A fundamental study of dynamic behavior of vehicles with unstable region under force control

Abstract

The primary method of improving steering dynamic response performance is expected to involve position control. However the driver uses not only the position of the steering wheel but also torque for control. It has been pointed out that particularly in regions that are close to straight-line driving, torque is the primary means of steering control. Therefore in order to achieve better high-quality dynamic response, it will be necessary to set higher natural frequencies and damping ratios for force control. A universal method for achieving this can be achieved by examining the symbolic expressions for these factors. Force control natural frequencies and damping ratios have been formularized for stable vehicles at all driving speeds. However these formulas cannot be used for vehicles which have unstable regions, and in fact there are vehicles which have such unstable regions. This paper examines a method of setting higher natural frequencies and damping ratios in order to improve the quality of dynamic response characteristics for vehicles that have unstable regions. I first envision a vehicle with neutral steering and steering system damping of 0, and confirm that the characteristic formula is a fourth-order equation for the Laplacian operator s. Next I show that when s is converted to a certain variable, the characteristic formula is written as a biquadratic equation for that variable. By solving this biquadratic equation, the damped natural frequencies and damping ratios are formularized. By considering these formulas, I show that increasing the cornering coefficient is a method that can simultaneously increase the damped natural frequency and damping ratio. I also show that this method can be applied to under-steer vehicles and vehicles which have steering system damping, and finally demonstrate the utility of this method with a time history response in transitional steering.

Keywords

• automobile
• vehicle dynamics
• handling and stability
• maneuverability
• force control
• free control
• natural frequency
• damping ratio
• steering system