Analysis of a Casted Control Surface using Bi-Linear Kinematic Hardening

Transcription

1 Analysis of a Casted Control Surface using Bi-Linear Kinematic Hardening Abdul Manan Haroon A. Baluch AERO, P.O Box 91, Wah Cantt Pakistan Abstract Control Surfaces or Fins are very essential parts of any aircraft structures for its dynamic stability and controls. In this case an investigation is carried out for stress analysis on an aluminum fin, manufactured through sand casting. Pressure due to aerodynamic loads is applied at one face of the fin. It is known from the experimental tests that permanent deformation occurs in the fin, after unloading. A Bi-Linear Kinematic material model is taken, to account the material non-linearity in the analysis. Time varying load is applied over certain period of time. To check the results accuracy two different integration methods, i.e. full and reduced, are taken into account with tetra elements. After the solution, residual stresses and strains are plotted, growth and evolution of plastic strains is determined. Experimental tests are conducted on more than five samples, with same loading conditions. Results are compared with experimental test. These two analyses, experimental and FEM, finally leads to the acceptance criteria for quality check of sand casting. Introduction Control surfaces are used for horizontal and lateral stability of any aerospace vehicle. Aerodynamic loadings are constantly acting on these surfaces at different flight conditions. The experimental and FEM analyses of such a control surface or fin are taken into account to check its strength against severe aerodynamic load. Geometry of fin is modeled in Pro/Engineer software and then transferred to ANSYS software by using IGES file format, (See Figure 1). The origin of coordinate system CSYS_PRT is at the center of pivot hole, where Y positive towards up and Z positive normal to fin front face.

2 Figure 1. Fin Geometry Aerodynamic Loading and Distribution All the aerodynamics loadings are taken from the report (Reference 1) provided by the Aerodynamics Department, AERO. Maximum loading is considered in the analysis i.e. 2560N at angle of attack of 20 º. Load is distributed as pressure on front face of the fin. Surface area is around 42274mm 2, which makes the pressure of MPa. Pressure is applied as a function of time, (See Figure 2). Total time is taken 60sec, in which pressure gradually increses to its maximum value in first 10sec and then holds for another 30sec and then released. Figure 2. Load Distribution FEM Analysis By using ANSYS/Mechanical software, FEM analysis is done. To check the results accuracy three different cases of analysis are to be discussed. In all the three cases two different types of tetra elements are used. Bi-Linear kinematic hardening BKIN material model is used with the properties of a standard Aluminum LM 24 (Reference 2) where E = MPa, ν = 0.33, Yield Strength = 110MPa, and Elongation = 2%. The descriptions of cases are as follows; 1. Case 1: Solution by using Solid Case 2: Solution by using Solid 187 (pure displacement) 3. Case 3: Solution by using Solid 187 (mixed U/P)

3 Solid92 is a higher-order fully integrated conventional displacement element. For the past many years, ANSYS recommends 18x elements for non-linear applications. The comparison of results by using two different elements is discussed in later section. As the pure bending is acting, chances of volumetric and shear locking are predicted, so case 3 takes care of this situation. To converge the solution, tolerance for volumetric compatibility, Vtol (1e-2), is given by using SOLCONTROL command. Compatibility equations are as follows (Reference 3); P P K dv Vtol V where: P = Pressure P = Pressure DOF K = Bulk Modulus To find out the yield surface translation vector, following equations are taken into account (Reference 3). pl { α} = C{ dε } T 2EE C = T 3( E E ) where: { α } = Yield surface translation vector E = Young s Modulus E T = Tangent Modulus E pl = Equivalent Plastic Strain Motion is restrained in all directions at pivot hole of the fin, (See Figure 3). After applying loads, transient solution is done, by using DO loop, with increment of 5 sec. from 1e-6sec. to 60sec.

4 Figure 3. Mesh and BC Experimental Testing By taking five samples of casted fins, experimental testing is performed. Same loads distribution is applied as stated in earlier sections, i.e. by constraining from its pivot hole and pressure is applied over the time of 60sec. Displacement readings are taken over the testing duration by putting a displacement meter on tip of each fin. Analysis Results & Discussion Both FEM and experimental results show that maximum deflection ranges from 3.4mm to 4.8mm. In maximum cases it lies between 4.3m to 4.4mm and experimental results are conforming to those of FEM. Comparison of deflections over time varying load, maximum, and residual deflection values are plotted in different figures (See Figure 4, Figure 5, Figure 6, and Figure 7).

5 Figure 4. Usum Plot Figure 5. Deflection vs. Pressure

6 Figure 6. Comparison of Maximum Deflection Figure 7. Comparison of Permanent Deformation

7 As stresses are not mesasured during experimental testings, so only stress comparison for FEM cases are plotted here for a node, lies near the pivot hole of the fin (See Figure 8 and Figure 9). It shows that residual stresses are ranging from 41MPa to 52MPa. Maximum values have crossed the yield strength of 110Mpa at around 0.04MPa pressure. FEM Case 3 shows a slight bigger values of stresses and starins, both maximum and residual. It may be due to volumetric relexation of Vtol i.e., 1e-2. Yield surface translation vectors for FEM 1 and 2 are almost same (See Figure 10 and Figure 11). As stated earlier stresses and strains for FEM Case 3 have greater values than those of the other two cases, so same scenario lies in the case of translation vectors. Figure 8. Comparison of Equivalent Stresses

8 Figure 9 - Comparison of Equivalent Plastic Strains Figure 10 - Yield Surface Translation; FEM 1 & 2

9 Figure 11 - Yield Surface Translation; FEM 3 Conclusion As for as FEM cases are concerned, solid92 and solid187 elements, with pure displacement, are making a slight difference in results, which is negligible. FEM Case 3 gives a good exercise of using mixed U/P option, which shows that slight relaxation in volume tolerance can still lead to fair agreement of FEM and experimental results. From above exercise one can made the benchmark for the quality check of sand casting. FEM analyses show that permanent deformation should be less than 0.22mm. If maximum samples of a lot exhibit permanent deformation more than 0.22mm, during experimental testing, can be regarded as rejected. Results show that maximum equivalent stress is crossing the limit of yield and there is still a room for design improvement. References 1) M. A. Zeshan, CFD Analysis of Control Surface, 25 th January, 2003, Aerodynamics Department, AERO, Pakistan. 2) Anonymous, The Properties of Aluminum and its Alloys, ALFED Aluminum Federation Ltd. UK, Ninth Ed. August 1993, UK. 3) Anonymous, ANSYS 7.0 Theory Reference, ANSYS Inc., USA.