Tec de Monterrey, 2021

The project’s purpose was to analyze and validate the natural frequencies of two components from a Mabe® refrigerator:  a cantilever aluminum beam and the compressor support bracket, to ensure they would not enter resonance during operation or transport.

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The study was grounded in a fundamental principle of mechanical design: resonance avoidance. When a component’s natural frequency matches an external excitation frequency, vibration amplitudes can grow indefinitely, leading to catastrophic failure; a phenomenon famously illustrated by the collapse of the Tacoma Narrows Bridge in 1940. The goal was therefore to ensure that both refrigerator parts would have natural frequencies far enough from the 60 Hz operating frequency of household AC power (the most likely excitation source).

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The project used three complementary methods for the cantilever beam:

1. Analytical Modeling – Using standard formulas for equivalent mass and stiffness of a cantilever, the team computed natural frequencies by hand. Moment of inertia values were calculated for two principal axes, leading to two distinct stiffness coefficients. The resulting natural frequencies were found to be 30.10 Hz and 177.36 Hz, both far from 60 Hz.

2. Experimental Testing – The beam was mounted as a cantilever, two accelerometers were installed, and an impact hammer test was performed. Data was collected using LabVIEW, and Fourier transforms were applied to determine natural frequencies.

3. Finite Element Simulation – The beam was modeled in SolidWorks and meshed for FEA modal analysis. Results confirmed the experimental findings, identifying the first mode at 26.20 Hz (vertical deflection) and the third mode at 164.46 Hz (lateral oscillation).

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The bracket, being an irregular geometry, was analyzed only through experimental and simulation methods. The component was suspended to isolate vibrations and subjected to impact testing with accelerometers.

• Experimental Results: 22 natural frequencies were identified, with the first significant mode appearing at ~24.9 Hz and higher modes distributed up to ~450 Hz.

• Simulation Results: 25 natural frequencies were captured through FEA, with the first at 148.28 Hz, confirming that the main operating frequency of 60 Hz was not a resonance risk.

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The team developed a clear process for data collection: mounting, instrumentation, impact excitation, LabVIEW acquisition, and FFT post-processing. They noted that although frequencies matched across accelerometer channels, amplitude readings varied based on sensor location, which provided insight into mode shapes. By comparing analytical, experimental, and simulation results, the team verified that neither component’s natural frequency coincides with 60 Hz. This means refrigerators can be transported without additional damping systems, reducing costs. However, they recommended adding a simple amortiguator (shock absorber) during transport as a preventive measure against unexpected road-induced frequencies.

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Please find attached below the relevant documents to this project. (Note: most, if not all documents, are in Spanish)