Parking-Specific Parameterization Method for FTire
Virtual steering system layout in the early development phase requires adequate tire models to predict realistic steering rack forces. An accurate representation of parking is particularly important, as the largest steering rack forces occur during this maneuver. Physical tire models are mainly parameterized for rolling conditions. Since the tire exhibits different mechanical behavior under nonrolling conditions, this article introduces a new parameterization procedure for the physical tire model FTire that characterizes the conditions during parking maneuvers. To this end, an additional full vehicle measurement setup is used to understand the tire motions, forces, and torques during parking. It is also shown that a tire model based on a standard parameterization procedure results in steering speed-dependent parking torque deviations of up to 17.5% when compared with component measurements. Thus, new measurement methods are developed to help parameterize the tire model for this maneuver. A linear friction tester is used to determine the friction interaction between tire and road at the relevant relative velocities. In addition, measurements are performed on a tire stiffness test rig, in which translatory and rotatory movements are overlaid. Furthermore, the contact patch shape, ground pressure distribution, and tire outer contour are digitalized and added into the model. A tire model based on the new parking optimized parameterization is then compared with the standard tire modeling approach and component measurements as well as the full vehicle measurements. In conclusion, improvements of up to 12% for drilling torque, up to 15% for longitudinal force, a more realistic lateral stiffness, a more realistic pressure distribution, and improvements of up to 8% when simulating the steering rack force can be stated. After the results are evaluated and interpreted, recommendations for future developments of this parameterization procedure and an extension of the virtual tire model are discussed.ABSTRACT
Static parking maneuver for steering design, according to Pfeffer and Harrer [1].
Components of steering rack force.
Full vehicle measurement setup [11].
fka’s tire test rigs: tire stiffness test rig (l), Flat-Trac CT+ (m), and cleat test rig (r).
Construction of the FTire friction map.
Sum tie rod force for standard FTire, 100°/s (l), 150°/s (m), 200°/s (r).
Drilling torque of standard FTire, 0.5°/s (l), 5°/s (m), 15°/s (r).
Longitudinal force for standard FTire, 0.9 mm/s (l), 4 mm/s (m), 12 mm/s (r).
Lateral force for standard FTire, 0.9 mm/s (l), 4 mm/s (m), 12 mm/s (r).
Contact patch of standard FTire, 0° camber angle (l), 9° camber angle (r).
Scheme (from above) of the mathematical tire model, according to [21].
Components of aligning torque.
Tire movements: one degree of freedom (l) and combined movement (r).
Influence of travel speeds in longitudinal (l) and rotational movement (r).
Ground pressure distribution at low (l) and high wheel load (r).
Linear friction tester [24].
Example of a friction test (l) [24] and sliding friction map of the tire (r).
Digitalization of tire outer contour.
Drilling torque, 0.5°/s (l), 4°/s (m), 15°/s (r).
Longitudinal force, 0.9 mm/s (l), 4 mm/s (m), 12 mm/s (r).
Lateral force, 0.9 mm/s (l), 4 mm/s (m), 12 mm/s (r).
Contact patch and pressure distribution 0° camber, measurement (l), standard FTire (m), optimized FTire (r).
Contact patch and pressure distribution 9° camber, measurement (l), standard FTire (m), optimized FTire (r).
Hull curve results, 0° camber angle (l), 9°camber angle (r).
Sum of pressure along the lateral profile, 0° camber angle (l), 9°camber angle (r).
Pressure histogram, 0° camber angle (l), 9°camber angle (r).
Sum of tie rod forces, 100°/s (l), 150°/s (m), 200°/s (r).
Boxplots of deviation of sum tie rod forces, standard FTire (l), optimized FTire (r).
Sum of tie rod forces normalized, 100°/s (l), 150°/s (m), 200°/s (r).
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