Journal of JSAM 61(4): 95～102, 1999

Research Paper

Method for Determining the Specification of

Rubber Track with Circular Grousers*

Desrial*1 and Nobutaka ITO*1

Abstract

Rubber tracks have generally straight grousers which are arranged perpendicularly or at an

angle to its direction of travel for better traction and soil removal. The new concept of circu-

lar grousers, together with the application of a pivot turn and the ability to control the con-

tact length proved to be successful in reducing turning motion resistance as well as attaining

better traction. This paper discusses the method for determining the specification of rubber

track with circular grousers, while taking in account tractive performance and track sinkage

on controlled pivot turns. The calculated track dimensions were validated by comparing them

to the track dimensions of commercial combine harvesters. It was revealed that the calculated

track dimensions were closely related to commercial ones.

[Keywords] rubber track, circular grouser, rolling resistance, sinkage, pivot turn with/without the control of contact length of track

Ⅰ Introductian

Recently, rubber tracked vehicles are com-

monly used on agricultural machinery that

perform agricultural operations on soft soil

with low bearing capacity. In agricultural

operations such as rice harvesting in paddy

fields, the maneuverability of the vehicle

plays an important role due to its need for

frequent changes in working directions. To

achieve good maneuverability, the sinkage of

traction device must be as shallow as possible

and its turnability must be high with a small

turning radius and less turning motion resist-

ance.

It is obvious that one effective way to pre-

vent the vehicle from sinking could be by

reducing the weight of the vehicle and by in-

creasing its track shape ratio1). In previous re-

search, Ito2) pointed out that the turnability

of tracked vehicles could be improved by

reducing their turning motion resistance. He

concluded that turning motion resistance

could be reduced by decreasing the contact

area of the track, especially the contact length

of the track. Practically, it can be done by ap-

plying a pivot turn with the control of con-

tact length of track to the braked track3)4)

In general, rubber track has a straight

grouser pattern which is arranged perpendic-

ularly or at an angle to its travel direction for

better traction and soil removal. However,

rubber track with straight grousers has a

comparatively high turning motion resistance

under the pivot turn without the control of

contact length of the track. In order to solve

this turning problem, Ito et al.3) proposed the

new concept of the circular grouser pattern

for rubber track which is suitable for reduc-

* presented at the 100th annual meeting of the Kansai

branch of Japanese Society of Agricultural Machinery

(Tottori University) in September 1998

*1 JSAM Member, Department of Bioproduction and

Machinery, Mie University, Tsu, Mie, 514-8507 Japan

〓059-231-9597

96 Journal of the Japanese society of agricultural machinery Vol. 61, No. 4(1999)

ing turning motion resistance as well as at-

taining better traction.

Considering the importance of the tur-

nability of rubber tracked vehicles, rubber

track with circular grousers will be designed

and its performance will be evaluated. The

objective of this paper is to develop a method

for determining the specification of rubber

track with circular grousers.

Ⅱ Theoretical Approach

The tractive performance and turnability of

tracked vehicles are obviously influenced by

track linkage due to the load acting on them.

Static sinkage of track can be determined

based on M. G. Bekker's6) theory of plate pene-

tration as follows:

(1)

where p is ground pressure, b is plate width,

z is static sinkage, and kc, kφ and η are soil

mechanical properties. Considering the vehi-

cle load, W, ground contact area of track, A,

track width, b, and contact length, l, ground

pressure under the track can be defined as:

(2)

Then, the relationship between vehicle wei-

ght, track dimension, soil properties, and stat-

ic sinkage of track due to vehicle weight can

be described by:

(3)

In this proposed method, first of all, the ex-

pected static sinkage should be given for the

further calculation. Based on the value of ex-

pected static sinkage, the dimension of mini-

mum contact area to support the vehicle

weight can be calculated by determining the

track width and the contact length of track.

In order to determine track width and con-

tact length of track, equation (3) can be rear-

ranged as:

(4)

Then, introduce the track shape ratio, K, as

the ratio of the contact length of track, l, to

the track width, b, which can be written as:

(5)

In general, the value of track shape ratio ran-

ges from 2 to 6 depending upon the terrain

where the vehicle will be operated5).

K=6, for standard bulldozers, excavator and

construction machinery

K=3, for bulldozers used in swampy area

and rice combine harvesters

K=2, for bulldozers used in extremely swam-

py areas.

Substituting l from equation (5), the equation

(3) can be rewritten as:

(6)

The above equation can be expressed as a

quadratic equation as follows:

(7)

By considering only the positive solution of

the above quadratic equation, the value of

track width, b, can be calculated by the fol-

lowing equation:

(8)

If the designed track is used for pivot turns

with the control of the contact length of

DESRIAL, IT0:

Method for Determining the Specification of Rubber Track with Circular Grousers 97

track, then the sinkage of braked track on

turning should be evaluated. On controlled

pivot turns, the contact length can be ad-

justed. In order to minimize turning motion

resistance, the contact length should be equal

to the track width because of less soil

bulldozing resistance to wipe out the soil due

to the soil cutting action by the edges of

braked track. There is no criteria for what

depth of sinkage is permissible on controlled

pivot turns. However, practically, if the

sinkage is too large, the vehicle will not be

level and there will be a lot of soil disturb-

ance while turning. In this proposed method,

the allowable sinkage of the braked track on

controlled pivot turns was assumed ranging

between 5 to 10cm. This assumption was de-

termined basing on the calculated sinkage on

pivot turn by using the specification data of

commercial combine harvesters. The sinkage

of braked track on controlled pivot turns

when can be calculated by the

following equation:

(9)

Regarding tractive performance, it is neces-

sary to evaluate the rolling resistance of the

designed track. Generally, tracked vehicles

running on deep muddy soil have the coeffi-

cient of rolling resistance in the range of 0.1

to 0.157). Hence, the rolling resistance of de-

signed track should meet that condition. The

rolling resistance of tracked vehicles is ex-

pressed by Bekker's6) formula as follows:

(10)

When the track width and the contact

length have been determined, the next step is

to calculate the total length of track and

number of grousers. Referring to Fig. 1, total

track length could be determined by the fol-

lowing formula:

L=Tp(2C+N) (11)

where L is the total length of the track (cm),

Tp is the track pitch (cm), C is the distance

between the centers of the sprocket and idler

expressed in number of pitch, and N is the

number of sprocket teeth.

Fig. 1 The sketch of the proposed rubber track

with circular shape grouser

The final step is the determination of the

number of circular grouser for the designed

track. Since the main purpose of circular

grouser is to minimize the turning motion re-

sistance, the outer diameter of the circular

grouser must be equal to the track width.

The value of L in equation (11) is the mean

length of the track. The outer length of the

track, Lo, can be determined by adding the

excrescent length due to one half of the

thickness of the rubber track in both

half-circular ends, which can be expressed as

follows:

L0=L+(tπ) (12)

98 Journal of the Japanese society of agricultural machinery Vol. 61, No. 4(1999)

where t is the thickness of the rubber track.

The number of circular grousers can be sim-

ply determined by the following formula:

(13)

where Ng is the number of grouser, Do is the

outer diameter of circular grousers (cm), and c

is spacing between the track grousers (cm).

However, occasionally it is not enough to de-

termine the number of grousers based on the

above equation only. In addition, manufactur-

ing requirements also have to be considered.

Practically, the center of the circular grousers

should be made by fitting them to one of the

track teeth center. For example, for small

tracked vehicles where the track pitch is rela-

tively narrower than the track width, one cir-

cular grouser will occupy 3 track pitches as

shown in Fig. 1. In this case, the total length

of track should be adjusted to cover the total

length of a certain number of circular

grousers.

Ⅲ Method

In this study, a computer program to deter-

mine the specification of rubber track with

circular grousers was developed. The program

inputs are total vehicle weight, soil mechani-

cal properties, estimated static sinkage and es-

timated track shape ratio. Program outputs

are the specification of circular grousers of

rubber track i.e. the track width, the contact

length of track which is equal to the distance

between the center of the sprocket and idler,

the total length of track and the number of

circular grousers. The algorithm flow chart of

the program is given in Fig. 2.

In this method, firstly, estimated static

sinkage and track shape ratio should be in-

putted into the program. Then based on the

data of vehicle and soil mechanical properties,

the minimum track width and contact length

Fig. 2 The flowchart for determining the specifica-

tion of rubber track with circular grousers

can be obtained. Secondly, the sinkage of the

braked track on pivot turns with the control

of the contact length of track can be

evaluated by assuming that in a pivot turn

one half of the vehicle weight (W/2=4.9kN)

is supported by the circular grouser only. If

the sinkage of braked track on pivot turns

with the control of the contact length of

track is larger than 10cm, the track width

should be reconsidered to meet the conditions

by enlarging the track width. Thirdly, the

rolling resistance of track tentatively derived

through calculations will be evaluated. If the

track rolling resistance is higher than 0.15

times the total vehicle weight, the increase of

the track shape ratio must be considered. Fi-

DESRIAL, ITO:

Method for Determining the Specification of Rubber Track with Circular Grousers 99

nally, the total length of track and number of

grousers can be determined.

In the numerical experiments, the total

weight of vehicle, W and the values of track

shape ratio, K were assumed to be 9.8kN and

3 respectively. Based on the calculated static

sinkage by using the specification data of

commercial combine harvesters, the estimated

static sinkage was varied from 0.5 to 2.5cm.

Three types of soil were selected in which

their constants are shown in Table 18).

Table 1 Soil constants used in the numerical experi-

ment by using the proposed methad8)

For the calculation of the total length of

track, the number of sprocket teeth, the track

pitch, and the thickness of rubber track were

assumed to be 11, 10cm, and 2cm, respective-

ly. In the computation of track pitch the cal-

culated results were rounded up to the

nearest integer number. This rounding up

will increase the total length of track, howev-

er this excess can be simply dissolved by ad-

justing the position of the track idler. Unlike

the computation for the total length of track,

the calculated results of the number of

grousers were rounded down to the nearest

integer number. This rounding down will

cause some blank spaces, which should be di-

vided equally to increase the spacing between

grousers.

Ⅳ Results and Discussion

The main objective of this study was to

find the optimally suitable specifications for

rubber track as it has been described earlier

in the introduction. In order to find the op-

timally suitable specifications of track, three

types of soil (sand, sandy loam and clay) were

selected for numerical experiments. Calcula-

tions were done by using the proposed meth-

od with different estimated static sinkage of

track, z, and the results are presented in

Tables 2, 3, and 4. In order to get better trac-

tive performance and turnability, the es-

timated static sinkage of track should be as

shallow as possible. It was considered that 1

cm of estimated static sinkage of track will be

comparatively better than the other estima-

tions. Tables 2, 3 and 4, show that as static

sinkage increases, the sinkage of braked track

on controlled pivot turns and rolling resist-

ance also increases. So, it could be said that

the static sinkage value directly influences

the sinkage of braked track on controlled piv-

ot turns and the rolling resistance of track.

Table 2 Specifications of rubber track with circu-

lar grousers for sand

Table 3 Specifications of rubber track with circu-

lar grousers for sandy loam

Table 4 Specifications of rubber track with circu-

lar grousers for clay

100 Journal of the Japanese society of agricultural machinery Vol. 61, No. 4(1999)

According to calculated results in Tables 2,

3 and 4, for 1cm of estimated static sinkage,

the minimum required track width to support

9.8kN the weight of a vehicle were 13.6cm,

24.5cm, and 29.5cm in sand, sandy loam and

clay soil respectively. As a final decision, the

terrain where the designed track will be ap-

plied should be considered. In these numeri-

cal experiments, for example, the designed

rubber track will be used for combine har-

vesters, which is mostly used in clayey soil.

Therefore, it can be decided that the best

suitable specifications of rubber track for that

purpose were rubber track having 29.5cm of

track width and 88.6cm of contact length re-

spectively.

In order to validate the proposed method,

Fig. 3 The comparison between the dimensions

of rubber tracks of Ya combine harvesters

and the calculated track dimensions by

the proposed method

Fig. 4 The comparison between the dimensions

of rubber tracks of Mi combine harvesters

and the calculated track dimensions by

the proposed method

the specification of rubber track of 103 models

of commercial combine harvesters which are

made by four agricultural machinery com-

panies in Japan named Ku, Mi, Ya and Is

Fig. 5 The comparison between the dimensions

of rubber tracks of Ku combine harvesters

and the calculated track dimensions by

the proposed method

Fig. 6 The comparison between the dimensions

of rubber tracks of Is combine harvesters

and the calculated track dimensions by

the proposed method

Fig. 7 The comparison between the calculated

track dimensions by the proposed method

and the dimensions of all collected data

of commercial combine harvesters

DESRIAL, ITO:

Method for Determining the Specification of Rubber Track with Circular Grousers 101

were collected. The collected data were com-

pared with the calculated dimensions of rub-

ber track by using the proposed method. The

comparison of calculated dimensions and the

dimensions of commercial tracks from each

brand are given in Fig. 3, 4, 5 and 6, while the

compilation of those graphs is given in Fig. 7.

These figures revealed that the calculated di-

mensions and the data fluctuate a little bit

but they are similar. For combine harvesters

with a total weight less than 20kN, the calcu-

lated track dimensions are less than commer-

cial ones and the reverse is true for those

which have a total weight greater than 20kN.

This can be explained as follows. In the cal-

culation using the proposed method, the

width and contact length of track are ob-

tained in minimum values to support the ve-

hicle weight to a certain depth of static

sinkage. However, in the selection of rubber

track for a commercial combine harvester,

other factors and adjustments are also taken

into account. For example, regarding econom-

ical considerations, the same sued rubber

tracks are usually used for combine har-

vesters in the same class within a certain

range of total weight.

Ⅴ Canclusian

From this study it can be concluded that

the specification of rubber track with circular

grousers can be determined satisfactorily by

considering two main factors: soil mechanical

properties and specifications of the vehicle.

As a result of numerical experiments for the

estimated static sinkage ranging between 0.5

to 2.5cm, the optimum calculated specifica-

tions of rubber track for vehicles having a to-

tal weight of 9.8kN were found to be: 29.5cm

of track width, 88.6cm of contact length, 29

pitch or 290cm of total length of track and 9

grousers, for example.

The obtained results were validated by

comparing them to the track dimensions of

commercial combine harvesters. The compari-

son showed that the calculated dimensions

were nearly concurrent with the commercial

ones.

References

1) Ito, N: Practical method of reducing turning motion re-

sistance of tracked vehicle, J. Terramechanics, 24(4),

251-261, 1987

2) Ito, N, Wang, X.: Effect of the distance between tracks

and pivoting location on turnability of the tracked ve-

hicle, J. Jpn. Soc. Agric. Mach., 50(5), 25-30, 1988

3) Ito, N, Kito, K., Takashima, T., Murase, H., Yamada, Y.: Design concept of the grouser pattern for reducing

turning motion resistance, J. Terramechanics, 30(1), 47-57, 1993

4) Ito, N: Evaluation of turnability of tracked vehicle, Ja-

pan Agricultural Research Quarterly 30(4), 259-253, 1996

5) Ito, N: Effect of track shape ratio on track sinkage for tracked vehicle, Proceedings of the 12th Int. Conf. of

the Int. Sac. For Terrain-Vehicle Systems, Beijing, 359-

366, 1996

6) Bekker M. G.: Theory of Land Locomotion, Univ. Michi-

gan Press, Ann Arbour, 1956 7) Japan Society of Agricultural Machinery: Hand Book

of Agricultural Machinery, Corona Co., 136-137, 1969

8) Sugiyama, N: Some Problems on Construction

Machines and Soil, Kashima Co., 1982

(Received: 21, Sept. 1998・Question time limit: 30. Sep. 1999)

「研究論文」

円形状 グローサを有する履帯の緒言決定法*

デス リアル*1,伊 藤信孝*1

要 旨

履帯 グローサは進行方向に直角に配置 したも

の、またはグローサ間への土の付着防止 とより良

好なけん引を目的 としてい くらか角度をつけたも

のが一般的である。接地長制御によるピボット旋

回ではより良いけん引に加えて旋回抵抗モーメン

トを著 しく低減できる円形状グローサが有効であ

ることが提案されている。

本研究はピボット旋回を前提 とした円形状グロ

ーサを有するゴム履帯の諸元を、けん引性能、履

帯の沈下を考慮 して検討 したものである。本報で

提案の方法による履帯諸元の計算結果 と市販のコ

ンバインのそれ を比較 した結果、その妥当性を検

証す ることができた。

[キーワード]ゴム履帯,円形グローサ,ころがり抵抗,沈下,

102 Journal of the Japanese society of agricultural machinery Vol. 61, No. 4(1999)

履帯接地長制御を有する(あ るいは有しない)ピ

ボット旋回* 1998年9月 第100回 農業機械学会関西支部例会(鳥 取大 学)

にて講演

*1 会員,三 重大学生物資源学部