In the development of modern electric SUVs, ensuring durability while meeting range requirements through lightweight design is critical. Traditional durability testing involves extensive real-world road trials, which are time-consuming and costly. This study presents a method for load identification in an electric SUV based on equivalent damage principles, utilizing road test data and multi-body dynamics simulation to derive wheel center forces efficiently. The approach reduces testing complexity and accelerates development cycles while maintaining accuracy.
Durability refers to the ability of a system to function normally over a specified period under operational conditions. For electric SUVs, lightweight design is essential to extend driving range, but it must not compromise fatigue life. Fatigue durability testing is the primary means to validate the lifespan of vehicles and components, typically conducted through user road tests, proving ground trials, or laboratory simulations. However, traditional methods are resource-intensive and slow to adapt to design changes. The Palmgren-Miner model is widely used for fatigue life prediction, as it handles complex load histories by accumulating damage from load cycles. This study focuses on estimating load spectra for an electric SUV by processing road test data and applying virtual iteration techniques to identify wheel center six-component forces, which include longitudinal force, lateral force, vertical force, pitch moment, yaw moment, and roll moment.
The technical route involves dynamic load identification, an inverse problem in dynamics where loads are estimated from measured responses using a multi-body model. Challenges include the distributed nature of dynamic loads in space, non-stationarity in time, and broad frequency content, leading to ill-posed mathematical equations. To address this, road load data from a prototype electric SUV were collected under various proving ground conditions. The data’s stationarity was verified using run tests, and equivalent damage principles were applied to reduce the number of road surfaces, simplifying the problem. A rigid-flexible multi-body model of the electric SUV was developed and correlated with experimental data, enabling accurate load decomposition through virtual iteration.
Road load data acquisition was conducted on a proving ground that replicates severe driving conditions, including high-speed tracks, rough roads, and off-road sections. Sensors were installed at key locations on the electric SUV, such as suspension knuckles and shock absorbers, to measure acceleration and displacement signals. The sensor types and parameters are summarized in the following table:
| Sensor Type | Location | Parameters |
|---|---|---|
| Accelerometer | Front Axle Knuckle | Range: ±20g, Frequency: 0-1000Hz |
| Displacement Sensor | Shock Absorber | Range: ±100mm, Resolution: 0.1mm |
| Six-Component Force Transducer | Wheel Center | Forces: ±10kN, Moments: ±500Nm |
Data were collected over 25 different road conditions, with signals sampled at high frequencies. For instance, the vertical acceleration at the front wheel knuckle exhibited peaks up to 18.65g, indicating severe loading. The stationarity of these signals was essential for subsequent analysis, as non-stationary data could lead to inaccurate fatigue assessments. The run test method, a non-parametric approach, was employed to verify stationarity. The algorithm divides the time series into equal segments, computes variances, and checks for random sequences of signs. For example, in a comprehensive road test, the run test resulted in a run count within acceptable limits, confirming stationarity. The run test statistic is calculated as follows: let the time series be divided into m segments, with variances σ²_i. The median variance is computed, and segments are labeled ‘+’ if above median and ‘-‘ if below. The number of runs r is compared to critical values; for large samples, the standardized statistic $$ z = \frac{r – \mu_r}{\sigma_r} $$ is used, where $$ \mu_r = \frac{2N_+N_-}{N} + 1 $$ and $$ \sigma_r^2 = \frac{2N_+N_-(2N_+N_- – N)}{N^2(N-1)} $$, with N_+ and N_- being counts of ‘+’ and ‘-‘, and N the total segments. If |z| < 1.96 at 5% significance, the data are stationary.
Fatigue damage accumulation is modeled using the Basquin equation and Palmgren-Miner rule. The Basquin equation relates stress amplitude S to cycles to failure N: $$ S = \alpha N^{-\beta} $$ where α and β are material constants. The total damage D is given by $$ D = \sum_{i=1}^{k} \frac{n_i}{N_i} $$ where n_i is the number of cycles at stress level S_i, and N_i is the fatigue life at that level. For load spectra, equivalent damage principles allow reduction of multiple road conditions to a subset. Suppose original roads have pseudo-damage values D_ji for road j and channel i, and reduced roads have D_ki. The equivalence condition is $$ \sum_{j=1}^{n} C_j D_{ji} = \sum_{k=1}^{n’} C_k’ D_{ki} \quad \text{for all } i $$ where C_j and C_k’ are cycle multipliers. Solving this system via linear fitting yields equivalent cycles for reduced roads. In this study, 25 roads were reduced to 9, with damage ratios for key channels staying within 0.5 to 2, ensuring accuracy. The table below summarizes the equivalent reduction:
| Original Road | Equivalent Road | Cycle Multiplier |
|---|---|---|
| Belgian Road | Rough Track A | 1.2 |
| Composite Road I | Rough Track B | 0.8 |
| Braking Road | Dynamic Path | 1.5 |
| Composite Road II | Resonance Path | 1.0 |
A multi-body dynamics model of the electric SUV was developed using ADAMS/Car software. The model included front MacPherson struts and a rear multi-link suspension, with flexible elements to capture real behavior. Correlation with experimental K&C (Kinematics and Compliance) data ensured model fidelity. For instance, the relationship between wheel vertical load and body roll angle was calibrated to match test rig measurements, as shown by the hysteresis curve. The model’s transfer function H(s) relates input forces F(s) to output responses Y(s): $$ Y(s) = H(s) F(s) $$. For load identification, the inverse problem is solved: $$ F(s) = H^{-1}(s) Y(s) $$, where H^{-1} is the generalized inverse. To avoid ill-conditioning, the number of output channels must exceed inputs; here, 38 outputs were used for 24 inputs.
Virtual iteration was applied to identify wheel center six-component forces. Starting with white noise inputs, the algorithm iteratively adjusted forces to minimize the difference between simulated and measured responses. The update step is $$ \Delta F = H^+ (Y_{\text{meas}} – Y_{\text{sim}}) $$ where H^+ is the pseudo-inverse of the transfer matrix. Convergence was achieved when damage ratios for all channels approached unity. For example, on a resonance road, after 10 iterations, the damage ratios ranged from 0.5 to 2, indicating satisfactory accuracy. The identified load histories can be used for component fatigue analysis in CAE tools.
The load identification method for this electric SUV demonstrates that equivalent damage reduction and virtual iteration effectively streamline durability assessment. By verifying data stationarity and employing a correlated multi-body model, accurate wheel forces are derived without extensive testing. This approach supports lightweight design goals for electric SUVs by enabling rapid fatigue life predictions. Future work could extend to different driving conditions or integrate with battery durability models.
In conclusion, this study outlines a comprehensive framework for load identification in electric SUVs, combining road testing, data processing, and simulation. The use of equivalent damage principles reduces computational effort, while virtual iteration ensures precise load estimates. This methodology enhances the development efficiency of electric SUVs, balancing durability and performance in a competitive automotive landscape.