Roving excitation or response? Uni-ax or Tri-ax? SIMO or MIMO?
A modal impact hammer test is broadly classified between two types: roving hammer and roving response. Each method has its own pros and cons.
Implementing the aforementioned methods to perform measurements in one direction (usually out-of-plane) using a single uni-axial accelerometer yields a row of FRF when roving hammer, or a column of FRF when roving sensor. In the case of a FRF column, it is necessary to switch the response and excitation of the DOF of each FRF signal to yield a row of FRF. Curve fitting the row of measured FRFs produces the modal parameters of the test structure.
However, some tests may use more than one accelerometer or measure data in more than one direction. Even though the basics are still the same, care must be taken while performing the experiment to ensure that there is either a complete row or a complete column of the frequency response function. If the resulting FRF signals does not contain this, then the natural frequencies, mode shapes and damping of the structure cannot be obtained.
1. Roving excitation – response measurement point is fixed (say point 3), and the hammer is roved over the entire structure. The disadvantage of this approach is long test durations. Another downside is that it might be difficult to excite structures with complex geometries. However, this approach does not induce any mass loading effect.
2. Roving response – the excitation point is fixed (say point 1), and the sensor is roved over the structure. This approach helps overcome the problem of achieving perpendicular impacts on intricate structures. Also, if multiple sensors are used then the experimentation times are reduced. However, roving the sensor induces a mass loading effect which affects the accuracy of the results.
Now let’s examine a case where we want three-dimensional mode shapes of the structure under test. Obtaining three-dimensional mode shapes of a structure requires acquiring data in all three directions.
1. Roving response (tri-axial accelerometer) with a fixed excitation point
Impacting the structure under test in the out-of-plane (z) direction at a fixed point (say point 1) and measuring the response in the x, y and z directions by roving a tri-axial accelerometer over the entire structure yields a complete column of the transfer function matrix. The advantage of this method is that it is relatively easier to excite the structure in the outward direction. However, roving the tri-axial accelerometer produces time variance which is the mass loading effect. To minimize this effect, a small or light weight tri-axial accelerometer can be used.
2. Roving excitation with a tri-axial accelerometer fixed at a measurement point
Measuring the response of the test object by fixing the tri-axial accelerometer at one location (say point 1) and roving the impact hammer to excite the structure in the z-direction yields the following set of FRFs (in black).
The above FRF matrix shows that the H matrix is incomplete as there is not a complete row in the transfer function matrix and thus curve-fitting the measured set of FRFs would not yield the modal properties of the structure under test.
To complete the H matrix shown above, each point would have to be impacted in all three directions (x, y and z).
The transfer function matrix now has three complete rows. It should be noted that there are now three references for this measurement set and so it is now a MIMO case. Note that it would still require switching the Excitation and Response DOFs before curve fitting. The disadvantage of this method is that it would not be possible to impact a flat surface in all three directions for most of the points. A quick work-around for this problem is to attach a block at each measurement point which would act as a protrusion of the test object. This block can then be excited in the x, y and z directions to obtain data for all the DOFs. Another significant disadvantage is the extra time required to excite all three directions at each measurement points. So, this is not the typical method used by most people.
We have discussed the different methods of hammer impact testing using uni-axial and tri-axial accelerometers. The last case we can look at examines what happens when we have more than one sensor while performing a hammer impact test.
Sometimes, the structure under test is large and capturing the response using one sensor is very tedious, thus multiple sensors are required to reduce experimentation times. Usually, all hammer impact tests are SIMO in nature. This can be observed by referring to the initial cases discussed. In the roving excitation test using a single uni-axial sensor, there are multiple outputs as the impact hammer is roved over the structure and the sensor is fixed at a single DOF. This signifies that there is a single reference and multiple outputs, which yields a transfer function matrix of a SIMO nature. Similarly, when the excitation is fixed, and a single uni-axial sensor is roved over the structure, there are multiple outputs for the single reference of the impact hammer. When a tri-axial accelerometer is used, the roving response yields a single column matrix of the transfer function and thus it is a SIMO case again. However, when the roving excitation method is implemented with a tri-ax then it is a MIMO case as there are three references for the x, y and z directions respectively.
Also, when a roving excitation hammer impact test is carried out with more than one uni-axial accelerometer, the transfer function matrix is MIMO in nature because of the presence of multiple references for the multiple sensors.
1. Roving excitation with multiple uni-axial sensors
The image shows that the transfer function matrix has two rows when a roving excitation impact hammer test is carried out with two uni-axial accelerometers fixed at measurement points 1 and 2. As it can be observed, the multiple sensors make this a MIMO case because of the multiple references.
2. Roving response with multiple uni-axial sensors
For an impact hammer test with a roving response, the H matrix is SIMO in nature because there is only one reference present (the excitation point, let’s say point 1). Again, as discussed previously, using multiple sensors reduces experimentation times but induces mass loading effect which can be minimized by using smaller or lighter sensors. Another solution is to use dummy blocks at other measurement DOFs to ensure no time variances while carrying out the test.
To conclude, there are two ways to carry out an impact hammer modal test. Based on the requirements, uni-axial or tri-axial sensors can be used to capture the response of the structure under test. Care must be taken to ensure while implementing these concepts to make sure that there is either a complete row or a complete column present in the transfer function matrix. If this is not achieved, then the modal characteristics of the test structure cannot be obtained. To reduce the mass loading effect, smaller or lighter sensors can be used. Also, dummy blocks can be attached at the other measurement DOFs. While carrying out a roving excitation in three directions, a small block can be used to excite the test structure in all the directions. Finally, more than one sensor can be used to reduce the experimentation times. The nature of the H (transfer function) matrix is SIMO or MIMO based on whether there is a single reference or multiple references present. The different combinations corresponding to these are also shown.
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