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AN INVESTIGATION OF THE MECHANICS OF SEVERING TREES
WITH AUGER CUTTERS

By

James Arthur Mattson

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Mechanical Engineering

1980

ABSTRACT

AN INVESTIGATION OF THE MECHANICS OF SEVERING TREES
WITH AUGER CUTTERS

By

James Arthur Mattson

The objective of this study was to analyze the mechanics of
severing trees with auger type cutters, and to document the force
and power requirements as functions of the major variables affecting
the process. The focus of the study was on the cutter parameters,
helix and rake angles; the machine variables, cutter rotational
speed and feed speed; and the workpiece parameters, species of wood
and the temperature of the wood being cut.

Cutter geometry was evaluated by the criteria of which combination
of parameters produced the lowest value of maximum torque and simultane—
ously the lowest axial force. With this criteria and the added constraint
of selecting a cutter geometry which is maintainable in practice, a
cutter configuration with a 40 degree helix angle and 30 degree rake
angle was judged to be an optimum compromise. Increasing values of
helix angle up to 40 degrees reduce the forces acting on the cutter,
but beyond this value the loadings increased. Increasing values of rake
angle were beneficial to the performance of the cutter but considerations
of the maintainability of the cutter preclude going above 30 degrees.

Investigations of the machine variables, cutter rotational speed
and feed speed, showed that these two variables could be combined into
a single parameter, feed rate, expressed as the feed per tooth, and the

loading on the cutter related to this one parameter. Over the range of

feed rates studied, the main loadings analyzed on the cutter were found
to be linearly related to the feed rate. The power requirement of the
cutter was found to be dependent on both the cutter rotational speed
and the feed speed, rather than only on the feed rate. It was found
that at a constant feed speed, or rate at which the cutter is moving
through the wood, the horsepower requirement decreased with a decrease
in the cutter rotational speed.

The species of the wood being cut and the temperature of the wood
were found to have significant effect on the force and power require-
ments of the cutting process. The forces on the cutter and the power
requirements follow the differences in specific gravity and hence the
differences in mechanical properties of the wood. Cutting frozen wood
was found to increase the loadings on the cutter by 20 to 25 percent
over those obtained with green wood.

The process of cutting wood with an auger cutter is a much more com-
plex operation than had been previously analyzed. However, the results
obtained by other investigators correlate with the results that were
obtained here. A logical expansion of this work would be to extend the
basic mathematical models of chip formation which have been developed
for the basic cutting processes to the more complex case of the auger
cutting process. A successful model of the mechanism of the auger cut-
ting process based on the results obtained in this study would extend
the usefulness of these results and increase the efficiency of applying

the auger cutting concept to practical cutting situations.

ACKNOWLEDGEMENTS

This work was done with the support of the Forestry Sciences Lab-
oratory, North Central Forest Experiment Station, Forest Service, U. S.
Department of Agriculture, Houghton, Michigan. Without the support and
assistance of many members of the staff, this work could not have been
completed, and sincere gratitude is expressed for this aid.

The patient guidance of Professor Roland Hinkle over the several
years that the completion of this project has taken is gratefully

acknowledged.

James A. Mattson

ii

TABLE OF CONTENTS

LIST OF TABLES
LIST OF FIGURES
INTRODUCTION
EXPERIMENTAL PROCEDURE
Experimental design
Cutters
Sample material
Test equipment
Data analysis
EXPERIMENTAL RESULTS
Cutter geometry
Cutting rate
ANALYSIS
Analytic methods
Chip formation with the auger cutter
DISCUSSION

BIBLIOGRAPHY

page
iv

10
10
14
17
28
35
39
39
58
88
89
92
104

109

Table

10.

11.

12.

13.

14.

15.

16.

17.

LIST OF TABLES

Suitability of severing devices for continuous
feller-bunchers.

Specified and measured parameters for the twelve
experimental auger cutters.

Summary
Summary
Summary
Summary
Summary
Summary

Machine

of

of

of

of

of

of

aspen trees cut for green samples.

sugar maple trees cut for green samples.
red pine trees cut for green samples.
aspen trees cut for frozen samples.

sugar maple trees cut for frozen samples.

red pine trees cut for frozen samples.

settings for test conditions.

Maximum axial force vs. helix angle for green and
frozen wood by species.

Maximum torque vs. helix angle for green and frozen
wood by species.

Summary of forces and power requirements for cutting
aspen with a 40° helix angle 30° rake angle auger cutter.

Summary of forces and power requirements for cutting sugar
maple with a 40° helix angle 30° rake angle auger cutter.

Summary of forces and power requirements for cutting red
pine with a 40° helix angle 30° rake angle auger cutter.

Regressions of maximum axial force vs. feed rate by
species and green or frozen wood.

Regressions of maximum torque vs. feed rate by species and
green or frozen wood.

Location within cutter cycle of maximum recorded torque
by spindle speed, table feed speed, and cutter.

iv

Page

18
22
23
24
25
26
27

30
46
50
65
66
67
73
74 ,

98

10.

11.

12.

13.

14.

15.

16.

LIST OF FIGURES

Geometry of auger cutter.
Orientation of sample material in original log.
Experimental auger cutters.

Arbor for mounting experimental auger cutters with
strain gage torque transducer.

Three component force transducer and fixture for
securing sample block.

Schematic of instrumentation system.

Equipment set up and instrumentation system for
experimental studies

Cutter position indicator.
Location on sample blocks for recording of test data.

Example of oscillograph output recording forces and
torque on cutter.

Maximum axial force vs. helix and rake angles for
green wood by species.

Maximum axial force vs. helix and rake angles for
frozen wood by species.

Maximum axial force vs. spindle rotational speed and
table feed speed by rake and helix angle combinations
for sugar maple cut green.

Maximum torque vs. helix and rake angles for green
wood by species.

Maximum torque vs. helix and rake angles for frozen
wood by species.

Maximum torque vs. spindle rotational speed and table
feed speed by rake and helix angle combinations for
sugar maple cut green.

Page
11
13

15

29

32

33

34
36

37

38

43

45

48

52

54

56

Figure Page

17. Maximum axial force and maximum torque vs. helix
and rake angles averaged over all tests. 57

18. Maximum axial force vs. spindle rotational speed and
table feed speed for green and frozen wood by species. 62

19. Maximum torque vs. spindle rotational speed and table
feed speed for green and frozen wood by species. 64

20. Maximum axial force vs. feed rate for green and
frozen wood by species and spindle rotational Speed. 70

21. Maximum torque vs. feed rate for green and frozen wood
by species and spindle rotational speed. 72

22. Linear regressions and ' 95% confidence limits for
maximum axial force as a function of feed rate for
green wood by species. 76

23. Linear regressions and 95% confidence limits for
maximum axial force as a function of feed rate for
frozen wood by species. 78

24. Linear regressions and 95% confidence limits for
maximum torque as a function of feed rate for green
wood by species. 80

25. Linear regressions and 95% confidence limits for
maximum torque as a function of feed rate for frozen
wood by species. 82

26. Maximum horsepower vs. spindle rotational speed and
table feed speed for green and frozen wood by species. 84

27. Maximum horsepower vs. feed rate by spindle rotational
speed and table feed speed for green and frozen wood

by species. 86
28. Principal configurations for orthogonal cutting

of wood. 90
29. Chips formed when cutting aspen at a constant feed

rate by rake and helix angles. 93
30. Chips formed when cutting aspen with cutter 8

by spindle RPM and table feed speed. 95
31. Identification of zones on cut surface of sample blocks. 96
32. Appearance of torn grain in zone 3 of sample block. 97
33. Schematic of indentation stage of cutting wood. 100

ml

INTRODUCTION

Forestry in the United States is approaching a position which agri—
culture in this country has occupied for many years. The industry must
increase the production of wood products to meet an ever increasing con—
sumer demand while, simultaneously, it must compensate for the loss of
timber producing land to other uses, e.g., urban development, highways,
recreational facilities, etc. The demand for forest products has been
projected to almost double by the year 2000, while the area of commer-
cial timber land available for the production of forest products is pro-
jected to decrease by as much as 5 million acres per decade (23)*. At
current levels of annual growth and utilization of available timber, the
balance between supply and demand is projected to become critical in the
near future, particularly for softwood sawtimber for use in lumber and
plywood.

The greatest potential for increasing the wood supply lies in the
development of new sources of fiber for the pulp and paper industry.

The lumber and plywood industries will continue to require large diame—
ter, high quality sawtimber for their products in the future, but the
pulp and paper industry, whose traditional source of supply has been the
wood chip, has the ability to utilize material produced from residue and

other low valued sources of fiber. Approximately 40 percent of the

 

* Number in parentheses refers to literature cited in the bibliography.

2
annual cut of timber goes into the production of pulp, including almost
20 percent of the annual cut of sawtimber. Therefore, if new sources
of supply for the pulp industry can be developed, the drain of sawtimber
for pulp can be reduced, and more high quality material will be avail-
able for higher valued products.

One of the promising approaches to increasing the supply of fiber
for the pulp and paper industry is "short rotation intensive culture"
(SRIC) forestry. Basically, the concept consists of establishing plan-
tations of genetically superior trees on well prepared sites, fertil-
izing and cultivating to maximize early growth at much higher than nor-
mal yields per acre, and harvesting whenever the annual growth rate
begins to fall off, usually before the trees are 15 years old. Several
investigators in various parts of the country have been studying the
potential of SRIC systems. Initial results have shown that yields can
be as high as seven times that of conventional timber growing systems
on a tons/acre/year basis 6;, 11,_1§, 12). In the North Central region,
the growth potential of a populus hybrid (Populus 'Tristis #1) growing
on a 4 by 4 foot spacing under intensively cultured conditions has been
projected to be about six times that of a natural aspen stand in the
same region (S). Some of the other tree species which are felt to be
compatible with short rotation systems are cottonwood, sycamore, and
red alder.

The potential of SRIC forests as a source of energy is also receiv-
ing attention (21). Because of rising fuel costs, depletion of fossil
fuel reserves, increasing dependence on imported oil and environmental
concerns over use of lower quality fossil fuels, the concept of a renew—

able source of clean fuel is very attractive. The technological

3
requirements of intensively cultured systems for site preparation,
planting, tending, harvesting and processing equipment are not drasti-
cally changed by whether the end product is used for pulping or fuel.
Thus the development of equipment for intensive culture systems will
advance the potential of both fiber and fuel production utilizing Silvi—
cultural systems based on intensive management concepts.

Once greenhouse tests and smallplot trials have established the
physiological requirements for maximizing the fiber yield from SRIC
plantations, the technology must be developed to apply these practices
on a commercial basis. Early estimates indicate that a minimum of 8,000
acres of SRIC plantations will be required to economically supply raw
material for pulping (4). Early estimates of acreages required for
fuel production are in the hundreds of square miles. Considering the
investment required to establish a fiber growing system of this magni-
tude, and the radical changes from a conventional fiber growing system,
all aspects of SRIC forestry will have to be thoroughly developed before
a company will consider switching its production of raw material to such
a system.

The harvesting of the wood fiber grown in SRIC plantations is one
aspect of the total system that has to date received little extensive
investigation. One advantage of these systems that most investigators
stress is that a completely mechanized harvesting operation would reduce
labor costs and be more conducive to a year round operation, but the
actual implementation of the harvesting has not been extensively studied.
The use of standard agricultural silage Choppers to harvest short rota-
tion fiber has been evaluated in one instance, but only on very small

material (one year old sycamore sprouts less than l-inch in diameter)

4
(19). Before short rotation fiber growing systems can be commercially
put to use, the harvesting technology will have to be developed to the
stage that an economically feasible system will be available that can
handle the required acreages.

In addition to the potential of intensively cultured fiber, the
use of previously non-commercial tree and brush species have been pro—
posed as a future source of fiber for pulping (EL-25). The development
of harvesting systems for intensively cultured fiber would also open
the door to the use of so-called "puckerbrush" since the material is
quite similar to short rotation trees, and the harvesting requirements
of both would be similar.

Two differences that exist between short rotation trees and conven~
tional timber that will have significant bearing on the final design of
a harvesting system are the size of the trees at harvest and the spacing
between the trees. In the field trials of short rotation systems thus
far conducted, the trees at harvest have been less than 5 inches in
diameter, and the spacings have varied from 6 feet by 5 feet to as
little as 9 inches by 9 inches. Both from the technical and economic
points of view, these factors will have a significant bearing on the
final design of a harvesting system.

Whole-tree chipping is the most likely system to be used for har-
vesting short rotation intensively cultured plantations (2). It is a
highly mechanized system capable of producing large quantities of wood
per-man-day. Besides its advantage of high productivity and reduced
labor requirements, the yield per acre of usable wood is greatly
increased due to the additional amounts of fiber recovered from the

tops, limbs, and the other residue materials normally left in the field

5
following a conventional harvesting operation. Additionally, the site
is left in a cleaner condition which is esthetically more acceptable,
and subsequent silvicultural operations are facilitated by the lack of
debris on the site.

The basic whole-tree chipping system consists of feller-bunchers
which sever the trees and accumulate them into bunches for subsequent
forwarding to the chipper site, grapple skidders to move the bunches
from the forest to the chipper, portable chippers which operate at a
woods landing to reduce the whole trees to chips, and chip vans which
transport the chips to the mill.

The felling-bunching phase of the harvesting operation is the area
where the current technology is the most deficient with respect to har-
vesting small trees. Current skidding and chipping equipment is basi-
cally designed as a multiple-tree operation, so the redesign of current
equipment should be merely an adjustment of the current technology to
the changed design parameters that the small trees of a SRIC plantation
would present. However, the basic design of current feller—bunchers is
based on handling one tree at a time. Considering the large trees in
conventional forest stands, this approach is reasonable, but for stands
of small trees, this assumption effectively puts an upper limit on the
potential productivity of the equipment (11).

To achieve a breakthrough in the productivity of felling—bunching,
the concept of continuous operation, as opposed to single tree Operation,
will have to be developed. The concept of continuous felling and bunch-
ing can be defined as severing and accumulating the trees in a swath of
timberstand on a nonstop basis. Development of this concept will require

the methods and machinery by which trees at random locations within the

6
swath and the severed trees can be accumulated into bunches and dropped
on the ground for subsequent skidding. To achieve high productivity in
stands of small trees, the operation must be continuous in that the
machine will not stop to sever and process each tree as it occurs in
the swath.

The primary problem involved in developing a continuous feller-
buncher, or swath cutter, will be the severing action of the felling
device. All existing fellers are designed to handle one tree at a time,
alignment between each tree and the machine is critical, and the machine
must stop to process each tree. If a means of severing the trees contin—
uously within the cutting swath of the machine can be devised, then the
problem is reduced to accumulating the trees into a bunch and dropping
them off for subsequent skidding.

There are three primary means by which existing mechanical fellers
sever the tree in the felling operation. The most common of these is
the mechanical shear. The shear has been developed to the point where
it is a highly productive and dependable means of felling timber. The
shear's main advantage over other mechanized severing methods is that
it is relatively insensitive to dulling. Its main disadvantage is the
large force required to drive the blade through larger trees and the
stability of the blade itself under these high forces. The shear also
has a tendency to split the butt end of the severed log, thus reducing
its applicability to felling sawtimber trees. For purposes of a contin—
uous cutter, the shear's main disadvantage is that it requires direct
alignment with the individual tree to be severed so that the stem falls

between the anvil and the blade.

7

The second means of severing commonly employed by mechanical fel—
lers is the saw. The manually operated Chain saw is the most common
application of saws for severing trees, but a few applications have used
a saw mounted on a meChanical feller. The main reason for using saws
on fellers is to reduce the butt damage that occurs in sawlogs when fel-
ling with a shear. The elimination of the butt damage and the ability
to handle larger diameter trees are the main advantages of saws; the
main disadvantages are that saws are a more mechanically complex system
and are highly sensitive to dulling. For a continuous feller, saws
would be a possibility for random selection of the trees. However, the
sensitivity to dulling and the expense involved in maintaining the sys-
tem would be major deterrents.

A third severing means employed by some mechanical fellers is the
auger cutter. As applied in tree fellers, the auger cutter looks like
an elongated milling cutter with either a straight or helical flute con-
figuration. Reduction of butt split was again the motivation for the
development of this concept. As opposed to the saw, auger cutters have
a simpler mechanical configuration, and the cutter is a heavier unit
than the individual tooth saw; thus dulling is a lesser problem than
with saws.

The relative advantages and disadvantages of shears, saws and
auger cutters are illustrated in Table 1. Based on these comparisons,
and not trying to speculate on what new technologies may be developed
in the future, the auger cutter concept appears to have the most promise
for the development of a continuous feller.

In addition to their potential for a continuous feller-buncher,

auger cutters are also the most promising device available for

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9
mechanizing the felling of sawtimber trees. Auger cutters eliminate
the butt log damage that occurs when using shears, and they are not as
limited by tree size as are the shears.

The use of auger cutters for tree fellers is a relatively new con—
cept, and the development of the current machine utilizing this concept
has been done on a trial and error basis without sound documentation of
the basic design parameters. Before this concept can be used as the
basis of the development of a continuous felling device, the technology
of auger cutting needs to be expanded. Cutter geometry, force and
power requirements, operational characteristics, material and fabrica-
tion constraints have to be investigated to establish the parameters
on which to base an efficient design.

The objectives of this study were to investigate the mechanics of
severing trees with auger cutters and to quantify the basic design
parameters needed to efficiently design a continuous felling device

utilizing this concept.

EXPERIMENTAL PROCEDURE

Experimental Design

 

An experimental investigation of auger cutters was conducted to
quantify the effects of cutter geometry, workpiece properties and cut-
ting conditions on the forces resulting on the cutter and the power
requirements. As previously stated, the auger cutter, as applied to
tree fellers, looks like an elongated milling cutter with either a
straight or helical flute configuration (Figure 1). The most signifi-
cant cutter parameters which affect the resultant forces and power
requirements of the cutter are the cutter diameter, cutter length,
number of flutes, rake angle and helix angle (1). For the main exper-
iment, rake angle and helix angle were studied. Two flutes were used
on the experimental cutters to eliminate the confusing effect of having
more than one edge cutting simultaneously. A cutter diameter of 2%
inches was used in all tests to minimize the expense of purchasing the
experimental units.

Besides the rake and helix angles of the cutter, the variables
expected to have the most effect on the results are the feed rate, most
conveniently expressed as the feed per tooth, which is a function of the
workpiece feed speed, and the cutter rotational speed, species of wood
being cut and the temperature of the wood. For the main experiment, a
series of 12 cutters constructed with combinations of 3 rake angles and
4 helix angles were evaluated along with 9 feed rates comprised of

10

11

 
   

HELIX ANGLE ANGENT TO HELIX RADIAL RAKE ANGLE
\ NORMAL TO AXIS
HA NORMAL TO or CUTTER
t”’——_- CUTTING EDGE r-~L\\
. \

/ G
/
/ \4/

\ SECTION - A A

)r

M\ / NORMAL

RAKE ANGLE
NORMAL TO
- CUTTING EDGE

SECTION - a a‘

\

 

+

 

 

 

 

 
   

CLEARANCE
ANGLE-‘//)r
SHARPNESS
ANGLE

—-'

 

Figure 1 Geometry of auger cutter.

12
combinations of 3 feed speeds and 3 cutter rotational speeds, on green
and frozen samples of 3 timber species-—sugar maple, a high density
hardwood; quaking aspen, a low density hardwood; and red pine, a soft-
wood. A standard sample width of 2 inches was used in the tests to
stay within the power capabilities of the test equipment.

Because of the anisotropic nature of wood, the orientation of the
cutter to the wood during the cutting process must be controlled to
avoid confounding the results with the variations in mechanical proper—
ties (9). For this experiment, the feed direction of the cutter was
taken to be perpendicular to the grain direction of the wood. This is
the orientation that a cutter would take if it were being used to fell
a standing tree. Significant differences in mechanical properties are
also observed between the spring and summerwood portions of the wood
structure (24). To minimize the effect of these differences, all the
2-inch by 4-inch samples cut from the sample logs were oriented so that
the 4—inch dimension of the sample 2 x 4 was orientated perpendicular
to a diameter of the original log (Figure 2). In this way a sample was
obtained where the measurements could be made while the cutter was oper-
ating perpendicularly to a radius of the original log, thus balancing
the effect of the differences between the spring and summerwood portions
of the wood.

For each species, the tests were run as a factorial experiment in
a randomized block design. Rake angle, helix angle and feed rate were
evaluated in a randomized factorial experiment with 3 replications per
cell with the frozen and green wood comprising the blocks. Using this
design, analysis of variance techniques were used to evaluate the effect

of the rake and helix angles, feed rate, temperature and interaction

13

 

 

 

rial in original log.

ion of sample mate

Figure 2 Orientat

14
between the variables. Regression analysis was then used to relate the
results to the cutter parameters and feed conditions and determine opti-
mum values of these variables.

The test runs made can be summarized as follows:

Rake angle 3
Helix angle x 4
Feed rate x 9
Replications '§;3
324

Temperature .§_£
648

Species x 3
Total 1944

Cutters

The nomenclature of an auger cutter is shown in Figure 1. The cut—
ter parameters which can be expected to affect the resultant forces on
the cutter and the power requirements are the cutter diameters, number
of flutes, rake angle and helix angle. Because of the significant
expense involved in procuring experimental cutters, it was decided to
hold the cutter diameter and number of flutes constant, and to investi-
gate rake angle and helix angle in detail, as the available literature
indicated rake and helix angles as being the most significant of the
parameters (1).

For the experimental cutters, a nominal diameter of 2% inches and
a two flute configuration were chosen. A nominal clearance angle of 10
degrees was specified. By contract with an independent machine shop
which specializes in fabricating such devices, 12 experimental cutters
were acquired (Figure 3). These 12 units varied in rake angle (15, 30
and 45 degrees) and helix angle (0, 20, 40 and 60 degrees) so that each

combination of rake and helix angle were represented as follows:

 

Figure 3 Experimental auger cutters.

16

 

Cutter Normal rake angle Helix angle
number (degrees) (degrees)
1 15 O
2 30 O
3 45 0
4 15 20
5 3O 20
6 45 20
7 15 4O
8 30 4O
9 45 4O
10 15 60
11 30 60
12 45 60

The cutters were fabricated from a medium carbon alloy steel and
induction hardened to maintain a ductile core while bringing the tooth
area to a hardness of 58-60 Rockwell C.

Subsequent to receiving the experimental cutters, measurements were
made to document the actual geometry of each unit. A Stocker and Yale
Inc. Model 11MB tool analyzer was used to measure helix angle, radial
rake and clearance angle on each flute from each end, and diameter on
each cutter. A plaster mold of each cutter flute was also made which
could be sawed in half so that the radial rake and clearance angles for
each flute could be measured with the tool analyzer at the center of each
flute.

Normal rake angle is related to radial rake angle by the following
expression (1):

tan w = tan r cos a

where,
w = normal rake angle
r = radial rake angle
a = helix angle.

17

This expression was used to relate the measured values of radial
rake angle to the corresponding value of the normal rake angle. Table 2
lists the specified and measured parameters for each of the 12 cutters.
As can be seen from Table 2, some errors were apparent in the manufacture
of the experimental cutters. Discrepancies of up to 40 in the helix
angle and up to 7° in the normal rake angle were found. In the discus-
sions which follow, the nominal values of the helix and normal rake angle
will be used, but the results must be tempered with the knowledge of the
discrepancies that were found. Errors in the clearance angle are also
apparent, but the errors are generally on the high side, and it is not
felt that they will have a significant effect on the results.

The sharpness of the cutter is a significant parameter in determin-
ing the forces and power requirements of the cutting process. For this
study, the cutters were resharpened using standard machine shop practice
after each 27 test runs, which was the number of tests conducted with
each cutter on each species within each replication. The objective was
to maintain a "work sharp" edge throughout the test program, meaning
that the cutters were not allowed to dull excessively but were not kept
in a freshly sharpened condition either.

Sample Material

 

Three tree species were selected for use as sample material--sugar
maple (Acer saccharum), a high density hardwood; bigtooth aspen (Populus
grandidentata), a low density hardwood; and red pine (Pinus resinosa),

a softwood. Besides providing a range of wood densities, these three
species are commercially important as sawtimber and as such, are species

on which the auger cutter may be used.

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Sample trees were obtained from several locations within Baraga
County, Michigan, where access to forests owned by the Ford Forestry
Center, of Michigan Technological University, and the Baraga State For-
est, Michigan Department of Natural Resources, was obtained. A total
of 26 trees were cut to obtain the required number of samples for the
green material and 20 trees for the samples run as frozen wood. The
green samples were cut during the period August 7-10, 1978, and the fro-
zen material was cut during the period November 7-9, 1978. The material
cut for the frozen tests was not yet naturally frozen at this point in
time, but the trees were well into their dormant period, and it wasn't
felt that cutting then and artificially freezing the sample blocks at
a later point would affect the test results. Enough trees of each spe-
cies were cut to supply 20 suitable logs for both the green and frozen
samples. Each tree cut was measured to obtain d.b.h. (diameter at breast
height) and total height and was marked with a north line to indicate
the original orientation of the tree.

After felling, each tree was bucked into as many 8—foot lengths as
were available. Each 8—foot log was measured for diameter at each end
and total length. Each bolt was given an identifying number so that
every eventual sample could be traced back to its original tree. Discs
were cut at 8—foot intervals from each tree, and these discs were taken
back to the lab for determination of tree age, specific gravity, green
density and moisture content. For these properties, the bark was
excluded and only the wood considered. The procedures contained in TAPPI
Standard T 18 m—53 were followed in making these determinations (22).
Tables 3 through 8 summarize the basic tree properties and the samples

that were obtained from each tree.

21

The material properties expected to have the most effect on the cut—
ting operation are the specific gravity and moisture content (24). Spe-
cific gravity in wood directly affects the strength properties and thus,
the forces and power requirements found in the wood cutting process.
Tables 3 through 8 show that the specific gravity values of the sample
trees chosen for aspen and red pine fell quite close together. This leads
to the expectation that the force and power requirements found for these
two species will be quite similar. This expectation is borne out in the
discussions which follow. Moisture content can have a very significant
effect on forces and power requirements in wood cutting operations (24).
In this work, the moisture content was maintained at green conditions so
its effect over a range of values was not documented.

The logs were transported to a commercial sawmill to be converted
into suitable 2 x 4'3 from which samples could be cut. Two 2 x 4'3 were
cut from each log according to the specification discussed earlier.

These 2 x 4'8 were then taken to the laboratory and stored in a controlled
humidity room to maintain the original moisture conditions. After cut-
ting the 6-inch test samples from the 2 x 4'3, the samples were bagged

in plastic and stored under controlled conditions until the tests were
run. The samples run at green conditions were stored at 400 F., while

the frozen material was kept at 30° F. A total of 1,359 samples were
prepared from the green material and 1,284 samples from.the frozen mate-
rial from.which the 972 samples used in each series of tests were selected

randomly.

 

22

qu owe ON HNHOH

 

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smouu

 

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23

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compo

 

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25

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cameo

 

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26

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somuw

 

mmHofimm amuoum now use mmmuu mafia omu mo Numaaaw .w oHHwH

28

Test Equipment

 

A Brown and Sharp No. 2 plain milling machine was acquired for use
as a test device. An arbor was fabricated which would hold the cutters on
the spindle plus would provide a suitable section for a strain gage
bridge to monitor the torque being exerted on the cutter (Figure 4).
The milling machine has a selection of 18 possible spindle speeds covering
a range of 40 to 1530 rpm and 18 possible table feed speeds over a range
of k to 20% inches per minute. Of the possible combinations, 3 spindle
rpm's of 520, 980, and 1530 were selected to use in the test program
along with 3 table speeds of 6-3/4, 13, and 20% inches per minute. A
factorial combination of these spindle and table speeds provide the 9
feed rates used in the test program. Each of the speed settings was

calibrated and the actual cutter feed rate calculated using the relation-

ship.
.1.
F = 2n
where,
F = cutter feed rate in inches/tooth
V = table speed in inches/minute
n = spindle speed in rpm.

Table 9 shows the nominal and measured speeds for the table and
spindle settings and the calculated feed rate for each of the combinations.
A special fixture was fabricated to secure the sample blocks. The

fixture was mounted on top of a 3 dimensional load measuring platform
which was secured to the table of the mill. The three-component measur—
ing platform used was a Kristal Model 9257 A piezoelectric transducer

built for the measurement of forces in three orthogonal directions

29

 

,7, 7 , 7 7 7 7 . ,7 7 7 7 x . 7 7 777 7. 77.7 _77_7.____7

Figure 4 Arbor for mounting experimental auger cutters
with strain gage torque transducer.

30

Table 9. Machine settings for test conditions.

 

 

Nominal Measured Nominal Measured Cutter
spindle spindle table speed table feed rate
rpm rpm in/min speed in/min in/tooth x 10"4
520 535 6-3/4 7.03 66
13 13.43 130
20—1/4 20.93 200
980 1006 6-3/4 7.03 35
13 13.43 67
20—1/4 20.93 100
1530 1567 6-3/4 7.03 22
13 13.43 43

20-1/4 20.93 67

 

31
(Figure 5) (8). For each of the three force components a proportional
charge is set up in the measuring platform. These Charges are fed into
charge amplifiers where they are converted into proportional voltages
which can be displaced or recorded as required. The particular unit
used in this study has a unique feature which makes it particularly
useful. Due to the construction of the unit, the point of application
of the forces to be measured can be anywhere in the space above the sur-
face of the platform without affecting the measurement. This was of
importance because the cutting action of the auger cutter changes loca-
tion as the cutting edge rotates through its cycle. Thus, the self
compensating feature of the device automatically adjusts for the changes
in the point of application of the forces.

The measurement of torque on the arbor was accomplished using a
4-arm strain gage bridge arranged to measure torque (Figure 6) (3).
Three hundred fifty ohm gages were used to increase sensitivity. The
signal from the strain gage bridge was amplified using 3 CBC model
1—161 amplifier and fed into a CEO model 5-124A recording oscillograph.
Figure 7 illustrates the complete test setup and the associated instru-
mentation. Both the torque transducer and the three—component force
measurement platform were calibrated using dead weights before the
test program was conducted.

Due to the rotary cutting action of the auger cutter, each 180
degree rotation of each cutting edge will experience a change in cutting
condition from cutting against the grain to cutting with the grain to
cutting against the grain. This change in cutting conditions has a
significant effect on the resultant forces. A cutter position indicator

was incorporated into the test setup to monitor the angular displacement

32

 

Figure 5 Three component force transducer and fixture
for securing sample blocks.

33

SLIP RING
ASSEMBLY

 
  
 
 
 
 

ROTATION

TORQUE TRANSDUCER

 

 

      
   

 

+
c
U
(9
<
.—
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o
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z o 350 OHM
9 - GAUGES X 4
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t
O
X
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- I
/‘

 

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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0, AMPLIFIERS
O O O O O
0 r0 | o o OAMPLIFIERS

 

 

 

 

 

 

 

 

 

 

 

RECORDING
OSCILLOGRAPH

 

CUTTER
POSITION

TORQUE
TRANSDUCER

\UTTER

 
 
    
  

FEED/v
DIBECTION

 

 

3 COMPONENT
DYNAMOMETER

Figure 6 Schematic of instrumentation system.

34

 

Figure 7 Equipment set up and instrumentation system
for experimental studies.

35
of the cutting edge and provide a means of relating the results to the
cutting condition being experienced at any given time (Figure 8).
Continuous recordings of all variables were thus made with the ability
to locate the angular position of the cutter at any given time.

Data Analysis

 

For each test run, the forces on the workpiece and the torque on the
arbor holding the cutter were recorded at the point on the sample where
the cutter was just reaching the imaginary radius of the original log
(Figure 9). This was done to maintain a constant orientation between
the cutter and the principal directions of the samples for all tests
conducted. For analysis of the data, one revolution of the cutter was
picked from the strip chart recordings where the loading had reached a
steady condition. Selection of one cycle was done by picking two
successive marks put on the recording by the cutter position indicator
(Figure 10).

From the cycle thus selected for each test run, the maximum and
minimum value of each force and the torque were picked off the recording.
After converting to pounds or inch-pounds, the results were divided
by the sample width to put the results on a per inch of cut basis. This
was done to permit easy extrapolation to other widths of cut. The
actual rotational speed of the cutter was also calculated from the
length of the cycle on the recording and the paper Speed of the recorder.
The calculated rpm of the cutter was used with the measured torque to

calculate the horsepower requirement of the cutting.

36

9

 

Figure 8 Cutter position indicator.

37

RADIUS OF
ORIGINAL
CROSS SECTION

I” T //

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

\\ M’
TIL‘ I
I
I /

 

Figure 9 Location on sample blocks for recording of test data.

38

 

Figure 10 Example of oscillograph output recording forces
and torque on cutter.

EXPERIMENTAL RESULTS

Cutter Geometry

 

An evaluation of an operation as complex as the auger cutting
process, with its several independent variables and numerous possible
output variables, initially requires a selection of the criteria by
which its performance will be judged. This work will consider the
maximum recorded torque and the maximum recorded axial force as being
the variables upon which selection of the optimum values of cutter
geometry will be based. The maximum torque is included because it is
directly related to the horsepower requirement of the cutting operation,
and it is dependent on both the Y and Z forces as measured in the exper-
iment. The Y and Z forces are both cyclical in nature, and when meas-
ured in the Y and Z directions as done here, would have to be resolved
into a radial and tangential component to be of significant value to
an evaluation of cutter parameters. The torque, as measured, is related
to the tangential component of the resultant force by the cutter diam-
eter, and thus besides relating the power requirement of the cutting,
partially relates the force loading on the cutter. The axial force is
significant from the aspect of the design of a subsequent cutting device
using this concept. Particularly when considering thrust loads on bear-
ing supports and structural requirements of the supporting frame, the

axial force would be significant in the design calculations.

39

40

The use of the maximum recorded torque and axial force implies that
the criteria for an optimum cutter would be the combination of rake and
helix angle that simultaneously produces the lowest value of torque and
axial force. However, it soon becomes obvious that a compromise will be
required as the geometry that will produce the lowest torque readings
will not be the same as those that produce the lowest axial force. This
will become evident in the discussion which follows.

The analysis of variance tests performed on the data showed all of
the major variables, species, helix angle, rake angle, table speed, spin-
dle r.p.m. and temperature, to have significant effect on the results.
The effect of these variables accounted for 71 percent of the variation
found in the analysis of maximum torque and 76 percent of the variation
found in the analysis of maximum axial force. Following is a discussion
of the effect of each variable on the selected outputs.

The helix angle is the single most important variable affecting

the axial force, F Sixty-two percent of the total variation in Fx is

x.
accounted for by the helix angle. As would be expected, increasing val-
ues of helix angle create increasing values of Fx- The effect is basi-

cally linear from 0° to 40° with a greater increase from 40° to 60° as

shown in the following tabulation.

Helix angle (degrees) Average Fx* (lb/in) Increment in Fx (lb/in)

 

0 - 0 -
20 21 21
40 42 21
60 77 35

*Averaged for all tests

41

Increasing rake angle has the effect of decreasing Fx, the average
decrease from 15° to 45° rake angles being 30 percent. This result is
consistent for the three species considered and both for green and frozen
wood (Figures 11 and 12). The frozen wood showed an average increase in
Fx of 26 percent over the green material. The average values of Fx for
the aspen, maple and pine by helix angle and green and frozen wood are
summarized in Table 10.

Spindle r.p.m. and table feed speed have consistent effects over the
range of the three species, green or frozen wood and the twelve combina-
tions of rake and helix angle. Increasing values of spindle r.p.m.
decrease the axial force while increasing values of table feed speed
increase the axial force. The general effect of the variables is illus-
trated in Figure 13 for sugar maple cut in the green condition. The
results for the other species and the frozen samples follow the same
general trends. Further discussion of the effect of spindle r.p.m. and
table feed speed will be included in a later section where their combina-
tion into a feed rate value and its effect on the cutter performance will
be considered. Further consideration of these two variables for selec—
tion of an optimum cutter geometry is not required.

The analysis of variance on the maximum torque (Tmax) indicated that
all the main variables, species, helix angle, rake angle, table speed,
spindle r.p.m. and temperature, have a significant effect on the results.
These main variables account for 71 percent of the variation found in
the results, but unlike the axial force analysis, no one variable has
a dominant effect. Spindle r.p.m. has the greatest effect but only

accounts for 18 percent of the variation in the data.

42

Figure 11 Maximum axial force vs. helix and rake angles
for green wood by species.

 

HXIHL FURCE (LE/INCH) HXIHL FURCE (LB/INCH)

HXIHL FDRCE (LB/INCH)

20D

ISZ

SB

238

ISZ

SB

ZZZ

ISZ

SE

 

1

 

 

43

HSPEN

RHKE HNELE
(DEGREES)
IE

HE

A A 1 J

20 HI GD
HELIX RNGLE (DEGREES)

SUEHR MHPLE

RHKE HNGLE
(DEGREES)

I 5
3B
H5

1

2B HE GB
HELIX RNGLE (DEGREES)

RED PINE

RHKE HNGLE
(DEIHREEIS)

A L l J

EB HZ ED
HELIX RNGLE (DEGREES)

Figure 11

44

Figure 12 Maximum axial force vs. helix and rake angles
for frozen wood by species.

HXIHL FDRCE (LB/INCH) HXIHL FDRCE (LB/INCH)

HXIHL FDRCE (LB/INCH)

2B8

ISE

SD

2GB

ISB

SE

ZZZ

ISZ

SD

 

45

 

 

 

 

 

' HSPEN
RFIKE FINGLE
(DEGREES)
IE
3B
- HS
2D HZ ED
HELIX HNGLE (DEGREES)
SUEHR MHPLE
' RFIKE FINGLE
(DEGREES)
IS
3D
I
I H5
28 H2 EU
HELIX HNGLE (DEGREES)
' RED PINE
RFIKE FINGLE
(DEGREES)
I l5
3!
.. ‘45
2a HE! 5a J

HELIX HNGLE (DEGREES)

Figure 12

46

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47

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48

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49

The effects of species and temperature are consistent throughout
the data and follow expected patterns, the frozen wood increased Tmax
by an average of 20 percent over the green material, and the results by
species showed maple to be higher than red pine and aspen, following the
differences in specific gravity.

The effect of helix angle on Tmax shows decreasing values of Tmax
with increasing values of helix angle from 0 to 40 degrees with a level-
ing out or increase in Tmax from 40° to 60° (Table 11).

Increasing rake angle has the effect of decreasing Tmax: the average
reduction from a 15° rake angle to 45° rake angle being 38 percent (Fig-
ures 14 and 15).

The effect of table speed and spindle r.p.m. are consistent over
the three species considered, green and frozen wood and the twelve cut-
ters, or twelve combinations of rake and helix angle. Increasing values
of spindle speed tend to decrease the value of Tmax while increasing val-
ues of table speed increase the resultant torque. The general effects
of these variables are illustrated in Figure 16 for maple cut in the
green condition. They will again be considered in more detail in the
next section.

The overall results of Tmax and Fx versus rake and helix angles are
shown in Figure 17. Using the selection criterion for the optimum cutter
of the combination of rake and helix angles which produces the lowest
Tmax and simultaneously the lowest Fx, it can be seen that a compromise
between the criteria must be made. The lowest Tmax occurs at a 60° helix
angle while the highest axial force also occurs at the 60° helix angle.
The combination of the lowest Tmax and lowest Fx occur at the 20° helix

angle and the 45° rake angle. However, a third consideration should be

50

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we ee ON mw soouO
oafim
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.moHooOo Ne e003 cowonm one noouw How once xaaox .m> oDOHOu Essfixez .HH oHeeH

51

Figure 14 Maximum torque vs. helix and rake angles
for green wood by species.

TDREUE (INCH LBS/INCH) TORQUE (INCH LBS/INCH)

TDREUE (INCH LBS/INCH)

32B

25B

2GB

ISZ

SE

BBB

25B

2B8 ~

ISO

SE

3Z2

25E

ZZZ

I50

50

VTVVVV‘

V'T‘V’WV'TYfY'TYVV'YVV

 

IrV’VV'

VV'YVV

 

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TY

 

H 2B HR GD

52

HSPEN

RRKE RNGLE
(DEGREES)

\ 32
HS

 

b

L

HELIX HNGLE (DEGREES)

SUGHR MHFLE

RRKE RNGLE
(DEGREES)

l l l _l

2D Ha GE
HELIX HNGLE (DEGREES)

at

RED PINE

RRKE RNGLE
(DEGREES)

EEEEEEEEETTTE‘NON #____,._ I:

v

\ 32
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H 2B HZ EB

HELIX HNGLE (DEGREES)

Figure 14

53

Figure 15 Maximum torque vs. helix and rake angles
for frozen wood by species.

TORQUE (INCH LBS/INCH) TDREUE (INCH LBS/INCH)

TURBUE (INCH LBS/INCH)

3GB

25B

EDD

I50

52

3GB

ESE

EDD

ISZ

IZZ

SD

3GB

25E

ZZZ

ISO

50

 

54

 

 

 

 

 

 

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r
I
I
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HELIX HNGLE (DEGREES)

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HELIX HNELE (DEGREES)
I RED PINE
I
; RHKE HNGLE
: (DEEWUEES)
IE

f \/ an
t -\
L “““‘-- HS
i

D 2B HR EB

HELIX HNGLE (DEGREES)

Figure 15

55

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56

 

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57

 

 

 

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RHKE HNELE
g (DEGREES)
5 ma -
\
l5
5}
V 3a
LL] P
&
E H:
E: SE ~
><
II:
B a 2B HE EB
HELIX HNBLE (DEGREES)
ZZZ .
2:15n -
3; I
z I RHKE HNELE
m . (DEGREES)
ND
—1 I
z b
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‘z‘aJ ’ H5
:5 f
E; 5n -
.I—
a A l L l l

 

Z 28 HZ 5a
HELIX RNELE (DEGREES)

Figure 17 Maximum axial force and maximum torque vs. helix
and rake angles averaged over all tests.

58
included at this point. The combination of a 200 helix angle and a 45°
rake angle gives a normal sharpness angle of 35 degrees (Table 2). For
practical cutting situations where the auger cutter would be employed,
experience in wood working has shown that this sharpness angle and the
implied fine edge, would create a significant problem in maintaining the
sharpness of the cutter, and also in providing enough mass in the tooth
to minimize damage due to hitting obstructions during the cutting process
(1;). For this reason, a cutter with a 300 rake angle, 40° helix angle
and a sharpness angle of 50 degrees is believed to be a better combina—
tion. The average Tmax found for this combination is only 14 percent
higher than for the 20° helix, 45° rake combination, while the sharpness
angle is about 40 percent greater.

Cutting_Rate

 

Any cutting process that has as its eventual application the commer-
cial felling of timber requires an analysis of the rate at which the
device can cut the wood, and the effect of the cutting rate on the forces
and power requirements for the device. This portion of the experimental
program was designed to develop the data needed to evaluate the effects
of cutting rate on the performance of the cutter and the resulting forces
and power requirements.

The experimental design used in this study was complete in that the
effect of cutting rate could be evaluated for any of the combinations of
cutter geometry, i.e., rake and helix angle, that were used in the test
program. However, since the combination of a 40° helix angle and 30°
rake angle has been selected as an optimum combination of cutter paramr
eters, the following analysis of the effect of cutting rate will be lim-

ited to that combination only. For identification purposes, the cutter

59
with the combination of the 40° helix angle and 30° rake angle was
labeled cutter number 8, and that identification will be used in the
discussion which follows.

The basis for the analysis of the effect of cutting rate on the cut-
ter performance was the 9 cutter feed rates built into the experimental
design. Within the limitations of the milling machine used for the test
setup, 3 nominal spindle speeds, or cutter rotationalspeeds, of 520,

980 and 1530 r.p.m., and 3 nominal table feed speeds of 6, 13 and 20
inches per minute were used in a factorial combination to provide 9 feed
rates for the experimental design. This combination gave a range of feed
rates from 22 x 10"4 to 200 x 10'4 inches/tooth. The following tabula-
tion gives the values of feed rate for each combination of rotational

speed and table feed speed.

Feed rates (inches/tooth x 10-4)

 

Nominal cutter rotational speed (r.p.m.)

 

 

520 980 1530
Nominal 6 66 35 22
table
speed 13 130 67 43
(in/min)
20 I 200 100 67

The values of cutter rotational speed and table speed used were spe-
cifically selected from those available so that a full range of values
was included, and also so that the values of feed rate on the diagonal
of the above matrix were as nearly equal as possible. A hypothesis of
this study was that the forces on the cutter and the power requirements
of the cutting operation were dependent upon the feed rate rather than

independently upon the cutter rotational speed or the table speed. Thus,

60
if the hypothesis is true, the values of the forces and power require-
ments observed for the three equivalent feed rates on the diagonal of
the above matrix should be equal. This hypothesis is partially borne
out in the following discussion of the experimental results of the effect
of cutting rate on the performance of the auger cutter.

The effect of cutter rotational speed and table feed speed on the
resulting torque and axial force are consistent for the three species of
wood considered and for green and frozen wood. Increasing values of cut-
ter rotational speed tend to reduce both the torque and the axial force,
while increasing values of table feed speed tend to increase both the
torque and axial force. In all cases, the axial force and torque are
higher for frozen wood than green wood. These results are illustrated
in Figures 18 and 19 for the three species of wood, both green and frozen.
The results by species follow the difference in specific gravity between
the three species, sugar maple being highest, with aspen and red pine
lower, but quite close.

Examination of the data in Figures 18 and 19 shows that for those
combinations of cutter rotational speed and table feed speed that create
the same feed rate of 66 x 10'4 inches/tooth, the resultant values of
axial force and torque are quite similar. The data in Figures 18 and 19
are taken from Tables 12, 13 and 14 where this trend can be seen in numer-
ical form. As previously stated, a hypothesis of this work was that the
resultant forces and power requirements for the auger cutter were depen—
dent on the feed rate of the cutting operation rather than independently
on the cutter rotational speed or the table feed speed. The effect this
has is that it allows the significant loadings on the cutter to be docu-

mented in terms of one variable instead of two, and greatly simplifies

61

Figure 18 Maximum axial force vs. spindle rotational speed
and table feed speed for green and frozen wood
by species.

HXIHL FURCE (LE/INCH) HXIHL FORCE (LB/INCH)

HXIHL FURCE (LB/INCH)

IZZ

BZ

SZ

HZ

ZZ

IZZ

EZ

HZ

ZZ

IEZ

IZZ

EZ

EZ

HZ

2Z

 

62

HSPEN

 

 

 

 

 

 

 

 

SPINDLE SPEED (RPM)

Figure 18

THBLE SPEED SYMBOL
IN/MIN GREEN FROZEN
E . ‘1‘
l3 D X
22 B *
1 22m A HZZ ‘ sun Liana AIZZZ“I2ZZ‘LIHZZ‘LIEZZAKIBZZ
SPINDLE SPEED (RPM)
SUEHR MHPLE
Alana LEHZZAAEEZZ A son AIZZZ‘LIZZZ‘ I nnlklszz‘glaaa
SPINDLE SPEED (RPM)
RED PINE
‘izzn ‘ HZZ Liana Liana 2IZZZ‘EIEZZJEIHZZ‘EIEZZAEIEZZ

63

Figure 19 Maximum torque vs. spindle rotational speed and
table feed speed for green and frozen wood by
species.

TURBUE (INCH LBS/INCH)

TUREUE (INCH LES/INCH)

TDREUE (INCH LBS/INCH)

64

 

 

 

 

 

 

 

 

 

22a .
I HSPEN
’ TFIBLE SPEED SYMBOL
' IN/MIN GREEN FROZEN
ISZ -
> E . +
’ [3 E] X
’ ‘I‘
IZZ -
I
so I
I
a L Lg L I 4 J L l L 1 - I I I L I L l
a 2mm HZZ EZZ BZZ IZZZ 12am [HZZ IEZZ IBZZ
SPINDLE SPEED (RPM) *
2am -
’ ESLHSFH? VHHFH_E:
ISZ -
b
I
IZZ -
L
SE -
L
z a ‘ 2mm L'HZZ A EZZ L‘saa LIZZZ ‘IZZZJEIHZZ‘ IEZZ RTBZZ
SPINDLE SPEED (RPM)
2mm -
L RED PINE
ISZ L
52 . T““‘r——~——___
L
b
a n A 22121 ‘ LIZZ L 52121 Rama AIZZZEIZZZ Ham 752m A IBZZ

SPIthE SPEED (RPMihi

Figure 19

65

 

 

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66

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67

 

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68
the explanation of the effect of cutting rate on the force and power
requirements of the cutting process.

The relationships between the axial force and torque and the feed
rate were found to be linear. Figures 20 and 21 show this linear rela-
tionship by plotting the data for the axial force and torque versus feed
rate. Linear regressions of the form Y = AX +-B were fitted to this
data, and the results are tabulated in Tables 15 and 16. The multiple
correlation coefficient, or degree of linear association between the
independent and dependent variables, varies between .70 and .94 for
these regressions, and the standard error of estimate is 8 lb/in or
less for the regression on the axial force, and 15 in lb/in or less for
the regression on the torque. The regressions plus 95 percent confidence
limits on the mean are plotted for these relationships in Figures 22, 23,
24, and 25. The closeness of the confidence limit curves to the regres-
sion lines indicate the good fit of the experimental data to these curves.

In addition to the loading on the cutter, the power requirement of
the cutting is of practical importance. The effect of cutter rotational
speed and table feed speed on the horsepower are illustrated in Figure
26. Slightly different than the effect found on the axial force and
the torque, increasing values of both cutter rotational speed and table
feed speed increase the power requirement. The axial force and torque
were found to increase with increasing table speed but decreased with
increasing cutter rotational speed. The power requirement of the cutting
is thus found not to be dependent only on the feed rate, but dependent
on both the cutter rotational speed and table feed speed.

The relationships between the power requirement, feed rate, cutter

rotational speed and table feed speed are illustrated in Figure 27.

69

Figure 20 Maximum axial force vs. feed rate for green and
frozen wood by species and spindle rotational
speed.

HXIHL FDRCE (LB/INCH) HXIHL FDRCE (LE/INCH)

HXIHL FURCE (LB/INCH)

IZZ

IZZ

EZ

HZ

ZZ

IZZ

IZZ

BZ

EZ

HZ

ZZ

IEZ

IZZ

BZ

EZ

HZ

EB

 

70

 

 

 

 

 

 

FISFDEWQ
SPINDLE SPEED SYMBOL
RPM GREEN FROZEN
EEO . +
EEO O X
ISEEI m #
LLzz L H! L an L an LIZZ lez LIHZ LIEZ LIBZ Lana
FEED RHTE (INCHES/TOOTH x Z.ZZZI)
SUERR MRRLE
L an L HZ LLEn L an LIZZ Liza LIHZ LIEZ LIBZ Liza
FEED RHTE (INCHES/TOOTH x Z.ZZZ|)
RED PINE
LL20 L ébLLREnLL ab LIZZ LIEZ IHZ LIEZ LIam Lana

FEED RHTE (INCHES/TOOTH X Z.ZZZI)

Figure 20

71

Figure 21 Maximum torque vs. feed rate for green and frozen
wood by species and spindle rotational speed.

TDRHUE (INCH LES/INCH)

TDREUE (INCH LES/INCH)

TUREUE (INCH LES/INCH)

ZZZ

ISZ

SZ

ZZZ

ISZ

SZ

ZZZ

ISZ

IZZ

SZ

 

72

 

 

 

 

 

 

I HSPEN

I SPINDLE SPEED SYMBOL

I RPM GREEN FROZEN

L 522: . +

I sazI n x

I Isaz a I

I

I'

b

I

a L an L HZ L an L an LlanLLizu Luau LIEZLRIBZLLZZZ
FEED RRTE (lNCHES/TDDTH x Z.ZZZI)

I SUERR MRPLE

I

b

I

I

L

F I l L L L I. L 1 L4 L l A l A l A I

a 2n HZ an an IZZ IZZ IHZ IEZ IBZ zna
FEED RRTE (INCHES/TOOTH x Z.ZZZ|)

I RED PINE

I

I

I

I

I

r

a L an L HZ an L an Luna LIZZ LIHZ LIEZ LlaaLLzza

FEED RHTE (lNCHES/TZDTH X Z.ZZZI)

«7‘ - Ah ._..__—I. A__._.. v; I , _ . .‘

Figure 21

73

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74

 

 

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75

Figure 22 Linear regressions and 95% confidence limits for
maximum axial force as a function of feed rate
for green wood by species.

HXIHL FURCE (LB/IN) HXIHL FDRCE (LB/IN)

HXIHL FURCE (LB/IN)

IZZ

IZZ

BZ

EZ

HZ

ZZ

IZZ

IZZ

BZ

EZ

HZ

ZZ

IZZ

IZZ

BZ

EZ

HZ

ZZ

 

L I I L A A A

 

 

76

HSPEN

RXIHL FORCE = 27.5Z + .IZ FEED RHTE

//

SZ L LlnzLLLL L LISZL L L Lzzz

FEED RHTE (IN/TDUTH X Z.ZZZI)

SUEHR MHPLE

RXIHL FORCE = 25.35 + .2! FEED RHTE

L L L A L LL L L L

SZ IZZ
FEED RRTE (lN/TDDTH X Z.ZZZI)

LISZL L 2am

 

RED PINE
HXIHL FORCE = 21.35 + .IH FEED RHTE
EZ IZZ ISZ ZZZ

FEED RHTE (IN/TOOTH X Z.ZZZI)

Figure 22

77

Figure 23 Linear regressions and 95% confidence limits for
maximum axial force as a function of feed rate for
frozen wood by species.

HXIHL FDRCE (LB/IN)

HXIHL FURCE (LB/IN)

HXIHL FORCE (LB/IN)

IZZ

IZZ

BZ

SZ

HZ

ZZ

IZZ

IZZ

BZ

EZ

HZ

ZZ

IZZ

IZZ

BZ

SZ

HZ

ZZ

 

 

 

 

HSPEN
RXIRL FORCE = 25.25 + .IH FEED RRTE
L L LLL SZ L L L LIsz L LISZL L Linn

FEED RHTE (IN/TZDTH X Z.ZZZI)

SUEHR MHPLE

/

RXIHL FORCE = 2H.EE + .H2 FEED RRTE

A A L -

SZ L IZZ LISZL 22a
FEED RPTE (lN/TDDTH x Z.ZZZI)

L . A

 

RED PINE
RXIRL FORCE = 23.35 + .l7 FEED RRTE
SZ L L LL LlaaL LL L LlsaLLLL L Lian

FEED RHTE (lN/TZUTH X Z.ZZZI)

 

Figure 23

79

Figure 24 Linear regressions and 95% confidence limits for
maximum torque as a function of feed rate for green
wood by species.

TDRBUE (IN-LES/IN) TDRGUE (IN-LBS/IN)

TORQUE (IN—LES/IN)

ZSZ

ZZZ

ISZ

IZZ

SZ

ZSZ

ZZZ

ISZ

IZZ

SZ

ZEZ

ZZZ

ISZ

IZZ

SZ

 

80

 

ffi'fi—Y

 

HSF‘EN
L TOROUE = EI.77 + .22 FEED RRTE
L-
I
I- //
z LL L L L SZLL LL L LIZZLL L LL LISZLL L L 2mm
FEED RHTE (lN/TDDTH x n.zzz1>
SUEFIR MFIPLE
E TOROUE = 53.5H + .35 FEED RRTE

 

 

 

I.
2 LL L L SE L L L LlnzL LL L LISZL L Lzzz
FEED RHTE (lN/TDUTH x Z.ZZZI)

I RED PINE

L

I TORQUE = H2.H2 + .BZ FEED RRTE

L

I.

I

a L LL L L SZLL L L LlaaL L ISZLL L LL Lana

FEED RHTE (lN/TZZTH X Z ZZZI)

Figure 24

81

Figure 25 Linear regressions and 95% confidence limits for
maximum torque as a function of feed rate for frozen
wood by species.

TDRZUE (lN-LES/IN) TDREUE (lN-LBS/IN)

TDRDUE (IN-LES/IN)

ZSZ

ZZZ

ISZ

IZZ

SZ

ZSZ

ZZZ

ISZ

IZZ

SZ

ZSZ

ZZZ

ISZ

IZZ

SZ

 

82

 

 

 

 

 

 

.
FISF'EN
I
. TDREUE = 52.47 + .az FEED RHTE
I
L
I
z LL L LLL 5n L L L LlanL LL L LISDLLLL L LGn
FEED RHTE (lN/TDDTH x n.2mzu>
I SUEFIR‘ MHF’LE
I. TOROUE = HE.H| + .78 FEED RRTE
L
I
I
a LLL L L SZ LLLL LIZZ L L LL LISZ L L LL Lzéa
FEED RRTE (lN/TDDTH x Z.ZZZI)
.
RED PINE
I
I. TOROUE = H7.2O + .35 FEED RRTE
z LL LLL LLSZ L L L LIZZL LL L LISZL LL LLLzaz

FEED RHTE (IN/TOOTH X Z.ZZZI)

Figure 25

83

Figure 26 Maximum horsepower vs. spindle rotational speed and
table feed speed for green and frozen wood by species.

HURSE PUNER PER INCH HURSE PDHER PER INCH

HURSE PDHER PER INCH

r‘LL‘\
H ‘i‘

 

 

 

HSPEN
THBLE SPEED SYMSnL
IN/MIN GREEN FRszN
S . +
l3 0 X
an a *

ZZZ

L 2am

L zaz

L HZZ L EZZ L BZZ LlanzLlennLLIszL IEZZL IBZZ
SPINDLE SPEED (RPM)

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87
A significant observation that can be made from this data is that at
a given table feed speed, which is the speed at which the cutter is
actually moving through the wood, the power requirement goes down signif—
icantly with increasing feed rate or decreasing cutter rotational speed.
Associated with the increase in feed rate is an increase in the force
loading on the cutter as seen in previous results, but a significant
reduction in the horsepower requirement may have important implications
for the total design of a felling device utilizing an auger cutter.
Quite often, the total horsepower available for a given machine is the
critical constraint around which the processing functions of the machine
need to be designed. For instance, in the case of a swath harvester as
discussed in the background section of this paper, the power source of
the machine would have to power the cutting device and associated mate-
rial processing equipment, as well as provide the motive power for the
machine. The actual cutting of the wood would be a major consumer of
the available horsepower, and thus any significant reduction in the power
requirement of the cutter itself could have major impact on the total

design.

ANALYSIS

Analytic analysis of wood machining processes has trailed the
analysis of metal cutting operations, and has usually attempted to
apply the basic techniques developed for metal cutting operations
to the more complex problem of predicting the action of a tool pene-
trating wood. The major factor complicating the analysis of wood cut-
ting is the anisotropic nature of wood which results in any analysis
being specific to a particular orientation between the cutting device
and the principal directions of the workpiece. Additionally, all pre-
vious analyses of wood machining operations have been directed at finish-
ing operations such as planing where the primary variable of interest
is the quality of the surface produced. This limits the applicability
of previous works to the case at hand where surface finish is of little
significance to the process.

Most wood machining operations can be considered as variations of
two basic processes, orthogonal cutting and peripheral milling (lg).
Orthogonal cutting is that machining situation where the cutting edge
of a straight tool is perpendicular to the direction of relative motion
between the tool and work piece, and the surface generated is a plane
parallel to the original work surface. Illustrative of this type of
process is the carpenter's hand plane. Specification of the relation-
ship between the cutting edge and the principal directions of the work-
piece in orthogonal cutting is commonly based on a system devised by

88

89
MtKenzie (lg) where a two number system is employed (Figure 28). The
first number gives the angle between the cutting edge and the grain direc-
tion of the wood, and the second number gives the angle between the veloc-
ity vector of the cutting edge and the grain direction of the wood. Thus,
crosscut shearing of wood.would be classified as a 900 - 90o cutting sit-
uation, planing with a hand plane is typically done in the 90° - 0° ori-
entation, and rotary veneer peeling is done in the 0° - 90° orientation.
Franz (1) investigated the 90° - 0° cutting situation extensively, while
‘McKenzie (13) has done an extensive investigation of the 900 - 900 cut-
ting situation.

The second basic cutting process, peripheral milling, is a rotary
cutting process in which wood is removed in the form of single chips.
These single chips are formed by the intermittent engagement with the
workpiece of knives carried on the periphery of a rotating cutter head.
The single surface rotary planer is illustrative of this type of process.
Koch (lg)'has investigated this cutting process and has also compiled a
thorough review of the information available on the basic cutting pro-
cesses (1;).

It is not the intent of this work to do a comprehensive review and
analysis of the work which has been done in the area of wood machining.
Rather, the findings and conclusions of several investigators will be
related to the findings of this study, and their results used to explain
and expand the work done here.

Analytic Methods

 

Because of the extreme anisotropy of wood, it is generally conceded
that a general analysis of the process of chip formation in wood cutting
is impossible. The common technique employed in most work has been to

experimentally observe the mechanism by which individual chips are formed

90

GRAIN DIRECTION
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\ \ I 0°-90°
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91

during the cutting operation and then through the use of an appropriate
model, relate the resultant loadings on the cutter to the properties
of the workpiece. This approach has also been useful in that the
mechanism of chip formation also determines the quality of the resultant
surface, and as previously stated, most wood machining operations previ—
ously analyzed have dealt with finishing operations where the quality
of the surface finish is the primary variable of importance. Franz (Z),
McKenzie (13): and Stewart (29) have reported good results with this
approach.

Application of this approach to this study was considered impractical
for the following reasons. The cutting action involved in the auger cutting
process is very complex compared to any analysis that have been previously

made. Franz's analysis was on the 90° - 0°, or plane milling configuration,

while McKenzie analyzed the 900 - 90°, or crosscutting configuration.
The auger cutting Operation is closer to the peripheral milling work of
Koch, but because of the cutting direction being through the workpiece,
it involves cutter contact throughout a 180° cycle of the cutter and a
complex combination of orientations between the helical shaped cutter
and the grain orientation, plus a continuously varying chip thickness
which is not found in the orthogonal cutting situations.

The observation of the actual mechanism of chip formation is critical
to this type of analysis of the wood machining process. In the studies
done previously, the geometry of the cutting permitted the placement of
a clear plastic plate adjacent to the workpiece through which the chip
formation process could be viewed, and which served to contain the edge

of the workpiece. The auger cutter with the helical knife configuration

92

is not conductive to this type of visual observation. Restraining
the edge is not practical because of the flow of chips in an oblique
direction, and if the edge is not constrained, extraneous modes of
chip formation can occur.

Chip_Formation with the Auger Cutter

 

A detailed analysis of the mechanism of chip formation was not
thought to be practical for the auger cutting process for the reasons
listed above, but an overview of the process can help to explain the
results obtained experimentally. Samples of the chipiformed by the
cutting process were collected during the test program for selected
combinations of cutter rotational speed and table feed speed, and also
for the twelve cutters studied. The sample blocks cut were also saved
for later observation of the appearance of the cut surface.

Examination of the chips formed under the various cutting conditions
showed very little change in the character of the resulting chips.

Within an individual test there was a variety of sizes and shapes of the
resultant chips but this would be due to the fact that the chip thickness
varies continuously from zero to a maximum halfway thru the cutter cycle,
and back to zero as each cutter flute completes a cycle. For comparison
purposes a representative sample of the major chip type formed was sorted
out for each test. Figure 29 illustrates the chip formation observed

for aspen cut by the twelve cutters at the same feed rate conditions.

It is seen that the basic form of the chips is very similar, and it can
be concluded that the rake and helix angle combinations have little effect
on the basic form of chip formation. The observation of the chips formed
for the other species and the other feed rate conditions showed a similar

effect of rake and helix angle.

93

 

Figure 29 Chips formed when cutting aspen at a constant
feed rate by rake and helix angles.

94

The effect of the feed rate combinations of table feed speed and
cutter rotational speed on chip type are illustrated in Figure 30
for aspen cut with cutter 8. Again the basic chip form is similar but
the size varies due to the difference in feed rate and thus the dif-
ference in chip thickness. The results again for other cutters and
species were similar. From these results it may be concluded that for
the range of conditions investigated in this work the basic chip form
encountered does not change on the macroscopic level. Microscopic ex-
amination of the mechanism of chip formation may lead to other conclus-
ions but was not investigated here.

Examination of the sample blocks saved showed a very similar pattern
of cut surface over the test conditions. Referring to Figure 31 to
identify zones on the cut surface of the sample blocks, zones 1 and 4
generally showed a smooth resultant surface due to the repeated action
of shaving off very thin chips. These zones are not of particular
interest because the primary cutting was done in zones 2 and 3. Zone 2
invariably showed a smooth cut surface while the resultant surface in
zone 3 showed varying degrees of what might be referred to as torn
grain. Figure 32 illustrates the appearance of the torn grain surface in
a sample block.

0n the suspicion that the marked difference in cut surface observed
could be related to the force and power requirements of the cutting
process, the strip chart recordings of all the test runs were analyzed
to determine the locations where the maximum values of the loading occur-
red. Analyzing the maximum torque and coding the peak locations within the
cutter cycle between 0 and l, 0 being the initial point of zone 2, and 1
being the final point of zone 3, the results in Table 17 were obtained.

This data shows that invariably the maximum torque values occurred in zone 3

95

SPINDLE RPM
980

 

Figure 30 Chips formed when cutting aspen with cutter 8
by spindle RPM and table feed speed.

96

 

 

 

 

 

 

Figure 31 Identification of zones on cut surface of sample blocks.

97

 

Figure 32 Appearance of torn grain in zone 3 of sample block.

98

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99

where the occurrence of the torn grain was observed.

The relationships between the cutter and the principal directions
of the workpiece are very complex in zone 3 but these results can be
related to the conclusions developed by McKenzie in analyzing the
90° - 90° cutting configuration (l2).

Microscopic examination of the action of a cutting edge by McKenzie
has shown two stages in what is referred to as the "indentation" stage
of cutting. In the first stage the wood is deformed or deflected before
the edge without apparent rupture, and in the second, rupture occurs
to separate the chips from the workpiece along the cutting plane.
This second stage is referred to as the "incision" stage of the cutting.
In the case of a cutter which is ideally sharp, the indentation stage
would be minimal as the ideally sharp cutter would produce a stress in-
tensity much in excess of the strength of the material and rupture of the
individual fibers would be immediate. However in practical situations,
ideal sharpness is never achieved and on the microscopic level a certain
degree of bluntness is alway present. Thus, under normal cutting circum-
stances wood deflection becomes significant before fiber severance
occurs. The wood immediately in front of the cutter is deflected and the
bending stresses build up until the stress on the fibers is sufficient
for severance to occur. The force then drops off until a new deflection
stage begins and the fiber deflection begins to build up again. Figure 33
taken from McKenzie, illustrates the progression through the indentation
stage of cutting.

The interaction between the parameters of the cutting edge and the
properties of the workpiece then determine the mode by which failure

, occurs at the cutting edge. If the combination of properties is such

 

 

 

101
that incision occurs before the deflection proceeds far enough to build
up the tensile stresses in the fibers to their limit, then the wood fails
by fiber severance at the cutting edge and the resultant cut surface is
uniform. This is labeled a type I failure by MbKenzie. This type of
failure was shown by McKenzie to be characterized by a normal stress
which has the tendency to pull the cutter into the wood.

If the conditions are such that the mode of failure is by the buildup
of tensile stresses in the fibers to their ultimate strength before inci-
sion severs the fibers, then the condition of torn grain appears. This
is classified as a type II failure by McKenzie. This type of failure
produces a very poor surface finish and is characterized by a normal
stress which tends to pull the cutter away from the workpiece. The type
II chip involves higher cutting forces as more energy is required to
deflect the fibers and raise the bending stress to their ultimate limit.

As previously stated, the cutting configuration in zones 2 and 3
are a more complex situation than that studied by MCKenzie but is par—
tially related. At the initial point in zone 2, with a 0° helix angle
cutter, the cutting would be in the 90° - 90° orientation as studied by
McKenzie. As the cutting edge moves through zone 2, the configuration
would move to a 90° - 0° orientation at the end of zone 2. As the cutter
progresses through zone 3, the cutting configuration would shift back
to 90° - 90° at the end of zone 3. Inclusion of a helix angle on the
cutter would complicate the configuration, and this effect will be dis-
cussed subsequently.

Considering the geometry of the auger cutter, it can be deduced that
the cutting action in zone 2 is such that the cutter is driving into the

wood. This would have effect of creating a normal stress into the

102
workpiece, and related to the findings of McKenzie should tend to create
a type I chip and a good surface finish. This is the type of surface
which was found in the sample blocks, and analysis of the force patterns
found in the cutting cycle such as are illustrated in Figure 10 bear out
this description of the force directions. The geometry would indicate
that in zone 3 the cutter would be pulling out of the wood which would
create a normal stress tending to pull up on the workpiece. The result
would be a type II chip form and the resulting torn grain appearance.
The force patterns and the observed surface again bear out this con—
tention.

Concludinthhat the observations made in this study agree with the
conclusions of McKenzie made on a microscopic study of cutting wood in
a 90° - 90° orientation, several of MtKenzie's deductions are significant
to the analysis of the auger cutter.

As a means of promoting the type I chip with its lower force require-
ments and better surface finish, McKenzie tried inducing a lateral veloc-
ity component to the cutting edge by vibration. The results of this
experiment and the following study by McKenzie and Franz (19) were that
the addition of a lateral velocity component improved the surface finish
and reduced the forces measured. These results bear out the results
obtained in this work on the effect of the helix angle. Inclusion of
the helix angle has the effect of creating an angle between the cutting
edge and the feed direction thus effectively creating a velocity component
along the cutting edge. The results shown for the maximum torque vs.
helix angle in Figures 14 and 15 reflect these results. Visual observa-
tion of the sample blocks saved from the tests also support this conten-
tion, as the amount of torn grain is evidently reduced by the inclusion

of the helix angle.

103

McKenzie's results also showed a small improvement in surface finish
with higher rake angles. This is credited to the creation of a sharper
edge which would facilitate the quicker incision of the wood. However,
the benefits of a higher rake angle are not very significant in that it
is the shape of the microscopic cutting edge that had the most bearing
on the chip formation. This result is also supported by the findings of
this study where increasing rake angle has the effect of lowering the
resultant forces observed but not significantly. This result also sup—
ports the earlier decision to select a cutter with a 30° rake angle as
preferred over one with a 45° rake angle.

McKenzie also found an improvement in the cutting was possible
through lubrication of the cutting edge with SAE 30 oil. This pos-
sibility was not investigated here, but should be considered as a

possibility when considering the design of a tree felling apparatus.

DISCUSSION

The objective of this study was to evaluate the major parameters
which affect the auger cutting process as it may be applied to tree
felling devices and document the force and power requirements of the
cutting as a function of the major variables. The focus of the study
was on the cutter parameters, rake and helix angle; the machine varia-
bles, cutter rotational speed and feed speed; and the workpiece param-
eters, species and temperature of the wood being cut.

The range of rake and helix angles studied covers the practical
range for this application. It was found that increasing values of
rake angle consistently decreased the forces and power requirements
of the cutting. However, increasing the rake angle decreases the
sharpness angle, which is the included angle of the tooth of the cutter,
and it is the sharpness angle of the cutter which would become the
limiting value. In practical situations experience has shown that
with a sharpness angle less than 45 degrees, and the resulting fine
edge, the cutter is difficult to maintain. The conclusion was that
a 30 degree angle was an optimum value.

Increasing values of the helix angle produced a linear increase
in the maximum axial force recorded up to a value of 40 degrees, and
simultaneously produced a decrease in the maximum torque recorded.

For helix angles above 40 degrees, the rate of increase in the axial
force accelerated and the maximum torque leveled out or increased.

104

105
Thus helix angles above 40 degrees do not appear to be beneficial, and
an optimum cutter geometry appeared to be a 40 degree helix angle and
a 30 degree rake angle.

Several parameters of the auger cutter which were not studied in
this work should be commented on. The cutter diameter is a Significant
parameter in that the torque on the cutter will be directly proportional
to the diameter. Increasing the diameter will create a larger cross
section to support the loading on the cutter but will also increase the
resultant torque. A need exists for an analysis of the stress created
on the cutter, and a determination of an optimum cutter diameter. This
was not undertaken as a part of this work, but the data presented in
this study would permit such an analysis to be made.

The cutters used in this study all were constructed with two flutes
to minimize the confusing effect of having more than one flute cutting
simultaneously. However, for a practical device, the possibility of
using more than two flutes should be considered. The cutting action
of this type of device creates very cyclic loading when considering
the action of a single flute. The use of 3 or possibly 4 flutes on the
cutter could have the’effect of balancing the loading and reducing the
wide fluctuation observed on a single flute. This would have significant
beneficial effects regarding the fatigue strength of the cutter.

The configuration of the cutter cross section was not evaluated in
this study. The shape of the cross section, particularly in the area
just below the tooth, could have a significant effect on the ability
of the cutter to convey the cut chips out of the cutting zone. If the
auger cutter were used on a very wide material, the ability to clean

the chips out of the cutting zone, and thus avoid plugging of the cutter,

106
would be of significance. The small sample width used in this study,
because of machine limitations, precludes any analysis of this problem,
but it is an item which needs to be considered in any subsequent design
of an auger cutting device.

The investigation of the machine variables, cutter rotational speed
and feed speed, covered a range of 500 to 1500 rpm for the cutter
rotational speed, and 6 to 20 inches/minute for the feed speed. The
significant finding was that the cutter rotational speed and the feed
speed could be combined into a single parameter, feed rate, expressed
as the feed per tooth, and the loadings on the cutter related to this one
parameter. The range of feed rates studied, 22 x 10'4 to 200 x 10"4
inches/tooth, is felt to cover the practical range for this type of de-
vice. The two main loadings on the cutter that were analyzed in this
study, the maximum axial force, and the maximum recorded torque, were
found to be linearly related to the feed rate (Figures 22, 23, 24 and
25).

The power requirement of the cutting was found to be dependent on
both the cutter rotational speed and the feed speed, rather than only
on the feed rate (Figure 27). It was found that at a constant feed speed,
or rate at which the cutter is actually moving through the wood, the
horsepower requirement decreases with increasing feed rate. That is, the
power requirement can be reduced by decreasing the cutter rotational
speed while still maintaining a constant feed speed through the workpiece.
This finding is contrary to commonly held beliefs and could have signifi-
cant implications for the design of a cutting device utilizing the auger
cutting concept, since total horsepower requirement is frequently a

major constraint in the total design of a felling device.

107

The three species of wood used for sample material in this study,
sugar maple, aspen, and red pine, illustrate the range of results that
will be obtained with varying species. The species selected are three
that the auger cutter could be used on, and therefore, in these cases,
the results would be directly applicable. If other species are of inter-
est, then additional work would be required. As noted in the results
of this study, the mechanical strength of wood, and the force requirements
for cutting wood vary directly with the specific gravity of the wood.
Additional study could possibly relate the variables of interest in the
cutting process to the specific gravity of the wood being processed.

If this type of relationship could be shown, then the required data on
cutting a wide range of woods would be available by knowing only the
specific gravity of the wood, which is commonly available for most
species.

The effect of the temperature on the cutting results Should also
be expanded. The results of this work showed a 20 - 25% increase in
forces from cutting at room temperature to cutting samples which were
frozen and held at 30 degrees F. Additional work needs to be done to
document the results at other temperature levels, particularly colder
temperatures since the auger cutter could well be used in cold climates
where temperatures could reach extremely low levels.

An overview of the process of chip formation in wood cutting has
helped to correlate the results obtained in this study with those ob-
tained by other investigators who have looked at the more basic aspects
of wood cutting. The location of the peak forces obtained in this
work can be explained by the mode of chip formation in the varying

zones of the cutting process. The effect of the helix angle which was

108
seen in this work also has basis in the literature. A needed expansion
of this work is to expand the basic mathematical models of chip forma-
tion which have been develOped for the basic cutting processes to the
more complex case of the auger cutting process. A successful model of
the basic mechanism of the auger cutting process could lead to further
refinements and greater efficiency in applying the auger cutting concept

to practical cutting situations.

BIBLIOGRAPHY

10.

11.

BIBLIOGRAPHY

The Cincinnati Milling Machine Co. 1951. A treatise on milling
and milling machines. Cincinnati, Ohio.

Deal, Earl L. 1972. Whole—tree chipping: its cost, advantages,
and drawbacks. Pulpwood Production 29 (7).

Dove, R. C., and P. H. Adams. 1964. Experimental stress analysis
and motion measurement. Charles E. Merrill Publishing Co., Columbus,
Ohio, 515 pp., illus. L

Dutrow, G. F. 1971. Economic implications of silage sycamore.
USDA, For. Serv. Res. Pap. 80-60, 9 pp.

Ek, A. R., and D. H. Dawson. 1976. Actual and projected growth
and yields of populus "'tristis #1" under intensive culture. Can.
J. For. Res. 6: 132-144.

Ethington, R. L., and H. C. Hilbrand. 1966. Anisotrophy in wood.
Orientation effects in the mechanical behavior of anisotropic struc-
tural materials. Am. Soc. Testing Mats. ST? 405, 21 pp.

Franz, N. C. 1958. An analysis of the wood cutting process. Ph.D
Thesis, Univ. of Mich., Ann Arbor, 152 pp.

Gautschi, G. H. 1971. Cutting forces in machining and their rou-
tine measurement with multi-component Piezo-electric force trans-
ducers. In Proceedings of the 12th International Machine Tool
Design and Research Conference, Manchester.

Hakkila, Pentti. 1973. Research project on short-rotation forestry.
Finnish Paper and Timber 24 (10): 125-126.

Herrick, A. M., and C. L. Brown. 1967. A new concept in cellulose
production--silage sycamore. Agri. Sci. Rev. 5: 8-13.

Kerruish, C. M. 1977. Developments in harvesting technology rele-
vant to short rotation crops. Appita 31 (1): 41-48.

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12.

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16.

17.

18.

19.

20.

21.

22.

2 3'".

24.

25.

110

Koch, P. 1954. An analysis of the lumber planing process.
Ph. D. Thesis, Univ. of Wash.

Koch, P. 1964. Wood machining processes, Ronald Press Co.,
New York, 530 pp, illus.

McKenzie, W. M. 1961. Fundamental aspects of the wood cutting
process. Ph. D. Thesis, Univ. of Mich., Ann Arbor, 161 pp.

McKenzie, W. M. 1962. The relationship between the cutting

properties of wood and its physical and mechanical properties.
For. Prod. J. 12(6): 287-294.

McKenzie, W. M. and N. C. Franz. 1964. Basic aspects of
inclined or oblique wood cutting. For. Prod. J. 14 (12): 555-565.

Schreiner, E. J. 1970. Mini-rotation forestry. USDA, For.
Serv. Res. Pap. NE-174. 32 pp.

Smith, J. H. G. and D. S. DeBell. 1973. Opportunities for short
rotation culture and complete utilization of seven northwest tree
species. For. Chron. 49: 31-34.

Steinbeck, K., R. G. McAlpine, and J. T. May. 1972. Short
rotation culture of sycamore: a status report. J. of For.
70: 210-213.

Stewart, H. A. 1971. Chip formation when orthogonally cutting
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