1. Introduction
Mechanical wear is a common and inevitable problem, and the general mechanical equipment parts are invalidated and scrapped due to wear. There are also wear phenomena in the joints of the aircraft NLG, such as the wear of washers, bushings and pins. Although the wear itself will not cause direct failure of the components, the joint clearance caused by wear will seriously affect the shimmy stability of the landing gear [
1,
2,
3,
4]. This will put forward higher requirements for the design of landing gear joints, such as the structural shape of joints, assembly dimensions and wear resistance of materials.
The wheel of the NLG may have a severe vibration that deviates from its central position, which is called shimmy [
5]. The shimmy of the NLG will seriously affect the stability of the body and the ride comfort and aircraft operation, cause damage to the body and landing gear and endanger the safety of life and property. There are numerous factors affecting the shimmy of the NLG, including linear and nonlinear factors, which can be summarized into four parts: NLG structural characteristics [
6,
7,
8,
9,
10], wheel characteristics [
11,
12,
13], fuselage characteristics [
14,
15,
16] and external conditions [
17,
18,
19]. Among them, the structural clearance has strong nonlinearity and discontinuity, which makes the dynamic behavior of the system very complicated, and it also causes great difficulties to the vibration analysis of the landing gear system and the practical application of the analysis conclusions.
The existing literature on the influence of joint clearance on the shimmy of NLG is mostly a general parameter. As early as 1980, Grossman D.T [
1] of the McDonnell-Douglas Company studied the influence of torsional clearance on the shimmy stability of the F-15 fighter, introduced the parameter of torsional clearance and constructed a mathematical model for shimmy analysis. In the early 21st century, Niranjan K. Sura [
20] and B Sateesh [
21] established a nonlinear shimmy dynamic model with torsional clearance. The results show that the torsional clearance reduces the stability of the NLG. Mohsen Rahmani [
22] used the simscape multibody method to study the coupling characteristics of coulomb friction and clearance. None of the above can reflect the specific location of the joint clearance. In addition, the clearance model is a mathematical model, which cannot reflect the three-dimensional characteristics of the clearance model.
The general structural clearance includes product assembly clearance and wear clearance, and the value of each position clearance is different. Filipe Marques [
23] proposed a new formula to simulate the spatial joints with radial and axial clearances; Yan et al. [
24] considered the radial and axial clearances between the rotating shaft and the shaft sleeve, and based on the analysis of the geometric characteristics of the motion pair, 13 contact modes and their conditions were given. In addition, the influence characteristics of different joint clearances are different [
25,
26,
27,
28].
The NLG system contains multiple joints. Joint clearance wear occurs during the service of the NLG. The vibration and noise caused by joint clearance and its wear directly affect the stability and service life of the NLG. Especially after long-term work, the joint clearance increases with the deepening of wear, and these problems are more prominent [
29,
30]. The transmission characteristics of each joint of the NLG are different, and little is known about the influence of different joint clearance on shimmy. At present, there are no studies in the literature to distinguish and discuss it. Although many scholars have studied the shimmy suppression method of the NLG [
31,
32,
33,
34,
35,
36,
37], it is impossible to establish the quantitative influence of joint clearance wear on NLG shimmy, which makes it difficult for the designer to analyze the reliability of the landing gear system, let alone accurately predict the joint life and monitor the motion state of the mechanism.
In this paper, taking a certain type of airliner as the research object, the shimmy MBD model with joint clearance at different positions is established based on LMS Virtual.Lab Motion. The clearance model is a three-dimensional space joint clearance model, considering the radial clearance, axial clearance and their coupling characteristics, which is more practical. The influence characteristics of different position clearance on shimmy are studied via the MBD model, and the critical clearance values of different joints are calculated quantitatively, which can easily determine the weak links that have a greater impact on the shimmy of NLG, so as to guide designers to improve the weak links in the aspects of joint design, material selection, manufacturing and so on. At the same time, it is also of great significance to provide a reference for the design and wear maintenance guidance of joint assembly dimension chain in different positions.
3. Evaluation Method
The sensitivity of NLG shimmy stability to joint clearance wear depends on two factors: the position of joint clearance in the NLG (referred to as “position factor”) and the amount of joint wear itself (referred to as “wear factor”). The influence of joint clearance on shimmy will be evaluated from the above two factors.
3.1. Position Factor of NLG Joint
Through the analysis of the joint characteristics of the NLG, it can be seen that the piston and the outer cylinder are cylindrical pairs; the upper resistance rod, the lower resistance rod and the lower locking brace rod form a compound hinge; the upper locking brace rod and the lower locking cylinder are ball pairs; and the others are rotating pairs. The motion mechanism diagram is depicted in
Figure 7. The NLG has a total of 12 parts, 14 rotating pairs, 1 ball pair and 1 cylindrical pair, with a total of 16 low pairs. The DoF
F of the NLG mechanism is
where
n is the number of parts,
pl is the number of low pairs, and
ph is the number of high pairs.
Based on Equation (24), it is calculated that the simplified NLG model contains the following four DoF: (1) the DoF of the NLG to realize the lower lock control; (2) the relative DoF between the outer cylinder and the turning sleeve around the axis to realize the turning function of the NLG; (3) the DoF of the piston relative to the turning sleeve and the outer cylinder moving along the axis to realize the landing shock absorber function of the NLG; (4) the DoF of wheel rotation around the axis to realize the taxiing function.
After the wheel of the NLG is excited laterally by the ground, the ground excitation is transferred from the wheel to the axle, and then from the lower torque link, the upper torque link, the turning sleeve and the outer sleeve to the fuselage. From the perspective of transmission path, there are mainly six positions that have influence on the shimmy. From top to bottom, they are as follows: (1) the joint clearance between the fuselage and the NLG; (2) the joint clearance between the outer cylinder and the turning sleeve; (3) the joint clearance between the upper torque link and the landing gear rotating sleeve; (4) the joint clearance between the upper torque link and the lower torque link; (5) the joint clearance between the lower torque link and the piston; and (6) the joint clearance between the pulley and the hub. Among them, the joint of the outer cylinder and the turning sleeve is connected by a rack and pinion, and the joint of the axle hub is connected by a pair of tapered roller bearings. In their actual design and use, the assembly clearance and wear clearance are small, which will not be considered in this paper. Therefore, this paper focuses on the influence of position (1), (3), (4) and (5) joint clearance on shimmy.
3.2. Wear Factor of NLG Joint
According to the manufacturing and assembly requirements of the NLG, the assembly dimension chain of each joint is analyzed,
Table 4 presents the assembly clearance range of joints at different positions.
Considering the influence of assembly clearance and wear factors, the radial and axial clearance of 0.1 mm is taken as the reference clearance, and the radial and axial clearance values are increased to 0.2 mm, 0.5 mm and 1.0 mm, respectively. The combination of wear factor studies is depicted in
Table 5.
5. Conclusions
In this paper, the shimmy MBD model of NLG with three-dimensional joint clearance is established, and the radial clearance, axial clearance and coupling conditions are analyzed, respectively. Based on this model, a method is proposed to evaluate the influence of joint clearance of NLG on shimmy stability from two aspects of position factor and wear factor. It is found that the joint clearance between the NLG and fuselage has almost no effect on shimmy, while the clearance between the turning sleeve and upper torque link and that between the lower torque link and the piston, upper and lower torque link will reduce the stability of NLG and is prone to shimmy. The axial clearance plays a greater role than the radial clearance in the process of causing the shimmy of the NLG.
The upper and lower torque link is the key component of the NLG to transfer torque, and only the joint axial clearance will make the front wheel shimmy; the radial clearance between turning sleeve and upper torque link, lower torque link and piston suppresses the axial clearance in space, and the coexistence effect is significant, in which case shimmy instability is prone to occur. To sum up, in the maintenance of the clearance of NLG, attention should be paid to the excessive axial clearance at the connection of upper and lower torque links, and to avoid the simultaneous existence of the radial clearance and axial clearance between the turning sleeve and upper torque link, and between lower torque link and piston. The influence characteristics of joint clearance at different positions on shimmy obtained in this paper are helpful for us to understand the influence mechanism of clearance on shimmy, and it can be applied to the design and maintenance of landing gear joints. The next research work can focus on the load transfer and the influence on shimmy of the NLG with multiple joints with clearance at the same time.