Vibration Qualification Campaign on Main Landing Gear System for High-Speed Compound Helicopter

Abstract

Vibrations in helicopters have strong implications for their performance and safety, leading to the increased fatigue of components and reduced operational efficiency. As helicopters are designed to land on several types of surfaces, the landing gear system dissipates the impact on the ground and maintains stability during landing and take-off. These vibrations can arise from a variety of sources, such as aerodynamic loads, mechanical imbalances, and engine instabilities. In the present work, the authors describe the vibration qualification process of the main landing gear tailored to fast helicopters within the Clean Sky 2 Racer program. The method entails devising preliminary load sets that deform the structure in its key excited mode shapes to assess stresses and address the experimental campaign. A full-scale prototype model is then tested for sine sweep and random vibrations as per the Airbus Helicopter requirements in order to reach the final qualification and acceptance stage. Although the discussion centers on a landing gear structure, the described process could be extended to other critical equipment as well.

1. Introduction

1.1. Vibration Characterization in Aerospace Field

The prediction and optimization of vibration are essential steps to determine the contributing sources of disturbance on the propeller vehicle’s performance. Propeller aircraft are generally subjected to the dynamic sources provided by the engine and airborne fluctuations. Consequently, dynamic analysis has received attention since the first phases of the aircraft design process [1,2,3,4]. The ground vibration test (GVT) is generally carried out by assessing the aircraft structural strength to verify the compliance with dynamic and aeroelastic requirements [5]. The technical–scientific literature on the vibration aspects of aero-structures is very extensive. However, most of the few existing works are purely based on numerical models [6], with no experimental validation or evaluation. The employment of composite materials has led to the development of more complex aircraft designs and consequently has imposed further challenges for GVT. This increase in structural complexity has resulted in a new scenario, where several research efforts [7,8,9,10,11] have been undertaken in order to reduce the testing time and cost, as well as improving its accuracy. The study in [12] focused on the details of the GVT of an all carbon-fiber-reinforced polymer (CFRP) composite unmanned aerial vehicle (UAV). Modal parameters including natural frequencies, mode shapes, and damping coefficients were numerically estimated for the full aircraft in a free-free condition and then compared to the experimental vibration characteristics measured by means of a shaker-table approach. Previous studies have performed finite element (FE) simulations and static and vibration testing of the wing assembly [13,14] and fuselage [15]. Gupta et al. [16] conducted a GVT on a flying wing aircraft within the NASA project entitled ‘Performance Adaptive Aeroelastic Wing’ (PAAW); in such a context, two tested configurations were designed (i.e., Sköll and Hati). Some studies have reported GVTs involving non-linear modal analysis and the inherent non-linear concerns [17,18,19]. The landing systems have long been the object of considerable interest regarding the study of the dynamic stability of the aircraft on the ground, especially for shimmy- and brake-induced vibrations [20]. Shimmy vibration is an unsteady behavior of the landing gear system during either takeoff or landing, endangering the safety and ride of the aircraft. Energy input for this type of vibration is provided by the kinetic energy of the forward motion of the aircraft [21]. As a result, this energy initiates a self-excited type of vibration in the wheels that may lead to an uncontrolled condition for ground maneuvering. An attempt was made in [22] to develop a dynamical model for the aircraft nose gear, to investigate its transient response to the lateral deviations and shimmy angles. Variations in different design parameters—namely, the energy absorption coefficient of the shimmy damper and the location of the gravity center of the landing gear—were studied. Both increasing the torsional damping and optimizing the stiffness distribution of the NLG can effectively improve the anti-swing performance, preventing the shimmy [23,24,25]. Several instability suppression strategies have been investigated in recent decades by developing multi-disciplinary formulations and the innovative design of active vibration absorbers [26,27,28,29,30,31,32,33]. Friction-induced vibrations are a major concern in the aircraft braking mechanism. Two significant non-linear phenomena have been recognized in the disk brakes during the taxi and landing phases: squeal and whirl. The other primary modal interactions were chatter and gear walk. Brake design parameters such as the working pressure, disk stiffness and geometry, and friction coefficient could be optimized to improve the brake roll conditions [34,35,36,37,38]. While modal interactions on the ground have been extensively discussed, a discussion of the in-flight conditions is lacking. The present authors aim to discuss the vibratory dynamics of the main landing gear (MLG) when exposed to the operative excitations of the aircraft. Despite the use of standard design and testing tools, the article presents novel activity within the certification of landing gear systems for the latest generation of high-speed vehicles.

1.2. RACER Main Landing Gear

The RACER MLG is based on a direct cantilever architecture, with an integrated nitrogen-oil shock absorber (S/A) consisting of one stage: a separator piston divides the oil and nitrogen phases. The MLG is sustained laterally by a side-brace actuator (SBA), which can extend and retract the leg and also lock it both in the down and up positions. In such a way, the actuator combines the dual function of the hydraulic power unit and structural bracing. The MLG system, including the hydraulic actuator and wheel and brake (W&B) assembly, is detailed in Figure 1.

1.3. Scope of the Research

The landing gear structure is designed to withstand the static and cyclic loads encountered during all the landing cases and the ground. Additionally, the dynamic loads comprise low-frequency sine waves and background random noise. The first are generally the excitation harmonics of the propeller source, namely the blade passing frequencies (BPFs), while the random noise—of a lower amplitude—is instead a consequence of the aero-structural interaction and turbulent boundary layer (TBL). A vibration analysis is usually essential when the expected acceleration levels may fall next to the structural natural frequencies. This paper describes a finite element (FE)-based procedure for the identification of the vibration levels of the MLG with regard to the in-flight inertial loads. The present study arises from the need to explore the system’s structural behavior due to the narrow distance between the helicopter (H/C) tonal loads and the predominant modal deformations. In the framework of the same research project, the authors have already performed the characterization of the vibration levels of the MLG composite door as a function of the propeller operating tonal loads [38]. Hence, to perform a structural strength analysis of the landing gear and conduct qualification tests, a numerical evaluation is performed to identify the main dynamic parameters (resonance frequencies, generalized masses). The central themes focus on the modeling strategies, dynamic analysis at harmonic and random loads, and final laboratory testing activities. Due to the various methods available to simulate the two mentioned load entities, an equivalent static load is considered as an engineering combination of them. The optimization of computational times for FE models based on a large number of nodes and elements is in fact a crucial topic currently addressed in the engineering literature. The approximation to a quasi-static type of analysis has the significant advantage of reducing the computational costs compared to an advanced analysis in the time or frequency domain. Transient analyses require the numerical integration of the differential equations governing the structural dynamics for all DOFs of the system. Spectral methods based on the extrapolation of eigenvectors possess the great advantage of replacing the dynamic equilibrium with a set of algebraic equations [39,40]. The normal modes and the corresponding modal mass distribution are employed to evaluate a possible equivalent static load and investigate the relevant stress effects in the resonance condition. In other words, the generalized mass calculation plays a key role in identifying the dynamic loads acting on the landing gear. The qualified modal base of the MLG system could represent proof of its compliance with airworthiness and safety regulations.

2. Materials and Methods

2.1. Numerical Model Design

The 3D FE models are conceived to be fully representative of the detailed MLG components; see Figure 2. The material characteristics are defined in

Table 1. MLG system: material properties of main items [42].

Item	Component	Material	Specification
[-]	[-]	[-]	[-]
MLG Leg	Main Fitting	Al 7050-T7452	AMS 4108
	Sliding Rod—Wheel Axle	Steel 300M	AMS 6257
	Torque Links	Ti-6Al-4V	AMS 4928
Actuator	End Cap—End Fitting	Ti-6Al-4V	AMS 4928
	Cylinder—Piston Rod	Steel 15-5PH	AMS 5659

. Structural FE analysis was carried out using 3D FEM modeling (in the Altair Hypermesh environment). Mesh modeling included the adoption of solid (ctet), rigid (rbe), and contact (cgap) elements, according to the formal classification of the MSC Nastran^® handbook [41] (MSC Software 2021, Newport Beach, CA, USA). Contact analysis allows us to simulate the load interaction among the sub-components. The main characteristics of the 3D FE model are summarized in

Table 2. Three-dimensional FE model’s total number of nodes and elements.

FE Entity	Number
Nodes	1,384,642
3D elements, ctet4	6,270,015
1D elements, cgap contact	32,785
0D elements, conm2	1
Rigid elements, rbe	36

.

2.2. FEM Boundary Conditions

The external constraints are representative of the actual attachments of the MLG leg and actuator vibration test fixture; see Figure 3. The wheel and brake component is assumed as a lumped mass (conm2, [41]) including the equivalent inertial properties; see

Table 3. W&B mass properties.

Mass, m	19.5	[kg]
Inertia moment, xy Ixx = Iyy	0.229	[kgm2]
Inertia moment, z Izz	0.331	[kgm2]

.

Some details of the contact modeling strategy are indicated in Figure 4.

2.3. Sine-on-Random Loading Conditions

The vibration performance and endurance test profiles from Airbus Helicopters combine a sequence of sine waves corresponding to the H/C tones and random noise; see

Table 4. Helicopter sine tones and random spectrum.

Frequency Band	Amplitude	Description
[Hz]	[g, linear], [g2/Hz, Random]	[-]
23.3	±1.0	5/rev MR
29.2	±1.0	1/rev LR
46.5	±0.67	10/rev MR
175.2	±0.67	6/rev LR
10–2000	0.01 (10; 300 Hz), 0.001 (f ≤ 2000)	performance Grms = 2.75 g
	0.02 (10; 300 Hz), 0.002 (f ≤ 2000)	endurance Grms = 3.89 g

linear acceleration confidential (indicated as normalized values); 1/rev: rotor vibration cycle occurring once for every complete rotor revolution.

. The numerical calculations were therefore performed with respect to the harmonics of the main rotor (MR) and lateral rotor (LR) and the random profile (10–2000 Hz); see Figure 5.

2.4. Computational Methodology for Dynamic Loads

The load conditions that are applied to the MLG structure and retraction actuator in the longitudinal (x), lateral (y), and vertical (z) directions are computed by carrying out the following equations. The total dynamic load combines both low-frequency harmonic force and a broadband random spectrum relying on the main participating normal mode shapes; see Figure 6.

• The harmonic sinusoidal load can be introduced as a factor of gravitational acceleration (a_in):

$$F_s=m_g\ast a_{in}\ast Q$$

(1)

where Q = 1/2ξ is the transmissibility at resonance occurrence and m_g is the generalized mass actually participating in the modal deformation.

2.

The random load to be applied is approximated by means of the Miles equation [43]:

$${\ddot{x}}_{rms}=\sqrt{\frac{\pi }{2}{f}_{n_i}Q{W}_{\ddot{u_i}}(f_n)}$$

(2)

$$F_r=m_g\ast {\ddot{x}}_{peak}$$

(3)

where f_n is the resonance frequency and $W_{\ddot{U}}\left(f_n\right)$ is the relevant auto-power spectral density (ASD) of the random enforced acceleration. The 3σ values of the random load factors are then applied considering an equivalent static peak load (${\ddot{x}}_{peak}=3{\ddot{x}}_{rms}$).

3. Numerical Results

3.1. MLG Normal Mode Analysis

The first stage was to characterize the dynamic properties of the MLG leg and re-traction actuator (natural frequencies, modal shapes, and participating mass) on the basis of FE models. The key mode shapes were identified in the bandwidth [0, 50 Hz]—considered significant for the dynamic displacement entity—by a linear modal solver [41]. For this reason, only the modes expected to be the most representative of a cantilevered telescopic LG (flexural deformations in fore and aft and lateral direction) and of a slender actuator strut (typical bending) are provided; see Figure 7. The following

Table 5. MLG dynamic parameters.

Frequency	Modal Mass	Description
[Hz]	[kg]	[-]
33.2	41.1	MLG leg first bending
34.8	27.8	MLG leg second bending
35.5	8.0	Actuator first bending

indicates the corresponding natural frequencies and modal masses calculated in the range of interest. Both the first MLG leg and hydraulic actuator mode shape fall close to the range of the second sine tone (i.e., 1/rev LR), which will be subsequently investigated for the structural analysis aspects. The other elastic deformations not reported are beyond the excitation bands and therefore not contemplated for the dynamic load evaluation.

3.2. Model Validation against Experiment

Considering the complexity of the main landing gear (MLG) and the severity of the qualification loads, with the aim of verifying the reliability of the numerical model, the MLG was subjected to trial tests before carrying out the whole vibration test campaign. For this reason, the MLG was subjected to sine sweep at 0.5 g from 10 Hz to 2000 Hz at 1 octave/min in all three directions. With reference to the directions defined in Section 4 (for excitation in the X and Z directions), the MLG was mounted on the shaker slip table; see Figure 8a,b. The response of the system was recorded at the same points as in the tests carried out along the Z axis (presented in detail in the Section 4).

In order to perform the trial test in the Y direction, the MLG was mounted on the shaker head expander; see Figure 9.

For a landing gear system, the wheel certainly represents one of the most stressed elements. Furthermore, the numerical results highlighted that the first resonance frequency for the MLG wheel was close in frequency to the second sinusoidal tone imposed by the tailoring of the standard and representative of the blade passage frequencies.

The results in

Table 6. Trial test. Comparison between numerical and experimental results.

Axis	First Numerical Frequency [Hz]	First Experimental Frequency [Hz]	Numerical Q Factor	Experimental Q Factor
X	33.2	27.24	20	1.86
Y		30.28		10.84
Z		31.23		11.45

refer to the accelerometer on the wheel system named AC4 and positioned as outlined in Section 4. In Figure 10, it is possible to see how this point was monitored during the experimental tests, as done in the numerical analysis (Figure 3). Although a modal analysis is the most appropriate process to identify all the dynamic characteristics, a sine-on-random vibration test is adequate to perform a survey of the natural frequencies and relevant amplification factors Q. The results demonstrate that the first natural frequencies measured are very close to those estimated numerically but above all confirm their closeness to the second excitation tone. A well-addressed numerical investigation was therefore considered of key relevance. Furthermore, the actual amplification factors Q are determined by the conservative preliminary choice.

The positive outcome of the trial test made it possible to verify that the numerical model was able to predict the behavior of the system in a conservative manner. The difference between the numerical and testing resonance frequencies may be due to the stiffness modeling approach of constraints, which will be tuned in a subsequent detailed phase of this research activity. Although the test was only required for the MLG system without the wheel, given the positive results of the trial test, along the axis considered most critical, i.e., the Z axis, the test was carried out with the wheel system. The other two axes, considered less critical, were tested without a wheel system, to avoid over-testing. The same analysis was also performed for the extended SBA; see Figure 11. For this EUT, the reference system is defined in Section 4, and since the most stressed point was the one positioned halfway along the extension of the actuator (see Figure 12), the results obtained during the trial test for this point are shown in

Table 7. SBA extended trial test. Comparison between numerical and experimental results.

Axis	First Numerical Frequency [Hz]	First Experimental Frequency [Hz]	Numerical Q Factor	Experimental Q Factor
X	35.5	No resonance up to 200 Hz	20	n/a
Y		29.03		7.03
Z		27.39		3.31

. Moreover, in this case, the results demonstrated the ability of the numerical model to test the system in a conservative manner.

The trial phase developed as described so far allows us to highlight potential critical issues in the system (and/or in the test setup) and to adopt the necessary corrective measures aimed at successfully carrying out the qualification tests. Vice versa, as in this case, the positive results of the trial test phase initiated the vibration test campaign with reasonable confidence in the success of the campaign itself.

3.3. FE Calculation of Quasi-Steady Structural Loads

The modal parameters allow for the evaluation of the stress distribution when the structure is subjected to the acceleration sets defined in Table 4. A structural damping coefficient ξ equal to 0.025 is assumed as an engineering choice for metallic assemblies with joints as per ref. [44]; a dynamic amplification factor Q = 1/2ξ = 20 is therefore used for the sine load estimation at the resonance condition. The equivalent static load is applied on the most excited point as established by the normal mode analysis. In this sense, the point at the wheel location would represent intuitively the MLG location with the maximum deformation due to the cantilevered architecture and the W&B lumped inertial effect, as demonstrated numerically in Figure 7a,b. For the actuator, a uniform inertial load is assumed to be applied, which induces a bending load according to the first flexural mode shape; see Figure 7b. The two assemblies—the MLG leg and actuator—are analyzed separately according to the qualification test procedure, which will be discussed in the next paragraph. The MLG equivalent loads with components (F_x, F_y, F_z) are applied at the point with the maximum modal displacement (α_x, α_y, α_z) and calculated for the n mode shapes according to Equation (4):

$${\left[\begin{array}{c}{F}_x\\ F_y\\ F_z\end{array}\right]}_i={\sum }_{i=1}^n{\left((F_s+F_r)\left[\begin{array}{c}{\alpha }_x\\ {\alpha }_y\\ {\alpha }_z\end{array}\right]\right)}_i$$

(4)

The normalized displacements for the three modes of interest are the following:

• α_x = 0.98; α_y = 1.00; α_z = 0.68; for the first MLG mode shape;
• α_x = 1.00; α_y = 0.68; α_z = 0.48; for the second MLG mode shape;
• α_x = 1.00; α_y = 0.00; α_z = 0.00; for the actuator first mode shape.

The equivalent deformations assuming the above (x,y,z) coefficients are given in Figure 13, providing a comparable pattern to the normal modes of Figure 7.

The Von Mises (VM) stress contours (combining principal stresses and shear) represented on the deformation patterns are represented in Figure 14; the details of the most loaded item are addressed in Figure 15. The results include both the MLG leg mode shapes in order to obtain a first conservative evaluation of the stress state. Tensile stresses are more likely to be a source of fatigue failure; therefore, the Max Principal (Max P) is worthy of verification in order to aid the identification of potential critical hotspots. Vibrations can lead to increased wear, particularly in areas where contact pressure could be significant; the oscillating loads with consequent bending deflections could in fact stress considerably the hydraulic actuator, whose nominal design is essentially a tie-rod/strut concept. For this reason, the Min Principal (Min P) stress needs to be investigated differently for the telescopic LG legs already normally sized against the high drag load conditions (spin-up/spring-back).

The FE analyses allowed us to better classify the critical areas to be monitored during the test and, in particular, for the post-test surface checks. The numerical results reported represent an overall view of all load conditions that precisely superimpose the static loads in the three axes simultaneously.

Table 8. MLG system: peak stress summary for worst condition (endurance levels).

Assy	Component	Stress Component	Yield Strength	Load Case
[-]	[-]	[MPa]	[MPa]	[-]
MLG leg	Main Fitting	139.0 (Max P)	400.0	x direction
	Sliding Rod	603.7 (Max P)	1586.0	x direction
	Wheel Axle	216.9 (Max P)	1586.0	z direction
	Upper Torque Link	168.7 (Max P)	792.0	x direction
	Lower Torque Link	176.1 (Max P)	792.0	x direction
Actuator	End Cap	<40.0	806.0	x direction (SBA reference frame)
	End Fitting	(−)43.6 (Max P)	806.0
	Cylinder	<40.0	1000.0
	Piston Rod	144.3 (Max P)	1000.0

recapitulates the maximum stress components (endurance acceleration levels) with the preeminent load direction. The Von Mises stress levels for the most loaded parts are below the yield strength (tension f_ty and compression f_cy) of the materials [42]. The most critical load for the MLG leg is in the x direction; in the same way as a cantilever beam, the bending moment trend of the LG structure is a dual function of the shear forces at the free end and the leg extension (arm). The load path passes through the torque links, which—given the eccentricity with respect to the wheel center—transfer a torque to the main fitting. The main fitting is in fact highly stressed at its interface lug with the torque links. Due to the rotation induced by the drag force (x dir.) around the S/A axis, both the torque links tend to deflect laterally with tension stress (Max P) near their common hinge. Moreover, the telescopic S/A could be perceived to be sustained at the two internal bearings (lower and upper). The stress magnitude on the sliding rod—occurring at the lower bearing—depends mainly on the S/A stroke (fully extended condition corresponds to the most conservative case). The loaded parts of the retraction actuator are located close to the mid-station: the scheme can be simplified to a double-pinned beam based on a normal load. Consequently, particular attention was given to the piston rod bending (Max P) and its contact interaction with the end fitting. The bearing stress (Min P) of the end fitting occurs, in fact, at the seal cavity and is emphasized by the global actuator deflection.

3.4. Vibration Preliminary Fatigue Analysis

The fatigue analysis is performed starting with the stress analysis results. The Goodman criterion is, in particular, used to obtain the damage for each fatigue cycle. Fatigue life assessment is performed with the available S-N discrete data, assuming a stress ratio R = −1.0 (pure sinusoidal oscillating load), and their corresponding best-fit curves, based on the data and equations reported in [42]. The materials’ S-N curves are processed with the following reduction factors:

-

surface finish factors [45];

-

surface treatment factor (confidential);

-

reliability factor [46].

The cycles required n_i are calculated according to the first MLG resonance frequency and the actuator, as well as with respect to the dwell time to be applied during the test; see

Table 9. MLG system: dwell testing duration and number of cycles.

Test	Duration	Cycles Required, ni
[-]	[min]	[–]
		MLG	Actuator
Performance	10.0	19,920	21,283
Endurance	20.0	39,840	42,566
Performance	10.0	19,920	21,283

.

The total damage in each load sequence is the sum of D_i, according to the Miner rule, as indicated in the

Table 10. MLG system: preliminary fatigue damage for main items.

Assy	Component	Max Principal (Performance/Endurance)	Cycles to Failure, Ni	Damage, D
[-]	[-]	[MPa]	[-]	${\sum }_{\mathit{i}}\frac{{\mathit{n}}_{\mathit{i}}}{{\mathit{N}}_{{\mathit{f}}_{\mathit{i}}}}$
MLG leg	Main Fitting	(39.4; 55.5)	1.0 × 107	0.000
	Sliding Rod	(184.1; 259.6)	1.0 × 106	0.415
	Wheel Axle	(45.0; 63.4)	1.0 × 107	0.000
	Upper Torque Link	(47.7; 67.3)	1.0 × 107	0.000
	Lower Torque Link	(49.8; 70.3)	1.0 × 107	0.000
Actuator	End Cap	<40 MPa	1.0 × 107	0.000
	End Fitting	<40 MPa	1.0 × 107	0.000
	Cylinder	<40 MPa	1.0 × 107	0.000
	Piston Rod	(118.1; 144.0)	1.0 × 107	0.004

. The damages are well below 1.0, except for that of the MLG sliding rod, which has a higher state of stress.

4. Vibration Qualification Process

4.1. Equipment under Test

The equipment under test (EUT) is reported in

Table 11. Equipment under test.

Description	Serial Number	Length [mm]	EUT Mass [kg]
MLG	TS100-G1033-00	1065.4	62.0
SBA	TS100-A1051-00	EXTENDED: 1326.7 RETRACTED: 810.8	14.0

and consists of the main landing gear (MLG), as shown in Figure 16, and the related side brace actuator (SBA), as shown in Figure 14. To simulate the operating conditions, the actuator was tested in both configurations: retracted (Figure 17a) and extended (Figure 17b). The EUT is designed to be installed on the Airbus Helicopter Racer compound helicopter high-speed demonstrator [47] currently being developed as part of the Clean Sky 2 research program [48]. The tests were conducted in the CIRA’s Space Qualification Laboratory [49].

4.2. Test Specification Tailoring

The purpose of the vibration test campaign was to prove the resistance of the test articles to qualification loads. In order to identify an efficient testing strategy, it was necessary to understand which loads were the most representative, and this led to an analysis of the aircraft configuration in relation to the flight profile.

The aircraft is able to perform vertical takeoff and landing like a helicopter, thanks to the main rotor and its capability to achieve the performance of the fixed-wing aircraft with propellers for the cruise phase. Hybrid aircraft like the racer are not regulated by any standards, and this necessitated a dedicated tailoring phase of RTCA-DO-160-F [50] in order to identify the most representative configuration of the real system and to test the equipment in a conservative condition in terms of the mechanical loads and test setup. The category identified was U2—Unknown Helicopter Frequencies. Each EUT was then tested with sine-on-random vibration loads. Test levels were calculated according to the aircraft source excitation frequency values outlined in Figure 18 [51], by following RTCA-DO-160-F (depending on the H/C vibration zone). The results contained in these tables are directly related to some information classified as confidential, and, for this reason, they are not shown in this paper.

Based on the previous analyses, each set of EUTs was assigned to the following zones:

• NLG and DBA are placed under the cockpit and therefore belong to area A;
• MLG and SBA are placed under the wing and therefore belong to zone B.

The duration of each test, as well as the random vibration levels, was the same for each set of EUTs.

A sine sweep test is not required within RTCA-DO-160-F. However, in order to detect any dynamic response variation or structural fault, highlighted by frequency peak changes or amplitude response modifications that could arise from the applied vibrational test loads, it was chosen, in line with what is established by the ECSS standard [52], to carry out a sine sweep at 0.5 [g] in the frequency range of interest, i.e., 10–2000 [Hz]. The sweep rate was chosen, in line with the sine-on-random tests, at 1 octave/min.

The test vibration sequence included the following steps:

• sine sweep at 0.5 g from 10 Hz to 2000 Hz at 1 octave/min;
• sine-on-random performance test level for a minimum of 10 min;
• sine-on-random endurance test level for a minimum of 20 min;
• repeat performance test level for a minimum of 10 min;
• repeat sine sweep at 0.5 g from 10 Hz to 2000 Hz at 1 octave/min.

The sine-on-random test is a combined test where several sine sweep tones are superimposed on the random background signal. The result of the RTCA-DO-160-F tailoring phase is summarized in

Table 12. Vibration test levels.

Sine-on-Random PERFORMANCE (600 s)						Sine-on-Random ENDURANCE (1200 s)
Background Random						Background Random
Frequency [Hz]			ASD [g2/Hz]			Frequency [Hz]		ASD [g2/Hz]
10			0.01			10		0.02
300			0.01			300		0.02
2000			0.001			2000		0.002
Sweeping Sine Tones						Sweeping Sine Tones
Item	Frequency [Hz]	23.25	29.20	46.50	175.20	23.25	29.20	46.50	175.20
MLG	X-Axis [g] *	1.00	0.67	0.67	0.67	1.00	0.67	0.67	0.67
	Y-Axis [g] *	1.00	0.67	0.67	0.67	1.00	0.67	0.67	0.67
	Z-Axis [g] *	1.00	0.19	0.19	0.19	1.00	0.33	0.33	0.33
SBA Retracted	X-Axis [g] *	1.00	0.67	0.67	0.67	1.00	0.67	0.67	0.67
	Y-Axis [g] *	1.00	0.67	0.67	0.67	1.00	0.67	0.67	0.67
	Z-Axis [g] *	1.00	0.19	0.19	0.19	1.00	0.33	0.33	0.33
SBA Extended	X-Axis [g] *	1.00	0.67	0.67	0.67	1.00	0.67	0.67	0.67
	Y-Axis [g] *	0.88	0.75	1.00	1.00	1.00	1.00	1.00	1.00
	Z-Axis [g] *	0.88	0.75	1.00	1.00	1.00	1.00	1.00	1.00

* normalized to the maximum value.

, where the vibrational loads to which it was subjected are indicated for each set of EUTs. The data are classified as confidential, and, for this reason, the reported sweeping sine tone amplitude values have been normalized to the maximum value. Meanwhile, the random values appear to be as per the standard [52] and therefore are reported.

According to RTCA-DO 160-F, the sinusoidal frequencies during the sine-on-random tests vary at a logarithmic sweep rate not exceeding 1 octave/min from 0.8∙fn to 1.2∙fn, where fn represents the sinusoidal frequencies of the test spectrum [50].

4.3. Test Setup

The tailoring phase made it possible to identify the qualification loads of the landing gear system. These loads are introduced into the system by the shaker through the fixtures. The design of the fixtures must ensure that, in the frequency range of interest, i.e., [20–2000 Hz], the fixtures do not dynamically amplify the input provided by the shaker, and the constraint conditions must be as realistic as possible. For this reason, the attachment points on the fixture were equipped, as in real operating conditions, with movable bearings and bushings. The orientation of the EUT with respect to the shaker plane (normal to the direction of the gravitational force) is irrelevant, since the effects of gravity are negligible on the dynamic response of the system. When we make this assumption, we consider that the structural configuration is evaluated relative to the static equilibrium point and there is essentially no significant deformation of the structure due to the effects of gravity. This was demonstrated on the FE model, in which a negligible value (less than 1 mm in both vertical and horizontal positions) was measured with the EUT unloaded, i.e., when the only force acting on the EUT itself was the force of gravity; see Figure 19.

Since the choice of the relative EUT/shaker orientation was equivalent, it was preferred to position the EUT horizontally (as shown in Figure 20) in order to minimize the unbalancing couples linked to the application of a non-barycentric dynamic load, which would have been balanced by the shaker bearings.

In order to verify that, in the test range, the fixture does not behave by amplifying the response provided by the shaker [51,52], for each set of EUTs, the fixtures were subjected to sine at 0.5 g in the test frequency range (10–2000 Hz, RTCA-DO-160-F Environmental Conditions and Test Procedures for Airborne Equipment, 6 December 2007) by monitoring the responses of the EUT attachment points to the fixtures themselves.

Due to the mass and dimensions shown in Table 12, each subsystem was tested individually on the vibration system coupled with the slip table (X and Z axes excitation) or with the head expander (Y axis excitation) by means of a mechanical fixture, as shown in Figure 16 and Figure 17.

Since the purpose of this paper is to provide a comparison between the experimental and the numerical results obtained when focusing on the MLG along the Z axis (see Figure 20a) and on the SBA in an extended configuration along the X direction (see Figure 20b), because they consider the elements in the most critical configuration, below, we refer to these sets of EUTs.

4.3.1. Test Setup: MLG

The control of the tests performed on the MLG was carried out on the average [50] of three accelerometers (CTR1, CTR2, and CTR3) located in the attachment points of the EUT with the fixture, as shown in Figure 21. Furthermore, four measuring accelerometers (AC1, AC2, AC3, and AC4) were positioned on the EUT, as shown in Figure 22.

For excitation in the Z direction, the EUT was mounted on the shaker slip table, as shown in Figure 23.

4.3.2. Test Setup: SBA in Extended Configuration

The control of the tests performed on the SBA in the extended configuration was carried out on the average of two accelerometers (CTR1 and CTR2) located in the attachment points of the EUT with the fixture; see Figure 24. Furthermore, four measuring accelerometers (AC1, AC2, AC3, and AC4) were positioned on the EUT, as shown in Figure 25.

Figure 26 represents the test setup of the SBA extended for the X direction.

5. Test Results

According to the test sequence reported previously, for each test article, a sine sweep before and after the sine-on-random sequences was performed for each axis. The sine sweeps were performed in order to detect any dynamic response variation or structural fault, highlighted by changes in the frequency of the peaks or amplitude response modifications, which could arise from the applied test loads [53].

In order to compare the results obtained numerically with the experimental ones, the resonance searches performed before (the blue curve) and after (the red curve) the sine-on-random sequences along the Z axis of the aircraft reference system, which corresponded to the Z axis of the MLG reference system and the X axis of the SBA reference system, are shown in Figure 27, Figure 28, Figure 29 and Figure 30 for the MLG and in Figure 31, Figure 32, Figure 33 and Figure 34 for the SBA in the extended configuration. Moreover, for the purposes of this paper, it is necessary to describe the responses of the accelerometers placed at the points in the structure considered most critical, which, for this reason, were subjected to in-depth numerical analyses before proceeding with the tests. These points, in particular, are

• AC4 for the MLG;
• AC2 for the SBA.

For these points, the FRFs are shown in Figure 30 and Figure 32, respectively.

Since the extended configuration is the most critical, results will be reported only for this configuration, although the same tests were also performed in the retracted configuration.

The overlapping of the two curves evidenced no significant peak variations, both in terms of amplitude and frequency, as highlighted in

Table 13. MLG: shift in the response of AC4 before and after the test along the Z axis direction.

Resonance ID	Frequency Shift [%]	Amplitude Shift [%]
1	0.29	0.00
2	−1.11	2.54
3	0.83	−3.96

, where the percentage shift in the response of the AC4 accelerometer before and after the S/N test along the Z axis direction is reported for the MLG. Similar results were also obtained for the other accelerometers in all three directions and for each EUT. For resonance searches, the success criterion established was, for modes with an effective mass greater than 10% [52], as indicated in Table 5,

• less than 5% in frequency shift;
• less than 20% in amplitude shift.

Table 13 highlights that the resonance search success criterion was satisfied.

Furthermore, at the end of the test sequence, the MLG and the SBA, in each configuration, were visually inspected and no evidence of oil leaks or structural failure was found [50], satisfying the test success criterion as established by RTCA-DO-160-F. The excitation in the X and Y directions showed similar results. Moreover, successive functional tests carried out by Magnaghi Aeronautica proved the correct functioning of the landing gear system and its capability to extend and retract without any problems. The experimental results were used as reference values to evaluate the accuracy of the developed numerical models.

6. Conclusions and Future Activities

For airframe structural components, it is crucial to quickly estimate the severity of the dynamic load conditions at which vibration loads could occur. The dynamic load increment plays a key role in affecting the structural strength assessment when the system’s natural frequencies are close to the excitation source characteristics. An engineering method of performing preliminary conservative evaluations of flight equipment is provided. Based on the resonance frequencies and participating masses, this paper analyzes the dynamic characteristics of an MLG conceived for high-speed applications against the operative vibration spectra. The mode shapes are sorted according to their participating mass entities, and less dominant modes are discarded to streamline the model. The FE-based results and those of the trial test are close, proving that the method can ensure good accuracy within the calculation and analysis process. Finally, the structural reliability of the MLG and its retraction actuator assembly are verified by a mechanical vibration test. Future activities could include the planning of an addressed modal analysis useful for the validation of the actual dynamic properties. The comparison of the present results with measurements carried out at the helicopter level would be another interesting task that would allow for the investigation of the influence of the actual boundary conditions with greater detail.