Simulation and Optimization for Tilt-rotor Rotating Mechanism Based on COMSOL Xiang-Bo MENG a and Ji-Yang ZHANG b,*

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1 2017 International Conference on Mechanical Engineering and Control Automation (ICMECA 2017) ISBN: Simulation and Optimization for Tilt-rotor Rotating Mechanism Based on COMSOL Xiang-Bo MENG a and Ji-Yang ZHANG b,* 1 National University of Defense Technology, College of Mechatronic Engineering and Automation, Changsha , China a xbmeng1993@163.com, b zjjyyang@163.com *Corresponding author Keywords: Tilt-rotor, Rotating Mechanism, COMSOL, Finite Element, Simulation. Abstract. Rotating mechanism is an important part of the tilt-rotor unmanned aerial vehicle (UAV), it plays a crucial role in the transition flight phase and even hover flight. The mechanical performance of the rotating mechanism affects directly flight safety and reliability of the tilt-rotor. In order to study the work process of rotating mechanism, and to find more suitable rotation modes, the rotating mechanism of tilt-rotor is set for the research object. A simulation model is built by using the finite element methods, and through the study of change regulation of speed, displacement, stress distribution and deformation, the movement process of rotating mechanism was made clear. Finally, material selection and structure design of the mechanism was optimized based on the simulation results. Introduction Tilt-rotor UAV is a composite aircraft, it not only has fixed wings, but also owns rotors. Meanwhile, it has two main flight modes, on one hand, tilt-rotor can hover, and thus take off and land vertically like a helicopter. On the other hand, it can reach a high speed in forward flight, just like a fixed-wing aircraft [1]. In order to realize the switching between the two flight modes, rotating mechanism plays an important role. It s rotors are upright in the hover mode, which be able to provide an upward lift force to the aircraft. In the second mode, the rotating mechanism rotates 90 degrees to promote the aircraft forward and the lift force is produced by the wings. In a word, rotating mechanism is the unique structure in tilt-rotor, analyzing the work process of the mechanism is helpful to improve the performance and broaden the application field of the tilt-rotor aircraft. However, it is not easy to study the tilting process only by mechanics equations because this phenomenon is involved in the multi-body problem and the implicit difference equation will be deduced. COMSOL Multiphysics simulation software is based on finite element method [2], it can perform the simulation of real physical phenomena by solving partial differential equations. COMSOL has efficient computing performance and multi-field bidirectional direct coupling capability, therefore, it has been used widely in the field of electromagnetism, hydrodynamics, quantum mechanics, semiconductors, structural mechanics and et al. This study uses COMSOL to simulate the rotating mechanism and analyze the relevant parameters, it is useful to imitate the real flight state of the tilt-rotor aircraft and get the effective theoretical guidance, and the simulation result could propose a more reasonable scheme of the mechanism. Rotating Mechanism Structure of Mechanism In this paper, the rotating mechanism has been implemented independently based on the engineering design, it is made up of several parts, including support frame, steering gear, linkage 128

2 mechanism, motor seat, motor and propeller. The mechanism is shown in Fig. 1(a) and Fig.1(b) shows the 3D model of the mechanism. (a) Figure 1. Rotating Mechanism (a) Archetype of Rotating Mechanism (b) Three-dimensional Geometric Model of Rotating Mechanism. According to the design requirements, the tilt-rotor UAV must be light and have a fast cruising speed. Meanwhile, it is required to have long flight time. Therefore, the material of the rotating mechanism should be light with high tensile strength, choosing the carbon fiber as the material of the support frame and the other structures that are applied to fixing use light metal material. The motor and the propeller are the most important parts of the mechanism, the motor will cause vibration when rotating at high speed, and the propeller needs to provide a static pull force bigger than 4kg. Therefore, the motor and the propeller must be carefully chosen. The Scorpion SII motor (Scorpion Power System Limited, has been selected and applied in the mechanism. It has reasonable size, suitable power, low noise, good heat radiation and dynamic balance when it works. Three engineering views of Scorpion SII motor and dimensions are shown in Fig.2. Tab 1 gives the specifications of the motor. At the same time, a three paddle propeller was matched to this motor. (b) Figure 2. Three Views of Scorpion SII Motor. Table 1. Motor Parameters. Motor Model Size Weight Maximum Power Maximum Current KV Value Scorpion SII Motor 48.9*48.9*78.4[mm] 288[g] 1850[W] 85[A] 555[RPM/V] 129

3 Movement of Mechanism A frame is fixed on the fuselage, supporting all of the parts of the mechanism. The steering gear rotates at a fixed angular velocity and drives the active lever of linkage mechanism to move. The motor is fixed on the motor seat, which is driven by the linkage mechanism. As shown in Fig.3. Due to the transmission of the linkage mechanism, the velocity of the end point of the passive lever is mutative. The relationship between rotation angle of the active lever and the velocity of the end point has been calculated in MATLAB (MathWorks, Inc.), as shown in Fig.4. Figure 3. Motion Diagram of the Rotating Mechanism Velocity of the end point of the passive lever (m/s) Rotation angle of the active lever (rad) Figure 4. Chart about the Transformation of the Velocity of the End Point. During the transform, the propeller has been spinning with a constant speed. The orientation of it rotates 90 degrees from vertical to horizontal, driven by a servo via the motor seat. It takes a short time to complete this process and achieve the power redistribution. Because of the geometrical transmission properties of linkage mechanism, the velocity of passive lever s end point is mutative when the steering gear drives the active lever to rotate with a fixed angle velocity. It is able to make the passive lever carry out a complex and irregular movement. This problem will bring a lot of trouble to the motion control strategy.therefore,it is necessary to study the relationship between the end point s velocity and the active lever s angle velocity. 130

4 Simulation in COMSOL Physical Field According to the structure of rotating mechanism, it could be simplified into a multi-body mechanism, choosing the Multi-body Dynamics physical field as a research environment. We can get the fundamental differential equations as = + (1) F=I+ u (2) Where ρ is the density of material, F is the volume force, u is the displacement at center of rotation, S is the force area and v represents the poison s ratio of material. In the multi-body dynamics physical field, we can simulate the movement of the linkage mechanism and make motor rotate forward, the value of velocity and displacement can be obtained. There is relative motion between the mechanism and air when the aircraft flies forward, at the same time, the propeller rotates with a high angular velocity. We choose the Rotating Machinery, Fluid Flow physical field to study. The differential equations are shown as ρ +ρ u u= pi+ μ+μ u+ u ρki +F (3) + ρu =0 dx=dx r,ω,t =w (4) (5) (6) where equation (3) is the momentum equation and (4) is the Navier-Stokes equation considered the compressibility of fluid[3], the equation (5), (6) are the rotation equation of the machinery[4], is the density from material, is the dynamic viscosity, is the velocity, is the pressure of fluid, is the angular velocity, is the distance to the rotation axis. We can get the pressure and velocity of the fluid in this physical field, the angular displacement of rotating machinery will be calculated. These numerical result can character the dynamics of the tilt machine qualitatively and reveal the detail of the work process of it. Methods in COMSOL The linkage mechanism will transmit a large force or a moment in the process of movement. It is important to choose a kind of material with large Young's modulus and low density, which ensures the mechanism works well and makes the flight safety. Therefore, preset a centrifugal force for the mechanism in the multi-body dynamics physics field, we can ascertain the most suitable material from a set of materials based on the deformation under the large centrifugal force. Then, according to actual requirements and the properties of the material that has been chosen, the size of rotating mechanism could be designed. Finally, we can get the final choice by testing the motion properties of the rotating mechanism. The end point of motor will has a vibrational velocity when the active lever has a fixed angle velocity. In order to ensure the velocity of the end point to be constant and the motor has a stable rotation process that from vertical to horizontal, it is important to design the angle velocity curve and set the most reasonable motion rule for the active lever, based on the corresponding velocity curve of the end point. 131

5 We can get the pressure of propeller from fluid, it is useful to study the relationship between the rotation rate of the motor and the pressure force. In addition, the velocity and direction of fluid will influence the pressure, it is able to find the regulation of pressure, confirm the extremism and direction in the rotating machinery, Fluid Flow physical field. The flow chart is shown in Fig.5. Figure 5. The Flow Chart of Study Results and Optimization Velocity of Mechanism and the Angular Velocity Optimization of Active Lever As mentioned above, we can get the simulation results about the motion of the rotating mechanism in the Multi-body Dynamics physical field, Fig.6 shows the states of the simplified mechanism at different rotation angles. 132

6 Figure 6. The Different States of the Mechanism at 0 Degree, 45 Degree and 90 Degree. Choosing the vertex of the motor as the end point, presetting a constant angle velocity for the active lever, we can get the velocity of the end point. The velocity curve is shown in Fig.7 when the angle velocity has been settled as 1.11 rad/s Optimized velocity curve of end point(m/s) t(s) Figure 7. Velocity Curve of the End Point. Adjust the angle velocity according to the velocity curve described above. Equation (7) was used as the angle velocity function after lots of experiments. ω t = 0.6 t (7) Where is time and is angle velocity. We can get a smoother velocity curve than the Fig.6. The optimized angular velocity curve is shown in Fig.8, and the smoother velocity curve is shown in Fig.9. Figure 8. Angular Velocity Curve of the Active Lever. 133

7 25 20 velocity of the end point (m/s) t(s) Figure 9. Optimized Velocity Curve of the End Point This result will make the motor rotate more stable than before, be helpful to simplify the control strategy. Deformation and the Material Optimization There is centrifugal force when the mechanism rotates [5], both in linkage mechanism and propeller. Combined with the value of density, we can compare the deformation of each material and choose the most suitable material for the mechanism. Taking into account the materials used in aeronautic industry, such as aluminum, aluminum alloy, iron, titanium alloy and carbon fiber, the deformation of every material was studied by applying the same force. Young's modulus is a physical quantity that describes the ability of a solid material to resist deformation [6]. Density can reflect the weight of the material with the same volume. Table 2 shows the Young's modulus and the density of several materials that mentioned above, the simulation results are shown in Fig.10. Table 2. Basic Attributes of Commonly Used Materials in Aeronautic Industry. Materials Young's modulus[n/m 2 ] Density[kg/ m 3 ] Aluminum 0.70 X X10 3 Aluminum Alloy 0.72 X X10 3 ~2.75 X10 3 Iron 1.0 X X10 3 Titanium Alloy 1.10 X X10 3 Carbon Fiber 1.08 X X10 3 ~1.79 X10 3 (a) 134

8 (b) (c) (d) (e) Figure 10. The Deformation Results (a) Titanium Alloy (b) Carbon Fiber (c) Iron (d) Aluminum Alloy (e) Aluminum. According to the study mentioned above, the deformation results of each material are different with the same experiment conditions. The deformation in order from large to small is aluminum, aluminum alloy, iron, carbon fiber, titanium alloy. On the other hand, when the mechanism has a definite size, the weight of every material is different, either.the order from heavy to light is iron, titanium alloy, aluminum, aluminum alloy and carbon fiber. Considering the deformation, density, heat resistance and price, choose carbon fiber as the material of the propeller to suffer a high rotation speed. It is suitable to combine the titanium alloy and motor rotor, using the heat resistance of titanium alloy. The aluminum alloy is enough to be used on the motor seat and linkage mechanism. Based on the material has been chosen, the size of structure could be designed to resist the deformation. The length of the active lever must be smaller than 40mm and the length of the passive 135

9 lever should be set between 25mm and 30mm. Otherwise, the linkage mechanism could have deformation when it moves with a high speed. Simulation of Pressure in Fluid Field For simplifying the model of mechanism, only the propeller s states was considered in fluid field. Firstly, the relative air speed is set as18m/s, which is the cruise speed of our UAV, the angle velocity of propeller is rad/s. The pressure and velocity of propeller was simulated by setting the study called Frozen Rotor. The pressure is shown in Fig.11, which contains three different states of propeller. (a) (b) (c) Figure 11. The Pressure of Propeller (a) Rotate 0 Degree (b) Rotate 45 Degree (c) Rotate 90 Degree. The lines in Fig.11 are contours, the pressure value is equal on one contour, and we can obtain the size of the value based on the color.as we can see, the fluid in the vertical direction produces the greatest pressure when the relative speed is the same.therefore, the mechanism will suffer the biggest pressure at the fixed wing mode. Then, by changing the angle velocity of propeller, we can observe the relationship between angle velocity and pressure. The results are shown in Fig.12. (a) Figure 12. The Relationship between Propeller s Angle Velocity and Pressure (a) Angle Velocity =733.04rad/s (b) Angle Velocity=852.37rad/s. According to Fig.12 we can see when the fluid speed is constant, the value of pressure increases as the angle velocity of propeller increases. Finally, we can see the real states of air around propeller and the size of the air flow rate is shown intuitively in Fig.13.When the tilt-rotor UAV flight with a cruise speed about 18m/s and the angle velocity of the propeller is rad/s, the airflow rate of the propeller s tip can reach 80m/s. (b) 136

10 Conclusion (a) (b) Figure 13. The Velocity of Air (a) The Front View (b) The Side View. In this paper, the rotating mechanism has been simulated in COMSOL Multiphysics, which is a powerful tool to realize the simulation in multi-physics fields. Based on the results, an optimized suggestion for mechanism s material and motion strategy was proposed. As a primary study, the intuitive results of propeller s pressure was simulated. These study is helpful to investigate the motion of tilt-rotor UAV, and thus to simplify the control strategy by numerical guidance. Combined with the aeronautic industry and the actual demand, this study is proved to be effective. Acknowledgement We acknowledge Tiantian Feng for her contribution to the structural design of the rotating mechanism. References [1] Jia Cheng, Linhong Ji. Two-dimensional simulation of inductively coupled plasma based on COMSOL and comparison with experimental data[j]. Journal of Semiconductors, 2013, 34(6). [2] Liu Haixu, Qu Xiangju, Wang Weijun. Multi-body Motion Modeling and Simulation for Tilt Rotor Aircraft[J]. Chinese Journal of Aeronautics. 2010, 23:415~422. [3] Zhen hongzhong. Simulation of Bubbles Excited Acoustically in a Deformable Tube with COMSOL Multiphysics[C]. China: Beijing, 2014:13~17. [4] G.L.Ghiringhelli, P.Masarati, P.Mantegazza. Multi-Body Analysis of a Tiltrotor Configuration. Nonlinear Dynamics[J]. 1999, 19:333~357. [5] Flores P, Lankarani H M. Contact Force Models for Multibody Dynamics[J] [6] Jinwei Shen, Matt Floros, Myeong Kyu Lee, Jai Moo Kim. Multibody Dynamics Simulation of a Tiltrotor UAV[A]. In: The 2nd International Basic Research Conference on Rotorcraft Technology. China: Nanjing, 2005:7~9. 137