Strength analysis of the rotor hub of an unmanned helicopter

This article presents a method of strength analysis of the rotorcraft component which is the rotor hub of an unmanned helicopter with a MTOW up to 150 kg. The simulation takes into account two materials of which individual elements are made, i.e. steel and aluminum alloy. The load scheme and element support were defined, and numerical calculations were performed in the Ansys Workbench software. The simulation results were presented in the form of stress maps and were subjected to detailed analysis for individual elements. In the last stage, critical places in the assessment of the strength of the elements were indicated. On the basis of the performed strength analysis, the obtained results were individually interpreted for each of the tested elements depending on the adopted safety factors.


Introduction
The aviation industry is a constantly developing branch of the economy. Therefore, numerous studies are carried out to develop and optimise new aircraft designs. A particularly important issue in the study of aircraft is the optimisation of their design in terms of reducing aerodynamic drag, increasing lift and minimising the weight [1][2][3]. The use of numerical methods in the design process significantly reduces the time of product development and costs compared to experimental methods. In recent years, unmanned aerial vehicles have gained in importance, hence many scientific works focus on this subject [4][5][6][7][8]. In this work, the rotor hub of the unmanned aerial vehicle was analysed. The main rotor hub is a key element in the rotorcraft structure. The rotor blades are attached to it using joints. The rotor is driven by the rotation of the shaft which transmits the torque from the engine. In addition, the rotor hub transmits the lift from the blades to the fuselage of the rotorcraft. This subassembly is mounted on a shaft and is therefore affected by inertia forces, aerodynamic forces and moments. The analysis of the aerodynamic effects on the main rotor blades or the hub rotor itself can be performed using a wind tunnel [9][10][11][12][13] or based on numerical CFD analyses (Computational Fluid Dynamics) [14]. CFD analyses in the field of aircraft make it possible to study their stability [15], aerodynamic effects occurring on aircraft components such as a stabilizer [16], fuselage [17], rotor [18] or occurring on the entire structure of the aircraft [19]. CFD analyses are extended by coupled analyses that enable the analysis of a coupled problem by dividing the system into different subsystems. Then, separate modelling and simulation processes are performed for these subsystems, and the interaction between them is synchronised at the defined discrete points. An example of such an approach is the combination of Multi-Body Dynamics modelling with CFD research [20]. The forces and moments on the rotor hub vary depending on the phase of flight. For this reason, the rotor hub should show high resistance to complex loads and high stiffness. There are four main types of helicopter rotor hubs. These are teetering, articulated, hingeless and bearingless designs [21].
To test the strength of the element, it is necessary to carry out strength tests to determine the behaviour of the structure (deformation or destruction) due to stresses in the material. To ensure adequate strength, it is necessary to choose the right material. Aluminum alloys play a special role in aviation due to their favorable strength-to-weight ratio [22].
The basic methods of strength testing are experimental, analytical and numerical methods. The works [23] and [24] present the results of the helicopter rotor hub fatigue test. The method for the detection and avoidance of static load limits on the main rotor hub [25] was also investigated. In the event of a failure of the main rotor hub, it is also possible to analyse the material structure [26].
Numerical methods are used for structures with a complex load state where obtaining results (stresses, strains, displacements) with analytical methods is highly complicated. The numerical method used to test the strength of aircraft components is the FEM method [27][28][29]. This method is favourable for detection of critical locations [30]. It consists in dividing the surface into finite elements that average the physical properties of the test object. Then, calculations are performed for the nodes of this division only, and the analysed physical properties are approximated on the basis of solutions for the nearest nodes [31]. The research of the helicopter rotor hub using this method is presented in [32]. Numerical FEM tests can also be used to analyse the fatigue life prediction of a helicopter main rotor blade [33].

Geometric model
The preliminary design of the rotor hub unit should be subjected to strength analysis. The implementation of the CAD model into the CAE environment requires the use of model simplifications and the appropriate definition of the external force system in accordance with the real system. The rotor hub ( Figure 1) is a kinematic chain of mechanisms with one degree of freedom. It aims to transfer the torque from the main gearbox to the blades of the main rotor. In addition, it transfers the lift force from the blades to the fuselage of an unmanned helicopter -in the example under consideration -with a takeoff mass of up to 150 kg. The third task is to change the blade angle of attack.
In the beginning, an analysis of the model was conducted to remove collisions of the elements in the model, the possibility of simplifying the geometry and the possibility of minimising the number of elements. Then the model was implemented in the CAE programme.
In the design stage, two materials were assigned to the individual elements. The first one is a lowalloy structural steel grade 42CrMo4 (40HM) which undergoes heat treatment [34]. The second is an aluminium alloy for the plastic processing AlZn6Mg2Cu (PA9 7075). Figure 2 shows the hub elements made of the materials listed above. Table 1 shows the assumed mechanical properties of the materials used to make the hub. The discretisation of the hub elements was done with tetra-type elements. The thickness of the grid was selected for each element, depending on its dimensions. Figure 3 shows the view of the shaft after the discretisation. Figures 4 and 5 show the selected key elements of the structure under investigation.

Results and analysis
The main purpose of the rotor hub is to transfer the torque from the engine to the rotor blades and the lift force from the blades to the helicopter support structure. The design assumptions are based on a helicopter's 30 kW engine. The rotor speed is defined as 1800 rpm. Based on the relationship between the engine power (P), rotor speed (n) and torque (Mo), the torque was calculated in the rotor hub. This was 159 Nm. A take-off mass of 150 kg was assumed. Therefore, a force of 1500 N was applied to the rotor shaft. The calculated centrifugal force was 14922.9 N. The analysis of the simulation results started with the analysis of the displacement map for the hub. The maximum displacement was 0.16 mm. These displacements are the sum of axial and angular displacements of all elements. The largest displacements occurred at the end of the shaft. This is due to both the displacement of all elements along the gravitational force and the angular displacement of the rotor head. Angular displacement resulting from joint deformations is visible as radial strips along the shaft. Stress analysis is carried out on the basis of the von Misses Huber hypothesis in which all stresses are comparable to tensile stresses. Stress values were analysed for each individual component. The article presents only selected elements. The first simulated element was the rotor hub shaft ( Figure 6). The maximum stresses occurred at the point the torque was applied. This is due to the small contact area, but their value (44 MPa) is safe for the structure. The part of the shaft between the bore and the splines was the most stressed as it is the torque-loaded section. The stresses in this zone did not exceed 19 MPa. The zone loaded with the longitudinal tensile force is minimally loaded at the bottom of the shaft (stresses do not exceed 5 MPa). In the upper part, due to the thinner wall, the stresses did not exceed 10 MPa. The spline transmits the torque only in the initial zone, which indicates the possibility of shortening its length. The second element subjected to the stress analysis was the rotor hub head. On the stress map (Figure 7), it can be seen that the maximum stresses occurred at the cut-out point of the head for the joint seat and amounted to 83.6 MPa. The zones of increased stresses occurred on the cross-sections of the joint pin fixtures, which results from stretching under the influence of centrifugal force. The stresses in this zone did not exceed 67 MPa. The next analysed element was the joint (Figure 8). The maximum stresses were 108.8 MPa. The joint was loaded in the area between the tilt axis bore and the yaw axis bore where the element is stretched. The stresses exceed the allowable stress tuv at the mounting point of the yaw axis of the rotor blade. Moreover, the stresses on the side wall between the vertical holes and the horizontal hole exceed the allowable stress kmv, and their value reaches 47 MPa. The cross-section shows the place where the stresses exceed the allowable stress tcc, which may lead to fracture.  The next tested elements were the rotor blade grip covers (Figure 9). The maximum stresses were 69.1 MPa and exceeded the allowable stresses tuv. They are located on the radius connecting the rib with the contact surface. They occur locally and can lead to a fracture at this point. In the remaining zones, the stresses did not exceed 33 MPa.

Conclusions
The strength analysis shows that depending on the accepted safety factors (tmv, tuv, tu) the strength of each element can be interpreted individually. The simplest interpretation is for the elements in which the permissible stresses tmv are not exceeded. These parts have been designed correctly and do not require any changes. This group includes the shaft, hub head, rotor blade swinging axis and rotor blade turning axis. Although the shaft construction seems oversized, it is correct. This is due to the use of the hole inside the shaft for the supply of hydraulic and measuring systems. The only element that may raise objections is the spline. The stresses on it show its operation in the initial section only. Therefore, its shortening should be considered. The calculation of the hub head has shown the design correctness in terms of strength. Alternatively, wall thickness and spline length optimisation can be considered.
The interpretation of the elements in which the stresses are in the range between tmv and tuv raises some doubts about the necessity of changes. Depending on individual cases, it is necessary to decide on structural changes or not. This group includes the rotor blade swing axis and the rotor blade twist axis. The rotor blade swing axis obtains the maximum stress on its cutting sections. Due to exceeding the admissible stresses, it is recommended to change the diameter of the workpiece for the diameter of the interaction. The stresses occurring at the point of interaction between the rotor blade and the swinging axis require a redesigning of this connection so that the axis does not break off. In a larger pivot diameter, the stress is low. Due to the bearing used, a change in diameter is not recommended. Instead, an axle bore can be made to reduce the weight of the component.
Another group consists of the elements in which the maximum stresses do not exceed the permissible tt, while the permissible tt is exceeded. Local changes in these parts are necessary, but usually there is no need to change the whole element. This group includes the hinge, the rotor blade deflection axis, the rotor blade cover, the rotor blade mounting yoke, the vibration damper holder and the rotor blade angle change holder. The last group are the elements in which the maximum stress is higher than the yield point Re. The elements which are in this range require thorough design changes because the material above the yield point is not usable (its shape changes permanently). Furthermore, in the simulation of displacement and stress for such an element, the elastic material is not reliable. In the last two groups, there are none of the elements under consideration. This indicates the correct design of the rotor hub.