1. Dept. Of Mechanical and Nuclear Engineering, Penn State University Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover A Comparative, Experimental Study of Model Suitability to Describe Vehicle Rollover Dynamics for Control Design John T. Cameron Pennsylvania State University Dr. Sean Brennan Pennsylvania State University

2. Dept. Of Mechanical and Nuclear Engineering, Penn State University 2/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover Outline 1.Goals 2.Analytical Vehicle Models 3.Experimental Model Validation 4.Conclusions

3. Dept. Of Mechanical and Nuclear Engineering, Penn State University 3/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover Goals  Examine various vehicle models to determine the effect that different assumptions have on:  Model order  Model complexity  Number and type of parameters required  Experimentally validate the models to:  Determine model accuracy  Relate modeling accuracy to assumptions made  Determine the simplest model that accurately represents a vehicles planar and roll dynamics

4. Dept. Of Mechanical and Nuclear Engineering, Penn State University 4/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover Analytical Vehicle Models  Standard SAE sign convention

5. Dept. Of Mechanical and Nuclear Engineering, Penn State University 5/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover Analytical Vehicle Models  Basic Assumptions Common to All Models  All models are linear  Result: Small angles are assumed making cos(θ)≈1, sin(θ)≈0 Constant longitudinal velocity (along the x-axis) The lateral force acting on a tire is directly proportional to slip angle Longitudinal forces ignored Tire forces symmetric right-to-left

6. Dept. Of Mechanical and Nuclear Engineering, Penn State University 6/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover Analytical Vehicle Models  Model 1 – 2DOF Bicycle Model

7. Dept. Of Mechanical and Nuclear Engineering, Penn State University 7/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover Analytical Vehicle Models  Model 2 – 3DOF Roll Model  Assumes the existence of a sprung mass  No x-z planar symmetry  Originally presented by Mammar et. al., National Institute of Research on the Transportations and their Security (INRETS), Versailles, France in 1999

8. Dept. Of Mechanical and Nuclear Engineering, Penn State University 8/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover Analytical Vehicle Models  Model 3 – 3DOF Roll Model  Assumes the existence of a sprung mass  x-z planar symmetry  Roll-steer influence  Originally presented by Kim and Park, Samchok University, South Korea, 2003

9. Dept. Of Mechanical and Nuclear Engineering, Penn State University 9/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover Analytical Vehicle Models  Model 3 (continued)  As a result of the assumption of roll steer, the external forces acting on the vehicle change accordingly

10. Dept. Of Mechanical and Nuclear Engineering, Penn State University 10/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover Analytical Vehicle Models  Model 4 – 3DOF Roll Model  Assumes a sprung mass suspended upon a massless frame  x-z planar symmetry  No roll steer influence  Originally presented by Carlson and Gerdes, Stanford University, 2003

11. Dept. Of Mechanical and Nuclear Engineering, Penn State University 11/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover Analytical Vehicle Models  Effect of assuming force equivalence  Slightly changes plant description (i.e. eigenvalues)  Additionally, causes a higher gain in roll response from the massless frame assumption

12. Dept. Of Mechanical and Nuclear Engineering, Penn State University 12/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover Model Fitting Procedures 1.Experimentally determine the understeer gradient to find the relationship between front and rear cornering stiffness values. Considering both frequency and time domains*: 2.Determine estimates on cornering stiffness values by fitting of the 2DOF Bicycle Model (Model 1). 3.Determine estimates on roll stiffness and damping by fitting of Models 2 – 4. * - Time domain maneuvers were a lane change and a pseudo-step

13. Dept. Of Mechanical and Nuclear Engineering, Penn State University 13/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover Time Domain Fit Results

14. Dept. Of Mechanical and Nuclear Engineering, Penn State University 14/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover Model Fitting Results  Results for Steering Input to Lateral Acceleration  Freq. Domain Fit

15. Dept. Of Mechanical and Nuclear Engineering, Penn State University 15/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover Model Fitting Results  Results for Steering Input to Yaw Rate  Freq. Domain Fit

16. Dept. Of Mechanical and Nuclear Engineering, Penn State University 16/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover Model Fitting Results  Results for Steering Input to Roll Rate  Freq. Domain Fit

17. Dept. Of Mechanical and Nuclear Engineering, Penn State University 17/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover Model Fitting Results  Inconsistency in roll rate measured response does not appear at lower speeds  Better sensors are required to clarify inconsistencies in data – especially lateral acceleration and roll rate

18. Dept. Of Mechanical and Nuclear Engineering, Penn State University 18/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover Remarks on Model Validation  As a result of overall accuracy and simplicity, Model 3 was chosen for further investigation. This entails:  The development of model-based predictive algorithms for rollover propensity  The development of control algorithms for rollover mitigation

19. Dept. Of Mechanical and Nuclear Engineering, Penn State University 19/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover Conclusions  A relatively simple dynamic model is capable of modeling both the planar and roll dynamics of a vehicle well under constant speed conditions.  Relatively accurate measurements may be taken with inexpensive sensors  The dynamics are seen even with commercial grade sensors  Important for industry because such sensors are typically found in production vehicles  Extra care should be taken when model fitting in the time domain

20. Dept. Of Mechanical and Nuclear Engineering, Penn State University 20/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover Time Response Tests  Pseudo-Step Response, 8.9 m/s, 0.09 rad amplitude, FR Params

21. Dept. Of Mechanical and Nuclear Engineering, Penn State University 21/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover Time Response Tests  Pseudo-Step Response, 8.9 m/s, 0.09 rad amplitude, TR Params

22. Dept. Of Mechanical and Nuclear Engineering, Penn State University 22/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover Time Response Tests  Lane Change Maneuver, 17.8 m/s, Right-to-Left, then Left-to-Right, FR

23. Dept. Of Mechanical and Nuclear Engineering, Penn State University 23/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover Time Response Tests  Lane Change Maneuver, 17.8 m/s, Right-to-Left, then Left-to-Right, Time

24. Dept. Of Mechanical and Nuclear Engineering, Penn State University 24/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover Experiments Performed  Determination of Understeer Gradient  Understeer gradient is a constant indicating the additional amount of steering necessary to maintain a steady-state turn per g of lateral acceleration (e.g. units are rad/g)  Provides a relationship between the front and rear cornering stiffness‘  Lateral acceleration was measured on a 30.5 m radius circle at 6.7, 8.9, and 11.2 m/s

25. Dept. Of Mechanical and Nuclear Engineering, Penn State University 25/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover Model Fitting Procedure  Step 1 – Determine understeer gradient  Plotting additional steering angle vs. lateral acceleration, the understeer gradient is simply the slope of the line

26. Dept. Of Mechanical and Nuclear Engineering, Penn State University 26/23 Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover Analytical Vehicle Models