The cutting of soil by narrow blades

The available models for predicting the forces acting on a narrow soil cutting blade have required separate measurements of the shape of the three-dimensional soil failure pattern ahead of the blade. It is proposed that a three-dimensional model consisting of straight line failure patterns in the soil can be used to predict both the draft forces and the volume of soil disturbed in front of a narrow blade. Limit equilibrium mechanics equations are written for the soil wedges in terms of an unknown angle of the failure zone and the theoretical draft force is minimized with respect to this angle. Force factors are thus found which are of the type to fit Reece's general earthmoving equation, but which vary with the width to depth ratio of the blade as well as with the rake angle of the blade and the friction angle of the soil. In addition the approximate geometry of the three-dimensional failure pattern in the soil is predicted for varying blade shapes and soil strengths. This allows the design of simple tools on the basis of their draft force requirements and their soil cutting efficiency. The draft force predictions and failure geometry calculations are shown to have considerable verification by experimental results.     

The inception and evolution of earthmoving soil mechanics

Soil and test conditions important to earthmoving machinery have been found to be significantly different from all other fields of endeavour with the partial exception of tillage studies. This could be the subject of a long dissertation. Broadly, however, soil conditions which produce critical mobility problems are much too soft and/or wet to be of concern to the earthmoving contractor who has to meet rigid specifications on acceptable types and moisture contents of fill soils. Occasional soft spots are considered as nuisances instead of indicators of the need for major design compromises.

Civil engineers are concerned with the same types of soil, but in a vastly different context. They must design soil structures which will never reach initial soil failure. Earthmoving processes, on the other hand, must accept soil failures in many different forms and degrees and utilize post-failure soil strength to perform their tasks efficiently.

Tillage studies display many important similarities to earthmoving studies, particularly in regard to the types of soil failures of importance. They are, in reality, merely another form of earthmoving; by definition, if nothing more. Earthmoving processes can range into much stronger soils, but this alone is insufficient to set them apart.

The term Earthmoving Soil Mechanics was introduced in 1962⁽²⁰⁾. This paper more clearly defines the implications of the new terminology and illustrates the first successful application of soil mechanics and model analysis principles in the earthmoving industry.     

Inverse problem of fracture mechanics for a disk fitted onto a rotating shaft

A plane problem of fracture mechanics for a circular disk fitted onto a rotating shaft is considered. The disk is assumed to be fitted tightly onto the shaft, and there are N randomly located straight-line cracks of length 2l_k (k = 1, 2, ..., N) near the inner surface of the disk. The interference between the disk and the rotating shaft, providing minimization of fracture parameters (stress intensity factor) of the disk, is theoretically studied on the basis of the minimax criterion. A closed system of algebraic equations is constructed, which allows the problem of optimal design to be solved. A simplified method of minimization of disk fracture parameters is considered. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 201–209, July–August, 2009.     

A dynamic model for soil cutting by blade and tine

A dynamic model for soil cutting resistance prediction by blade and tine was developed, taking account of shear rate effects both on soil shear strength and soil-metal friction, besides the conventional soil slice inertia, for both brittle and flow failure of soil. The model was verified with a series of tests in a soil bin with a blade and a tine, and the results were acceptable.     

Finite element analysis of plane soil cutting

This study develops the finite element method (FEM) of solution to provide a theoretical means for determination of soil performance under the actions of a cutting blade—and the forces required to promote cutting. The developed FEM takes into account the effect of progressive and continuous cutting of the clay soil at the tip of the blade, with possible development of failure zones in the soil whenever the shear strength of the soil is exceeded. The solution provides detailed information on stress and deformation fields in the soil, together with tangential and normal pressures developed at the blade soil interface Correspondence between theoretically computed displacement fields and measured values has been obtained. In addition, the theoretically computed and experimentally measured values for forces developed in blade thrust are seen to be in close agreement.     

Large rotating states of a conducting elastic wire in a magnetic field: subtle symmetry and multiparameter bifurcation

In this paper we consider large-amplitude, steadily rotating states of a flexible, nonlinearly elastic, current-carrying wire in a magnetic field. Our formulation leads naturally to a multiparameter bifurcation problem. A detailed local analysis is ostensibly intractable, due to the presence of the rotation group SO(2). However, we identify an additional, more subtle symmetry, which enables a standard local bifurcation analysis via group-theoretic methods. In contrast to well known methods of local equivariant bifurcation theory, we first exploit the group invariance of the full problem (before performing a local reduction) to construct a reduced problem that is also amenable to a global analysis, which we provide.Supported in part by the U.S. Army Research Office through the Mathematical Sciences Institute of Cornell University, Contract DAAG29-85-C-0018, and by the Air Force Office of Scientific Research, Grant No. AFOSR-88-0222.     

The dynamic calibration of a hot wire by means of a sound wave

Hot wires of various design, operated by the constant resistance method, were calibrated by means of a plane sound wave of 2500 Hz. This is achieved by locating a small open resonance tube axially in a homogeneous incompressible airflow. Its third harmonic is excitated by superimposing a coaxial, damped, progressive, plane wave on the main airstream. The hot wire to be calibrated is situated in an anti-node of the particle velocity. The amplitude at this station is known from the pressure gradient of the standing wave measured at two small holes in the wall by a probe microphone. This device in turn is calibrated in a specially developed “pistonphone”. Numerical results of the diverse designs are communicated; an absolute accuracy of ±2% is achieved.     

Measurement and interpretation of space-time correlation functions and derivative statistics from a rotating hot wire in a grid turbulence

A family of autocorrelation functions and derivative statistics are measured by a rotating hot wire in a grid turbulence. The autocorrelation functions, at various probe radii and speeds, can be rescaled with the probe effective velocity suggesting that Taylor's hypothesis is satisfied. The effects of the random convecting speed and the temporal change which would violate the hypothesis are however effectively removed in computing the autocorrelation functions. For the derivative statistics, it is shown that the eulerian temporal derivative statistics can be determined from the time derivative statistics measured by the moving probe at two different speeds based on the principle of Galilean invariance. The Reynolds number dependence of the eulerian temporal derivative mean square values suggests that the main contribution comes from the nonlinear acceleration terms in the limit of high Reynolds number.     

The stability of a compressed rotating rod

The classical stability problem of a compressed hinged elastic rod rotating with constant angular velocity about the axis that passes through the hinges is considered. It is assumed that the compressive force is constant and the line of its action coincides with the axis of rotation of the rod. The stability of a solution of the nonlinear problem that describes deformation of the rod under the action of the compressive force and the distributed centrifugal load is studied within the framework of the stability theory of dynamic systems with distributed parameters. The buckling paramcters of the problem are determined. Calculation results are given. Technology Institute, Altai State Technical University, Biisk 659305. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 190–197, July–August, 2000.     

Experimental study of frontal resistance force in soil cutting

The paper presents an experimental study of the frontal resistance forces in soil cutting, with emphasis on their dependence on tool displacement during the loading and unloading stages under quasistatic and dynamic regimes. Laboratory tests on undisturbed soil, using specially developed equipment, showed that:During the loading stage, at pre-limiting levels of the frontal resistance force, the soil undergoes both reversible and residual deformations.At the onset of the unloading stage, the restoring force undergoes a downward jump.The limiting value of the frontal resistance force increases considerably in the cutting velocity interval of 0.1 to 3–5 mm/s; at higher velocities, up to 25 mm/s, this force slowly. At the initial velocity of 3 m/s, the limiting value of the frontal resistance force exceeds by about 20% its counterpart appearing at the velocity of 0.1 mm/s.The frontal resistance force is linearly related to the tool width and non-linearly to the depth of cutting.     

Stratification of a gas by an incandescent wire

The propagation of a shock wave in a gas in which there is a wire rendered incandescent by a pulsed electrical discharge enables one to discover the stratified structure in space acquired by the gas as a result of nonuniform heating.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 175–176, July–August, 1984.     

The flow external to a rotating torus

Imparting a sudden rotation to a torus (or other symmetric smooth object) in an otherwise quiescent, viscous fluid serves to generate boundary layers at the object’s surface. These boundary layers are known to exhibit a finite-time singularity at the equator which manifests in a thickening of the boundary layer and subsequent development of an equatorial jet. Here we consider the post-collision flow dynamics, demonstrating that the equatorial jet serves to shed a finite amplitude toroidal vortex pair. The radial jet is also shown to develop an absolute instability at suitably high Reynolds numbers.     

The flow past a freely rotating sphere

We consider the flow past a sphere held at a fixed position in a uniform incoming flow but free to rotate around a transverse axis. A steady pitchfork bifurcation is reported to take place at a threshold \(Re^\mathrm{OS}=206\) leading to a state with zero torque but nonzero lift. Numerical simulations allow to characterize this state up to \(Re\approx 270\) and confirm that it substantially differs from the steady-state solution which exists in the wake of a fixed, non-rotating sphere beyond the threshold \(Re^\mathrm{SS}=212\). A weakly nonlinear analysis is carried out and is shown to successfully reproduce the results and to give substantial improvement over a previous analysis (Fabre et al. in J Fluid Mech 707:24–36, 2012). The connection between the present problem and that of a sphere in free fall following an oblique, steady (OS) path is also discussed.     

Asymmetric snap-buckling of a column restrained by a stiff wire

Summary A relatively simple example of asymmetric snap-through buckling in a continuous structure is the nonlinear problem of a cantilevered column restrained at its tip by a stiff wire, which is inclined at an acute angle to the column centerline, and loaded at its tip by a force perpendicular to the centerline. A parameter called , which is the nondimensional ratio of the flexural rigidity of the column to the combined extensional stiffness of the wire and the column centerline, determines the essential features of the buckling. If is zero, or is small compared to unity, the bending of the column is small enough to justify the use of linear bending theory for the column. Hence, even though the constraint is nonlinear, the solution to this problem is obtained in closed form. The critical point for the structure is found to be an asymmetric branching point for =0, while for positive, the critical point is a snap-through type. The effect of is similar to that induced by initial imperfections in more complex structures. For very small , the critical load is markedly decreased from the value for =0. Moreover, the graph of the load vs. tip deflection has the appearance of having an acute discontinuity in slope at the critical point for very small, although it is actually found that the graph has a horizontal tangent there.

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Sommario Un esempio relativamente semplice di collasso asimmetrico per carico di punta in una struttura continua è il problema non lineare di una colonna incastrata ad una estremità e vincolata all'altra estremità da un filo rigido che forma un angolo acuto con l'asse della colonna e caricata a quella estremità con una forza perpendicolare allo stesso asse. Un parametro chiamato , che è il rapporto adimensionale fra la rigidità flessionale della colonna e la rigidezza longitudinale del filo e dell'asse della colonna, determina le caratteristiche essenziali del cedimento. Se è zero o è piccolo rispetto all'unità, l'inflessione della colonna è sufficientemente piccola per giustificare l'uso della teoria lineare di inflessione per la colonna. Di conseguenza anche se il vincolo non è lineare la soluzione del problema è ottenuta in forma compatta. Il punto critico della struttura si trova nel punto di biforcazione asimmetrica per =0, mentre per positivo, il punto critico rappresenta un punto di collasso. L'effetto di è simile a quello prodotto da imperfezioni iniziali in strutture più complesse. Per molto piccolo il carico critico è notevolmente ridotto rispetto al valore per =0. Inoltre il grafico del carico in funzione della curvatura all'estremità sembra avere una netta discontinuità nella pendenza dal punto di biforcazione per molto piccolo benchè, in realtà si trovi che il grafico ha lì una tangente orizzontale.

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This research was supported by the Advanced Research Projects Agency (Project DEFENDER) and was monitored by the U.S. Army Research Office, Durham, under Contract DA-31-124-ARO-D-257.     

Experimental evaluation of cutting dynamic models in soil bin facility

Computer Aided Engineering methods in earthmoving machines design and their automation require the development of soil-cutting models. These models both in two or three dimensions, static or dynamic, fitted for frictional or cohesive soils, must be mutually compatible and must function with soil transportation models and with machine locomotion characteristic models. In this work two different methods of soil cutting have been evaluated, both of them based on the classical wedge method, in order to verify their applicability to test conditions in the new soil bin facility of CEMOTER. From experimental results the possibility of using dynamic models of soil cutting in the frequency domain is discussed, to improve earthmoving machinery performance by automation and implementation of open and closed-loop control. After a preliminary analysis of a plane blade under different test conditions in sandy soil, soil cutting theoretical models of a simple implement are compared with respective scale models by tests performed in a soil bin facility at various operating speeds and depths, in order to investigate their applicability and the dynamic behaviour of the soil cutting force.