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Soil deformations induced by a moving cutting blade, an expanding tube and a penetrating sphere
J. agric. Engng Res. (1972) 17, 371-375
Soil Deformations Induced by a Moving Cutting Blade, an Expanding Tube and a Penetrating Sphere A. R.
DEXTERt; D.
w. TANNERt
1. Introduction It is possible to observe the soil deformations on a plane of symmetry of a soil deforming tool by cutting the tool in half along this plane, and by pushing one of the halves through soil alongside a sheet of glass which lies in the original plane of symmetry. Provided that there are no frictional or other forces acting in the plane of the glass, the soil deformations which can be seen to occur through the glass are the same as those which would have occurred on the plane of symmetry with the complete tool moving through an unbounded mass of soil. Tanner! has made use of this glass-sided box technique to study the deformations of sand, loam and clay on the planes of symmetry of rigid tines at several different rake angles and each with two different values of soil to tool coefficients of friction. Where soil deformations occur in only two dimensions, it is also possible to observe the total deformations by measuring the initial and final positions of markers buried in the bulk of the soil. This method has the advantage that any effects caused by friction at the walls of the apparatus are eliminated, together with the disadvantage that only the final positions of the buried markers are measured, and no information is obtained during the deformation process. This method has been used by Gill" to determine the deformations induced in clay soils by the passage of wide wedgeshaped tools. Here we report measurements of soil deformations around a moving rectangular cutting blade and an expanding tube which were made with the buried marker method, and measurements of soil deformations around a penetrating sphere which were made with the glass-sided box technique. 2. Soil deformation around a rectangular cutting blade It was required to investigate the flow of soil around a cutting blade as part of a study of abrasive wear of agricultural implements," and to determine what increase in density of bulk soil can be produced during soil cutting operations in tillage processes. The measurements were made in a soil box 650 mm square and 204mm high which could be split into 2 pieces each 102mm high. The wide walls of the box were covered with grit to prevent slipping, and the top and bottom were covered with P.T.F.E. to aid sliding in the two required dimensions. A loamy sand was used whose size distribution was well described by a log-normal distribution with a log-mean diameter of 0·4 mm and a standard deviation of the mean of 0·7. This soil was prepared in the box to a density of approximately 1940kg m- a and a water content of 13·5 %measured on a dry weight basis, as these were the same values of these properties that were found in the field during the abrasive wear experiments. The maximum density for this soil with this water content is about 2100 kg m". The soil was first prepared in the bottom half of the box. Steel pins were pushed into the soil in a grid pattern with the aid of a perspex template. The positions of the centres of these pins were measured with a 2-dimensional travelling microscope which could be located on a special measuring frame over the box. The pins were covered with a 5 mm deep layer of dry, loose sand in order to facilitate their later excavation. The remaining top half of the box was then filled with soil prepared to the same condition as that in the bottom half, and the top of the box was bolted on. t Engineering Research Department, National Institute of Agricultural Engineering, Wrest Park, Silsoe, Beds. 371
372
SOIL DEFORMATIONS INDUCED BY A MOVING CUTTING BLADE
The vertical blade had a thickness of 14·3 mm and like the box it was made in 2 halves. The blade entered the soil through a slit in the middle of one end of the box. On completion of a run, the lower half of the blade was clamped into position. The top of the box was unbolted, and the upper half of the soil was removed. The dry sand and any remaining soil were extracted with a vacuum cleaner to avoid disturbing the pins. In this condition the blade was well into the box and its upper half had to be removed before the measuring frame and the two dimensional microscope could be used to measure the final positions of the centres of the pins. The initial and final positions of the pins were fed into a computer programme. This gave the displacement of each pin in magnitude and direction in addition to the percentage volume strain between each group of four adjacent pins. Fig. 1 (top) shows the magnitude and directions of the pin displacements and Fig. 1 (bottom) shows the percentage volume strains around the cutting blade. There is some uncertainty in the positions of the volume strain contours because they are based on the average strain between four pins. Since the pins were spaced 25 mm apart, the uncertainty on the positions of the contours is probably of the order of ±5 mm on the full scale.
p
Fig. 1. Deformations produced by rectangular blade cutting through sandy soil. Only half of the box is shown. The blade has enteredfrom the right and has stopped at P. In the top drawing, contours ofequal pin displacements are given in mm, the broken lines with arrows show the directions of soil movement. The bottom drawing gives contours joining places having equal percentage volumetric compression
3. Volume strain in soil around an expanding tube A pure cylindrical radial strain is one of the simplest types of 2-dimensional deformation. Although no existing types of agricultural machinery impose this mode of soil deformation, it is induced naturally under certain conditions by the roots of plants. When growing plant roots reach regions in soil where there are large mechanical shear strengths or where there are high hydrostatic pressures acting, it has been demonstrated that they temporarily cease axial growth and that instead they thicken by radial expansion." This radial expansion mechanism is thought to result in a weakening of the soil ahead of the root tip which enables axial growth to be re-established." Radial strain was produced in this experiment by inflating a length of colotomy tubing in the soil. A similar technique has been used previously to study the effects of soil parameters on
373
A . R. DEXTER; D. W . TANNER
compaction.' The experimental arrangement was very similar to that described above for the cutting blade investigation, and the same soil was used prepared to the same condition. The colotomy tubing had an initial diameter of 9·5 mm and was held rigid by a core of brass about 75 mm long . The soil was constrained from moving in the third dimension (in the direction of the tube axis) by the rigid top and bottom of the box. The tube was inflated with compressed air until its diameter had doubled to 19 mm. The changes in the positions of the buried needles were used to calculate the percentage volume strain or compression of the soil, and this is shown as a function of the distance from the tube axis in Fig. 2.
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Radius fr om l ube axi s (mm )
Fig. 2. Percentage volume strain induced by an expanding tube as a fun ction ofdistance from the tube axi s. Points are marked X and Y to refer to the axis of measurement
4.
The flow of sand and clay around penetrating spheres
Abrasive wear of agricultural implements has been found to be caused mainly by the stones in the soil being pushed out of the way. Stones have been simulated by steel spheres in this study of flow patterns. When a sphere is pushed into soil, the required force increases with the depth of penetration and finally levels off towards a maximum limiting value.' It was decided to investigate the flow pattern of soil around a penetrating sphere , and to determine how this changes with the dimensionless depth of penetration, LjR, where L is the distance of penetration and R is the radius of the sphere . The experiments were carried out with both a dry sand and a moist clay as these represent 2 of the extremes of soil types, being frictional and cohesive respectively. The moist clay was remoulded to a bulk density of 1470 kg nr" and had a water content of43 %by weight measured on a dry weight basis . Since the plastic limit of this clay is 41 % and the liquid limit is 78 %, the clay was just within its plastic consistency range. The dry sand had a density of approximately 1550kgm- 3 •
374
SOIL DEFORMATIONS INDUCED BY A MOVING CUTTING BLADE
A steel hemisphere of 25·4 mm diameter was pushed slowly and steadily down into the soil with its flat surface against the glass plate by a lead screw which was driven from an electric motor. In order to observe the soil movements, markers had to be placed in the surface of the soil which was in contact with the glass. In the case of the sand, some of the grains were dyed blue to make them stand out photographically. In the case of the clay, the surface was sprinkled with some crushed and sieved pieces of white porcelain which were then pushed into the surface. The interface between the sand and the glass was not lubricated because the angle of sand/glass sliding friction is approximately half that of the angle of internal friction of the sand." The interface between the clay and the glass, however, was lubricated with a proprietary silicone anti-stick and mould release agent in order to reduce the adhesive and frictional forces acting in the plane of the glass. Soil to glass friction and its reduction by lubricants has been the subject of a recent investigation by Krause. 7 As the hemisphere was driven into the soil, a cine camera was run at 24 frames/sec. The films were later examined with an analytical projector, and the tracks of certain chosen particles were drawn on the sheet of paper which was being used as a projection screen. The tracks were drawn for a run of 36 frames when the hemisphere had just penetrated the surface (L/R = I), and again on a fresh sheet of paper when the hemisphere was much deeper (L/R = 5). During the 36 frames of the analysis, the hemisphere penetrated an additional depth of approximately half a radius. It was found that the tracks of the particles were approximately straight lines for this small distance of penetration. Contours were drawn joining the mid-points of lines of the same length, and it has been assumed that these contours represent the particle velocities when the hemisphere was in the mid-point of its travel-s-that is, after 18 frames from the start of the analysis. Fig. 3 (top) and (bottom) show these contours of constant particle velocity in sand where the velocity of the sphere has been normalized to unity, together with the streamlines which are the
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Fig. 3. Streamlines and contours of equal particle speed in dry sand. The numbers give sand particle speeds with respect to that ofthe sphere. In the top drawing, the sphere is near the sand surface, in the centre drawing, the sphere is deeper
375
A. R. DEXTER; D. W. TANNER
directions of particle movement. The particle flow patterns in the case of clay were qualitatively similar to those in the sand, but in the clay the particle velocities at any given position were approximately 40 % greater. Attempts to find velocity potential functions to describe these flow patterns have not been entirely successful."
Acknowledgement The authors would like to express their indebtedness to the late Dr R. C. D. Richardson who initiated the work reported here. REFERENCES
Tanner, D. W. Further work on the relationship between rake angle and the performance ofsimple cultivation implements. J. agric. Engng Res., 19605 (3) 307 2 Gill, W. R. Soil deformation by simple tools. Trans. A.S.A.E., 1969 12 (2) 234 3 Richardson, R. C. D. The wear of metallic materials by soil-practical phenomena, J. agric. Engng Res., 1967 12 (1) 22 4 Abdalla, A. M.; Hettiaratchi, D. R. P.; Reece, A. R. The mechanics of root growth in granular media. J. agric. Engng Res., 196914 (3) 236 5 Hovanesion, J. D.; Buchele, W. F. Development of a volumetric transducer for studying effects of soil parameters on compaction. Trans. A.S.A.E., 1959 12 (2) 234 6 Witney, B. D. The determination ofsoil particle movement in two dimensional failure. J. Terramechanics, 19685 (1) 39 7 Krause, R. Die Grenzfliichenreibung bei Untersuchungen in Bodenrinnen mit Glaswdnden (Boundary surface friction in investigations in soil bins having glass walls). LandbForsch-VOlkenrode, 197020 (2) 83 (N.LA.E. translation No. 292, 1971) 8 Dexter, A. R.; Tanner, D. W. The flow of sand and clay around penetrating spheres. N.LA.E. Departmental Note DNjERj122j1162, 1971 1
Soil Deformations Induced by a Moving Cutting Blade, an Expanding Tube and a Penetrating Sphere A. R.
DEXTERt; D.
w. TANNERt
1. Introduction It is possible to observe the soil deformations on a plane of symmetry of a soil deforming tool by cutting the tool in half along this plane, and by pushing one of the halves through soil alongside a sheet of glass which lies in the original plane of symmetry. Provided that there are no frictional or other forces acting in the plane of the glass, the soil deformations which can be seen to occur through the glass are the same as those which would have occurred on the plane of symmetry with the complete tool moving through an unbounded mass of soil. Tanner! has made use of this glass-sided box technique to study the deformations of sand, loam and clay on the planes of symmetry of rigid tines at several different rake angles and each with two different values of soil to tool coefficients of friction. Where soil deformations occur in only two dimensions, it is also possible to observe the total deformations by measuring the initial and final positions of markers buried in the bulk of the soil. This method has the advantage that any effects caused by friction at the walls of the apparatus are eliminated, together with the disadvantage that only the final positions of the buried markers are measured, and no information is obtained during the deformation process. This method has been used by Gill" to determine the deformations induced in clay soils by the passage of wide wedgeshaped tools. Here we report measurements of soil deformations around a moving rectangular cutting blade and an expanding tube which were made with the buried marker method, and measurements of soil deformations around a penetrating sphere which were made with the glass-sided box technique. 2. Soil deformation around a rectangular cutting blade It was required to investigate the flow of soil around a cutting blade as part of a study of abrasive wear of agricultural implements," and to determine what increase in density of bulk soil can be produced during soil cutting operations in tillage processes. The measurements were made in a soil box 650 mm square and 204mm high which could be split into 2 pieces each 102mm high. The wide walls of the box were covered with grit to prevent slipping, and the top and bottom were covered with P.T.F.E. to aid sliding in the two required dimensions. A loamy sand was used whose size distribution was well described by a log-normal distribution with a log-mean diameter of 0·4 mm and a standard deviation of the mean of 0·7. This soil was prepared in the box to a density of approximately 1940kg m- a and a water content of 13·5 %measured on a dry weight basis, as these were the same values of these properties that were found in the field during the abrasive wear experiments. The maximum density for this soil with this water content is about 2100 kg m". The soil was first prepared in the bottom half of the box. Steel pins were pushed into the soil in a grid pattern with the aid of a perspex template. The positions of the centres of these pins were measured with a 2-dimensional travelling microscope which could be located on a special measuring frame over the box. The pins were covered with a 5 mm deep layer of dry, loose sand in order to facilitate their later excavation. The remaining top half of the box was then filled with soil prepared to the same condition as that in the bottom half, and the top of the box was bolted on. t Engineering Research Department, National Institute of Agricultural Engineering, Wrest Park, Silsoe, Beds. 371
372
SOIL DEFORMATIONS INDUCED BY A MOVING CUTTING BLADE
The vertical blade had a thickness of 14·3 mm and like the box it was made in 2 halves. The blade entered the soil through a slit in the middle of one end of the box. On completion of a run, the lower half of the blade was clamped into position. The top of the box was unbolted, and the upper half of the soil was removed. The dry sand and any remaining soil were extracted with a vacuum cleaner to avoid disturbing the pins. In this condition the blade was well into the box and its upper half had to be removed before the measuring frame and the two dimensional microscope could be used to measure the final positions of the centres of the pins. The initial and final positions of the pins were fed into a computer programme. This gave the displacement of each pin in magnitude and direction in addition to the percentage volume strain between each group of four adjacent pins. Fig. 1 (top) shows the magnitude and directions of the pin displacements and Fig. 1 (bottom) shows the percentage volume strains around the cutting blade. There is some uncertainty in the positions of the volume strain contours because they are based on the average strain between four pins. Since the pins were spaced 25 mm apart, the uncertainty on the positions of the contours is probably of the order of ±5 mm on the full scale.
p
Fig. 1. Deformations produced by rectangular blade cutting through sandy soil. Only half of the box is shown. The blade has enteredfrom the right and has stopped at P. In the top drawing, contours ofequal pin displacements are given in mm, the broken lines with arrows show the directions of soil movement. The bottom drawing gives contours joining places having equal percentage volumetric compression
3. Volume strain in soil around an expanding tube A pure cylindrical radial strain is one of the simplest types of 2-dimensional deformation. Although no existing types of agricultural machinery impose this mode of soil deformation, it is induced naturally under certain conditions by the roots of plants. When growing plant roots reach regions in soil where there are large mechanical shear strengths or where there are high hydrostatic pressures acting, it has been demonstrated that they temporarily cease axial growth and that instead they thicken by radial expansion." This radial expansion mechanism is thought to result in a weakening of the soil ahead of the root tip which enables axial growth to be re-established." Radial strain was produced in this experiment by inflating a length of colotomy tubing in the soil. A similar technique has been used previously to study the effects of soil parameters on
373
A . R. DEXTER; D. W . TANNER
compaction.' The experimental arrangement was very similar to that described above for the cutting blade investigation, and the same soil was used prepared to the same condition. The colotomy tubing had an initial diameter of 9·5 mm and was held rigid by a core of brass about 75 mm long . The soil was constrained from moving in the third dimension (in the direction of the tube axis) by the rigid top and bottom of the box. The tube was inflated with compressed air until its diameter had doubled to 19 mm. The changes in the positions of the buried needles were used to calculate the percentage volume strain or compression of the soil, and this is shown as a function of the distance from the tube axis in Fig. 2.
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Radius fr om l ube axi s (mm )
Fig. 2. Percentage volume strain induced by an expanding tube as a fun ction ofdistance from the tube axi s. Points are marked X and Y to refer to the axis of measurement
4.
The flow of sand and clay around penetrating spheres
Abrasive wear of agricultural implements has been found to be caused mainly by the stones in the soil being pushed out of the way. Stones have been simulated by steel spheres in this study of flow patterns. When a sphere is pushed into soil, the required force increases with the depth of penetration and finally levels off towards a maximum limiting value.' It was decided to investigate the flow pattern of soil around a penetrating sphere , and to determine how this changes with the dimensionless depth of penetration, LjR, where L is the distance of penetration and R is the radius of the sphere . The experiments were carried out with both a dry sand and a moist clay as these represent 2 of the extremes of soil types, being frictional and cohesive respectively. The moist clay was remoulded to a bulk density of 1470 kg nr" and had a water content of43 %by weight measured on a dry weight basis . Since the plastic limit of this clay is 41 % and the liquid limit is 78 %, the clay was just within its plastic consistency range. The dry sand had a density of approximately 1550kgm- 3 •
374
SOIL DEFORMATIONS INDUCED BY A MOVING CUTTING BLADE
A steel hemisphere of 25·4 mm diameter was pushed slowly and steadily down into the soil with its flat surface against the glass plate by a lead screw which was driven from an electric motor. In order to observe the soil movements, markers had to be placed in the surface of the soil which was in contact with the glass. In the case of the sand, some of the grains were dyed blue to make them stand out photographically. In the case of the clay, the surface was sprinkled with some crushed and sieved pieces of white porcelain which were then pushed into the surface. The interface between the sand and the glass was not lubricated because the angle of sand/glass sliding friction is approximately half that of the angle of internal friction of the sand." The interface between the clay and the glass, however, was lubricated with a proprietary silicone anti-stick and mould release agent in order to reduce the adhesive and frictional forces acting in the plane of the glass. Soil to glass friction and its reduction by lubricants has been the subject of a recent investigation by Krause. 7 As the hemisphere was driven into the soil, a cine camera was run at 24 frames/sec. The films were later examined with an analytical projector, and the tracks of certain chosen particles were drawn on the sheet of paper which was being used as a projection screen. The tracks were drawn for a run of 36 frames when the hemisphere had just penetrated the surface (L/R = I), and again on a fresh sheet of paper when the hemisphere was much deeper (L/R = 5). During the 36 frames of the analysis, the hemisphere penetrated an additional depth of approximately half a radius. It was found that the tracks of the particles were approximately straight lines for this small distance of penetration. Contours were drawn joining the mid-points of lines of the same length, and it has been assumed that these contours represent the particle velocities when the hemisphere was in the mid-point of its travel-s-that is, after 18 frames from the start of the analysis. Fig. 3 (top) and (bottom) show these contours of constant particle velocity in sand where the velocity of the sphere has been normalized to unity, together with the streamlines which are the
2
4
.c
a. Q)
6
0
0-15
7
Fig. 3. Streamlines and contours of equal particle speed in dry sand. The numbers give sand particle speeds with respect to that ofthe sphere. In the top drawing, the sphere is near the sand surface, in the centre drawing, the sphere is deeper
375
A. R. DEXTER; D. W. TANNER
directions of particle movement. The particle flow patterns in the case of clay were qualitatively similar to those in the sand, but in the clay the particle velocities at any given position were approximately 40 % greater. Attempts to find velocity potential functions to describe these flow patterns have not been entirely successful."
Acknowledgement The authors would like to express their indebtedness to the late Dr R. C. D. Richardson who initiated the work reported here. REFERENCES
Tanner, D. W. Further work on the relationship between rake angle and the performance ofsimple cultivation implements. J. agric. Engng Res., 19605 (3) 307 2 Gill, W. R. Soil deformation by simple tools. Trans. A.S.A.E., 1969 12 (2) 234 3 Richardson, R. C. D. The wear of metallic materials by soil-practical phenomena, J. agric. Engng Res., 1967 12 (1) 22 4 Abdalla, A. M.; Hettiaratchi, D. R. P.; Reece, A. R. The mechanics of root growth in granular media. J. agric. Engng Res., 196914 (3) 236 5 Hovanesion, J. D.; Buchele, W. F. Development of a volumetric transducer for studying effects of soil parameters on compaction. Trans. A.S.A.E., 1959 12 (2) 234 6 Witney, B. D. The determination ofsoil particle movement in two dimensional failure. J. Terramechanics, 19685 (1) 39 7 Krause, R. Die Grenzfliichenreibung bei Untersuchungen in Bodenrinnen mit Glaswdnden (Boundary surface friction in investigations in soil bins having glass walls). LandbForsch-VOlkenrode, 197020 (2) 83 (N.LA.E. translation No. 292, 1971) 8 Dexter, A. R.; Tanner, D. W. The flow of sand and clay around penetrating spheres. N.LA.E. Departmental Note DNjERj122j1162, 1971 1