COEFFICIENT OF FRICTION OF WHEAT GRAINON GRAIN AND STEEL

Girja Sharan

Agricultural Engineering DepartmentCornell University

Ithaca, N.Y., U.S.A.

J. H. A. LeeMember CSAE

School of Agricultural EngineeringUniversity of Guelph

Guelph, Ontario

INTRODUCTION

A law of granular friction first described by Coulomb in 1776 can beexpressed as

t = <r tan $ -f- C

where r is the shear stress or strengthat failure, <r the stress normal to thefailure surface, <j> the angle of internalfriction and C the cohesion. Airy (1),Janssen (9), and Ketchum (11) usedthe tangent of the angle of repose ofthe material as its true coefficient ofinternal friction. Collins (7) observedthat there were other characteristicangles seen during the flow of material which could be taken to represent the frictional characteristics ofthat material. Brubaker (6) observedthat not only the external and internalangles of repose of a material weredifferent but the latter also variedwith boundary conditions. Differentmethods have been used to measurethe coefficient of friction of agricultural grains to obtain design information for grain bins, conveyors andnumerous other agricultural machines. Different methods of forminga natural pile to measure angle of repose have been reported (9, 11).Direct shear methods have been usedto measure shear strength and eventually coefficient of friction (10). Balis(2) compared the different methodsfor determination of the coefficient offriction of agricultural materials. It isgenerally recognized that the frictional properties are important sincethey effect the flow behavior, pressure exerted and behavior under deformation of granular materials.

The objective of this study was todetermine the effective coefficient ofwall friction during the flow of grain.A model bin and Genessee wheatgrain were used to carry out thisstudy.

EQUIPMENT

The model bin used was the sameas that described by Dwivedy (8). ARECEIVED FOR PUBLICATION

SEPTEMBER 3- 1969

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schematic diagram is shown in Figure1. The first cylinder (7), about 100inches high, 30 inches diameter andmade of 16 gauge steel sheet was supported by a rugged steel frame (4).A second cylinder (5), 21 inches high,31 inches diameter, and made of 16gauge sheet steel was placed underthe first cylinder. The junction of thetwo cylinders was used as a referencelevel for measurement of the heightof the grain column. The second cylinder was supported on a replaceableplywood bottom (3). There were 17holes of 0.75 inch diameter symmetrically arranged in the bottom. Therate of flow of grain through theseholes was about five inches of cylinder depth per minute. Only one flowrate was tested, since Dwivedy reported that the rate of flow did notaffect the frictional force. The plywood bottom was supported on aweigh scale (6) by an angle ironframe (1). A slanting steel trough(2) was placed underneath the bottom of the bin to collect the grainand channel it to the elevator. (12).The elevator returned the grain to thestorage bin. The depth of grain abovethe reference level was measured using a wooden float (8). The heightof the float was indicated by a pointerattached to a balance weight (11)moving along a scale (10). The pointer was attached to the float by acord (9).

A grain spreader was mounted ontop of the first cylinder to spread thegrain uniformly across the bin.

Beam Transducer

A schematic diagram of a pressuretransducer referred to as the beamtransducer is shown in Figure 2. Itwas used to measure radial and shearforces at the inside surface of the binwall. The transducer was fastened tothe wall by four screws through aplate (5). When properly fitted thepressure plate (2) was flush with theinside surface of the wall. A horizontal beam (3) connected the pressure

plate to the cantilever (4) and curvedbeam (7). The horizontal force dueto grain mass inside the bin acting onthe pressure plate produced bendingstress in the cantilever beam. Similarly the shear force due to grain massproduced bending in the curvedbeam. The resulting stresses were determined by means of strain gauges.The cantilever and the curved beamswere designed to obtain maximumsensitivity and minimum deflection.To facilitate construction and avoid

Figure 1. Schematic diagram of verticalforce measuring apparatus

Figure 2. Schematic diagramof beam transducer

CANADIAN AGRICULTURAL ENGINEERING, VOL. 12, No. 1, MAY 1970

machining, the cantilever beam wasmade in two parts (1) and (4) whichwere firmly fastened together. Thecurved beam was made by bendinga cold rolled steel bar of the requireddimension and then two machinedconical points were attached, at oneend of each of the two horizontalarms. An adjusting schew (6) wasused to level the horizontal beam.Weights were attached by a cord topin (8) in order to calibrate thetransducer for radial forces. The internal connection of gauges in eachcase was made to obtain double sensitivity, provide temperature compensation and independence from axialstrains. Double-shielded strain gaugecables were used as lead wires. Thetransducer was calibrated separatelyfor shear and radial forces. There wasa linear relationship between thetransducer response and the radialand shear forces.

Smooth and Rough Bins

The original surface of the bin isreferred to as the smooth bin. Theoriginal surface lined with expandedmetal of 21 gauge thickness and 0.187x 0.875 inch center distance is referred to as the rough bin.

PROCEDURE

Emptying and Filling of Bins

A general procedure for emptyingand filling the model bin was followed. At the beginning of every experiment the grain spreader was checkedto insure that it delivered the grainuniformly across the bin. To fill thebin, steel plates were pushed underthe bottom to close the holes. Thegrain spreader and the elevator wereswitched on and the outlet of thestorage bin was opened to let thegrain pour into the model bin. Afterthe model bin was filled, the spreaderwas switched off. The grain surfacewas then inspected to insure that itwas level. To empty the bin, the steelplates were rapidly pulled out to obtain a uniform commencement offlow. The grain was returned to thestorage bin by the elevator.

Smooth Bin Measurements

(i) radial force

The beam transducer was used toobtain radial force at the wall surface.It was checked to insure that the pressure plate was flush with the wall surface. The clearance between the hole

and the pressure plate was filled witha heavy-duty grease to prevent deposition of cracked grain kernels. Thebin was filled. The filling was interrupted to balance the strain indicatorwhen the grain surface was at thecenter of the pressure plate. Thedepth indicator was lowered into thebin to measure the depth of the graincolumn. Strain readings were recorded at every six inches of depth as theemptying proceeded.

(ii) shear force

The pressure plate was againchecked to insure that it fitted flushwith the inside surface of the wall.The plate surface was rubbed witha clean cloth to insure that it was freefrom grease, dirt, etc. The bin wasfilled completely after balancing ofthe strain indicator. The emptyingwas begun and shear force recordedat depth intervals of six inches.

(Hi) vertical force

The weight of grain supported bythe bottom was measured by theweigh scale. Filling of the bin wasbegun, then interrupted to record thetare weight when the grain surfacereached the lower end of the first cylinder. The tare weight was the fixedforce exterted on the bottom of thebin when no grain was present in thefirst cylinder. This depth was considered to be zero depth for referencepurposes. The bin was then completely filled. Emptying was begunand the weigh scale reading recordedat every six inches of depth. The tareweight was then subtracted from theweigh scale readings to yield the totalvertical force.

Rough Bin Measurements

The original surface of the bin andthe pressure plate were lined with expanded metal. The lining did not

cover the second cylinder. The sametechniques as used for the smooth binwere employed to measure radial,shear and vertical forces. To insurethat the pressure measured by thetransducer was free of location effects, it was fitted at another locationin the bin. Similar results were obtained (Figures 5 and 6). The moisture and bulk density of the wheatused were measured several timesduring the experiment to account forany change in these factors. The results are shown in Table I.

2 3 4

DEPTH OF GRAIN IN FEET

Figure 3. Stress on smooth bin wall

DEPTH OF GRAIN IN FEET

Figure 4. Shear load supported bysmooth bin wall

TABLE I. BULK DENSITY AND MOISTURE CONTENT OF WHEAT USEDFOR EACH REPLICATION

Replication

I

2

3

% M. C.(w. b.)

7.8%

7.3%

7.1

Bulk Density

48.6 lbs/ft"

50 lbs/ft"

50 lbs/fr

CANADIAN AGRICULTURAL ENGINEERING, VOL. 12, No. 1, MAY 1970 15

RESULTS AND DISCUSSION

At least three replications of eachtest were made and the results areshown graphically in Figures 3 to 9.The wheat grain used was considereda cohesionless material, i.e.: the valuefor C in Coulomb's equation assumedto be zero. The values of the normaland shear stresses were used in thisequation to determine the coefficientsof friction. In the rough bin shearoccurred in the grain mass and therefore, the coefficient obtained wasequal to the effective coefficient ofinternal friction. In the smooth binthe coefficient obtained was considered to be equal to the coefficient offriction of grain on steel.

The area under the shear stressversus depth of grain curves obtainedby means of the beam transducer represented the shear load per unitlength of the bin perimeter. The areasunder the curves (Figures 3, 6) weredetermined by a planimeter and multiplied by the perimeter of the bin(94.5 inches) to obtain the total shearload supported by the wall. The shearload was also obtained by subtractingthe vertical force acting on the bottom of the bin from the total weightof grain inside the bin. Both thevalues of shear load are shown inFigures 4 and 7 for the smooth andrough bins respectively. The shearload obtained by the beam transducerdiffers from the weigh scale value bya maximum of 15% in the smoothbin. This may have occurred due tothe difference in the roughness of theinside surfaces of the bin and thepressure plate of the beam transducer.In the rough bin the values obtainedby each method did not differ bymore than 5%. This indicates that thecoefficient of friction values obtainedby the use of the beam transducer arethe values actually existing at thewall surface.

The coefficient of friction of grainon grain increased with an increasein the depth of grain (Figure 8).The complex nature of the coefficientof internal friction has led many research workers to believe that it wasdependent only on the bio-physicalproperties of the kernels and could berepresented by the tangent of thestatic angle of repose. Brubaker (6)stated that the coefficient of frictionof grain was independent of normalpressure whereas Collins (7) pointedout that it was affected by the orient

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ation of the kernels and questionedits relationship with the tangent ofthe angle of repose.

The variation of the coefficients offriction may be due to the changesin the normal pressure and the arrangement of kernels on the slidingsurface (Figure 8). If the kernelswere randomly oriented and interlocked in a static granular mass theywould tend to offer greater resistanceto sliding in the early stages of flow.With the onset of flow the kernelswould tend to reorient themselves inorder to minimize their resistance tosliding. This would explain the difference in the values of coefficients offriction between an early and laterstage of flow (Figure 8). Again it islogical to assume that the major reorientation of mass occurred in thefirst few inches of flow and thereforethe greatest reduction in the coefficient of friction should occur in thesame period. The experimental evidence is contrary to this because it isseen that the coefficient of internalfriction continued to decrease untilthe bin emptied and the coefficientof friction of grain on steel decreaseduntil about two and a half feet offlow had occurred. This indicatesthat the reorientation of the kernelsmay be only one of the factors affecting the coefficient of friction, whichis in agreement with Collins's observation.

Radial pressure exerted by thegrain column normal to the slidingsurface may be another factor affecting the coefficient of friction. Thecoefficient of internal friction increases with the normal pressurewhereas the coefficient of friction ofgrain on steel remains constant up to0.5 psi of pressure and then increases(Figure 9). This indicates that theradial pressure has a greater effect onthe coefficient of internal friction thanthe coefficient of friction of grain onsteel. The coefficient of internal friction and the radial, pressure becameconstant at depths greater than fiveand one-half feet in the rough bin. Itis possible that the limiting value ofthe coefficient may be higher thanthat obtained in the experiment. Inorder to ascertain the limiting valuea larger normal pressure, hence adeeper bin, would be required. Therefore the effect of further increase ofpressure on the coefficient of frictioncould not be observed. The variability of the coefficient of friction with

the depth of bin contradicts the common assumption, made in order tosimplify the development of grainpressure theories, that the coefficientof friction is independent of pressure.The coefficient of friction of grain onthe steel was readily obtained fromthe results of the smooth bin experiment. The values obtained are lowerthan the coefficient of internal friction because sliding of grain occurredalong the surface made of smoothsteel. The coefficient of friction ofgrain on steel increased from 0.20 to0.26 as the normal pressure increasedto 0.6 psi. Brubaker (6) reported avalue of 0.33 for about the samemoisture content and normal pres-

DEFTH OF GRAIN IN FEET

Figure 5. Radial stress on rough bin wall

- Original locat i on

-Another location

DEPTH OF GRAIN IN FEET

Figure 6. Shear stress on rough bin wall

• Hydrostat ic

Vertical Force

' Shear Load (Scale)

Shear Load (Transducer)

DEPTH OF GRAIN IN FEET

Figure 7. Shear load supported byrough bin wall

CANADIAN AGRICULTURAL ENGINEERING, VOL. 12, No. 1, MAY 1970

Internal friction

Grain on Steel

DEFTH OF GRAIN IN FEET

Figure 8. Coefficients of friction of grainon bin wall

/Internal Friction

Grain on St#el

RADIAL PRESSURE IN POUNDS PER SQ. IN.

Figure 9. Variation of coefficients of frictionwith normal pressure

sure; however, he concluded that thecoefficient of friction of grain on steelwas not affected by normal pressure.

CONCLUSIONS

From the results of the experimentsand discussion the following conclusions may be drawn.

1. The coefficient of friction of grainon grain and on steel vary with thedepths of grain in a bin at least upto depths of 60 inches, when thebin is 30 inches in diameter.

2. The tangent of the angle of reposeof grain may not represent the truecoefficient of internal frictionunder all circumstances since thelatter appears to vary with bothnormal pressure and orientation ofkernels.

REFERENCES

1. Airy, W. 1898. The pressure ofgrain. Minutes and proceedingsof the Institution of Civil Engineers, 121: 347-358.

2. Balis, J. S. 1961. Methodology onthe determination of friction coefficients of agricultural materials. Unpublished Master ofScience Thesis, Library, PurdueUniversity, Lafayette, Indiana.

3. Barre, H. J. 1958. Flow of bulkgranular, materials. AgriculturalEngineering, September, 534-536.

4. Brown, R. L. and Richards, J. C.1958. Exploratory study of theflow of granules through apertures. Transactions, Institute ofChemical Engineers, 37: 108-119.

5. Brown, R. L. and Hawksley, P.G. W. 1958. The internal flow ofgranular masses. Transactions,Institute of Chemical Engineers,36(6): 159-173.

6. Brubaker, J. E. and Pos J. 1965.Determining static coefficients offriction of grains on structuralsurfaces. Transactions, AmericanSociety of Agricultural Engineers,8(1): 53-55.

7. Collins, S. H. and Yin, P. K. K.1965. A model study of the binflow of dry grains. CanadianAgricultural Engineering, January.

8. Dwivedy, R. C. 1965. Stresses inwheat flowing steadily in a vertical cylindrical bin. Master ofScience Thesis, University ofGuelph Library, Guelph, Ontario,Canada.

9. Janssen, H. A. 1895. VersucheLiber Getreidedruck in SilozellenBand. XXXIX (35): 1045-59.

10. Jenike, A. W. 1961. Gravity flowof bulk solids. Bulletin of University of Utah, 52(108).

11. Ketchum, M. L. 1929. The designof walls, bins and grain elevators.McGraw Hill Book Co. Inc.,Third Edition.

12. Means, R. E. and Parcher, J. V.1964. Physical properties of soils.Constable and Co. Ltd., LondonWC2, Second Printing.

13. O'Callaghan, J. R. 1960. Internalflow in moving beds of granularmaterials. Journal of AgriculturalEngineering Research, 5: 200-217.

14. Rose, H. E. and Tanaka, T. 1959.Rate of discharge of granular materials from bin and hoppers. TheEngineer, October, 465-469.

15. Sharan, G. 1967. Stresses in moving grain. Master's Thesis, University of Guelph, Guelph, Ontario, Canada.

CANADIAN AGRICULTURAL ENGINEERING, VOL. 12, No. 1.. MAY 1970

BALLAST FOR OPTIMUM . . .

continued from page 13

thumb" maximum. Finally, it shouldbe realized that the tractor enginestorque and power also limit the drawbar pull and maximum DBHP. Thisis particularly so at the higher groundspeeds.

CONCLUSIONS

A traction loss mechanics was developed resulting in a simple expression for the optimum dynamictractive tire weight. The expressioncan be used to estimate the requiredballast for maximum tractive efficiency. In its present form it can be auseful teaching tool. The accuracyand limitations of the mechanics aresuch that field application should beapproached with caution.

REFERENCES

1. Barger, E. L., Liljedahl, J. B.,Carleton, W. M., McKibben, E. G.,1963. Tractors and their powerunits. John Wiley and Sons, Chap.13, p. 285.

2. Bekker, M. G., 1955. A proposedsystem of physical and geometricalterrain values for the determination of vehicle performance andsoil trafficability. Interservice Vehicle Mobility Symposium, April.

3. Domier, K. W. and Friesen, O. H.,1969. Performance parameters oftractors equipped with singles,duals and* four-wheel drive. Can.Agr. Engr. 11 (1): p. 16.

4. Friesen, O. H. and Domier, K. W.,1967 Traction tests. Manitoba Department of Agric. Publication.

5. Reece, A. R., 1967. Tractor designand tractive performance. Proc.Agric. Eng. Symposium - Inst, ofAgr. Engs., Paper No. 3/4/E/34.

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