thesis fem Begum a? M. S.
EEEEEESML SKATE URLYERSITY
exzfilez‘me Carma

(fig-i.
tan:

 

This is to certify that the

thesis entitled

Wheel Bevameter

presented by

Guillermo N. Carrera

has been accepted towards fulfillment

of the requirements for

M.S. degree inAglifllLural Engineering

/ Major professor

 

Date erh 7. 1963

0-169

 

 

LIBRARY

3 11:

 

WHEEL BEVAMETER

BY

Guillermo Carrera

AN ABSTRACT

Submitted to the
College of Agriculture of Michigan State University
of Agriculture and Applied Sciences in partial
fulfillment of the requirements for the
degree of

MASTER OF SCIENCE

DEPARIMENT OF AGRICULTURAL ENGINEERING

1962

Approved by

 

ABSTRACT
WHEEL BEVAMETER
by Guillermo Carrera

Many workers are now conducting research in which
soil trafficability is being related to measurable psycho-
geometrical parameters which pertain to both the soil and
the vehicle. This investigation studied the feasibility of
measuring soil values by means of a forced-slip test wheel,
instrumented for determining the following: towing force,
horizontal component of resistances to motion and sinkage at
a pre-determined fixed-slip value.

An automotive tire was asSembled in a carriage where
it was free to move vertically under the action of a variable
weight and the vertical reaction of the supporting soil.

The amount of sinkage was measured with respect to the
ground surface. The towing force and a horizontal opposing
force were electronically recorded with a Brush direct
writing oscillograph.

By recording the towing force and the opposing slip-
force to various loads, it was possible to define the
horizontal retarding force and relate it as the motion
resistance of the test tire for different loads and soil
conditions.

The results indicated that meaningful soil parameters
can be obtained and with further modifications, an acceptable

range of accuracy will be gained in which practical problems

GUILLERMO CARRERA

involving the evaluation of soil trafficability can be
studied without moving the prototype vehicle across the

problem soil.

WHEEL BEVAMETER

BY

Guillermo Carrera

A THESIS

Submitted to the
College of Agriculture of Michigan State University
of Agriculture and Applied Sciences in partial
fulfillment of the requirements for the
degree of

MASTER OF SCIENCE
Department of Agricultural Engineering

1962

ACKNOWLEDGMENTS

The author is grateful to the many peOple who have
given of their time and assistance in the develOpment of
this research project. The guidance of Dr. Wesley F. Buchele
has been most helpful and the author is Specially pleased
to have been associated with him during his period of gradu-
ate study.

The writer is grateful to Dr. Arthur W. Parrall, head
of the Department of Agricultural Engineering, for the
interest shown toward the progress of the program. The
friendly and highly scholastic atmOSphere of the Department
made the training period a fruitful and joyful experience.

Appreciation is extended to Dr. Carl W. Hall,
professor of the Agricultural Engineering Department, and
to Dr. Guy E. Timmons, professor of the College of Education,
members of the guidance committee, for their many suggestions.

The author would like to acknowledge the valuable
assistance of Mr. Arnold G. Berlage, graduate assistant, for
helping the writer in setting-up the experiments.

Finally, the author is indebted to his family for
their loving faith and for the many sacrifices that they

encountered during the course of the study.

ii

TABLE OF CONTENTS
Page

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . 1
REVIEW OF LITERATURE . . . . . . . . . . . . . . . . . 4
DESIGN AND DEVELOPMENT OF THE TEST WHEEL . . . . . . . 8

The Principle of the Forced-Slip Tester . . . . . 8
Description of the Tester . . . . . . . . . . 10
Determination of Load- -Sinkage Parameters . . . . 13
Determination of Soil Strength Parameters . . . 15

INSTRUMENTATION . . . . . . . . . . . . . . . . . . . 19

Sinkage Measurements . . . . . . . . . . . . . 19
Values of the Vertical Load . . . . . . . . 20
Forward Thrust and Horizontal Component of

Resistant Forces Measurement . . . . . . . . . 20

TESTING PROCEDURE . . . . . . . . . . . . . . . . . . 22
RESULTS AND ANALYSIS OF DATA . . . . . . . . . . . . . 24
SUMMARY AND CONCLUSIONS .'. . . . . . . . . . . . . . 33
RECOMMENDATIONS FOR FURTHER STUDIES . . . . . . . . . 36

REFERENCES . . . . . . . . . . . . . . . . . . . . . . 38

iii

Figure

OO\]O\U'I

10.

ll.

12.

LIST OF FIGURES

Forced Slip principle . . . . . . . . . . .
Variable weight principle . . . . . . . .

Portable type wheel bevameter model
(Negative NO. 62529-4) . . . . . . . . .

Stationary frame wheel bevameter model
(Negative NO. 62529-1) . . . . . .

Force distribution on wheel bevameter . . .
Load vs. sinkage curves (lst approach) . .
Load vs. sinkage curves (2nd approach) . .
Shearing stress vs. normal pressure curves

Sinkage measuring device
(Negative No. 62195-4) . . . . . . . . .

Direct measurement of sinkage
(Negative NO. 621652-4) . . . . . . . . .

Setting the ink marker on the sinkage plate
(Negative NO. 621652-1) . . . . . . . . .

Slip pattern when operating at 10 per cent
slip (Negative No. 621652-8) . . . . . .

iv

Page

11

11
18
26
26
29

31

32

32

35

Table

II

III

LIST OF TABLES

Page

Load sinkage values vs. width Of
tire

. O O O C O O I O O O O O 0

Average values of towing and resistant
forces and calculated unit pressures and
soil-tire contact area

Experimental soil values

INTRODUCTION

The mechanical properties of the soil, as far as
agriculture is concerned, has been a neglected field of
investigation due primarily to the lack of workable principles
and fundamental knowledge upon which to build a systematic
study. Only recently, and as a result of the investigations
by Bekker (4) and others, it has been possible to establish
a solid criterium for research.

Another reason for this apathy toward furthering the
knowledge of the soil as a supporting medium of agricultural
vehicles and implements is that, in the past, the traffic-
ability of agricultural soils was not of major concern due
to the limited power and weight of the farm tractor and the
weight of the trailed implements. Because of the modern
trend in farming, more powerful tractors and larger machines,
the soil may no longer provide adequate support. As a re-
sult, the soil is often seriously disturbed, thus reducing
the yielding potential of the soil and the performance of
the machines.

The farm machinery manufacturing industry, soil
scientiSts and farmers are well aware of the difficulties
arising from the consequences of extensive agricultural soil
traffic and have sought a reliable approach to the problem
of relating the behavior of moving equipment to variable

conditions imposed by different soil characteristics.

1

Using soil mechanics, they would like to predict the traffic—
ability of the soil as well as the effects of the traffic
upon tillage, subsequent Operations, and plant growth.

As a result Of this endeavor a new branch of
Scientific investigation has emerged. This new field, which
has been called Land Locomotion, or even in a wider sense
"Terramechanics,” is the concern of many scientists in U.S.A.
and abroad.

During the past several years intensive research work
has been conducted by governmental as well as private
institutions, each one in terms of their own objectives, but
all of them using the same premises and theoretical values
long used by civil engineers in foundation design.

The trafficability of a soil can be determined if
certain values can be measured. These values, called para-
meters, are of paramount importance when evaluating the
strength of the soil and its relation to sinkage and slippage
of vehicles. Besides this purely mechanical problem, soil
values may be related to even more complex problems of seed-
ling impedance and plant growth, provided that a more ex-
tensive study of soil-plant interaction is undertaken.

To measure these values, different methods and pro-
cedures have been prOposed. The shear-vane principle is
used to determine the parameters in Coulomb's equation and
a penetrometer is used to gather data used to calculate the
parameters for Bernstein's equation. The Land Locomotion
Laboratory of OTAC (Ordnance Tank-Automotive Command, U. S.

Army) has develOped a series Of apparatus, most of them to

be used under laboratory-controlled conditions, for this
purpose.

The Objective of this project is to develop a simple
method Of measuring the effects of a variable-weigh towed
wheel upon the soil's strength parameters developed by
Bekker (l).

The wheel bevameter discussed contains the geared
forced—Slip tester suggested by Reece (11).

It is hoped that with further refinements this device
can be used to measure soil values rather quickly (within an
acceptable range of accuracy) and thus be used where compara—

tive study of mechanical properties of soils are desirable.

REVIEW OF LITERATURE

Terzaghi, in his book Theoretical Soil Mechanics, de-

 

fines the scope of soil mechanics as the branch of applied
mechanics which includes the study of the following:

1. Theories of behavior of soils under stress,
based on radically simplifying assumptions.

2. The investigation of the physical properties
of real soil.

3. The application of our theoretical and em—

pirical knowledge of the subject to practical
problems.

He emphatically excluded agricultural soils from his
consideration. Nevertheless, his work served as a basic
analytical tool from which other investigators derived funda-
mental knowledge applicable tO various problems encountered
in off-the-road locomotion.

Micklethwait (3) was the first to call the attention
of automotive and agricultural engineers to the possibility
of using Terzaghi's "stability problem" to study the relation
between sOil and tires in automotive vehicles. Nevertheless,
the problem of cross—country locomotion has not been the Sub-
ject of scientific investigation until recently when a series
of studies has been undertaken by the U. S. Army, univer-
sities, automotive industry, and others.

Immediately after World War II, and as a result of

the difficulties encountered by the fighting vehicles when

crossing unusually rough terrains, a full scale research

4

program was established by the Land Locomotion Research
Branch, Ordnance Corp, U. S. Army.

This laboratory, in addition to other contributions,
has developed an apparatus for measuring the vertical stress-
strain function and a pneumatic tire test device (3).

The National Tillage LaboratOry, in COOperation with
the Alabama Polytechnic Institute, has conducted a series of
research investigations in order to study the relationship
of wheels and lugs to soils under various conditions, in-
cluding rolling resistance and the distribution of forces
from lugs throughout the soil (9).

Pavlics (10) reports the progress of a new test
method using rigid wheels for measuring physical soil para-
meters instead Of the sinkage plates and shear annulus ring
plate proposed by Bekker (4). The approach was intended to
provide a quick and continuous method for soil testing in
the field. His conclusions Show clearly that the wheel type
measuring instruments are not only feasible, but practical
for field tests. He reports that the soil parameters ob-
tained by this method are in close agreement with the values
Obtained from conventional bevameter tests. The only ob-
jection that could be raised is that it required extensive
instrumentation; this limits the usage to well equipped
laboratories with highly specialized personnel for setting
up the eXperiments.

Parallel to the U. S. Army, the Department of Tractor
Research Center in Agricultural Engineering Center in.

Braunschweig (Germany) conducted a number of investigations

on the relationship between vehicles and agricultural soils.
A considerable number of measuring devices and methods were
investigated; these instruments enabled them to correlate
research data on the traction, performance of vehicles in
relation to slippage and rolling resistance, as well as the
determination of shearing resistance and vertical deformation
under loaded plates and wheels. Sohne (12) developed a
forced slip single-wheel tester and used it under field
conditions.

Reece and Wills (11) reported the develOpment Of an-
other Similar apparatus which can measure the tractive ef-
fort, rolling resistance, and slippage of a wide range Of
rigid as well as resilient wheels and tracks. In the same
way as Sohne's instrument, this device also works on the
forced-Slip principle, in which the test wheel mounted on a
frame is obliged to rotate at a controlled slip by unwinding
a wire rope from a drum which is geared to the wheel or
track under test. The input torque and output thrust are
simply measured by instruments hooked to the towing tractor
and a cable.

The field Of Land Locomotion is rapidly gaining
popularity in American universities; several courses on this
subject matter are actually Offered within the Agricultural
Engineering curricula, either as a distinctive type Of
studies or included in the content of courses in Power and
Machinery. The interest of including this subject matter
within the training framework of Agricultural Engineering

students has been stimulated by the appearance of Bekker‘s

book (4) and the publication of the research work done by
the Land Locomotion Research Center of the Ordnance Tank-
Automotive Command, U. 5. Army.

At Michigan State University, an active and well
oriented research program supported by a meaningful graduate
course has already produced its first accomplishments shown
by the research work carried on by Stong (13, 14), Trabbic

(16), Dahir (5), VanderBerg (l7), and Hovanesian (7).

DESIGN AND DEVELOPMENT OF THE TEST WHEEL

The Principle of the Forced-Slip Tester

The apparatus under consideration operates on what
Reece and Wills (11) called a geared forced-slip principle.
In short, the forced-slip tester consists of a towed free-
floating test wheel Of a rolling radius “r" (Figure l). The
angular velocity of the wheel was increased Over a normally
towed wheel by means Of a gear-chain drive and a drum. Steel
cable (wound around the drum) was led off and anchored behind
the wheel, which is pulled forward by a tractor. The linear
diSplacement of the wheel equalled the length of unwound
cable from the drum. In order tO obtain a Constant slip of
the test wheel, the peripheral Speed of the drum was made
proportionally less than the linear diSplacement of the
wheel. Since the cable was unwound at no Slip, the wheel
was forced to slip in an amount proportional to the speed
ratio. If ”n" is the ratio of the number of teeth on the

drum-shaft to the number of teeth on the wheel sprocket,

then:
i = l - a (1)
n?—
When:
i = Slippage in per cent
a = Drum effective radius
n = Speed ratio of Sprocket
r = Test wheel effective radius
or:

 

 

 

 

\
.- -\V|\\\V\\ \‘\\\‘\‘\‘\ \ ‘ \‘

Pig. 2 Variable Weight Principle

 

lO

i=1__A_ (2)
I'

Where:

A = a is the effective drum radius.
n

With the arrangement described, it was possible to

obtain a constant slip at all times.

In order to Obtain a variable sinkage ”Z," which would

enable us to determine the load sinkage function in the

modified Bernstein equation, two rigid bars, mounted length-

wise at each side of the test wheel, provided a means of

varying the vertical load upon the tire as it was towed for-
ward with the variable force F against a horizontal component

of the resistances P. The arrangement is shown in Figure 2.

Description of the Tester
Prior to the construction of the tester for measuring

the above soil parameters, three different scale models were

constructed using a FAC X-2 mechanical construction kit.

The models (Figures 3 and 4) not only showed the best

mechanical arrangement, but also gave an indication of the

possible causes of unbalancing forces under dynamic condition.

Once the "best" arrangement was chosen a prototype
was constructed.

The test wheel used, a 6.50 x 16 automotive tire, was
assembled on a hub keyed to a 1—1/2 inch steel shaft, the
tire was held in the middle of a rectangular angular frame
with pillow block bearings.

The cable drum and its corresponding Sprockets were

mounted at the rear of the frame. Another Sprocket was

ll

 

Portable type wheel bevameter model.

Fig. 3.

II)
.LIOfi
KL

3.111."

.' I'-

i!
j!

 

Fig. 4. Stationary frame wheel bevameter model

12

located on the wheel-hub shaft and a chain transmitted the
peripheral velocity of the cable drum to the wheel Sprocket.

The assembly was then attached to the middle of two
above-ground suspended tracks by placing the hangers' tips
into guide sleeves protruding at each corner of the wheel
frame assembly. To allow a free up—and—down movement of the
wheel assembly, the connecting guide Sleeves were provided
with linear ball bearings.

The arrangement allows a linear diSplacement of the
wheel aSsembly within the length of the tracks with a minimum
of friction.

In order to provide a means Of varying the vertical
load upon the test tire, which, in turn, will cause a vari-
able sinkage, two T-Shaped l/4-inch thick steel bars were
mounted lengthwise and located on both Sides of the wheel.
One end of the bars was hinged to the frame structure and
the other end was free. The bars rested upon the wheel
shaft and the weight transmitted to the shaft depending on
the distance from the hinge. Figures 10 and 11 Show the
overall View, as well as the details of the arrangement.

The dimensions and Specifications of the device were

as follows:

1. The effective rolling radius of the tire was
13.5 inches at an inflation pressure of 30 psi.

2. The motion of the towed wheel was transmitted
to an 8-inch diameter forced-slip drum
mounted behind and above the wheel by a gear-
chain drive.

3. The sprocket of the wheel had 56 teeth, while
the sprocket Of the drum-shaft had 20 teeth;
hence, the Speed ratio was 0.34.

l3

4. The cable wound around the drum was a 1/8—
inch wire cable.

5. The tracks used were two tubular-type barn
door tracks with matching rolling hangers
mounted 36 inches apart to the structural

assembly.

The dimensions of the components are substituted in

Equation 1 and the constant Slip value is calculated as

follows:
Equation 1: i = 1 -_2
nr
Where:
a.= Drum radius 4.1 inches
n = 20/56 0.35
r = Effective radius Of the wheel = 13.5 inches
1 = 1 4'1 = 15.6%

 

' (0.35) (13.5)

Figure 12 Shows the Slip pattern imprinted on the rut

created by the tire on the test soil.

Determination of Load-Sinkage Parameters
The relation between load and sinkage has been deter-
mined by Bekker and expressed by the equation:
p = (kc/b + kpl) zn (3)
This equation has been applied to Simple sinkage
plates, tracks, and pneumatic tires, but it was further

modified when applied to rigid towed wheels, and eXpressed

 

as follows: 1
z = 3W *1 2n + l
(3 - n) (kc + bk¢9D1/Z

14

Where:
Z = Sinkage in inches
W = Normal load on the tire in pounds
D = Effective diameter of the wheel
b = Width of the ground contact area
n = Exponent of sinkage
KC and K5 = Cohesive and frictional modulus Of

deformation, reSpectively
If two successive measurements of Sinkage 21 and 22 are
taken correSponding to two different loads W1 and W2 under

constant Slip conditions, we have two equations:
2

 

21 = f 3W1 ..._.._..__..
[(3 — n) (kc + blkfi) Dl/2 ] 2n + 1
‘ 2

3W2

Z : r 1 _—_..._
2 [(3 - n) (kC + b2k¢) lez J 2“ + 1

Rearranging terms and taking logarithms of the above equations:

 

 

log W1 = 2n + 1 log 21 + log (3 - n) (k + blk ) D1/2
“‘27" 3 C d
log W1 = 2n + 1 log Zg + log (3 - n) (kc + bZKM) D1/2
2 3

Now varying the load W and plotting log W vs. log 2 we get
two straight lines, the slope of which is:

cx.= 2n + 1
___:T_.

And the exponent of Sinkage can be expressed as:
n=tan0£ -l/2
The ordinates at Z = 1 are equal to:

a1 = (3 - n) (kc + b13¢> D1/2
3

a2 = (3 - n) (kc + bgkfl) D1/2
'3

Hence, the values of kc and k¢ can be determined, being

15

 

 

 

equal to:
kc: 3 [ii-2]blb2
(3 - n) BUSES b1 b2 b2 - bl
and:
3 a — a
k = _______

Another analytical approach to the problem has been
suggested by Bekker and Janosi (3). Using equation 3:

p = (kc + bkfl) zn
Taking logarithms: I

log p = n log Z + log (kc/b + kg)

If the equation is plotted on a log-log paper for two
different tires width, b1 and b2, correSponding to two
different normal unit pressures, pl and p2, we get two
straight lines leping to angle 6.. The tangent Of 0‘ equals

the unknown n value. The ordinates at Z = 1 are equal to:

al kC/b1+ kg '

32 = kC/b2+ kfi

 

 

Hence:
kc = (a2 - a1) D1 D2: (4?
b2 ' b1
and:
kg = (a2 b2 - a1 b1) (5)
bZ-bl

Determination of Soil Strength Parameters
The evaluation of Shear-Slip parameters are much
more involved and requires the computation of different Slip
values. Nevertheless, following Reece's analysis (11), it

is possible to make a rough estimate of the soil's shear

16

strength for different normal pressures of the test tire.
In fact, from Figure 5 we can evaluate the condition Of
equilibrium of the forced Slip system.

In order to simplify the analysis we rationalize that
the geared-drum assembly has been hypothetically replaced
for a drum having the same peripherical speed and has been
directly attached to the tire's shaft (broken line). Then:

ZFX=0;‘>=L+E-I>-R
LQR=P-E ‘
L - R

But: Thrust

P - F

Therefore: Thrust
Bekker (4) defines the maximum soil thrust of a track or
soft pneumatic tire in terms of Coulomb's equation:

H = Ac + W tan fl (6)
For our purpose we can say:

P - F = Ac + W tan d

For our purpose we will consider that the above
equation maximizes at the design dynamic Slip value of 15.68
per cent (normally, maximum draw bar pull of pneumatic tires
occurs at 15 to 18 per cent slip). Then:

P - F = c + p tan fl = SS
__KL_

Where Ss is the Shearing strength of the 5011.

For two

different normal pressure values, we have:

S c + p1 tan d

51

$52 = C + p2 tan fl

Thus:

tan fl = Ssl - ng
pl'pz

Knowing tan d, c is defined.

17

18

Motion ———>

 

 

 

 

Fig. 5 Force distribution on Wheel Bevameter

INSTRUMENTATION

In order to provide the necessary information for
evaluating the soil value system, the following measurements
were required:

1. Sinkage values under variable loads.

2. Values of vertical loadS_upon the test
tire.

3. Forward thrust and horizontal component
of the resistant forces.
Sinkage Measurements

Figure 9 shows the device used to record sinkage
under increasing load. It consists Of a 10-inch circular
plate keyed to one end of the tire's shaft and rigidly
following the rotational and up-and—down movement of the
tire. A marker held at a constant height by the barn door
track and moving along with the wheel carriage draws a
circular line which shows the vertical displacement as well
as the angular displacement of the tire with reference to
the stationary frame.

By marking the distance travel on the chart and refer-

ring to the actual weight on the wheel at various distance

of travel, the Operator can relate weight to sinkage of wheel.

At the end of each run and before returning the wheel

carriage to the initial position, a set of S1nkage measure-

y from the rut of the tire (Figure 10).

a

ments were taken directl

19

20

Both measurements were then compared to secure repre-

sentative values of Sinkage correSponding to the loads im-

posed on the test tire.

Values of the Vertical Load
Once the loading bars were positioned on the track
structure, the weight variation from the free ends were

recorded at each two feet interval by a suSpension method,

using a conventional Spring Scale. Thus, the total weight

imposed to the soil was the sum of the weight of the wheel
assembly plus the weight of the bars at each particular
interval.

Average values of the load on SOil at various dis-
tances are as follows:

Distance feet
from free end 2 4 6 8 10 12 14

Weight lb.
total 320 356 376 406 452 506 636

Forward Thrust and Horizontal Component of Resistant
Forces Measurement

Three different methods were studied for measuring
the force variation of the forward pull and the horizontal
component of the resistances:

1. Direct reading dynamometer scales.

2. Hydraulic dynamometers.

3. Strain gauges test rings.

Direct measurement of forces by means of Spring scale
dYnamometerS linked between the towing cable and tractor and

between the anchor and drum cable were used during the early

OH

to:

GU

run
WU

tr

 

 

 

 

21

stages of development of the tester. It was soon discarded

after a few trials because the vibration of the scales pre-
vented accurate readings and the elongation of the spring of

the scale prevented the maintenance of constant slip during

the run.

The replacement of Spring-scales by hydraulic dynamo-
meters could minimize the vibration and elongation problem

on the drum cable, but the recording of dataappeared to be

too involved.
Finally, it was decided to use proving rings and

oscillagraph recording. Four SR—4 strain gauges were mounted

on each ring to measure the imposed strain. Since the

transmitted forces were within the elastic range of the test
rings, a linear stress-strain relationship was assured. A

Brush amplifier and a Brush Direct Writing oscillograph were

used to record the data.

FJ‘

Cf

'17)

TESTING PROCEDURE

A plot of ground was plowed to a depth Of eight
inches and thoroughly mixed with a rotary hoe tO secure a
uniform surface; all stones were removed before the surface
was leveled.

The structural assembly was supported on two long
boards placed on each side of the prepared plot and, once
positioned in place, the height of the tracks were checked
against the ground level to be Sure that the tracks were
parallel. At the end of each run the soil was renovated by
Spading and the surface was smoothed and releveled.

A series of comparative tests were performed using a
bevameter with a Shear annulus plate and circular Sinkagg
plates.

Prior to each run, a hand. Wench was used to place an
initial tension in the drum cable, thus assuring that the
tire would rotate at the designed slip from the start Of the
test. An ink pen mark, on the sinkage graph paper, showed
the starting point. A tractor was used to tow the wheel at
the lowest Speed available, approximately 2 mph, in order to
neglect the velocity factor as well as tO insure proper read-
ing and recording on the oscillograph.

The starting point of each run was Set at two feet

from the free ends Of the loading bars and the final distance
was twelve feet from the starting point when the bars

22

 

 

 

.y'

.u

23

touched the ground surface.
Two kinds Of tests were performed in order to secure
two different values of sinkage:

l. The average width of the tire was 5.5 inches
when the inflation pressure was 30 psi.

2. The average width of the tire was 6.5 inches
when the inflation pressure was zero psi.

Besides these two tests a number of other tests were

run without the Slip—causing cable attached to the anchor.

RESULTS AND ANALYSIS OF DATA

More than fifty tests were performed in the same
testing plot. Each set correSponding to a certain soil
moisture content as determined on the testing days.

A group of tests with 12 per cent moisture content
were selected for analysis as they were more uniform than
tests at other moisture contents.

Prior to each run the test rings were calibrated at
zero load and the drum cable was tightened.

To evaluate the force required to overcome the
friction of moving parts Of the wheel assembly, a number
Of runs were made without the tire touching the ground.

It has been found that this, on the average, amounted to
approximately 10 per cent of the total towing force. These
values were taken into account when processing the data.

The values which appear in Tables I and II are aver-
age Of all values recorded in each run under identical

condition and correSponding to the set selected for analysis.

24

25

Table I. Load-sinkage values vs. width Of tire.
“WM—“W

 

Sinkage

Distance b = 5.5 b = 6.5 Load
ft. inches 1b.

3 1.118 0.400 329

5 1.253 1.000 349

7 1.331 1.050 366

9 1.331 1.100 389

11 1.440 1.200 426

 

Using the procedure outlined on pages 14 and 15, the
above data were plotted on log-log paper to Obtain the two
parallel lines shown in Figure 6. The angle of inclination
was equal to 47°. The tangent of that angle was 1.0724.
Hence:

n = tan 47°- 1/2

 

 

 

n = .5724
a1 = 290
a2 = 349
k = 3 290 - 349 (6.5)(5.5)
C (3*- 0;3721)(5.1962) 373 '673 1
kc = -8.24
kg = 3 349 — 29o

 

(3 - 0.5724D(5.l962) 6.5 - 5.5

kg = 14.16

Using the second approach from pages 15 and 16, the

' ' re
values of unit normal pressure 1n pounds per square 1nchve

calculated. The area of contact for width b = 5.5 inches was

. 2 .
33 in.2 and for b = 6.5 inches was 39 1n. . The unit

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

500'
)4.
400
f . J
.;-—< <1
.0
A] Rd
c 322/ v
I
3‘21
———200
2 3
Sinkage, z, inches
Fig. 6 Load 75. Sinkage Curves (lat. approach)
19
b
”7
310
.3 ./
-——-9 a
_____J
lie
a,
£1 4
7 2 3

Fig. 7 Load vs. Sinkage Curves (2nd. approach)

27

pressure (psi) for different travel distances follows:

 

 

M
M

Distance Feet
Width- 3 . 5 7 9 11

 

Pounds per square inch

U
II

5.5 in. 9.97 10.57 11.09 11.79 12.91

0'
II

6.5 in. 8.44 8.95 9.38 9.97 10.92

 

Plotting the logarithm form Of the equation proposed

by Bekker on log-log paper, two parallel straight lines were

drawn through the points and are shown in Figure 7. The angle

Of inclination is C! = 48.50, the tangent of the angle is
equal to the unknown parameter "n".
n = 1.0176

The ordinates at Z = 1, are:

a2 = 8.95

a1 = 8.30
Then:

kg = 12.52
And:

k = 23.95

28

Table II. Average values of towing and resistant forces and
calculated unit pressures and soil-tire contact

 

 

area.
W
A P-F
Distance P P Area A p
ft. lbs. lbs. in.2 psi psi
3 174.57 77.80 39 2.48 8.44
5 188.38 83.43 39 2.69 8.95
7 190.40 80.61 39 2.81 9.38
9 197.35 78.75 39 3.04 9.97
11 216.22 88.65 39 3327 10.92

 

We said that the dynamic soil strength can be calcu-

lated if P - F is set equal to shearing stress, SS. Then:
A

SS = c + p tan d
Plotting SS values vs. the normal pressure per unit of area
"p," we obtain the straight line shown in Figure 8.

The slope of which represent the angle of internal
friction d, and for that particular sample is equal to 180.
Having defined this unknown parameter, the value of cohesion
"c" is also determined.

In this form all the values of the soil parameters
have been defined for that type of soil and for a Specific

moisture content. These values are in Table III.

29

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unannouh Huauoz .u> unoaum waauuoam w .wam
«an unannoum Huauoz

Na OH m m 4
r _

_ p _
1.
“up

N
(L

 

qasucans 3911.398

IA]

3O

 

 

 

TABLE III. Experimental soil values.*
Conventional
Parameter Wheel Bevameter Bevameter
lst 2nd
Approach Approach

Cohesive modulus
of deformation kc -8.24 23.95 -7.5
Frictional modulus
of deformation kg 14.16 12.52 37.00
Exponent of sinkage

n 0.5724 1.0176 1.1184
Angle of internal :0
friction 180 36
Cohesion c 0 psi 0.73 psi

 

*Moisture content:

12%, bulk density:

1.3 Gram/cc.

 

31

.COH>DC meflusmmos wmmxcflm .o .mflm

 

 

 

Fig. 10. Direct measurement of Sinkage.

 

Fig. 11. Setting the ink marker on the sinkage plate.

 

 

 

 

 

 

 

 

 

 

SUMMARY AND CONCLUSIONS

Soil trafficability as it has been generally accepted
can be assessed only if the physicogeometrical values per—
taining to both the soil and the vehicle have been determined.
This project dealt with only a fraction of the whole problem;
that is, to prove the feasibility of measuring soil values
by means of a forced-slip test wheel, instrumented for deter—
mining: towing force, horizontal component of reSiStances
to motion and Sinkage under a predetermined fixed-slip value.

The wheel used, an automotive tire, was assembled in
a carriage where it was free to move vertically under the
action of a variable weight and vertical reaction of the
soil. The amount of Sinkage was measured with respect to
the ground surface. The towing force and a horizontal Op-
posing force was electronically recorded with a Brush
analyzer.

At the present stage of development it was only
possible to get approximate values of the parameters in the
modified Bernestein equation, i.e., kc: cohesive modulus of
deformation, kg: frictional modulus of deformation, and:

n, the exponent of sinkage reflecting the rate of strain
change with load.

Relating the towing force (F) and the opposing Slip-
force (P) to various loads (W), it was possible to define
the horizontal retarding force and relate it as the motion

33

IE

CC

It

34

resistance Of the test tire for different loads and soil

conditions.
A complete evaluation of soil trafficability factors

required the determination Of additional soil values, ex-

pressed in Coulomb's equation, that is: cohesion ”c" and

the angle of internal Shear d. TO accomplish this, certain

modifications will have to be introduced to the basic design
of the tester which will allow not only the measurements Of

the thrust but the maximum thrust attainable at certain Slip

values.

Some of the causes of unbalancing forces of the free—
floating wheel assembly will have to be overcome in order
to have net force readings. The effect of inflation pressure

and carcass stiffness have to be taken into account.

‘..
‘vbfafirfi‘s

. \a'_”,. M9

0—
H
H
U!
4.:
C:
Q)
U
H
M
D.
O
H
+.:
N
00
E
'Fl
4.:
d
H
G)
D.
O
8:
Q)
.C:
3
E}
H
G)
.1.»
4.1
N
D.
D.
'H
v-l
U)

F'g. 12.

 

 

 

 

 

RECOMMENDATIONS FOR FURTHER STUDIES

The wheel bevameter has proved to be a fairly reliable

instrument for measuring load-Sinkage parameters under con-

trolled field conditions. To make it a more worthy instru-

ment, the following features should be considered:

1. A precise sinkage reading may be obtained by
replacing the Sinkage-recording—plate with
linear potentiometers.

2. It has been found that the use of linear bear-
ings intended to allow a free floating action
of the wheel assembly introduced serious prob-
lems of dirt inclusion and friction. Test
tires free to rotate around crankshaft-like
shafts would eliminate this problem.

3. As all the tests were performed without moving
the tester from the same plot, no tranSportation
wheels were provided. But, if the apparatus is
going to be used extensively for practical
field measurements, some kind of retractable
wheels should be provided.

4. To get accurate sinkage readings and to eliminate
the terrain uneveness factor, it is advisable

to have some sort Of built-in tilling and

leveling device.

36

37

In order to determine the Sinkage parameters,
according to standard procedures, it is necessary
to record the load Sinkage values for two differ-
ent contact patch widths. Therefore, the addition
of another test tire of same rolling radius and
different width may provide the required inform-
ation without recurring to the artificial
procedure followed during the tests.

It has been already mentioned that the evaluation
of the shear-strength parameters require the
determination of maximum soil thrust attainable
at optimum slippage. If the resistance to motion
and power demand were the only objective, the
fixed—Slip arrangement is satisfactory, but if
the parameters in Coulomb's equation are to be
defined, it is necessary to incorporate some
method of varying the Slippage within a wide
range of values; some kind of electromagnetic

friction brakes might do the job.

10.

REFERENCES

A

Bekker, M. G. (1950) Relationship between soil and a
vehicle. SAE Transactions No. 3.

Bekker, M. G. (1957) Terrain evaluation in automotive
off-the-road operations. Research Report No. 13. De-
partment of the Army, Ordnance Tank-Automotive Command,
Research and Development Division. Land Locomotion

Research Branch.

Bekker, M. G. and Janoski, Z. (1958) Terrain evalu-
ation of pneumatic tires in soft soils. Report No. 5.
Department of the Army, Ordnance Tank—Automotive Com-
mand, Research and Development Division. Land Loco-

motion Research Branch.

Bekker, M. G. (1960) Off-the-road locomotion. The
University of Michigan Press. Ann Arbor. 220 pp.

Dahir Abdallah George (1961) The effect of liquid and
dry ballast on the stability of pneumatic tired
tractors. Unpublished M.S. thesis. M.S.U.

Harris, W. Lamar (1961) Dynamic stress transducers
and the use Of continuum mechanics in the study of
various Soil stress—strain relationship. Ph.D. thesis.

M.S.U.

Hovanesian, Joseph der. (1958) Development and use Of
a volumetric transducer for studies Of parameters upon

soil compactation. Ph.D. thesis. M.S.U.

Janosi, Z. (1961) An analysis of pneumatic tire per-
formance on deformable soils. Paper No. 45. Proceedings
of the lst International Conference on the Mechanics of
Soil-Vehicle Systems. Mechanics of Soil Vehicle Systems

Edizione Minerva Tecnica. Torino, Italy.

Nichols, M. L. (1958) Purpose and history of the
National Tillage Laboratory. Proceedings of seminar on;
tillage and traction equipment. ARS 42-16. Agricultural

Research Service. USDA.

Pavlics, Ferenec. (1961) Bevameter-100. A new type

of field apparatus for measuring locomotive stress—
strain relationships in soils. Paper No. 22. Pro-
ceedings of lst International Conference on the Mechanics
of Soil-Vehicle Systems. Mechanics of Soil Vehicle
Systems. Edizione Minerva Tecnica. Italy.

38

11.

12.

13.

14.

15.

16.

17.

39

Reece, A. R. and Wills, B. M. D. (1961) Forced-slip
wheel and track tester. Paper No. 25. Proceedings of
the list International Conference on the Mechanics of
Soil-Vehicle Systems. Mechanics of Soil Vehicle
Systems. Edizione Minerva Tecnica. Torino, Italy.

 

Sohne, Walther. (1960-1962) Personal correSpondence.

Stong, J. V. (1961) The effect of liquid and dry
ballast on the stability Of pneumatic tired tractors.
M.S. thesis. M.S.U.

Stong, J. V. and Buchele, W. F. (1962) Effect of
soil parameters on strength of tillable tools. ASAE
Paper NO. 62—132.

Terzaghi, Karl. (1959) Theoretical Soil Mechanics.
9th Ed. John Wiley and Sons, Inc., New York.

Trabbic, W. G. (1959) The effect of drawbar load and
tire inflation on soil-tire interface pressure. M.S.
thesis. M.S.U.

VandenBerg, G. E. (1958) Application Of continuum
mechanics to compaction in tillable soils. Ph.D.
thesis. M.S.U.

ROOM USE ONLY

at!“ 1 , .h‘. .2-

“61685

[CH 113;: LEA-.313.

 

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