Brake Rotors & Operational Deflection Shapes
Automobiles are subject to many forces during operation. Vibrations from the engine or the road surface transmit through the vehicle’s chassis and suspension to the most essential mechanical component of the vehicle, the brake system. In this example (setup seen left), a 14” diameter brake disc from a heavy-duty truck was transiently excited and analyzed with the VIC-3D High-Speed Vibration Analysis (FFT) technology. Because all operational deflection shapes (ODSs) under 3,000Hz were of interest, a framerate of 6,250fps was used to capture images with high-speed cameras.
Before frequency domain data could be computed, displacement data needed to be obtained via the standard VIC-3D DIC analysis. After the displacement data was measured, a Fast Fourier Transformation (FFT) was applied to the time history of the displacement data for each point on the surface of the brake rotor. The FFT data then displayed full-field amplitudes of the surface of the brake rotor and the average amplitude at each frequency in the x, y, and z directions for easy identification. From this data, three unique operational deflection shapes (ODSs) were easily identified and animated for further analysis using the VIC-3D HS Vibration Analysis FFT software.
Three shapes were found to be at frequencies 120.0 Hz, 932.7 Hz, and 2,087.4 Hz. These frequencies are seen in the left graph (out-of-plane amplitude vs. frequency). The right graph shows the out-of-plane displacement in the time domain. This information is important because it displays frequencies where large average amplitudes occur, how much the specimen actually displaces after the excitation and the duration of image capture.
Figure 1. The Maxima tab in the FFT Workspace shows a graph of each data point’s maximum amplitude and maximum frequency in the z direction on the left. On the right, a plot of frequency vs. average amplitude is shown.
Figure 2. The full-field deflection shape, phase, frequency, and average amplitude of the brake rotor at 120.0Hz. This shows the first operational deflection shape at ~120.0 Hz. The full-field plots show the out-of-plane motion and phase at this frequency. An average amplitude of 84 nanometers was measured as the ODS at ~120 Hz, as seen in the plots and graphs above.
The out-of-plane motion is animated in 3D below to better show the maximum values, the minimum values, and the nodes of the operational deflection shape. At this frequency, the brake rotor experienced a total out-of-plane deformation of approximately +/- 268 nanometers.
Figure 3. Animated 3D view of the brake rotor at 120.0Hz.
Figure 4. Animated 3D view of the brake rotor at 932.7Hz.
Figure 5. The full-field deflection shape, phase, frequency, and average amplitude of the brake rotor at 932.7Hz. The full-field left and right plots show the out-of-plane shape and phase respectively at this frequency. An average amplitude of 183 nanometers was measured for this ODS, as seen in the left graph.
The out-of-plane motion is animated in 3D below to better show the maximum values, the minimum values, and the nodes of the operational deflection shape. At this frequency, the brake rotor experienced a total out-of-plane deformation of approximately +/- 375 nanometers.
Figure 5. Animated 3D view of the brake rotor at 932.7Hz.
Figure 6. The full-field deflection shape, phase, frequency, and average amplitude of the brake rotor at 2,087.4Hz. he full-field left and right plots show the out-of-plane motion and phase respectively at this frequency. An average amplitude of only 25 nanometers was measured for this ODS, as seen in the left graph.
The out-of-plane motion is animated in 3D below to better show the maximum values, the minimum values, and the nodes of the operational deflection shape. At this frequency, the brake rotor’s ODS was measured to have an out-of-plane amplitude of +/- 64 nanometers as shown in the animation below.
Figure 7. Animated 3D view of the brake rotor at 2087.4Hz
For this test, the out-of-plane amplitude noise signal was measured to be approximately 4 nanometers, which is excellent. The system also shows excellent dynamic range in the frequency domain. For a more in-depth analysis, the average measurements can be compared to reference points and point extractions. For easy finite element analysis and modal analysis validation, the full-field 3D data can be exported in the form of animations, .csv’s, and other various formats.
This example shows that measurements with amplitudes as small as 64 nanometers and frequencies over 2,000Hz with up to 1 million data points at every time step are achievable. Compared to traditional and laser measurement techniques, this non-contact full-field measurement tool provides more data in less time. The VIC-3D HS FFT system analyzes and displays multiple operational deflections shapes at different frequencies after a single excitation from any transient event. Furthermore, the system concurrently computes valuable 3D strain and displacement data that can be displayed alongside the vibration data.