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Abstract

The centering mechanism of the nose landing gear is crucial for aircraft operational safety, particularly during the takeoff and landing processes. To address the failure of the return function observed in a certain aircraft, this paper establishes a dynamic model that can effectively characterize the return motion characteristics of the landing gear, considering the synergistic effect of the landing gear buffer device, the shimmy damper, and the centering mechanism comprehensively. On this basis, the four key parameters are studied in depth, including the initial filling pressure of the buffer device, the friction moment of the shimmy damper, the damping coefficient of the shimmy damper, and the contact friction coefficient of the centering mechanism. The results reveal that the return driving moment acting on the piston rod of the nose landing gear increases slowly with the increase in steering angle. At the 90° steering angle, the peak value of the return driving moment is 43.97 Nm. Among the parameters studied, compared with the initial filling pressure and the friction moment of the shimmy damper, the contact friction coefficient of the cam has the most significant effect on the return function.

Keywords

Nose landing gear buffer device centering mechanism cam contact parameter influence analysis

Introduction

The aircraft landing gear is an important load-bearing component of the aircraft.^1,2 It bears static and dynamic loads when the aircraft is in contact with the ground and has an extremely important mission in ensuring the safety of the aircraft.^3,4 The centering mechanism applied to the nose landing gear is the key component to ensure the safe take-off and landing process. It is responsible for driving the wheel from any turning position to a neutral position before the aircraft takes off or lands.⁵ The centering mechanism is designed inside the landing gear buffer strut. Through a pair of cam devices (an upper cam fixed on the piston rod, and a lower cam fixed on the outer cylinder of the landing gear), the wheel is automatically guided back to the neutral position, and the return driving moment is provided by the compressed gas inside the buffer.⁶

During ground taxiing, the buffer device slightly compresses, causing the upper and lower cams to separate, allowing the nose wheel to deflect left or right as needed.^7,8 However, the stuck problem of the centering mechanism may lead to serious security risks. Once stuck, it may lead to structural damage or attitude imbalance in the aircraft, thus affecting the landing safety.

Through research, Peng et al.⁹ found that friction and wear are the main reasons for the increase in the required minimum pressure angle for the centering mechanism, which affects the return ability of the nose landing gear. By appropriately increasing the pressure angle of the cam, the cam can still maintain its return function after cam wear, thereby improving the safety of the aircraft. Miao et al.¹⁰ conducted a comprehensive analysis of the fault location and underlying mechanisms associated with the slow return issue at small angles in the return process of a tail landing gear. They identified the critical factors that influence the return performance and verified the effectiveness of the proposed solutions through rigorous durability return testing. The research of Tao et al.¹¹ focused on the friction stuck problem of the external centering mechanism of the helicopter landing gear. They developed a mathematical model for analyzing the friction stuck and solved the critical friction coefficient of the friction stuck. Their research demonstrated that friction stuck will not happen in the centering mechanism with adequate coaxiality. They reduced the risk of friction stuck by optimizing the structure size that affects the critical friction coefficient, which provides a new idea for improving the reliability of the centering mechanism. To return the nose wheel to the centered position after takeoff, Chen¹² proposed a new type of centering mechanism through the analysis and transformation of design requirements and carried out the return performance analysis and experimental verification of the mechanism. In the previous studies, the kinematic model was usually established to discuss the fault causes of the landing gear centering mechanism, but the detailed analysis was not carried out from the perspective of dynamics motion. In addition, there is a lack of quantitative evaluation of the impact of various parameters.

The primary contributions of this study can be summarized as follows:

A novel dynamic response model was developed, specifically characterizing the centering process of the nose landing gear. Unlike existing models that focus solely on kinematics, this model incorporates the interaction of multiple components, including the buffer device, shimmy damper, and centering mechanism, to analyze the full dynamic behavior during the centering motion. This comprehensive approach provides a more detailed representation of the system’s response under various conditions.

A quantitative analysis of key design parameters was performed, focusing on the effects of the initial filling pressure of the buffer, the friction moment and damping coefficient of the shimmy damper, and the contact friction coefficient of the centering mechanism on centering failure. The boundary conditions for parameter combinations leading to centering failure were defined, addressing a gap in previous studies, which lacked detailed parameter analysis.

The remainder of the paper is structured as follows: Section “Return dynamic response model of nose landing gear” first establishes a dynamic simulation analysis model, focusing on the returning dynamics of nose landing gear. Then, Section “Influence of shimmy damper on return function of nose landing gear” investigates the influence of the shimmy damper on the return function. In Section “Analysis of influencing parameters on return dynamic characteristics,” the quantitative impact of four parameters on the return function are analyzed. Finally, conclusions are given in Section “Discussion.”

Return dynamic response model of nose landing gear

The nose landing gear of the studied aircraft and its centering mechanism is depicted in Figure 1. The primary components of the nose landing gear include the outer cylinder, piston rod, torque link, wheel, shimmy damper, and centering mechanism. Notably, the lower cam is affixed to the outer cylinder, while the upper cam is attached to the piston rod. A sealing ring is installed on the outer side of the upper cam to prevent oil leakage during the buffer compression process.¹³ The right side of Figure 1 shows the situation of the centering mechanism in its initial state and the −30° steering angle of the nose landing gear.

Figure 1.

Schematic diagram of nose landing gear and centering mechanism.

When the aircraft takes off, the motion of the nose landing gear piston rod is mainly affected by the buffer load, the contact load from the centering mechanism, and the anti-swing moment of the shimmy damper.¹⁴ The translational and rotational dynamic equations of the landing gear piston rod can be described by the following equations:

{\begin{matrix} ma = F_{NLG} - F_{CON} \\ J β = M_{CON} - M_{D} - M_{FRI} \end{matrix}

(1)

where $m$ and $J$ are the inelastic mass of the nose landing gear and its moment of inertia along the buffer axis, respectively. $a$ and $β$ are the axial acceleration of the piston rod and the angular acceleration around the buffer axis. $F_{NLG}$ is the resultant force generated by the landing gear buffer, acting on the upper cam, while $F_{CON}$ is the force component of the resultant force generated by the centering mechanism. In addition, the piston rod will be subjected to the friction resistance moment $M_{FRI}$ generated by the sealing ring during the rotation process. $M_{D}$ is the resistance moment generated by the nose landing gear shimmy damper. Finally, $M_{CON}$ represents the resultant moment generated by the centering mechanism around the buffer axis. The detailed analysis and modeling of the aforementioned loads are presented in subsequent sections.

Dynamic model of buffer device

The buffer device of landing gear primarily consists of key components such as the buffer cylinder, piston rod, orifice, and sealing rings. Its operation is based on a combination of hydraulic and pneumatic forces: when the aircraft lands, the piston rod enters the buffer cylinder, compressing the gas inside and pushing the hydraulic oil through the orifice. The flow of hydraulic oil generates damping force, thereby absorbing and mitigating the impact energy. The compressed gas provides the elastic restoring force, pushing the piston rod back to its initial position. In the centering process of the nose landing gear, the buffer device provides the returning driving moment through gas pressure, driving the landing gear from the deflected angle back to the neutral position. Additionally, the damping effect of the hydraulic oil helps smooth the centering process, preventing excessive shocks and vibrations.

The axial resultant force $F_{NLG}$ of the nose landing gear buffer acting on the upper cam mainly includes^15,16: gas spring force $F_{AIR}$ , oil damping force $F_{OIL}$ , and friction force $F_{FRI}$ (the structural limiting force of the buffer after complete compression is not considered here). The calculation equation is as follows:

F_{NLG} = F_{AIR} + F_{OIL} + F_{FRI}

(2)

The internal gas of the buffer will be compressed when there is a relative displacement between the piston rod and the outer cylinder. Assuming that the internal gas is in an adiabatic environment and the volume of the buffer gas chamber is constant, the gas spring force can be expressed as:

F_{AIR} = A_{a} [P_{ini} (V_{ini} / (V_{ini} - A_{a} \cdot X_{R}^{N}))^{n} - P_{atm}]

(3)

where $X_{R}^{N}$ is the buffer compression displacement, $n$ is the gas polytropic exponent, $P_{atm}$ is the atmospheric pressure, and $P_{ini}$ is the initial filling pressure of the gas inside the buffer. $A_{a}$ is the effective pressure gas area of the buffer, $V_{ini}$ is the initial gas chamber volume.

The oil damping force of the buffer is calculated as follows¹⁷:

F_{OIL} = | V_{R}^{N} | V_{R}^{N} (\frac{ρ_{oil} \cdot A_{o}^{3}}{2 C_{d}^{2} \cdot A_{d}^{2}})

(4)

where $V_{R}^{N}$ is the compression velocity of the buffer, $ρ_{oil}$ is the oil density, $A_{o}$ is the pressure oil area of piston rod, $C_{d}$ is the shrinkage coefficient of oil hole, $A_{d}$ is the oil hole area.

There is a significant difference in the oil hole area when the movement direction of the buffer piston rod is different. The total area of the oil hole can be calculated using the following equation:

A_{d} = {\begin{matrix} A_{d}^{z} + A_{d}^{f}, V_{R}^{N} > = 0 \\ A_{d}^{f}, V_{R}^{N} < 0 \end{matrix}

(5)

where $A_{d}^{z}$ is the oil hole area that takes effect only when the buffer is compressed during the positive stroke process, $A_{d}^{f}$ is the oil hole area that always takes effect throughout the whole process.

The outer cylinder of the buffer and the piston rod will produce axial friction when there is relative motion. After the nose landing gear is off the ground, the friction of the buffer piston rod is mainly generated by the sealing ring. The empirical expression is as follows:

F_{FRI} = μ_{h} \cdot F_{air} \cdot \tanh (k_{h} \cdot V_{R}^{N})

(6)

where $μ_{h}$ is the equivalent friction coefficient along the axial direction of the buffer. To avoid the discontinuity of friction force in the numerical simulation process, the hyperbolic tangent function is introduced to reduce the sudden change in friction load caused by the buffer compression velocity near 0.

Dynamic model of shimmy damper

The shimmy damper provides damping moment and friction moment during the return process of the piston rod. The calculation equation is as follows¹⁸:

M_{D} = c_{D} \cdot ω_{N} + M_{D}^{F}

(7)

where $c_{D}$ is the equivalent damping coefficient of the shimmy damper, $M_{D}^{F}$ is the constant friction moment generated by the shimmy damper, $ω_{N}$ is the angular velocity of the piston rod around the axis direction.

Dynamic model of centering mechanism

The actual contact between the upper and lower cams in the centering mechanism is surface-surface contact.¹⁹ Given the complex nature of constructing a mathematical model for surface contact, which hinders further research on the coupling influence of multiple parameters, this section employs the point-line contact method to determine the contact load between the upper and lower cams of the centering mechanism. The corresponding diagram, shown in Figure 2, illustrates that the cam edge is expanded into a straight line.

Figure 2.

Equivalent modeling diagram of contact force.

The specific modeling process is as follows:

As the lower cam is fixed to the outer cylinder of the landing gear, when the global coordinate system $O_{g} x_{g} y_{g} z_{g}$ is fixed to the outer cylinder, the coordinates of the upper edge line of the lower cam remain unchanged and can be expressed by a fixed function. The origin of the global coordinate system is located at the center of the lower end face of the lower cam;

The local coordinate system $O_{b} x_{b} y_{b} z_{b}$ is established at the center of the upper cam. The contact reference points are then selected equidistantly on the lower edge curve, and the coordinates of each point in the $O_{b} x_{b} y_{b} z_{b}$ coordinate system are defined, which lays a foundation for solving the depth and embedding speed of each point embedded in the lower cam during the subsequent motion process.

Considering the unreasonable phenomenon of the contact force model established by the linear spring-damping system, this paper introduces the Gonthier contact force model to calculate the contact force between each contact reference point and the lower cam one by one.²⁰ The equation is:

P_{n} = k_{n} \cdot δ_{n}^{1.5} + \frac{1 - c_{n}^{2}}{c_{n}} \cdot \frac{k_{n}}{V_{n 0}} δ_{n}^{1.5} \cdot V_{n}

(8)

where $P_{n}$ is the contact force of a single reference point, $k_{n}$ is the contact stiffness coefficient, $c_{n}$ is the corresponding recovery coefficient. $δ_{n}$ , $V_{n}$ , and $V_{n 0}$ are the compression amount, compression velocity, and compression velocity at the initial moment of contact between the reference point and the lower cam.

Considering the accuracy and consuming time of contact load calculation, this paper compares and analyzes the number of reference points. Finally, the number of contact reference points is determined to be 30, and 15 reference points are arranged on the left and right sides of the upper cam. The contact load analysis process of each reference point is basically the same, so this paper only selects one of the reference points to carry out the detailed derivation of the force analysis process, and the reference point is recorded as point $n$ .

Firstly, the position of point $n$ in the local coordinate system $O_{b} x_{b} y_{b} z_{b}$ of the upper cam is measured, and the normal vector and tangential vector of the lower edge line of the upper cam at point $n$ are measured. The equations are as follows:

{\begin{matrix} R P_{n} = [38.84; 21.33; - 58.28] \\ R V_{n} = [- 0.16; 0.31; 0.94] \\ R H_{n} = [- 0.45; 0.82; - 0.35] \end{matrix}

(9)

where $R P_{n}$ is the coordinate of the reference point, $R V_{n}$ and $R H_{n}$ are the normal vector and tangent vector at the reference point respectively.

The representation function of the vertical coordinate $H$ of the points on the upper edge line of the lower cam in the global coordinate system $O_{g} x_{g} y_{g} z_{g}$ is established as follows:

H = 52 - 16.55 \cdot | θ |

(10)

where the definition of $θ$ , as shown in Figure 3, indicates that a positive rotation around the $z_{g}$ axis is considered positive, with the unit being radians.

Figure 3.

Definition of lower cam edge height.

Subsequently, as the upper cam moves with the piston rod, the embedding depth $X_{n}$ of point $n$ into the lower cam edge line is calculated. Then the projection length of the embedding depth in the normal direction of the contact point is calculated and the value is used as the compression distance $δ_{n}$ . The equation is as follows:

δ_{n} = [0, 0, \max (H - X_{o b} - X_{R}^{N} - R P_{n} (3), 0)] \times R V_{n}

(11)

in which, $R P_{n} (3)$ is the coordinate of point $n$ in the $Z$ direction of the local coordinate system $O_{b} x_{b} y_{b} z_{b}$ , $X_{ob}$ is the initial coordinate of the origin of the local coordinate system in the $Z$ axis direction of the global coordinate system. The absolute velocity of the point $n$ is affected by the coupling influence of the buffer compression velocity and the piston rod rotation speed. At the same time, the compression velocity of the reference point is the projection of the absolute speed in the normal direction of the reference point. The equation is as follows:

V_{n} = - {([0; 0; ω_{N}] \times R P_{n} + [0; 0; V_{R}^{N}])}^{T} \times R V_{n}

(12)

By substituting the compression distance and compression velocity of the reference point $n$ into equation (8), the contact resultant force $F_{n}^{c}$ at the reference point $n$ can be solved. At the same time, the contact surface will produce friction resistance $F_{n}^{f} = F_{n}^{c} μ_{hz}$ during the contact movement of the upper and lower cams. Therefore, the vector form of the load ${\vec{F}}_{n}$ at the reference point $n$ is expressed in the $O_{b} x_{b} y_{b} z_{b}$ coordinate system as follows:

{\vec{F}}_{n} = R V_{n} \cdot F_{n}^{c} + R H_{n} \cdot F_{n}^{c} \cdot μ_{hz}

(13)

Then, considering the comprehensive influence of each contact point, the force vector ${\vec{F}}_{c}$ and moment vector ${\vec{M}}_{c}$ generated by the centering mechanism on the upper cam are derived. The equations are as follows:

{\begin{matrix} {\vec{F}}_{c} = \sum_{i = 1}^{30} {\vec{F}}_{i} \\ {\vec{M}}_{c} = \sum_{i = 1}^{30} (R P_{i} \times {\vec{F}}_{i}) \end{matrix}

(14)

Since only the component of the contact load in the axial direction of the buffer and the moment generated around the axial direction of the buffer are considered when establishing the dynamic model of the centering mechanism, the relevant state can be expressed as follows:

{\begin{matrix} F_{CON} = {\vec{F}}_{c} (3) \\ M_{CON} = {\vec{M}}_{c} (3) \end{matrix}

(15)

Influence of shimmy damper on return function of nose landing gear

This section will first analyze the effective return driving moment generated by the centering mechanism under different steering angles of the piston rod and then discuss the concrete influences of the shimmy damper on the landing gear return dynamics. The key parameters of the nose landing gear required for subsequent simulation are shown in Table 1.

Table 1.

Key parameters required for return simulation of nose landing gear.

Name	Unit	Value
Inelastic mass of nose landing gear, $m$	kg	77.43
Moment of inertia of inelasticmass around Z axis, $J$	kgm²	2.98
Damping coefficient of shimmydamper, $c_{D}$	Nm/(rad/s)	10
Friction moment of shimmydamper, $M_{D}^{F}$	Nm	27.7
Initial filling pressure of buffer, $P_{ini}$	MPa	1.5e⁶
Initial gas chamber volumeof buffer, $V_{ini}$	m³	1.4e⁻³
Pressure gas area of buffer, $A_{a}$	m²	6.4e⁻³
Pressure oil area of buffer, $A_{o}$	m²	4.8e⁻³
Oil density, $ρ_{oil}$	kg/m³	860
Gas polytropic exponent, $n$	/	1.15
Atmosphere pressure, $P_{atm}$	MPa	1.01325e⁵

Return driving moment at different steering angles

Based on the above dynamic response model, the return driving moment of the centering mechanism under different steering angles is calculated. The simulation results are shown in Table 2. It can be seen that when the steering angle increases from 0° to 1°, the driving moment generated by the centering mechanism increases rapidly to 37.59 Nm. Since then, the return moment has increased slowly with the increase in the steering angle. When the steering angle increases to 90°, the return driving moment generated by the centering mechanism is 43.97 Nm. According to the mechanism of the return moment, the current moment change is mainly due to the change of the buffer compression distance, which changes the gas spring force. Therefore, when the steering angle is larger, the gas spring force is greater, which increases the contact force between the upper and lower cams.

Table 2.

Return driving moment under different piston rod steering angles.

Piston rod steering angle (°)	Return drivingmoment (Nm)
0	0
1	37.59
2	37.65
10	38.15
20	38.78
30	39.44
40	40.11
50	40.81
60	41.53
70	42.26
80	43.00
90	43.97

To ensure the validity of the model, a simple experiment was conducted to measure the return driving moment at various steering angles of the nose landing gear. As shown in Figure 4, the pentagram represents the obtained data. It can be found that the maximum relative difference of the return driving moment between simulation and test data is 4.8%. Therefore, the simulation results have a certain degree of matching with the test results obtained from the test of nose landing gear return function. The dynamic model of the return function can be utilized for the later research.

Figure 4.

The relative difference of the return driving moment between simulation and test results.

Influence of shimmy damper on return motion of nose landing gear

Figure 5 shows the motion state curves of the piston rod under three different initial steering angles of −30°, −60°, and −90°. The centering mechanism is fixed to the initial steering angle at 0–1 s in the simulation process and begins to move under the action of the return driving moment and the resisting moment generated by shimmy damper after the fixed constraint is removed. Comparing Figure 5(a) with Figure 5(c), it can be found that the return rate of the piston rod decreases greatly under the action of the shimmy damper. When the piston rod is not affected by the shimmy damper, the three types of working conditions only need 1–2 s to complete the return process. At the same time, after the intervention of the shimmy damper, the piston rod cannot be restored to the median state, and finally it is stationary at the position of −3.26° steering angle.

Figure 5.

Influence of the shimmy damper on nose landing gear return process: (a) change of steering angle without shimmy damper, (b) change of steering angular velocity without shimmy damper, (c) change of steering angle with shimmy damper, and (d) change of steering angular velocity with shimmy damper.

It can be seen from Figure 5(c) and (d) that, taking the −30° steering angle condition as an example, the peak steering angular velocity of the piston rod without the influence of the shimmy damper is 127.89°/s, which is much larger than the steering angular velocity of 2.69°/s after the shimmy damper is installed. The main reason for this difference is that the shimmy damper provides a large damping moment during the piston rod steering process.²¹

Figure 6 shows the return driving moment and hindering moment of the piston rod during the movement under the condition of −90° steering angle. It can be seen that the piston rod is subjected to the effective moment that drives its own steering only during the period from 1 to 1.2 s, causing the steering angular velocity to rise rapidly. Subsequently, the resultant moment is negative, which is unfavorable for its own steering, causing the steering angular velocity to gradually decrease until it approaches 0.

Figure 6.

Driving moment and hindering moment of nose landing gear piston rod in return process.

Analysis of influencing parameters on return dynamic characteristics

This section focuses on four parameters: the friction moment of the shimmy damper, the damping coefficient of the shimmy damper, the contact friction coefficient of the cam, and the initial filling pressure of the buffer device. It analyzes the influence of these parameters on the return dynamic characteristics of the landing gear. The fourth condition of each parameter represents the actual value for the current landing gear. The research conditions are set at 70%, 80%, 90%, 100%, and 110% of the actual values, respectively. By conducting numerical simulation studies under various conditions, the specific influence degree of different parameters can be explored, so as to provide guidance for the future comprehensive optimization of landing gear parameters. The research conditions are as shown in Table 3.

Table 3.

Parameters which affect nose landing gear return characteristics.

No.	Friction momentof shimmydamper $M_{D}$ (Nm)	Damping coefficient of shimmy damper $c_{D}$ (Nm/(rad/s))	Initial filling pressureof buffer device $P_{ini}^{l}$ (MPa)	Contact friction coefficient of cam $μ_{hz}$
1	19.39	7	1.05	0.14
2	22.16	8	1.20	0.16
3	24.93	9	1.35	0.18
4	27.70	10	1.50	0.20
5	30.47	11	1.65	0.22

Influence of friction moment of shimmy damper

Figure 7 illustrates the return motion characteristics of the landing gear under the influence of different friction moments of the shimmy damper. It can be observed from Figure 7(a) that the friction moment of the shimmy damper has a significant impact on the return process of the studied landing gear. For the first three conditions, the nose landing gear is capable of returning the piston rod to the center position, with the required times being 3.59, 4.84, and 8.71 s, respectively. When the friction moment increases to 30.47 Nm, the piston rod will move from steering −60° to −45.21° and stop at the current position. It can be found from Figure 7(b) that when the friction moment of the shimmy damper is only 19.39 Nm, the steering angular velocity of the piston rod increases rapidly to 29.19°/s, which makes the landing gear return in a very short time. Subsequently, a collision occurs between the upper and lower cams at the end of the motion, causing the steering angular velocity to quickly decrease.

Figure 7.

The influence of the friction moment of the shimmy damper on the return dynamic characteristics of the nose landing gear: (a) the trend of changes in the piston rod steering angle and (b) the trend of changes in the piston rod steering angular velocity.

Therefore, the numerical selection of the friction moment value for the shimmy damper should take into account two factors: it should ensure the realization of the landing gear’s return function, and it should not be set too low, which could lead to frequent collisions between the upper and lower cams, resulting in wear.

Influence of damping coefficient of shimmy damper

Figure 8 illustrates the return motion characteristics of the nose landing gear under the influence of different damping coefficients of the shimmy damper. For the landing gear studied, the change of damping coefficient has little effect on the movement of piston rod, and there is no difference in the time tending to be stationary and static angle of piston rod. For the damping coefficients of 7 and 11 Nm/(rad/s), the maximum peak values of the steering angle velocity are 7.03 and 6.09°/s, respectively.

Figure 8.

The influence of the damping coefficient of the shimmy damper on the return dynamic characteristics of the nose landing gear: (a) the trend of changes in the piston rod steering angle and (b) the trend of changes in the piston rod steering angular velocity.

Influence of contact friction coefficient of cam

Figure 9 demonstrates the variation of the landing gear’s return motion characteristics with different contact friction coefficients of the upper and lower cams in the centering mechanism.

Figure 9.

The influence of the contact friction coefficient of the cam on the return dynamic characteristics of the nose landing gear: (a) the trend of changes in the piston rod steering angle and (b) the trend of changes in the piston rod steering angular velocity.

The contact friction coefficient significantly influences the return process of the studied landing gear. For the first three conditions, the nose landing gear is able to achieve the whole return process of the piston rod, with the required times being 2.49, 3.32, and 5.71 s, respectively. When the friction coefficient of the contact surface increases to 0.22, the piston rod will move from a steering of −60° to −56.64° and then stop at the current position. Changes in the cam contact friction coefficient will lead to a decrease in the return driving moment of the piston rod generated after the upper and lower cams come into contact, which results in it being insufficient to overcome the friction resistance moment produced by the landing gear buffer and the shimmy damper.

Influence of initial filling pressure of buffer device

Figure 10 illustrates the landing gear’s return motion characteristics under different initial filling pressures of the buffer device.

Figure 10.

The influence of the initial filling pressure of the buffer device on the return dynamic characteristics of the nose landing gear: (a) the trend of changes in the piston rod steering angle and (b) the trend of changes in the piston rod steering angular velocity.

From the figure, it can be observed that when the initial filling pressure of the buffer device is only 70%, 80%, and 90% of the actual value, the driving moment produced by the centering mechanism is not sufficient to drive the nose landing gear to perform the return motion. When the filling pressure of the buffer device is increased to 110% of the actual value, the landing gear piston rod can be restored to its initial position at 6.43 s.

Quantitative evaluation of parameter influence degree

The core of the landing gear centering mechanism relies on the return driving moment acting on the piston rod being greater than the combined resistance moment it encounters during its motion. According to the data results in Table 2, it is evident that the return driving moment generated by the mechanism gradually decreases as the steering angle reduces. Therefore, this paper quantitatively evaluates the influence degree of three parameters on the return motion characteristics of the studied landing gear through the moment difference in the state of −1°, containing shimmy damper friction moment $M_{D}$ , cam contact friction coefficient $μ_{hz}$ , and buffer device initial filling pressure $P_{ini}$ .

When the moment difference under the −1° state is larger, the reliability of the return function is higher. The equation is expressed as follows:

V_{e} = M_{CON} - M_{D} - M_{FRI} = M_{CON} (- 1 °) - M_{D}^{F} (- 1 °)

(16)

Figure 11 illustrates the influence patterns of the shimmy damper friction moment $M_{D}$ and the cam contact friction coefficient $μ_{hz}$ on the return performance of the studied nose landing gear. The horizontal and vertical coordinates represent the ratios of the cam contact friction coefficient and the shimmy damper friction moment to their initial reference values under corresponding conditions, which are listed in Table 1. It can be seen from the figure that when the cam contact friction coefficient is kept constant, a 50% reduction in the shimmy damper friction moment will result in an increase of the moment difference $V_{e}$ by 13.85 Nm. In contrast, when the shimmy damper friction moment is kept constant, a 50% reduction in the cam contact friction coefficient will lead to an increase of the moment difference $V_{e}$ by 23.74 Nm. Therefore, during the design and subsequent maintenance phases, special attention should be paid to monitoring the cam contact friction coefficient to prevent wear from long-term use, which could affect the effectiveness of the return function.

Figure 11.

The coupling influence law of two parameters on the landing gear return process.

At the same time, combined with the simulation results, the failure boundary of the nose landing gear return function has been drawn in Figure 11. Maintaining the initial filling pressure of the buffer unchanged, it should be ensured that the parameter combination of $M_{D}$ and $μ_{hz}$ is located at the lower left of the failure boundary.

Figure 12 demonstrates the coupled influence of three parameters on the return performance. The five surfaces from bottom to top correspond to the buffer device’s initial filling pressures of 0.90, 1.20, 1.5, 1.80, and 2.10 MPa, respectively. It can be observed from the figure that the initial filling pressure of the buffer device $P_{ini}$ and the cam contact friction coefficient $μ_{hz}$ have a significant coupled influence on the return function. When the friction moment of the shimmy damper is held constant and the cam contact friction coefficient is 0.1, an increase of 40% in the initial filling pressure of the buffer will result in a growth of the moment difference $V_{e}$ by 26.31 Nm, significantly enhancing the landing gear’s return capability. However, when the friction moment of the shimmy damper is held constant and the cam contact friction coefficient is increased to 0.3, the same 40% increase in the initial filling pressure only leads to a growth of the moment difference $V_{e}$ by 6.63 Nm, greatly reducing the impact of the buffer filling pressure on the return performance.

Figure 12.

The coupling influence law of three parameters on the landing gear return process.

Based on the simulation analysis results, it is clear that the contact friction coefficient between the upper and lower cams plays a crucial role in the performance of the centering mechanism, and thus should be closely monitored during use and maintenance.

Actual inspections of the studied nose landing gear have indicated that the primary cause of the failure of return function, is due to wear on the contact surfaces of the upper and lower cams, which leads to an increase in the friction coefficient compared to the initial design value.

Discussion

This section discusses the trends and key findings from the return dynamics analysis of the nose landing gear, focusing on the influence of critical parameters, as depicted in Figures 4 to 12.

As shown in Figure 4, the return driving moment increases nonlinearly as the steering angle increases from 0° to 90°, reaching a peak value of 43.97 Nm. This trend can be attributed to the increased compression of the buffer, which generates greater spring force from the compressed gas. The simulation results closely match the experimental data, with a maximum relative error of only 4.8%, confirming the validity of the model in predicting the return motion.

Figure 5 explored the effect of the shimmy damper on the return motion of the nose landing gear. The inclusion of the shimmy damper significantly reduced the return speed, causing the system to stop at a steering angle of −3.26° across three different conditions. In contrast, without the damper, the nose landing gear returned to the neutral position within 1–2 s. This behavior highlights the critical role of the shimmy damper in dissipating kinetic energy, effectively slowing the return motion.

As illustrated in Figure 7, the results show that an increased friction moment significantly delays the return motion. For instance, with a friction moment of 30.47 Nm, the piston rod stopped at a steering angle of −45.21°. In contrast, with a smaller friction moment of 19.39 Nm, the return was completed more rapidly, and the maximum angular velocity reached 29.19°/s. These results underline the critical role that the friction moment of the shimmy damper plays in the return process, suggesting that controlling the friction moment is essential for optimizing the performance of the centering mechanism. In Section “Influence of damping coefficient of shimmy damper,” Figure 8 shows that variations in the damping coefficient of the shimmy damper have minimal impact on the return motion of the nose landing gear. Both the return time and final stopping angle showed little change across different damping coefficients, suggesting that the damping coefficient plays a limited role. The impact of the contact friction coefficient between the upper and lower cams was examined, with results shown in Figure 9. As the friction coefficient increased to 0.22, the piston rod failed to return completely, stopping at a steering angle of −56.64°. This happens because the increased friction torque surpasses the return driving moment, thus preventing full return motion. This result confirms that the friction coefficient is a critical factor in the design of the centering mechanism, as excessive friction can lead to incomplete return motion. The findings agree with existing studies, which also highlight the detrimental effects of high friction on mechanical systems.⁹

At last, a quantitative evaluation of the influence of key parameters was conducted. Figure 11 shows that the contact friction coefficient of the cam had the most significant impact on the return function, while the friction moment of the shimmy damper had a lesser effect. When the contact friction coefficient was reduced, the return driving moment increased substantially. This observation underscores the importance of controlling the friction coefficient in both design and maintenance to ensure optimal performance and prevent failure due to wear.

Conclusions

This paper conducts a detailed analysis of the return function of a certain nose landing gear, establishing a dynamic simulation model that effectively characterizes the return process. The study evaluates the influence of various parameters on the return dynamics through multi-condition simulations, leading to the following key conclusions:

Considering the impact of the landing gear buffer and the shimmy damper, a mathematical model for the return motion of the piston rod is developed based on a simplified contact force model, and the return driving moment produced by the upper-lower cam mechanism at different steering angles is derived. The simulation results show a reasonable match with the data collected during the return driving moment test of the nose landing gear, confirming the validity of model for investigating the causes of return function failures;

The presence of the shimmy damper plays a critical role in the effectiveness of the return function. For the studied nose landing gear, without the shimmy damper, it can quickly return to the center within 2 s. However, the intervention of the shimmy damper will cause it to stop at a steering angle of −3.26°;

An influence study is conducted on three parameters: the friction moment of the shimmy damper $M_{D}$ , the cam contact friction coefficient $μ_{hz}$ , and the initial filling pressure of the buffer device $P_{ini}$ . It is known that the change in the cam contact friction coefficient has the most significant impact on the return function. When the friction moment of the shimmy damper remains constant, a 40% increase in the buffer’s filling pressure coupled with an increase in the friction coefficient from 0.2 to 0.3 leads to a 19.68 Nm reduction in the effective return driving moment. This highlights the importance of carefully controlling the contact friction coefficient in design and maintenance.

Footnotes

Handling Editor: Aarthy Esakkiappan

Author contributions

Conceptualization, Y.Z.; methodology, S.Z.; formal analysis, S.Z.; writing-original draft preparation, S.Z.; writing-review and editing, S.Z.; visualization, Y.Z.; supervision, Y.Z.; project administration, Y.Z. All authors have read and agreed to the published version of the manuscript.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Data availability

Data are contained within the article.

ORCID iD

Ye Zhao

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Effects of design parameters on the centering performance of nose landing gear for a certain aircraft

Abstract

Keywords

Introduction

Return dynamic response model of nose landing gear

Dynamic model of buffer device

Dynamic model of shimmy damper

Dynamic model of centering mechanism

Influence of shimmy damper on return function of nose landing gear

Return driving moment at different steering angles

Influence of shimmy damper on return motion of nose landing gear

Analysis of influencing parameters on return dynamic characteristics

Influence of friction moment of shimmy damper

Influence of damping coefficient of shimmy damper

Influence of contact friction coefficient of cam

Influence of initial filling pressure of buffer device

Quantitative evaluation of parameter influence degree

Discussion

Conclusions

Footnotes

Author contributions

Declaration of conflicting interests

Funding

Data availability

ORCID iD

References