In situ characterization of exemplary rail vehicle structure borne sound sources Jenny Böhm 1 , Haike Brick 2 German Centre for Rail Traffic Research August-Bebel-Str. 10, D-01219 Dresden

ABSTRACT A narrowband characterization of structure borne sound sources is needed for an accurate prediction of rail vehicle interior noise. Typical rail vehicle sources are relatively large and heavy structures. In 2019, a measurement method for the indirect determination of the blocked force was standardized. It can be applied in situ, with the source connected to an arbitrary receiving structure and was found to be promising for rail vehicle applications in recent re- search projects. One major challenge is the need to measure the coupled velocity and mobility of all relevant degrees of freedom (six directions per coupling point).

Within the European Shift2Rail project DESTINATE, measurements were carried out using a traction motor and an HVAC unit as exemplary sources to investigate the suitability of the in situ method for rail vehicle sources. The measurements include translational and rotational degrees of freedom. Recently, they were further analyzed to investigate the effects of neglecting degrees of freedom. The results will be shown in this contribution.

1. INTRODUCTION

Structure-borne sound prediction is important for rail vehicle interior noise. A correct prediction needs receiver independent data of the source strength as input, such as the free velocity or the blocked force. The direct measurement of these quantities requires a special test set-up to ensure free or blocked boundary conditions at the source’s coupling points. This can be difficult to achieve for typical rail vehicle sources, which are usually large and heavy structures and often comprise excita- tion mechanisms that prevent a source operation under free boundary conditions. The in situ method determines the blocked force on an arbitrary receiver without a special test set-up, so that coupling conditions can be close to reality. The measurement can even take place in the target installation. Although determined on an arbitrary receiver, the blocked force measured in situ is theoretically a receiver-independent quantity that is suitable for predicting structure-borne sound for different re- ceiving structures. The in situ method was standardized in 2019 in ISO 20270 [1]. A recent European research project recommends the in situ method for rail vehicle application [2].

In practice, there are some challenges linked to the in situ method, mainly because it involves inverse force determination and thus matrix inversion. The correct in situ determination of the re- ceiver-independent blocked force requires including all relevant degrees of freedom (DOF), which are up to three translational and three rotational DOFs at each coupling point. ISO 20270 is only applicable for sources where the complete measurement of all relevant DOFs is possible. However, in practice, it is often not possible to measure all DOFs, especially when the coupling geometry is 1 BoehmJ@dzsf.bund.de

2 BrickH@dzsf.bund.de

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complex. Neglecting relevant DOFs leads to errors and the true blocked force cannot be determined. On the other hand, irrelevant DOFs should not be included, because they increase the possibility for inversion errors [1].

For the above reasons, knowing which DOFs to include is crucial for the correct in situ determi- nation of the blocked force. This paper aims to give some insight into the consequences of neglecting DOFs for the in situ blocked force and to describe conditions that influence the relevance of certain DOFs. The paper contains theoretical considerations as well as measurement results from typical rail vehicle sources.

2. THEORETICAL BACKGROUND

2.1 The blocked force and the in situ method The blocked force 𝐹 𝑏𝑙 is a quantity that characterizes the source strength independent of a receiving structure. It is the force, which occurs at the coupling points when the source operates on a perfectly rigid receiver (blocked boundary conditions). In practice, these boundary conditions are difficult to achieve especially for heavy sources and complex coupling geometries. The blocked force can be determined indirectly from the free velocity 𝑣 𝑓𝑠 and the inverted source mobility 𝑌 𝑆 :

−1 𝑣 𝑓𝑠 . (1)

𝐹 𝑏𝑙 = 𝑌 𝑆

The receiver independent free velocity is the velocity at the coupling points when the source op- erates under free boundary conditions. In equation (1), the force and velocity are vectors containing as many components, as there are contact DOFs and the mobility is a matrix.

The in situ method determines the blocked force indirectly from the inverse mobility of the pas- sive, coupled source-receiver interface (coupled mobility 𝑌 𝑐 ) and the velocity of the coupled interface when the source operates (coupled velocity 𝑣 𝑐 ) [3,4]:

𝐹 𝑏𝑙 = 𝑌 𝑐

−1 𝑣 𝑐 . (2)

The coupled velocity and mobility are measured at the source side of the interface at the same measurement positions. They must include all relevant DOFs. Coupling elements can be treated as part of the source or the receiver. Equation (2) can be seen as a generalization of equation (1) [5].

Although looking simple, equation (2) includes a matrix inversion, which obscures the importance of contributing DOFs and may lead to the increase of small measurement errors. ISO 20270 contains an on-board validation (OBV) method to evaluate the quality of the in situ blocked force estimate. The OBV consists of predicting a validation velocity 𝑣 𝑣𝑎𝑙 on the receiver using the in situ blocked force and a measured transfer mobility from the coupling points to the validation point 𝑌 𝑡𝑟,𝑣𝑎𝑙 :

𝑣 𝑣𝑎𝑙,𝑐𝑎𝑙𝑐 = 𝑌 𝑡𝑟,𝑣𝑎𝑙 𝐹 𝑏𝑙 . (3)

The predicted validation velocity 𝑣 𝑣𝑎𝑙,𝑐𝑎𝑙𝑐 is compared to the actual velocity at the validation point measured during operation 𝑣 𝑣𝑎𝑙,𝑚𝑒𝑎𝑠 . In lack of an alternative, the OBV is sometimes used to examine the effects of neglecting DOFs. However, the results are only valid for the validation point.

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2.2 Measuring rotational degrees of freedom As pointed out earlier, it is necessary to include all relevant DOFs in the measurement. The finite difference method [6] allows for the measurement of rotational DOFs with standard measurement equipment. To measure all DOFs it is necessary to mount at least six or seven accelerometers per coupling point (depending on the coupling geometry) and – when using the method given by equa- tion (2) – to apply a force near these positions.

3. NEGLECTING DEGREES OF FREEDOM

This section briefly discusses some consequences of neglecting DOFs on a theoretical basis. A more detailed discussion can be found in [5]. As pointed out earlier, neglecting relevant DOFs leads to errors. Previous investigations indicate that the in situ blocked force indirectly accounts for neglected DOFs for a given coupling situation [4,7].

Generally, the 𝑁 coupling points of a source have 6 𝑁 DOFs, the vectors of the coupled velocity and blocked force have 6 𝑁 components and the coupled mobility matrix has 6 𝑁 x 6 𝑁 elements. Neglecting a DOF means to delete it from the coupled velocity vector (one element) and likewise from the coupled mobility matrix (one row and the corresponding column). In the following, quantities derived from an incomplete description with less than 6 𝑁 DOFs are labelled with the exponent 𝑟 (reduced). If the remaining components of a quantity are altered because of the incomplete description, the exponent 𝑟′ is used. A relevant DOF is a DOF that cannot be neglected without altering the remaining components of the blocked force vector. With this notation, equation (2) becomes

𝑟′ = 𝑌 𝑐

−1,𝑟′ 𝑣 𝑐

𝐹 𝑏𝑙

𝑟 , (4)

when relevant DOFs are neglected. The remaining components of the directly measured quantities 𝑣 𝑐

𝑟 and 𝑌 𝑐

𝑟 are obviously not altered by neglecting DOFs. However, when a mobility matrix is reduced and then inverted, the components of the inverted mobility are generally altered [8]. The in situ blocked force is also generally altered. The dependency of the inverted mobility on the included DOFs makes general predictions on the relevance of specific groups of DOFs difficult.

𝑟′ is called in situ force in this paper, in order to discriminate it from the true blocked force with reduced components 𝐹 𝑏𝑙

The altered quantity 𝐹 𝑏𝑙

𝑟 . With a reduced blocked force vector, it is generally not possible to correctly predict the reduced coupled velocity vector. This can be expressed by:

𝑟′ = 𝑌 𝑐

𝑟 . (5)

𝑟 𝐹 𝑏𝑙

𝑣 𝑐

The 𝑖 -th component of the coupled velocity is given by:

6𝑁

𝑣 𝑐,𝑖 = ෍𝑌 𝑐,𝑖𝑘 𝐹 𝑏𝑙,𝑘 .

(6)

𝑘=1

When relevant DOFs are neglected in equation (6), the resulting coupled velocity component is not correct. However, there are conditions when certain DOFs are irrelevant for the correct prediction of 𝑣 𝑐,𝑖 . The 𝑘 -th DOF can be neglected when i) 𝐹 𝑏𝑙,𝑘 is zero or very small (small depending on the

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magnitude of the cross-transfer mobility 𝑌 𝑐,𝑖𝑘 ) or ii) 𝑌 𝑐,𝑖𝑘 is zero or very small (small depending on the magnitude of 𝐹 𝑏𝑙,𝑘 ). In the special case that the neglected DOFs are irrelevant for all remaining components of the coupled velocity, equation (5) becomes:

𝑟 . (7)

𝑟 = 𝑌 𝑐

𝑟 𝐹 𝑏𝑙

𝑣 𝑐

Solving equation (7) for the blocked force shows, that the in situ force corresponds to the correct blocked force when the neglected DOFs are irrelevant for the determination of the coupled velocity, i.e. when cases i) or ii) occur. Case i) requires the blocked force to be negligibly small. The blocked force depends only on the source and cannot be influenced. Furthermore, it is not known. An analysis of the principal internal exitation mechanisms could possibly help to estimate the magnitude of the blocked force and thereby the relevance of specific DOFs. However, it should be kept in mind that the dimension of blocked forces and moments is not comparable. Case ii) requires a negligibly small cross-coupling of the neglected DOF. The coupling conditions can be influenced to a certain extent by altering the receiver. When a DOF is blocked by the receiver, it can be neglected.

In contrast to the reduced true blocked force, the reduced in situ force necessarily predicts the coupled velocity correctly (inverse of equation (4)), because the reduced coupled velocity is used as input. This explains that the in situ force indirectly accounts for neglected DOFs as indicated in [4,7].

The incorporation of neglected DOFs can result in a correct prediction of a validation velocity for an OBV. It should be clear that this is case specific and dependent on the particular transfer mobility to the validation point. 4. MEASUREMENTS AND RESULTS

4.1. Measurements Two typical rail vehicle structure-borne sound sources were used for measurements: a traction motor mounted on a test structure and an HVAC-unit mounted on a light rail vehicle, see Figure 1. The measurement equipment consisted of up to 32 accelerometers and an impulse hammer for force ex- citation. All signals were captured simultaneously. A detailed description of the measurements can be found in [5].

The traction motor mounts are three spherical bearings. The mounts can be treated as part of the receiver or part of the source. Both possibilities were examined. In the first case (mounts are part of the receiver), the response measurement and excitation points are located at the motor surface sur- rounding the bearings. This source-receiver interface (IF) is called IF1. In the second case (mounts are part of the source), the response measurement and excitation points are located at the metal part of the spherical bearings connecting the motor to the test structure (IF2). The measurement includes all translational DOFs and two rotational DOFs (rotations around the 𝑥 - and 𝑧 -axis for IF1 and around the 𝑦 - and 𝑧 -axis for IF2). It was difficult to ensure a correct measurement set-up due to the complex coupling geometry and lack of space. Adapter wedges had to be employed for some excitation points. The operational measurement used in this paper had a duration of 30 s and was repeated three times with a constant rpm of 1500 and no load. One validation point for the OBV was located centrally at the back of the test structure in 𝑦 -direction (vertical direction).

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Figure 1: Measurement objects: traction motor mounted on test structure (left) and HVAC-unit on light rail vehicle (right) (pictures newly assembled from [5]).

The mounts of the HVAC-unit were specially designed for the measurement, see Figure 2. They are part of the receiver. The middle element is exchangeable, which allows characterizing the HVAC- unit with stiff and elastic coupling. The measurement includes all translational DOFs and two rota- tional DOFs, rotations around the 𝑧 -axis were neglected. Due to the restricted space, excitation was difficult at some points, but much easier than at the traction motor. The operational measurement had no controlled operating conditions. It took place under a catenary wire with the vehicle turned on and a sample of about 15 s with constant peak frequencies was chosen for evaluation.

Figure 2: HVAC coupling elements: stiff metal cylinder (left), elastic rubber element (right) (pictures newly assembled from [5]).

4.3. Measurement results and discussion The measurement quantities were the acceleration ( 𝑎= 𝑗𝜔𝑣 ) and the accelerance ( 𝐴= 𝑗𝜔𝑌 ). To evaluate effects of neglecting DOFs, the in situ force was first calculated using all five DOFs (expo- nent “ 𝑎𝑙𝑙 ”, e.g. 𝐹 𝑏𝑙

𝑎𝑙𝑙 ). Then, rotational DOFs were neglected (exponent “ 𝑥𝑦𝑧 ”) and last only one direction was included (exponent “ 𝑧 ”, when only 𝑧 -components were considered, etc.). To simplify the interpretation of the figures, vector and matrix elements of the same direction are added energet- ically over all coupling points in the last step. For example, all 𝑧 -components of the in situ force are added ( 𝐹 𝑏𝑙,σ 𝑧 ), or all components of the inverted accelerance, where excitation and response are both in 𝑧 -direction ( 𝐴 𝑐,σ 𝑧

−1 ). As pointed out in section 3, the inverted accelerance is dependent on the included DOFs. Figure 3 gives an example of potential changes when DOFs are neglected, here for the summed 𝑧 -components for IF1 of the traction motor. In the lower frequency region up to about 250 Hz the inverted accelerance shows spurious peaks. These stem from a rather high measurement uncertainty and the amplification of errors by the inverse solution. Neglecting DOFs reduces these spurious peaks. In general, the condition number of a matrix decreases with decreasing matrix size. Some local maxima also display spurious peaks, e.g. around 350 Hz. In the given case, neglecting DOFs does not seem to reduce this second type of spurious peaks.

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Figure 3: Influence of neglecting DOFs on the inverted accelerance ( 𝑧 -components) of IF1 of the traction motor; grid distance = 10 dB.

ft 100 sy} 200 300 500 1700 frequency in Hz

In some frequency regions, the inverted accelerance shown in Figure 3 is hardly affected by neglecting DOFs. The biggest changes can be seen in regions with local maxima (anti-resonance regions). Maxima are shifted towards lower frequencies and partly become more prominent. Therefore, damping the receiver in order to avoid high resonances and anti-resonances could have a positive effect, when planning to neglect DOFs.

Figure 4 shows the changes in the summed 𝑧 -components of the inverted accelerance of the HVAC-unit for different coupling conditions. Neglecting rotational DOFs has a bigger effect on the inverted accelerance when the HVAC-unit is coupled elastically. This is probably due to a stronger cross coupling of translational and rotational DOFs for elastically coupled sources, because the rota- tional movement of the coupling points is less restrained. The examinations in [5] show that neglect- ing rotational DOFs also results in bigger changes of the in situ force of the elastically coupled HVAC-unit. This is an important difference to structure-borne sound power transmission. For power transmission, the relevance of rotational components was found to be lower when the source is cou- pled elastically, e.g. in [9].

Figure 4 also shows that neglecting translational, in-plane components does not have a big effect on the inverted accelerance of the HVAC-unit for both coupling conditions.

ndB Ente frequency in Hz Lyx in eB 100 300 frequency in Hz

Figure 4: Influence of neglecting DOFs on the inverted accelerance ( 𝑧 -components) of the HVAC unit: stiff coupling (left), elastic coupling (right); grid distance = 10 dB.

Of course, changes of the inverted accelerance do not necessarily correlate with changes of the in situ force. The measurement analysis in [5] shows that the in situ force can change substantially even though no effect is observed in the inverted accelerance. This probably occurs when the cross cou- pling to the neglected DOFs is small (only slight changes in the inverted accelerance), but the ne- glected DOFs contribute substantially to the considered components of the coupled acceleration. In

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some frequency regions, the changes of the in situ force were lower than the changes of the inverted accelerance, but this occurred less frequently.

Finally, some results are presented to underline that the OBV is not suitable to assess the effect of neglecting DOFs. Figure 5 shows the added 𝑦 -components of the blocked force and the predicted validation velocity in 𝑦 -direction of IF2 of the traction motor. In order to make changes in the in situ force more visible the level difference of the in situ force calculated with 𝑦 -components only and calculated with all measured DOFs Δ𝐿 𝐹,σ𝑦

𝑦−𝑎𝑙𝑙 = 𝐿 𝐹𝑏𝑙,σ 𝑦

𝑦 − 𝐿 𝐹𝑏𝑙,σ𝑦

𝑎𝑙𝑙 is shown. A substantial level dif- ference indicates that at least one component of the in situ force in 𝑦 -direction changes significantly due to neglecting relevant DOFs. Results below 200 Hz are not included because the measurement uncertainty is too high.

Figure 5: Influence of neglecting DOFs on the 𝑦 -components of the in situ blocked force (above) and the predicted validation acceleration (below) for IF2 of the traction motor; grid distance = 10 dB.

Figure 5 shows different effects depending on the frequency region. In the region of 220 to 240 Hz the added 𝑦 -components of the reduced in situ force are similar to the more complete solution indi- cating that the neglected DOFs are irrelevant. The predicted validation acceleration is close to the measured acceleration for all DOF-combinations. Around 350 Hz the reduced in situ force deviates substantially from the more complete solution indicating that the neglected DOFs are relevant. Nev- ertheless, the measured validation acceleration is predicted correctly. In this region, the OBV does not show that relevant DOFs are neglected. Around 1.5 kHz the reduced in situ force is similar to the more complete solution, once more indicating that the neglected DOFs are irrelevant. Nevertheless, the measured validation acceleration is not predicted correctly. In this frequency region, the 𝑦 -com- ponents of the blocked force are not sufficient to predict the validation acceleration correctly.

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5. CONCLUSIONS

The in situ determination of the blocked force requires the measurement of all relevant degrees of freedom. However, this requirement is often violated in practice. This paper aims to give some insight into the consequences of neglecting DOFs and to describe conditions that influence the relevance of certain DOFs.

It is shown that DOFs that are irrelevant for predicting the coupled velocity from the true blocked force and the coupled mobility are also irrelevant for the inverse case of determining the blocked force from the coupled velocity and the inverse coupled mobility (in situ method). It follows that a DOF is irrelevant when its blocked force is negligibly small or when the cross coupling of the ne- glected DOF to the considered DOFs via the coupled mobility is negligibly small.

Measurements on typical rail vehicle sources indicate that damping the receiving structure could be advantageous when having to neglect DOFs. Furthermore, the results suggest that rotational DOFs gain importance for determining translational components of the blocked force in situ when the source is elastically coupled. The measurements underline that an on-board validation is not suitable to as- sess the effect of neglecting DOFs. 6. ACKNOWLEDGEMENTS

The measurements were part of the Shift2Rail project DESTINATE funded by the European Com- mission under Grant Agreement No: 730829. The results shown are part of a PhD-thesis written at the chair of rail vehicles at the Technical University of Berlin. 7. REFERENCES

1. ISO 20270, “Acoustics - Characterization of sources of structure-borne sound and vibration -

Indirect measurement of blocked forces”, 2019. 2. Guiral, A.: FINE 1 Deliverable D8.4 - Standardization proposals and specifications for IP1, 2019.

url: https://projects.shift2rail.org/s2r_ipcc_n.aspx?p=FINE%201. 3. Moorhouse, A. T.; Elliott, A. S.; Evans, T. A. In situ measurement of the blocked force of struc-

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situ Methode zur Bestimmung der blockierten Kraft. Dissertation, TU Berlin, 2022. 6. Elliott, A. S.; Moorhouse, A. T.; Pavić, G. Moment excitation and the measurement of moment

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