Simulating Track/Sprocket and Track/Wheel/Terrain Contact in Tracked Vehicles

Size: px

Start display at page:

Download "Simulating Track/Sprocket and Track/Wheel/Terrain Contact in Tracked Vehicles"

Amelia Long
6 years ago
Views:

1 Simulating Track/Sprocket and Track/Wheel/Terrain Contact in Tracked Vehicles Z.-D. Ma C. Scholar N. C. Perkins University of Michigan

2 Objective Efficient simulation of vehicle response including track vibration, track/sprocket contact, and track/wheel/terrain interaction. n Overview of recent efforts n New effort: Track/Sprocket Contact n New effort: Track/Wheel/Terrain Interaction

3 Track Models QUASI-STATIC MULTI-BODY CHAIN HYBRID DISCRETE-CONTINUOUS ELEMENT

4 Continuous Track Model IN-PLANE RESPONSE TRANSVERSE LONGITUDINAL

5 Continuous Track Model u 2 (s,t) s, u 1 (s,t) V Longitudinal Response (quasi-static) d V - track speed d - static sag k - static curvature T - static tension f(t) - dynamic strain s u 1 (s,t) = f (t)s + k u 2 (η,t)dη 0 Transverse Response m(u 2,tt + 2Vu 2,st + V 2 u 2,ss ) + keaf (t) = Tu 2,ss f (t) = k L L 0 u 2 (η,t)dη

6 Experimental Validation

7 M1 Tank Traversing Profile 4

8 Track Transverse Vibration

9 Including Track/Sprocket Contact Objective: To model of dynamic shoe-tumbler seating process n n Inputs: shoe pitch elongation, tumbler lug wear, track tension, interface friction, applied torque, ground conditions. Outputs: pin loading, shoe/tumbler contact forces, animation of seating process P&H 4100A Crawler

10 P&H 4100A Crawler n Operating weight: 1,200 tons n Max. speed: 0.56 mph. n n Max. applied torque: 1,580,000 ft-lbs Max. design tension: 1,480,000 lbs

11 Shoe/Tumbler Seating Process

12 Hybrid Track Model Shoes Tumbler Rear Idler Guide Rollers Front Idler Multibody Model of Shoes Continuous Model of Track Segments

13 Shoe/Tumbler Interface a) Slight Wear b) Heavy Wear

14 Prescribed Tumbler Velocity

15 Machine Travel Speed

16 Shoe/Tumbler Normal Contact Force For Shoe shoe 5 shoe shoe 3 shoe 6 shoe 7

17 Vertical Load For Pins 01 to 03 Under Rear Idler pin 01 pin 02 pin 03

18 Case: Slight Wear, Very Tight

19 Case: Heavy Wear, Extremely Loose

efficiently predict the loading on the vehicle due to

20 Including Track/Wheel/Terrain Contact Objective: To develop track/wheel/terrain interface model to efficiently predict the loading on the vehicle due to the ground pressure and shear. Track/Wheel/Terrain Interaction

21 Track/Wheel/Terrain Interaction Model (Force Element) Inputs (X 1, Z 1, φ 1 ) (X 2, Z 2, φ 2 ) z t (x) Z F X 1 F Z 1 Wheel 1 φ 2 φ 1 z t (x) O 1 (X 1, Z 1 ) A o τ 1 F X 2 F Z 2 s P(x,z) α Terrain x l B Wheel 2 O 2 (X 2, Z 2 ) τ 2 x Outputs (F X1, F Z1, τ 1 ) (F X2, F Z2, τ 2 ) O z g X

22 Track/Wheel/Terrain Interaction o x Equilibrium T θ f x ds P f z ds θ+dθ T+dT T cos θ + ( T + dt)cos( θ + dθ ) f ds = 0 T sin θ + ( T + dt )sin( θ + dθ ) f ds = 0 Kinematic Relationships x z o z θ P ds dρ dx dz θ+dθ x dx cosθ =, cos( θ + dθ ) = dρ dz sinθ =, sin( θ + dθ ) = dρ Constitutive Law T = EA( dρ ds) / ds dx + dρ dz dρ + d ds d ds dx ds dρ dz ds dρ z

23 x z O 1 (x 1, z 1 ) -f z r 1 z-z 1 f -f x P(x, z) x-x 1 Contact Models Track/Wheel Track/Terrain f k = w ( r r1 ) for r < r1 0 for r r f x = τ + mg sinα and τ ( x, z) = τ m x x 1 exp K τ = C p(z) tanφ m + k W c n p ( z) = + kφ ( z zt ) = p mg cosα (Janosi & Hanamoto) (Bekker) (x t,z t ) B P(x,z) A f α x f o z Terrain x g z t f z

24 Solution Procedure n Re-write BVP in incremental form n Discretize by FE n (Modified) Newton-Raphson Iteration of nonlinear BVP

25 Example: Case of Zero Sinkage Trapezoid Bump Round Bump

26 Example: Case of One Inch Sinkage Trapezoid Bump Round Bump

27 Example: Effect of Ground Stiffness K=3.6e4 K=1.8e4 K=0.9e4

28 Effect of Track Extensibility EA (lbs) Tension (lbs) Fx (lbs) Fz (lbs) 2.5e e e e6 2.5e e e e6 2.5e e e e6 2.5e e e e6 5.0e e e e6 1.0e e e e6

Continuous to Multibody Formulation Nel Tension (lbs) FX (lbs) FZ (lbs) 100

29 Continuous to Multibody Formulation Nel Tension (lbs) FX (lbs) FZ (lbs) e e e e e e e e e6

30 Conclusions Continuous track model n Captures low frequency track vibration in an efficient manner n Can be married to multibody track models (track/sprocket contact) n Can be extended to capture track/wheel/terrain interaction

CHAPTER 71 NUMERICAL INTEGRATION

CHAPTER 71 NUMERICAL INTEGRATION CHAPTER 7 NUMERICAL INTEGRATION EXERCISE 8 Page 759. Evaluate using the trapezoidal rule, giving the answers correct to decimal places: + d (use 8 intervals) + = 8 d, width of interval =.5.5.5.75.5.65.75.875.