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Method for modeling and simulation of aircraft taxiing with unilateral and non-holonomic constraints
XU Ziyao, WANG Qi
School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Abstract:The motion of the aircraft taxiing along the ground was related to wind load and asymmetric braking torque. The method for modeling and simulation of the aircraft was presented on the basis of the dynamics of the non-smooth multibody system with non-holonomic constraints in order to analyze the dynamic behavior of the aircraft taxiing along the ground. The aircraft was treated as the multibody system which consisted of a rigid fuselage, two wheels of main landing gears and a wheel of nose landing gear. Two wheels of main landing gears rolled on the ground without slip. The lateral slip of the wheel on the nose landing gear was taken into account when the aircraft taxied along the ground. The dynamic equations of the system were obtained by Routh's equations and the constraint-stabilized method to reduce constraint drift. The frictional model between the wheels and the ground was the model of Coulomb friction which was described by the set value of function to determine whether the wheel of the nose landing gear slipped in lateral direction or not. Finally, numerical examples were presented to analyze the dynamic behavior of the aircraft undertook the wind load and the asymmetric braking torque.
Key words: aircraft taxiing     multibody system     non-smooth     unilateral constraint     non-holonomic constraint

1 飞机滑跑的力学建模

1.1 基本假设

1.2 飞机滑跑的运动模型

 图 1 飞机滑跑平面运动主视图Fig. 1 Main view of aircraft taxiing planar motion

 图 2 飞机滑跑平面运动俯视图Fig. 2 Top view of aircraft taxiing planar motion

1.3 非完整约束方程

1.4 飞机前轮的非光滑约束条件

2 动力学方程及数值计算方法

2.1 系统的动力学方程

Φ对时间求导可得

2.2 气动力计算

2.3 支撑力计算

2.4 摩擦力计算

3 数值仿真算例

3.1 无侧风时刹车力矩不对称对飞机滑跑的影响

 图 3 刹车力矩不对称时前轮侧向滑移速度变化Fig. 3 Lateral slip speed change of front wheel when braking torque is asymmetric

 图 4 刹车力矩不对称时飞机质心运动轨迹Fig. 4 Motion trajectory of aircraft mass center when braking torque is asymmetric
 图 5 刹车力矩不对称时航向角时间历程Fig. 5 Time history of heading angle when braking torque is asymmetric

3.2 刹车力矩对称时侧向风力对飞机滑跑的影响

 图 6 刹车力矩对称时前轮侧向滑移速度变化Fig. 6 Lateral slip speed change of the front wheel when braking torque is symmetric

 图 7 刹车力矩对称时飞机质心运动轨迹Fig. 7 Motion trajectory of the aircraft mass center when braking torque is symmetric

 图 8 刹车力矩对称时航向角时间历程Fig. 8 Time history of the heading angle when braking torque is symmetric

 图 9 刹车力矩对称时刹车力矩与跑偏量的关系Fig. 9 Relationship between Mf and x when braking torque is symmetric

3.3 对约束方程漂移的修正效果

Φ2表示系统约束方程列向量Φ的二范数.在刹车力矩对称时侧向风力干扰的算例中,取u0=0.7和u1=0.5的情况,图 10给出了||Φ||2的时间历程图.由图可知,约束稳定化方法有效地抑制了约束漂移.

 图 10 刹车力矩对称时||Φ||2时间历程Fig. 10 Time history of ||Φ||2 when braking torque is symmetric

4 结 论

1) 给出了在不对称刹车力矩和侧风载荷作用下飞机在跑道上滑跑的数值仿真.仿真结果表明,不对称刹车力矩和侧风载荷都能引起飞机滑跑跑偏,跑偏量与不对称刹车力矩和侧风载荷的大小正相关.当飞机与地面间的摩擦系数较小时,还会引起飞机前轮的侧滑,侧滑导致飞机滑跑出现较大的跑偏量,并且前轮侧滑现象发生在滑跑的初期.

2) 采用约束稳定化方法,有效地避免了数值仿真时出现约束方程的漂移,保证了数值仿真结果的正确性.数值仿真算例验证了本文给出方法的有效性.

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#### 文章信息

XU Ziyao, WANG Qi

Method for modeling and simulation of aircraft taxiing with unilateral and non-holonomic constraints

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(5): 835-840.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0342