臺灣博碩士論文加值系統

直昇機之減振設計已是許多年來國外研究的課題之一，在主動式減振法當中最讓人感興趣的為高階諧模控制法 (Higher Harmonic Control (HHC))。這些控制輸出端賴於針對某一葉片做轉距角的調整，因此有獨立葉片控制法 (Individual Blade Control (IBC)) 產生。然而利用葉片根部的連桿來改變轉距角的傳統方法已漸漸不被採用了，取而代之的為機翼後緣的伺服襟翼。因此，本研究將建立一套整合葉片結構形變及後緣襟翼非穩態空氣動力環境的理論模式，利用耦合系統動態響應分析，以提供新一代直昇機設計的資訊及高階諧模控制 (HHC) 減振技巧參考的數據。本研究將建立一套整合直昇機主旋翼之複材結構葉片、尾流 (wake) 造成之誘導流 (induced flow) 及允許機翼後緣襟翼做任意角度調整之空氣動力流場的耦合模式。並進而分析這一套耦合系統在直昇機懸停時，隨著後緣襟翼角度的改變對於整個主旋翼氣體彈性系統之影響。本研究將著眼於系統的動態響應分析，據筆者所知，目前尚無任一項研究建立在後緣襟翼變化對整個耦合系統影響之理論分析。本研究將可對這一項直昇機主旋翼的裝置做一較深入的理論研究，相信對於其後續發展將提供許多重要資訊。

目 錄
中文摘要………………………………………………………………..I
英文摘要………………………………………………………………III
目 錄 V
圖目錄 VII
表目錄 IX
第一章 緒論 1
一、1研究動機 1
一、2文獻回顧 4
第二章 複材彈性葉片─尾流耦合模式之建立 11
二、1 複材葉片結構動力方程的推導 11
二、1.1 弦向 (擺振向lead-lag) 類非線性方程之比較 16
二、1.2 揮舞向 (flapping) 類非線性方程式之比較 17
二、1.3 扭轉 (torsional) 之類非線性方程比較 18
二、2 葉片上空氣動力表示式之推導 20
二、2.1 葉片上的空氣動力表示式之推導 20
二、2.2 後緣襟翼之空氣動力流場 23
二、3 尾流函數 32
第三章 複材葉片─尾流耦合方程式 33
三、1 類非線性耦合方程式之展開 33
三、2 複材葉片─尾流耦合方程式 33
三、3 類非線性複材葉片振動模態之建立 35
三、4 複材葉片動態耦合方程之求解 39
三、4.1 題目之敘述 39
三、4.2 動態耦合方程之求解 39
第四章 結果與討論 42
四、1 Peters TEF模式之比較 42
四、2 等向均質葉片之結果 43
四、3 複材葉片之結果 45
第五章 結論 49
五、1 結論 49
五、2 未來的研究方向 50
附錄一、 後緣襟翼 Matrix Form (Eq.17) 之相關參數定義 51
附錄二、動態響應方程式外力項有關所有空氣動力的展開 52
附錄三、均質葉片比較函數 63
附錄四、NACA 0012 葉片翼剖面動態失速之函數參數 65
參考文獻 98
圖目錄
圖一、空氣動力座標 66
圖二、後緣襟翼的幾何位置圖 67
圖三、後緣襟翼及葉片示意圖 68
圖四、TEF在不同弦向位置時的升力與Garrick之比較 69
圖五、TEF在不同弦向位置時的扭力矩與Garrick之比較 70
圖六、不同的襟翼角所造成的扭矩與實驗值之比較圖 71
圖七、TEF每單位襟翼角所造成之扭矩的理論及實驗比較圖 72
圖八、襟翼角所造成的升力影響 73
圖九、RPM所造成的升力影響 74
圖十、TEF的中心位置在0.7R、0.75R、0.8R時襟翼角對扭力矩之影響 75
圖十一、TEF的中心位置在0.7R、0.75R、0.8R時RPM對扭力矩之影響 76
圖十二、TEF的中心位置向外移 (0.7R~0.75R~0.8R) 襟翼角的改變對升力的影響 77
圖十三、TEF的中心位置向外移 (0.7R~0.75R~0.8R) RPM的改變對升力的影響 78
圖十四、不同TEF鉸接點扭力矩相對襟翼角的結果 79
圖十五、不同TEF鉸接點扭力矩相對RPM的結果 80
圖十六、不同TEF鉸接點升力相對襟翼角的結果 81
圖十七、不同TEF鉸接點升力相對RPM的結果 82
圖十八、不同襟翼角時的等長複材及均質葉片升力之比較 83
圖十九、升力在不同RPM的等長複材及均質葉片升力之比較 84
圖二十、不同襟翼角時等長複材及均質葉片的扭力矩比較 85
圖二十一、不同RPM時等長複材及均質葉片的扭力矩比較 86
圖二十二、複材葉片TEF在不同鉸接位置襟翼角對升力的影響 87
圖二十三、複材葉片TEF在不同鉸接位置RPM對升力的影響 88
圖二十四、複材葉片TEF在不同鉸接位置襟翼角對扭力矩的影響 89
圖二十五、複材葉片TEF在不同鉸接位置RPM對扭力矩的影響 90
圖二十六、複材葉片TEF中心在不同翼展位置襟翼角對升力的影響 91
圖二十七、複材葉片TEF中心在不同翼展位置RPM對升力的影響 92
圖二十八、複材葉片TEF中心在不同翼展位置襟翼角對扭力矩的影響 93
圖二十九、複材葉片TEF中心在不同翼展位置襟翼角對扭力矩的影響 (放大圖) 94
圖三十、複材葉片TEF中心在不同翼展位置RPM對扭力矩的影響 95
表目錄
表一、兩個葉片旋翼的參考數據 Ref.[8] 96
表二、選用的複材資料 97

[1] McCloud ,J.L.Ⅲ, “An Analytical study of a Multicyclic Controllable Twist Rotor,” AHS Forum, 1975.
[2] McCloud, J.L.Ⅲ, and Weisbrich ,A.L., “Wind-Tunnel Test Results of a Full-Scale Multicyclic Controllable Twist Rotor,” AHS forum, 1978.
[3] McHugh , F.J., and Shaw , J., Jr , “Benefits of Higher-Harmonic Blade Pitch : Vibration Reduction, Blade Load Reduction, and Performance Improvement, ” American Helicopter Society Mideast Region Symposium on Rotor Technology , Essington , PA, August, 1976.
[4] Gates A.A., Adrezin, R.S., and Wei, F.-S., ”Servo-Flap Rotor Power Improvement Though Wind Tunnel Testing,” AHS. 55th Annual Forum, Montreal ,Quebec, Canada, May 25-27,1999.
[5] Gates, A.A., Adrezin, R.S., and Wei, F.-S., ”Thin Body Shape Optimization Technique Using Wind Tunnel Test Data,” AIAA paper, AIAA-99-0836,1999.
[6] Wei, F.-S., “Advanced Servo-Flap Rotor Using Variable Blade Index Angle Control,” 38th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, & Materials, Kissimmee, Florida, April 7-10, 1997.
[7] Wei F.-S., and Tomashofski, C.A., “HHC and IBC For a Servo-Flap Controlled Main Rotor,” the 7th International Workshop on Dynamics and Aeroelastic stability modeling of Rotor craft Systems, St. Louis, Missouri, October, 14-16, 1997.
[8] Fulton, M.V., and Ormiston, R.A., “Hover Testing of a Small-Scale Rotor with On-Blade Elevons, ” Journal of the AHS, April, 2001, pp.96-106.
[9] Nikhil, A.K., and Chopra, I., “Open-Loop Hover Testing of a Smart Rotor Model,” AIAA Journal, Vol. 40, No.8, August, 2002, pp. 1495-1502.
[10] Kurdila, A.J, Li, J., Strganac, T., and Webb, G., “Nonlinear Control Methodologies for Hysteresis in PZT Actuated On-Blade Elevons,” Journal of AerospaceEngineering, October, 2003, pp.167-176.
[11] Shang, X., Hodges, D.H., and Peters, D.A., “Aeroelastic Stability of Composite Hingeless Rotors in Hover with Finite-State Unsteady Aerodynamics,” Journal of the American Helicopter Society, Vol. 44, No.3, July 1999, pp. 206-221.
[12] de Andrade, D., and Peters, D. A., “Correlation of Experimental Flap-Lag-Torsion Damping - A Case Study,” Mathematical and Computer Modeling - Rotorcraft Modeling, Part II, Pergamon, pp. 135~158, 1994.
[13] Donizeti de Andrade, “Application of Finite-State Inflow to Flap-Lag-Torsion Damping in Hover,” Ph. D. Thesis, School of Aerospace Engineering, Georgia Institute of Technology, May, 1992.
[14] Pai, P. F., and Nayfeh, A. H., “Fully Nonlinear Theory of Curved and Twisted Composite Rotor Blades According for Warpings and Three-Dimensional Stress Effects,” International Journal of Solids and Structures, Vol.31., No.9, pp.1309-1340, 1994.
[15] Gray, R. B., “On the Motion of Helical Vortex Shed from a Single-Bladed Hovering Helicopter Rotor and Its Application to the Calculation of the Spanwise Aerodynamic Loading,” Princeton University, Aeronautical Engineering Report No. 313, Sept. 1955.
[16] Gray, R. B., “An Aerodynamic Analysis of a Single-Bladed Rotor in Hovering and Low Speed Forward Flight as Determined from Smoke Studies of the Vorticity Distribution in the Wake,” Princeton University, Aeronautical Engineering Report No. 356, Sept. 1956.
[17] Landgrebe, A. J., “An Analytical and Experimental Investigation of Helicopter Rotor Performance and Wake Geometry Characteristics,” USAAMRDL Technical Report 71-24, Eustis Directorate, U.S. Army Air Mobility Research and Development Laboratory, Ft. Eustis, Virginia, June 1971.
[18] Kocurek, J.D., A Lifting Surface Performance Analysis with Circulation Coupled Wake for Advanced Configuration Hovering Rotors, Ph.D. Thesis, Texas A & M University, May 1978.
[19] Summa, J.M., Potential Flow about Three Dimensional Lifting Configurations with Application Wings and Rotors, AIAA paper 75-126, January, 1975.
[20] Summa, J.M., and Clark, D.R., A Lifting Surface Method for Hover and Climb Airloads, Paper presented at Annual National Forum of the American Helicopter Society, May 1979.
[21] Bridgeman, J.O., Strawn, R.C., and Caradonna, F.X., An Entropy and Viscosity Corrected Potential Method for Rotor Performance Prediction, Paper presented at the 44th Annual National Forum of the American Helicopter Society, 1988.
[22] Chen, C.S., Bridgeman, J.O., Three Dimensional Viscous Rotor Flow Calculations Using a Viscous-Inviscid Interaction Approach, NASA TM 102235, February, 1990.
[23] Ormiston, R. A., and Peters, D. A., "Hingeless Helicopter Rotor Response with Nonuniform Inflow and Elastic Blade Bending," Journal of Aircraft, Vol.9., No. 10, October, 1972.
[24]Ormiston, R. A., "Application of Simplified Inflow Models to Rotorcraft Dynamic Analysis," Journal of the American Helicopter Society, Vol. 21, No.3, July, 1976, pp. 34 - 37.
[25] Peters, D. A., "Hingeless Rotor Frequency Response with Unsteady Inflow," Rotorcraft Dynamics, NASA SP-352, 1974.
[26] Hodges , D. H., “Nonlinear Equations of Motion for Cantilever Rotor Blades in Hover with Pitch-Link Flexibility, Twist, Precone, Droop, Sweep, Torque Offset and Blade Root Offset,” NASA TM X-73,112, May, 1976.
[27] Hodges , D. H. and Dowell , E. H., “Nonlinear Equations of Motion for the Elastic Bending and Torsion of Twisted Nonuniform Rotor Blades,” NASA TN D-7818, December, 1974.
[28] Hodges, D. H., Crespo da Silva, M. R. M., and Peters, D. A., “ Nonlinear Effects in the Static and Dynamic Behavior of Beams and Rotor Blades ,” Vertica, Vol. 12, pp.243-256, 1988.
[29] Clark, D. R., and Leiper, A. C., “The Free Wake Analysis - A Method for the Prediction of Helicopter Rotor Hovering Performance,” the 25th Annual National Forum of the American Helicopter Society, Washington, D. C., May, 1969.
[30] Sadler, S. G., “Development and Application of a Method for Predicting Rotor Free Wake Positions and Resulting Rotor Blade Airloads, “NASA CR-1911 Vol. I; Model and Results, NASA CR-1912, Program Listing, 1971.
[31] Landgrebe, A. J., “An Analytical Method for Predicting Rotor Wake Geometry,” Journal of the American Helicopter Society, Vol. 14, No.4, October, 1969.
[32] Landgrebe, A. J., “The Wake Geometry of a Hovering Helicopter Rotor and Its Influence on Rotor Performance,” Journal of the American Helicopter Society, Vol. 17, No.4, October, 1972.
[33] Peters, D. A., Boyd, D. D., and He, C. J., "Finite State Induced Flow Model fo Rotors in Hover and Forward Flight," Journal of theAmerican Helicopter Society, Vol. 34, No.4, October, 1989.
[34] He, C. J., “Development and Application of a Generalized Dynamic Wake Theory for Lifting Rotors,” Ph. D. Thesis, School of Aerospace Engineering, Georgia Institute of Technology, July, 1989.
[35] Peters, D. A., and He, C. J., "Comparison of Measured Induced Velocities with Results From a Closed Form Finite State Wake Model in Forward Flight," the 45th Annual National Forum of the American Helicopter Society, Boston, Massachusetts, May 22-24, 1989.
[36] Wang, Y.-R., “The Effect of Wake Dynamics on Rotor Eigenvalues in Forward Flight,” Ph. D. Thesis, School of Aerospace Engineering, Georgia Institute of Technology, May, 1992.
[37] Wang, Y.-R., and Peters, D.A., '''' The Lifting Rotor Inflow Mode Shapes and Blade Flapping Vibration System Eigen-Analysis," Computer Methods in Applied Mechanics and Engineering,Vol. 134, pp.91-105, 1996.
[38] Wang, Y.-R., '''' The Frequency Response on Lift of Helicopter Rotor Blade Flapping with Three-Dimensional Wake Effect in Forward Flight," Transactions of the Aeronautical and Astronautical Society of the Republic of China, Vol. 26, No.4, pp. 299-309, 1994.
[39] 王怡仁，“三維尾流及旋翼葉片拍撲-延遲-扭轉耦合模式之建立及應用-II，”國科會結案報告。NSC Contract. Contract No. NSC 88-2212-E-032-006. July 1999.
[40] 王怡仁，唐鵬駿，彭暉元，“三維尾流及非線性旋翼葉片耦合模式之葉片弦向阻尼分析”，中華民國航空太空學會第四十一屆學術研討會，桃園 龍潭 中正理工學院, December 1999.
[41] Hirsch, C., Numerical Computation of Internal and External Flows, John Wiley & Sons, 1988.
[42] 王怡仁, 蔡健民, 楊文中, "尾流效應對直昇機前飛時旋翼彈性葉片之影響," 中華民國航空太空學會第三十七屆學術研討會, 淡水 淡江大學, December, 1995.
[43] 王怡仁, 張 立, "直昇機旋翼在前飛及滯空時相對於不同的葉片弦長之空氣動力分析," 中華民國航空太空學會第三十七屆學術研討會, 淡水 淡江大學, December, 1995.
[44] 張永康, 王怡仁, 洪健君 "直昇機滯空時旋翼葉片之最佳化設計," 中華民國航空太空學會第三十七屆學術研討會, 淡水 淡江大學, December, 1995.
[45] 王怡仁, 張永康, 洪健君 "前飛時直昇機旋翼葉片外形最佳化設計及性能分析,"中華民國力學學會第十九屆學術研討會,桃園 中正理工學院, December, 1995.
[46] 王怡仁,"A Flapping Mode Identification of Rotary Wing Blades and Wake Coupled System in Forward Flight," 第一屆海峽兩岸航太科技研討會,淡水 淡江大學, December, 1995.
[47] 王怡仁, "直昇機旋翼尾流力學之理論發展及其背景," 第一屆海峽兩岸航太科技研討會, 淡水 淡江大學,December, 1995.
[48] Su, A., and Wang, Y.-R., "The Effect of Wake Dynamics on Rotor Elastic Flap-Lag Damping in Hover and Forward Flight," presented at the 2nd Pacific International Conference on Aerospace Science and Technology, Melbourne Australia, March, 20-23, 1995.
[49] Wang, Y.-R., Lee, S.-M., and Tsai, J.-M., "A Numerical Simulation of Helicopter Rotor Blade Flapping and Wake Vibrating Mode Shapes," presented at the 36th Conference of Aeronautical and Astronautical Society of the Republic of China, December, 1994.
[50] Wang, Y.-R., "The Frequency Response of Helicopter Rotor Blades and Three-Dimensional Unsteady Wake Coupled Systems in Vertical and Forward Flight," presented at the Japan Society for Aeronautical and Space Sciences 8th Aircraft Symposium International Sessions, Kitakyushu, Japan, October 5-7, 1994.
[51] Wang, Y.-R., "An Eigen-Analysis of Rotary Wing Blades and Wake Coupled System with the Finite-State Inflow Model," presented at the 1st Pacific International Conference on Aerospace Science and Technology, National Cheng Kung University, Tainan, Taiwan, R. O. C., December, 1993.
[52] Wang, Y.-R., and Peters, D. A., " The Effect of Wake Dynamics on Rotor Eigenvalues in Forward Flight," presented at the Fourth Workshop on Dynamics And Aeroelastic Stability Modeling of Rotorcraft Systems, University of Maryland, College Park, Maryland, November, 1991.
[53] Wang, Y.-R., and Tsai, J.-M., "A Study of Wake Effects on Elastic Helicopter Rotor Blades by Using Floquet Theory," the Japan Society for Aeronautical and Space Sciences 9th Aircraft Symposium International Sessions, Hiroshima, Japan, November 8-10, 1995.
[54] Wang, Y.-R. , and Yang, W.-C., " Frequency Response of The Wake Oscillation on An Elastic Bladed Flapping Rotor," Journal of The Chinese Society of Mechanical Engineers，Vol. 20, No.4, pp. 399-408, 1999.
[55] Tang, D., and Dowell, E.H., “Damping Prediction for a Stalled Rotor in Flap-Lag with Experimental Correlation,” Journal of the American Helicopter Society, Vol. 40, No.4, October 1995, pp. 79-89.
[56] Tang, D., and Dowell, E.H., “Damping Prediction for Hingeless Rotor Aeroelastic Stability with Experimental Correlation,” Journal of Aircraft, Vol. 33, No.6, November-December 1996, pp. 1071-1078.
[57] Tang, D., and Dowell, E.H., “Nonlinear Rotor Aeroelastic Analysis with Stall and Advanced Wake Dynamics,” Journal of Aircraft, Vol. 34, No.5, September-October 1997, pp. 679-687.
[58] Barwey, D., and Gaonkar, G.H., “Dynamic-Stall and Structural-Modeling Effects on Helicopter Blade Stability with Experimental Correlation,” AIAA Journal, Vol. 32, No.4, April 1994, pp. 811-819.
[59] Chunduru, S.J., Subramanian, S., and Gaonkar, G.H., “Dynamic Stall and Wake Effects on Trim and Stability of Hingeless Rotors with Experimental Correlation,” Journal of the American Helicopter Society, Vol. 42, No.4, October 1997, pp. 370-382.
[60] S. Subramanian, G. H. Gaonkar, S. J. Chunduru, “Dynamic Stall and Wake Effects on Trim and Stability of Hingeless Rotors with Experimental Correlation”, Department of Mechanical Engineering, Florida Atlantic University, Boca Raton, FL33431, October 1997.
[61] Nagabhushanam, J.,and Gaonkar, G. H., “Hingeless Rotors Aeromechanical Stability in Axial and Forward Flight with Wake Dynamics”, Journal of the American Helicopter Society, Vol.44, 1999, pp. 222-233.
[62] Greenberg, J.M., “Airfoil in Sinusoidal Motion in a Pulsating Stream,” NACA TN 1326, June 1947.
[63] Garrick, I.E., “Propulsion of Flapping and Oscillating Airfoil,” NACA TR567, May 1936.
[64] Abourahma, Ahmed Ali Mohammed Hassan, The Analysis of Wake-Induced Unsteady Aerodynamics as Related to Higher Harmonic Control, Ph.D. Dissertation, Naval Postgraduate School, December 1993.
[65] Peters, D.A., and Johnson, M.J., ”Finite-State Airloads For Deformable Airfoils on Fixed and Rotating Wings,” AD-Vol.44, Aeroelasticity and Fluid Structure Interaction Problems, ASME, 1994, pp.1~28.
[66] Sharpe, D. L., “An Experimental Investigation of the Flap-Lag-Torsion Aeroelastic Stability of a Small-Scale Hingeless Rotor in Hover,” NASA TP-2546, January, 1986.
[67] Hodges, D. H., Atilgan, A. R., Cesnik, C. E. S., and Fulton, M. V., “ On A Simplified Strain Energy Function for Geometrically Nonlinear Behavior of Anisotropic Beams,” Composite Engineering Vol. 2, 513-526, 1992.
[68] Pai, P. F., and Nayfeh, A. H., “Three-Dimensional Nonlinear Vibrations of Composite Beams - I. Equations of Motion,” Nonlinear Dynamics 1, Kluwer Academic Publishers, pp.477-502, 1990.
[69] Pai, P. F., and Nayfeh, A. H., “Three-Dimensional Nonlinear Vibrations of Composite Beams - II. Flapwise Excitations,” Nonlinear Dynamics 2, Kluwer Academic Publishers, pp.1-34, 1991.
[70] Pai, P. F., “Nonlinear Flexural-Flexural-Torsional Dynamics of Metallic and Composite Beams,” Ph. D. Thesis, Dept. of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA, April, 1990.
[71] Pai, P. F., and Nayfeh, A. H., “A Nonlinear Composite Beam Theory,” Nonlinear Dynamics 3, Kluwer Academic Publishers, pp.273-303, 1992
[72] Pai, P. F., and Palazotto, A. N., “Large-Deformation Analysis of Flexible Beams,” International Journal of Solids and Structures, Vol.33., No.9, pp.1335-1353, 1996.
[73] Pai, P. F., Anderson, T. J., and Weather, E. A., “Large-Deformation Tests and Total-Lagrangian Finite-Element Analysis of Flexible Beams,” International Journal of Solids and Structures, Vol.37., No.21, pp.2951-2980, 2000.
[74] Crespo da Silva, M. R. M., “A Comprehensive Analysis of The Dynamics of A Helicopter Rotor Blade,” International Journal of Solids and Structures, Vol. 35, No. 7-8, pp. 619-635., 1998.
[75] 王怡仁，彭暉元，唐鵬駿，"三維尾流及非線性旋翼葉片耦合模式之葉片弦向阻尼分析"，中華民國航空太空學會第四十一屆學術研討會，桃園 龍潭 中正理工學院, December, 1999.
[76] 王怡仁，唐鵬駿，"三維尾流及旋翼葉片拍撲-延遲-扭轉耦合模式之建立及應用- I. 均質穩態之模擬"，中華民國航空太空學會第四十屆學術研討會，台中 逢甲大學, December, 1998.
[77] 李明峰，“動態失速下主旋翼懸空及前飛時的平衡態分析,” 淡江大學航太系碩士班碩士論文，民國八十九年六月。
[78] Jeon, S.-M., and Lee, I., “Aeroelastic Analysis of a Hingeless Rotor Blade in Forward Flight,” AIAA Journal, Vol.38, No.5, May 2000, pp. 843-850.
[79] Pai, P. F., “Nonlinear Flexural-Flexural-Torsional Dynamics of Metallic and Composite Beams,” Ph. D. Thesis, Virginia Polytechnic Institute and State University, April, 1990.