1 Extension of Terrestrial Excavation Mechanics to Lunar Soil Jason R. Florek, M.S. Rutgers University Department of Mechanical and Aerospace Engineering June 5, 2007

2J. R. Florek. Extension of Terrestrial Excavation Mechanics to Lunar Soil. 6/5/07. Motivation Nearly all lunar base designs call for some form of regolith shielding. Moving regolith also necessary for paving roads and collecting natural resources. Digging and excavating forces must be well understood for first generation design. Forces directly related to required power and size, weight and cost of equipment.

3J. R. Florek. Extension of Terrestrial Excavation Mechanics to Lunar Soil. 6/5/07. Design of Equipment Grader with extended frame Combination grader blade Smooth roller Hemispherical dome wheel All from Banks et al. (1990).

4J. R. Florek. Extension of Terrestrial Excavation Mechanics to Lunar Soil. 6/5/07. Modeling Required Cutting Forces Analytical Models  Two-Dimensional  Three-Dimensional  Static  Dynamic Finite Element Models Empirical Models

5J. R. Florek. Extension of Terrestrial Excavation Mechanics to Lunar Soil. 6/5/07. Experiments on Lunar Soil Simulants W. W. Boles, W. D. Scott, and J. F. Connolly, Excavation forces in reduced gravity environment. J. Aerospace Engng. 10(2) (1997). Scaled experiment aboard KC 135 aircraft to predict force to fail JSC-1 simulant. Required force in reduced gravity did not scale by factor of 1/6. Proposed using results at 1/6 g and 1 g as lower and upper bounds of force.

6J. R. Florek. Extension of Terrestrial Excavation Mechanics to Lunar Soil. 6/5/07. Experiments on Lunar Soil Simulants B. M. Willman and W. W. Boles, Soil-tool interaction theories as they apply to lunar soil simulant. J. Aerospace Engng. 8(2) (1995). Measured average required drawbar forces: 192 N, 522 N and 825 N, respectively. Values compared to four predictive models. One model: 627 N, 1157 N and 1639 N. Average of other models: 35 N, 112 N, 187 N. All predictive models rejected. Not all necessary parameters provided.

7J. R. Florek. Extension of Terrestrial Excavation Mechanics to Lunar Soil. 6/5/07. Cutting and Excavating the Lunar Soil A. Wilkinson and A. DeGennaro, Digging and pushing lunar regolith: Classical soil mechnaics and the forces needed for excavation and traction. J. Terramech. 44(2) (2007). S. Blouin, A. Hemami, and M. Lipsett, Review of resistive force models for earthmoving processes. J. Aerospace Engng. 14(3) (2001). Numerous models for needed digging (drawbar) forces, each with varying complexities. Authors hold back recommendation until after experimental validation. Reducing failure plane angle to between deg. creates a match between Gill model and Willman experimental data.

8J. R. Florek. Extension of Terrestrial Excavation Mechanics to Lunar Soil. 6/5/07. Logarithmic Spiral Failure Plane Locate spiral center. Moment balance about center. d 2 most difficult distance to calculate. Minimize pushing forces. Failure model of Osman (1964).

9J. R. Florek. Extension of Terrestrial Excavation Mechanics to Lunar Soil. 6/5/07. Cutting Parameters Depth Cohesion Surcharge Adhesion From Blouin et al. (2001). Fundamental earthmoving equation from Reece (1964). From Luengo et al. (1998).

10J. R. Florek. Extension of Terrestrial Excavation Mechanics to Lunar Soil. 6/5/07. Parameter Notations [5]-Willman & Boles (1995), [7]-Wilkinson & DeGennaro (2007), [11]-Luengo et al. (1998), [13]-Osman (1964)

11J. R. Florek. Extension of Terrestrial Excavation Mechanics to Lunar Soil. 6/5/07. Horizontal Force vs. Tool Depth Depth and tool-soil terms most important. Cutting force in Gill Model arbitrary.

12J. R. Florek. Extension of Terrestrial Excavation Mechanics to Lunar Soil. 6/5/07. Horizontal Force vs. Rake Angle Depth and tool-soil terms most important. Negative tool-soil contribution possible for Swick model.

13J. R. Florek. Extension of Terrestrial Excavation Mechanics to Lunar Soil. 6/5/07. Horizontal Force vs. Gravity Depth and tool-soil terms most important for Gill Model. Only depth term important for Swick model.

14J. R. Florek. Extension of Terrestrial Excavation Mechanics to Lunar Soil. 6/5/07. Horizontal Force vs. Cohesion & Internal Friction Depth and tool-soil terms most important when changing friction angle. Cohesion only important for high values.

15J. R. Florek. Extension of Terrestrial Excavation Mechanics to Lunar Soil. 6/5/07. Horizontal Force vs. Density & Surcharge Depth and tool-soil terms most important. Surcharge, cohesion and kinetic terms can in most cases be neglected.

16J. R. Florek. Extension of Terrestrial Excavation Mechanics to Lunar Soil. 6/5/07. Depth vs. Soil Density vs. Cohesion vs. Friction Angle

17J. R. Florek. Extension of Terrestrial Excavation Mechanics to Lunar Soil. 6/5/07. Parameter Dependencies Failure plane angle is a function of all other angles—rake angle and two friction angles. Cohesion, friction angles and density are all related to soil depth. Major problem in determining values for input to equations.

18J. R. Florek. Extension of Terrestrial Excavation Mechanics to Lunar Soil. 6/5/07. Depth-Varying Density Assumed constant density of 1.68 g/cm 3 [7]. First model matches density at 9 cm. Second model matches density at 30 cm.

19J. R. Florek. Extension of Terrestrial Excavation Mechanics to Lunar Soil. 6/5/07. Effect of Density Change with Depth Assumed constant density of 1.68 g/cm 3 (Wilkinson). First model matches density at 9 cm. Second model matches density at 30 cm.

20J. R. Florek. Extension of Terrestrial Excavation Mechanics to Lunar Soil. 6/5/07. Conclusions Required forces do not scale by 1/6 in reduced gravity. Although some Earth based models correlate poorly with experimental results, others compare surprisingly well. Depth and tool-soil terms appear to be most important. Parameter dependencies should be accounted for in model.