The Study of Three-Dimensional Tank Dynamics 石珈豪、陳志鏗
E-mail: [email protected]
ABSTRACT
This thesis develops the mathematical models of tank motion for the applications of real-time simulation. Three dimensional models including hull, turret and barrel are deduced by the Euler-Lagrange equations in quasi-velocity. The contact points between the road wheel and the road surface are computed. To reduce the load of real-time computation, all the forces from the ground are assumed to concentrate on the tracks under the ground wheels. The normal force and frictional force at these contact points are computed to simulate the tractive and braking behavior of the tank dynamics. The model developed is verified in a case of computer simulations.
The symbolical mathematical software MAPLE is used to derive the equations of motion. The different computation simulations are given to test the applicability of the dynamical model. Some of the simulation results are compared and verified with those from ADAMS.
Keywords : Tank ; contact force ; quasi-velocity ; real-time simulation Table of Contents
第一章 緒論 ...1 1.1前言 ...1 1.2文獻回顧
...2 1.3研究目的與本文架構 ...6 第二章 三維坦克車輛系統數學模式 ...9 2.1坦克車輛系統簡介 ...9 2.2運動方程式推導 ...12 2.2.1 座標系統轉換矩陣之定義 ...12 2.2.2八自由度數學模式推導 ...18 2.2.3七自由度數學模 式推導 ...25 2.3地輪接觸點位置與作用力推導 ...27 2.3.1 地輪接觸平面分析
...28 2.3.2承載系統幾何關係 ...30 2.3.3接觸平面判斷
...33 2.4坦克車輛行駛作用力之計算 ...35 2.4.1地輪與履帶簡化模式 ...36 2.4.2地輪與地面接觸力之推導 ...38 第三章 坦克車輛之數值模擬
...41 3.1程式架構 ...42 3.2數值模擬與驗證 ...44 3.3三維 路面資料庫之建立 ...49 3.4接觸作用驗證 ...52 第四章 坦克車輛電腦模型 建立 ...57 4.1質量特性與參數定義 ...57 4.2運動條件設定
...59 4.2.1設定限制條件 ...59 4.2.2地輪承載系統參數建立與設定 ...60 4.2.3 地輪與路面間接觸碰撞力之設定 ...62 4.3地輪單一承載系統模型
...65 第五章 模擬結果分析與驗證 ...67 5.1數學模型與電腦模型之數值模擬驗證 ...67 5.2不同路面之直線行駛加速與減速 ...72 5.3坦克車輛行駛於上下坡地形
...79 5.4轉向彎行 ...85 5.5砲彈射擊 ...91 第六章 結 論 ...97 參考文獻 ...99 附錄A 三維坦克車輛系統之物理量
...103 附錄B 三維坦克車輛系統運動方程式推導之MAPLE程式 ...105 REFERENCES
[1] Ahmadi, M., Polotski, V., and Hurteau, R., "Path Tracking Control of Tracked Vehicle," Proceedings of the IEEE International Conference on Robotics ＆ Automation, pp. 2938-2943, 2000.
[2] Bekker, M. G., "Parametric Analyses of Tracks and Tracklayers Update Sample of Engineering Problems and Their Solutions in Off Road Locomotion," SAE Technical Papers, pp4.1083-4.1103, 1987.
[3] Bodin, A., "Development of A Tracked Vehicle to Study the Influence of Vehicle Parameters on Tractive Performance in Soft Terrain,"
Journal of Terramechanics, pp. 167-181, 1999.
[4] Choi, C. G., and Kwak, B. M., "Analysis of Tracked Vehicle Suspension Systems Using a Frictional Contact Problem Formulation," Mech.
Struct. & Mach, Vol. 21, pp. 123-149, 1993.
[5] Choi, J. H., Lee, H. C., and Shabana, A. A., "Spatial Dynamics of Multibody Tracked Vehicles Part I: Spatial Equations of Motion," Vehicle System Dynamics, Vol. 29, pp. 27-49, 1998.
[6] Choi, J. H., Lee, H. C., and Shabana, A. A., "Spatial Dynamics of Multibody Tracked Vehicles Part II: Contact Forces and Simulation
Results," Vehicle System Dynamics, Vol. 29, pp. 113-137, 1998.
[7] Conwell, J. C. and Johnson, G. E., "Design, Construction and Instrumentation of A Machine to Measure Tension and Impact Forces in Roller Chain Drives," Mech. Mach. Theory, Vol. 31, No. 4, pp. 525-531, 1996.
[8] Dhir, A. and Sankar, S., "Analytical Track Models for Ride Dynamic Simulation of Tracked Vehicles," Journal of Terramechanics, Vol. 31, No. 2, pp. 107-138, 1994.
[9] Dhir, A., and Sankar, S., "Ride Dynamics of High-Speed Tracked Vehicles: Simulation with Field Validation," Vehicle System Dynamics, Vol.
23, pp. 379-409, 1994.
[10] Guo, K., and Guan, H., "Modelling of Driver/Vehicle Directional Control System," Vehicle System Dynamics, Vol. 22, pp. 141-184, 1993.
[11] Hohl, G. H., "Torsion-Bar Spring and Damping Systems of Tracked Vehicles," Journal of Terramechanics, Vol. 22, No.4, pp. 195-203, 1986.
[12] Hoogterp, F. B., Saxon, N. L. and Schihl, P. J., "Semiactive Suspension for Military Vehicles," SAE Technical paper, No.930847, pp.47-52, 1993.
[13] Huh, K., and Hong, D., "Track Tension Estimation in Tracked Vehicles Under Various Maneuvering Tasks," ASME Journal of Dynamics Systems, Measurement, and Control, Vol.123, pp. 179-185, 2001.
[14] Low, K. H., "Computer-Aided Selection of Roller Chain Drives," Computer & Structures, Vol. 55, No. 5, pp. 925-936, 1995.
[15] McCullough, M. K., "Terra-Dynamics of High Mobility Track Vehicles," Ph. D. dissertation, The University of Iowa, 1985.
[16] Mechanical Dynamics, Inc, ADAMS User's guides, 2000.
[17] Muro, T., Tingji, H. and Munehito, M., "Effects of A Roller and A Tracked Vehicle on the Compaction of A high Lifted Decomposed Granite Sandy Soil," Journal of Terramechanics, Vol.35, pp. 265-293, 1998.
[18] Nakanishi T., Yin, Xuegang and A. A. Shabana, "Dynamics of Multibody Tracked Vehicles Using Experimentally Identified Modal Parameters," ASME Journal of Mechanisms, Transmissions and Automation in Design, 1993.
[19] Thuvesen, D., "A Single Track Module in Multibody Systems Sense for Simulation of Steering of Vehicles on Hard Ground," ISTVS Conference, Vienna, Austria, September 28-30, 1994.
[20] Thuvesen, D., "Steering of Tracked Vehicles on Solid Ground," ISTVS Conference, Ferrara, Italy, October 8-10, 1997.
[21] Thuvesen, D., "Transient Steering of Tracked Vehicles on Hard Ground," Chalmers University of Technology, Engineer Thesis, Chalmers University of Technology, Goteborg, Sweden, Report No. 1997-06-09, June 1997.
[22] Wang, G. G., Wang, S. H., and Chen, C. W., "Design of Turning Control for a Tracked Vehicle", IEEE Control Systems Magazine, pp.
122-125, 1990.
[23] Wong, J. Y., Theory of Ground Vehicle, John Wiley & Son, Third edition, 1993.
[24] Wong, J. Y., and Gao, Y., "Applications of a computer aided method to parametric study of tracked vehicles with rigid links," Proceedings of the Institution of Mechanical Engineers, Journal of Automobile Engineering, Vol. 208, pp. 251-257, 1994.
[25] Wyk, D. J., Spoelstra, J., and Kierk, J. H., "Mathematical modelling of the interaction between a tracked vehicle and the terrain," Applied Mathematics Modelling, Vol. 20, pp. 838-846, 1996.
[26] 林振昱, 履帶車輛承載系統設計參數最佳化之研究分析, 中正理工學院兵器系統工程研究所碩士論文, 1999.
[27] 紹清安, 戰甲車承載系統之扭力桿動力分析, 中正理工學院兵器系統工程研究所碩士論文, 1998.
[28] 江明德, 趙毓芹,祝嘉光, 坦克行駛原理, 國防工業出版社, 1983.
[29] 韓雪海, 劉侃, 履帶車輛行駛力學, 陸軍戰甲車發展中心研究發展處, 1988.
[30] 丁建仁, 履帶車輛三維運動模擬與動態分析, 大葉大學機械工程學系碩士班論文, 2000.
