For the occupants of a vehicle the operating sound and vibration responses are directly perceivable, contributing to the overall impression of vehicle refi nement. It is the development task of the sound and vibration engineer to design the vehicle hardware in such a way that customer expectations, legal requirements and vehicle manufacturing targets with respect to the sound and vibration characteristics are met. This requires a detailed under- standing of the complex generation and transfer of sound and vibration to the occupants of the vehicle cabin (Kronast and Hildebrandt, 2000).
A fi rst step in reducing complexity can be attained if the vehicle response is separated into the contributing excitation forces on the one side, and the structural and acoustic properties of the vehicle on the other side. The structural and acoustic properties are then characterized by the sound and vibration transfer functions, which contain all relevant information on the structure’s dynamic properties, so these are often also used for comparing vehicles and setting targets. Transfer functions derived by testing a struc- ture can be broken down further through the application of modal analysis.
The breakdown into the modal characteristics delivers valuable informa-
Excitation spectrum System FRF Response spectrum
Force
Frequency
H(f) Response
= x
Frequency Frequency
6.1 Distortion of the system response to a linear force input by the transfer characteristics (courtesy of Ford of Europe, Germany).
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tion for the sound and vibration development engineer, yielding a tool that can be used to assess, change and predict a structure’s dynamic properties.
In the next sections we will discuss the outlined process.
6.2.1 Spatial, modal and response model
There are several ways to gain an understanding of the root cause of a distinct response. The one with the least amount of analysis work uses sound pressure or vibration data obtained at several locations on the oper- ating vehicle together with a geometrical shape, allowing the generation of
‘operating defl ection shapes’ (ODS) (Johansen and Madsen, 1992). These animated patterns of motion are processed and made visible using a com- puter. They show areas of high and low response and thus help in identify- ing the root cause of poor vehicle sound or vibration performance. Near a dominating resonance the ODS can look very similar to an animation of modal analysis eigenvectors, and indeed, as shown in Fig. 6.2, there is a direct relation between a mode shape and an operating defl ection shape (de Siqueira and Nogueira, 2001). Often this type of ODS investigation already allows one to draw fi rst conclusions with respect to an NVH concern, but remember that both force excitation and the structural properties are mixed into the result and cannot be separated from each other at this point.
When the density of resonances is high but there is no dominating reso- nance, the ODS will show a complex pattern of motion since several reso- nances will then be contributing to a defl ection pattern at one frequency.
At this point it clearly becomes diffi cult to identify the root cause for an NVH concern.
When the result of an ODS analysis does not yield suffi ciently clear information, then modal analysis might be the right tool for the task. Modal analysis employs structural and/or acoustic response data derived through a test with artifi cial excitation, or a computer model of the object’s mass,
System characteristics Dynamic forces
Imbalance Combustion Shock Aerodynamic Pressure
System responses Operating deflection shapes
Natural frequency Damping factor Mode shape vector
Sound Vibration
Stress Modal analysis
6.2 Contribution of excitation and modal characteristics to a system’s forced response (courtesy of Ford of Europe, Germany).
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stiffness and damping distribution properties. If the object under investiga- tion fulfi lls the prerequisites for applying this method, which we will discuss later, then we are able to determine the modes of a structure in a chosen frequency band. Each mode of a structure is characterized by its natural frequency, the modal damping value and the mode shape vectors. Figure 6.3 shows the principle and details for analytical and experimental modal analysis. Avitabile (1998–2008) describes the basics of this method, while Allemang (1992) and He and Fu (2001) present more details.
6.2.2 Application to vehicle NVH development
Having determined the modal parameters as described above, we now have the possibility of formulating a mathematical model of the dynamic pro- perties of the object under investigation (Inman, 2000). This then allows us to calculate the frequency response function, i.e. acceleration/force or pressure/force, between all defi ned structure points although, in the case of experimental modal analysis, we may not have explicitly measured them.
Multiplication of the vibration or noise transfer functions by the respective excitation forces acting on the vehicle and summation of all these contribu- tions then yields the absolute response, or forced response, at the defi ned response location, as shown in Fig. 6.4. Vice versa, looking at the vehicle development process where absolute vehicle noise and vibration levels are targeted at important response locations, one is now, at least in theory, able to break this down into modal contributions. At the model level the con- tribution of each mode to the response at a certain frequency can be ranked against the other mode contributions, sensitivity investigations can be performed and the fi ndings can be used to modify the modal model. The
Acoustic/structural
model Modes Response
properties Analytical approach (FE)
Experimental approach Physical properties:
Mass Stiffness Damping
Modal model:
Natural frequency Modal damping Mode shape vectors
Frequency response function
6.3 Analytical and experimental approach to modal analysis (courtesy of Ford of Europe, Germany).
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modifi ed model then allows a prediction of how the responses will change if the structural or acoustic dynamic properties of the investigated object are changed. This relation yields a powerful tool for vehicle NVH development.
Often during vehicle development one is not interested in using the modal model to perform calculations. The pure knowledge of a structure’s mode frequencies and mode shapes already gives the experienced develop- ment engineer suffi cient information, enabling him or her to set up a plan for the distribution of these over frequency. This concept is often called modal alignment, although it is really a method to avoid having several modes strongly coupling at one frequency or having a strong excitation and relevant modes near one common frequency. Figure 6.5 shows typical
H1
H2
H3
Xseat F2 engine
X2 engine X1 engine F1 engine
F3 road
X3 road
= +
+
6.4 Multiple excitation and transfer path contributions to the structural response of a vehicle (courtesy of Ford of Europe, Germany).
Rigid P/T modes
Suspension modes
Full vehicle body modes
Steering column modes
5 10 15 20 25 30 35 40
Frequency (Hz) 1
2 3 4
6.5 Typical resonance frequencies of important vehicle systems.
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frequency bands for major passenger vehicle modes. Other usages of the modal properties include the possibility to compare the full vehicle, subsys- tems or components with competitor dynamic performance, to correlate models to test derived results, or to set targets for system and component development.