Technical Report TR–2016–08

NG-NRMM Phase I Benchmarking: Chrono Tracked Vehicle Simulation Results Summary

Radu Serban, Michael Taylor, Daniel Melanz, Dan Negrut

Simulation Based Engineering Lab University of Wisconsin – Madison

August 15, 2016 Contents

1 Brief Overview of Chrono 2

2 M113 Model Overview and Assumptions 2

3 Deformable Terrain Model 3

4 Simulation Results 3 4.1 Steering Performance ...... 3 4.1.1 Wall to wall turning radius ...... 3 4.1.2 Steady state cornering ...... 4 4.1.3 Double lane change paved ...... 7 4.1.4 Double lane change gravel ...... 8 4.2 Side slope stability ...... 9 4.2.1 Paved conditions ...... 9 4.2.2 Deformable terrain conditions ...... 10 4.3 Grade climbing ...... 12 4.3.1 Steerable limiting slope ...... 12 4.3.2 Speed on slope – paved conditions ...... 13 4.3.3 Speed on slope – deformable terrain conditions ...... 14 4.4 Ride quality ...... 15 4.4.1 Random terrain ride limiting speeds ...... 15 4.4.2 Half round obstacle ride limiting speeds ...... 16 4.5 Obstacle Crossing ...... 17 4.5.1 Step climb height limit ...... 17 4.5.2 Gap crossing limits ...... 18 4.5.3 Trapezoidal fixed barrier limits ...... 19 4.5.4 Trapezoidal ditch crossing limits ...... 20 4.6 Off road trafficability ...... 21 4.6.1 Single pass soil strength ...... 21 4.6.2 Multi pass soil strength limit ...... 21 4.6.3 Drawbar pull vs slip performance curve ...... 22 4.6.4 Motion resistance ...... 23 4.7 Fuel Economy ...... 23 4.7.1 On-road conditions ...... 23 4.7.2 Off-road conditions ...... 26

1 1 Brief Overview of Chrono

Chrono [2] is an open source multi-physics engine whose development is led by teams at the University of Wisconsin – Madison and the University of Parma, Italy. It supports the simulation of systems of rigid bodies, flexible bodies, and fluids interacting through traditional multi-body constraints, friction, and contact. To lower the learning curve for new users, several toolkits are currently under development or have already been developed. The most relevant of these is Chrono::Vehicle which supports the simulation of both wheeled and track vehicles through a template interface.

2 M113 Model Overview and Assumptions

The Chrono::Vehicle module provides a model of an M113 vehicle as a demonstration instan- tiation of its tracked vehicle templates. This model was modified to bring it in alignment with the data provided by the NATO RTG along with engineering approximations to fill in the remaining required parameters. The track shoes were modeled as geometric primitives (cylinders and rectangular prisms) and were connected together by revolute joints. Although Chrono supports the ability to use triangular contact meshes, this higher level of fidelity was not used for these benchmarking simulations due to the fidelity of assumptions made in the provided benchmarking data and benchmarking effort’s focus on rigid terrain. The sprocket profile was setup as a 2D contact profile whose geometry was based on the M113 demon- stration model. Based on the track assembly algorithm developed for the Chrono::Vehicle Tracked Vehicle Toolkit, the idler was not fixed in place, but was put on a carrier with a TSDA and a translational joint, acting as a hydraulic tensioner, to preload the track. This track tension method is consistent with the information we found on the M113 in public domain (http://www.army-guide.com/eng/product1424.html). The missing mass properties for the M113 model were generated based on rough engi- neering approximations. For example, the inertia for the vehicle’s chassis was generated by assuming a hollow rectangular prism with 1.75 in thick walls, the largest armor thickness stated in the provided documents, and the calculated mass of the chassis. The drive sprocket mass and inertia was calculated by assuming a solid cylinder with the provided radius of 0.214 m and width of 0.236 m (9.3 in) with a density a quarter of that of steel to account for the voids in the actual sprocket design. The idler’s mass properties were generated in a similar manner, except two spaced solid cylinders were used. The road wheel mass was calculated by solving for the remaining unsprung mass and the inertia was calculated assum- ing two solid spaced cylinders with this combined mass. Assumptions were made for other parameters, but they are not listed here for brevity. They can be provided upon request.

2 3 Deformable Terrain Model

While Chrono provides full support for Discrete Element Method (DEM) granular dynamics and coupled vehicle – granular terrain simulations, due to time and resource limitations, for the purpose of these tests we opted to use a more expeditious model for deformable terrain, based on the Soil Contact Model (SCM) [1]. The Chrono implementation provides several extensions to the original SCM; e.g. non-uniform and adaptive griding and ability to load terrain profiles from height field or mesh data.

4 Simulation Results

4.1 Steering Performance 4.1.1 Wall to wall turning radius Wall to wall turn radius (Neutral axis spin maneuver): slow speed, maximum steer input (drive right reverse and left tracks in forward direction to achieve a clockwise vehicle spin), compute the maximum diameter of a plan view trace of vehicle chassis outer most points that will impinge upon a wall of any height and thus prevent the turn maneuver, spinning at least a 360 degrees. Repeat in the counterclockwise direction.

Figure 1: Event 1a: Clockwise wall to wall turning radius.

3 Figure 2: Event 1a: Counterclockwise wall to wall turning radius.

4.1.2 Steady state cornering Steady state cornering: Per SAE J266, asphalt skid pad (friction coefficient = 0.8), 100 feet turn radius, starting at 5 mph increase velocity at constant acceleration rate to achieve ap- proximate expected max speed in 100 seconds. Continue acceleration until loss of traction or unable to maintain turn radius. Plot turn angle and vehicle roll angle vs lateral acceleration. Repeat to get both right and left turns.

Note: For this maneuver, the vehicle was power limited and did not slide out of the turn. The steering required at the peak speed was greater than 0.5, meaning that a reverse torque was applied to the inside track.

4 Figure 3: Event 1b: Steady state cornering (counterclockwise). Speed vs. time.

Figure 4: Event 1b: Steady state cornering (counterclockwise). Vehicle path.

5 Figure 5: Event 1b: Steady state cornering (counterclockwise). Kinematic turn ratio.

Figure 6: Event 1b: Steady state cornering (clockwise). Speed vs. time.

6 Figure 7: Event 1b: Steady state cornering (clockwise). Vehicle path.

Figure 8: Event 1b: Steady state cornering (clockwise). Kinematic turn ratio.

4.1.3 Double lane change paved Double lane change paved: Determine max attainable speed per AVTP 03-160W, hard sur- face, mu= 0.8

7 Note: For this maneuver, the vehicle was power limited. The steering required was greater than 0.5, meaning that opposite torques were applied to each track.

Figure 9: Event 1c: Animation snapshot for a double lane change maneuver.

Figure 10: Event 1c: Double lane change maneuver on paved road.

4.1.4 Double lane change gravel Double lane change gravel: Determine max attainable speed per AVTP 03-160W, hard sur- face, mu=0.5

8 Note: For this maneuver, the vehicle was power limited. The steering required was greater than 0.5, meaning that opposite torques were applied to each track.

Figure 11: Event 1d: Double lane change maneuver on gravel.

4.2 Side slope stability 4.2.1 Paved conditions Paved (mu=0.8) surface serpentine steerable slope speed limit: Determine maximum 30% side slope speed maneuverable. This is defined as the maximum speed on a 30% side slope for which the vehicle can traverse across a 30% side slope, first in a straight path line for 20 meters, then execute a downhill obstacle avoidance maneuver in less than 30 meters of traverse path length, around a 3 meter wide obstacle while recovering to the original straight line path and elevation on the slope.

9 Chrono::Vehicle M113 - Event 2a - Side slope stability 10 Speed = 4 m/s 9 4.5 m/s 5 m/s 8 5.5 m/s 6 m/s 7

6

5

4 y-position (m) 3

2

1

0 -20 -15 -10 -5 0 5 10 15 20 x-position (m) Figure 12: Event 2a: Vehicle position for side slope stability (paved conditions).

Conclusion: 5 m/s is the maximum speed.

4.2.2 Deformable terrain conditions Deformable terrain serpentine steerable 20% slope speed limit. Determine maximum maxi- mum speed for obstacle avoidance (per 2a description) on a 20% side slope on sand defined by the LETE sand in Ref 3 (Wong, Garber, and Preston-Thomas, 1984).

10 Figure 13: Event 1c: Animation snapshot for side slope obstacle avoidance simulation (vehicle speed: 4 m/s).

Chrono::Vehicle M113 - Event 2b - Side slope stability 7 Speed = 1 m/s 6 2 m/s 3 m/s 4 m/s 5 5 m/s

4

3

2 y-position (m)

1

0

-1 -20 -15 -10 -5 0 5 10 15 20 x-position (m) Figure 14: Event 2b: Vehicle position for side slope stability (deformable conditions).

11 Conclusion: 4 m/s is the maximum speed.

4.3 Grade climbing 4.3.1 Steerable limiting slope Max steerable/brake-able up slope and down slope. For paved (mu=0.8) surface determine max up slope and down slopes for which a 3 meter wide obstacle avoidance maneuver can be executed in 30 meter s of path length while recovering original path line.

Chrono::Vehicle M113 - Event 3a - Grade Climbing Chrono::Vehicle M113 - Event 3a - Grade Climbing 4 8 Slope = 60% Slope = 60% 3.5 65% 7 65% 70% 70% 3 75% 75% 80% 6 80% 2.5 85% 85% 5 2 4 1.5 3 y-position (m) 1 Vehicle Speed (m/s) 2 0.5

0 1

-0.5 0 -30 -20 -10 0 10 20 30 0 5 10 15 20 25 30 35 x-position (m) Time (s) (a) (b)

Figure 15: Event 3a: Vehicle position for upward grade climbing for paved conditions.

Conclusion: Maximum slope is 75% at approximately 1 m/s.

Chrono::Vehicle M113 - Event 3a - Grade Climbing Chrono::Vehicle M113 - Event 3a - Grade Climbing 6 12 Slope = -30% Slope = -20% -40% -30% 5 10 -50% -40% -55% -50% 4 -60% 8 -55% -65% -60%

3 6

2 4 y-position (m) y-position (m) 1 2

0 0

-1 -2 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 x-position (m) x-position (m) (a) (b)

Figure 16: Event 3a: Vehicle position for downward grade climbing at 2 m/s (left) and 3 m/s (right) for paved conditions.

12 Chrono::Vehicle M113 - Event 3a - Grade Climbing Chrono::Vehicle M113 - Event 3a - Grade Climbing 20 20 Slope = 0% Slope = 0% -5% -5% -10% 15 15 -10% -15% -15% -20% -20% -30% 10 -30% -40% 10 -40%

5

5

y-position (m) y-position (m) 0

0 -5

-5 -10 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 x-position (m) x-position (m) (a) (b)

Figure 17: Event 3a: Vehicle position for downward grade climbing at 4 m/s (left) and 5 m/s (right) for paved conditions.

Conclusion: Max slope for 2 m/s: -60%; Max slope for 3 m/s: -50%; Max slope for 4 m/s: -30%; Max slope for 5 m/s: -5%

4.3.2 Speed on slope – paved conditions Speeds on grades. Determine maximum speed on grades up to maximum steerable up slope.

Figure 18: Event 3b: Vehicle top speed for grade climbing (paved conditions).

13 4.3.3 Speed on slope – deformable terrain conditions Deformable terrain grade limits and speeds (initial benchmark on dry sand). For LETE sand from Ref 3 (Wong, Garber, and Preston-Thomas, 1984) determine maximum steerable up slope and down slopes and maximum speed on grades up to the maximum up slope.

Chrono::Vehicle M113 - Event 3b - Grade Climbing Chrono::Vehicle M113 - Event 3b - Grade Climbing 4 5 Slope = 35% Slope = 35% 3.5 40% 4.5 40% 45% 45% 3 50% 4 50% 55% 55% 3.5 2.5 60% 60% 65% 65% 3 2 2.5 1.5 2

y-position (m) 1 1.5 Vehicle Speed (m/s) 0.5 1

0 0.5

-0.5 0 -30 -20 -10 0 10 20 30 0 5 10 15 20 25 30 35 x-position (m) Time (s) (a) (b)

Figure 19: Event 3b: Vehicle position for upward grade climbing for deformable terrain.

Conclusion: Maximum slope is 55% at approximately 1.75 m/s.

Chrono::Vehicle M113 - Event 3b - Grade Climbing Chrono::Vehicle M113 - Event 3b - Grade Climbing 6 4.5 Slope = -25% Slope = -25% -30% 4 -30% 5 -35% -35% -40% 3.5 -40% -45% -45% 4 3 -50% -50% 2.5 3 2 2 1.5 y-position (m) y-position (m) 1 1 0.5 0 0

-1 -0.5 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 x-position (m) x-position (m) (a) (b)

Figure 20: Event 3b: Vehicle position for downward grade climbing at 2 m/s (left) and 3 m/s (right) for deformable terrain.

14 Chrono::Vehicle M113 - Event 3b - Grade Climbing Chrono::Vehicle M113 - Event 3b - Grade Climbing 6 18 Slope = 0% Slope = 0% 5 -5% 16 -5% -10% -10% 4 -15% 14 -15% -20% -20% 3 12 -25% -25% 2 10

1 8

0 6 y-position (m) y-position (m) -1 4

-2 2

-3 0

-4 -2 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 x-position (m) x-position (m) (a) (b)

Figure 21: Event 3b: Vehicle position for downward grade climbing at 4 m/s (left) and 5 m/s (right) for deformable terrain.

Conclusion: Max slope for 2 m/s: -45%; Max slope for 3 m/s: -45%; Max slope for 4 m/s: -10%; Max slope for 5 m/s: -5%

4.4 Ride quality 4.4.1 Random terrain ride limiting speeds Random terrain ride limiting speeds: Determine 6 watt ride limiting speeds due to vertical driver accelerations on standard 2D profiles provided.

15 Figure 22: Event 4a: Example absorbed power simulation run (Single speed).

Figure 23: Event 4a: Random terrain ride limiting speeds for each profile.

4.4.2 Half round obstacle ride limiting speeds Half round obstacle ride limiting speeds: Determine 2.5G ride limiting speeds due to vertical driver accelerations on standard half round profiles from 4 inches to 12 inches.

16 Figure 24: Event 4b: Animation snapshot for a 4 inch obstacle crossing simulation.

Figure 25: Event 4b: Half-round obstacle. Ride limiting speeds.

4.5 Obstacle Crossing 4.5.1 Step climb height limit Step climb height limit: determine maximum traversable height in forward direction.

Note: For this maneuver, the vehicle was able to climb over a maximum vertical wall of

17 30 inches. Due to the powertrain assumptions and the contact model used for the track, after a couple of attempts the track would catch the top of the step and would pull the vehicle over the vertical wall.

Figure 26: Event 5a: Animation snapshot for a max step climb simulation.

Figure 27: Event 5a: Step climb height limit; maximum step height: 30 inches

4.5.2 Gap crossing limits Gap crossing limits: determine maximum gap traversable in forward direction.

18 Note: For this maneuver, the vehicle started from a stop shortly before the gap and then accelerated with full throttle. The maximum gap was determined to the nearest 5 inch to be 125 inches.

Figure 28: Event 5b: Gap crossing limit; maximum gap width: 125 inches

4.5.3 Trapezoidal fixed barrier limits Trapezoidal fixed barrier limits: determine traversability limits for obstacles parameterized by trapezoidal slope angle, barrier height, and barrier top surface width. Assume 12 differ- ent obstacles generated by the combinations resulting from the following obstacle parameter values: height (30 inches), top/bottom widths :6”, 30”, 140”; up angles: 16 deg, 26 deg, 38 deg, 68 deg.

Note: The vehicle was able to climb all of the specified trapezoidal barriers.

19 Figure 29: Event 5c: Trapezoidal fixed barrier; Vehicle CG Position for the 6” wide, 16◦ barrier

Figure 30: Event 5c: Trapezoidal fixed barrier; Vehicle CG Position for the 140” wide, 68◦ barrier

4.5.4 Trapezoidal ditch crossing limits Trapezoidal ditch crossing limits: determine traversability limits parameterized by trape- zoidal slope angle, ditch depth, and ditch bottom surface width. Assume 12 different ditch

20 obstacles generated by the combinations resulting from the following obstacle parameter val- ues: depth (30 inches), top/bottom widths : 6”, 30”, 140”; down angles (for ditch obstacles): 16 deg, 26 deg, 38 deg, 68 deg.

Note: The vehicle was able to traverse all of the specified trapezoidal ditches.

Figure 31: Event 5d: Trapezoidal Ditch Crossing; Vehicle CG Position for the 140” wide, 68◦ ditch

4.6 Off road trafficability 4.6.1 Single pass soil strength Single pass soil strength limit. Determine maximum gross vehicle weight traversable in one pass including reversing back through the path per standard VCI measurement methods.

4.6.2 Multi pass soil strength limit Multi pass soil strength limit. Determine max GVW traversable for 50 passes (forward and reverse).

21 Chrono::Vehicle M113 - Event 6 - Multi-Pass Chrono::Vehicle M113 - Event 6 - Multi-Pass 9 5.6

5.4 8.5 5.2 8 5

7.5 4.8

4.6 Time/pass (s) 7 Speed/pass (m/s) 4.4 6.5 4.2

6 4 0 5 10 15 20 25 0 5 10 15 20 25 Weight (kN) Weight (kN) (a) (b)

Figure 32: Event 6a: Average time (left) and speed (right) per pass for 10 passes as a function of vehicle weight.

Note: In an effort to speed up computation times, 10 passes were used instead of 50 and the time per pass was recorded.

4.6.3 Drawbar pull vs slip performance curve Drawbar pull vs slip performance curve. For the LETE sand and standard M113 GVW, determine the drawbar pull at 2 mph and at stall, assuming drawbar attached at rear hitch location. See Ref 3 (Wong, Garber, and Preston-Thomas, 1984).

22 40

30

20

10

0 Drawbar Pull [kN]

-10

-20

-30 -1.5 -1 -0.5 0 0.5 1 Slip [-]

Figure 33: Event 6c: Drawbar pull vs slip performance curve.

4.6.4 Motion resistance Motion resistance (MR) (powered , towed). Determine powered and towed motion resistance coefficients in LETE sand. Powered motion resistance is defined to be MR at zero drawbar pull.

4.7 Fuel Economy 4.7.1 On-road conditions On-road. For a given 3D path loop determine net terrain dependent motion resistance coef- ficient.

Note: The vehicle was given a target speed of 7m/s. This required the vehicle to brake downhill in order to maintain this speed. Uphill, the vehicle was power limited and could

23 not maintain the target speed of 7m/s. The final value for the Motion Resistance Coefficient was 0.1082.

Figure 34: Event 7a: Vehicle CG Position vs. Vehicle Speed.

Figure 35: Event 7a: Vehicle CG Position vs. Powertrain Power.

24 Figure 36: Event 7a: Vehicle CG Position vs. Energy Used by the Powertrain.

Figure 37: Event 7a: Distance Traveled vs. Motion Resistance Coefficient (Cumulative En- ergy/(Cumulative Distance x GVW)).

25 4.7.2 Off-road conditions Off-road deformable terrain. For a given 3D path loop of LETE sand determine net terrain induced motion resistance coefficient.

While Chrono is capable of performing this test on deformable terrain, we were unable to do so due to time and resource limitations. As an example of what the results might look like, a comparison between the motion resistance coefficient for rigid and LETE sand deformable terrain was generated for the first 500m of the Fuel Economy path.

Figure 38: Event 7b: Distance Traveled vs. Motion Resistance Coefficient (Cumulative En- ergy/(Cumulative Distance x GVW)) for the first 500m.

Acknowledgments

The development of Chrono has been supported with funding from the following projects: • U.S. Army Research Office RIF W56HZV-14-C-0254 ”A Physics-based High Perfor- mance Computing Capability for Ground Vehicle Mobility Analysis” • U.S. Army TARDEC, CREATE-GV project, W56HZV-08-C-0236 ”Development of a High Performance Computing Software Infrastructure for the Modeling and Simulation of Multibody Dynamics Applications: Part 1” (wheeled vehicles) • U.S. Army TARDEC, CREATE-GV project, W56HZV-08-C-0236 ”Development of a High Performance Computing Software Infrastructure for the Modeling and Simulation of Multibody Dynamics Applications: Part 2” (tracked vehicles)

26 • U.S. Army Research Office, W911NF-15-1-0386 ”An Instrumentation Request for Up- grading a Mid-size Heterogeneous Computing System Supporting Research and Edu- cational Activities in Computational Dynamics”

• U.S. Army Research Office, Math Division, W911NF-12-1-0395 ”A Homogenization- Driven Multiscale Approach for Characterizing the Dynamics of Granular Media and its Implementation on Massively Parallel Heterogeneous Hardware Architectures”

References

[1] Rainer Krenn and Andreas Gibbesch. Soft soil contact modeling technique for multi- body system simulation. In Trends in computational contact mechanics, pages 135–155. Springer, 2011.

[2] A. Tasora, R. Serban, H. Mazhar, A. Pazouki, D. Melanz, J. Fleischmann, M. Taylor, H. Sugiyama, and D. Negrut. Chrono: An open source multi-physics dynamics engine. In T. Kozubek, editor, High Performance Computing in Science and Engineering – Lecture Notes in Computer Science, pages 19–49. Springer, 2016.

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