techniques of experimental stress analysis and statistics - 1956 - bigsby

8/13/2019 Techniques of Experimental Stress Analysis and Statistics - 1956 - Bigsby

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TE HNIQUES OF EXPERIMENT L STRESS ANALYSIS ND ST TISTI SFOR DETERMIN TION OF FOR ES IN MOUNTED IMPLEMENT LINK GESFloyd W. Bigsby

Member C S A ECanada Department of AgricultureExperimental Farm, Swift Current, Saskatchewan

byKenneth K. Barnes

Department of gricultural EngineeringUniversity of Arizona,

Tucson ArizonaThe three-point implement hitch

came into general use after 1939 followinga development period of abouttwenty years. Three - point hitcheshave gained popularity because theimplement and tractor become acompact unit easily maneouvered inlimited space. Control of the implement and transportation from fieldto field are simplified when an implement is attached by a three - pointhitch.The two main types of three-pointhitches in general use have been described by Clyde (1). The first type,known as the free-link hitch, is sonamed because the lifting links arefree of any load during normal operation. The depth of operation is controlled by adjusting the length of thetop link which controls the angle theimplement makes with a plane paralel to th e soil sur face . Because th elinks are not parallel this anglehanges as the implement enters theThe implement will then reachilibrium at some point determinedy the length of the top link. Thecond type, the restrained link hitch,r ives i ts name from th e fact that th eift links hold the implement in thesired operating position. The coniguration of the linkage is such thate implement seeks a depth greaterhan that desired before reachingThe hydraulic system

are connected into the l inksystem so that either th e draft orhe position of the implement may besed to control the hydraulic system.Advertising statements discussinghe virtues of mounted implementsressthe increase in traction resultingrom carrying the downward forces ofplement weight and soil reactionn the tractor. Clyde (1) and Heitshu2) have presented analyses of theatics of tractor-implement combina

and have calculated rear wheelunder assumed loads. Rogersnd Johnston (5) have measuredin th e links of a free-link, three-hitch, in which the links werewith hydraulic cylinders. Verypublished mater ia l present ing

of m e a su re m e nt o f forces in aimplement was found, alundoubtedly such informationin th e files o f s ev er al t r ac to r m a n u

This paper discusses the use of electrical resistance strain gages in measurement of forces in a fixed-l ink implement hitch, the statistical designof an experiment to facili tate estimation of simultaneous strain readingsin five links when only two-channels train recording equipment is available, and the r es ul ts o f one field testwith a mounted plow.EXPERIMENTAL EQUIPMENT

A ND P RO CE DU R ESA Ferguson Model TO-35 tractorand Dearborn plow with two 14-inchbottoms were chosen for this study.The tractor and plow, blocked up inplowing position and with the linkspar tial ly seen in phantom, are shownin figure 1. The tractor is equipped

Figure I. Three point implement hitch showingposition of links.with a two-position hydraulic system1.The system may be set to keep theimplement in constant position in relation to the tractor, or it may be setto keep the draft of the implementconstant. The only change from astandard linkage was that both hangerlinks were adjustable. The left hangerl in k, however , was se t to th e samelength as the standard f ixed l ink.

The weight distribution of thet ractor was determined by weighingthe front and rear separately, and byweighing the right and left side separately. When th e sides of th e tractorwere weighed the left side was raisedsix inches above the right side tosimulate a plowing position. Theweight di st ribution is given in table

I. The dimensions of th e tractor ar egiven in figure 2. The forces shownin figure 2 will be discussed later.TABLE I. WEIGHT DISTRIBUTION

F O R T RA CT OR O NL YComponent Weight lb s

R e a r W h e e l s 1880F r o n t W h e e l s 1 0 9 0

T o t a l 2970L e f t W h e e l s 1 3 5 0Right Wheels 1620

T o t a l 2970

Figure 2. Dimensions of Tractor and Linkage.Link forces under field operatingconditions were determined from

strain measurements in th e links. SR4type C7 strain gages were affixed toeach of the links (numbered 1through 5 in figure 1). The two bott om li nk s were mil le d down 5 inchesahead of the rear ball joint for approximately 2 inches to a rectangularsection \i 2 inches by inch. Gageswere th en attached to this mil leddown section as follows: on the topl ink 4 inches ahead of the rear balljoint, and on t he male section of theadjustable hanger links 3 inches abovethe upper end of the threads. Thestrain gages were placed on the linksand connected into a bridge as shownin figure 3. Two model BL-320 Brush

SECTION OF LINKWITH GAGES ATTACHED BRIDGE DIAGRAM

JFor a description of th e action of thissystem see T he New Ferguson Hydraulic System: How it works , Farm Mechanization 8, No. 89 : 345-347, 1956. Figure 3. Arrangement of strain gages and electricalresistance strain gage hookup.


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analyzers, and a two-channel ModelBL-222 Brush oscillograph were usedto amplify and record the unbalanceof the strain gage bridge. Duringtests the instruments were carried ina three-wheel trailer fastened to th eside of the tractor. The wheels ofth e trailer were of the caster type,thus allowing the trailer to follow thetractor around curves. In addition tothe instruments a small 110 - voltgenerator was carried in the trailerto supply power for the instruments.The leads from th e instruments tothe gages consisted of two four-conductor shielded cables. Snap connectors on the cables and gage leadswith color coding on both cables andgages made it easy to change from onel ink to another.

The links were calibrated beforeand after testing by applying a forcein the direction of the load as itnormally occurred in the field. Thetwo bottom links are subjected tobending as well as tension duringoperation in the field. However, theplacement of the gages on the linkswas such that bridge unbalance because of bendingstrainswas cancelledout (4).

Field tests were conducted on asilty clay loam with a cover of weedgrasses. The soil moisture contentwas approximately 13 per cent. Theplow was fitted with new shares,adjusted for operation at a 6-inchdepth as recommended by Hull 3),and operated at 1 miles per hour.It was necessary to know the simultaneous strains in all five of the linksbetween the plow and the tractor inorder to calculate the resultant reactions on the tractor. This could notbe accomplished directly with a two-channel recorder. An experimentaldesign involving simultaneous recording of strains in all possible pairs oflinks was used to make an estimateof the variance of the forces. Thepairs of links to be used in each runwere chosen so that all possible pairswere represented, and the order oftesting pairs was chosen at random.When runs were made with all possible pairs being used, four traceswere obtained for each link. Recordsin field tests were made alternately illposition control and in draft controlThe test runs were approximately 1UUfeet long and the chart speed was 5millimeters per second, giving a chartlength of 24 centimeters for each run.Dafa used in the analyses were_ takenfrom a 10-centimeter section in themiddle ofeach chart. This section wassubdivided into four 2.5-centimeterlengths, and a 0.5-centimeter lengthwas chosen at random from each of

the 2.5-centimeter subsections. Thepoints chosen on one trace were carried across the chart to th e othertrace on th e chart; thus the sectionschosen gave simultaneous values ofdeflection. Typical charts marked outfor analysis are shown in figure 4.

Figure 4. Section of os ci ll og raph cha rt .T h e area u n d e r each trace was m easured with a planimeter and dividedby the base length to give the averagedeflection. The average deflection of

th e 10-centimeter sections was usedto compute an over-all average deflect ion in each l ink fo r th e fo ur ru ns inwhich a particular l ink was represented. An estimate of th e variance of th edeflection in each link was computedfrom value s o f d ef le ct ion ove r the 0.5-centimeter lengths of the chart. Defle ctio n valu es obtained from th echarts were converted to forces usingthe l ink calibration data.FORCE ANALYSIS AND RESULTS

Forces in th e links were resolvedinto horizontal longitudinal, vertical,and horizontal transverse forces atthe points of attachment of the plowto the bot tom links and the top link.Figure 5 shows a free-body diagram ofthe right bottom link and the righthanger link. Figure 5 and the examples following used the notation:

PLAN

ELEVATIONFigure 5. Resolution of Forces of Drag and HangerLink Assembly. (Not to Sca le .)

fj, f2measured axial force in link,subscript refers to link number int igure 1.

Hj, H2horizontal longitudinalcomponent of force at end ofl i n k .

V1( V2vertical component of forcea t e n d o f l in k.

Tl f T2horizontal transverse component of force at end of link.Vj'resultant vertical component at

e n d o f li nk .Ti resultant horizontal transversecomponent at end of link.

R f l vertical reaction on left fronwheel .

Rrf vertical reaction on righf ront wheel .

R rl vertical reaction left rearwheel .

Rrr vertical reaction on r ight rearwheel .

P l trac ti ve for ce on left reawheel .

Pr tractive force on right reawheel .

From geometric relationships:Hi = V(32)2 - (0.4)2 _ (4,4)2 f

32= 0.990 fi 1Vx = 0.4 fx = 0.0116 ft

= V(32)2 - (31.7)2 - (0.4)2 32= 0.136 fj

By similar application of geometrirelationships:

H2 = 0.620 f2V2 = 0.780 f2T2 = 0.0097 f2The resultant vertical and transverscomponents are obtained by summinmoments abou t 0.In a vertical plane:5Mo = 31.7 Vi - 2.9 V2 - 0.4 H

- 15.7 H2 = 0Vi' = 2.9 V2 + 0.4 Hi -f- 15.7 H

31.7In a horizontal plane:5Mo = 31.7 TV + 15.7 T2 + 2.2 H- 4.4 Hi 0Ti = 4.4 Hx - 15.7 T2 - 2.2 H31.7


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TABLE II AVERAGE MEASURED LINK FORCES AND COMPONENTS OFFORCES AT ENDS OF LINKS FROM TESTS OF A MOUNTED PLOW

Link LengthDraft Control Position Control

Link f H V T f H V TNo in lbs lbs lbs lbs lbs lbs lbs lbs1 32 1315 13 2 15 18 1386 1372 16 192 2 5 192 119 15 2 131 81 1 2 13 25 1384 136 249 62 1439 1414 259 654 2 2 782 5 588 6 7 7 452 532 1 55 32 163 1614 62 223 1758 174 67 4

given in table III. It must be recognized that these resul ts are from oneset of conditions of soil and plowadjustment. They are presented as examples of the type of information thatcan b e obtained.

STATISTICAL ANALYSISIn this study the statistical analysiswas made on oscillograph chart de

flections rather than on forces tofacilitate computation. Variances andcovariances computed for deflectionswere then multiplied by suitable constants to convert them to variancesand covariances of forces. Since eachlink was represented on four tracesand four def lect ion values were takenfrom each trace, an estimate of thevariance of deflections was computedfrom the following equation:

Sd2 =4

r l

4S (drf -dr)2i l

4 3 14The subscript r refers to runs, thesubscript i refers to items within runs,and d is the average deflection of a0.5-centimeter length of trace.

Estimates o f t he de fle ctio n covariances were made for each pair of linksfrom the following equation:

on the tractor, it is necessary to writethe equation for the resultants interms of deflections. The general formof this equation is:R= l 1*2 -.In Jn 16Where k isconstant, dependent on theconfiguration of the machine and thecalibration constant of the link, thevariance of a resultant is then givenby:SR = k 2 S 2+ k22 S22+ ...kn2 Sn2+ 2kjk2Cil h +2k2 k3 Cd^+ 2kn_i kn C4.1 dn. 17The above equation gives the varianceof a resultant calculated from a singleset of link forces. The variance estimate of an average resultant shouldbe divided by factor N, which is thenumber of independent observationsthat can beconsidered to make up thetrace over which the average wastaken. An approximate estimate ofthe number of observations may bemade by observing the number ofcycles in the trace. The number ofcomplete cycles may then be considered as equal to the factor N. Thelength of the cycles varied considerably throughout a trace and from onetrace to another. However, in thisstudy examinations of the chartsshowed that the cycle length was approximately 0.5 cent imeters for runsin fast response and 4 centimeters forruns in slow response. Each link wasrepresented on four traces, making at ot al l ength of 40 centime ters . Thefactor N for draft control was 80, andfor positioncontrol 10. Table IVgivesth e variances and standard deviationsof average resultant components asestimated by the method describeda b o v e .

Table II gives the values of the axialorces determined from strain meaurements in the l inks fo r draf t control and position control, and alsoives the results using these forces insimilar to the foregoing, to

ermine the horizontal, vertical, andransverse component s o f forces ac tg at the ends of the five links. Withhe forces acting at the ends of theinks and the gravitational forces

th e soil reactions on the traco r c an be de te rm ined . T h e determin

of th e vertical soil reactions one front wheels will be used as anReferring to the elevationin figure 2, and summingabout point O:2Mo = 70.2 (Rfl -f Rfr; +31.0 V3 + 24.0 Hs + 31.7 V'5-f20.1 Hi -f 31.7 Vj - 24.8 W 4 1 . 4 H 3 6 P l 0 11l may be determined by summingin the horizontal longitudinalirection, neglecting rolling resish = Hi + Hs - Hs - PrP l = 0 12

of the d i ff e r en t i al in the f inalof th e tractor P r is a ss um ed toPl and

r = Pl = Hi + H= - H2 13

P l knowne determined.

Rfl f RFr may TABLE IV. VARIANCES AND STANDARD DEVIATIONS OF AVERAGERESULTANT COMPONENTS

T LE III. SOIL RE CTIONSON TRACTOR FROM TESTS OF A

MOUNTED PLOWNotation Draft Cont r ol Po si ti on Cont ro l(see fig. 2) (lbs) (lbs)

r , P lr + Plf l -f R frr l -f- R rrf l -f- T frrl -j- Trr4- Rrlr 4 Rrr

7781 5 5 6

7 3 32818

588 4

1 6 4 91 9 0 2

8 4 91 6 9 8

72 92 7 7 6

7298

1 6 2 41 8 8 1

By similar analyses the magnituded location of all forces acting upone tractor may be determined. Thesults of these computations are

D r a f t Cont ro l Posi t ion ControlDirect ion ofComponent

Hor izon ta lVer t ica lT r a n s v e r s e

V a r i a n c e15 11 3 3

3 .4

Q Jk 3 715The subscripts a and b refer to the2 links in a run and d is the averagedeflection of the 0.5-centimeter lengthof trace. To make use o f the values ofvariance and covariance computed

for the links and pairs of links to estimate th e var ia nc e o f resultant force

2 (dadt)- 3daSdb

St a n d a r dDevia t ion

12.511.5

1 .8

V ar i an ce35,817

428361

St a n d a r dDeviat ion

18920.719.0

DISCUSSION AND CONCLUSIONSThe results of this study verifysome important relationships concerning the forces on a tractor whenan implement is attached by a restrained link three-point hitch. Onewill observe that the differences inwheel reactions and draft are notlarge when comparing the calculated


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TABLE V. TRACTOR WHEEL LOADSR e a r F r o n t T o t a l

T r a c t o rTractor ca rry ing plowPlowing with three-point h itchPlowing with standard drawbaran d pull type plow

lb s1 8 8 02 6 3 528182253

lb s1090

7 657 3 37 1 7

lb s2 9 7 03 4 0 03 5 5 12 9 7 0

re su lt s fo r draft control with thosefor position control. It should benoted, however, that the rear wheelreaction for draft control is greaterthan for position control, whereas thedraft is greater for position control.Referring to figure 5 and comparingthe force in link 2 for draft controland in link 2 for position control, onewill note the greater variation andhigher peaks for the run in draftcontrol. These rapid fluctuations andhigh peaks of force in the hangerlinks for draft control are undoubtedly caused by the hydraulic system ofthe tractor adjusting to varying draftconditions by raising and lowering theplow slightly and probably accountfor the greater wheel reaction in draftcontrol. Because of the approximationsmade in computing the standarddeviations, it is impossible to computea confidence interval for the averageresultant components. A rough estimate of the upper limit may be madeby adding to the average resultant,twice its standard deviation, and similarly a lower limit by subtractingtwice the standard deviation. A statistical test was not used to compare theaverage resultants in draft control andposition control because the standarddeviations of the average resul tantsand position control are large enoughin themselves to indicate no differenceat a 5 per cent level except perhapswith a vertical component.Table 5 compares the tractor wheelreactions under several conditions.The reactions given for plowing witha pull type plow was calculated, assuming that the draft of the pull typeplow was the same as the mountedplow and the drawbar was pullinghorizontally at a 15-inch height. Itshould be noted that the rear wheelreactions determined in this study are20 to 25 per cent greater for themounted plow than those calculatedfor a pull type plow while the frontwheel reactions are essentially thesame. This study shows that under theconditions of the test the sum ofthe wheel react ions of the tractor wasgreater than the total weight of thetractor and plow. This is probably nottrue for all implements. A comparison of the calculated standard deviations of the resultant horizontal components for draft control and position control shows that the draft control mechanism does keep the draftalmost constant. This is also evidentfrom the appearance of the char s see link 3, figure 5). The method ofobtaining the link forces in a three-point implement hitch outlined inthis study appears to be quite satisfactory. Strain gages can be attached

to links readily and it is not difficultto calibrate the links. If strain recordingequipment is already on hand, themethod is not expensive. Applicationof statistical techniques makes possible estimates of the reliabili ty of themean cha rt deflections used in calculating forces and their resultants.

REFERENCES1. Ciayde, A. W. Mounted Plowsand 3-Point Linkage. Farm Implement News 73, No. 12: 34, 35,74, 78. 1952.

2. Heitshu, D. C. The Kinematicsof Tractor Hitches. AgriculturalEngineering 33: 343-346, 356.1952.

3. Hull, Dale O. Suggestions forThree-point Hitch Plow Adjustment. Iowa State College, Agricultural Extension Service Pamphlet 219. 1955.

4. Perry, C. C. and H. R. Lissner.The Strain Gage Pr imerMcGraw - Hill Co., New York.1955.

5. Rogers, I. C, and G. M. Johnston. Measuring the Forces inTractor Linkage. AgriculturalEngineering 34: 542-544. 1953.

WAFERING IN FORAGEScontinued from page 3

REFERENCES1. Barger, E. L., latest report onField Hay Wafering. CanadianFarm Implements, May, 1962.2. Bruhn, H. D., Zimmerman, A.and Niedermeier, R. P., Developments in Pelleting Forage Crops.Agricultural Engineering 40,April, 1959.3 Butler, J. L. andMcColly, H. F.,Factors Affecting the Pelleting ofHay. Agricultural Engineering40, August, 1959.

4. Dobie, J., Engineering Appraisaof Hay Pelleting. AgriculturaEngineering 40, February, 1959.5. Haenlein, F. W., Richards, C. Rand Mitchell, W. H., Effect o

Size of Gr in d and Lev el o f Intakof Pelleted Alfalfa Hay on itNutri t ive Value in Cows anSheep. ADSA Annual MeetingJune, 1962, College Park, Maryl and .

6. Holdren, R., Wafering ResearcProgress. Proceedings of Seminaon Wafer ing, Massey-FergusonDecember, 1962.

7. Holekamp, E. R., Equipment anLabor Required for HarvestinHay Crops. Paper presented aPacific Northwest Section ASAEPenticton, B.C. Canada, Octobe1956.

8. Lamp, B. J. and Peterson, M. HExperiences with a CommerciaHay Wafering Machine. PapeNo. 62-603. Presented ASAWinter Meeting, December, 196

9. Pickard, G. E., Roll, W. M. anRamser, J. H., Fundamentals oHay Watering. Transactions othe ASAE (4), 1961.

10. Proposed Wafering StandardsASAE Wafering and PelletinCommittee , 1963.

11. Reece, F. N., Mensch, R. anJudy, H. E., Hay Wafering oKansa s Farms . Kan sa s S ta te Unversity Progress Report No. 6February, 1963.

12. Ronning, M., Pelleted anWatered Hay for Milk Prodution. Proceedings of SeminarWafering, Massey-Ferguson, Dcember, 1962.

13. Unpublished data from MichigState University, Lansing, Micgan .

14. Vander Noot, G. W. and O Conor, J. J., Effect of WaferingAlfalfa Hay. ProceedingsSeminar on Wafering, MassFerguson, December, 1962.

techniques of experimental stress analysis and statistics - 1956 - bigsby

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