SAE TECHNICAL
PAPER SERIES
972731
Belt and Tire Tractive Performance
Frank M. Zoz
John Deere Product Engineering Center
Reprinted from: Belt and Tire Traction in Agricultural Vehicles
(SP-1291)
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972731
Belt and Tire Tractive Performance
Frank M. Zoz
John Deere Product Engineering Center
Copyright 1997 Society of Automotive Engineers, Inc.
GT / Wd = Gross Traction Ratio, GTR
NT /Wd = Net Traction Ratio, NTR
MR /Wd = Motion Resistance Ratio = GTR - NTR
ABSTRACT
Numerous traction tests of tires and belts have
been conducted over the last few years. These tests
cover a range of tire sizes, weights, and tire pressures as
well as a range of belt sizes tested on vehicles of various
configurations. Use of wider belts provides the greatest
tractive performance improvement under the more
adverse tractive conditions. Larger diameter tires with
longer footprint operating at correct low pressure nearly
equal the performance of belts when tractive conditions
are good.
The theoretical travel speed, Vt, depends upon
the effective radius, r, and the rotational speed. Input
power is the product of the theoretical speed, Vt, and the
gross thrust, GT. Output power is the product of the
actual travel speed, Va, and the net pull, NT. Tractive
efficiency, TE, is the ratio of the output power to input
power.
Tractive Efficiency (ratio) =
INTRODUCTION
Over the last few years numerous traction
performance tests have been conducted on tires and
belts. Tires of various size, and pressure have been
tested in different soil conditions with various axle
weights. More recently belts of various sizes and tread
configurations have also been tested on vehicles of
various weights and configurations. While full vehicle
performance and productivity tests (1) (2) have also been
conducted, the objective of this paper is to present
specific performance data and general characteristics of
the tractive mechanism only, comparing belts and tires.
The mechanics of the belt drive mechanism
(Fig.2) is similar to the wheel in many respects; but the
distribution of the load is dependent upon vehicle
parameters. Location of the dynamic load resultant, eh
(dynamic balance ratio) (3) depends upon the static
distribution and vehicle weight transfer characteristics.
TRACTION MECHANICS REVIEW
Tractive "inefficiency" is caused by both velocity
losses and pull losses. The loss in travel speed is
commonly referred to as "slip" although it should more
properly be called 'travel reduction". It is the result of the
theoretical travel speed not being entirely converted to
actual speed due to losses within the soil, between the
soil surface and the tractive device (slip?), and within the
tractive device (tire windup or belt slippage). The other
component of tractive "inefficiency" which is less visible
and often overlooked is a loss of pull when motion
resistance reduces the amount of gross thrust that is
converted to useful output (net traction). This is
especially relevant to belts as internal losses within a belt
are greater than those within the tire. On soft soils the
internal losses are generally compensated for by lower
external motion resistance than for tires.
A review of traction mechanics is helpful in
understanding differences in tractive performance. The
basic forces involved in a powered wheel are shown in
Figure 1. The torque input, Q, develops a gross thrust,
GT, acting at the wheel's loaded radius, Lr. Part of the
gross thrust is required to overcome motion resistance,
MR, which is the resistance to the motion of the wheel,
including internal and external forces. The remainder is
equal to the net thrust, NT. Dividing by the dynamic
weight on the wheel, Wd, results in dimensionless
relationships.
2
Fig.3 Tractor Dynamic Weight Distribution
TRACTIVE EFFICIENCY
Fig.1 Deformable Wheel on Soft Surface
The following is a generalized plot of the traction
relationships using radial ply tires and the Brixius (5)
traction equations. While traction data has been
traditionally plotted with "slip" as the independent
variable, it's becoming more evident that pull, that is, net
traction is the independent variable. For a properly
ballasted and inflated farm tire, tractive efficiency tends
to maximize at a net traction ratio of approximately 0.40.
This was also recognized by Dwyer (6). Motion
resistance tends to be a linear function of either slip or
NTR unless (slip) sinkage becomes a factor.
Fig.2 Belt Drive
In general, the best tractive performance and the
most uniform ground pressure on a belted tractor can be
obtained with a dynamic balance ratio of near 50 % (3).
The ratio obtained depends not only upon tractor
dimensional parameters and the location and angle of
the line of draft but also upon the drawbar pull level. The
following chart shows the effect of draft angle and Net
Traction Ratio upon the dynamic balance for a tractor
with 60% of the static weight at the front. A wheel tractor
is shown for simplicity but the weight transfer mechanics
are the same for belted and wheel tractors. Note that it
only takes a 5 deg draft angle to give a 50% dynamic
balance ratio at a typical Net Traction Ratio of 0.40.
Figure 3 is for hitching to the drawbar. Even higher
weight transfer and hence, higher front weight
requirements may result from use of three point hitch
equipment.
Fig.4 Generalized Traction Relationship
The travel and pull losses making up tractive
"inefficiency" do not have official terminology. The
simplest way to understand them is to look at a "Velocity
Ratio" and "Pull Ratio". From Eq 1,
The Velocity Ratio is shown as a function of Net
Traction Ratio in Fig.5. At zero NTR (zero pull) the actual
velocity, Va, is about equal to the theoretical velocity, Vt,
depending somewhat on the definition of "zero" slip (7)
3
and the Velocity Ratio is near unity. As pull increases,
slip increases and the Velocity Ratio decreases. Velocity
Ratio losses depend upon the characteristic shape of the
pull-slip curve.
Fig.7 Overall Tractive Efficiency with Velocity and Pull
Losses
The overall tractive efficiency cannot be greater than
either the Pull or Velocity Ratio and thus it reaches a
maximum value at NTR of about 0.4 with radial ply tires.
It will be shown later that a similar value exists for belts.
Fig.5 Velocity Ratio Losses
Pull Ratio is shown as a function of NTR in
Figure 6. At zero pull, the ratio of Net Traction Ratio to
Gross Traction Ratio approaches zero (the difference
between GTR and NTR is motion resistance which is in
the range of 0.05 to 0.15). Due to motion resistance, the
Net Traction Ratio can never equal the Gross Traction
Ratio and the Pull Ratio approaches but never reaches
unity.
Pull Ratio, Velocity Ratio, and overall tractive efficiency
are shown for real data in Figure 8. Data is for radial ply
tires in medium (tilled) tractive conditions. The curves are
the result of regression analysis (4) of the field test data.
Both velocity (slip) and pull (motion resistance) losses
contribute to the overall tractive efficiency.
Fig.8 Velocity and Pull Losses with real data
Fig.6 Pull Ratio Losses
TRACTION DATA
Tractive efficiency is defined as output power / input
power. It can also be expressed as the product of Pull
Ratio and Velocity Ratio. Figure 7 shows how Velocity
Ratio and Pull Ratio combine for overall tractive
efficiency.
Typical traction data plots are shown by Figures 9 and
10. Figure 9 shows an example of the traditional plot with
slip as the independent variable.
4
Fig.11 Performance of 20.8R42 Duals on Three Surfaces
Fig.9 Traditional Slip Plot of Traction Data
Figure 12 is an example of operating at overpressure on
the tires. Peak tractive efficiency is reduced as well as
the maximum Net Traction Ratio. While the maximum
tractive efficiency is only reduced about 5 percentage
points, the effect on vehicle performance may be
significantly greater depending how implements are
matched to the tractor. For example, at an NTR of 0.5,
more than 10 percentage points difference results in
about 17 % difference in drawbar power and significantly
higher slip.
Each data point represents the average for 1.5 seconds.
This example shows the merging of 3 replications of the
test run. Also shown as a smooth curve is the results of a
regression of the Net Traction Ratio and Motion
Resistance ratio data. These are examples only and all
subsequent comparisons are made using the regression
coefficients.
Fig.10 Net Traction Ratio data plot
Fig. 12 Performance at Two Air Pressures
TIRE PERFORMANCE COMPARISONS
Performance of two size tires at correct pressure is
shown by Figure 13. The larger diameter 520/85R46 tire
shows significantly higher power efficiency at the same
slip. This means the wider smaller OD tire has greater
motion resistance loss. Both provide similar maximum
pull capability which may give the operator the
impression that there is no performance difference
between the tires.
Figure 11 shows the performance of 20.8R42 Duals on
three tractive surfaces. Note that the peak tractive
efficiency is reduced as the soil becomes softer and
looser but that the peak occurs at a Net Traction Ratio of
approximately 0.4 on all soils. Maximum NTR is also
reduced as the soil becomes less firm.
5
Figures 15 to 17 show the performance of the 3 widths
from one manufacturer in comparison to the dual tires on
three surfaces. Under firm untilled conditions there is not
a lot of performance difference between the four
treatments at normal field pulls (NTR approx 0.4 to 0.5).
Duals tend to drop off more at the higher pulls and the
wider belt provides higher maximum NTR (limited by
slip).
Fig. 13 Performance of Two Sizes at Correct Pressures
Performance of the same tire at different weights, both
with correct pressure is shown by Figure 14. Using the
correct pressure for the weight keeps the tire operating at
it's design deflection ratio where optimum performance is
obtained. Maximum Tractive Efficiency comes at about
the same Net Traction Ratio for each weight. It should be
noted that this means drawbar pull in proportion to the
weight. In other words, if only the weight is changed,
performance may suffer from not operating at the
optimum NTR.
Fig.15 Belt Width Comparison on Firm Untilled soil
As the tractive conditions become softer and looser, the
difference becomes more evident between belts and tires
with the belts maintaining their relative position with each
other.
Fig. 14 Performance at Two Wts with Correct Pressures
BELT-TIRE COMPARISONS
Fig.16 Belt Width Comparison on Tilled soil.
In June of 1996 a series of tests were carried out in
Texas to determine the effect of belt width on tractive
performance. Three belts of 400, 630, and 810 mm width
(16, 25, and 32 in) were available from one
manufacturer (A). A 400 mm (16 in) belt was available
from a second manufacturer (B). At the same time a set
of 20.8R42 dual tires were available for comparison.
Tests were to be conducted on untilled and tilled tractive
conditions. However, in the process of testing, a
subsoiler was used on the load tractor to provide a
portion of the load. This then provided a soft subsoiled
condition upon which further tractive comparisons were
made. Soil was in a good moist condition as rain was
experienced shortly before tests were to begin. All tests
were carried out over a two day period and test
conditions had little time to change.
Differences between the belts and tires becomes
greatest as the soil becomes soft and loose (Figure 16
and 17). Note that the maximum tractive efficiency for
tires still comes at NTR of about 0.4 whereas the belts
tend to maximize at a slightly higher pull and
demonstrate a wide range of pulls at near maximum
efficiency. It should be noted that these tests were all
carried out with a minimum of steering. Matching
implements at higher NTR on the skid steer belted
machine may result in limited steering control under load.
6
Fig.17 Belt Width Comparison on Subsoiled land
Fig.20 Belt Manufacturer Comparison on Subsoiled
Two manufacturers' 16 inch belts were available for test.
Figures 18 to 20 show that there was very little difference
in performance between the two belts on the three
surfaces tested. It should also be noted that under the
firm untilled conditions the dual 20.8R42 tires at 12 psi
equaled or outperformed the 16 inch belts.
Figures 21 and 22 compare the performance of 25 inch
belts and dual 20.8R42 tires on the three surfaces tested.
Fig.21 Performance of 25 inch belt on Three Surfaces
Fig.18 Belt Manufacturer Comparison on Firm Untilled
Fig.22 Performance of 20.8R42 Duals on Three Surfaces
Fig.19 Belt Manufacturer Comparison on Tilled Soil
7
CONCLUSIONS
Both velocity (slip) and pull (motion resistance)
losses are important to the overall tractive efficiency of
both belts and tires. Proper tire sizing and pressures are
important if optimum tire performance is to be obtained.
Wider belts and larger tires provide the greatest tractive
performance improvement under the more adverse
tractive conditions. Larger diameter tires with longer
footprint operating at correct low pressure nearly equal
the performance of belts when tractive conditions are
good.
REFERENCES
1.
2.
3.
4.
5.
6.
7.
Shell, L. R., Field Performance of Rubber Belt and
MFWD Tractors in Texas Soils. SAE 97F-65
Tumer, R, Field Performance of Rubber Belt and
MFWD Tractors in Southern Alberta Soils. SAE 97F66
Corcoran, Paul T and Gove, Daniel S. Understanding
The Mechanics of Track Traction._lnt'l Conference
On Soil Dynamics, 1985
Upadhyaya, S.K., Chancellor, W. J., Wulfsohn D.,
Glancey J. L., Sources of Variability in Traction Data.
Journal of Terramechanics, Vol. 25, No. 4, pp. 249272, 1988
Brixius, W. W., Traction Prediction Equations For
Bias Ply Tires, American Society of Agricultural
Engineers, ASAE 87-1622
Dwyer, M. J., The Tractive Performance of Wheeled
Vehicles, Journal of Terramechanics, Vol 21, No 1
pp. 19-34, 1984.
Brixius, W. W. and Wismer, R. D. The Role of Slip in
Traction, American Society of Agricultural Engineers,
ASAE 78-1538