The classical method of noise source identifi cation is to conduct a discon- nection test. If a source is disconnected (e.g. by decoupling the engine mount, putting a total muffl er on the air intake system, etc.) and the noise amplitude at the receiving point is reduced signifi cantly, the main root cause is found. However, this only works well if there is a single dominant source (or very few). Even then there is an inherent risk that the disconnection test changed the other contributions, which is often the case if engine mounts are decoupled. With multiple sources of similar contributions this method is not able to give clear results.
In such cases, Transfer Path Analysis (TPA) works better. The TPA models each connection between the noise source (e.g. vibrating engine) and the receiver (e.g. interior compartment noise or seat vibration) as an excitation (e.g. force input, N) and a transfer function (e.g. receiver sensitiv- ity, Pa/N or (m/s2)/N). Figure 9.1 shows the source–receiver model. The general thinking is:
respij= excij× TFij (9.1)
where
respij= response at point i caused by excitation at path j excij= excitation at path j
TFij= transfer function between points i and j.
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If all paths are modelled correctly the complex sum of all responses should be equal to the response under operation:
respoper, resp
,
i ij
i j
=
∑
(9.2)where respoper,i= response at point i measured under operation.
The difference between the calculated response and the measured response can be used as an indicator of the quality of the TPA model.
However, even if the calculated response equals the measured response under operation, this is not a proof that the TPA model is exact in every detail.
The main problem of the TPA is to get the force input.1–3 There are four principal methods:
1. Force method: measure excitation force by introducing a force sensor.
2. Stiffness method: estimate excitation force through, e.g., rubber mounts by multiplying measured relative displacement by measured dynamic stiffness.
3. Matrix method: estimate excitation force by measuring and inverting the inertance transfer matrix.
4. Operational TPA: estimate excitation force by a least-squares approach of operational data.
The features of each method are:
1. Introducing a force sensor (e.g. 15mm high) will modify the vehicle (mass and stiffness at the connection point and position of force input) and therefore potentially all path contributions. It can only be applied in special cases. The advantage is that the problems of other methods do not arise (see below).
Vibration
•
• •
• Source
Receiver
Noise radiation Vibration
Noise
9.1 Source–receiver model.
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2. The measurement of relative displacement can be diffi cult for complex mounts such as engine mounts. The dynamic stiffness of a rubber mount depends on the frequency and the preloads in all directions. Unfortunately the preload changes during operation (wide open throttle = WOT, or overrun = OVR) due to changing engine torque and with temperature, so it is very diffi cult to test the engine mount under real-world condi- tions. Commercially available 3D mount testing machines are extremely expensive and work only up to 100Hz, so they cannot provide the required data.
3. The matrix method only works if all relevant transfer paths are included in the model. A typical vehicle model will include at least 25 structural paths, a model of a rear- or all-wheel drive vehicle may include up to 80 paths (see Table 9.1).
4. The least-squares approach assumes that transfer functions are constant over, e.g., all engine rpms. Since the engine torque changes over rpm this is not valid in detail. As the desired response is used as a target for the least-squares optimisation, the difference between the measured response and the calculated response can no longer be used as a quality indicator of the TPA model.
For the fi rst method the vehicle must be modifi ed signifi cantly; for the second method the vehicle must be modifi ed if the original mounts are to be used. For the fi rst, second and third methods, the transfer functions should be measured with a decoupled excitation side, which again is a modifi cation of the vehicle. These modifi cations may change the vehicle signifi cantly, therefore making validation of the model impossible.
During the measurement of the transfer functions the vehicle is at room temperature, has no occupants (missing volume and mass load) and is not preloaded with reaction torques from the powertrain. All these conditions differ more or less from operational conditions and may adversely affect the result.
Table 9.1 Typical paths to be included in a TPA
Count Component Directions Paths
3–4 Engine/transmission mounts XYZ 9–12
1 AC hose XYZ 3
1 Clutch cable XYZ 3
3–8 Exhaust hangers Z or XYZ 3–8
2 Airborne noise sources S (scalar) 2
1 Powertrain radiated noise S (scalar) Typically 6
2 (4*) Side shafts* XYZ 6–12
* If the contribution of the side shafts is to be further analysed, they must be split down to link arm (XYZ) + top mount (XYZ) per side shaft.
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The only way to avoid this is to conduct operational TPA, which unfor- tunately gives the least insight into the vehicle because the excitation forces are not calculated; only the path contribution and the transfer functions (Pa/(m/s2)) are calculated, which are only valid under the operating condi- tions used.4,5
This situation can be improved by performing noise transfer function (NTF) (Pa/N) and point inertance measurements ((m/s2)/N). With these values one could better understand the body structure and calculate the exciting forces. However, for physically exact results it is required to discon- nect the body and excitation sides in order to ensure that the exciting force is introduced only into the body. Unfortunately this gives the method a disadvantage.
Airborne noise sources such as intake and exhaust orifi ce noise can be included in the model, e.g. by measuring the noise under operation (Pa) and the transfer function with noise excitation at the orifi ce (Pa/Pa). Even the radiation from surfaces can be included by measuring the surface aver- aged acceleration (m/s2), multiplying it by the surface (m2) and measuring the volume acceleration transfer function (Pa/(m³/s2)).
As the TPA calculates a vector sum of contributions it can only deal with coherent signals with constant phase relationship (e.g. engine excitation).
For incoherent excitation (e.g. road noise) the inputs must fi rst be repre- sented by a set of orthogonal vectors (principal components, PRC) by means of a principal component analysis (PRCA).
The number of principal components is identical to the number of refer- ence signals. Nevertheless, a certain principal component cannot be inter- preted as being correlated with a certain reference signal. In order to explain the measured response best a high number of PRCs are required.
However, for each set of PRCs one has to solve a complete TPA. Therefore it is desired to fi nd the lowest number of reference signals that can explain the measured response well enough in the problem areas. The quality of a road noise TPA depends highly on the selection of the reference signals.
The index of the highest contributing PRC is not constant, so problem range A may be explained mainly by PRC 1 whereas problem range B may be explained mainly by PRC 2. In general a noise phenomenon (e.g., a response peak at a certain frequency) is explained not just by a single PRC but by a combination of PRCs. This requires that the results of multiple TPAs have to be judged in parallel or one has to work with the sum of PRCs.