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In recent years, the conversion of vehicles to electric power has been accelerating, and if a full conversion to electric power is achieved, further advancements in vehicle kinematic control technology are expected. Therefore, it is thought that kinematic performance in the critical cornering range could be further improved by significantly controlling not only the steering angle but also the camber angle of the tires through the use of electromagnetic actuators. This research focused on a method of ground negative camber angle control that is proportional to the steering angle as a technique to improve maneuverability and stability to support the new era of electric vehicles, and the effectiveness thereof was clarified. As a result, it was found that in the critical cornering range as well, camber angle control can control both the yaw moment and lateral acceleration at the turning limit. It was also confirmed that both stability and the steering effect in the critical cornering range are improved by implementing ground negative camber angle control that is proportional to the steering angle using actuators. Dramatic improvements in cornering limit performance can be achieved by implementing ground negative camber angle control that is proportional to the steering angle.

Since the proposal of four-wheel steering (4WS), vehicle motion performance technology has focused on im- proving the lateral, longitudinal, and vertical movements of vehicles by controlling chassis components, such as the steering, brakes, powertrain, and suspension. 4WS is relatively simple to describe using mathematical control models, making this topic an often investigated topic for the application of advanced control rules and leading to the development of various control algorithms for improving vehicle performance. At small lateral accel- erations, the tire slip angle can be effectively controlled by steering. However, steering becomes less effective as lateral turning acceleration increases, because the tire sideslip angle also increases, resulting in a saturated tire side force. In order to counteract this weakness in 4WS, [

On the other hand, in recent years, the conversion of vehicles to electric power has been accelerating, and if a full conversion to electric power is achieved, further advancements in vehicle kinematic control technology are expected. When vehicles are converted to electric power, in-wheel motors located in each of the four wheels will be used for braking and driving, and independent control of braking and driving at each of the four wheels will be possible. In addition, it will also be easier to independently control the steering angle of all the wheels using electromagnetic actuators. For these reasons, much research is being conducted on direct yaw moment controland active steering of electric vehicles [

The following notation is used in the present study:

Will become apparent from the moment method the effects of ground negative camber angle control. The vehicle equation of motion cannot be solved analytically when the tire characteristics are nonlinear. Therefore, we assumed that the vehicle (

The relationship between Equations (3) and (4) is shown in

A

Vehicle model and analysis condition

can express all states of the vehicle motion: linear, nonlinear, steady, and transient.To determine this relationship with respect to lateral acceleration,

The tire model uses the magic formula [

The side force

Are shown in

Notation used in the displacement analysis model

: Wheel load

To this end, we adopt the quasi-stable state approach proposed by Abe (

. Magic-Formula coefficient

Symbol | |
---|---|

BCD_{y}, B_{y} | Constant indicating the stiffness |

C_{y} | Constant that determines the shape of the entire curve |

D_{y} | Constant indicating the maximum value of the curve |

E_{y} | A constant representing the curvature of the curve before reaching the maximum value |

S_{hy} | Shift in the horizontal direction at the origin |

S_{vy} | Shift in the vertical direction at the origin |

Tire side force characteristics (Camber angle change)

. Parameters used in calculation

Symbol | Value |
---|---|

a_{0} | 1.3 |

a_{1} | −0.0274 |

a_{2} | 1.05 |

a_{3} | 1.18 |

a_{4} | 7.69 |

a_{5} | 0.009 |

a_{6} | −0.257 |

a_{7} | 0.224 |

a_{8} | 0.025 |

a_{9} | 0.01 |

a_{10} | 0.015 |

a_{11} | 0.00849 |

a_{12} | −0.0103 |

a_{13} | 0.0395 |

Model for the analysis of load distribution [11]

Tire load vs. lateral acceleration

Numerical computations were performed using the parameters listed in

. Parameters used in calculation

Symbol | Value | Unit |
---|---|---|

M = (W/g) | 1600 | kg |

0.48 | - | |

0.52 | - | |

h_{f} | 0.046 | m |

h_{r} | 0.05 | m |

h_{g} | 0.52 | m |

t_{f} | 1.47 | m |

t_{r} | 1.459 | m |

Yaw moment diagram (zero camber angle). (a) β-yaw moment diagram; (b) Y_{G}-yaw moment diagram

Yaw moment diagram (front wheel negative camber angle 20 deg. Rear wheel positive camber angle 20 deg). (a) β-yaw moment diagram; (b) Y_{G}-yaw moment diagram

Yaw moment diagram (front wheel positive camber angle 20 deg. Rear wheel negative camber angle 20 deg). (a) β-yaw moment diagram; (b) Y_{G}-yaw moment diagram

Yaw moment diagram (front wheel negative camber angle 20 deg. Rear wheel negative camber angle 20 deg). (a) β-yaw moment diagram; (b) Y_{G}-yaw moment diagram

(

In

^{*} is 0. By changing the balance between the front- and rear-wheel camber angles, the yaw moment is changed from the turn-in side to the restoring side at the cornering limit. In the case of moment control through steering, the cornering force reaches a saturated state at the critical cornering range, and therefore, yaw moment cannot be generated. However, in the case of camber angle control, yaw moment can be generated without becoming narrow even in the critical cornering range.

The following notation is used in the present study:

(

The vehicle model for analysis was a model having three degrees of freedom (yaw rate, body slip angle, and roll). Moreover, it was assumed that the suspension characteristics were linear, and that the slip angle and camber angle of the tires were the same for the right and left tires. The equation of motion is expressed by the following Equation (21) [

for the tire slip angle:

for the tire camber angle:

Yaw moment diagram

where

It uses a Magic-Formula tire model shown in Section 2.2 as a model for cornering characteristics of the tire, and using the same tire characteristic.

In addition, when the

wheel load of each

Input a step steering with a front wheel actual steering angle of 4˚ while traveling at a vehicle speed of 95 km/h. For camber angle control, implement front and rear wheel ground negative camber angle control (20˚) simultaneously with the steering angle.

We verified the computation results through the following experiment using a model car. Using a remotely controlled model car, we clarified the effectiveness of four-wheel negative camber control proportional to steering.

The model car used in the experiment is shown in

In order to achieve four-wheel negative camber control proportional to steering in the model car, we controlled the camber angle by moving the link mechanism using the servo motors on each of the tires. The camber angle,

Simulation results

Remote controlled model vehicle

. Specifications of the model vehicle

Value | Unit | |
---|---|---|

Weight | 4 | kg |

Wheel base | 256 | mm |

Tread | 188 | mm |

Movable toe angle | ±30 | degree |

Movable camber angle | ±20 | degree |

The model car experiment was performed with the vehicle driving in a circle, as shown in

The representative results of the experiment in which the car ran a circular course are shown in

This research focused on a method of ground negative camber angle control that is proportional to the steering

Circle-turn course

Experimental results

angle as a technique to improve maneuverability and stability to support the new era of electric vehicles, and the effectiveness thereof was clarified. As a result, it was found that camber angle control can control both the yaw moment and lateral acceleration at the turning limit in the critical cornering range as well. It was also confirmed that both stability and the steering effect in the critical cornering range are improved by implementing ground negative camber angle control that is proportional to the steering angle using actuators. Dramatic improvements in cornering limit performance can be achieved by implementing ground negative camber angle control that is proportional to the steering angle.