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.
AntinodeAntinode AntinodeAntinode 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: ?=?2−?12?0
Damping coefficients can then be calculated using the classical equations provided in the notes. This method is generally valid for damping ratios below 0.1.
Figure 5: Half-power bandwidth method for estimating damping
Matlab Model:
Figure 6 shows a section of the matlab script. The values provided here should be replaced and edited as part of your parameter study. The values provided in the raw file are default values to get you started. You need to calculate your own values from the data provided and then perform a parameter study on these values (note that some values require scaling – see the excel file for details). You should note the order of magnitude of the default parameters in Figure 5; this provides an indicator of the correct order of magnitude for your calculated results.
As part of your study you should investigate the influence of the parameter values on the propensity to generate instability in the model (mode coupling). Consider the effect of the parameters, and of the suitability and limitations of the model with reference to your literature study.
Note: Any other change to the Matlab code is at your own discretion.
MAE7031-B Assignment Help Sheet
Figure 6: Matlab script
In Abaqus I change seed part on a mesh from 0.014 to 0.007
Frist material
FE model:
Density = 7250 kg/m^3
Modulus of elasticity = 96*10^9 pa
Poisson’s ratio = 0.25
2 Diameter
9 Diameter
Second material
Grey cast iron:
Density = 7060 kg/m^3
Modulus of elasticity = 124*10^9 pa
Poisson’s ratio = 0.25
2 Diameter
9 Diameter
Calculation:
Kd = w^2*m = 2.683*10^10
Kp = w^2*m = 2.989*10^10
, then I used half-power bandwidth to determine the estimating damping, however I used interpolation method to find the missing points(frequency)
X = x1+(y-y1)*((x2-x1)/(y2-y1))
f1 = 5930 + (-0.883625105+1.576476925) * ((5940-5930)/(1.218115793+1.576476925))
f1 = 5932.4792
f2 = 5950+ (-0.883625105 – 2.116374895) * ((5960 – 5950)/(-2.207068477 – 2.116374895))
f2 = 5956.9389
, then zeta = (f2-f1)/(2f0)
= 0.00205
This data given by prof, and I used 7th mode which is frequency of interest.
| Diametral Mode orders | ||
| Mode | Frequency (Hz) | Angle (°) |
| 2 | 620 | 90 |
| 3 | 1500 | 60 |
| 4 | 2540 | 45 |
| 5 | 3650 | 36 |
| 6 | 4790 | 30 |
| 7 | 5950 | 25.71429 |
| 8 | 7100 | 22.5 |
| 9 | 8280 | 20 |
This graph represent the result from FE Model, grey cast iron, and the orange graph for diametral mode orders. For the previous table.
Matlab
I multiply by 2*k3, and I got this graph.
Use this reference for the new material.
http://www.substech.com/dokuwiki/doku.php?id=grey_cast_iron_astm_40
