How are transfer paths measured?
To create a TPA model the global system has to be divided into an active and a passive part, the former containing the sources, the latter the receiver points where the responses are measured. Loads are defined at the interface between the active and passive part and the so-called Noise Transfer Functions (NTF’s), also referred to as Frequency Response Functions (FRF’s), characterize the relationship between a load and a receiver. The paths are represented by these NTF’s. See figure 1. The individual contribution of each transfer path to the total response can be calculated by multiplying the load with the corresponding NTF. This model presupposes that the load-response relationship is causal and the paths are system characteristic of the global system. Using this model, a pressure target response can be expressed as follows:
Figure 1: TPA Model schematic: Sources, receivers, loads, transfer functions on a vehicle model
The test procedure to build a conventional TPA model typically requires two basic steps: 1. identification of the operational loads during in-operation tests (e.g. run-up, run-down, etc.) on the road or on a chassis dyno: and 2. estimation of the FRF from excitation tests typically under laboratory conditions (e.g. hammer impact tests, shaker tests, etc.). The procedure is similar for both the structural and the acoustical loading cases, but the practical implementation is of course governed by the nature of the signals and the loads.
The separation into “loads” and “transfer” is the key to the use of the TPA results to identify dominant causes and propose solutions (act on specific load inputs, act on mount stiffness, act on specific system transfer).
Building on evolutions on experimental TPA, the methodology has found its way into simulation, resulting in the introduction of “contribution analysis” concepts in numerical modeling, extending the traditional “unit-force” FE validation models to true engineering models with realistic loads and interpreting the results in terms of critical problem area’s, panels, structural parts, etc.. Experimental TPA has become a key part towards successful simulation modeling by providing accurate load estimates.
Today, the main driver for innovations in TPA is the industry’s demand for simpler and faster methods. Several attempts have been made to speed up the TPA process. One example is the Operational Path Analysis (OPA) approach. This approach attracts quite some attention as it requires only operational data measured at the path references (e.g. passive-side mount accelerations, pressures close by vibrating surfaces, nozzles and apertures, etc.) and target point(s). The OPA method is indeed very time-efficient, but has several limitations, that are discussed in the “advanced transfer path analysis techniques” section.
A fast, test-based procedure which supports troubleshooting of vibro-acoustic problems in a very efficient way is LMS OPAX. This approach is nearly as accurate as conventional TPA and almost as fast as purely operational path methods that often fail to identify the root cause of vibrations and find remedies to NVH problems. The LMS OPAX solution separates loads and transfer paths so that vibro-acoustic energy can be traced right from the source. This helps engineers identify the problem quicker than ever before with the minimum of time-consuming measurements.
1. Loads identification
Loads identification is probably the main accuracy factor for a successful TPA campaign. Different methods may be employed to identify both vibro-acoustics and acoustics loads.
1.1 Direct measurements
1. Loads identification
Loads identification is probably the main accuracy factor for a successful TPA campaign. Different methods may be employed to identify both vibro-acoustics and acoustics loads.
1.1 Direct measurements
Direct measurement of the loads is done by placing force transducers between the engine and the engine mounts. Although the most effective method, direct measurement of the loads is not possible in the majority of cases as the load cells require space and well-defined support surfaces, which often makes application impractical or even impossible without distorting the natural mounting situation. In those cases where direct measurement is possible (i.e. large machinery) it remains the preferred method.
1.2 Mount stiffness method
In case the active and passive structures are connected through flexible mounts, the mount stiffness method can be used. The operational forces can be determined from a knowledge of the complex dynamic stiffness of the mounts K(w) and of the differential displacement over the mount during operation.
When applying the mount stiffness method, it is required to measure the operational displacement at both the source and the receiver side. It is therefore important to place the accelerometers as close as possible to the mount connection points – even though this is not always easy. If measured further away, the measured acceleration signals will not be representative for the problem at higher frequencies
1.2 Mount stiffness method
In case the active and passive structures are connected through flexible mounts, the mount stiffness method can be used. The operational forces can be determined from a knowledge of the complex dynamic stiffness of the mounts K(w) and of the differential displacement over the mount during operation.
When applying the mount stiffness method, it is required to measure the operational displacement at both the source and the receiver side. It is therefore important to place the accelerometers as close as possible to the mount connection points – even though this is not always easy. If measured further away, the measured acceleration signals will not be representative for the problem at higher frequencies
Nevertheless, this method has its limits as accurate mount stiffness data are seldom available and furthermore depend on the excitation amplitude due to their non-linear behavior: modern mounts have a stiffness that changes depending on the operational load on the mount.
1.3 Matrix inversion method
For transfer paths which comprise of rigid connections, or where the mount stiffness is very large with respect to the body impedance, inducing even the minimum relative displacement over the mount is not possible, and thus the mount stiffness method can not be used to identify the load.
1.3 Matrix inversion method
For transfer paths which comprise of rigid connections, or where the mount stiffness is very large with respect to the body impedance, inducing even the minimum relative displacement over the mount is not possible, and thus the mount stiffness method can not be used to identify the load.
In these cases, a technique based upon inversion of a measured accelerance matrix between structural response on the receiver side due to force excitation at all transfer paths can be used. This accelerance matrix must be measured when the source is disconnected from the receiver. This matrix is then combined with operational measurements of the structural vibration at the receiver side in order to obtain force estimates.
In the matrix inversion method so-called “indicator accelerations” are measured in a first step at multiple locations on the support structure during operating conditions. Typical locations for indicators are points at the passive side on the subframe to which the engine mount is connected. In a second step, the relation between the interface forces and the motion/deformation is characterized by a measured accelerance matrix in the form of multiple complex transfer functions in the frequency domain (FRF). These FRFs from the passive side mount location to the indicator locations are measured in controlled, non-operational conditions.
The FRF accelerance matrix data and the operational indicator acceleration data are combined to calculate the forces as shown in the following equation:
with Fi the calculated operational force through path i, FRFik(w) the local transfer function between the transfer path location i and indicator point k, and ak(w) the operational accelerations at indicator location k. So, the FRF matrix describes the local relationship between a known force input at the transfer path location and a measured response acceleration output due to this known input. It is this very relationship that is also valid in an operational situation (such as the runup of a vehicle) and allows to calculate the force by inverting this matrix and multiplying it with the operational accelerations.
Calculating the inverse of the accelerance matrix in practise requires some numerical stability issues to take into account. The number of measured indicator acceleration signals should therefore well exceed the number of forces to be identified. This allows calculation of a pseudo-inverse with a least squares optimized estimation of the forces. The condition number of the accelerance matrix (ratio between the largest and smallest eigenvalue) is a measure of the potential amplification of errors. Small or large inaccuracies in the FRF of the accelerance matrix, as well as in the operational indicator acceleration vector can lead to large errors in the force estimation if the condition number is high. Singular value decomposition elimination or smoothing can not compensate for thus introduced bias errors.
The disadvantage of the inverse method is that all potential and correlated forces that act need to be analyzed simultaneously because all forces may cause motion/deformation throughout the structure. Also, to limit the errors in the identification, an over-determination (at least 2 times more indicator responses than excitations) is advised, leading to a relatively large number of signals and a large number of measurements to fill the FRF matrix. Furthermore, all constraints with respect to impact location and direction and FRF phase accuracy also apply to this problem.
For FRF measurements, reciprocal techniques can be used, allowing the reuse of the in-operation response instrumentation (and exciting at the indicator positions). This not only saves time, but also guarantees consistency. The reciprocal method will be discussed in more detail in the section VII.
1.4 OPAX
OPAX is a parametric force identification method, which is based on operational data and complete vehicle reciprocal FRF measurements.
1.4 OPAX
OPAX is a parametric force identification method, which is based on operational data and complete vehicle reciprocal FRF measurements.
The OPAX approach differentiates from the existing methods in the identification of the operational loads. Key is the use of parametric models characterizing the operational forces and acoustics loads as a function of measured paths input such as mount accelerations and acoustics pressures. The parametric load models are estimated from (i) in-situ measured operational path inputs and target response signal(s) and from (ii) transfer path FRFs.
The OPAX method is discussed in more detail in the section ”Advanced transfer path analysis techniques".
2. FRF measurements
2.1 Direct measurements
Direct measurement of vibro-acoustic FRF is often done by instrumented hammer excitation of the structure, where a normal microphone measures the pressure response. When more accurate data are needed, an electro-mechanical shaker is used for excitation. But, access to the correct location is often impossible with normal shakers, and even difficult with an instrumented hammer. In the example of a vehicle, surrounding parts are sometimes disassembled to be able to reach locations like strut towers, ventilation system supports, screen wiper supports, etc.
The estimation of the vibro-acoustic (or acoustic-acoustic) FRF is probably the easiest to determine. Still, direct measurements are often complex with respect to setup constraints (apply a force at the connection points or apply an acoustic load near the radiating surface) and accuracy (direction errors when using impact testing, connection lateral or moment constraints when using shakers).
2.2 Reciprocal measurements
2.2 Reciprocal measurements
Using reciprocal measurements (exciting at the target locations, measuring the response at the interface) has alleviated this problem significantly. Verification experiments show that acoustic-acoustic and acoustic-structural reciprocity hold in nearly all cases, for large ranges of excitation amplitudes and types of structures. Even in case non-linear and/or local damping effects may cause a slight breakdown of reciprocity, the corresponding errors are typically an order smaller than these of impact location and orientation, sensor cross-talk and sensor sensitivity.
The reciprocal determination of vibro-acoustic FRF is attractive when multiple FRF need to be determined, and when access to the suspension support location is constrained. A low frequency volume acceleration source is positioned at ear location, and the acceleration response at the suspension locations is measured in parallel for multiple suspension connection points and for multiple directions per location. Accelerometers are easily placed in narrow and concealed places.
According to theory exactly the same information is measured. In practice the experiments have shown that the vibro-acoustic FRF, thus measured, are very close to direct measurements. Small residual differences exist. These deviations in the observed reciprocity are only partially caused by non-linearity of the vehicle body structure. The imperfect alignment of the force excitation in a direct measurement and alignment of the accelerometers in a reciprocal measurement have proved to be highly critical in obtaining good vibro-acoustic reciprocity.
Especially on complete vehicle, reciprocal transfer function tests have a major advantage in required effort and in positioning accuracy around mounts. Acoustics excitation at the ear location, and response accelerometers around the mounts, allow more freedom in positioning the sensors close to mount center, and it is more feasible to surround mounts with sensors.
2.3 New excitation methods
An important contribution to speeding up TPA measurements while supporting the improvement of accuracy is offered by the advances in instrumentation technology, for excitation as well as measurement.
Reciprocal tests for example require accurate acoustic sources which behave like point sources and have approximately omni-directional characteristics in the applicable frequency ranges while not disturbing the sound field too much. For these tests, engineers need calibrated Volume Velocity Sources (VVS) such as LMS Qsources, with dimensions and characteristics adapted to specific frequency ranges. To have access to the in-situ source levels, volume velocity sources need to have integrated volume acceleration sensors. For structural excitations, advanced and lightweight (inertial) shaker systems can be used.
Figure 2: From left to right: LMS Qsources mid-high frequency volume velocity source, integral shaker, and low-frequency volume velocity source. These sources provide an accurate real-time reference signal of the acoustic source strength.
Other innovative measurement techniques find their way into transfer path analysis, such as using strain sensors the measure displacement as used in the mount stiffness method. This indirect force identification approach uses strain responses and easy-to-apply strain sensors. Strain responses are much more localized than acceleration responses, eliminating to a large extent the concerns on cross-coupling between the interface locations.
Important when mixing different signal types in level-sensitive procedures like the matrix inversion, is the proper balancing of the different quantities (acceleration-pressure, acceleration-strain) since acceleration levels are generally much higher than pressure levels. This is a well-known problem from modal analysis, addressed in vibro-acoustic and strain modal analysis.
When (burst) random excitation techniques are unable to excite the structure at sufficiently high levels this results in signal to noise ratio problems, long measurement times (many averages) and noisy FRFs. High quality FRFs can be measured using stepped sine excitation techniques that are able to concentrate the excitation energy at a single frequency and excite the structure at much higher energy levels. A MIMO sine testing technique has been introduced that used a digital implementation of the classical swept sine excitation. The technique acquires leakage-free spectra, which are processed into multiple-input-multiple-output FRFs. A ‘system identification’ approach is implemented to control the excitation level during the test without using a time-consuming online closed loop control scheme. For vibro-acoustic noise transfer functions, the new technique was compared with the traditional burst random and stepped sine techniques. It was proven that this technique is able to measure FRF and coherence function of similar high quality as the stepped sine technique, but at drastically reduced measurement times, which are comparable with the burst random technique.
2.4 Decoupling the system
Because of the system’s modal behavior, a single force in one of the mounts causes vibrations at all path references. Excitation at a transfer path point would also cause energy to travel through the engine mount, passed via the engine through a second engine mount, and from there travels to the receiver location (e.g. the driver’s head). So the response at the receiver is not anymore directly caused by energy traveling directly from the excitation point to the receiver. Therefore, Noise Transfer Functions should be measured after disassembling the sources from the assembly structure to eliminate source coupling, or cross-coupling. In case of a vehicle, this means that the engine needs to be removed.
In some cases, the effect of cross-coupling is not significant. This can be the case if the mounts are rigid, and the excitation at the transfer path points is low due to e.g. reciprocal measurements.
Apart from the theoretical reason to remove the engine, practically, there is a severe lack of physical space between the engine and engine mount to place force transducers. A pragmatic approach is to remove the engine to gain access to the body-side of the mount directly, and use a hammer or shaker to directly excite the system. Likewise, the suspension should be removed when measuring body side FRFs related to road noise.
