Research on the Vibration Characteristics of Aviation Hydraulic Clamp and Pipeline Based on Hard Coating

Abstract

Aviation hydraulic clamp-piping systems often experience damage due to vibration, which poses a great threat to the reliability and safety of the aircraft. In this paper, a hard coating is used as a new damping method to study the vibration characteristics of aviation hydraulic clamp-piping systems. Three kinds of coated clamp entities are obtained by optimization and preparation, and the combination of finite element simulation and experiment is used to analyze the vibration response of the high- and low-pressure rotor under fixed-frequency simple harmonic excitation, and the resonance response under sweep-frequency excitation of the aviation hydraulic clamp-piping system. Through orthogonal experiments, it is clear that 304 stainless steel clamps coated with 200-μm-thick YSZ-PTFE coating have the best vibration damping effect on the clamp-piping system; that is, the damping rate can reach 24.67% under fixed-frequency excitation, and swept frequency damping can reach 19.93%. The maximum error between the simulation and the experimental vibration response amplitude is 7.9%, which proves the correctness of the model and verifies that the YSZ-PTFE hard coating can significantly improve the vibration damping effect with very good application prospects.

1. Introduction

The aero-engine is equivalent to the “heart” of the aircraft [1]; the aero-engine hydraulic clamp-piping system provides power to actuators all over the aircraft when the aero-engine is in operation [2,3]. The level of development of aero-engines can be said to reflect a country’s level of scientific and technological development, industrial hard power, and comprehensive national strength standards [4]; therefore, the hydraulic clamp-piping system in aircraft engines is a very important prerequisite for the normal operation of aircraft. Statistically, the failure of hydraulic clamp-piping systems accounts for 36.7% of aircraft engine failures every year [5], while the failures caused by other major engine components account for only 6%, with most being produced by the mechanical vibration effects of the hydraulic system. When the aircraft engine is working normally, due to the foundation excitation of the external frame and the fluid pulsation excitation of the pump source, fluid–structure interaction occurs, which leads to forced vibration, strong vibration, noise, and other phenomena, leading to different problems resulting in failure of the clamp management system. Therefore, solving the problem of vibration in the hydraulic piping system is of utmost importance [6].

There are a number of methods of passive vibration isolation. Michał Stosiak [7] proposed a broadband pressure fluctuation damper with sound filtering function. Experiments showed that this scheme was able to effectively reduce the impact of vibration and noise over a wide frequency range. M. Stosiak [8] and others used a spring-type vibration isolator with linear characteristics, so that the vibration acceleration amplitude of the valve shell was successfully reduced at a certain external vibration frequency. Mechanical vibrations are common in various types of hydraulic systems. Feng Gao [9] selected the specific benchmark of NiCoCrAlY + YSZ hard coating deposited on the detuned blisk for numerical calculation, and studied the vibration reduction characteristics of the detuned blisk with a hard coating. Cross [10] and Patsias S [11] applied ceramic coatings to the surface of engine blades, analyzing and comparing the damping characteristics of the blades before and after coating. Du Guangyu [12] and others found that hard coatings made of metal-based and ceramic-based materials have obvious vibration damping effects. Yin Zeyong [13] and Kwong [14,15] established a finite element model of the stiffness of aero-engine pipeline clamps based on the finite element method. The vibration characteristics of the model were calculated by simulation, and the feasibility of the model was verified by vibration experiments.

The hard coating was found to effectively consume external energy due to the friction effect of the particles inside the coating, reducing the structural vibration after coating and offering a good suppression effect for the fatigue caused by vibration [16,17,18]. The use of hard coatings for vibration damping has become a new research direction [19,20,21,22,23,24], and therefore research has been conducted on the damping of aero-engine hydraulic clamp-piping systems based on hard coatings. Aerohydraulic clamp-piping systems are generally affected by the vibration of the dual-rotor system of aero-engines and the vibration of the casing, resulting in local vibration and random vibration. By changing the characteristics of the clamp, the pipeline vibration can be effectively reduced [25,26].

This paper applies hard coatings made from three kinds of composite material (8%Y₂O₃-Z_rO₂, Al-Cu-Fe-Cr, YSZ-PTFE) to the clamp and pipeline system to minimize vibration. A dynamic analysis of the clamp and pipeline systems incorporating clamps coated with the hard coatings is carried out, and a finite element model under real conditions is established and verified by experiments. The influence of different hard coating materials and thicknesses on the vibration characteristics and damping effect of clamp-piping systems was investigated, which is significant in reducing the vibration of clamp-piping systems of aeroengines.

2. Materials and Methods

2.1. Selection and Preparation of Test Materials

To prepare a coating material that would offer the best performance with respect to the vibration characteristics and damping effect of the clamp-piping system, three experimental coating materials were optimized and screened via experimental research. The performance characteristics of the three coating materials are as follows:

(1)

YSZ (8%Y₂O₃-Z_rO₂) (Beijing Chemical Company, Beijing, China) ceramic coating. Ceramic coatings have a high melting point and good stability at high temperatures and a thermal expansion coefficient similar to that of metal materials. Since the state of the pure Z_rO₂ coating itself is unstable and cannot be used as a thermal barrier coating, Z_rO₂ with the addition of Y₂O₃ was selected as the coating material. Generally, the content of Y₂O₃ in zirconia used as a thermal barrier coating is between 6 wt% and 8 wt%. This YSZ coating is currently the material most widely used in thermal barrier coatings, and offers good stability, corrosion resistance, and a high thermal cycle life.

(2)

Al-Cu-Fe-Cr (Beijing Chemical Company, Beijing, China) quasicrystalline coating. Quasicrystals have the properties of high hardness, oxidation resistance, and low thermal conductivity. However, due to their inherent high brittleness, they can only be attached to the surface of other substrates in the form of a film or a coating; thus, they are able to exert their outstanding mechanical and thermal properties while the substrate alleviates their brittleness. Professor Chungen Zhou of Beijing University of Aeronautics and Astronautics and others have used plasma spraying to prepare Al-Cu-Fe-Cr quasicrystalline coatings on titanium alloy substrates. After systematic research, they found that the quasicrystalline system had very good vibration damping performance.

(3)

YSZ-PTFE composite coating. PTFE (Fuxin Chemical Company, Fuxin, China) is a polytetrafluoroethylene-containing polymer chemical material with an excellent low-loss tangent and low dielectric constant. PTFE has a variety of properties, such as high-temperature resistance, corrosion resistance, and self-lubrication. This soft coating can effectively reduce the friction coefficient of surfaces onto which it is sprayed, improving the surface’s corrosion resistance. The combination of PTFE with a ceramic filler changes its material properties; PTFE can be mixed into a ceramic filler, following which it can be used as a damping material to absorb the vibration energy caused by external vibrations, thereby achieving the effect of vibration reduction and noise reduction. After many mixing–spraying experiments, YSZ and PTFE were finally mixed at a ratio of 16:1.

2.2. Design of the Test Plan

Oerlikon Metco 9MC plasma spraying equipment (Oerlikon Metco Surface Technology, Shanghai, China) was used to plasma spray the clamps to prepare three kinds of hard-coated clamp. Images of the clamps following the coating are provided in Figure 1. During the orthogonal experiments, the coating material, the coating thickness, the clamp material, and three other parameters were studied with respect to their vibration damping effect on the clamp-piping system, as shown in

Table 1. Horizontal factor table.

Factor Level	Coating Material A	Coating Thickness B (μm)	Clamp Material C
1	8%Y2O3-ZrO2	100	Galvanized iron
2	Al-Cu-Fe-Cr	150	304 stainless steel
3	YSZ-PTFE	200

. On this basis, a 3-level 3-factor orthogonal test table L9(3³) was designed. The resulting spraying experiment scheme is shown in

Table 2. Spraying experiment scheme.

Test Number	Horizontal Combination	A	B (μm)	C
P1	A1B1C1	1(8%Y2O3-ZrO2)	1(100)	1(Galvanized iron)
P2	A1B2C2	1(8%Y2O3-ZrO2)	2(150)	2(304 stainless steel)
P3	A1B3C2	1(8%Y2O3-ZrO2)	3(200)	2(304 stainless steel)
P4	A2B1C2	2(Al-Cu-Fe-Cr)	1(100)	2(304 stainless steel)
P5	A2B2C2	2(Al-Cu-Fe-Cr)	2(150)	2(304 stainless steel)
P6	A2B3C1	2(Al-Cu-Fe-Cr)	3(200)	1(Galvanized iron)
P7	A3B1C2	3(ZrO2-PTFE)	1(100)	2(304 stainless steel)
P8	A3B2C1	3(ZrO2-PTFE)	2(150)	1(Galvanized iron)
P9	A3B3C2	3(ZrO2-PTFE)	3(200)	2(304 stainless steel)

.

3. Establishment of a Hard-Coated Clamp-Piping Model Based on Finite Elements

According to the experimental spraying scheme, Solidworks was used to establish the finite element three-dimensional model, and the x-t file of the model was imported into ANSYS Workbench for finite element simulation analysis which consisted of defining the geometric model, setting its boundary conditions, applying loads to the system, and finally obtaining the simulation results, thus verifying the model. The specific process is shown in Figure 2.

3.1. Straight Pipe-Clamp Model Establishment

According to the aviation standard HB 6665, the geometric size of the clamp used with a diameter of 20 mm was obtained, the solid geometric model of the clamp was established, and the geometric model of the clamp was simplified within the range allowed by the simplification principle of the finite element model. The simplified clamp position and a comparison of the simplified front and rear clamp models are shown in Figure 3.

3.2. Material Parameters

In this study, the material parameters of the aviation hydraulic clamp-pipeline components in the finite element analysis are shown in

Table 3. Material parameters of the aviation hydraulic clamp-piping model.

Part	Material	Elastic Modulus (Pa)	Poisson’s Ratio	Density (kg/m3)
Pipeline	Nitronic40 (XM-10) S21900 Stainless steel	180 × 109	0.298	7830
The first type of clamp	304 stainless steel	1.98 × 109	0.3	7830
Rubber liner	Rubber	1 × 109	0.49	930
The second type of clamp	Galvanized steel	2 × 1011	0.31	7870

and

Table 4. Hard coating material parameter table.

Material	Elastic Modulus (Pa)	Poisson’s Ratio	Density(kg/m3)
8%Y2O3-ZrO2	180 × 109	0.31	5850
Al-Cu-Fe-Cr	168 × 109	0.23	4492
ZrO2-PTFE	169.4 × 109	0.32	5633

.

3.3. Mesh and Add Constraints

Different meshing methods can be implemented in ANSYS Workbench for a model. Aviation hydraulic clamp-piping systems are small, but have many parts. To improve the quality of the divided mesh, the mesh was refined for the three main research components: the rubber gasket, the clamp, and the hard coating; the grid size was 1 mm. Other parts uniformly used the automatic division method (Automatic), where the size of the grid was 2 mm. Figure 4 shows the grid diagram of the aviation hydraulic clamp-piping model. The number of nodes divided was 166,821, and the number of grids was 84,524.

According to the basic theory of the finite element method, accurate constraints need to be added to the model. With respect to the specific situation of vibration testing, the pipeline is mainly constrained by the clamp, and the clamp is fixed on the experimental support; therefore, constraints are added for the fixed support to fix the two bases of the clamp-piping system, as shown in Figure 5.

4. Clamp-Piping System Finite Element Modal Analysis and Vibration Test

4.1. Finite Element Model Analysis

The 10 natural modes and natural frequencies of the uncoated 304 stainless steel and galvanized steel clamp-piping systems were obtained on the basis of the finite element model simulation analysis, as shown in Figure 6 and Figure 7. The first four natural modes are presented in detail in

Table 5. First 10 natural frequencies/Hz of uncoated clamp-piping system.

	304 Stainless Steel Clamp-Pipeline Natural Frequency/Hz	Galvanized Steel Clamp-Pipeline Natural Frequency/Hz
1	488.62	487.65
2	692.59	692.71
3	1014.1	1013.6
4	1730.8	1730.1
5	1939.8	1939.8
6	2420.8	2421.2
7	3200.9	3202.8
8	3836.6	3835.6
9	4019	4019.9
10	4118.5	4117.2

. The natural frequencies of 304 stainless steel and galvanized steel clamps with different coating thicknesses of Z_rO₂-PTFE are listed in

Table 6. First 10 natural frequencies/Hz of 304 stainless steel clamps coated with different thicknesses of Z_rO₂-PTFE.

	Thickness 100 (μm)	Offset Rate (%)	Thickness 150 (μm)	Offset Rate (%)	Thickness 200 (μm)	Offset Rate (%)
1	497.77	1.87%	523.92	7.22%	542.64	11.06%
2	696.52	0.57%	700.81	1.19%	704.9	1.78%
3	1019.1	0.49%	1047.9	3.33%	1072	5.71%
4	1728.9	−0.11%	1735.9	0.29%	1739.8	0.52%
5	1941	0.06%	1948.7	0.46%	1955.3	0.80%
6	2417.4	−0.14%	2431.3	0.43%	2442.6	0.90%
7	3208.6	0.24%	3244.3	1.36%	3271.6	2.21%
8	3848.7	0.32%	3873.7	0.97%	3892.9	1.47%
9	4020.5	0.04%	4035.3	0.41%	4048.4	0.73%
10	4134.9	0.40%	4171.8	1.29%	4212.2	2.28%

and

Table 7. First 10 natural frequencies/Hz of galvanized steel clamps coated with different thicknesses of Z_rO₂-PTFE.

	Thickness 100 (μm)	Offset Rate (%)	Thickness 150 (μm)	Offset Rate (%)	Thickness 200 (μm)	Offset Rate (%)
1	497	1.92%	523.34	7.32%	542.15	11.18%
2	696.61	0.56%	700.87	1.18%	704.94	1.77%
3	1018.8	0.51%	1047.5	3.34%	1071.6	5.72%
4	1728.3	−0.10%	1735.3	0.30%	1739.2	0.53%
5	1940.9	0.06%	1948.7	0.46%	1955.3	0.80%
6	2418	−0.13%	2431.8	0.44%	2443.1	0.90%
7	3210.3	0.23%	3245.9	1.35%	3273	2.19%
8	3847.9	0.32%	3873.1	0.98%	3892.5	1.48%
9	4021.5	0.04%	4036.3	0.41%	4049.4	0.73%
10	4133.4	0.39%	4170.2	1.29%	4210.4	2.26%

. By comparing and analyzing the results calculated by finite element simulation, it can be seen that the thicker the coating, the greater the deviation of the natural frequency of the clamp-piping system, with the first-order natural frequency deviation reaching up to 11.18%, which satisfies the requirement of preventing resonance by changing the natural frequency of the clamp-piping system.

4.2. Clamp-Piping System Vibration Response Test

The working state of an aviation aircraft under different working conditions was simulated, taking 11 different aviation hydraulic clamp-pipe systems before and after the application of a hard coating as the research object. The vibration response test of clamp-pipe systems supported by double clamps was carried out by a method that combines simulation and experiment, using fixed-frequency and frequency-sweep excitation methods. The vibration response characteristics of aviation hydraulic clamp-pipeline system were explored in combination with different hard coating materials and coating thicknesses, as well as different clamp materials, and the change rule of the vibration suppression effect caused by the hard coating was investigated in order to select the optimal vibration reduction scheme. The instruments used in this experiment include a vibration test bench, an acceleration sensor, a clamp-pipeline system, a signal acquisition instrument, and the Coinv DASP V11 analysis software.

(1)

Test bench

The test system adopted was the vibration test system of Suzhou Dongling Vibration Company. The electromagnetic vibration table is composed of a vibration table, a power amplifier, a cooling system, and a controller. There is an excitation coil inside the shaker to create a magnetic field. Under the coil, driven by circulating alternating current, the table vibrates back and forth to simulate the basic excitation of the pipeline system under working conditions.

(2)

Data acquisition and analysis system

The data acquisition and analysis system used in this experiment is composed of and INV3060S 24-bit network-distributed acquisition instrument and the signal test and analysis software Coinv DASP V11. The pickup of the signal is fixed on the outer surface of the pipeline by the ICP type sensor (INV9822 type), which is connected with the data channel of the acquisition instrument. The sensor parameters are provided in

Table 8. Parameter table for the INV9822 acceleration sensor.

Parameter	Configuration	Parameter	Configuration
Reference sensitivity	100 mv/g	Mounting thread	M5
Frequency Range	0.5–9000	Resonant frequency	>25 KHz
Measuring range	50 g	Resolution	0.002 m/s2
Weight	10 g	Dimensions	13 × 22 mm

.

The experiment used a Nitronic40 (XM-10) S21900 stainless steel pipe with an outer diameter of 20 mm and a wall thickness of 1 mm. The pipeline was installed on the vibration test bench by fixing it with clamps at both ends; two acceleration sensors were placed onto the surface of the pipeline; an INV3062 V type 24-bit network-distributed acquisition instrument was used to collect the vibration model of the No. 1 sensor near the clamp and the No. 2 sensor in the middle of the pipeline. Figure 8 shows the setup for the vibration response test of the clamp-piping system, and

Table 9. Hard-coated aviation hydraulic clamp-pipeline vibration response test table.

Test Number	A	B (μm)	C
P1	1(8%Y2O3-ZrO2)	1(100)	1(Galvanized iron)
P2	1(8%Y2O3-ZrO2)	2(150)	2(304 stainless steel)
P3	1(8%Y2O3-ZrO2)	3(200)	2(304 stainless steel)
P4	2(Al-Cu-Fe-Cr)	1(100)	2(304 stainless steel)
P5	2(Al-Cu-Fe-Cr)	2(150)	2(304 stainless steel)
P6	2(Al-Cu-Fe-Cr)	3(200)	1(Galvanized iron)
P7	3(ZrO2-PTFE)	1(100)	2(304 stainless steel)
P8	3(ZrO2-PTFE)	2(150)	1(Galvanized iron)
P9	3(ZrO2-PTFE)	3(200)	2(304 stainless steel)
P10			304 stainless steel
P11			Galvanized iron

shows the test table for the vibration response test of the hard-coated aviation hydraulic clamp-piping system.

4.2.1. Fixed Frequency Vibration Test of Clamp-Piping System

The hydraulic clamp-pipeline system of an aero-engine is stimulated by a rotor system, the fluid–structure coupling vibration of hydraulic fluid, gas excitation, etc. Aircraft typically use dual-rotor engines, which include two systems: a low-pressure rotor and a high-pressure rotor. This article selects a high-pressure speed of Nj = 12,000 r/min and a low-pressure speed of Ni = 9000 r/min as examples; that is, when the engine is working normally, the excitation frequency fi = 9000/60 = 150 Hz, fj = 12,000/60 = 200 Hz, the excitation force acceleration is 2 g. Thus, it is possible to carry out a vibration response analysis of the clamp-piping system under fixed-frequency excitation. The vibration response results of the aviation hydraulic clamp-piping system under low-pressure fixed-frequency excitation at 150 Hz before and after application of the hard coating are shown in Figure 9, Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14.

It can be seen from Figure 9, Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14 that, under 150 Hz fixed-frequency excitation, the minimum value of vibration response of the 304 stainless steel clamp-piping system coated with YSZ with a layer thickness of 200 μm was 1.196 g, which is 17.79% lower than that of the uncoated layer; the minimum value of vibration response of the galvanized iron clamp-piping system coated with Al-Cu-Fe-Cr with a layer thickness of 200 μm was 1.346 g, which is 16.71% lower than that of the uncoated layer; the minimum vibration response of the galvanized iron clamp-piping system coated with YSZ-PTFE with a layer thickness of 150 μm was 1.407 g, which is 12.93% lower than that of the uncoated layer; the minimum value of vibration response of the 304 stainless steel clamp-piping system coated with YSZ-PTFE with a layer thickness of 200 μm was 1.139 g, which is 21.45% lower than that of the uncoated layer. It can be seen from this the degree to which the value of vibration response of the clamp-piping system after coating decreases to different degrees, with vibration response value gradually decreasing with increased coating thickness. Among the tested systems, the 304 stainless steel clamp with the coating material 3 (ZrO₂-PTFE) coating and a coating thickness of 200 mm exhibited the greatest reduction in vibration response and the best vibration reduction effect.

The vibration response results of the aviation hydraulic clamp-piping system at low pressure and a fixed frequency of 200 Hz before and after the application of the hard coating are shown in Figure 15, Figure 16, Figure 17, Figure 18, Figure 19 and Figure 20.

From Figure 15, Figure 16, Figure 17, Figure 18, Figure 19 and Figure 20, it can be seen that, under 200 Hz fixed-frequency excitation, the minimum value of vibration response of the 304 stainless steel clamp-pipeline system coated with YSZ with a layer thickness of 200 μm was 2.289 g, which is 23.06% lower than that of the uncoated layer; the minimum value of vibration response of the galvanized iron clamp-piping system coated with Al-Cu-Fe-Cr with a layer thickness of 200 μm was 2.485 g, which is 17.99% lower than that of the uncoated; the minimum value of vibration response of the 304 stainless steel clamp-pipeline system coated with YSZ-PTFE with a thickness of 200 μm was 2.241 g, which is 24.67% lower than that of the uncoated layer. It can be seen from this, that the vibration response value of the clamp-piping system following hard coating is significantly reduced compared to that of the uncoated layer. In addition, different coating thicknesses, different coating materials, and different clamp materials have different effects on the vibration response.

According to

Table 10. Orthogonal test results of vibration response under low-voltage 150 Hz fixed-frequency excitation.

Test Number	A Coating Material	B Coating Thickness (μm)	C Clamp Material	Damping Rate
P1	1(8%Y2O3-ZrO2)	1(100)	1(Galvanized iron)	3.22%
P2	1(8%Y2O3-ZrO2)	2(150)	2(304 stainless steel)	7.17%
P3	1(8%Y2O3-ZrO2)	3(200)	2(304 stainless steel)	17.79%
P4	2(Al-Cu-Fe-Cr)	1(100)	2(304 stainless steel)	1.59%
P5	2(Al-Cu-Fe-Cr)	2(150)	2(304 stainless steel)	10.41%
P6	2(Al-Cu-Fe-Cr)	3(200)	1(Galvanized iron)	16.71%
P7	3(ZrO2-PTFE)	1(100)	2(304 stainless steel)	4.28%
P8	3(ZrO2-PTFE)	2(150)	1(Galvanized iron)	12.93%
P9	3(ZrO2-PTFE)	3(200)	2(304 stainless steel)	21.45%
P10			304 stainless steel
P11			Galvanized iron
Sum value K1	28.18%	9.09%	32.86%
Sum value K2	28.71%	30.51%	62.69%
Sum value K3	38.66%	55.95%
Mean K1	9.39%	3.03%	12.37%
Mean K2	9.57%	10.17%	13.43%
Mean K3	12.89%	18.65%
Extremum R	3.32%	15.62%	1.07%
Excellent solution	A3	B3	C2

and

Table 11. Orthogonal test results of vibration response under high-voltage 200 Hz fixed-frequency excitation.

Test Number	A Coating Material	B Coating Thickness (μm)	C Clamp Material	Damping Rate
P1	1(8%Y2O3-ZrO2)	1(100)	1(Galvanized iron)	3.83%
P2	1(8%Y2O3-ZrO2)	2(150)	2(304 stainless steel)	13.82%
P3	1(8%Y2O3-ZrO2)	3(200)	2(304 stainless steel)	23.06%
P4	2(Al-Cu-Fe-Cr)	1(100)	2(304 stainless steel)	2.18%
P5	2(Al-Cu-Fe-Cr)	2(150)	2(304 stainless steel)	10.69%
P6	2(Al-Cu-Fe-Cr)	3(200)	1(Galvanized iron)	17.99%
P7	3(ZrO2-PTFE)	1(100)	2(304 stainless steel)	3.16%
P8	3(ZrO2-PTFE)	2(150)	1(Galvanized iron)	16.73%
P9	3(ZrO2-PTFE)	3(200)	2(304 stainless steel)	24.67%
P10			304 stainless steel
P11			Galvanized iron
Sum value K1	40.71%	9.17%	38.55%
Sum value K2	30.86%	41.24%	77.58%
Sum value K3	44.56%	65.72%
Mean K1	13.57%	3.06%	12.37%
Mean K2	11.73%	13.75%	13.43%
Mean K3	15.00%	21.91%
Extremum R	3.27%	18.85%	1.07%
Excellent solution	A3	B3	C2

, in the case of vibration caused by 150 Hz low-voltage fixed-frequency excitation and 200 Hz high-voltage fixed-frequency excitation, the coating thickness has the greatest impact on the vibration response of the clamp-piping system, the coating material has a great impact on the vibration response of the clamp-piping system, and the clamp material has little effect on the vibration response of the clamp-piping system. The optimal combination of orthogonal experiments would be to use a clamp-piping system comprising 304 stainless steel with a YSZ-PTFE composite material coating with a thickness of 200 μm. The damping rate reaches 21.45% under 150 Hz low-voltage fixed-frequency excitation vibration, and the damping rate reaches 24.67% under 200 Hz high-voltage fixed-frequency excitation vibration.

ANSYS Workbench software was used to carry out the simulation calculations for the 150 Hz and 200 Hz fixed-frequency vibration response characteristic and to calculate the simulation error relative to the experimental value. The specific values are shown in

Table 12. Simulation and experimental data comparison of the aeronautical hydraulic clamp-pipeline system under fixed-frequency excitation before and after hard coating.

Comparison of Simulation and Experiment Under 150 Hz Excitation
Test Number	150 Hz Vibration Experimental Sensor Vibration Acceleration Amplitude (g)	150 Hz Vibration Simulation Vibration Acceleration Amplitude (g)	Error Rate
P1	1.564	1.485	5.05%
P2	1.346	1.288	4.31%
P3	1.192	1.183	0.76%
P4	1.427	1.477	−3.50%
P5	1.299	1.314	−1.15%
P6	1.346	1.276	5.20%
P7	1.388	1.439	−3.67%
P8	1.407	1.308	7.04%
P9	1.139	1.136	0.26%
P10	1.450	1.494	−3.03%
P11	1.616	1.504	6.93%
Comparison of Simulation and Experiment under 200 Hz Excitation
Test Number	200 Hz vibration Experimental Sensor Vibration Acceleration Amplitude (g)	200 Hz Vibration Simulation Vibration Acceleration Amplitude (g)	Error Rate
P1	2.912	2.857	1.89%
P2	2.564	2.454	4.29%
P3	2.289	2.241	2.10%
P4	2.910	2.882	0.96%
P5	2.657	2.506	5.68%
P6	2.485	2.306	7.20%
P7	2.881	2.863	0.62%
P8	2.523	2.494	1.15%
P9	2.241	2.273	−1.43%
P10	2.975	2.884	3.06%
P11	3.030	2.905	4.13%

.

Table 12 shows that the maximum error between the acceleration response results of the hard-coated aviation hydraulic clamp-piping system and the experimental test data obtained on the basis of the finite element simulation calculation was 7.20%, which verifies the rationality and feasibility of the aviation hydraulic clamp-piping system model established by the simulation calculations.

4.2.2. Frequency Sweep Vibration Test of Clamp-Piping System

The vibration response of the hard coating material, coating thickness and clamp material of the aviation hydraulic clamp-piping system was analyzed in a nonresonant state under basic excitation. The sampling frequency was set to 5120, the frequency sweep range was 150 Hz-1500 Hz, and the frequency sweep time was 120 s. The results for the frequency sweep vibration response of the aviation hydraulic clamp-piping system before and after application of the hard coating are shown in Figure 21, Figure 22, Figure 23, Figure 24, Figure 25 and Figure 26.

From Figure 21, Figure 22, Figure 23, Figure 24, Figure 25 and Figure 26, it can be seen that, in the case of 150 Hz–1500 Hz frequency sweep range, the minimum value of the vibration response of the 304 stainless steel clamp-pipeline system coated with YSZ with a layer thickness of 200 μm was 15.21 g, which is 15.78% lower than that of the uncoated layer; the minimum value of vibration response of the galvanized iron clamp-pipeline system coated with Al-Cu-Fe-Cr with a layer thickness of 200 μm was 16.88 g, which is 12.06% lower than that of the uncoated layer; the minimum vibration response of the galvanized iron clamp-piping system coated with YSZ-PTFE with a layer thickness of 150 μm was 17.32 g, which is 9.93% lower than that of the uncoated layer; the minimum value of the vibration response of the 304 stainless steel clamp-pipeline system coated with YSZ-PTFE with a thickness of 200 μm was 14.46 g, which is 19.93% lower than that of the uncoated layer.

According to

Table 13. Frequency sweep excitation vibration response orthogonal test conclusion table.

Test Number	A	B (μm)	C	Damping Rate
P1	1(8%Y2O3-ZrO2)	1(100)	1(Galvanized iron)	3.33%
P2	1(8%Y2O3-ZrO2)	2(150)	2(304 stainless steel)	9.97%
P3	1(8%Y2O3-ZrO2)	3(200)	2(304 stainless steel)	15.78%
P4	2(Al-Cu-Fe-Cr)	1(100)	2(304 stainless steel)	2.55%
P5	2(Al-Cu-Fe-Cr)	2(150)	2(304 stainless steel)	9.52%
P6	2(Al-Cu-Fe-Cr)	3(200)	1(Galvanized iron)	12.06%
P7	3(ZrO2-PTFE)	1(100)	2(304 stainless steel)	4.21%
P8	3(ZrO2-PTFE)	2(150)	1(Galvanized iron)	9.93%
P9	3(ZrO2-PTFE)	3(200)	2(304 stainless steel)	19.93%
P10			304 stainless steel
P11			Galvanized iron
Sum value K1	29.08%	10.09%	25.32%
Sum value K2	24.13%	29.42%	61.96%
Sum value K3	34.07%	47.77%
Mean K1	9.69%	3.36%	12.37%
Mean K2	8.04%	9.81%	13.43%
Mean K3	11.36%	15.92%
Extremum R	3.31%	12.56%	1.07%
Excellent solution	A3	B3	C2

, in the case of the frequency sweep, consistent with the conclusion obtained for fixed-frequency excitation, the coating thickness has the greatest impact on the acceleration of the first-order resonance response of the clamp-piping system, while the hard coating material has a great impact. The hard-coated clamp material has less influence. The optimal combination of orthogonal experiments is to use a coating consisting of YSZ-PTFE composite material. The damping effect of the clamp-piping system of 304 stainless steel with a coating thickness of 200 μm can reach 19.93%.

ANSYS Workbench software was used to analyze the first-order resonance response of the aviation hydraulic clamp-piping system. Comparison of the acceleration response obtained for the aviation hydraulic clamp-piping system coated with a hard coating with the experimentally collected data reveals a maximum error of 7.9%. Taken with the conclusions obtained for the fixed-frequency basic excitation, it can be seen that the aviation hydraulic clamp-piping system model used in the simulation calculations is reasonable and meets the requirements of engineering calculations, as shown in

Table 14. Simulation and experimental data comparison of the aeronautical hydraulic clamp-pipeline system under frequency sweep excitation before and after coating.

Test Number	Experimental Vibration Frequency Sweep Acceleration Amplitude (g)	Simulation Vibration Frequency Sweep Acceleration Amplitude (g)	Error Rate
P1	18.59	17.32	6.83%
P2	16.26	15.97	1.78%
P3	15.21	14.25	6.31%
P4	17.6	16.21	7.90%
P5	16.34	15.38	5.88%
P6	16.88	15.74	6.75%
P7	17.3	15.97	7.69%
P8	17.32	16.01	7.56%
P9	14.46	13.69	5.33%
P10	18.06	17.49	3.16%
P11	19.23	18.73	2.60%

.

5. Conclusions

This article combines the vibration theory of clamp-piping systems with an experimental investigation. Three different hard coating materials were optimized and prepared for use in simulation analysis and experimental research on their effect on the vibration characteristics and the damping effect of an aviation hydraulic clamp-piping system. The main conclusions are as follows:

(1) By establishing a finite element hard-coated clamp-pipeline model, and on the basis of the simulation calculation and analysis results, it can be seen that: the natural frequency of a clamp-piping system coated with hard coating is improved, and the natural frequency increases with increasing coating thickness, that is, the greater the coating thickness, the greater the deviation of the natural frequency of the clamp-piping system. When the coating thickness is 200 μm, the first-order natural frequency deviation can reach 11.18%, which is better able to prevent the occurrence of resonance.

(2) From the vibration test analysis of the aviation hydraulic clamp-piping system before and after application of the hard coating, the acceleration amplitude of the forced vibration response was compared and analyzed, both under the fixed-frequency excitation of the high- and low-pressure rotor and under frequency sweep simple harmonic excitation, the acceleration amplitude of the forced vibration response is compared and analyzed, and it can be seen that the same conclusion can be drawn for both the frequency sweep and fixed-frequency excitation; that is, the thickness of the coating has the greatest impact on the vibration response of the clamp-piping system. With the gradual increase in coating thickness, the vibration response of the pipeline gradually decreases. The hard coating material has a greater impact, while the clamp material has a smaller impact.

(3) According to the orthogonal experimental test, the optimal combination consists of a clamp-piping system with a YSZ-PTFE (yttria-stabilized zirconia-polytetrafluoroethylene) composite material coating. For a 304 stainless steel material with a coating thickness of 200 μm, the damping rate reaches 21.45% under 150 Hz low-voltage fixed-frequency excitation vibration, 24.67% under 200 Hz high-voltage fixed-frequency excitation vibration, and 19.93% under frequency sweep excitation vibration. It is verified that the YSZ-PTFE composite coating has the best vibration damping effect among the three hard coating materials.

(4) The maximum error is 7.9% between the finite element simulation results and the experimental data of the aviation hydraulic clamp-piping system coated with a hard coating under constant frequency and frequency sweep excitation. The rationality and feasibility of the aviation hydraulic clamp-piping system model were verified on the basis of simulation calculations.