MAE7031-B Assignment Help Sheet

The aim of this help sheet is to give you guidance on your results from ABAQUS, Matlab and

the experimental testing. There are also some comments on what to look for in your data.

FEA Results

Figure 1 shows the mode shapes that you should be extracting from your FE model. They

are diametral mode shapes which means that the shape can be divided by drawing diametral

lines across the disc. A 2 diameter mode of vibration is therefore where the disc has been

split into 2 ‘diameters’, resulting in 4 antinodes.

The mode shapes appear in pairs – the frequencies are closely spaced – so it is acceptable to

take an average of the two values.

There will be other mode shapes, but these can be ignored as they are not relevant to your

assignment.

2 Diameter 3 Diameter 4 Diameter

5 Diameter 6 Diameter 7 Diameter

8 Diameter 9 Diameter 10 Diameter

Figure 1: Example diametral mode shapes

MAE7031-B Assignment Help Sheet

The mode shapes are formed from antinodes (the peaks of the waveform which vibrate up

and down) and nodes (the stationary points) – these are shown in Figure 2 below.

2 Diameter 9 Diameter

The vibration of the disc in these mode shapes is out-of-plane. The FRF data recorded from

the ‘tap’ testing of the disc measured acceleration in the out-of-plane direction. The

predicted (simulated) and measured results can be plotted against each other to validate the

accuracy of the predictions. You can plot a graph of mode shape against frequency for your

FEA results. It should look similar to Figure 3.

It is expected that you undertake a mesh sensitivity study (also known as mesh

independence) to ensure that the results are insensitive to the quality and density of the

mesh elements. To do this you can plot a particular result against the number of elements

and determine if the results are stable.

Antinode

Node

Figure 3: FEA results

Figure 2: Out-of plane

motion

Vibration

MAE7031-B Assignment Help Sheet

Experimental Results

The results from the experimental “tap” testing of the brake disc will look similar to Figure 4

below. Your frequency values may be different to this example. Each peak frequency will be

an out of plane natural frequency. You are only interested in the major frequencies – these

relate to the diametral modes.

The first frequency will be a 2-diameter (2D) mode of vibration

The next frequency will be 3-diameter (3D) and so on as below.

How many modes are visible will depend upon the quality of your data. You can

see below that the 9-diameter mode is difficult to discern from the other excited

frequencies.

2D

3D

4D 5D

6D

7D

9D

8D

Figure 4: Experimental results

MAE7031-B Assignment Help Sheet

Estimating Damping Using the Half-power bandwidth method:

Using the FRF data as shown in figure 5 and by assuming damping is small, the following

equation can be used to estimate damping:

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