Steering body-tire angle control strategy optimization of wide-body airplane ground turning

The wide-body airplane’s unsynchronous coordination of the inner and outer steering body-tires turning angle during the ground turning process will increase the lateral force of the tires and cause side slip accidents. This paper considers the dissymmetry of the inner and outer steering body-tire turning angles during the ground turning process, calculates the theoretical turning angle mathematical relationship between nose-tire and steering body-tire, optimizes the steering body-tire control strategy from "symmetric turning angle control strategy" to "dissymmetric turning angle control strategy". By comparison, the optimized "dissymmetric turning angle control strategy" can effectively reduce the lateral force of steering body-tires during the ground turning process, decrease the risk of side slip accidents and tire abrasion. Besides, the optimized "dissymmetric turning angle control strategy" can reduce the lateral force difference between the inner and outer steering body-tires during the ground turning process, making the lateral force distribution more balanced, reducing the damage to landing gear structure caused by unbalanced lateral force and extending the service life of body landing gear.


Introduction
The safety and performance of airplane are closely related to the ground turning control skill [1] . With the development of large airplane technology, foreign wide-body airplane such as A380 and B747 generally use nose-tire and steering body-tire cooperative turning control when turning on the ground. Since the turning radius of the body landing gear on both sides are different when turning, the inner steering body-tires needs larger turning angle, the outer steering body-tires needs smaller turning angle. If the inner and outer steering body-tires can't keep synchronous coordination, steering body-tires' lateral force will increase and cause side slip accidents when the airplane is turning at large angles or high velocity [2] . In this paper, the steering body-tire control strategy is optimized based on the lateral force of tires on body landing gears.

Steering body-tire control strategy
The landing gear layout of the certain type wide-body airplane is shown in figure 1. It includes a nose landing gear, two body landing gears, 14 tires in total [3].During the ground turning process, when the nose-tire turn through a certain angle, the steering body-tire will turn rotate a small angle in reverse direction to help nose-tire complete the airplane ground turning action.  Figure 1. Landing gear layout. Figure 2. Symmetric turning angle control strategy.

Dissymmetric turning angle control strategy
According to the Ackermann principle [4], to ensure the smooth and controllable process of the airplane ground turning, there can only be one turning center point at any time, as shown in figure 3. Based on the airplane landing gear layout, the theoretical turning angle mathematical relationship between nose-tire and steering body-tire turning angle is calculated by equation 2, 3, the result is shown in figure 4.   It is calculated that when the nose-tire turning angle is less than 13°, the theoretical turning angles of the steering body-tire on both sides don't exceed 1°. It can be approximated that the steering bodytires haven't participated in the turning process at this stage. Besides, the wide-body airplane such as A380, B747 adopt linear steering body-tire control strategy currently. After comprehensive consideration, modifying the theoretical turning angle mathematical relationship between nose-tire and steering body-tire turning angle, obtaining the "dissymmetric turning angle control strategy", as shown in figure 5. At this point, the angle of nose-tire and steering body-tire satisfies the equation 4, 5. Since the inner steering body-tire turning angle is always larger than the outer under this control strategy, it is called "dissymmetric turning angle control strategy".  angle control strategy". So the optimized "dissymmetric turning angle control strategy" is more suitable for ground turning control of the airplane.

Ground turning motion model
Based on the ground turning motion of the airplane, the following assumptions are made for the kinetic model: the airplane keeps the height of the gravity center unchanged during the turning process; and the fuselage is parallel to the ground [5]; using the trajectory of the airplane's gravity center to represent the airplane's trajectory; airplane ground turning is usually low-speed movements, the aerodynamic forces influence can be ignored [6]; ignoring the instantaneous center's own acceleration influence [7]; the multi-tire landing gear is simplified as a single tire [8].
Taking any moment of the airplane's ground turning as analysis scene, the airplane's force situation is shown in figure 6. Establish a fixed ground coordinate system xoy and a dynamic coordinate

Analysis of airplane ground motion
The airplane's velocity along the y x、 direction and angular velocity around the z axis is:

Analysis of airplane ground turning forces
The airplane's resultant force along the y x、 direction and torque around the z axis is:

airplane ground motion equation
The airplane's motion equation along the y x、 direction and around the z axis is: Establish force balance equation along the n o' direction: (15) In combination with the above equations, the lateral force of the body landing gear is:

Lateral force calculation of steering body-tire
The calculation method of each tire's lateral force of multi-tire landing gear can be found in the aircraft design manual. To calculate the actual lateral force of steering body-tire, the steering body-tire turning angle influence need to be taken into account [9], as shown in figure 7. The calculation formula of the actual lateral force and friction force of the steering body-tire satisfies the equation 22, 23.   [10]. In conclusion, the ground turning velocity of the airplane selected in this paper is 3m/s, 5m/s and 7m/s, and the nose-tire turning angle's range is 20°-70° [11].

Comparative analysis of steering body-tire's lateral force
The body landing gears include four steering body-tires, tire 7, tire 8 on the outer body landing gear, tire 13, tire 14 on the inner body landing gear. The lateral force calculation results are shown in the  table 1, table 2. According to table 1, the optimized "dissymmetric turning angle control strategy" can reduce the lateral force of tire 7, tire 8, and the lateral force reduction effect is more obvious when the airplane is