Analysis and Experimental Study for Fatigue Performance of Wing-Fuselage Connection Structure for Unmanned Aerial Vehicle

Abstract

(1) Background: As the principal structural element of an unmanned aerial vehicle (UAV), a lightweight, high-performance wing-fuselage connection structure plays an important role in UAV structural integrity. Previous studies focused on the static strength characteristics of aluminum and high-strength steel wing-fuselage connection structures. With the widespread usage of titanium material in aviation, research should address the fatigue performance of titanium wing-fuselage connection structures. This paper aims to investigate the fatigue performance of the titanium wing-fuselage connection structure by using analysis and experimental methods, and to develop a reliable fatigue assessment method based on the experimental results. (2) Methods: General and detail finite element models were established, and the stress distribution at the detail fatigue design point was obtained via finite element analysis. Based on the equivalent life curve theory, a dimensionless value, detail fatigue value (DF), was proposed to characterize the fatigue performance for structure. By using detail fatigue value (DF) method, the theoretical fatigue performance value was calculated. The fatigue test of the wing-fuselage connection structure was conducted, and the fatigue life was determined according to the test results. (3) Results: For the wing joint with fatigue failure in the test, the test fatigue performance was close to the theoretical value. It can be concluded from the DF value that the analysis and test results are consistent, and the values obtained from the analysis are more conservative than test results. (4) Conclusions: The error between the test DF value and the theoretical analysis DF value is small, and the theoretical analysis of fatigue performance can represent the fatigue characteristics of the wing-fuselage connection structure. The detail fatigue value (DF) method can predict the fatigue performance of the structure quite well.

1. Introduction

With the trend of pursuing sufficient strength and maintenance economy in unmanned aerial vehicle (UAV) design, the principal structural components of UAVs are facing great challenges of high performance, light weight and long life. Among them, the wing-fuselage connection structure is the key and main load transmission structure, which is very important for the structural integrity of the UAV. The wing-to-fuselage connection is a structural design style common to different UAV models. UAVs in service will encounter aerodynamic loads, ground loads and so on. These loads will lead to fatigue damage to the structure, especially when high-strength steel or titanium alloy materials are used in the connection structure; the fatigue problem of the structure will replace the static strength and become a new big challenge. Therefore, in order to ensure the structural safety of the UAV during its operational life, the wing-fuselage connection structure must be evaluated to demonstrate that the fatigue life of the structure meets the design requirements and has sufficient reliability during the service life of the UAV.

The design of the wing-fuselage connection structure has become a key technology for the structural integrity of the aircrafts and UAVs, and an increasing number of analyses and tests have focused on the aluminum and high-strength steel wing-fuselage connection structure. Force transmission characteristics [1,2,3,4,5,6], stress distribution and analysis [7,8,9,10,11,12,13,14], fatigue characteristics [15] and crack growth characteristics [16,17] of the structure, joints and lug of the wing-fuselage connection area were obtained through finite element analysis methods.

For the fatigue assessment of structures, there are traditional stress-life-based methods and strain-life-based methods. The above two methods are based on the deterministic damage accumulation law under the elastic or plastic deformation conditions, and do not consider the uncertainties in the manufacture, assembly and service of the structure, such as material defects, manufacturing defects and the service environment. Therefore, the detail fatigue value (DF) method, as a probabilistic assessment method, is an evolution of the traditional fatigue analysis methods applied to the fatigue assessment of civil aircraft structures [18].

In this paper, the DF method was applied to the analysis of the wing-fuselage connection structure, and the analysis results were evaluated through tests.

2. Wing-Fuselage Connection Structure

The wing-fuselage connection structure is the most critical load transmission structure of a UAV. According to the UAV structural design, the UAV fuselage and wing are connected through eight joints, including four inner joints and four outer joints. The four inner joints on the fuselage frame are connected to the joints on 1# rods, as shown in Figure 1a. The material of all tie rods and joints is Ti-6Al-4V (TC4).

Since the outer joint mainly transmits the vertical load of the fuselage and its damage could have a great impact on the safety of the UAV, the outer tie rod and its connecting joint between the 2# wing rib on the rear spar and the 33# frame were selected as the object of evaluation, as shown in Figure 1b.

3. Numerical Analysis of Fatigue Performance

3.1. General Finite Element Analysis of Wing-Fuselage Connection Structure

In order to reduce the complexity and workload of finite element modeling, the structure was simplified as necessary, and the finite element analysis model of the wing-fuselage connection structure was established using the MSC. PATRAN software (2008_r2 version), see Figure 2. The purpose of establishing the detail finite element model is to obtain the stress of the detail design part and simplify the test part design to ensure the consistency of the stress level between the test part and the real structure. A convergence test was performed for the finite element model.

The model adopted 3D solid elements (16,346 CTETRA10 and 10,275 CHEXA10); the bolts were simulated by bush elements CBUSH. The unit stiffness k was 10⁶ N/m according to modeling experience, and the rotational stiffness was infinite. Material property MAT1 was defined as 113.00 GPa for Young’s modulus, 0.34 for the Poisson ratio and 4.45 × 10³ kg/m³ for mass density. According to the fatigue load and the general finite element model (GFEM) of the UAV, the loads of the connection structure were extracted; the external force of the model was along the Z-axis direction, and the load P was 197.96 kN, applied by RBE2 elements at the upper end of the model. The lower end of the model was clamped with supported constraints.

Due to the GFEM stress analysis, the stress value level of the wing joint was higher than that of the fuselage joint and tie rod, making the wing joint the high stress structure. Because the wing-fuselage connection structure is a single-load-path structure, the wing joint was the fatigue-weakness structure. We established the detail model of the wing joint for further study and focused on the fatigue performance of the wing joint.

3.2. Detail Finite Element Analysis of Wing Joint

The detail model of the wing joint also used 3D solid elements (11,563 CTETRA10 elements); the bolts were simulated by bush elements CBUSH, as shown in Figure 3a. The analysis was performed with the support end clamped (six degrees of freedom constraints), and a concentrated load of 197.96 kN was applied to the wing joint lugs along the negative Z-axis via RBE2 elements. The stress cloud diagram of the wing joint is shown in Figure 3b; the maximum principal stress at the wing joint lug area was 95.00 MPa, and the high-stress level zone was the hole edge of lug.

According to the stress distribution, the hole edge of the lug was the fatigue-weakness location. We focused on the fatigue performance of the lug and carried out the analysis and experimental study for the lug of the wing joint.

3.3. Theoretical Fatigue Life Analysis for Wing Joint Lug

The maximum principal stress of the lug σ_max is 95.00 MPa, and this value is lower than the material yield strength value of titanium. Based on the maximum principal stress of the lug, the stress spectrum for the hole edge of the lug can be obtained. The peak stress value was 95.00 Mpa, with a stress ratio R = 0.06, as shown in Figure 4.

For any stress spectrum, the stress spectrum can be converted to an amplitude spectrum with a stress ratio R = −1 using Goodman–Soderberg theory, as shown in Equation (1):

$${\mathrm{S}}_{\mathrm{a}}^{\prime }={\mathrm{S}}_{\mathrm{a}}({\displaystyle \frac{{\sigma }_{0.2}}{{\sigma }_{0.2}-{\mathrm{S}}_{\mathrm{m}}}})$$

(1)

where ${\mathrm{S}}_{\mathrm{a}}^{\prime }$ denotes the converted amplitude value for the stress spectrum with a stress ratio R = −1 and σ_0.2 denotes the material yield strength value, which for titanium alloy is 820.00 Mpa, S_m is the mean value of the stress spectrum, S_a is the amplitude value of the stress spectrum and S_m and S_a can be calculated from the maximum value σ_max and the stress ratio R in the stress spectrum as follows [19]:

$${\mathrm{S}}_{\mathrm{m}}={\displaystyle \frac{(1+{\mathrm{R})\mathsf{\sigma }}_{\max }}{2}}$$

(2)

$${\mathrm{S}}_{\mathrm{a}}={\displaystyle \frac{{(1-\mathrm{R})\mathsf{\sigma }}_{\max }}{2}}$$

(3)

Then, Corten–Dolan theory can be used to analyze the theoretical fatigue life of the wing joint lug, as shown in Equation (4):

$$N={\left({\displaystyle \frac{{\mathrm{S}}_{-1}}{{\mathrm{S}}_{\mathrm{a}}^{\prime }}}\right)}^d\times {10}^7$$

(4)

where N denotes the theoretical fatigue life of the lug, S₋₁ denotes the material fatigue limit, which for titanium alloy is 550.00 Mpa, ${\mathrm{S}}_{\mathrm{a}}^{\prime }$ denotes the converted amplitude value for the stress spectrum with a stress ratio R = −1 and d is the material characteristic factor, which for titanium alloy is 4.8.

3.4. Detail Fatigue Value Analysis

Because the fatigue life of the structure has a large dispersion, based on the equivalent life curve theory, we proposed a dimensionless value, the detail fatigue value (DF), to characterize the fatigue performance for structure. The detail fatigue value (DF) is a ratio that represents the ratio of the maximum nominal stress that allows the fatigue life of the structure to reach 10⁵ cycles under a constant amplitude fatigue load with a stress ratio of 0.06, which corresponds to a 95% reliability and 95% confidence requirement [18] relative to the material yield strength value. The DF represents the fatigue performance of the structure; a higher DF means better fatigue performance and a longer fatigue life.

The DF can be defined as follows:

$$\mathrm{DF}={\displaystyle \frac{{\mathrm{S}}_{{10}^5}}{{\sigma }_{0.2}}}$$

(5)

where ${\mathrm{S}}_{{10}^5}$ denotes the fatigue limit stress that allows the fatigue life of the structure to reach 10⁵ cycles under a constant amplitude fatigue load with a stress ratio of 0.06, which corresponds to a 95% reliability and 95% confidence and σ_0.2 denotes the material yield strength value.

It is assumed that the fatigue life follows a two-parameter Weibull distribution, and the reliable fatigue life N can be determined by fatigue analysis or test results. Under the assumption that the fatigue life follows the two-parameter Weibull distribution, according to Goodman–Soderberg theory, the S-N curves at different confidence levels and reliability levels share the same slope value in logarithmic coordinates. Therefore, the DF value can be obtained by conducting one group of fatigue tests at a specific stress level and stress ratio. Equation (6) shows the relationship between fatigue life N and DF as follows:

$$N={\left[{\displaystyle \frac{\left({\sigma }_{\mathrm{m}0}-0.53\cdot \mathrm{DF}\cdot {\sigma }_{0.2}\right){\mathrm{S}}_{\mathrm{a}}}{0.47\cdot \mathrm{DF}\cdot {\sigma }_{0.2}({\sigma }_{\mathrm{m}0}-{\mathrm{S}}_{\mathrm{m}})}}\right]}^B\times {10}^5$$

(6)

where σ_m0 denotes the material characteristic value, which for titanium alloy is 620.00 Mpa, σ_0.2 denotes the material yield strength value, which for titanium alloy is 820.00 Mpa, B is the shape factor related to material type, which for titanium alloy is −3.32, S_m is the mean value stress spectrum and S_a is the amplitude value stress spectrum.

The theoretical value of DF can be obtained according to the fatigue life and load spectrum using Equations (4) and (6). Meanwhile, the structural properties and processing state of the material can affect the actual DF value. For the lug of the wing joint, because the fit clearance between the connecting pin and the lug hole is small and the fit is tight, there is inevitable wear on the lug hole and the shaft during the process of force application. A large number of theoretical and experimental studies show that micro-wear has an obvious effect on fatigue life; therefore, the fatigue damage caused by micro-wear must be considered. Actual DF value (${\mathrm{DF}}^{\prime }$) can be calculated as follows:

$${\mathrm{DF}}^{\prime }=\mathrm{DF}\cdot \mathrm{Lt}\cdot \mathrm{Lc}\cdot \mathrm{Ls}\cdot \mathrm{Ld}\cdot \mathrm{L}\mathsf{\theta }\cdot \mathrm{Tm}\cdot {\mathrm{R}}_{\mathrm{C}}\cdot \mathrm{WF}$$

(7)

where DF denotes the theoretical value of DF from Equations (4) and (6), Lt is the thickness factor, Lc is the margin coefficient, Ls is the lug shape factor, Ld is the hole fit coefficient, Lθ is the lug slant load factor, Tm is the alloy and surface treatment factor, R_c is the structure fatigue rating factor and WF is the wear correction factor for titanium alloy. According to ref. [20], the input parameters and DF values for the calculation of the structure details are shown in

Table 1. Input parameters and DF values for wing joint lug structure.

Parameters	Wing Joint Lug
Theoretical DF value (DF) from Equations (4) and (6)	0.14322
Thickness factor (Lt)	1.00
Margin coefficient (Lc)	1.16
Lug shape factor (Ls)	0.88
Hole fit coefficient (Ld)	1.00
Lug slant load factor (Lθ)	1.00
Alloy and surface treatment factor (Tm)	1.00
Structure fatigue rating factor (RC)	1.00
Wear correction factor for titanium alloy (WF)	0.60
$\mathrm{Actual} \mathrm{DF} \mathrm{value} ({\mathrm{DF}}^{\prime }$)	0.08772

.

4. Fatigue Test and Implementation

4.1. Test Piece and Test Program Design

The outer joint between the 2# wing rib on the rear spar and the 33# frame was the object of this test. The test piece contained the tie rod and the joint at both ends (one connected to the frame and the other connected to the wing rib), and the connecting bolt, and was appropriately simplified. The test piece is shown in Figure 5a, and the strain gauges were located on the test piece, with the strain gauges on the wing joint as shown in Figure 5b. The length of the test piece was 510 mm and there were five test pieces (Test piece No.1#~5#).

The fatigue test was conducted on the hydraulic fatigue tester MTS-500T (Mechanical Testing & Simulation, Eden Prairie, MN, USA). The test fixture and loading are shown in Figure 6, which includes the loading fixture, connection fixture, transition fixture and support fixture. The test piece and test fixture were assembled as shown in Figure 6. The contact and friction areas of the test parts (lug and tie rod) were lubricated with grease in accordance with the lubrication requirements of the real structure of the UAV. The temperature of the test lab was 25 °C ± 2 °C.

4.2. Fatigue Test Load Spectrum

The fatigue test load spectrum is an equal amplitude spectrum with a stress ratio R = 0.06. The test loading frequency f is controlled from 5 Hz to 10 Hz, which can be adjusted according to the test condition up to 10 Hz. The target life of the test piece is six times the design service goal (DSG); if no fatigue crack appears after six times the DSG cycle, the load spectrum is adjusted, and the test is continued until the test piece is damaged.

The maximum load of the real fatigue load spectrum was 197.96 kN with a stress ratio R of 0.06. The test load spectrum is shown in Figure 7, where the first and second test pieces were suitably scaled up to determine the damage mode and the rest of the test pieces used the given load spectrum. The loading error was controlled within ±1%.

4.3. Fatigue Test Results

The test was performed by applying the load according to the specified load spectrum until the test piece was damaged.

Before 300,000 cycles, a detailed visual inspection (with the aid of a magnifying glass) of the test piece was carried out every 30,000 cycles and a shutdown inspection was carried out every 60,000 cycles, and if suspicious conditions were found, non-destructive testing methods were used for inspection.

After 300,000 cycles, a detailed visual inspection (with the help of a magnifying glass) was carried out every 15,000 cycles on the test piece and a shutdown inspection was carried out every 30,000 cycles, and if suspicious damage conditions were found, non-destructive testing methods were used for inspection. The test results are shown in

Table 2. Test results.

Test Piece No.	Number of Test Cycles	Cumulative Number of Test Cycles	Fatigue Fracture Position
1#	93,799	93,799	Fuselage joint and tie rod connection pin *
	53,082	146,881	Fuselage joint and tie rod connection pin *
	1981	148,862	Wing joint lug
2#	108,756	108,756	Wing joint and tie rod connection pin *
3#	616,564	616,564	Wing joint lug
	281,986	281,986	Wing joint and tie rod connection pin *
4#	86,345	368,331	Fuselage joint and tie rod connection pin *
	155,327	523,658	Wing joint lug
	378,676	378,676	Wing joint and tie rod connection pin *
5#	21,218	399,894	Fuselage joint and tie rod connection pin *
	34,782	434,676	Fuselage joint and tie rod connection pin *
	74,003	508,679	Wing joint lug

* Note: The joint shaft is not the test part, and the joint shaft was replaced after breaking to continue the test.

, and the fatigue fracture of the test parts is shown in Figure 8. For the wing joint, the fracture position was the hole edge of the lug.

During the fatigue test, the experimental stress of the wing joint was obtained. The maximum principal stress at the hole edge of the lug was 77.29 MPa.

5. Discussion

The test load spectra of all test pieces were the same equal amplitude spectrum. For the computation, according to each test data, the fatigue cycle before wing joint lug damage were recorded in

Table 3. Computed test result data for wing joint lug.

Test Piece No.	Test Cycles
1#	148,862
3#	616,564
4#	523,658
5#	508,679

. Due to no damage occurring during the test, the data for test piece 2# was removed, and the data from the other four test pieces were used to calculate the DF.

According to the test results in Table 3, the estimated value of characteristic life β can be calculated as follows:

$$\beta ={\left[{\displaystyle \frac{1}{n}}{\displaystyle \sum _1^n{N_i}^S}\right]}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$s$}\right.}}$$

(8)

where n denotes the number of effective specimens, N_i is the commuted test life cycles of the ith specimen and S is the shape factor related to material type, which for titanium alloy is 3.0.

The test fatigue life N_T can be calculated as follows:

$$N_{\mathrm{T}}={\displaystyle \frac{\mathsf{\beta }}{\mathrm{ST}\cdot \mathrm{SR}\cdot \mathrm{SC}}}$$

(9)

The input parameters are according to ref. [20]. The test DFs of the corresponding structures can be calculated using Equations (6), (8) and (9). The results are shown in

Table 4. Test DF results.

Parameters	Wing Joint Lug
Number of effective specimens	4
Specimen coefficient (ST)	1.30
95% confidence coefficient (SC)	1.24
95% reliability coefficient (SR)	2.70
Estimated value of characteristic life (β) (cycle)	504,265
Test fatigue life (NT) (cycle)	115,859
Test DF value	0.08897

.

The test DFs in Table 4 were compared with the DF results obtained from the theoretical calculation of the lug in Table 1, and the comparison results are shown in

Table 5. Comparison of test and calculation.

DF Value		Maximum Principal Stress of Hole Edge (MPa)
Test value	Analysis value	Test value	Analysis value
0.08897	0.08772	77.29	95.00

. It can be seen from Table 5 that the analysis DF value is smaller than the test result, and the analysis maximum principal stress value is higher than the test result.

The fracture position during the fatigue test was the hole edge of the lug and is consistent with the high-stress level zone by finite element analysis.

Based on the fracture position, high-stress level zone, stress value and DF value, it can be concluded that the analysis and test results are consistent, and the values obtained from the analysis are more conservative than the test results.

6. Conclusions

In this paper, the general and detail finite element models were established, and the stress level at the detail design point was determined via finite element analysis. Based on the equivalent life curve theory, a dimensionless value, the detail fatigue value (DF), was proposed to characterize the fatigue performance of the structure. Through analysis, the analysis DF was obtained.

For the lug structure with small clearance, the effect of micro-motion wear on fatigue life should be considered. From the results of this paper, both the analysis and test results indicated that the hole edge of the lug is the initial area for fatigue crack generation.

The results of this paper showed that the DF obtained from the test was greater than the analysis DF, and the analysis maximum principal stress value was higher than the test result, which indicates that the analysis results were conservative and safe, and could certainly lead to an underestimation in the life calculation.

In the experimental study of this paper, although the fracture of the pin was not the purpose of the assessment, attention needs to be paid to the life and fatigue assessment of the pin in the actual UAV operations, and the influence and effect of the pin on the fatigue life of the connection structure should be evaluated and considered in subsequent studies.