Research Article  Open Access
JaeSang Park, DoHyung Kim, Sanghyun Chae, YeLin Lee, JeongIn Go, "Vibration and Performance Analyses Using Individual Blade Pitch Controls for LiftOffset Rotors", International Journal of Aerospace Engineering, vol. 2019, Article ID 9589415, 13 pages, 2019. https://doi.org/10.1155/2019/9589415
Vibration and Performance Analyses Using Individual Blade Pitch Controls for LiftOffset Rotors
Abstract
This work attempts to reduce the hub vibratory loads of a liftoffset rotor using IBC (individual blade pitch control) in highspeed forward flight. As a liftoffset rotor for the present study, the rigid coaxial rotor of a XH59A compound helicopter is considered and CAMRAD II is used to predict the hub vibration and rotor performance. Using the IBC with a single harmonic input at 200 knots, the vibration index of the XH59A rotor is minimized by about 62% when the 3/rev actuation frequency is applied with the IBC amplitude of 1° and control phase angle of 270° (/1°/270°); however, the rotor effective lifttodrag ratio decreases by 3.43%. When the 2/rev actuation frequency with the amplitude of 2° and control phase angle of 270° (/2°/270°) and the 3/rev actuation frequency using the magnitude of 1° and control phase angle of 210° (/1°/210°) are used in combination for the IBC with multiple harmonic inputs, the vibration index is reduced by about 62%, while the rotor effective lifttodrag ratio increases by 0.37% at a flight speed of 200 knots. This study shows that the hub vibration of the liftoffset rotor in highspeed flight can be reduced significantly but the rotor performance increases slightly, using the IBC with multiple harmonic inputs.
1. Introduction
Liftoffset helicopters using ABC™ (Advancing Blade Concept, [1]) have been developed to solve the lowspeed flight performance of conventional helicopters. As seen in Figure 1 [2, 3], the liftoffset helicopter uses a counterrotating rigid coaxial rotor. Since most lift is generated by the advancing blades, the liftoffset rotor can avoid the dynamic stall on the retreating side of a rotor and may produce more lift as compared to a conventional helicopter rotor. Therefore, the rotation speed of the liftoffset rotor can be reduced moderately and highspeed flight is possible with the help of auxiliary propulsions [4].
(a) XH59A Technology Demonstrator [2]
(b) X2 Technology Demonstrator [2]
(c) S97 Raider [3]
Although liftoffset compound helicopters have showed excellent highspeed flight performance, they have a serious vibration problem during highspeed flights. In flight tests of the XH59A compound helicopter, significant 3/rev cockpit vibration was observed because of the use of a rigid coaxial rotor and the absence of a vibration control system [5]. To solve this vibration problem in highspeed flights, the X2 Technology Demonstrator and S97 Raider apply the AVCS (active vibration control system, [6]) to their airframes. The AVCS consists of accelerometers and circular force generators with electric motors and eccentric masses. The X2 Technology Demonstrator using the AVCS reduced the 4/rev cockpit vibration significantly in highspeed flights [7]. The AVCS can successfully alleviate the airframe vibration of liftoffset helicopters; however, it cannot reduce the vibration of a rigid coaxial rotor, which is the main source of vibration for the liftoffset helicopter. Therefore, the high levels of rotor vibration may still lead to serious constraints such as a restricted flight envelope, low fatigue life of the structural components, and a resultant high operating cost.
There have been numerous experimental and numerical works on active rotor controls such as HHC (higher harmonics pitch control, [8–11]), IBC (individual blade pitch control, [12–15]), active trailingedge flap rotor [16–20], and active twist rotor [21–23] in order to reduce the rotor vibration of conventional helicopters. These active rotor controls usually excite the fixed or rotating system of a rotor with a single higher harmonic input to modify directly the periodic aerodynamic loads acting on the rotor blades for vibration reduction. The HHC demonstrated successfully the vibration reduction of full and smallscale rotors of helicopters in flight tests [8, 9] and wind tunnel tests [10, 11], but the available actuation frequency range is limited since actuators are located below the swashplate. The IBC was developed to overcome the actuation frequency limitation of HHC. Since IBC uses the pitch link actuators in the rotating frame, each blade can be individually actuated and it has a wide range of actuation frequency. Using this advantage over HHC, IBC showed excellent vibration reduction capability for the fullscale rotors in wind tunnel tests [12, 13] and flight tests [14, 15]. The vibration of helicopter rotors can be reduced significantly using the active trailingedge flap in the advanced numerical analyses [16, 17], wind tunnel tests [18, 19], and flight tests [20] while the power required to actuate flaps is approximately an order of magnitude less than the power required for the HHC and IBC systems. The ATR using piezoelectric fiber composites such as AFC (active fiber composites) and MFC (macro fiber composites) in wind tunnel tests and numerical analyses [21, 22] reduced significantly the vibratory loads of smallscale rotors. Recently, the International Cooperative Program, STAR (SmartTwisting Active Rotor), has a plan to conduct the wind tunnel test in DNW (GermanDutch Wind Tunnels) using a scale rotor incorporating MFC actuators to investigate the vibration reduction [23]. In addition, there have been other active rotor controls such as the SHARCS (smart hybrid active rotor control system, [24]) with the smart spring and the active gurney flap [25] to alleviate vibratory loads of helicopter rotors. Although the extensive works using active vibration control techniques [8–25] have been conducted for conventional helicopter rotors as described above, there is only one research using the active rotor control to reduce the vibration of the liftoffset rotor [26]. In this work [26], HHC was applied to both the upper and lower rotors to reduce the vibration of the XH59A rotor. Although the HHC in the numerical analysis could significantly reduce the vibration of the XH59A rotor in highspeed flights, the actuation frequency of the HHC is restricted as the (), , and frequency. In addition, the rotor performance was not investigated when HHC was used to reduce the vibration of the XH59A liftoffset rotor. It is known that it is not easy to obtain rotor vibration reduction and rotor performance improvement simultaneously by using active rotor control with a single harmonic input [13].
There are limited works on vibration analyses of the liftoffset rotor using rotorcraft comprehensive analyses [26–28]. The RCAS (rotorcraft comprehensive analysis system, [29]) was used to conduct the trim optimization for the vibration reduction and performance improvement of the XH59A rotor in highspeed forward flight [27]. In addition, a validation study of the performance, loads, and vibration was conducted using CAMRAD II (comprehensive analytical method of rotorcraft aerodynamics and dynamics II, [30]) for the XH59A rotor in hover and forward flight conditions [28]. However, there is no research using the rotorcraft comprehensive analyses for the vibration reduction of the liftoffset rotor using IBC. The IBC has an advantage that the actuation frequency is not limited and is more appropriate for the liftoffset rotor than the active trailingedge flap and active twist rotors since the liftoffset rotor uses rigid blades with high stiffness.
Therefore, this paper is aimed at reducing the vibration of the liftoffset rotor using IBC in highspeed flights. As the liftoffset rotor, the XH59A rotor is considered and CAMRAD II is used to analyze the vibration and performance of the XH59A rotor using IBC. When 3/rev hub vibratory loads are minimized using the IBC with a single harmonic input, a decrease in the rotor effective lifttodrag ratio is investigated. In addition, it is shown that the vibration reduction and performance improvement of the liftoffset rotor can be simultaneously obtained when 2/rev and 3/rev actuations are applied in combination for the IBC using multiple harmonic inputs. This study for the XH59A liftoffset rotor using IBC does not correlate the analysis results of vibration reduction and performance improvement with the measured data, since there is not the test data for vibration and performance of a liftoffset rotor using IBC. Furthermore, the present work is the first attempt for the study of the liftoffset rotor using IBC. However, it is believed that this work will show reasonable prediction results because the present analysis model without IBC has already been validated well in the authors’ previous work [28] and CAMRAD II has moderate or good prediction capability to investigate the vibration and performance of the rotor using IBC [13].
2. Analytical Methods
2.1. Analytical Model
The XH59A liftoffset rotor is used as an analysis model using IBC in this work. The XH59A helicopter using ABC™ was initially developed as a pure helicopter configuration without auxiliary propulsions in 1964 [1]. After flight tests in pure helicopter mode were conducted successfully in 1973, two auxiliary propulsions were added to the aircraft for transformation into a compound helicopter ([1], Figure 1). Table 1 summarizes the general properties of the XH59A helicopter [1]. It is well known that the hub vibration characteristics of a liftoffset rotor are dependent of the crossover angle [26]. The crossover angle is defined as the rotor azimuth angle where the upper and lower blades of a rigid coaxial rotor crossover each other (Figure 2). When a crossover angle of 0° is used for the XH59A rotor, the 3/rev hub axial force, normal force, and pitch moment are only transmitted to the fuselage because of interrotor cancellation [5, 26]. In addition, the pitch inputs with higher harmonics do not alter the interrotor cancellation characteristics of a rigid coaxial rotor [26].

(a) Crossover angle = 0°
(b) Crossover angle = 90°
2.2. Analytical Tool
This work uses CAMRAD II [30], which is a comprehensive analysis code for the performance, the aerodynamic and structural loads, and the aeroelastic stability of rotorcrafts. CAMRAD II includes nonlinear finite elements, multibody dynamics, and rotorcraft aerodynamics along with various inflow or wake models. The finite elements of nonlinear elastic beam components are used for the structural dynamics modeling of isotropic or composite rotor blades. A finite beam element has a total of 15 degrees of freedom. The liftingline theory with the unsteady aerodynamics is used to calculate the aerodynamic loads acting on the rotor blade. In addition, CAMRAD II has the prescribed wake, rolledup wake, multipletrailer wake, and multipletrailer wake with consolidation. The NewtonRaphson method with a Jacobian matrix is used for trim tasks in CAMRAD II analysis. The thrust, rolling moment, and pitching moment are considered as the trim targets. The trim analysis usually uses a low azimuthal resolution of 15°.
2.3. Modeling and Analysis Techniques
The CAMRAD II model for the XH59A rotor using IBC in the present study is based on the model constructed in the authors’ previous work [28]. Therefore, most modeling and analysis techniques of the present CAMRAD II analysis are the same as those given in reference [28]. Figure 3 shows the CAMRAD II model for the XH59A rotor with the crossover angle of 0° in this work. A blade of the XH59A rotor is represented using seven nonlinear finite beam elements. The pitch hinge is located at the 5% blade radius. The rotor control system including the pitch link, swashplates, and pitch horn is also modeled. It is assumed that the stiffness of the pitch link with the IBC actuator is the same as that of the original XH59A rotor model used in the previous work [28]. In this work, the pitch motion by the IBC inputs applied to both the upper and lower rotors is represented using equations (1) and (2).
For a single harmonic input,
For multiple harmonic inputs, where is the IBC equivalent blade pitch, is the blade azimuth angle, and , , and are the actuation frequency, amplitude, and control phase angle, respectively, of the IBC inputs.
Since the actual airfoil data for the XH59A rotor are not available, the airfoils similar to the actual airfoil characteristics of the XH59A rotor are used as given in Figure 4. However, the drag increment is used appropriately in order to correct the aerodynamic characteristics of the airfoils used in the present analyses. Further detailed explanation for the adjustment of drag coefficients in the C81 airfoil tables is given in reference [28]. The aerodynamic loads on each blade are calculated using 16 aerodynamic panels. Unlike the authors’ previous work [28], which used a general free wake model, the prescribed wake model is used in the present analyses to avoid the convergence trouble due to the application of the IBC inputs.
(a) Actual airfoils
(b) Present airfoils
The trim analyses are conducted using the six primary rotor controls of the upper and lower rotors. The pitch angle of the XH59A compound helicopter is fixed at 0° since it provides the best performance for the liftoffset rotor [1]. The trim targets in the validation examples in Section 3.1 are set as the vertical force equivalent to the aircraft weight, the torque offset of the upper and lower rotors, and the hub pitching and rolling moments of the upper and lower rotors. In particular, the hub rolling moment () can be prescribed using the assumed liftoffset (LOS) value given in the following equation: where is the thrust of each rotor.
For the propulsive trim, which will be used in Sections 3.2 and 3.3, the drag force of each rotor is considered as the trim target instead of the pitching moment of each rotor. In the present analyses, the drag forces obtained from the validation examples in Section 3.1 are used as the target values of drag forces for the propulsive trim.
The 3/rev hub vibratory loads of the XH59A rotor are calculated using the following: where and are the hub forces and moments, respectively. In addition, the superscripts upper and lower mean the upper and lower rotors, respectively, and the subscripts and represent the cosine and sine components, respectively, of the hub loads.
The vibration index () [31] to evaluate the vibration level of the XH59A rotor is defined as where is the aircraft weight. In addition, and are assumed as unity in this work. It should be noted that the interrotor cancellation of a liftoffset rotor [26] is considered when the vibration index is calculated. Furthermore, the 6/rev hub load components are not considered in equation (5) since the 3/rev hub vibratory loads are the most dominant for the XH59A rotor [26] and predictions of the 6/rev hub vibratory loads are not validated in this paper.
The rotor power () of each of the upper and lower rotors for performance calculation of the liftoffset rotor is defined as where , , and are the induced power, profile power, and parasite power, respectively.
The rotor effective lifttodrag ratio () to evaluate the rotor performance is defined as where is the power of the liftoffset rotor which is the sum of each power of the upper and lower rotors. In addition, and are the flight speed and drag force, respectively, of the liftoffset rotor.
3. Results and Discussions
3.1. Validation
The modeling and analysis techniques of CAMRAD II using the prescribed wake model are validated for the XH59A rotor without IBC in this section. For the analyses, the XH59A rotor in compound helicopter mode with auxiliary propulsions (gross weight of 13000 lb) is considered and the liftoffset of 0.25 is used. Figure 5 shows the correlation of the rotor effective lifttodrag ratio in forward flight between the present prediction and flight test data [32]. The flight test data in Figure 5 are for a gross weight ranging from 11000 to 13000 lb. As seen in the figure, the present prediction compares well with the flight test data since the CAMRAD II analysis result is within the upper and lower bounds of the flight test data and the variation of the predicted result is similar to that of the test data. Figure 6 compares the predicted 3/rev hub pitch moment with the flight test data [1] for the XH59A rotor with a crossover angle of 0°. Although correlations between the present analysis and test data are given at only two flight speed conditions in the figure, the present CAMRAD II analysis predicts well the 3/rev hub pitch moment. As given in Figures 5 and 6, it is considered that the present modeling and analysis techniques to predict the rotor performance and vibration are well established.
3.2. IBC Using a Single Harmonic Input
In this section, the 3/rev hub vibratory loads and rotor performance are investigated when the IBC with a single harmonic input (equation (1)) is used for the XH59A rotor at a flight speed of 200 knots. For the IBC with a single harmonic input, three actuation frequencies () of 2, 3, and 4/rev and two IBC amplitudes () of 1 and 2° are used. The control phase angle () from 0 to 360° is considered with an increment of 30°. The propulsive trim is used for the analyses with and without the IBC, as previously described.
3.2.1. Rotor Vibration
Figure 7 shows the change in the vibration index (equation (5)) of the XH59A rotor in terms of the control phase angle. The baseline indicates the result when the IBC is not applied. As seen in the figure, the vibration index of the XH59A rotor changes (increases or decreases) significantly when the IBC with a single harmonic input is used. The vibration index is reduced by about 59.3% from the baseline value when the actuation frequency of 2/rev, IBC amplitude of 2°, and control phase of 180° (/2°/180°) are used for IBC. In addition, when the IBC with /1°/270° is used, the vibration index is minimized with a reduction of about 62% as compared to the baseline value. The IBC using /1°/330° also moderately reduces the vibration index by approximately 44%. However, the vibration index is reduced by about 3% only when the IBC with /2°/270° is applied. The maximum reduction in the vibration index is summarized in Figure 8 for various IBC input conditions. As shown in Figures 7 and 8, the IBC inputs using /2°/180° and /1°/270° both show excellent vibration reductions of the XH59A rotor by about 59.3 and 62%, respectively.
Changes in the 3/rev hub load components in terms of the control phase angle are investigated in Figure 9. As given in the figures, the variation trends for two different IBC amplitudes of 1 and 2° are similar to each other with the given actuation frequency. The 3/rev hub axial force in Figure 9(a) is minimized by approximately 73.1% from the baseline value when the IBC using /2°/120° is applied. Figure 9(b) shows that the 3/rev hub normal force is minimized by about 83.8% when the IBC input of /1°/270° is used. The IBC using /1°/240° in Figure 9(c) minimizes the 3/rev hub pitch moment by about 65.4% to the baseline value. As shown in Figure 9, the IBC input conditions are different to minimize the 3/rev hub axial force, normal force, and pitch moment. However, all of the 3/rev hub load components are minimized by the IBC using the 3/rev actuation frequency.
(a) Axial force
(b) Normal force
(c) Pitch moment
Figure 10 summarizes the maximum reductions in the 3/rev hub axial force, normal force, and pitch moment for the given actuation frequency and IBC amplitude and shows the corresponding control phase angles. Particularly, the IBC using /2°/330° minimizes the 3/rev hub pitch moment but its reduced value is higher than the baseline value by 50%. As shown in the figures, there is no control phase angle, which simultaneously minimizes the 3/rev hub axial force, normal force, and pitch moment for the given actuation frequency and IBC amplitude. Furthermore, when two IBC amplitudes of 1 and 2° are considered with the given actuation frequency, the control phase angle is the same to minimize the 3/rev hub load component.
(a) /1°/φ
(b) /2°/φ
(c) /1°/φ
(d) /2°/φ
(e) /1°/φ
(f) /2°/φ
As shown in Figures 7–10, two IBC input conditions, /2°/180° and /1°/270°, are appropriate to reduce significantly the vibration index of the XH59A rotor at 200 knots. In addition, the control phase angle to minimize the vibration index is the same as that to minimize the 3/rev hub normal force when the actuation frequency and IBC amplitude are given. For these two IBC input conditions, the 3/rev hub normal force is minimized the most as compared to the reductions in the other 3/rev hub load components. Therefore, the control phase angle to minimize the vibration index is also the same as the control phase angle, which provides the greatest maximum reduction in the 3/rev hub load components. However, it is known that the 3/rev pitch moment of the XH59A rotor is the most dominant to excite the airframe in highspeed flights when a crossover angle of 0° is used [1, 26].
3.2.2. Rotor Performance
The variations of the rotor effective lifttodrag ratio are given in Figure 11 when the IBC with a single harmonic input is used for the XH59A rotor at 200 knots. As shown in the figure, the rotor performance increases or decreases by the IBC application. When Figures 7 and 11 are compared, it is easily known that the IBC input to minimize the vibration of the XH59A rotor reduces the rotor performance. For an example, the IBC using /1°/270° which minimizes the vibration index by about 62% reduces the rotor effective lifttodrag ratio by about 3.43% as compared to the baseline performance. In other words, it is difficult to obtain the vibration reduction and performance improvement of a liftoffset rotor simultaneously when using the IBC with a single harmonic input. Figure 12 summarizes the maximum improvement of the rotor effective lifttodrag ratio for various IBC input conditions. The IBC with /2°/0° maximizes the rotor performance of the XH59A rotor by 3.18% to the baseline value. However, the IBC using the 4/rev actuation does not increase the rotor effective lifttodrag ratio but decreases the rotor performance, as seen in Figures 11 and 12, although the IBC using 4/rev actuation reduces the vibration index discussed previously in Figures 7 and 8.
3.3. IBC Using Multiple Harmonic Inputs
As shown in the previous section, the IBC using a single harmonic input reduces significantly the vibration index of the XH59A rotor at a flight speed of 200 knots; however, the rotor effective lifttodrag ratio is reduced when the IBC condition to minimize the rotor vibration is used. Therefore, a new input scenario of IBC is required to reduce significantly the hub vibratory loads while maintaining or increasing the rotor performance of a liftoffset rotor in highspeed flights. In this section, the IBC using multiple harmonic inputs is proposed to reduce the vibration index and increase the rotor effective lifttodrag ratio (or at least maintain the baseline value) of the XH59A rotor at 200 knots, simultaneously. The different actuation frequencies (), IBC amplitudes (), and control phase angles () are combined using equation (2) for the IBC with multiple harmonic inputs.
Two actuation frequencies of 2/rev and 3/rev, two IBC amplitudes of 1 and 2°, and control phase angles from 0 to 360° with an increment of 30° are combined for the IBC with multiple harmonic inputs. As previously discussed in Section 3.2, since the IBC using a 4/rev actuation does not increase the rotor performance, the 4/rev actuation is not considered for multiple harmonic inputs of IBC. Actually, it is an optimization problem to find the conditions of multiple harmonic inputs for IBC, which simultaneously minimizes the vibration and maximizes the performance of the liftoffset rotor in highspeed flights. However, the goal of this study is not to search for the optimal input condition for simultaneous vibration minimization and performance maximization of the XH59A rotor. Instead, this paper shows an example using the IBC with multiple harmonic inputs, which reduces the vibration index significantly and increases slightly the rotor effective lifttodrag ratio of the XH59A, simultaneously. Two input conditions of /2°/270° and /1°/ are combined for the IBC using multiple harmonic inputs.
3.3.1. Rotor Vibration
Figure 13 shows the variation of the vibration index of the XH59A rotor at 200 knots, using the IBC with the multiple harmonic inputs; . As shown in the figure, the vibration index increases or decreases as the control phase angle for the 3/rev actuation () varies. The vibration index is minimized by about 62% from the baseline value when a control phase angle () of 210° is used for the IBC with multiple harmonic inputs. The capability of this vibration reduction is exactly equivalent to that using the IBC with the single harmonic input of /1°/270° given in Figures 7 and 8.
Figure 14 exhibits the variations of the 3/rev hub axial force, normal force, and pitch moment in terms of the control phase angle () for the IBC using multiple harmonic inputs. Although the vibration index is reduced seriously from the baseline result given in Figure 13, the 3/rev hub axial force in Figure 14(a) is not reduced than the corresponding baseline value since its minimized value is higher than the baseline value by about 48.8%. The 3/rev hub normal force in Figure 14(b) is minimized by approximately 64.5% to the baseline value when the IBC using the multiple harmonic inputs with a of 240° is used. The variation of the 3/rev hub pitch moment is given in Figure 14(c). The multiple harmonic inputs using a of 210° minimize the 3/rev hub pitch moment with a reduction of about 87.6% from the baseline value. Figure 15 summarizes the maximum reduction in 3/rev hub load components and the corresponding IBC input conditions using multiple harmonic inputs. When the IBC using multiple harmonic inputs is applied, the 3/rev hub pitch moment is minimized the most as compared to the other 3/rev hub load components. As shown in Figures 14 and 15, the control phase angle for the 3/rev actuation () to minimize the vibration index is the same as the control phase angle (), which gives the greatest maximum reduction in the 3/rev hub load components.
(a) Axial force
(b) Normal force
(c) Pitch moment
3.3.2. Rotor Performance
Figure 16 shows the variation of the rotor effective lifttodrag ratio in terms of the control phase angle () for the IBC using multiple harmonic inputs; . When the control phase angle () is 150°, the rotor performance is maximized by 3.16% as compared to the baseline value. The rotor effective lifttodrag ratio increases by 0.37% when a control phase angle () of 210°, which minimizes the vibration index as given in Figure 13, is used. Therefore, the IBC using multiple harmonic inputs, , significantly reduces the rotor vibration while it slightly increases the rotor performance for the XH59A liftoffset rotor at 200 knots.
When two present prediction result sets using control phase angles () of 180 and 210° are interpolated, the vibration reduction and rotor performance improvement of the XH59A rotor are summarized as shown in Table 2. As given in the table, when a control phase angle () of 200° is used for the present multiple harmonic inputs of IBC, the rotor vibration is reduced by about 50% from the baseline value and the rotor performance is improved by approximately 1.01% as compared to the baseline result, simultaneously. It is not easy to obtain this outperformance in the simultaneous vibration reduction and performance improvement of the XH59A rotor when the IBC using a single harmonic input is used.

4. Conclusions
In this work, the vibration and performance of the XH59A liftoffset rotor using IBC were investigated by the rotorcraft comprehensive analysis code, CAMRAD II. At a flight speed of 200 knots, the vibration index was minimized by about 62% from the baseline value but the rotor effective lifttodrag ratio was reduced by about 3.43% to the baseline result when the actuation frequency of 3/rev, amplitude of 1°, and control phase of 270° (/1°/270°) were used for the IBC with a single harmonic input. However, when the IBC with multiple harmonic inputs, , was used for the XH59A rotor at 200 knots, the rotor vibration was reduced by about 62% and the rotor performance was improved by about 0.37% from the baseline value. Using the obtained prediction results, the vibration index was reduced by approximately 50% while the rotor effective lifttodrag ratio increased by about 1.01% when the IBC using was applied to the XH59A liftoffset rotor at 200 knots. In the future, a physical understanding of the analysis results given in this paper will be investigated thoroughly along with other prediction results including the trimmed pitch control angles, rotor airloads, blade structural loads, blade elastic deformations, and blade tip clearance. In addition, an optimization study of the input scenario for the IBC using multiple harmonic inputs, which minimizes the vibration reduction and maximizes the rotor performance of the liftoffset rotor simultaneously, will be conducted.
Nomenclature
:  Actuation amplitude of IBC (deg.) 
:  Drag force (lb) 
:  3/rev hub force (lb) 
:  Lift force (lb) 
:  Rotor effective lifttodrag ratio 
:  3/rev hub moment (lb·ft) 
:  Hub rolling moment (lb·ft) 
:  Actuation frequency of IBC (/rev) 
:  Number of blades of each rotor 
P:  Per revolution (/rev) 
:  Rotor power (hp) 
:  Coaxial rotor power (hp) 
:  Induced power (hp) 
:  Profile power (hp) 
:  Parasite power (hp) 
:  Radial position of the rotor (ft) 
:  Radius of the rotor (ft) 
:  Thrust (lb) 
:  Flight speed (ft/sec) 
:  Hover tip velocity of the rotor (ft/sec) 
:  Weight of the aircraft (lb) 
:  Wind axis drag force of the rotor (lb) 
:  IBC equivalent blade pitch (deg.) 
:  Solidity of the rotor 
:  Control phase angle of IBC (deg.) 
:  Azimuth angle (deg.). 
Data Availability
The data used to support the findings of this study are included within the article.
Disclosure
This paper was presented at the 44th European Rotorcraft Forum, Delft, the Netherlands, September 1821, 2018.
Conflicts of Interest
The authors declare that there is no conflict of interest regarding the publication of this paper.
Acknowledgments
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (NRF2016R1C1B1007199). This work was supported by the research fund of the Korea Aerospace Research Institute. This work was conducted at the HighSpeed Compound Unmanned Rotorcraft (HCUR) research laboratory with the support of the Agency for Defense Development (ADD).
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Copyright © 2019 JaeSang Park et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.