Zheng-Dong Ma & Noel C. Perkins Department of MEAM The University of Michigan

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1 A G e n e r a l T r a c k E l e m e n t F o r T r a c k e d V e h i c l e S i m u l a t i o n Zheng-Dong Ma & Noel C. Perkins Department of MEAM The University of Michigan

2 Major Features of the Track Element u Coupling a vibration track model with the multibody dynamic system. u Mixed Eulerian/Lagrangian description of motion. u Coupled multibody dynamics equations including rigid body motion, longitudinal vibration, and transverse vibration of the track.

3 Coupling a vibration track model into the multibody dynamic system Vibration Track Model Multibody Dynamic System

4 Mixed Eulerian/Lagrangian description of motion Eulerian description of motion Lagrangian description of motion

5 Track Multibody Dynamics Equations Rigid Body Motion Equations + Track Vibration Equations + Coupling Terms

6 Major Features of the Track Element (Continued) u Using component mode syntheses method for discretization. u Solving track equations within DADS framework. u General purpose element. u Integrated with DADS menu. u Various fidelity/accuracy available.

7 Using component mode syntheses method for discretization u Rigid body mode u Constraint mode u Longitudinal vibration modes u Transverse vibration modes

8 Solving track equations within DADS framework Traditional Force Elements: u Stiffness, Damping New Force Element For Track Span: u Added mass term u Need to solve differential equations u Convergence issues u Accuracy issues

9 Six Different Track Models u Static (spring-damper) model u Lumped mass-spring-damper model u Quasi-static (Guyan reduction) model u Dynamic model with longitudinal vibration u Dynamic model with transverse vibration u Dynamic model with coupled longitudinal and transverse vibration

10 Integrated With DADS Menu Easy-To-Use User Interface

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14 Possible outputs u Tank rigid body dynamics u Longitudinal track vibration u Transverse track vibration u Dynamic track tension u Track contact forces u Dynamic responses of all components u Animation

15 Possible Applications Track/Belt/Chain

16 Integration For System Optimization CORBA I n t e r f a c e On Board Vibration x' x' 1 x' Road Arm Shape Optimization Powertrain System Design

17 Support Roller M1 Abrams Tank Model Track Turret Hull Idler Wheel Track Adjusting Link Torsion Bar Road Arm Road Wheel Drive Sprocket

18 M1 TANK CROSSING PROFILE 4

19 M1 TANK CROSSING PROFILE 4

20 TRACK TRANSVERSE VIBRATION

21 Example Results: Dynamic Tension of the Track long. & trans. long. only static

22 Dynamic Tension (Zoomed In) long. & trans. static long. only

23 FFT of the Dynamic Tension long. & trans. long. only static f 1 trans =3.7Hz f 1 long =14.0Hz

24 FFT of Normal Contact Force long. & trans. static long. only f 1 trans =3.7Hz f 2 trans =5.5Hz

25 Current Limitations/Future Developments u Idealized track/terrain contact u 2-D model u Ideal engagement of track/sprocket u Do not model loss of contact between track and rollers u Delivery of new software and user manuals at TACOM and GD

26 Frequency response to polygonal action 3.5 Simulation Results #1 #2 SPAN #3 #4 #5 3 Mid-span Transverse Response (in.) #4 #2 #1 #5 0.5 # Frequency (rad/s) AUTOMOTIVE RESEARCH CENTER ~ 7 mph

27 Polygonal Action Physics Action coarseness proportional to the difference in the inscribed and circumscribed pitch polygon circles Modeled as a mechanism equivalent to a four-bar linkage Excitation amplitude increases with increasing pitch length or decreasing sprocket radius Phasing determined by the fractional number of pitches within the track spans AUTOMOTIVE RESEARCH CENTER

28 Polygonal Action Excitation source to the track at the sprocket, idler, and front/rear roadwheels Implemented as a transverse boundary condition at these sites Occurs as linked track conforms to circular components as a polygon Excitation amplitude and frequency are a function of vehicle parameters - pitch length, sprocket radius, track speed, track geometry, etc. AUTOMOTIVE RESEARCH CENTER

29 Response to Actual Roadwheel Input θ f (t) - Front Roadarm Angle θ r (t) - Rear Roadarm Angle Roadarm data supplied by John TACOM ft (One-way coupling to track) θ f (t) SPAN #3 MID-SPAN TRANSVERSE DEFLECTION, SPAN #3 θ r (t) ft Time ZOOM VIEW ~3.7 Hz Time (sec.) AUTOMOTIVE RESEARCH CENTER

30 Example Simulation Results Response computed by low-order modes 0.16 f 1 = 3.7 Hz #2 #3 #4 Acos(2πft) Mid-span Transverse Amplitude (ft.) SPAN #3 f 3 = 7.3 Hz f 2 = 5.5 Hz f 4 = 7.6 Hz SPAN #4 SPAN # Frequency (Hz) AUTOMOTIVE RESEARCH CENTER

31 Vibration Mode Shapes f 1 = 3.7 Hz f 2 = 5.5 Hz f 3 = 7.3 Hz f 4 = 7.6 Hz AUTOMOTIVE RESEARCH CENTER

32 Low Order Track Vibration Modes M1A2 Upper Span Track Circuit v 2u2 SPAN # 2 v 3 v 4 u 3 u 4 SPAN # 3 SPAN # 4 SPAN # 1 u 1 v1 SPAN # 5 u 5 v 5 Displacement Coordinates and Track Span # s u i - Longitudinal v i - Transverse AUTOMOTIVE RESEARCH CENTER

33 Longitudinal Vibration Element Model x, u 1 (x,t) EA - section modulus m - mass/length c longitudinal = 920 ft/s Transverse Vibration Element Model u 2 (s,t) s, u 1 (s,t) d V V - track speed d - static sag k - static curvature T - static tension f(t) - dynamic strain c transverse = 63 ft/s (45 mph) Longitudinal Response: Transverse Response: AUTOMOTIVE RESEARCH CENTER

34 Simulation of Tracked Vehicles University of Michigan Dept. of Mechanical Engineering and Applied Mechanics Noel Perkins - Associate Professor Craig Scholar - Research Assistant Zheng-Dong Ma - Associate Research Scientist Matt Castanier - Assistant Research Scientist AUTOMOTIVE RESEARCH CENTER

35 Transverse Vibration Modes 6.0 Hz 10 K lbs. static tension 7.2 Hz 15 K lbs. static tension AUTOMOTIVE RESEARCH CENTER

36 Longitudinal Vibration Modes 10 K lbs. static tension 97.5 Hz Rod Theory f 1 = 97.5 Hz Hz 15 K lbs. static tension f 1 = Hz AUTOMOTIVE RESEARCH CENTER

37 Experimental Test Stand Track-mounted accelerometers 7-pitch test specimen AUTOMOTIVE RESEARCH CENTER

38 Full Vehicle Simulation with Coupled Track Vibration Modelling Options for 2D Track+Tank Dynamics: QUASI-STATIC TRACK+TANK MODEL: DYNAMIC AND CONTINUOUS TRACK+TANK MODEL: DYNAMIC AND MULTI-BODY TRACK+TANK MODEL: 15 DOF 31 DOF AUTOMOTIVE RESEARCH CENTER 96 DOF (no stretching) 246 DOF (with stretching)

39 Coupled Longitudinal and Transverse Track Element Model Transverse Longitudinal New Features Coupled Longitudinal-Transverse Motions Initial Track Sag AUTOMOTIVE RESEARCH CENTER