Simulate Bearing Fault Signals by Constructing Bearing Fault Simulation Signals

Using MATLAB to simulate bearing fault signals by constructing bearing fault simulation signals. According to the given conditions, we know that the bearing's natural frequency fn is 3000Hz, displacement constant y0 is 5, damping coefficient ξ is 0.1, impact fault occurrence period is 0.01s, sampling frequency fs is 20kHz, and number of sampling points N is 4096. We now need to construct bearing fault simulation signals based on these conditions and plot their time-domain waveform and frequency spectrum diagram. For code implementation, the simulation typically involves generating impulse responses using a second-order system model that represents the bearing vibration characteristics. The key algorithm can be implemented using the following approach: 1. Create time vector based on sampling frequency and number of points 2. Generate impulse train at fault frequency (100Hz = 1/0.01s) 3. Apply exponentially decaying sinusoids with the given natural frequency and damping ratio 4. Use convolution to combine the impulse train with the bearing system response Critical MATLAB functions for implementation include: - `linspace` for time vector creation - `square` or impulse generation functions for fault period simulation - Filter design functions for implementing the second-order system - `fft` for frequency spectrum analysis - `plot` and `subplot` for waveform visualization The simulation should demonstrate characteristic bearing fault features including periodic impacts in the time domain and sidebands around the natural frequency in the frequency spectrum.