Design and strength simulation of hub mechanism of variable pitch propeller

The hub mechanism is an important force bearing mechanism of variable pitch propellers and an important actuator of variable pitch control in tilting ducted propeller UAV. To solve the problem of the connection between the blades and the fuselage of the tilting ducted propeller UAV, according to the parameters of the blades, the force of the hub mechanism is analyzed, and the design parameters of the hub mechanism are obtained by using the theoretical calculation method, such as the power density method. The strength of the parts is analyzed by using the finite element method. A variable-pitch propeller hub mechanism was developed for tilting ducted unmanned aerial vehicles. A design flow of the hub mechanism is formed, including the design of the parts of the hub mechanism and the strength check. This will facilitate the design and development of ducted UAVs.


Introduction
According to its structure and flight principle, UAVs can be roughly divided into fixed wing UAVs and rotary wing UAVs [1].To explore a more efficient aircraft, the tilting ducted propeller UAV was developed to consider the advantages of fixed wing UAVs and rotary wing UAVs [2][3].The new UAV has the advantages of long-range and fast speed of fixed-wing UAV and has the characteristics of vertical take-off and landing of rotary-wing UAV.Compared with the rotor, the ducted propeller has higher aerodynamic efficiency under the same diameter [4].And the conversion between helicopter mode and fixed wing mode is completed using a tilting ducted propeller [5][6][7].In the conversion process, to adapt to the lift demand under different modes, the pitch of the propeller blades needs to be changed within a certain range.Hence, the ducted propeller needs to be designed as a variable-pitch propeller.
The hub mechanism is an important load-bearing mechanism of the variable pitch propeller system, which connects the blade and the fuselage and drives the blade to rotate.At the same time, it is the actuator of variable pitch control, which cooperates with the variable pitch mechanism to complete the variable pitch movement of the blade.
For the research of propeller hub, domestic scholars have mainly done the following research: Hu et al. [8] analyzed the strength of each component in the hub mechanism of CPP by using the finite element analysis method considering the geometric structure of hub components and the assembly contact relationship between parts.Shi et al. [9] proposed a design method for the hub mechanism of marine CPP by combining engineering design and software design.
In this paper, a kind of variable pitch propeller hub mechanism for tilting ducted propeller UAV is designed, and the strength of its main bearing parts is checked and simulated to ensure that the hub mechanism can meet the functional requirements and strength requirements.

Working principle and design idea of propeller hub
The working states of the tilting ducted propeller UAV include helicopter mode, transition mode, and fixed wing mode.In the design stage, considering the rotating speed, power, load, and other factors, we refer to the form and requirements of the rotor hub in helicopter mode to design the rotor hub mechanism.Hub mechanism includes hub, pitch shaft, blade clamp, bolt, bearing, etc.The basic design input parameters of the hub mechanism are shown in Table 1.
Table 1.Input parameters for the design of the propeller hub mechanism.

Symbol of parameter
Name of parameter V a l u e n propeller speed 5400 rpm R blade radius 0.35 m M b blade weight 0.095 kg The conventional fully articulated hub consists of a pitch hinge, a flapwise hinge (horizontal hinge), and a lag hinge (vertical hinge).The blade pitch movement can adjust the blade angle of attack and change the propeller pull.The blade flapping motion can compensate for the uneven lift of the forward blade and the backward blade of the propeller disk and reduce the fatigue of the blade.The blade shimmy motion can reduce the alternating force and alternating moment produced by blade flapping and reduce the fatigue damage of the blade.
(1) Outward displacement of equivalent flapping hinge This paper selects the hub as a hingeless hub, which cancels the flapping hinge in the structure.Still, to realize its inherent characteristics in dynamics, the hinged blade with flapping hinge outward displacement is adopted, that is, the equivalent flapping hinge.
The first-order natural frequency of the flapping joint is defined as Formula (1): The precone angle of the propeller hub can offset the bending moment at the root of the propeller hub caused by the propeller pulling force and balance the bending moment at the root of the propeller hub caused by the centrifugal force and the pulling force. is defined as Formula (2): where  is the precone angle.T is the blade pull force, herein 135N T  . N is the blade centrifugal force,

Design flow of propeller hub mechanism
In this design, the working condition of the propeller blade is high-speed rotation, and the hub is under high load, so the design and selection of the main load-bearing components in the hub mechanism is particularly important.The main parts need to be checked for strength.To form a design process with a short design period, high calculation accuracy, and convenient design change, various factors in the design process are analyzed and summarized to form a simple, fast, and reasonable design process for the hub mechanism.At the same time, based on the design process, the technical application verification is carried out, and the optimization of the design scheme is realized by computer software combined with the engineering machinery design method and software design method.If the safety factor of a part of the hub cannot meet the requirements, it is necessary to change the local structure size of the part or increase the diameter of the hub and re-check, and finally give the optimal scheme.
In the design of the rotor hub, first of all, the diameter of the rotor hub is preliminarily estimated.The estimation methods include the estimation method of hub diameter ratio and the estimation method of power density.The power density is the ratio of the power of the main engine to the area of the blade disk, as shown in Formula (3): where L is the power density, The flow chart of the propeller hub mechanism design is shown in Figure 1.

Structure design of propeller hub mechanism
The invention discloses a variable-pitch propeller hub mechanism, which comprises a propeller hub, a propeller hub connecting bolt group, a propeller clamp blade variable-pitch component, a rotating shaft, and a locking bolt group.The outline diagram of the hub mechanism is shown in Figure 2, and the detailed design structure is shown in Figure 3.

Strength check of propeller hub mechanism
The hub mechanism designed in this paper mainly includes a hub shell, blade clamp, pitch shaft, bearings, bolts, and other parts.The hub, pitch shaft, blade clip design, and strength calculation for the bolt type selection are among them.According to the strength design code, to ensure the safety and rationality of the design, the load at the working state of the maximum point in the helicopter mode is selected as the strength calculation load.The hub, pitch shaft, and blade clamp are all made of 7075 aluminum alloy, and the yield strength of this material is 455 MPa.12.9 grade high strength bolts shall be selected for blade fixing bolts n is the safety factor,  s is the material yield strength, and max  is the maximum stress.
The blade fixing bolt mainly bears the centrifugal force generated by the blade.The allowable safety factor is selected as 8 because the load the mechanism bears is dynamic.The strength check results of the main parts are shown in Table 2.  2 that the designed parts meet the strength requirements.It can be seen from Figures 5(b)-7(b) that the magnitude of strain is less than 10 -6 , which does not need to be checked and meets the stiffness requirements.

Conclusion
In this paper, a kind of propeller hub mechanism of variable pitch propeller, suitable for tilting ducted propeller, is designed and simulated.
1) A propeller hub mechanism design flow with a short design period is formed, with high calculation accuracy and convenient design change.
2) The propeller hub mechanism designed in this paper can meet the functional requirements and adjust the collective pitch range with the pitch control mechanism.
3) The important parts in the mechanism meet the strength requirements and have a certain static stability margin.
The mechanism provides a general design idea for the propeller hub of a small rotor-wing UAV or a propeller UAV and has good engineering application value.

where 1 
is the first order flapping natural frequency. is the blade speed, 30 n   .e l is the equivalent flapwise hinge outward displacement.e I is the moment of inertia of the blade, operation power of the main engine, D is the propeller diameter, andd A Ais the disk ratio.

Figure 1 .
Figure 1.Flow chart of propeller hub mechanism design.

Figure 2 .
Figure 2. Outline drawing of propeller hub mechanism.The propeller hub adopts a combined split type layout, divided into an upper and lower propeller hub.The upper propeller hub is connected with the lower propeller hub through a propeller hub connecting bolt group.The inner parts of the upper propeller hub and the lower propeller hub are provided with rotating grooves for mounting bearings and a variable pitch shaft.The combined split propeller hub benefits the installation and later maintenance of other parts.The paddle clamp blade pitch assembly consists of a pitch shaft, thrust bearing, deep groove ball bearing, pitch connecting bolt, paddle clamp, blade, and blade fixing bolt set, as shown in Figure4.The variable pitch shaft is stepped and vertically arranged along the circumferential direction of the propeller hub.The shaft head of the variable pitch shaft is arranged in a rotating groove in the propeller hub, the shaft body of the variable pitch shaft is connected with the inner rings of the thrust bearing and the deep groove ball bearing, and the outer rings of the thrust bearing and the deep groove ball bearing are arranged on the inner walls of the upper propeller hub and the lower propeller hub.The blade is arranged on the blade clamp through the blade fixing bolt group, and the blade clamp is fixedly connected with the pitch shaft through the pitch connecting bolt.The blade clamp blade pitch change assembly also comprises a joint bearing joint, wherein the joint bearing joint is arranged on the blade clamp.A pitch change pull rod can be arranged on the joint bearing joint, and the pitch change pull rod is connected with a pitch change mechanism to complete pitch change motion.

Figure 3 .
Figure 3. Detailed design drawing of propeller hub mechanism.

Figure 4 .
Figure 4. Detailed design drawing of blade pitch assembly of propeller clamp.

Table 2 .
Strength check results of main parts.