Keywords

1 General

The ambient temperature envelope of civil aircraft is large, and the influence of thermal stress on its static strength and fatigue strength cannot be ignored [1, 2]. Usually the calculation of the skin surface temperature field often only considers the external pneumatic environment, which is not consistent with the actual skin overall thermal environment. Therefore, it is necessary to establish a reasonable thermal analysis model and calculation method to analyze the skin temperature field and influencing factors [3,4,5].

2 Test Data

The lower panel of the center wing of a civil aircraft is formed by connecting the skin of 2024HDT-T351 and the stringer of 2026-T3511 through fasteners, and 15 stringers are arranged in total (the number from the front spar to the rear spar is stringer 1 to stringer 15 respectively). The heading length is 2890 mm, the span width is 3664 mm.

This test mainly investigates the strain of the center wing lower panel skin under different temperature gradients under local thermal load. The investigation area is 1000 mm × 560 mm, as shown in Fig. 1. The circle in the inspection area is a schematic diagram of the location of the heat source (heat lamp used in the test).

Fig. 1
A schematic diagram of the inspection area presents 15 horizontal stringers between the front and rear spars. The length and height of the area are 3664 and 2890 millimeters, respectively. Grids are formed over the area. Two vertical elements are in the center.

Schematic diagram of the main inspection area of the test

Distributed optical fiber sensors are arranged in the main inspection area of the center wing lower panel for temperature field and strain field reconstruction, and fiber grating sensors (FBG) are arranged on the central skin of the main inspection area for point-type high-frequency real-time measurement, as shown in Fig. 2. The monitored strains are all wing spanwise.

Fig. 2
A diagram of the main inspection area. The optical fiber sensors are arranged in 7 rows and 3 columns. F B G is placed on the central skin.

Monitoring area and sensor arrangement

In the test, a heat lamp was used to irradiate and load, as shown in Fig. 3. During the test, a total of 6 heat lamps were used and three heating-cooling cycles were performed. The position of the heat lamp is the same in the first two cycles, and the position of the heat lamp is slightly adjusted in the third cycle, so that the temperature of the fiber grating sensor (FBG) at the center skin of the monitoring area increases.

Fig. 3
A photograph of the loading of a hot lamp presents 4 lamps with light.

Hot lamp loading photo

The temperature loading and unloading process curve of the three cycles is shown in Fig. 4, and the thermal strain change curve of the inner and outer surfaces is shown in Fig. 5.

Fig. 4
A multi-line graph of temperature versus number of sampling points plots oblong, sawtooth wave-shaped trends for the outer and inner surface temperatures. The spikes for the outer surface temperature are higher.

Heating cycle temperature change curve

Fig. 5
A multiline graph of thermal strain versus the number of sampling points plots oblong, sawtooth wave-shaped trends for the outer and inner surface thermal strains. The spikes for the outer surface are higher.

Heating cyclic strain change curve

As can be seen from Figs. 4 and 5, the outer surface temperature of the skin in the first two cycles is up to about 72 °C. In the third cycle, the position of the heat lamp is adjusted so that the heat lamp directly hits the central area of the test, that is, the position of the FBG sensor, so The maximum temperature reaches about 80 °C, while the maximum temperature of the inner skin is about 60 °C. Correspondingly, the maximum thermal strain of the outer skin in the first two cycles is about 544 με, the maximum thermal strain of the inner skin is about 444 με, the maximum thermal strain of the outer skin in the third cycle is about 552 με, and the maximum thermal strain of the inner skin is about 452 με.

According to the temperature-strain change data of the inner and outer surfaces of the three cycles, the corresponding graphs are drawn as shown in Figs. 6, 7, 8, 9, and 10.

Fig. 6
A graph of thermal strain versus temperature. It plots trends for outer and inner surfaces. The trends ascend in a concave downward manner first and retract. The trend for inner surface lies inside the area formed by the outer surface trend.

Temperature-strain change curve of inner and outer surfaces in the first cycle

Fig. 7
A multiline graph of thermal strain versus temperature. It plots leaf-shaped trends for the inner and outer surfaces. The width for the inner surface trend is smaller than that for outer surface trend.

Temperature-strain curves of inner and outer surfaces in the second cycle

Fig. 8
A multiline graph of thermal strain versus temperature. It plots leaf-shaped trends for the inner and outer surfaces. The width for the inner surface trend is smaller than that for outer surface trend.

Temperature-strain change curve of inner and outer surfaces in the third cycle

Fig. 9
A multiline graph of thermal strain versus temperature. It plots leaf shaped loops labeled first, second and third cycles.

Temperature-strain variation curves of three cycles on the outer surface

Fig. 10
A multiline graph of thermal strain versus temperature. It plots trends for first, second, and third cycles that ascend first and then retract.

Temperature-strain variation curves of three cycles on the inner surface

It can be seen from Figs. 6, 7, and 8 that in all three cycles, the inner surface temperature-strain curve has a good linearity, while the outer surface is a typical hysteresis loop. The reason for the analysis may be that the outer surface is directly irradiated by a heat lamp, which is more sensitive to temperature, causing the temperature to rise and fall faster than the structural strain change rate.

As can be seen from Figs. 9 and 10, the three cycle cooling processes on the outer surface have good linearity and repeatability, and the heating process is different due to the different position of the heat lamp; except for the first cycle heating process, the rest of the heating and cooling processes on the inner surface have good linearity and repeatability.

The temperature distribution results of the three cycles of the distributed optical fiber sensor are shown in Figs. 11, 12, and 13.

Fig. 11
A line graph traces variation in temperature across length and is divided into 7 parts. phases. Length ranges from 0 to 5 meters. The temperature ranges from 0 to 100 degrees Celsius. The highest spike is in part 7.

Outboard temperature results of center wing lower panel (first cycle)

Fig. 12
A line graph traces variation in temperature across length and is divided into 7 parts. phases. Length ranges from 0 to 5 meters. The temperature ranges from 0 to 100 degrees Celsius. The highest spike is in part 7.

Outboard temperature results of center wing lower panel (second cycle)

Fig. 13
A line graph traces variation in temperature across length and is divided into 7 parts. phases. Length ranges from 0 to 5 meters. The temperature ranges from 0 to 100 degrees Celsius. The highest spike is in part 7.

Outboard temperature results of center wing lower panel (third cycle)

The thermal strain distribution results of the three cycle temperatures of the distributed optical fiber sensor are shown in Figs. 14, 15, and 16.

Fig. 14
A line graph traces variation in thermal strain across length and is divided into 7 parts. phases. Length ranges from 0 to 5 meters. The thermal strain ranges from 0 to 700. The highest spike is in part 6.

Thermal strain results of center wing lower panel (first cycle)

Fig. 15
A line graph traces variation in thermal strain across length and is divided into 7 parts. phases. Length ranges from 0 to 5 meters. The thermal strain ranges from 0 to 700. The highest spike is in part 6.

Thermal strain results of center wing lower panel (second cycle)

Fig. 16
A line graph traces variation in thermal strain across length and is divided into 7 parts. phases. Length ranges from 0 to 5 meters. The thermal strain ranges from 0 to 700. The highest spike is in part 6.

Thermal strain results of center wing lower panel (third cycle)

3 Finite element analysis

A natural mesh model and a fine finite element model are used to analyze the thermal load of the center wing lower panel. The temperature on the node is applied according to the real temperature in the test. Among them, the temperature applied at the nodes in the natural mesh model (GFEM0, GFEM1) is taken from the average value of the temperature of the fiber measuring point at the adjacent position of the node in the test, as shown in Fig. 17; the fine model (DFEM0) The temperature applied at the node is basically consistent with the temperature of the fiber measuring point at the corresponding position of the node in the test, as shown in Fig. 18.

Fig. 17
A 2 quadrant graph of temperature versus coordinates. It plots 2 datasets labeled 5 ascending to descending trends labeled G F E M 1 to 5 and G F E M 1 to 7. It also plots 5 ascending to descending trends labeled measured temperatures 5, 6, and 7 and G F E M 0 to 5 and G F E M 0 to 7.

Schematic diagram of temperature applied at nodes in natural mesh model of center wing lower panel

Fig. 18
A 2 quadrant graph of temperature versus coordinates. It plots fluctuating trends labeled measured temperatures 3, 4, 5, D F E M 0 to 3, D F E M 0 to 4 and D F E M 0 to 5.

Temperature applied at nodes in fine model of center wing lower panel

As shown in Figs. 19 and 20, the strain value of the natural mesh model (GFEM0) has a high degree of fit with the test value.

Fig. 19
A 4 quadrant graph of strain versus coordinates. It plots fluctuating trends labeled thermal strain 4, G F E M 0 to 4, G F E M 1 to 4 and D F E M 0 to 4.

Strain comparison of center wing lower panel at monitoring area 4

Fig. 20
A 4 quadrant graph of strain versus coordinates. It plots ascending to descending trends labeled thermal strain 6, G F E M 0 to 6, G F E M 1 to 6 and D F E M 0 to 6.

Strain comparison of center wing lower panel at monitoring area 6

4 Conclusions

After comparative analysis, the strain value of the natural mesh model (GFEM0) has a high degree of fit with the test value, and the analysis results of the natural mesh model can be used to analyze the thermal stress intensity of the center wing lower panel.