richard l. echols, b.s. a thesis in

ANALYSIS OF ENERGY REQUIREMENTS

FOR SHREDDING MESQUITE

by

RICHARD L. ECHOLS, B . S .

A THESIS

IN

AGRICULTURAL ENGINEERING

Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for

the Degree of

MASTER OF SCIENCE

IN

AGRICULTURAL ENGINEERING

Approved

Accepted

IDe n ofluie Graduate School

May 1973

80 b T3 (373

ACKNOWLEDGEMENTS

I gratefully acknowledge the guidance of Dr.

Thomas G. Carpenter, my committee chairman and

project director, for his tireless help during my

research, I would also like to thank Dr. W. L, Ulich,

Dr. W. M. Lyle, and Dr. H. Y. Lee for their helpful

criticism.

- 1 1 -

CONTENTS

/ PAGE

ACKNOWLEDGEMENTS ii

LIST OF TABLES v

LIST OF FIGURES vi

1. INTRODUCTION 1

Statement of the Problem 2

Objectives ..• 2

II. LITERATURE REVlEl'/ 4

Related Work 4

Brush Pvelated Research • 7

III, PROCEDURAL PLAN 10

Static Test Procedure e. 11

Dynamic Test Procedure ..•.,• H

Instrumentation ..,,.. 12

Theory of Operation .,,.,, 12

IV. ANALYSIS OF DATA AND FINDINGS .... 17

Feed Speeds 19

Log Diameter, Blade Tip Speed, and Blade Sharpness 28

Applications of Results 43

111-

V. SUMMARY AND CONCLUSIONS 47

Summary • 47

Conelusions .•...•..,..,••.,,••• 50

Recommendations for Further Study 51

REFERENCES 52

APPENDICES

Appendix I •••,,,• , •.•••.•••• 53

Appendix II ...•••••• 57

-iv-

LIST OF TABLES

TABLE PAGE

1. Energy ratios 20-22

2. Total energy, energy per area, and energy per diameter .•,,,••••,,. 25-27

3. Energy ratio for diameter ratio for a given blade tip speed ••,.,,•••• 33

4. Summary of dynamic test data obtained after data reduction and analysis ...... 40

5. Summary of static test data obtained after data reduction and analysis ...... 41

«v-

LIST OF FIGURES

FIGURE PAGE

1. Dynamic cutting test apparatus 13

2. Belt driven carriage table 13

3. Counterweight and blade ...,., , 14

4. Rotating shaft torque transducer ,.,. 14

5. Energy ratios at equal blade tip speeds but different feed speeds 24

6. Blade tip speeds vs. total energy 29

7. Blade tip speeds vs. energy per square inch of cross-sectional area ,.,..., 30

8. Blade tip speed vs. energy per inch of diameter ••.••,., •• •«.•• 32

9. Diameter ratios vs. energy ratios for sharp blade dynamic tests 35

10. Diameter ratios vs. energy ratios for dull blade dynamic tests 36

11. Blade tip speed vs. slope for dynamic sharp blade tests .•••,•••• 37

12. Blade tip speed vs. slope for the dynamic dull blade tests 38

13. Relationship between energy, diameter, and speed for sharp and dull blades 42

-vi-

CHAPTER I

INTRODUCTION

Great strides have been achieved in agriculture in

the past few years. Farming has advanced from mule or

horse drawn shares to highly mechanized, high speed, high

horsepower equipment. During this period of advancement,

however, the Texas rancher has allowed mesquite brush to

invade and infest his ranchland and choke out the native

grasses on an estimated 88 million acres (8). This

infestation has spurred research towards the development

of methods for controlling mesquite and other undesirable

brush growth with the ultimate objective of killing out

the brush infestation.

A simple brush control method advocated by some

researchers is shredding. Shredding which has been a

popular method of weed control, highway right-of-way

maintenance, and lig^t brush control for many years

appears to offer a rapid, effective, and economical

approach to brush control. A number of researchers are

currently involved in research programs pertaining to the

various aspects of shredding as a brush control method.

From an engineering viewpoint, additional information is

needed pertaining to machine requirements and shredder

design. ^-^^

-2-

Increased use of shredding might be realized for

mesquite control if power and energy requirements for

shredding can be determined and this information is

subsequently used in shredder design. Instrumented

laboratory cutting tests in combination with limited

field information was thought to supply the needed

design information.

Statement of the Problem

Shredding appears to be a very realistic and

practical method of mesquite control, but basic design

information pertaining to or defining the power and

energy requirements of shredding brush is not available,

and is needed. Because of this need, a laboratory study

was conducted to define the power and energy requirements

of a blade when cutting mesquite.

Objectives

The objectives of this study were to determine the

energy requirements for cutting mesquite under various

conditions. More specific objectives were as follows:

1, To determine the energy requirements of a

blade for a relatively static cutting

condition. This requires the determination

of the energy required to cut restrained

mesquite logs with a slov; speed blade.

-3-

2. To determine the energy requirem.ents of a

blade for a relatively dynamic cutting

condition. That is, a blade traveling at a

speed equivalent to blade tip speeds of a

field machine,

3. To determine the energy requirements of a

dull blade for breaking or crushing mesquite

at both high and low speeds.

The information obtained will be analyzed on a

comparative basis and utilized to more accurately

define optimum conditions and requirements for shredding

mesquite.

CHAPTER II

LITERATURE REVIEIV

Since shredding has not been a widely used method

of mesquite control, very little information has been

reported in literature concerning shredder designs for

large brush. Information relating to brush shredding

consists primarily of field and laboratory tests of

forage harvesters. One series of brush shredding tests

was reported by Smith (9), A personal interview with

1^. Charlie Fisher (6), head of the brush control program

at the Texas Agricultural Experiment and Research Station

at Lubbock, Texas, provided the outlook that all shredders

used in brush were adaptations of crop shredders V7ith no

additional engineering. Mr. Fisher believes that shredders

will become a more important tool for the initial treat

ment of brush when a shredder unit is designed for the

purpose of shredding brush.

Related V>'ork

Laboratory Tests

Feller's (5) research consisted of a pendulum type

apparatus designed to cut standing stalks and to measure

the energy required for cutting. The apparatus permitted

observations of the effect on the stalks after one pass -4-

-5-

of the knife. Alfalfa and Sudan grass stalks, fixed in

a holder, were cut at relatively low velocities up to

1900 feet per minute. Angles between the knife edge and

the direction of motion were varied from 7 to 90 degrees.

A sharp knife and a dull knife were used in the tests.

The results of these tests showed that the sharp

knife cutting was best at about 60 while the dull knife

performance was best at 90°. The cutting quality of the

dull knife v/as very poor and the energy requirement v/as

high. Feller further reported that knife angles below

60° had little effect on cutting. Also the velocity of

the knife did not have any effect on the energy of cutting

for short alfalfa and Sudan, but had a great effect on tall

plants. High speed cameras showed that the stalks were

pushed about one inch before cutting took place.

Feller gives the energy requirements for cutting

alfalfa V7ith a conventional shredder as 0.125 to 0.223

ft.-lb. per stalk. This energy was determined on the basis

of the speed loss of the pendulum after the cut.

Bosworth and Yoerger (2) report in their research

that improved design for flail knives vjould decrease

power and maintenance requirements and result in a

machine that was safer to operate. The/designed and

built a laboratory test stand that consisted of a rotor

-6-

assembly with tV7o flail knives, counter v/eights, and a

carriage table. One Icnife v/as strain gauged for torque

measurements and the other blade carried a linear variable

differential transformer for a knife deflection measure

ment. Rotor speeds used were 820, 1145, 1359, and 1640

revolutions per minute.

Corrugated cardboard vzas cut in an attempt to give

a good simulation of a crop and maintain a constant

medium. The forward speed of the feed table was 4 miles

per hour. The samples required an average energy of

0.80 ft.-lbs. per stem with a density of 100 stems per

square foot.

Field Tests

Hephard and Hebblethwaite (7) field tested forage

harvesters in England. Of the harvesters tested, tv7o

were direct-throw flail type. They stated that ground

speeds from 2 to 5 miles per hour had no visible differ

ences on the length of cut. The report states that the

flail machines had a higher power requirement than

conventional type machines, even though the flail type

results in a longer length of cut. The researchers

concluded that the higher power requirement of the flail

type machine V7as due to laceration during cutting. The

researchers also stated that the basic simplicity of the

-7-

flail design is bound to have advantages as far as

mechanical reliability is concerned.

Bockhop and Barnes (1) ran a series of tests on a

Lundell forage harvester (flail type) to analyze the

power requirements, to acquire information on the peak

torques, and to establish the requirement for a power

unit for flail type forage harvesters.

Power requirements vrere determined by using strain

guages to measure torque on the rotor shaft. Their

research revealed an energy requirement of one horse

power per 14.5 Ib./min. which is equal to 2.3 Hp.-Hr. per

ton. It was concluded that the flail type machine re

quires more horsepower than a conventional harvester,

especially at full capacity.

Brush Related Research

As previously mentioned, the only series of tests

conducted for determining machine requirements for flail

shredding of brush were reported by Sm.ith (9), To deter

mine the energy of cutting. Smith dropped a v/eighted

knife a known distance. He measured the depth of cut and

multiplied this depth times the stem diameter. This

product was called the effective area. The given energy

was then divided by the effective area and the results

were assumed to be the energy required to cut mesquite.

-8-

Smith further states that the energy requirement for

cutting was found to be 1210 in.-lbs. per sq. in. of

effective area. The results would appear to be

questionable, however, because his effective area and

the actual area of cut are not proportional except for

a complete cut or when the log is cut exactly half-way

through. Smith further stated that he found that a

1307o to 250% increase in energy v/as required for a dull

knife.

In additional work conducted by Smith, it was

reported that 10 horsepower per foot of shredder width

appears to be a good rule of thumb for the power re

quirements for shredding brush. Smith further judges

that the flail shredder should contain approximately

40,000 ft.-lbs. of kinetic energy when running at rated

speed. This estimate he bases upon field observation of

a heavy flail shredder operating over a range of rotat

ional speeds in various size brush. The 40,000 ft.-

Ibs., he states, is not all available for shredding

large intermittent loads, but an acceptable rotational

speed drop of 35% would result in utilization of

approximately 23,000 ft.-lbs. of energy per foot of v/idth.

Smith also found through field observations that the

energy requirements for shredding mesquite could be

-9-

expressed as approximately 3.4 Hp,-Hrs, per ton of

material shredded. This is equivalent to approximately

3400 ft,-lbs, of energy per pound of mesquite. Comparing

this value against the available 23,000 ft.-lbs, per foot

of v/idth and assuming a 10-foot wide shredder, one could

shred an almost instantaneous intermittant load of

approximately 70 pounds. Actually, the load could no

doubt be significantly higher than this because the load

is not shredded instantaneously which results in energy

contribution from the engine pov/er source itself.

In summary. Smith's findings were:

(1.) The power requirement for shredding mesquite

is 3.4 horsepov/er per ton per hour.

(2.) A guideline for designing a flail shredder

for brush appears to be 10 horsepower per

foot of width.

(3.) A kinetic energy level of approximately

40,000 foot-pounds per foot of width appears

most desirable.

A summary of Smith's v/ork by Carpenter (3) states

that exceptionally high blade tip speeds are not nec

essarily desirable for brush shredding because of a finer

degree of shredding and a higher power requirement. Blade

tip velocities within the range of 10,000 to 14,000 feet

per minute were judged to be most desirable.

CHAPTER III

PROCEDURAL PLAN

Since engineering data on power and energy require

ments of a shredder for mesquite appears to be limited

to Smith's work, laboratory tests were undertaken to

determine the energy required to cut or break mesquite

over a range of blade cutting speeds with both sharp

and dull blades. This required the use of two distinctly

different laboratory machines. The first laboratory

tests v/ere conducted with a relatively slov/ moving blade

which was weighted and dropped from a height v/hich was

just sufficient enough to sever the log.

The other laboratory set-up involved a high speed

rotating blade v/hich v/as traveling at velocities in the

range of 7,000 to 16,000 feet per minute. These

velocities generally encompass the range of blade speeds

encountered in existing shredders and suggested by

Carpenter, Special instrumentation was constructed to

measure speed-torque relationships and integrate these

measurements into a total energy value required for a

particular cut.

Both machines were equipped v/ith first a sharp

blade and then a dull blade to obtain a comparative

energy requirement. Both blades were 0.5 inch thick

-10-

- 1 1 -

steel. The sharp blade was ground to 45°angle on both

sides and the dull blade was rounded on a 0,25 inch

radius. The mesquite logs used in these tests were

obtained from a local ranch. Sam.ples were selected at

random from several locations on the ranch.

Static Test Procedure

Relatively static or slow speed tests were performed

by placing a mesquite log on a block and dropping a

blade of a given mass a kno\7n distance. By trial and

error, a correct distance was found that cut the mesquite

log. Calculations of the energy required to make the cut

was accomplished by assuming the kinetic energy of the

blade at impact was equal to the potential energy prior

to release.

Therefore, Energy = % IW^ = WD

Where, W = total weight of blade and

the attached mass

D = height of drop

Dynamic Test Procedure

The d3''namic cutting tests v/ere performed with a

single counterweighted rotating high speed blade. The

entire cutting apparatus consisted of a 36-inch square

box constructed of ^-inch steel plate. The blade was

mounted to a 2'2-inch diameter shaft which was driven by

a six-cylinder industrial engine. The complete setup

-12-

is shown in Figure 1. A belt driven carriage table , as

sho\^ in Figure 1 and 2, was used to move the mesquite

log into the blade. The count erweighted blade is shov/n

in Figure 3. Special instrumentation was assembled to

measure the energy of cutting.

Instrumentation

A strain-gauged rotating shaft torque transducer,

as shown in Figure 4, was mounted in the driveline between

the cutter and the engine and a counter type digital speed

pickup with an analog converter was connected to the

ignition system of the engine to monitor torque-speed

relationships. Since it was assumed that engine speed

v/ould vary somewhat during the cutting process, a

special multiplier-integrator circuit was constructed

to integrate the product of torque and speed with

respect to time. The results produces the total energy

required for cutting a given mesquite log.

Theory of Operation

The torque transducer available for use on this

project v/as a four leg, self nulling bridge with

sensitivity of 0.181 mv/1000 in.-lb./volt across bridge.

From a study by Passmore (8) it was found for an input

voltage of 10 VDC, the resulting sensitivity is 1.81

mv/1000 in.-lbs. In order to increase the sensitivity of

the transducer to a usable level, an operational

amplifier was connected across the output legs of the

-13.

Figure 1. Dynamic cutting test apparatus

Figure 2, Belt driven carriage table

-14-

Figure 3. Counterweight and blade

Figure 4. Rotating shaft torque transducer

-15-

bridge. The amplifier has an adjustable gain of

approximately 552 which gives an output sensitivity

of 1,0 volt/1000 in,-lbs, torque.

The offset null of the operational amplifier v/as

used to null the steadystate error introduced by

frictional losses within the shredder,

A peak reading volt meter was used to measure the

peak torque from the transducer. The peak reading volt

meter follov/s the bridge amplifier v/ith unity gain.

This provides an output of 1 volt/1000 in.-lbs, torque.

The output is displayed on a 100 UA meter calibrated in

1000 in.-lbs./units.

In order to measure the total energy required v/ith

a variable speed engine, the integral of the product of

the engine speed and the instantaneous torque with

respect to time must be computed. The speed of the

engine was determined by a digital to analog converter

being driven by the points of the engine. The sensitiv

ity of this measurement was 1 volt/300 RPM.

The digital to analog conversion was performed by

one-shot triggered b}'' the signal from the points. The

one-shot v/as averaged by a high speed integrator. Follow

ing the integrator, an inverting amplifier which determines

the sensitivity of the measurement was used.

An analog multiplier was used to perform the multipli

cation. The gain of the multiplier was determined to be

-16-

XY/10. This provides an output sensitivity of 0.1

volt/300 RPM/1000 in.-lbs. torque.

Following the multiplier, an integrator v/ith a

selectable time constant was used. The output of the

integrator was set 0.10 volts. The sensitivity depends

upon the value of the multiplier selected and is 1

volt/3 X 10" multiplier in.-lbs.

The reset function sets the total torque and peak

torque indicators to zero by discharging the storage

capacitors holding the required charge to produce the

output. This is equivalent to setting zero initial

conditions into the instrument.

The basic formula used in the calculation of power

and energy requirement in the dynamic situation is as

follows:

Energy = 2 ^ \^2

^1

(n)(T) dt

V/hen speed and torque do not vary with respect to

time, this equation reduces to:

Energy = 2rr nTt

Where; E = energy in ft.-lbs.

t = time in minutes

T = torque in lb,-ft.

n = revolutions per minute

The wiring diagram for the instrumentation set-up is

shown in Appendix I.

CHAPTER IV

ANALYSIS OF DATA AND FINDINGS

The data obtained in this study is presented in

Appendix II. This data shows the energy values required

for cutting mesquite logs over a range of diameters,

blade speeds and feed speeds for moving the log into

the cutter blade for the dynamic tests.

The maximum size log which could be cut in the static

type tests was found to be three inches in diameter.

This was for a sharp blade. For the dull blade tests,

the maximum log size was a two-inch diameter. Larger

logs could have been cut, but the amount of weight re

quired becomes difficult to hoist by hand with the

arrangement used. The maximum energy for these tests

was 1190 ft,-lbs, which was developed by dropping a

total weight of 170 pounds from a drop height of seven

feet.

Trial tests utilizing a number of different weight

and drop heights were conducted to determine the amount

of energy which would consistently result in complete

cutting of the log.

During the course of the high speed tests, a

drive line failure was experienced while trying to

-17-

-18-

cut a 4-inch diameter log. Although the drive line

was then repaired and strengthened, subsequent tests

were restricted to logs of 4-inch diameter and smaller.

The results of these tests consist of data for 2, 3,

and 4-inch diameter logs, cut at blade tip speeds

ranging from 7540 ft./min. to 15,910 ft./min. and

at feed speeds of 2, 4, and 6 MPH. Three data points

are shown for each combination of test conditions and

the average energy value was calculated for these

three points.

This average energy value was then used in

the subsequent data analysis. Some scatter was evident

in the data, but this could be attributed to different

strengths in the mesquite log samples.

The strength of the mesquite logs seemed to vary

with the time of year when they were cut, with the

moisture conditions when they were cut, and with the

length of time they were allowed to season before the

sample was used. These conditions, however, will be

present in the field situation, so no attempt was

made to hold them constant.

The results of the dynamic tests were analyzed

-19-

to deteirmine significant relationships between the

energy levels required for cutting and the other

variables which include; feed speed, log diameter,

blade tip speed, and blade sharpness. The results

of the slov/ speed tests were then compared to the

high speed test results.

Feed Speeds

The ratio of the energy requirements for cutting

equal size logs at equal blade tip speeds but at

different speed rates were calculated and tabulated

to determine if feed speed is a significant factor

affecting the total energy requirements. These ratios,

which are summarized for all log diameters in Table 1

indicate a slight increase in energy requirement as the

diameter of the log increases, but the average value

of this increase for the 2 inch to 4 inch log is only

8.237o, For the 2 inch to 6 inch log the increase is

8,58%, and for the 4 inch to 6 inch log the increase

is only 0,3%, Thus, this indicates that the energy

level was slightly lower for the 2 MPH feed speed but

that there is essentially no difference between 4 and

6 MPH. The relationship involved is shown graphically

-20-

Table 1. Ratio of energy requirements for cutting selected size logs at selected blade tip speed but at different feed speeds

Blade Speed (Ft./min.)

2

7540 9210 10855 12560 14230 15910

^l-k

Inch Diamet

.741 ,844 ,732 ,700 ,736 ,785

2 <"

er Sharp

,654 ,844 ,667 ,913 ,855 ,861

^3^^

Blade

,883 1,000 ,912

1,304 1.162 1.097

Average

.759

.896

.770

.972 ,917 .914

Avg. .756 .799 1.050 .817

2 Inch Diameter Dull Blade

Avg.

7540 9210 10855 12560 14230 15910

m» mm

1.162 1.086 1.074 1.056 .946

1.061

•• ..

1.078 1.003 .926 .870 .822 .940

,. ^

.928

.923

.862

.824

.869

.881

•» a>

1.055 1.004 .954 .917 .879 .962

*A.

'VA/

^'A.

Ratio of energy at 2 MPH to energy at 4 HPK.

Ratio of energy at 2 MPH to energy at 6 >'LPH.

Ratio of energy at 4 MPH to energy at 6 MPH.

Table 1. (cont inued)

- 2 1 -

Blade Speed

( F t . / m i n . ) A 1* ^2* ^3''^ Average

Avg.

3 Inch Diameter Sharp Blade

7540 9210 10855 12560 14230 15910

.887 1.033 1.211 1.046 1.002 .933

1.109

.598

.852 1.090 .978 .913 .969 .900

.675

.824

.900

.934

.911 1.038 .880

.720

.903 1.067

.986

.942

.980 "T933


Avg.

7540 9210 10855 12560 14230 15910

•D «•

.984

.927

.930

.920

.933

.939

- •

1.005 1.000 .899 .891 .919 .943

. .

1.021 1.079 .966 .969 .985

1.004

. .

1.003 1.002 .932 .927 .946 .962

-22-

Table 1. (continued)

Avg.


4

7540 9210 10855 12560 14230 15910

IVc ^2''f

Inch Diameter Sharp

1.376 ,905 ,743 ,782 ,697 .698 ,867

1,010 1.094 1.141 1.109 1.080 1.073 1.084

3 >

Blade

1.734 1.208 1.536 1.418 1.549 1.537 1.330

Average

1.040 1.009 1.140 1.103 1.109 1.103 1.084


Avg.

O v e r a l l Averages

7540 9210 10855 12560 14230 15910

.912

.919

.912

.949

.927

.930

.824

.868

.849

.899

.868

.874

.903

.944

.931

.947

.936

.939 .925

.924

.864

.921

.933

.997

.880

.910

.897

.932

.910

.914

.907

.947

O v e r a l l % I n c r e a s e 8,23% 8,58% 0,3%

- 23-

in Figure 5 where the energy at a given feed speed

for one diameter is plotted on the ordinate and the

corresponding energy value at a different feed

speed is plotted on the abscissa. This plot provides

a visual comparison of the scatter involved. If

feed speed has no effect on energy requirement, then

all values should fall on the 45° line shovm, or

due to random error the values should be evenly

distributed on either side of the line. This graph

helps to verify that the effect of feed speed upon

energy is relatively unimportant. Therefore, the

energy values obtained at the three different feed

speeds were averaged together for further analysis of

the effect of the other variables involved. These

average energy values are summarized in Table 2, for

each log diameter and blade tip speed included in the

study. Values of energy per inch of log diameter

and energy per square inch of cross-sectional area

were calculated and included in this table for further

analysis of log diameter and blade tip speed effects.

- 24 -

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00 C3N 00 CJN O ON VD CM CO i n CM r>. i n vo vo r^ 00 CO

m m cMinco <f CO r^ CO COCM vD vo vci r^ r^ 00 00

td p o H

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r H CO CO VO CO < t 00 CO CO m r H r>. CO <}• <t- m vO vD

1—I r ^ CM CM CO CO < t vo CJN CM < t r> . CM CM CM CO CO CO

C M m CO O CM CM o rH CO m vD r>. CM CM CM CM CM CM

m CM CM r^ o r^ CJN VO CO < t < f r H I-H CO m r^ CJN r H 1-H f-H f-H r H f-H CM

o r^co CO o CO o CO r^ r*. vD CO r^ COO CM <)- vD t-H rH CM CM CM CM

r > . o v o m m <t CO o CM <^ CJN m m r^ ON rHCM < t CM CM CM CO CO CO

o o m o oo <t rH m VD CO rH m CM 03 m CM CJN r>. CJN o c M <t m

o o m o o o < t r H m VO CO r H m CM CO m CM CJN r ^ CJN o CM < f m

o o m o o o vJ- f-H m vO CO r H m CM 00 m CM CN r^ CJN o CM < f m

CM CO

-27-

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m CM CO r- CO CM vD r^ r^ <t vD o CO ON

CM CM CM CO oo CO

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CM r H rH f-H r H rH

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<}• < t vo r^ CJN f-H

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m m o m o CMm r o

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to P to 0 H O

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td r-4 CQ

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m omr^ o • • • •

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-28-

LoR Diameter, Blade Tip Speed, and Blade Sharpness

The relationships between log diameter, blade tip

speed, and blade sharpness is sho -m graphically in

Figure 6, As one might expect the energy required for

cutting increases with log diameter and increased blade

tip speed. The higher energy values for a dull blade

are also to be expected. The energy values obtained

in the static type tests were also plotted in Figure 6,

but these values appear to be rather inconsistent.

Although definite patterns are evident v/hen energy

versus blade speed for various diameters was plotted,

further analysis appears to be needed in an attempt to

develop a meaningful and useful general relationship

between the variables,

A reasonable expectation is that the required

energy would vary with the cross-sectional area of the

log. Thus, energy per square inch of cross-sectional

area v/as calculated and plotted as shown in Figure 7,

Hov/ever, the figure does not result in a satisfactory

collapse of the data. This graph indicates that the

increase in energy v/ith increased diameter is less than

the corresponding increase in area. This is apparent

because the energy per unit area is lowest for the

larger diameter.

- 2 9 -

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-31-

An additional consideration is the possibility

that energy varies directly with diameter. Thus, the

energy/diameter ratio was calculated and plotted as

shown in Figure 8, The resulting relationship

between energy/diameter versus blade tip speeds appear

to be much better than the previous relationships,

because the values tend to fall closer to one average

line, but this graph indicates that perhaps blade tip

speed also influences the magnitude of energy increase

with increase in log diameter.

One approach to analyzing the data is to examine

energy ratios at given diameter ratios for given values

of blade tip speed. In keeping with this approach,

energy ratios were calculated for the possible diameter

ratios of 2.00, 1.50, and 1.33. These values are shown

in Table 3. for each blade tip speed and for both the

sharp and dull cutting blade. It should be pointed out

that diameter ratio of 1.0 also results in an energy

ratio of 1,0. If energy ratios are subsequently

plotted versus diameter ratios, then this forces the

plot through coordinates of (1,1). The energy ratios

at a given diameter ratio are not constant, thus this

indicates that energy and diameter are not independent

of blade tip speed.

A plot of energy ratio versus diameter ratio is

- 3 2 -

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-33-

Table 3. Energy Ratio for diameter ratio at a given blade tip speed.

Speed (Ft./min.)

7540 9210 10855 12560 14230 15910

7540 9210 10855 12560 14230 15910

2.00

3,91 3,48 3,14 2,62 2,19 2,08

2,12 1,98 1.91 1,80 1,70 1,63

harp

Diameter

1,50

Blade

2,24 2,18 1.98 1.60 1.52 1.50

Dull Blade

1.42 1.39 1.36 1.30 1.27 1.24

Ratio

1.33

1.74 1.59 1.58 1.64 1.43 1.39

1.49 1.43 1.41 1.38 1.34 1.31

1.00

1.00 1.00 1.00 1.00 1.00 1.00

1.00 1.00 1.00 1.00 1.00 1.00

-34-

shown in Figure 9 and 10 for the sharp and dull

blade, respectively. This results in an equation of

the form,

Ej/E2 = (dj/d2)^

where, K is the slope of the line or effectively

the exponent to which the diameter must be raised to

result in a collapse of the data. The slope or K-

values shown directly in Figures 9 and 10 range from

0.70 to 1.97. Each value is for a given blade tip speed

with the larger values corresponding to the slower

speeds.

Plots of K-values versus blade tip speed are shown

in Figures 11 and 12. An excellent linear relationship

is shown and the equations for K were found to be as

follows:

Sharp Blade: kg = 2.840 - 0.000113 S

Dull Blade: kj = 1.420 - 0.000045 S

where, S is blade tip speed in feet per minute and

k and kp. are exponents to be used for collapsing the

data. In other words, the following plots should

result in a single relationship for the sharp blade

and another for the dull blade.

Sharp Blade: E/d^s Vs. Speed

Dull Blade: E/d^D Vs. Speed

- 3 5 -

c\j

a H EH <

C5 P4

Pxl

K va lues

4 ^

3 .

2 -

DIAMETER RATIO d^/d^

E-^/E^ = (d-^/d^) K

where K is slope of the line

u

I I i

Figure 9- Diameter ratios vs energy ratios for the sharp blade dynamic tests

- 3 6 -

CVJ

r-i

CO O H

cr> p:;

H

K values

1.08 0.99 0.95 0.85 0.77 0.70

E^/E^ = (dj /d^) K

where K is slope of the line

DIAMETER RATIO d^/d^

Figure 10- Diameter ratios vs energy ratios for the dull blade dynamic tests

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-39-

Values of K and E/d^ were calculated for data

points and tabulated in Table 4. An inspection of

this data shows that the E/d^ values are very nearly

constant for all diameters at a given speed. The

equations for k^ and k^ were also used to calculate

values of E/d for the slow speed tests. The re

sulting values for the slow speed tests are shov/n in

Table 5.

The graphs of the average E/d versus blade speeds

are shown in Figure 13. Two separate relationships

are shown; one for the sharp blade and one for the

dull blade. The slow speed test results are also

plotted to form a continuous relationship with the

dynamic or high speed tests. The dull blade tests

are somewhat erratic at the lov/ speeds.

The analysis appears to result in an excellent

reduction of the data obtained and all data points

with the exception of the energy for slow speed cutting

of a 1,5 inch diameter log are represented very well

by the graphs in Figure 13,

The results obtained indicate the importance of

utilizing a sharp blade if possible, even though this

may not be practical in field application. The

results also indicate a significant increase in

energy as blade speeds are increased. In fact, this

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-41-

Table 5, Summary of static test data obtained after data reduction and analysis.

Dia, Speed Energy Vi* d^ d ^

Sharp Blade

1,0

1,5

2,0

2,25

2,5

2.75

3,0

1.0

1.5

1.75

2.0

480

1120

1220

1175

1265

1269

1265

480

830

1120

1175

75

412

487

600

770

910

1190

Dull Blade

75

215

550

750

2,786 1,00 75,0

2,713 3.00 137.3''«v

2.702 6.51 74.8

2.707 8.98 66.8

2.697 11.84 65.0

2,697 15.31 59.4

2.697 19,36 61,5

1,398 1,00 75.0

1.383 1.75 122.9

1.370 2.15 255.0

1.367 2.58 290.7

'«"Calculated on basis of equation obtained in dynamic

tests.

*' This value is unusually high and, therefore, was

not included in the subsequent analysis.

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-43-

indicates that a roller chopper type device would be

most effective from the standpoint of energy require

ments ,

From a practical viewpoint for shredding, however,

the shredder blade must be traveling at some reasonable

speed in order to maintain rotary motion and to provide

kinetic energy for smooth continuous power flow.

Application of Results

Although field application of the results of

the cutting tests was not outlined as an objective of

this study, some consideration of the usefulness of the

information obtained appears to be in order. Some of

the trends or implications of the results were pointed

out in the previous section, but meaningful application

methods must include an additional detailed study of the

size distribution of shredded brush for various field

situations.

The results of this study can be compared with the

recommendations as presented by Smith. He shows that

the results of his static cutting tests produce a range

of energy for cutting mesquite of 101 to 161 ft. lbs.

per square inch of cross-sectional area. Thus, the

maximum energy required for cutting a 3-inch diamioter

log should be 1139 ft.-lbs. In addition to this. Smith

assumes that 258 ft.-lbs, of energy would be dissipated

-44-

due to collision of the flail with the wood and an

additional 96 ft.-lbs. of energy would be required

to accelerate the wood mass. This then yields a total

of approximately 1500 ft.-lbs. of energy to cut the

3-inch diameter log.

The energy requirement for cutting a 3-inch

diameter log based upon the results of this study

can be determined as follows:

Assuming a blade tip speed of 10,000 ft./min.

and a dull flail blade;

From Figure 13: E ^^c — ^ = 725

d^

For a dull blade,

K = 1.42 - .000045(s) = 1.42 - .000045(10000) Therefore, K = 0.97

Thus, the energy requirement can be expressed as,

E = 725d^ = 725d^'^^

Therefore, for a 3 inch diameter log,

E = (725) (3)'^^ = 2105 ft.-lbs. of energy

This value is approximately 40% higher than the

maximum value obtained by using recommendation from

earlier work. The values obtained in this study would

appear to be more reliable since it is based upon actual

dynamic cutting tests.

-45-

Another example of how one might use the infor

mation obtained in this study is as follows:

For a typical field situation:

Assume:

10,000 ft./min. blade tip speed

16 blades per foot

10 foot cutting width

8 blades per foot under maximum load

Then:

(8)(10) = 80 blades under full load

For a dull knife and a 4 inch diameter log the

energy required for one cut is:

E = 725d-^^ = (725)(4)-^^ = 2781 ft.-lbs.

Therefore:

(80)(2781) = 222,549 ft,-lbs, of energy

If a 357o speed reduction can be tolerated then

this corresponds to using 587o of the total energy

available.

Thus, the total energy stored in the machine must

be:

^^^^33^ = 383,705 ft,-lbs.

This indicates approximately 38,000 ft,-lbs, of

energy per foot of width would be needed for the machine

to handle 4 inch diameter logs. As larger logs are

-46-

encountered, this energy requirement would go up.

Smith concluded from field observations that

approximately 40,000 ft,-lbs. of energy per foot of

shredder width is an appropriate design value.

The method of analysis presented is valid for the

range of variables used in this study, but caution

should be exercised in trying to extrapolate energy

values for higher blade speeds and larger log diameters<

CHAPTER V

SUMMARY AND CONCLUSIONS

Summary

Shredding appears to be a very realistic and

practical method of mesquite control, but basic design

information pertaining to the energy requirements

needed for shredding was lacking. This study determined

the energy requirements for dynamic cutting and static

cutting of mesquite for both sharp and dull blades.

After a review of pertinent literature, it was

decided that a weighted blade would be dropped on

restrained mesquite logs for the static tests to

determine by trial and error an appropriate energy

for a consistent cut, A rotor with one blade and

counter weight was used in the high speed tests. The

blade speed was varied between 7000 and 16,000 feet

per minute. The energy required was measured by means

of a torque transducer mounted in the driveline and a

multiplier-integrator circuit, which integrated the

product of speed and torque with time.

The maximum size log cut with the static tests was

-47-

-48-

3 inches in diameter with a sharp blade and 2 inches in

diameter with a dull blade. In the dynamic tests, a 4

inch diameter log was the largest to be cut.

The results of the dynamic tests were analyzed

to determine the relationship between feed speed, log

diameter, blade tip speed, and blade sharpness. The

results of the slow speed tests were then compared to

the high speed test results.

Very little effect of feed speed upon the required

energy was found when the feed speed was kept in the 2

to 6 mile per hour range. A graphical relationship

between the log diameter, blade tip speed, and blade

sharpness was established. This relationship yields

values of energy required for cutting mesquite logs up

to 4 inches in diameter, through a range of blade speeds

up to 16,000 ft./min. Extrapoluted values for larger

log diameters or higher blade speeds would be question

able.

A large increase in the required energy between

sharp blade and dull blades was found. However, it

is very reasonable to expect the dull blade to require

more energy. In fact, when designing a shredder, one

probably should use the dull blade values because most

shredders operate with dull blades due to the adverse

conditions of use and the operator's lack of service to

the machine.

1 1

•49-

The investigation yielded results which agree

reasonably well with values previously observed in

the field by Smith and Carpenter.

-50-

Conclusions

Specific conclusions drawn from this study are as

follows:

(1) Although the relative energy requirements

of a dull versus sharp blade varies consid

erable with speed and brush size, energy

requirements are significantly higher for

the dull blade. For a given blade speed,

the percent increase in energy required

for a dull blade is greatest for small

diameter logs.

(2) There is a significant increase in energy

requirements cutting as the speed of the

blade or flail increases.

(3) The effect of log size upon energy require

ment becomes less significant at higher

blade speeds.

(4) In the design of a brush shredder, the lowest

practical blade speed should be utilized

because of the lower energy requirement at

slow blade speeds.

-51-

Rec_o.mmendations for Further Study

The following is presented as suggestion for

additional study:

(1) A detailed study of the size distribution

of shredded brush for various field

situations,

(2) A study of the energy required to cut

mesquite logs of 5 inch to 8 inch diam

eter,

(3) Further study in defining the duration of

load on a shredder when shredding brush,

(4) A field study with shredders using

different knife shapes and rotor speeds,

(5) A field study with roller choppers.

REFERENCES

1, Bockliop, C, W, and Barnes, K, K,; "Power Distribution and Requirements of a Flail-Type Forage Harvester," Agricultural Znpaneerin.q;. Vol, 36, July 19^5, Pg, 455-457,

2, Bosworth, D, L, and Yoerger, R, R,, "Dynamic Considerations for Flail Knives," American Society of Agricultural Engineers Paper Number 65-613, A.S.A.E., St. Joseph, Michigan, 1965.

3, Carpenter, Dr. T, G,, Personal Interview, Texas Tech University, Lubbock, Texas, Sept. 1971, Dec. 1972.

4, Eshbach, 0, V/., Handbook of Sn.Q;ineering. Fundamentals, New York: John \/iley and Sons, Inc., 1965.

5, Feller, R,, "Effects of Knife Angles and Velocities on Cutting of Stalks without a Conter-edge," The Journal of Agricultural Engineering; Research. British Society for Research in Agricultural Engineering, Volume 4, Number 4, 1959,

6, Fisher, Charlie, Personal Interview, Texas Agricultural Experiment and Research Station, Lubbock, Texas, June, 1972,

7, Hepherd, R, Q, and Hebblethwaite, P,, "A Comparison of Fielci Performance of Forage Harvester Mechanisms," The Journal of Agricultural Engineering Research, British Society for Research in Agricultural iingineering. Volume 4, Number 1, 1959,

8, Passmore, P, M., Personal Interview, Lubbock, Texas, January, 1972,

9 Smith, Clayton, C,, "Analysis and Design of Mechanical Shredders for the Control of Noxious Brush." M.S. Thesis, Texas Tech University, May, 1971

-52-

APPENDIX I

Electrical Diagram of Instrumentation

til III

-53-

-54-

Rl

Wiring Symbols

Gail offset for transducer

^2 Offset adjust

^^ 3000 RPM peak set

^^ 0 RPM null set

R5 X-offset null

R6 Y-offset null

R7 X-Y = 0 null

Kl Power on-off

K2 Null set

K3 Reset

K4 Gail select

AlA Transducer amplifier

AlB Peak voltmeter amplifier

A2A RPM signal conditioner

A2B RPM signal conditioner

A3A Multiplier gain set

A3B Integrator

Ml Null meter

M2 Peak torque indicator

M3 Total energy indicator

-55-

M P

M

OH

HI—-»

OJ

ft

k..xj !bf l«RN«nMP«

LJjTti<»wmTfnMiPl

1 1 I I III I III • III i M i i I II I I I m w i i II

•At,^W-\,,A

- 5 6 -

Ti 0

P fi o o

CD < i-H

P a

M

vw<g)-* K^ S

III

APPENDIX II

Results of Tests

-57-

-58-

DYNAMIC TEST RESULTS

Sharp Blade

Log Blade Feed Dia, Speed Speed (in,) (Ft./min,) (MPH)

Measured Energy Required (Ft.-lb.)

Replication

Average

7540

9210

10855

12560

14230

15910

2 4 6

2 4 6

2 4 6

2 4 6

2 4 6

2 4 6

262 314 366

366 576 628

628 628 681

681 890 734

890 1309 1204

942 1361 1204

209 471 471

471 471 471

419 733 785

942 1152 786

1047 1257 1100

1099 1518 1310

419 419 524

576 628 576

524 785 890

576 1099 890

838 1204 943

1204 1257 1255

297 401 454

471 558 558

524 716 785

733 1047 803

925 1257 1082

1082 1379 1256

- 5 9 -


S h a r p Blade

Log Blade Feed Dia. Speed Speed (in.) (Ft./min.) (I4PH)

Measured Energy Required (Ft.-lb.)

Replication

1 Average

7540

9210

10855

12560

14230

15910

2 4 6

2 4 6

2 4 6

2 4 6

2 4 6

2 4 6

944 785 995

944 1099 1361

1570 995 1361 1570 995 1361

1580 1623 1675

1832 1937 1728

628 942 785

944 890 1204

1411 1257 1309

1411 1257 1309

1727 1466 1885

1623 1832 1832

472 576 1099

1411 1204 1308

1411 1308 1361

1727 1308 1361

1520 1728 1728

1937 1990 1990

681 768 1138

1100 1064 1291

1569 1209 1343

1569 1209 1343

1609 1605 1762

1797 1920 1849

- 6 0 -


S h a r p Blade

Log Blade Dia. Speed (in.) (Ft./min.)

Feed Measured Energy Required Speed (Ft.-lb.) (MPH) Replication

1 Average

7540

9210

10855

12560

14230

15910

2 4 6

2 4 6

2 4 6

2 4 6

2 4 6

2 4 6

1623 1675 1832

1885 1832 1675

1990 2670 1728

2147 2880 1832

2042 2932 1990

2147 3455 2251

1832 1361 1623

1780 1728 1675

1937 2513 1832

2042 2722 1937

1990 3036 2042

2153 3194 2147

1518 576 1466

1728 2513 1518

1990 2775 1623

2199 2565 1990

2356 3194 1885

2251 3246 2042

1657 1204 1640

1832 2024 1675

1971 2652 1727

2128 2722 1919

2128 3053 1971

2303 3298 2146

- 6 1 -


D u l l B lade

Log Blade Dia, Speed (in,) (Ft,/min.)

Feed Measured Energy Required Speed (Ft.-lb.) (MPH) Replication

Average

7540

9210

10855

12560

14230

15910

2 4 6

2 4 6

2 4 6

2 4 6

2 4 6

2 4 6

995 1152

1414 1257 1204

1675 1414 1571

1780 1728 1728

1885 1675 2251

1990 1990 2356

1099 1308

1623 1152 1518

1518 1414 1518

1623 1518 1990

1832 1780 2042

2199 2042 2408

1361 1256

1361 1361 1361

1623 1518 1623

1832 1623 1832

1937 1885 2147

1990 2147 2251

1150 1240

1465 1260 1360

1575 1450 1570

1740 1620 1880

1880 1780 2160

1940 2050 2360

-62-


Dull Blade

Log Blade Feed Dia, Speed Speed (in.) (Ft./min.) (MPH)

Measured Energy Required (Ft.-lb.) Replication

Average

7540

9210

10855

12560

14230

15910

z 4 6

2 4 6

2 4 6

2 4 6

2 4 6

2 4 6

1832 1728

1780 1788 1885

1937 2094 1990

2199 2251 2304

2356 2565 2565

2513 2670 2775

Ml wm

1728 1623

1937 1937 1885

2147 2304 1937

2356 2303 2408

2251 2618 2513

2565 2513 2565

1623 1832

1832 2041 1832

2042 2147 2147

1937 2408 2460

2408 2461 2670

2461 2775 2827

1670 1730

1880 1910 1870

2020 2180 2020

2140 2300 2380

2300 2500 2580

2500 2680 2720

- 6 3 -


D u l l B lade

Log Dia. (in.)

4


7540

9210

10855

12560

14230

15910

Feed Measi Speed (MPH)

2 4 6

2 4 6

2 4 6

2 4 6

2 4 6

2 4 6

1

2356 2461 2775

2565 2617 2722

2723 2932 3194

3037 3089 3089

3089 3455 3560

3403 3508 3612

jred Energy Required (Ft.-lb.) Replication

2

2461 2670 2670

2513 2879 2872

2775 3037 3298

2880 3141 3298

3141 3351 3508

3246 3613 3822

3

2147 2513 2932

2461 2670 3089

2565 2827 2984

2775 3246 3560

2984 3194 3403

3037 3298 3612

Average

2300 2520 2790

2500 2720 2880

2680 2940 3158

2980 3140 3315

3060 3300 3525

3220 3460 3682

-64-

SLOW SPEED TEST RESULTS

Log Dia. (in.)

1.00 1.00 1.00

1.50 1.50 1.50 1.50

2.00 2.00 2.00

2.25 2.25 2.25

2.50 2.50 2.50

2.75 2.75 2.75

3.00 3.00 3.00

Drop Height (ft.)

0.50 0.75 1.00

3.00 4.00 5.00 5.50

6.00 7.00 6.50

5.00 5.50 6.00

6.00 6.50 7.00

6.00 6.50 7.00

7.00 7.00 7.00

Sharp

Total Weight (lb.)

75 75 75

75 75 75 75

75 75 75

100 100 100

no 110 110

130 130 130

150 160 170

> Blade

Total Energy (ft.-lb.

37.5 56.2 75.0

225.0 300.0 375.0 412.0

450.0 525.0 487.0

500.0 550.0 600.0

660.0 715.0 770.0

780.0 845.0 910.0

1050.0 1120.0 1190.0

Comment

)

Not a complete Not a complete Complete cut

Not a complete Not a complete Not a complete Complete cut

Not a complete Complete cut Complete cut





cut cut

cut cut cut

cut

cut cut

cut cut

cut cut

cut cut

-65-

SLOW SPEED TEST RESULTS

Dull Blade

Log Dia. (in.)

1.00 1.00

1.50 1.50 1.50

1.75 1.75 1.75

2.00 2.00 2.00 2.00 2.00

Drop Height (ft.)

0.50 1.00

2.00 2.50 3.00

4.00 5.00 5.50

5.00 6.00 5.00 6.00 6.00

Total Weight (lb.)

75 75

75 75 75

100 100 100

75 75 100 100 125

Total Energy (ft.-lb.

37.5 75.0

140.0 187.5 215,0

400,0 500,0 550,0

375,0 450,0 500,0 600,0 750,0

Comment

)

Not a complete Complete cut



Not a complete Not a complete Not a complete Not a complete Complete cut

cut

cut cut

cut cut

cut cut cut cut

richard l. echols, b.s. a thesis in

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