Drilling on Mars

Abstract

The Drill Automation for Mars Exploration (DAME) project started in 2003 to develop facilitative technology for exploration of the surfaces of planets. The control software for the drill monitors it at all times and will adjust it accordingly to account for the uncertain environment of the Martian terrain. To develop models of the drill, hammers and shakers are used to tap the drill and collect the natural frequencies of the drill augers. Sometimes the drill becomes encroached in the rock, and the location of the encroachment is unknown. However, the location of the encroachment can be found by using the natural frequency collected by tapping the drill. Since, because of encroachment, the effective length of the beam has changed, the natural frequency also changes. By solving the inverse problem and knowing the new natural frequency, a new length of the beam can be found and therefore the location of the encroachment.

First, the initial problem about the oscillation of the beam will be solved. This is a boundary value problem with a partial differential equation of the fourth order and four boundary conditions. It will be reduced to an ordinary differential equation of the fourth order. It will then be solved as a general solution with four constants involved: C₁, C₂, C­₃, C₄. These constants will then be plugged into the four boundary conditions to get a system of four linear equations for four variables. After solving, the natural frequencies and their dependence on the beam length will be found.