Optimization of the cushion properties of amphibious aircraft landing gear by simulation and drop test

Abstract

This paper proposes a method of optimizing the cushion properties for a certain amphibious aircraft landing gear, which is establishing an accurate simulation model in least mean square by adjusting parameters. First, carry out a drop test under initial parameters to get the friction between the tire and platform, and the elastic parameters of the wheel to simulate the interactions of components. Second, repeatedly modify the model by analyzing the results of comparisons between the drop test and simulation until an accurate model with optimal parameters is established. Finally, verify that the cushion properties of the landing gear with the optimal parameters meet the requirements of airworthiness rules and the properties are greatly improved. The study shows that an adjusting-parameter drop test for establishing a simulation model is an available and reliable way to optimize the cushion properties of an amphibious aircraft landing gear.

Keywords

Cushion properties drop test landing gear LMS simulation parameter optimization

1. Introduction

Landing gear plays a vital role in developing a new aircraft and ensures that the aircraft has enough safety and maneuverability at gliding, taking-off and landing. At touch down during landing, dynamic loads applied on the landing gear are mainly undertaken by shock absorbers, and are then of great interest in the design process of the shock absorber, as an influencing factor of structure damages (Aviation Industry, 2002).

So how to make a shock absorber have optimal cushion properties is a concern in design. Some relevant researches have been conducted to investigate the impact process and cushion properties of landing gear. Milwitzky and Cook (1724) studied theoretically the behavioral analysis of landing gear in the process of touch down. William and McGehee (1991) did a drop test for landing gear to research the cushion properties. Daugherty and Vogler (1990) researched the property control of F-106B airplane landing gear through a drop test. Along with the rapid development of computer technology, virtual prototype technology emerged. Thus, some researchers (Kruger, 2002; Maemori et al., 2003; Lernbeiss and Plöchl, 2007; Kruger and Morandini, 2011) widely used a method of simulation to analyze the properties of landing gear. However, a study of optimizing cushion properties of landing gear has not been done with the comprehensive consideration of a simulation and verification test.

Therefore, this paper aims to establish a complete methodology of optimization for the cushion properties of certain amphibious aircraft landing gear, including a simulation and verification test. In the process of simulating, it is necessary to modify the model of landing gear by adjusting parameters such as filling parameters (James, 1951) and diameters of the oil holes to obtain the accurate model for optimizing the cushion properties. It must be verified that the optimized property indexes satisfy those of airworthiness rules (Wang and Li, 2010).

2. Drop test under initial parameters

2.1. Testing equipment

The test rig used in this article is designed for a free drop test on light aircraft landing gear. It is vertical in style, consisting of column, slide way, lift motor, wheel turning speed system, impact platform and clamp of test pieces, shown in Figure 1. The impact platform supports the impulsive force when the landing gear drops, and provides the friction of tires and the ground. The frictional coefficient can be changed through adjusting the layout pattern of the platform.

Figure 1.

Drop test rig for landing gear.

In the study, the theoretical value of a valid cast-weight is adopted as an initial value for carrying on multiple drop tests to collect data met with cast-absorbing energy, such as valid drop-weight and so on. The final cast-parameters are shown in Table 1.

Table 1.

Initial cast-parameters of drop test

Cast-height $\frac{H}{mm}$	Valid cast-weight $\frac{W_{e}}{Kg}$	Diameter of main oil holes $\frac{d_{m}}{mm}$	Diameter of one-way oil holes $\frac{d_{s}}{mm}$	Initial pressure $\frac{P_{o}}{MPa}$	Wheel turning speed $\frac{r}{min}$
410	329.8	2.6	1.8	0.6	1300

2.2. Results of test

It is necessary to deal with the sensor data gained by a measurement system, thus getting the parameters to justify the cushion properties of the shock absorber. Here are some equations presenting relations between test parameters, shown as equations (1) to (5).

2.2.1. Vertical load of wheel

F_{Z} = F_{1} + F_{2} + F_{3} + F_{4}

(1)

Where F_Z is the vertical load, from the curve of which can be obtained the maximum $F_{z}^{max}$ . Besides, F₁ to F₄ are the vertical forces exerted on the four corners of the platform, measured by force sensors.

2.2.2. Absorbing energy of absorber system A_c

A_{c} = \int_{0}^{h} F_{Z} dh

(2)

Where h is the cast-height. The data of $F_{z} - h$ are read into ORIGIN software to plot a curve, and then make an integral to the curve. The value of integral is the A_c.

2.2.3. Absorbing energy of shock absorber $A_{s}$

A_{s} = \int_{0}^{S_{c}} F_{s} d S

(3)

Where S_c is the maximum stroke of shock absorber, $S$ a stroke of shock absorber and F_s the axial force of shock absorber. A_s can be obtained in reference to A_c.

2.2.4. Efficiency coefficients of absorber system and shock absorber, η and $η_{s}$

η = A_{c} / F_{z}^{max} h

(4)

η_{s} = A_{s} / F_{s}^{max} S_{max}

(5)

Where $F_{s}^{max}$ is the maximum axial force of the shock absorber, obtained in accordance to $F_{z}^{max}$ , and $S_{max}$ is the maximum stroke of the shock absorber.

Calculate the formulas above by using the initial experimental data, thus listing some parameters measuring properties in Table 2 and describing the absorbing energy curves of the shock absorber and absorber system shown in Figure 2.

Figure 2.

Absorbing energy curve of test under initial parameters.

Table 2.

Drop test results based on initial parameters

$S_{max}$ /mm	$\frac{F_{z}^{max}}{N}$	$\frac{A_{c}}{J}$	$\frac{η_{s}}{%}$	$\frac{η}{%}$
126	17980	1521	64.9	55.1

In order to make performance parameters in Table 2 better meet the requirements of Table 3, it is necessary to implement a parameter-adjusting simulation test. The accuracy of a model can be evaluated by controlling the deviation within 10% between analytical value and experimental value of the cushion properties.

Table 3.

Requirements of cushion properties

No.	Cushion property	Requirement
1	Efficiency coefficient of absorber system	$A_{c} \geq$ 50%
2	Efficiency coefficient of shock absorber	$A_{s} \geq$ 60%
3	Service energy $A_{sy}$	$A_{s} y$ = 1967 J
4	Ground load under service energy F_z	F_z ≤ 15362 N
5	Stroke of shock absorber under service energy S	S ≤ 156.3 mm
6	The first round time t	t ≤ 0.8 s

3. Dynamic simulations on drop

3.1. Establishment of simulation model

The nose landing gear is a type of pillar, consisting of rotating shaft, pillar, twisting force arm, and wheel-fork, wheel and so on, among which the pillar is the shock absorber. According to the CATIA 3D digital model, there are some steps to establish a virtual prototyping model in least mean square (LMS) Virtual. Lab Motion, such as model simplicity, definition of motion pair, definition pavement, definition of elastic parameters of tire and shock absorber above, initial conditions and so on. So the final simulation model of landing gear is shown in Figure 3.

Figure 3.

Simulation model of landing gear.

Because setting a different friction coefficient in simulation produces different cushion properties, soothe input of the curve of $μ_{g}$ against δ obtained from the initial drop test, as shown in Figure 4, in which $μ_{g}$ is the friction coefficient between the platform and the tire and δ is the compression amount of the wheel. Other parameters are listed in Table 1. Then a simulation for the drop under initial parameters is carried out.

Figure 4.

The curve of $μ_{g} - δ$ .

3.2. Simulation results compared with test data

The simulation results and the comparison with test data are shown in Table 4. It is known from this that the deviation of maximum vertical load is 3.4%, that of maximum stroke of shock absorber 1.5% and that of absorbing energy of absorber system 3.5%. Considering these deviations are small enough, parameter simulation can be carried out for optimization analysis, in order to obtain the optimal parameters.

Table 4.

Simulation results in comparison with test data under initial parameters

Performanceof system	$\frac{S_{max}}{mm}$	$\frac{F_{z}^{max}}{N}$	A_c/J	$η_{s}$ /%	η/%
Value of simulation	126.0	18590	1885	65.8	53.6
Value of test	126.0	17980	1721	64.9	55.1
Deviation %	0	3.4	9.5	1.4	2.7

4. Parameter-adjusting technology for drop

4.1. Optimization procedures of parameter-adjusting

4.1.1. Optimization model

Look for the optimal parameter configuration to reach the requirements of cushion properties. In fact, in the process of optimization make the parameters of the shock absorber as design variables, and the specific optimization model can be described as follows:

Objective function: absorbing energy of shock absorbing system A_c.

Design variables: the diameter of main oil hole d_m, the diameter of one-way oil hole d_s (considering the diameter of four oil holes equal), initial pressure of shock absorber P_o. Combined diameter of oil hole with the actual minimum adjusting limit of the initial pressure, specify d_m, d_s, V_o as discrete variable, 0.2 mm and 0.2 Mpa as discrete scales respectively.

Constraint function: the maximum stroke of shock absorber $S_{max}$ , vertical load of wheel $F_{z}^{max}$ , the first buffer cycle time t, efficiency coefficients of absorber system and shock absorber as listed in Table 3.

According to the experimental results under the initial parameters, ascertain that increasing the diameter of oil holes and initial pressure of the shock absorber, to make the constraint function within the scope of constraint. Based on practical experiences, define the variation ranges of design variables, as followed in equation (6).

{d_{m} \in (2.8, 3.0, 3.2, \dots, 5.2) d_{s} \in (1.8, 2.0, 2.2, \dots, 3.6) P_{0} \in (0.60, 0.62, 0.64, \dots, 0.80)}

(6)

4.1.2. Optimization analysis for the cushion properties

Set design variables and response function in simulation mode, and add the validated ranges of design variables in equation (6), and then exert variation range on the constraint function and make the objective function as max A_c. So the simulation model for optimization can be established with the specific parameter settings, as shown in Figure 3 above. Carry out optimizing by running LMS software, so the iterative curve of objective function can be obtained, described in Figure 5. And then some specific values of objective function and design variables can be extracted from the iterative curve, listed in Table 5.

Figure 5.

The iterative procedure.

Table 5.

A_c in response to kinds of parameters

$\frac{d_{m}}{mm}$	$\frac{d_{s}}{mm}$	$\frac{P_{o}}{MPa}$	A_c/J
3.4	1.8	0.6	1943
3.8	1.8	0.6	1973
4	1.8	0.6	1988
2.6	2	0.6	1924
3	2	0.6	1948
3.4	2	0.6	1974
3.8	2	0.6	2002
4	2	0.6	2014
4	2	0.62	2012
4	2	0.64	2011
4	2	0.68	2007
4	2	0.7	2006

From Figure 5 above, it can be seen that where the objective function gets maximum, the parameters get optimum, and the specific optimization results are listed in Table 6

Table 6.

First optimization results of cushion properties

$\frac{d_{m}}{mm}$	$\frac{d_{s}}{mm}$	$\frac{V_{o}}{MPa}$	$\frac{S_{max}}{mm}$	$\frac{F_{z}^{max}}{N}$	$\frac{t}{s}$	$\frac{A_{c}}{J}$
4.0	2.0	0.6	153.0	16170	0.38	2014

4.1.3. Test under the optimized parameters

According to the values of parameters in Table 6, alter diameters of the main oil holes and the one-way oil holes. The specific steps are as followed: (a) drill the stigmas of the oil holes referring to the diameters above; (b) replace the stigmas in oil hole flange of the shock absorber; (c) complete the assembling of landing gear, and then fill nitrogen gas to make the initial pressure 0.6 MPa.

Other parameters like wheel turning speed, casting height, valid cast-weight and so on keep the same as those of Table 1, and then carry out the drop test. The results are the absorbing energy of the shock absorber and absorber system as shown in Figure 6, and some main property parameters as listed in Table 7.

Figure 6.

Absorbing energy curve of drop test under 4 mm oil holes.

Table 7.

The results of drop test under 4 mm main oil hole

$\frac{S_{max}}{mm}$	$\frac{F_{z}^{max}}{N}$	$\frac{A_{c}}{J}$	$\frac{η_{s}}{%}$	$\frac{η}{%}$
152.9	15789	1841	64.6	56.8

Compared to the curve of the initial test, its fuller curve indicates that the cushion property has been improved from before. Specifically speaking, the maximum stroke of the shock absorber has been increased; the maximum vertical load has been deduced; the absorbing energy of the absorber system has been greater. However, in comparison to the requirements of design, the maximum vertical load is a little bigger; the absorbing energy of the absorber system slightly trends to the small side. Therefore, it needs adjusting to certain extent, including the enlargements to oil holes and initial pressure of the shock absorber.

4.1.4. Further optimization for parameters considered friction between rolling wheel and rollaway nest

As the friction between the rolling wheel and rollaway nest in the simulation model is not considered, there is a loss of sink speed. So, the optimization model needs further modifying. The specific methods are as follows: a) cast-height is modified as 410 mm; b) consider the friction between guide roller and guide rail; c) set the fall-acceleration as

9.8 \times (1 - 3.7 %) = \frac{9.44 m}{S^{2}}

. Then carry out a simulation for modified model. Finally, the results of the simulation and the comparison to optimized test are showed in Table 8.

Table 8.

Simulation results for further optimization in comparison with drop test

Property of absorber system	$\frac{S_{max}}{mm}$	$\frac{F_{z}^{max}}{N}$	$\frac{A_{c}}{J}$
Value of simulation	158.2	15480	1992
Value of test	152.9	15789	1841
Deviation %	3.5	2.0	8.2

Seen from the table above, the deviations are all within 8%, thinking the further optimization model has enough accuracy. Therefore, the next optimization can be pursued. First, increase the cast height to 427 mm. The variation range of design variables can be determined by the comparison relation of test results and the design objectives, as expressed in equation (7). Thus, the final parameter optimization results are listed in Table 9.

{d_{m} \in (3.8, 4.0, 4.2, 4.4, 4.6) d_{s} \in (2.0, 2.2, 2.4) P_{0} \in (0.66, 0.68, \dots, 0.76)}

(7)

Table 9.

The final optimization results of cushion properties

$\frac{d_{m}}{mm}$	$\frac{d_{s}}{mm}$	$\frac{V_{o}}{MPa}$	$\frac{S_{max}}{mm}$	$\frac{F_{z}^{max}}{N}$	$\frac{t}{s}$	$\frac{A_{c}}{J}$
4.2	2.0	0.70	152.7	15030	0.71	1987

4.2. Drop test under optimal parameters

Based on the final optimization results, triple drop tests are carried out under the conditions where the cast height is increased to 427 mm, the diameter of main oil hole altered to 4.2 mm, the initial pressure of airspace kept as 0.7 MPa and other parameters unchanged.

Take the absorbing energy curves of the second test, as shown in Figure 7, to compare with that of Figure 6. It turns out the two curves look similarly, having the same four peaks and the near compression strokes where these peaks occur. On the other hand, the absorbing energy curve is fuller under the optimal parameters, thereby testifying the cushion property boosted.

Figure 7.

Absorbing energy curve of drop test under optimal parameters.

Then calculate the values measuring the cushion properties, as listed in Table 10. From the table, it can be seen that the results of these three tests keep higher coherence, and both meet the airworthiness requirements, consequently accomplishing the purpose of adjusting parameters.

Table 10.

Experimental results under optimized parameters

No.	Properties	1	2	3	Average
1	$\frac{S_{max}}{mm}$	155.6	157.6	155.2	156.1
2	$\frac{F_{z}^{max}}{N}$	15283	15018	15146	15149
3	$\frac{A_{c}}{J}$	1964	2013	1972	1983
4	$\frac{η_{s}}{%}$	70.7	69.2	64	67.9
5	$\frac{η}{%}$	55.3	59	55.3	56.5

5. Conclusion

In order to improve the cushion properties of certain amphibious aircraft landing gear, the paper presents the method of an adjusting-parameter test to establish an accurate simulation model based on LMS. By research, not only it obtains the optimal parameters of simulation model through optimization, but also verifies the reliability of the landing gear with the optimal parameters through a drop test. The optimization results of properties are summarized as: the maximum stroke increases from 126 mm to 156.1 mm; the maximum vertical load decreases from 17980 N to 15149 N; the absorbing energy improves from 1521 J to 1983 J; efficiency coefficients of the absorber system and shock absorber are both boosted. The improved cushion properties of the landing gear better meet the airworthiness standard technology index compared to that of the initial test. Therefore, this study proves the effectiveness of the proposed approach and it can be applied to amphibious aircraft for improving cushion properties of landing gear.

Footnotes

Funding

This work was supported by the Fundamental Research Funds for the Central Universities, (grant number NS2012081) and the Foundation of Graduate Innovation Center in Nanjing University of Aeronautics & Astronautics, (grant number KFJJ20110201).

References

Aviation Industry (2002) 14th Section of Aircraft Design Manual. Beijing, People's Republic of China: Aviation Industry Publishers.

Daugherty

Vogler

(1990) F-106B Airplane active landing gear drop test performance control. NASA Langley Research Center. 19: 1–3.

James

(1951) Investigation of the air-compression process during drop tests of an oleo-pneumatic landing gear. NASA Technical Note 2477.

Kruger

(2002) Design and simulation of semi-active landing gear for transport aircraft. Mechanics of Structures and Machines. 4(30): 493–526.

Kruger

Morandini

(2011) Recent developments at the numerical simulation of landing gear dynamics. CEAS Aeronautical Journal. 1–4(1): 55–68.

Lernbeiss

Plöchl

(2007) Simulation model of an aircraft landing gear considering elastic properties of the shock absorber. In: Proceedings of the Institution of Mechanical Engineers. 1(221): 77–86.

Maemori K Tanigawa

Koganei

(2003) Optimization of a semi-active shock absorber for aircraft landing gear. Proceedings of 29th Design Automation Conference: Sept. 2–6, Chicago, IL597–603.

Milwitzky B and Cook FE (1953) Analysis of landing-gear behavior. NASA TR-1154.

Wang

(2010) Airworthiness rule alteration and analysis for drop test on transport category airplanes. Development of Aerospace Engineering. 1(4): 10–13.

10.

William

McGehee

(1991) Landing gear drop testing. Aerospace Engineering. 6(11): 42–44.