Penetration Rates and Stability of Motions of a Harmonically Forced Fore-Aft Vibrating Plow

Abstract

A fore-aft vibrating plow with applied harmonic and bias forces, and with soil-blade interaction modeled by a constant tip resistance in uncut soil and zero skin friction is studied analytically. Necessary conditions are found which must be satisfied by transition crank angles if steady state motions with velocity period equal to an integer number of harmonic force periods are to exist. The infinitesimal stability of these motions is examined and the range of parameters over which stable and unstable motions exist is delineated. Average plowing speeds corresponding to these regular motions are computed and the variation of plowing speed with system parameters is found. These results are useful, both for estimating penetration rates of conceptual plows and for adjusting machine parameters to obtain optimum performance.