The Dynamic Characteristics Analysis of Rotor Blade Based on ANSYS

Transcription

1 The Dynamic Characteristics Analysis of Rotor Blade Based on ANSYS Nian-zhao Jiang, Xiang-lin Ma, Zhi-qing Zhang The Research Institute of Simulation Technology of Nanjing, No. 766 Zhujiang Road, Nanjing,210016, PR China Abstract: The three-dimension finite element model of helicopter rotor blade has been built with APDL language. Then using this model, the static strength and the dynamic characteristics about rotor blade has been analyzed with ANSYS software package. During the analysis of dynamic characteristic, the influence of aerodynamic force and centrifugal force applying to blade has been totally considered. Furthermore, the resonant chart of rotor blade has been presented in this paper. Introduction The dynamic characteristics analysis of rotor blade is mainly involved in the calculation about natural frequency and modal shape. The objective to calculate the natural frequency and modal shape of rotor blade is modulating those frequencies and avoiding resonance at rotational speed, thus the vibration level of helicopter may reduce. There are many methods to compute the natural frequency of rotor blade, such as the method about calculating vibration characteristics of non-uniform beam. Because of the complex structure about rotor blade, such as three-dimension elasticity with minus twist angle, taper tip and complex blade root configuration, and modeling is difficult. A general dynamic characteristic analysis about rotor blade is simplified the blade by a one-dimension beam. In other words, the theory for dynamic characteristics analysis about rotor blade is simplified the blade, viz. simplified infinite DOF vibration by finite DOF vibration, or applying some displacement function to simulate the modal shape of rotor blade or dividing the rotor blade into finite element. In terms of the theory, many methods are applied to calculate the natural frequency, such as Lagrange's method, Rayleigh's method, Galerkin's method, three-moment equation method, matrix transfer method and dynamic finite element method. If the number of element is enough, the result of computing is satisfactory. Now the dynamic finite element method has been in wide use. Based on those methods, a lot of analytic software about helicopter is developed, such as CAMRAD, UMARC, 2GCHAS and FLIGHT LAB [1][2]. Because of the different of emphasizing particularly on and developing time, calculation results are different. But these results can fit the dynamic characteristics analysis of rotor blade well. In the other hand, these softwares need much specialty knowledge about helicopter and finite element; they are not applicable to common CAE technician. So it is necessary to apply general CAE software to analyze and compute the dynamic characteristics analysis of rotor blade. Type structure about rotor blade is three-dimension elastic with minus twist angle, taper tip and made up of composite material, it is difficult to built geometric model about rotor blade. Moreover, rotor blade performs complex flights, such as rotating round the rotor shaft of helicopter, level flight and hovering so on, and that the load applying to rotor blade is complex, thus 3-D FE model to fit flight state of rotor blade is difficult to built too. On the other hand, using 3-D finite element model, the analysis may consume much more CPU times, and that modeling and loading are not easy to be modulated, thus three-dimensional model and dynamic characteristics analysis of rotor blade have not been in wide use before. A general method of dynamic characteristic analysis about rotor blade was simplified the blade by a one-dimension beam. As every mechanical engineer knows that a perfect geometric model and mechanical model may play a key role in analyzing and computing the dynamic characteristics of structure, so this method can't simulate the state of rotor blade truly. With APDL language, complex geometric model and mechanical model are easy to built in ANSYS software. In this paper, the three-dimension finite element model of helicopter rotor blade has been built with APDL language, and analysis to strength and dynamic characteristics of rotor blade has been developed.

2 Modeling Just like other analysis about structure, the dynamic characteristics analysis about helicopter rotor blade must build exact structural modeling and apply true load too. Load analysis The mainly loads applying in rotor blade of helicopter are aerodynamic force and inertial force. When helicopter performs motion, such as forward flight, hovering, level flight, sideward flight and backward flight, the movement of flapping, lagging and twisting occurs in blade. Furthermore, these movements are coupled each other. That is to say, precision load is not easy to apply; the lower step loads are difficult especially. In this paper, the centrifugal force is computed by. where, ρ = 2 F = ρω r R 0 ra( r) dr 3 Density ( Kg / m ) of rotor blade, A (r) = 2 m ) of section where distance to rotor shaft is r, area ( ω = rotational speed ( radian / s ) of rotor blade, r 0 = distance (m) between root blade to rotor shaft, R = radius (m) of rotor blade. Inputting rotational speed and material properties, it's easy to apply centrifugal force with APDL language in ANSYS. These commands can be use, such as: mp,dens,1,5e3 omega,100 The aerodynamic force of blade includes: aerodynamic force and moment about center of rotor blade's gravity. They are computed by (1) Fx H Fy = T F S z MR (2) where, subscript "MR" represents the coordinate system of reference frame of fuselage, the other is reference frame of right-handed coordinate system.

3 Formula (2) is the computing equation of force. The left hand side of equation represents the force of x, y and z direction at reference frame of fuselage coordinates, and ( H, T, S ) represents the force at reference frame of right-handed coordinates, viz. H represents rearward-pointing component of rotor, T represents thrust of rotor, and S represents sideward-pointing component of rotor. Mx Mx 0 zmr ymr Fx M y Q zmr 0 x = + MR Fy M z M z ymr xmr 0 F z MR where, ( x MR, y MR, z MR ) is the position which calculates the force and moment at reference frame of fuselage; the other symbol is the same as formula (2). Formula (3) is the computing equation of moment. The left hand side of equation represents the moment of x, y and z direction at reference frame of fuselage coordinates, Q represents rotor-shaft torque, and others are moments at reference frame of right-handed coordinate system. MR (3) Three-dimension finite element model Rotor blade of helicopter is made up of composite material. Type rotor blade is composed of crossbeam, cover skin, foam core and back edge. Each constituted structure is different material and the direction of each fiber is different too. So rotor blade is anisotropic, and has different material property. These different are not easy to embody and model. In addition, rotor blade is three-dimension elasticity with minus twist angle and taper tip. In theory, the stiffness of composite material is not the simple summation of stiffness of EI each constituted material, viz. EiI. On the other hand, the interlaminar constrainer has little effect on stiffness ( < 2% ), so the interlaminar constrainer can be ignored. So in engineering, section EI = characteristic and the stiffness of rotor blade are still deal with material mechanics, viz. EiI, and built the model of rotor blade with equivalent Young s Modulus E, equivalent Poisson s Ratio µ and equivalent density ρ. This paper calculated the property of blade-section and got the equivalent Young s Modulus E, equivalent Poisson s Ratio µ and equivalent density ρ. In ANSYS software, the three-dimension finite element model of helicopter rotor blade has been built with APDL language for the first time. As applying the APDL, minus twist angle and taper tip are easy to model. Figure 1 is three-dimension structure with APDL language in ANSYS. Figure 2 is the three-dimension finite element model. There are elements and nodes with SOLID185 element.

4 Figure 1. Three-dimension structure of rotor blade Figure 2. Three-dimension finite element model of rotor blade Strength Analysis In other References, the analysis of rotor blade was worked on as a beam. It's not enough to simulate the blade's flying state. This paper has built the three-dimension model of rotor blade and considered the influence of aerodynamic force and centrifugal force to strength. Figure 3 is deforming chart and figure 4 is Von Mises stress chart. The maximum stress locates at blade root where is dangerous as figure 4 show. Although blade root's centrifugal force is lower than other location, but the area of section is smaller than other, thus the average stress of blade root is maximum stress that caused by centrifugal force. What's more, the blade root connect hub, leading to the force route and the stiffness break, which is the source of stress concentration. So especial attention must be provided to blade root. Aimed at the stress concentration, some techniques must be taken.

5 Figure 3. Deforming of rotor blade Figure 4. Von Mises of rotor blade

6 Dynamic Characteristics Analysis In order to avoid the resonance, the designer must calculate the natural frequency and modal shape of rotor blade and analyze dynamic characteristics. The first three step flapping and lagging natural frequency and modal shape should be focused on, because those natural frequency and modal shape are mainly influence on dynamic characteristics of rotor blade. What's more, they are enough to avoid the resonance of helicopter. The boundary condition of flapping blade is different from lagging blade while analyzing and computing, Flapping constrainer is fix support and lagging constrainer is pin support. Furthermore, the influence of aerodynamic force and centrifugal force on dynamic characteristics about rotor blade is totally considered. The reason is that the stiffness of blade is influence by aerodynamic force and centrifugal force and the natural frequency and modal shape by the stiffness. Thus, this paper may simulate the rotational state of rotor blade truly. With ANSYS software, pre-stress modal analysis can simulate those loads by APDL language and the command can be applied, Such as: "pstres,on" The natural frequency at rating rotational speed and frequency ratio are shown as table 1. With those results, the blade's natural frequency avoided the resonance. Table 1. The natural frequency at rating rotational speed Mode Flap Frequency(HZ) Frequency ratio Lag Frequency(HZ) Frequency ratio

7 Figure 5. Flapping mode shape 1 of rotor blade Figure 6. Flapping mode shape 2 of rotor blade

8 Figure 5, 6, 7, 8 are the first three step mode shape of flapping and lagging. Figure 7. Flapping mode shape 3 of rotor blade Figure 8. Lagging mode shape 1 of rotor blade

9 Figure 9 is the resonant chart of blade flapping and figure 10 is resonant chart of blade lagging. Figure 9. The resonant chart of blade flapping

10 Figure 10. The resonant chart of blade lagging Conclusions 1) In this paper, the three-dimension finite element model of rotor blade has been built with APDL language. Using ANSYS software package, the static strength and the dynamic characteristics have been analyzed. The result is more accurate than before, because the aerodynamic force and centrifugal force have been reckoned in to the FEM of rotor blade. Based on the dynamic characteristic result, the rotor blade has been designed and manufactured. Using this rotor blade, the flight-testing of helicopter has been successful. It's also shown that the modeling and analysis method about rotor blade are feasible. 2) The blade root is easy to fail. The reason is that the maximum stress locates at blade root, as shown figure 4. It is the place where one must pay more attention to. With the method of modulating frequency, the rotor blade can avoid the resonance in the working rotational speed. 3) Applying the FEA with ANSYS software, the design cycle of rotor blade has been shortened; the expense of test outlay has been saved; the effect is marked. In conclusion, the analysis of the dynamic characteristics about rotor blade with ANSYS is feasible and provides a new field of applying ANSYS software too. Furthermore, the result of calculating by ANSYS is helpful to flight-testing of helicopter. References [1] Hodges, D. H., Review of Composite Rotor Blade Modeling AIAA Journal, Vol.28. No pp 561~565. [2] Johnson, W., Rotorcraft dynamics models for a comprehensive analysis, Presented at the 54th Annual Forum of the AHS, Washington, DC, May 20-22,1998

11 [3] ANSYS, Inc. ANSYS Structural Analysis Guide Release 7.0 [4] ANSYS, Inc. ANSYS Basic Procedure Guide Release 7.0