Full-paper template – The International Symposium on Agricultural and Biosystem Engineering (ISABE) 2013
Title: A method of workload application for tractor transmission
Su Chul Kim1 Yong Joo Kim2 Seung Jae Park3
1
R&D Center, LSMtron
E-mail: sckim@lsmtron.com
2
R&D Center, LSMtron, Korea
3
Division of Bioresource System Engineering, Chonbuk National University, Korea
Abstract
Workload has been evaluated to use load spectrum for an agricultural tractor. The
studies of the working load are concentrated on how to analyze the load spectrum, but only a
few studies are about how to apply the load spectrum to transmission design for life
expectancy calculation. Moreover, it is hard to figure out the level of the working load
intuitively through only the load spectrum and its severity. In this paper, we present several
methods for applying and rating the load spectrum to calculate the transmission life. The
methods are based on field survey, S-N curve of materials, and Palmgren-Minor rule. The
international standard for gear rating, ISO 6336, is used for simplification and its KA Factor
to evaluate the working load.
Keywords: Working load, Tractor, Transmission life, KA Factor
Introduction
Agricultural tractors are a working vehicle under high work load and used for various
farm works. In high load conditions, it is important to secure high reliability of the machinery
as it is directly connected to safety of workers. Tractor transmission that composes a tractor
body is the biggest component thus it is the most closely related to the reliability. For the
reason above, engineers who design tractor transmission ought to secure sufficient reliability.
In addition to, they also need to optimize the transmission design because the transmission is
forming a great part of tractor prices. Workload conditions are a very important factor for the
transmission design optimization between the reliability and the transmission prices.
The basic load conditions are the wheel slip torque and the engine rated torque for the
transmission design. It can be used for the transmission design but it is easy to be
overdesigned because the workloads are generally lower than the rated torque and the slip
loads. To optimize the design, the engineer needs to analyze workload levels of the
transmission.
Load spectrum analysis is the method which has been used to show the characteristic
of the workloads. Applying the load spectrum to transmission design, it is possible to reflect
the workload. However, it is hard to apply to the transmission design that has to consider all
load cases according to speeds because the calculating procedure is significantly complicated
by the factors such as speed, works, and theirs load spectra.
Kim et al. [1, 2] analyzed and evaluated the transmission load of agricultural tractors
in Korea. They showed the load measurement system, the load spectrum according to farm
works, and theirs severity. The severity can show the level of the workloads, but it cannot
apply directly to the transmission design because it is expressed as scale of the cycle instead
of the load. In order to apply a more intuitive the workload for the transmission design, the
Full-paper template – The International Symposium on Agricultural and Biosystem Engineering (ISABE) 2013
application factor in the standards of gear durability calculation such as KA in ISO 6336-6 [3]
can be used. It adjusts the nominal load in order to compensate for incremental gear loads
from external sources, the workload can be evaluated.
In this paper, the method of application of workloads to transmission design is
proposed and the workloads are evaluated by using the application factor.
Materials and methods
Load measurement
The loads can be varied depending on the measurement location, input or output
shafts because there are some factors to affect on the measured loads such as transmission
efficiency and damping between the input and output shafts. To reduce the load measurement
errors, input and output loads should be measured. The input loads can be measured from the
engine shaft and the output loads can be measured from the axle shaft.
Load spectrum
Workload that is measured by using torque sensors such as strain gages is expressed
as Fig. 1. These data will be cycle-counted using some methods like the level crossing
counting or peak counting or rain-flow counting to be used in fatigue analysis [4]. After
cycle-counting, it is necessary to transfer the counted loads to the representative load for
considering the effect of mean torque. The Smith-Watson-Topper (SWT) method [5] is a
reasonable choice to consider the mean torque. To obtain the load spectrum such as Fig. 2,
the calculated loads is divided into bins or classes. Each bin contains the number of load
occurrences recorded in its load range.
60
Torque, kgf.m
Torque, kgf.m
50
40
30
20
10
0
0
20
40
60
80
Time, sec
Figure 1. Mesured workload data
45
40
35
30
25
20
15
10
5
0
1
10
100
1000
10000
Cycle
Figure 2. Load spectrum
The load cycles in S-N curve
A fatigue life is based on the S-N curves, applicable to fatigue failure property of
material. Tractor transmission life can be calculated by using the curves and the load spectra.
To apply the load spectra to the transmission life calculation, the cycle of load spectrum
should be converted the load cycle to S-N curve. There are two types of the converting
process by the workload shape acting at some components. One of them is when the
Full-paper template – The International Symposium on Agricultural and Biosystem Engineering (ISABE) 2013
components are continuously under loads such as bearing and shaft regardless of its rotating
speed. The other type is the specific case of which the load cycles are affected by rotating
speed such as gears.
For the former case, each cycle of the load spectrum can be converted as follows:
ni = 3600nLiωiT
where,
ni : The number of load cycles for bin i (in S-N curve, see Figure 3), cycle;
nLi : The number of load cycle in a bin of load spectrum, cycle/s;
ωi : A ratio of a load cycle for total cycle in load spectrum;
T : Required life that has been taken from a field survey, h;
For the latter case, the load cycle is not related to the measured time in contrast with
above case because the load cycle of gears in fatigue life is regarded a one-cycle per
revolution. Thus, the total required cycle can be taken into account by multiplying required
time by the rotating speed when it measures the workloads. In this case, the load cycles in SN curve is determined in accordance with following equation.
ni = 60RPMLiωiT
where,
RPMLi : The rotating speed of the gear when it measures the workloads,
revolution per minute;
ωi : A ratio of the load cycle for total cycle in load spectrum;
Stress spectra in S-N curve
The loads spectra are generally expressed as torque spectra, but it is necessary to
convert the torque spectra to stress spectra because the loads in S-N curve for calculating the
fatigue life are expressed in stress. An example of torque and stress spectrum is given in
Figure 3.
The stress spectra are formed on the basis of the torque spectra [4]. The method for
calculating the stress is obtained by the fatigue life calculating method of each component
such as ISO and DIN standards. These methods have some factors to reflect the other effects
influencing the life. This would enable the life calculation to predict more accurately. The
design engineer should determine which method is applied for the stress calculation.
Palmgren-Miner rule
The Palmgren-Miner rule [6] is a widely used and well-known linear damage
accumulation method. This rule operates on the hypothesis that the portion of useful fatigue
life used by a number of repeated stress cycles at particular stress is equal to the ratio of the
total numbers of cycles during the fatigue life at particular stress level according to the S-N
curve established for the material [3, 6].
According to the rule, the fatigue failure could be expected when;
∑
𝑖
𝑛𝑖
=1
𝑁𝑖
Full-paper template – The International Symposium on Agricultural and Biosystem Engineering (ISABE) 2013
where,
Ni : The number of load cycles to failure for bin i
(taken from the appropriate S-N curve, see figure 3)
Figure 3. Torque and associated stress spectrum with S-N curve
Application factor KA
The gear design standards for calculating the fatigue life such as ISO 6336 and
AGMA usually have included the application factor to adjust the nominal load in order to
compensate for incremental gear loads from external sources. It can reflect the workload
instead of the load spectrum. The empirical guidance values have given in ISO 6336-6 but it
is necessary to calculate the application factor to reflect the workload using the load spectrum.
The calculation method given by ISO 6336-6 is defined as follows [3]:
𝐾𝐴 =
𝑇𝑒𝑞
𝑇𝑛
where,
KA : The application factor;
Tn : The nominal torque;
Teq : The equivalent torque.
The equivalent torque is defined as follows [3]:
𝑝
𝑇𝑒𝑞
𝑛1 𝑇1𝑝 + 𝑛2 𝑇2𝑝 + ⋯
=(
)
𝑛1 + 𝑛2 + ⋯
Full-paper template – The International Symposium on Agricultural and Biosystem Engineering (ISABE) 2013
where,
Ti is the torque for bin i;
p : The slope of the Woehler-damage line.
The slope exponent, p, is determined by S-N curves of gears. The S-N curves depend
on material, heat treatment and fatigue failure case (pitting or tooth root). The values are
shown in Table 1 [3]:
Table 1. The slope in S-N curves plotted in a log-log scale, p.
Heat treatment
Case carburized
Pitting
6.610
Tooth root
8.738
Through hardened
Nitrided
Nitro-caburized
6.610
5.709
15.715
6.225
17.035
84.003
Results and discussion
Transmission life calculation
Using above methods, the method for calculating the fatigue life is shown in Fig. 4. ni
that is factor in Miner’s rule is calculated from ni in load spectrum and required life from
field survey. Ni is calculated from Ti in load spectrum and S-N curve. U is the total damage
values compared to the required life.
Figure 4. The calculation process of fatigue life
Through this process, the fatigue life about one load condition can be calculated, but it
should be applied differently in transmission because the transmission generally has variety
load condition according to speeds and variable operations. It means the transmission has to
consider many different cases of load spectrum. To take account of the fatigue life about a
specific speed in transmission, the rate used of the operations has to be applied to the number
of load cycles for bin. The number of load cycles is defined as follows:
nit = ψi x ni
where,
nit : The number of load cycles for a operation in the specific speed;
ψi : The rate used of speeds according to the field survey;
Full-paper template – The International Symposium on Agricultural and Biosystem Engineering (ISABE) 2013
The damage of fatigue failure for a specific speed is defined as follows:
𝑈𝑡 = (∑
𝑖
𝑛𝑗𝑡
𝑛𝑖𝑡
𝑛𝑘𝑡
) +(∑
) + ⋯ (∑
)
𝑁𝑖
𝑁𝑗
𝑁𝑘
1
𝑗
2
𝑘
𝑛
where,
Ut : The sum of the workloads damage parts at a specific speed;
n: The number of the considered operations at specific speed;
i, j, k : The number of bins;
Total transmission damage is the sum of Ut that is the damage of a specific speed. The
load spectrum can be applied to the transmission design using above equation. The best case
of the transmission design is to apply the whole case of load spectrum for tractor operations,
but it is costly and time consuming. If the whole case of load spectrum is not available, the
nominal load can replace the spectrum according to follows:
∑
𝑖
𝑛𝑖𝑡 𝑛𝑖𝑛
=
𝑁𝑖 𝑁𝑖𝑛
where,
nin : The number of load cycles for nominal load;
Nin : The number of load cycles to failure for nominal load;
This method is more useful to the design engineer because it is irrational to apply the
whole data, considering costs and time. The simplified method that is applied the workloads
compared to the method of using load spectrum is to use the modified nominal loads by the
application factor, KA. This calculation method is less precise than the load spectrum, but
useful for a beginning design stage.
Example of evaluation of the workloads
The application factor that is calculated by load spectra shows the level of the
workloads compared with the nominal loads. Table 2 shows the application factors calculated
using the measured load in wheel at tractor operations, Figure 5. The nominal torque was
used the severe load between rated torque and slip torque. In this result, the plowing
operation is the most severe, the baler and rotovating operation showed values, less than 50%
compared to the nominal torque. It means that the external load is half level as compared with
the nominal load in same cycles. The size of the axle load and engine load are different as
shown in Table 2, the gear designer applies to the application factor greater than any of these
values.
Full-paper template – The International Symposium on Agricultural and Biosystem Engineering (ISABE) 2013
Torque(kgf.m)
100
P_L3
P_L4
R_L1P1
R_L1P2
R_L2P1
R_L2P2
B_L4P1
B_M1P1
B_M1P2
10
1
1
10
100
0.1
1000
10000
Cycle
Figure 5. Load spectrum of tractor operations in Korea (P:Plowing, R:Rotovating, B:Baler)
Table 2. The calculated application factor in farm work
Speeds
Baler
Axle loads
Max
Pitting
Tooth root
Pitting
Tooth root
L3
0.899
1.028
0.805
0.949
1.028
L4
0.916
1.047
0.749
0.879
1.047
L1P1
0.198
0.224
0.133
0.150
0.224
L1P2
0.183
0.209
0.122
0.136
0.209
L2P1
0.204
0.235
0.120
0.132
0.235
L2P2
0.173
0.191
0.125
0.139
0.191
L4P1
0.382
0.443
0.317
0.366
0.443
M1P1
0.201
0.236
0.183
0.217
0.236
M1P2
0.434
0.491
0.391
0.445
0.491
Plowing
Rotary
Engine loads
Conclusion
In this study, we discussed the application method for calculating the fatigue life in
tractor transmission to apply the workloads and the evaluation of the workloads by the
application factor. The life calculation procedure is suggested using load spectrum, stress
spectrum and Palmgren-Miner rule. The field survey such as a rate used of speeds also has to
consider in transmission life. The workloads of the tractor can be evaluated by severeness and
it is also possible to be measured through the application factor. The application factor can
assess the magnitude of the workload in various operations easily because it is calculated
based on the load. Furthermore, the application factor is able to be utilized to calculate the
life considering the workload without applying the load spectrum. Of course, the load
spectrum is more precise to calculate the gear life, thus the evaluation method is useful for
Full-paper template – The International Symposium on Agricultural and Biosystem Engineering (ISABE) 2013
the first estimation during the beginning design stage when the geometry data of a gear drive
is not fixed.
References
1. Kim, J. H. (2000). Analysis of transmission load of agricultural tractors. Journal of
Terramechanics, Vol. 37, pp. 113-125.
2. Kim, Y. J. (2011). Evaluation of tractor PTO severeness during rotary tillage operation.
Journal of Biosystems Engineering Vol. 36(3), pp. 163-170. (In Korean)
3. ISO 6336-6. (2006). Calculation of load capacity of spur and helical gears – Part 6:
Calculation of service life under variable load.
4. ASTM Standards:E1049 – 85. Standard practices for cycle counting in fatigue analysis.
5. Dowling, N. E. (2004). Mean stress effects in stress-life and strain-life Fatigue. 2nd SAE
Brasil International Conference on fatigue, São Paulo, 22-23th June.
6. Miner, M. A. (1945). Cumulative damage in fatigue. Journal of Applied mechanics, Vol.
12, A159-164.