Constitutive model for high speed tillage using narrow tools

Dynamic effects on soil–tool cutting forces are important when operating at elevated speeds. The rate-dependent behavior of narrow tillage tools was investigated in this study. A hypoelastic soil constitutive relationship with variable Young's modulus and Poisson's ratio was developed to describe the dynamic soil-tool cutting problem. An initial finite element formulation with viscous components incorporated in the stiffness matrix resulted in severe numerical oscillations. A modified model that incorporated lumped viscous components in the equation of motion (independent of the stiffness matrix) was proposed. Numerical oscillations still occurred, but at sufficiently high tool displacements (1–10 mm) to enable the determination of peak draft forces. Experimental data for flat and triangular edged narrow tools were obtained using a 9-m long linear monorail system designed to accelerate narrow tools through a linear soil bin to high speeds. Steady-state speeds from 0.5 to 10.0 m/s over a distance of 1 to 3 m were attained using this system. A reference-tool inverse procedure was used to estimate the dynamic soil parameter in the soil model using draft data obtained for the flat tool. Predictions of triangular tool draft produced correct trends but overestimated experimental data. Draft was overpredicted by less than 1% at a tool speed of 2.8 m/s and by 25% at 8.4 m/s.