Achieving Quality in Modal Excitation

The quality of the experimental modal model is directly proportional to the quality of the Frequency Response Functions (FRFs). This quality is, in turn, highly dependent on the energy source, that is, the input used for the excitation. With focus on electromagnetic vibration exciters, this article provides a short introduction to the reasoning behind this and a short introduction to the new line of dedicated Brüel & Kjær modal exciters.

Introduction
From being a highly useful but "academic" method requiring nothing short of expert knowledge, Experimental Modal Analysis has, within the last two decades, evolved into one of the common tools in the sound and vibration analysis toolbox, readily available to most test engineers. The reason behind this development is not difficult to comprehend. The advent of the PC and the development of inexpensive, user-friendly modal parameter extraction software packages, have been the primary reasons for the current widespread use of Experimental Modal Analysis.

Yet, despite its recent widespread use and advances in software technology, Experimental Modal Analysis, or Modal Testing, remains a notoriously difficult application especially in critical applications where high accuracy and high precision are of paramount importance. Understanding and correctly applying the rigorous mathematical processes involved in developing the modal model is no easy task without in-depth knowledge of structural dynamics.

At the same time, the experimentalist is confronted with the fact that modal testing explicitly assumes an ideal physical model - time-invariant, linear, causal and observable. Most structures, however, seldom behave in an ideal fashion and a multitude of concomitant problems have to be dealt with (or anticipated) in any modal test setup. Typical questions include which test strategy -Single Input Single Output (SISO), Single Input Multiple Output (SIMO), Multiple Input Single Output (MISO), Multiple Input Multiple Output (MIMO) - to choose? Which type of boundary condition should be sought? What transducer technology and which operating range to choose? How many transducers to use and which mounting method to apply? And finally, what type and how many excitation sources are optimal for the test in hand?

Achieving the Highest Quality FRFs - the Role of the Modal Exciter
For a high precision modal test setup, where one or several exciters is the natural choice of excitation, the latter question has, in combination with positioning and orientation of the exciter(s), far-reaching implications.

Contrary to what many experimentalists think, the input (force) measurement, is one of the most critical aspects of a successful modal test. Errors originating here will not only affect each and every FRF measurement, but even worse, the errors will typically be hidden bias errors and not the random type of errors often associated with the output response measurements that can manifest themselves in a visual way allowing easy detection. On the input side, other significant challenges confront the experimentalist as well.

Minimising Exciter/Test Structure Interaction
Effective mechanical de-coupling of the structure under test and the modal exciter(s) minimises the mechanical impedance "disturbance" caused by the exciter(s).
At resonance frequencies, where modal parameters are subsequently being extracted, force drop-offs are inevitable , thereby decreasing the accuracy of the residue (mode shape displacement) determination.

Force drop-offs are caused by the fact that, at resonance, the structure becomes highly compliant (high vibration amplitudes at low input force levels). The exciter may then use all the available energy to accelerate its own mechanical components, leaving no force with which to drive the structure under test. Very little force is therefore being put into the structure and the signal level of the force may then drop towards the normal noise level in the instrumentation. The lighter the mass of the moving element in the exciter, the lesser this problem will be.

Obtaining Valid Force Measurements
Any force transducer/impedance head is, to a certain degree, sensitive to unwanted environmental effects as well as to bending moments and transverse movements. There are many causes for side loads and bending moments that have to be dealt with in a modal test setup:
· Rotational motion of the test structure at the location of the force transducer.
· Translational motion of the test structure in any direction other than the driven axis.
· Rotational or translational motion of the modal exciter on its stand or suspension system, as well as stinger bending modes.

The purpose of the stinger (the component that connects the modal exciter to the force transducer/structure) is to faithfully transmit axial forces, as well as to isolate and decouple the force transducer/impedance head from side loads and bending moments. Present state-of-the-art stinger designs are accordingly all based upon the tension wire concept.

A thin metal (piano) wire will have zero compression and negligible bending stiffness. A tension wire test setup is therefore utilised in such a way that there is a constant tension in the wire, upon which the oscillatory force (typically a burst random based signal) is superimposed. A piezoelectric-based force transducer/impedance head is by definition an active transducer that requires a dynamic force input in order to give an output. Hence, the constant tension provides no output from the input transducer and only the oscillatory part of the signal will be measured.

In practice, the tension wire technology is implemented by using a "through-hole" design of the modal exciter and exciter fixture, whereby the exciter can be "slid" along the wire. A chuck assembly that clamps the exciter to the wire at the desired position replaces the traditional exciter table. In connection with a lateral exciter stand, the tension wire concept becomes especially simple and elegant. The piano wire goes through the exciter, then goes around a pulley and connects to a spring fastened to the base of the exciter stand. A double threaded boss, placed in between the spring and the base, achieves adjustable pre-tensioning.

This pre-tensioning feature can also be achieved by using the DC Static Centering Unit Type 1056 - optional with Power Amplifiers Types 2732 and 2720 but mandatory with Type 2721. This allows for use of piano wire stinger technology without a dedicated horizontal exciter fixture as described above - especially useful when limited space or skewed angle mounting is necessary.

The DC Static Centering Unit Type 1056 has another significant advantage for modal testing, namely that of providing the test specimen with a pre-load capability. Many structures require an accurately controlled static preload force in order to take up the slack in bearings, gears, or joints. Failure to apply such a preload will often add significant problems to the modal parameter extraction algorithm.

Distributing and Minimising Dynamic Force Levels
There are several reasons why exciting the structure under test with the smallest possible force level, at more than one input location, is desirable. Firstly, force levels that are too high may drive the structure into non-linear behaviour. Secondly, higher force levels require larger exciters, which, by necessity, have more massive armatures - leading to increased force drop-offs at resonance frequencies. Thirdly, large and complex structures that exhibit local modes generally require force inputs at several distributed locations in order to excite all modes sufficiently well.

In addition to the above, two modes occurring at the same frequency - a situation commonly known as "repeated roots" - may occur in certain, mostly bi-symmetrical, structures. The only way to obtain a valid modal model in such a situation is by employing a modal test setup with multiple inputs (i.e., a MISO or MIMO test strategy ).

Choosing the Best Exciter Location
Theoretically, exciting at any arbitrary location should excite all modes except those that have a node line at that exciter location. In practice, however, it is necessary to have a good exciter location for a given mode. This is much more demanding than simply requiring that bad locations, i.e., node lines, be voided. It is, therefore, usually necessary to evaluate many exciter locations before picking the best and fewest numbers. This process is often referred to as an exciter location survey. One key is to try as a many exciter locations as possible.

Obviously, using a lightweight modal exciter is a definite advantage because it is quick and easy to move and set up. A rugged and dedicated lateral exciter stand, allowing for easy positioning in several degrees of freedom, is a definite advantage.

Low Frequency Modal Test Performance
Even though, as previously discussed, smaller and distributed force inputs are generally preferred, it is evident that the signal-to-noise ratio of the instrumentation will pose a limit as to how far this principle can be stretched.

Knowing the residual noise of the instrumentation and knowing (or, more likely, assuming) the stiffness between a given input and output, one can easily calculate the force necessary to obtain a minimum acceleration level at a specific frequency. Following the well-known frequency-squared relationship between vibration displacement and acceleration, the force that has to be applied in order to obtain the same minimum acceleration level rises exponentially with the inverse of the frequency.

At lower frequencies, the attainable input force level is, concomitantly, determined by the maximum peak-to-peak displacement of the exciter. As modal testing is generally conducted at low frequencies (say, below 4 kHz), high displacement capability of the modal exciter is of paramount importance. The de facto industry standard for peak-to-peak displacement of general modal exciters seems to be hovering around 1" (2.54 cm).

Conclusion
From the above it is evident that the input (force measurement) aspects of a modal test based upon electromagnetic exciters is of paramount importance for a successful Experimental Modal Analysis session.

With the new line of modal exciters Brüel & Kjær has taken an integral modal test approach to ensure the highest possible quality, accuracy and consistency of the FRF measurements.

The line consists of five dedicated modal exciters, all with the following important features:

- High force to weight ratio
- High force to price ratio
· Full 1" peak-to-peak displacement for best low-frequency performance
· Armature (moving element) with high rigidity and low mass
· Low total weight of exciter allowing for easy positioning and orientation relative to test object
· Dedicated robust lateral exciter stand for easy positioning and orientation. Prepared for attachment and pre-tensioning of piano wire stinger technology
· Wide frequency ranges
· Through-hole design for choice of piano wire stingers or traditional stingers
· Complete line of accessories, including various stingers and additional inertial masses