Measurement Technique and Result Analysis of Helicopter Rotor Blade Structural Vibration Load

Te measurement of helicopter rotor blade structural load amid fight has always been the difculty in fight test. In this paper, the principle of the existing blade structural load measurement method (electrical measurement method) was analyzed, and the problem of physical decoupling in the use of this method was expounded. As a weak signal measurement, the electrical measurement method also has electromagnetic interference problems, which will afect the fight test period of blade structural load measurement. Terefore, a numerical decoupling measurement method based on fber Bragg grating (FBG) was proposed. Ten, the new method was applied and verifed in the load equation modeling test and the fight test under the real atmospheric environment was carried out. Trough comparing and analyzing the measured data of the new method and the electrical measurement one, the correctness of the FBG data decoupling method was validated. Te results indicate that the method proposed in this paper can efectively improve the efciency of blade load equation modeling engineering and has good application value.


Introduction
In the course of fight, the helicopter obtains the required lift force and handling force through the rotor, specifcally the movement of the blade. In the process of rotation, the blade is easily subjected to the action of periodic aerodynamic force, which undergoes fapwise motion, edgewise motion, and torsional motion. From the point of view of structural load, the blade bears the fapwise bending moment, edgewise bending moment, torque, and other multiaxis loads. Te structural load level of the blade cross-section has been a concern in the design process, which determines the static strength and fatigue strength of the blade and refects the aerodynamic design results of the rotor blade to a certain extent. Terefore, the measurement of the structural load of the rotor blade is always a necessary work in the course of a fight test.
Te helicopter rotor structural load is currently measured based on the traditional electrical measurement method [1][2][3][4][5]. However, it, as a weak current signal measurement method, is susceptible to electromagnetic interference, which to a certain extent afects the fight test period of blade structural load measurement.
In this paper, the characteristics of helicopter rotor blade structural load measurement based on FBG technology [6,7] were analyzed and investigated. Figure 1 is the structural load diagram of the helicopter rotor blade cross-section, in which fapwise bending moment is perpendicular to the chord direction of the blade, edgewise bending moment is parallel to it, and α is the blade pitch angle relative to the hub plane. Torque is the resultant moment about the blade pitch axis, located at the quarterchord point. Figure 2 shows the principle of the blade structural load measurement by the traditional electrical measurement method. It is to install resistance strain gauges at the upper and lower surfaces of the blade, respectively. Tat is to say, 4 resistors, namely, R1′, R2′, R3′, and R4′ in Figure 2, were used to form a strain bridge for fapwise bending moment measurement; from the 10 resistors R1∼R10, as shown in Figure 2, 4 resistors were selected to form a strain bridge, and the edgewise bending moment was measured. Te selection principles is determined by the coupling coefcient of fapwise and edgewise strain bridges, which is usually no more than 5% among the engineering.

Analysis of Blade Structural Load Measurement Method
Electrical measurement method was proposed based on the physical decoupling idea of blade fapwise and edgewise loads [8]. When it is used to measure blade structural loads, in addition to the aforementioned weak current signal electromagnetic interference, there is also the work of repeated selection of the strain gauge, which afects the test progress to a certain extent.
What is more, due to the limitation of the fatigue life of the electric strain gauge, in the use of the method, the fapwise bending moment bridge and edgewise bending moment bridge are prone to being damaged, which results in a failure to measure the blade fapwise structural load and edgewise structural load synchronously during the fight test period.
As the communication medium of the FBG sensor, optical fber has good tensile and bending resistance [9][10][11][12], and good adaptability in the helicopter blade vibration environment. Terefore, it can be used to measure the blade structural loads by using the idea of numerical decoupling [13][14][15]. Te measurement principle is shown in Figure 3. For the fapwise and edgewise bending moments measurement, along the blade pitch axis, two FBG sensors were arranged on the upper and lower surfaces of the blade, respectively; along the blade edgewise direction, two FBG sensors were assembled on the leading and trailing edges of the blade, respectively. For the torque measurement, on the upper and lower surfaces of the blade, two FBG sensors were installed at ±45 deg angles with the blade pitch axis, respectively.
In Figure 3, F up and F down represent the linear strains measured along the blade pitch axis, on the upper and lower surfaces of the blade, respectively. Lfront and Lback denote the linear strains measured on the leading and trailing edges of the blade, respectively. φ u+ and φ u-refer to the strains for the torque measurement on the upper surface of the blade. φ d+ and φ d-represent the strains for the torque measurement on the lower surface of the blade.
Te linear strains F up and F down can be calculated by the following formulas: where F, M F , M L , and T represent the centrifugal force, fapwise bending moment, edgeswise bending moment, and torque of the blade cross-section, respectively. For strain components on the right-hand sides of equations (1) and (2), there are the following formulas: It can be obtained from equations (1) and (2) that Tat is to say, along the blade pitch axis, the linear strain diference between the upper and lower surfaces of the blade is a binary function of fapwise bending moment and edgewise bending moment.
Similarly, the linear strain diference between the leading and trailing edges of the blade is a binary function of the edgewise bending moment and fapwise bending moment. Ten, for ∆F and ∆L, there is the following relation: For the strains of the torque measurement on the upper surface of the blade, there is Flapwise bending moment Flapping gauge strain resistor Lead-leg gauge strain resistor It can be drawn from equations (6) and (7) that the strain components are caused by the centrifugal force, fapwise bending moment, edgewise bending moment, and torque, respectively. For these strain components, the following relations exist: It can be obtained from equations (6) and (7) that Evidently, ∆ϕ, the strain diference of the two FBG sensors for the torque measurement on the upper surface of the blade is a linear function of the cross-section torque. For the lower surface, the same conclusion is reached. Hence, the following formula can be obtained Based on the above analysis, the principle of multiaxis numerical decoupling can be used to measure the blade structural loads by FBG method.

Load Equation Modeling
Te blades were instrumented with 28 FBG sensors to measure structural loads at seven radial stations, as shown in Table 1. Flapwise, edgewise, and torsion moments were measured at 6, 6, and 1 radial stations, respectively.
Te corresponding load data were obtained through static loading tests on the ground. Te loading conditions contain a pure fapwise bending moment, a pure edgewise bending moment, a combined fapwise-edgewise bending moment, and pure torsion moment. Te represented results of these tests are shown in  It can be seen from Figure 4 that the fapping and torsion output responses of section 1 were basically unchanged when it was loaded in the edgewise direction. As can be seen from Figure 5, when section 1 was loaded in the fapwise direction, the output response of torsion was roughly unchanged, while the output response of lag varied within a small range. According to Figure 6, the output responses of fapping and torsion of section 2 remained basically unchanged when the load was applied in the edgewise direction. Likewise, as can be seen from Figure 7, when section 2 was loaded in a fapwise direction, the output response of torsion kept basically unchanged, while the output responses of fapping and lag presented a linear variation. Te above phenomena verify the correctness of the measurement principle of the FBG method.
Te load comparison curves of sections 1 and 3 are shown in Figures 8 and 9. It can be seen that the estimated and measured fapwise and edgewise bending moments have the same variation trend for both sections. Tables 2 and 3 show the error analysis of the bending moments of sections 1 and 3. It can be seen that the maximum error of the fapwise bending moment of section 1 was 1.3%, while that of the edgewise bending moment was 5.1%. For section 3, the maximum error of the fapwise bending moment was 2.7% and that of the edgewise bending moment was 4.9%, which meets the engineering requirements. Figure 10 shows the comparison of estimated and measured torques of section 2. It can be seen that the     Table 4 shows the corresponding error analysis. Te maximum error between the estimated value and the measured one was 4.3%, satisfying the engineering requirements.

Analysis of Flight Test Results
Te test equipment installation is shown in Figure 11. Typical hover and forward fight conditions were selected for fight test measurement. Blade structural load Figure 12 obtained by the FBG method Figure 13 are compared with Figure 14 those obtained by electric Figure 15 measurement method. Te results for two blade cross-sections at radial stations of 0.20R and 0.40R under two diferent advance ratios (μ � 0.20 and μ � 0.23) are shown in Figures 12-16. It can be seen from Figures 12-16 that blade structural loads have almost the same variation trends for the two measurement methods. Tis indicates that the FBG sensor shows good following performance for the blade structural dynamic load measurement. It should be noted that the maximum or minimum values of the blade structural loads are also captured by the FBG method, which are important for fatigue characteristic analysis of the blade.
Te diference, mainly refected in the load magnitude, may be caused by the takeof weight or the air density.
Furthermore, the blade structural loads obtained by the FBG method were analyzed in the frequency domain.    Load times (-) calculated test    It is evident that the frst three harmonic coefcients are dominant, which correctly refects the typical characteristic of blade vibration. Figure 20 shows the variations of the harmonic coefcients of blade fapwise bending moment with radial stations at advance ratio of 0.23.

Shock and Vibration
For the same harmonic coefcient, its value generally increases as the radial position of the blade increases.
In summary, the blade structural loads obtained by FBG numerical analysis method were compared in time domain  and frequency domain, and the feasibility of the method was validated.

Conclusion
Trough aforementioned research, the following conclusions are drawn as follows: (1) In view of the problems arose by the traditional electrical measurement method, a new numerical decoupling method based on FBG sensor was proposed to measure the blade structural loads (2) Te correctness and feasibility of the new method are verifed by load equation modeling test and fight test (3) Te method proposed in this paper can be used for the blade structural load measurement efectively.

Data Availability
Te test and fight data used to support the fndings of this study are available from the corresponding author upon request.

Conflicts of Interest
Te authors declare that there are have no conficts of interest.  10 Shock and Vibration