NVH Analysis of an Electric Vehicle using Reduced Order Models
Tesla
Mentors: Wei Cai (Stanford), Hussein Sanaknaki (Tesla)
Goal:
To develop reduced order models for an electric vehicle using analytical (Python) and CAE (Abaqus) methods. The time and frequency domain responses obtained using these models would eventually be validated with actual data provided by Tesla. Another parallel goal was to develop a convenient way of generating random road inputs analytically, for different ISO class roads and different vehicle velocities.
Problem:
While solving analytically in time domain, a second order system of equations needs to be converted to a first order system, which is then solved as an Initial Value Problem. Meanwhile, in frequency domain, a transfer matrix (n x n ) has to be generated using matrix manipulation of the equation of motion. This transfer matrix can then be used to obtain a frequency domain response and even a PSD response. For the CAE model, the reduced order model was built using masses, springs and dampers. The transient and frequency domain responses were evaluated using Abaqus Explicit Dynamics and Abaqus Steady State Dynamics respectively. The random input was obtained using the PSD = G (f) [1], by generating two random numbers from different distributions with variance Gd and covariance coh(f)*Gd . These were assigned as the amplitudes for the front wheel inputs, and were combined with randomly generated phases. The rear wheel inputs were obtained by setting a time delay for the corresponding front input.
What did the team do?
For building the vehicle model, the team split the entire project into three phases - single mass model, motorbike model and full vehicle model. Each phase includes the validation between their Python analytical model and their Abaqus CAE model using different inputs in both time domain and frequency domain. As part of the analytical model, multiple Python scripts were developed for different tasks like generating random input, obtaining equations of motion using Lagrangian parameters, solving the system in time and frequency domain. Once the analytical and CAE models were developed, their output responses were validated using sinusoidal and random inputs. Finally, the model response was compared with the actual response provided by Tesla. This showed that the reduced order model is qualitatively able to capture the trends of the actual response, thus providing a good estimate with fewer computational resources.
