)nejnα V n(r0, k · cos(θ))

H ′n(kr0 sin(θ)) sin(θ)(6)

for points on a spherical surface with the radius R aroundthe source. Comparisons with BEM simulations as de-picted in Fig. 4 show a good compliance for the cylindermodel, considering the required computation time.

Figure 4: Comparison between BEM (top) and cylindermodel (bottom) results (left) for the 6th circular and 0th axialmode at various frequencies.

Piston Model

The on axis radiated sound pressure by a circular pis-ton moving with the velocity v at a given distance r isdenoted as ([6])

p(r, t) = ρ0cvejωt(e−jkr − e−jk

√r2+a2

). (7)

Using the directivity factor

R(θ) =2J1(ka sin θ)

ka sin θ(8)

with the angle θ relative to the main axis it is possible tocalculate the sound pressure at any given point in frontof the piston.

Transfer Paths

The goal of the simulation chain is to generate binau-ral sound pressure signals at the driver position for theassessment of the drive train noise. Therefore, the cal-culated sound pressure, forces and velocities are fed intomeasured binaural transfer paths.

Airborne Transfer Path

The airborne transfer paths are measured in a half-anechoic chamber, using a directional loudspeaker in theengine compartment and a dummy head on the driver

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seat. The drive train is removed for the measurements.The directional loudspeaker is moved along a sphericalsurface around the original position of the drive traindirected in the surface normal direction, matching thesimulated positions of the radiation simulation.

Structure Borne Transfer Path

The structure borne transfer paths are also measured ina half-anechoic chamber. The drive train is removed forthe measurements. An impulse hammer is used to ex-cite the three coupling points in all three axes. Triax-accelerometers at the input positions record the velocity,a dummy head at the driver position records the binauralsound pressure. Fig. 5 shows the setup with the dummyhead in the passenger cabin, as well as some accelerom-eter positions and the impulse hammer excitation.

Figure 5: Dummy head in passenger cabin (top), triax-accelerometer in engine compartment (middle), impulse ham-mer excitation (bottom).

Simulation Performance and Drive TrainEvaluation

Fig. 6 shows the left ear results for an exemplary partialload run-up with standard parameters for the simulatedmachine and drive train structure. The calculation ofthe binaural time signals in the passenger cabin basedon the velocities and forces of the structural simulationtakes about 1.7s per simulated signal minute. Thus, themodel fulfills the criterion of a fast simulation. The bin-aural time signal can be evaluated objectively and subjec-tively. The combination of several methods allows electri-cal drive developers to get a quick analysis of the effectsof changes to drive train components.

Figure 6: Exemplary partial load run-up, results shown forthe left ear. Time signal (top), total loudness over time ([8],middle), spectrogram (bottom).

Fig. 7 shows an example for the simulation of a vari-ant with additional elastic decoupling in the drive trainstructure. The goal is to diminish the dominant reso-nances in Fig. 6 for machine speeds around 3000 rpm.As it can be seen in the comparison between the original(red) and new (blue) loudness curve in Fig. 7, the goalhas been accomplished. Due to resonance shifts causedby the decoupling, new dominant resonances appear atmachine speeds that correspond to vehicle velocities ofabout 70 km/h, which are a very frequent use-case, re-sulting in a clear contraindication for this variant. Thisdemonstrates how the application of a fast integrativesimulation helps to identify unexpected effects that onlyappear in the coupled systems.

Figure 7: Exemplary partial load run-up, results shown forthe left ear. Reference run-up (red), additional elastic decou-pling (blue). Total loudness over time.

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References

[1] Rick, S.; Franck, D.; Hameyer, K., Hybrid NVHSimulation for Electrical Vehicles I - Force Excita-tion Model for Electrical Machine, Fortschritte derAkustik : DAGA 2015, Nurnberg, Germany, 16–19March, 2015.

[2] Wegerhoff,M.; Schelenz, R.; Jacobs, G., HybridNVH Simulation for Electrical Vehicles II - Struc-tural Model, Fortschritte der Akustik : DAGA 2015,Nurnberg, Germany, 16–19 March, 2015.

[3] Blum, J.; Pollow, M.; Muller-Trapet, M.; vander Giet, M.; Dietrich, P. , Simulationskette zurPradiktion der abgestrahlten Schallleistung elek-trischer Maschinen, Fortschritte der Akustik : DAGA2011, Dusseldorf, Germany, 21–24 March, 2011.

[4] Williams, E. G., Fourier Acoustics: Sound Radiationand Nearfield Acoustical Holography, Academic Press,(1999).

[5] Junger, M.; Feit, D., Sound, structures and their in-teraction, MIT Press, (1986).

[6] Kuttruff, H., Acousitcs, Taylor & Francis, (2007).

[7] Dietrich, P., Uncertainties in Acoustical TransferFunctions, RWTH Aachen, Dissertation, (2013).

[8] DIN ISO 226.

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