Computer aided analysis of the effects of design parameters on the performance of tracked vehicles

Journal ofTerramechanics, Vol. 23, No. 2, pp. 95-124, 1986.

Printed in Great Britain.

0022--4898/8653.00+0.00 Pergamon Journals Ltd. © 1986IS'I'VS

COMPUTER AIDED ANALYSIS OF THE EFFECTS OF DESIGN PARAMETERS ON THE PERFORMANCE OF TRACKED VEHICLES J. Y. WONG*

Summary--Th.is paper describes the application of a computer simulation model, known as NTVPM-85, to the evaluation of the effectsof design parameters on the performanceof tracked vehiclesover varioustypesof terrain. It demonstratesthat the computersimulationmodelis a useful tool for the vehicle designer and the user in the evaluation of competing designs and in the examination of the effectson performanceof design modificationsand terrain conditions. INTRODUCTION THE DEVELOPMENTand design of tracked vehicles have been, for a long period of time, guided

by empiricism and the "cut and try" methodology. In this technologically advanced era, this approach is, however, being seriously challenged, as it has become extremely inefficient and prohibitively expensive. Coupled with a growing demand for improved mobility over a wide range of terrains, it has created a need for a comprehensive and yet realistic mathematical model to guide the development and design of tracked vehicles. To be useful to the development and design process, a mathematical model for tracked vehicle performance should take into account all major vehicle design parameters and terrain characteristics. The performance of a tracked vehicle is primarily dependent upon the normal and shear stress distributions on the track-terrain interface. It appears, therefore, that a basic issue in the mathematical modelling of tracked vehicle performance is the development of the proper relationship between the interacting forces on the track-terrain interface and vehicle design parameters and terrain characteristics [1, 2]. To develop a realistic mathematical model, the mechanical behaviour of the terrain, which forms an integral part of the input, should be measured under loading conditions similar to those exerted by a tracked vehicle. Among the various terrain measuring techniques currently available, the bevameter technique pioneered by Dr. M. G. Bekker [3] appears to provide a close approximation of the loading conditions of a tracked vehicle. In the development of the computer simulation model presented in this paper, the bevameter technique was, therefore, selected to measure the. behaviour of the terrain. To reduce the uncertainty in extrapolating terrain data obtained using the bevameter to the prediction of full-size vehicles, the size of the test pieces used in the pressure-sinkage tests was comparable to that of the contact area of a track link. Also, the size of the shear ring used in the shear tests was made as large as practicable. Since an element of the terrain under a moving track is subject to the repetitive loading of consecutive roadwheels, to provide data for predicting the multipass performance of the vehicle running gear, the measurement of the response of the *Departmentof Mechanicaland AeronauticalEngineering,Carleton University,Ottawa, Ontario, Canada, and VehicleSystemsDevelopmentCorporation, Nepean, Ontario, Canada. 95

96

J.Y. WONG

terrain to repetitive loading was included [1]. Furthermore, additional sinkage may be induced by the slip of the track, and the slip-sinkage relationship was, therefore, also monitored during shear tests. These characteristics of the terrain were used as inputs to the detailed analysis of the mechanics of track-terrain interaction, upon which a mathematical model for tracked vehicle performance was developed [1, 2]. The mathematical model takes into account all major design parameters of the vehicle, including track system configuration, number of roadwheels, dimensions of roadwheels, roadwheel spacing, track dimensions, initial track tension, suspension heave stiffness, location of the centre of gravity, and sprocket, idler, and supporting roller arrangements. The model can be used to predict the normal and shear stress distributions on the track-terrain interface, and the external motion resistance, tractive effort and drawbar pull of the vehicle as functions of slip. It is particularly suited for predicting the performance of tracked vehicles with relatively short track pitch designed for high speed operation. The basic features of the model have been validated by means of full-scale tests made with an instrumented vehicle on three types of terrain, namely, sandy terrain, muskeg and snow

[1, 2]. In this paper, the application of the model to the evaluation of the effects of vehicle design parameters on the tractive performance over various types of terrain is described. The results demonstrate that the model is an extremely useful tool for the evaluation of competing designs and in the examination of the effects on performance of design modifications and operational environments. BASIC FEATURES OF THE COMPUTER SIMULATION MODEL When a tracked vehicle travels over deformable terrain, the load applied through the track system causes the terrain to deform. The track segments between roadwheels take up load and as a result they deflect and have a form of a curve. The shape of the deflected track is primarily govemed by terrain characteristics, track tension, and roadwheel spacing. Furthermore, an element of the terrain under the moving track is subject to the repetitive loading of consecutive roadwheels. To predict the normal pressure distribution on the track-terrain interface, the pressure-sinkage relationship and the response to repetitive loading of the terrain, measured using the bevameter technique, are required as input. When the terrain characteristics are known, the prediction of the normal pressure distribution is reduced to the determination of the shape of the deflected track in contact with the terrain. This is achieved through a detailed analysis of the mechanics of track-terrain interaction. In the analysis, it is assumed that the track is equivalent to a flexible belt. This assumption is considered quite reasonable for a track with relatively short track pitch and for a rubber-belt type of track. A system of equations for the equilibrium of forces and moments acting on the track system (as shown in Fig. 1)and for the conservation of overall track length are derived. They establish the relationship between the shape of the deflected track in contact with the terrain and vehicle design parameters and terrain characteristics. The solution to this set of equations defines the sinkage of the roadwheels and the shape of the track segments between roadwheels. From these, together with the known pressure-sinkage relationship and the response to repetitive loading, the normal pressure distribution under a moving tracked vehicle can be predicted. To predict the shear stress distribution under the track, the shear stress-displacement relationship of the terrain and its response to repetitive shearing are used as input to the analysis of the characteristics of track-terrain shearing. The shear displacement developed under a flexible track as a function of slip can be determined through a kinematic analysis of

C O M P U T E R A I D E D ANALYSIS O F T R A C K E D V E H I C L E P E R F O R M A N C E

97

0 FIG. I.

Forces acting on a tracked vehicle.

the track based on the concept of slip velocity [3, 4]. From these, the shear stress distribution under a moving track can be predicted. When the normal pressure and shear stress distributions have been determined, the external motion resistance, tractive effort and drawbar pull as functions of slip can then be predicted. The external motion resistance is calculated by integrating the horizontal component of the normal pressure over the contact area, while the tractive effort is determined by integrating the horizontal component of the shear stress over the entire track-terrain interface. The drawbar pull is obtained by subtracting the external motion resistance from the tractive effort. The details of the analysis are described in references [1] and [2]. It should be mentioned that in the latest version of the mathematical model, the track longitudinal elasticity, which determines the elongation of the track under tension, and the belly drag, which occurs when track sinkage is greater than vehicle ground clearance, have been taken into account [2]. Furthermore, improvements in the analysis of track-terrain interaction have also been incorporated. The procedures that implement the mathematical model are currently programmed on an advanced microcomputer. The computer simulation model is of an interactive type and

LETE Sand @

.

em

IB'

Dra~ar

S1 i p = l .BX

{a3

0 (3.. 188 ,e v

280 QJ $_

388 {4

at

488 588

FIG. 2.

~

Measured

Predicted

Measured and predicted normal pressure distrbutions under the track pad of an M I 13A I on LETE sand.

98

J.Y. WONG

highly "user friendly". The latest version o f the m o d e l that incorporates the newest d e v e l o p m e n t s is referred to as N T V P M - 8 5 . The basic features o f the c o m p u t e r simulation m o d e l N T V P M - 8 5 have been validated with full-scale tests o f an instrumented vehicle over three types o f terrain, namely, sandy terrain, m u s k e g , and snow. Figures 2, 3 and 4 s h o w a c o m p a r i s o n between the predicted and

Petawawa

Muske B R

Dr awbar

E

C~

40

51 i p=2.2~.

0 O_

50 L

188

150 -

FIG. 3.

-

Measured

Predicted

Measured and predicted normal pressure distributions under the track pad of an M 113A I on Petawawa Muskeg A.

Pet awawa

Snow

R Draubar

E

I

)

g

-~

2s I Sl i p = 2 . 4 ~ ,

n

L

to to t._ O_

100

280

300 400

FIG. 4.

~

Measured

Predlcted

Measured and predicted normal pressure distributions under the track pad of an M I t3A I on Petawawa Snow A.

measured normal pressure distributions under the track pad of an M I I 3 A 1 armoured personnel carrier over a sandy terrain, m u s k e g , and snow, respectively. Figures 5, 6 and 7

COMPUTER AIDED ANALYSIS OF TRACKED VEHICLE PERFORMANCE

99

show a comparison between the predicted and measured drawbar pull as a function of track slip over various types o f terrain [1].

Terrain:

LETE

Sand

58 Z

40 30

O_

e~ B ¢o

28

Measured Predicted

18 0

FIG. 5.

+

(NTVPM-B5)

-~÷

28

0

40 S l i p (%)

80

68

Measured and predicted drawbarpefformanceofan M I I 3 A I o n LETEsand.

Terrain: Petawawa Muskeg B B0

___t._----

Z

60 D

(2.

40 ,+4.

& 20

Predicted

0

20

48

60

Slip FIG. 6.

(NTVPM-85)

,÷ +

80

180

(%)

Measured and predicted drawbar performance of an M II3AI on Petawawa Muskeg B.

Terrain:

Petawawa

Snow R

30 z

25

++

28 D

n

15 +

Measured Pred

i ct.ed

(NTVPM-85)

s 0

PO

40 SIip

FIG. 7.

60

80

(%)

Measured and predicted drawbar performance of an M 113AI on Petawawa Snow A.

100

J.Y. WONG

It should be p o i n t e d out that N T V P M - 8 5 gives a m u c h more realistic prediction of tractive p e r f o r m a n c e t h a n the c o n v e n t i o n a l m e t h o d in which the track is a s s u m e d to be equivalent to a rigid footing with a u n i f o r m contact pressure. In general, the c o n v e n t i o n a l m e t h o d overestimates the p e r f o r m a n c e of a tracked vehicle [5].

APPLICATION OF THE COMPUTER SIMULATION MODEL TO EVALUATION OF THE EFFECTS OF DESIGN PARAMETERS ON PERFORMANCE OVER VARIOUS TERRAINS The a p p l i c a t i o n of the c o m p u t e r s i m u l a t i o n model N T V P M - 8 5 to p a r a m e t r i c analysis of tracked vehicle p e r f o r m a n c e is d e m o n s t r a t e d t h r o u g h an example. The baseline vehicle used in the analysis has p a r a m e t e r s similar to those of a widely used a r m o u r e d personnel carrier. The m a j o r design p a r a m e t e r s of the baseline vehicle with five roadwheels (on each of the two tracks) are given in Table 1. T o examine the effects of track system c o n f i g u r a t i o n on p e r f o r m a n c e , two derivatives of the baseline vehicle, one with six roadwheels a n d the other with eight o v e r l a p p i n g roadwheels (on each of the two tracks), are selected. Their design p a r a m e t e r s are also given in T a b l e 1.

TABLE I.

BASIC PARAMETERS OF THE TRACKED VEHICLES USED IN THE STUDY

Vehicle parameters Weight, kN C.G.X--co-ordinate*, cm C.G.Y-co-ordinate, cm Number of roadwheels (per track) Roadwheel radius, cm Roadwheel spacing, cm Sprocket pitch radius, cm Sprocket center X-co-ordinate, cm Sprocket center Y-co-ordinate,cm Idler radius, cm Idler center X-co-ordinate, cm Idler center Y-co-ordinate, cm Drawbar X-co-ordinate, cm Drawbar Y-co-ordinate, cm Suspension stiffness (per track), kN/cm Track weight per unit length, kN/m Track width, cm Track pitch, cm Height of grouser, cm Track elasticity, kN Number of track supporting rollers

Baseline vehicle

Vehicle Vehicle with with six eight overlapping roadwheels roadwheels

104.62 136 99 5 30.5 66.8 24.3 -65 55.3 21.4 338 41.4 362.5 68 4.8 0.56 38 15 4.7 3000 0

104.62 141.9 99 6 25 55.8 24.3 -59, 1 55.3 21.4 343,9 41.4 368.4 68 4.8 0.56 38 15 4.7 3000 3

104.62 142.5 99 8 25 40 24.3 -58.5 55.3 21.4 345.5 41.4 369 68 4.8 0.56 38 15 4.7 3000 3

*Co-ordinate origin is at the bottom of the front roadwheel.

To evaluate the effects of terrain c o n d i t i o n s on vehicle p e r f o r m a n c e , three types of terrain, referred to as Hope Valley snow, Petawawa Muskeg A, a n d L E T E sand, are used in the study. They are selected to represent a wide range of terrain c o n d i t i o n s , from highly compressible to fairly firm. The Hope Valley s n o w had an average depth of 128 cm, which represents a challenge to vehicle m o b i l i t y [6]. The Petawawa Muskeg A had a surface mat of approx. 5-10 cm thick a n d a n u n d e r l y i n g peat of a b o u t 5 m deep [7]. It was a muskeg with a fragile surface easily disturbed by vehicles. The L E T E sand was a fairly firm terrain [1].

COMPUTER AIDED ANALYSISOF TRACKEDVEHICLEPERFORMANCE

101

Table 2 summarizes the values of the pressure-sinkage and repetitive loading parameters of the three types of terrain used in the study. The basic mechanical properties of the Hope Valley snow are taken from reference [6]. Certain parameters that are required as input to the simulation model are not available from reference [6]. For these parameters, estimated values based on those of similar terrains are used. Terrain parameters for Petawawa Muskeg A and LETE sand are taken from references [1] and [7]. TABLE 2.

VALUES OF THE PRESSURE-SINKAGE AND REPETITIVE LOADING PARAMETERS

Parameters kr, k N / m "+' k , , k N / r d '+2 n kin, k N / m 3 M.,, k N / m 3 k0, k N / m ~ .4., k N / m 4

HopeValleySnow PetawawaMuskeg A 6.16 149.35 1.525 0 40,000

290 51 123 23,540

LETESand 102 5,301 0.793 ~ 0 503,000

For Hope Valley snow and LETE sand, the Bekker equation is used to characterize the pressure-sinkage relationship, that is

p = (kc/b +k s) z"

(1)

where p is pressure, z is sinkage, b is the smaller dimension of a rectangular plate (or the radius of a circular plate), and kc, ks and n are pressure-sinkage parameters. For Petawawa Muskeg A, a second order equation of the following form is used to describe the pressure-sinkage characteristics [7]: p = k m z + 2 (Mm/b)z ~

(2)

where km and M,, are pressure-sinkage parameters for muskeg. When the terrain is subject to repetitive loading, the pressure-sinkage relationship during the unloading and reloading cycle is assumed to be linear and is expressed by (1): P = Pu-ku

(Zu-Z)

(3)

where Pu and z~ are the pressure and sinkage, respectively, when unloading begins; and k~ is a parameter representing the average slope of the pressure-sinkage curve during the unloading-reloading cycle [1]. It is found that ku is a function ofz~ and their relationship, as a first approximation, may be described by: ku = ko + A u z u

(4)

where k0 and Au are repetitive loading parameters. Table 3 summarizes the values of the shear strength parameters of the three types of terrain used in the study [l, 6]. It should be mentioned that for the three types of terrain, an

102

J. Y. WONG

exponential equation relationship,

is used to characterize the shear stress-shea r displacement

that is, s = Sm~ [1 - - exp (-j/K)] TABLE 3.

Terrain

(5)

VALUES OF SHEAR STRENGTH PARAMETERS

Type of shearing

Angle of Shear Cohesion shearing deformation (adhesion), resistance, modulus, c (kPa) ~b(°) K (cm)

Hope Valley Snow

Internal Rubber-snow Vehicle belly-snow

0.76 0.12 0

23.2 16.4 5.7

4.24 0.39 -

Petawawa Muskeg A

Internal(peat) Vehicle belly-muskeg

2.83 0

39.4 13.5

3. I -

LETE Sand

Internal Rubber-sand

1.3 0.7

31.3 27.5

1.2 1.0

where s and Smax are the shear stress and maximum shear stress, respectively; j is shear displacement; and K is a parameter usually referred to as the shear deformation modulus. The maximum shear stress Sma~ is assumed to obey the M o h r - C o u l o m b relation, Sma, = C + p tan~

(6)

where c is the cohesion, ~b is the angle of shearing resistance, and p is the normal pressure. It should be pointed out that although in this study, the equations described above are selected to characterize the behaviour of the terrain, the computer simulation model can accept other forms of terrain inputs. Advancements in the characterization of the mechanical properties of terrain can readily be incorporated in the computer simulation model. Parametric analysis was performed using the computer simulation model NTVPM-85 to examine the effects of design parameters on the tractive performance over the three types of terrain. The prime vehicle design parameters examined in this study include track system configuration and initial track tension.

Effects of design parameters on performance on Hope Valley snow The drawbar pull to weight ratio as a function of slip for three different track system configurations (five roadwheels, six roadwheels and eight overlapping roadwheels) at various initial track tension to weight ratios, To/W, over Hope Valley snow are shown in Figs. 8, 9 and 10, respectively [2]. The initial track tension referred to in this study is the tension in the track when the vehicle rests on firm, level ground. It should be mentioned that To/W = 0.096 corresponds to an initial track tension of 10 kN, which is the recommended value for the baseline vehicle. It can be seen that for a given track system configuration, increasing the initial track tension noticeably improves the drawbar performance of the vehicle. For the baseline vehicle with five roadwheels, increasing the value of To/W from

COMPUTER AIDED ANALYSIS OF TRACKED VEHICLE PERFORMANCE

103

Track System With 5 Roadwheels .25

(Hope Valley Snow)

(-

o i o°

\ .15 .J

To/N .1 ..0 3

~ .05

/

i/

// I/

8.89B

-"

l

8.287

~

0O

.

i

i

i

i

20

40

60

80

.

.

.

8.382 i

100

$1 Jp (~.) FIG. 8.

Drawbar performance of a track system with five roadwheeis at various ratios of initial track tension to weight on Hope Valley snow.

.25

Track

System N i t h 6 Roadwheels

(Hope Valley Snow)

c-

I o o ~ "°"

-e \ O_

.15

.1

L

'"

f

/f

//

/ / "

To/N

t

8.89B 8. 191

3

~ .05

--'-.... i

00

FIo. 9.

20

i

8. 287 8,382

i

40 60 $1 ip (X)

88

188

Drawbar performance of a track system with six roadwheels at various ratios of initial track tension to weight on Hope Valley snow.

0.096 to 0.382 results in an increase of the drawbar pull to weight ratio from 0.006 to 0.130 at 20% slip. This indicates that when the initial track tension is set at the recommended value, the vehicle is close to immobilized on Hope Valley snow. However, the mobility of the vehicle is greatly improved with the increase of the initial track tension. It can also be seen from Figs. 8 and l0 that for the same initial track tension to weight ratio o f 0.191, the track system with eight overlapping roadwheeis has a drawbar pull to weight ratio of0.122 at 20% slip, as compared with a value of 0.049 for the track system with five roadwheels. This represents an increase of 248% in drawbar pull.

104

J.Y. WONG

Track System N1th 8 Roadwheeis

.3

V a l l e y Snow)

(Hope

.25

i/

• L

~-~

/"

.2

.05

1

-

To,

/

0

0

- -

0.096

---....

0.287 8.302

i

i

l

i

J

20

40

60

80

100

Slip (~) FIG. I0.

Drawbar performance of a track system with eight overlapping roadwheels at various ratios of initial track tension to weight on Hope Valley snow.

Figures 11 and 12 show the normal pressure distributions under the track system with eight overlapping roadwheels at initial track tension to weight ratios of 0.096 and 0.287, respectively. It is shown that for a given track system configuration, an increase in the initial track tension greatly increases the load supported by the track segments between roadwheels over soft terrain. Consequently, the normal pressure is more uniformly distributed and the peak pressure is reduced. This results in the reduction of sinkage and in the improvement of tractive performance. Figure 13 shows a comparison of the effects of initial track tension on drawbar pull at 20% slip for the three track systems over Hope Valley snow. It is interesting to note that on this snow the drawbar performance of the track system with five roadwheels at an initial track

Orambar

E

I )

g U1

0

60

$I 1p=207.

8

CL L

L

20 40 60 80

FIG. II. Predicted normal pressure distribution under a track system with eight overlapping roadwheels at initial track tension to weight ratio of 0.096 on Hope Valley snow.

C O M P U T E R A I D E D A N A L Y S I S OF T R A C K E D V E H I C L E P E R F O R M A N C E

LL +

E

0 b~

÷

105

9ra=bar

~.

~

I

~'

50

S I i p=207.

0

n

28 48

~

68

88 FIG. 12. Predicted normal pressure distribution under a track system with eight overlapping roadwheels at initial track tension to weight ratio of 0.287 on Hope Valley snow.

Hope V a l l e y Snou .3

.c

(Slip:

20~)

.25

03

~

.J

.2

\

..f

//'" 7

/ -

/ ."

.15

O.

.-

./ L

f

J

f

5 Roadwhee I s E~--~ 6 Roaduheels

///

JO 3

/''~/

. 05

/ "/

.... i

0 0

.1 Initial

FIG. 13.

.°~

.2 lr~ck

.i

.3 Tension

8 Roadwheels

.4 /

,

,

=

.5

Height

A comparison of the effects of initial track tension on drawbar pull at 20% slip for three track systems on Hope Valley snow.

tension to weight ratio of 0.382 is approximately equal to that of the track system with eight overlapping roadwheels at an initial track tension to weight ratio of 0.20. Figure 14 shows a comparison of the effects of initial track tension on tractive efficiency, defined as (drawbar pull/tractive effort) × ( 1- slip), for the three track systems. It can be seen that for a given track system, the tractive efficiency increases significantly with the increase of initial track tension, For the track system with five roadwheels, the tractive efficiency increases from 0.03 to 0.429 when the initial track tension to weight ratio increases from 0.096 to 0.382. For the track system with eight overlapping roadwheels, an increase in the initial track tension to weight ratio from 0.096 to 0.382 results in an increase in tractive efficiency from 0.222 to 0.585.

106

J.Y. WONG

Hope V a l l e y

.8 >, u c

(Slip:

.6

N-

La

. /

/ /"

5 Roadwhee Is B Re adtuhee I s

1 /

.2

/ /

/

/ / ~ /

I--

B Roadwhee I s

/

@

i

I

i

i

i

.1

.2

.3

.4

.5

Initial FIG. 14.

/

4

+~ o r~ £_

Snow

20%)

Track

Tension

/

Weight

A comparison of the effects of initial track tension on tractive efficiency at 20% slip for three track systems on Hope Valley snow.

The performance parameters of the three track systems with various initial track tensions at 20% slip on Hope Valley snow are summarized in Tables A-l, A-2 and A-3 of the Appendix. It can be seen from the tables that on Hope Valley snow the belly of all three vehicles comes into contact with the snow surface. As a result, part of the vehicle weight is supported by the belly and additional drag due to belly contact is introduced. It should be noted that the load supported by the belly decreases with the increase of initial track tension. For the same initial track tension, as the number of roadwheels increases, the load supported by the belly decreases.

Effects of design parameters on performance on Petawawa Muskeg A Figures 15, 16 and 17 show the variations of the drawbar pull to weight ratio with slip at Track

i I

System

N1th

5 Roadwheels

(Petawawa Muskeg R)

J o

FIG. 15.

0

20

40 60 $1 11o (X)

B@

i@0

Drawbar performance of a track system with five roadwheels at various ratios of initial track tension to weight on Petawawa Muskeg A.

COMPUTER AIDED ANALYSIS OF TRACKED VEHICLE PERFORMANCE

Track System Nith 6 Roadwheels (Petawawa Muskeg FI)

I [ ~

.8

\

.6

/7

.

~/-~

ii//

o

FIG.

107

-

O

20

-

40 60 Slip (%)

80

100

16. Drawbarper~rmanceofatracksystem withsixroadwh~lsatvariousratiosofinitial tracktensionto weighton Petawawa Muskeg A.

Track System Nith B Roadwheels (Petawawa Muskeg R)

1 I .e

~-

//,'y .4

2

IL//

--

8.896

I/

--

8. 191

-

.28,

V/

o

B

20

40

68

80

108

Slip (%) FIG.

17. Drawbarper~rmanee ofatraeksystem witheightoverlappingroadwheelsatvarious ratiosofinitialtracktensionto weighton ~tawawa Muskeg A.

various initial track tension to weight ratios for the three track systems over Petawawa Muskeg A. It can be seen that over this muskeg, the initial track tension again has a significant effect on tractive performance. For the baseline vehicle with five roadwheels, increasing the value of the initial track tension to weight ratio, To~W, from 0.096 to 0.382 results in an increase of the drawbar pull to weight ratio from 0.454 to 0.649, at 20% slip, representing an improvement of 43%. It can also be keen from Figures 15 and 17 that for the same initial track tension to weight ratio of 0.191, the track system with eight overlapping roadwheels has a drawbar pull to weight ratio of 0.603 at 20% slip, as compared with a value of 0.509 for the track system with five roadwheels. This represents an improvement of approx. 18.5%.

108

J.Y. WONG

Figures 18 and 19 show the normal pressure distributions under the track system with six roadwheels at initial track tension to weight ratios of 0.096 and 0.287, respectively. It again demonstrates that an increase in initial track tension results in a decrease in peak pressure and hence improved tractive performance.

41I~

~

b

ar

S I p=20X 0 20 CL "~

40 60

(8 42

80

ot 1o~ 120

FIG. 18.

Predicted normal pressure distribution under a track system with six roadwheels at initial track tension to weight ratio of 0.096 on Petawawa Muskeg A.

-~ u~

=bBr 4B

S l i p =20~.

100 FIG. 19,

Predicted normal pressure distribution under a track system with six roadwheets at initial track tension to weight ratio of 0.287 on Petawawa Muskeg A.

Figure 20 shows a comparison of the effects of initial track tension on drawbarpull at 20% slip for the three track systems. It is interesting to point out that o n this muskeg the drawbar performance of the track system with five roadwheels at an initial track tension to weight ratio of 0.382 is approximately equivalent to that of the track system with eight overlapping roadwheels at an initial track tension to weight ratio of about 0.25. Figure 21 shows a comparison of the effects of initial track tension on tractive efficiency for the three track systems. It is interesting to note that on this muskeg the initial track tension has a m o r e

COMPUTER AIDED ANALYSIS OF TRACKED VEHICLE PERFORMANCE Petauawa Muskeg R

.75 ~z

(Slip: 20%)

.7

/

.65

\

109

-/

/,"

/.,

/

/

o~ 0,~¢0 -Q

•

55

/

3

/

~

Q

.45

0

/

~

//

Roadwheels

-

6 Roadwheels

"

B Roadwhee

i

i

I

i

i

.2

.3

.4

.5

Track Tension

14eight

I

A comparison of the effects of initial track tension on drawbar pull at 20% slip for three track systems on Petawawa Muskeg A.

Petauawa Muskeg R

.?5

(Slip: L)

..

C

o qqW

20%)

-......

Z--C

.7

/

>

/

/

'

~

.05 u

/

/

t.. I--

-f 46

i

0

.l Initial

5 Roadwheels

~

to

FIG. 2 I.

Is

.1

Initial FIG. 20.

/

/

-- 6 Roadwheels

.... i

.2 Track

B Roadwhee

i

.3 Tension

/

ls

i

i

.4 Neight

.5

A comparison of the effects of initial track tension on tractive efficiency at 20% slip for three track systems on Petawawa Muskeg A.

significant effect on tractive efficiency of the track system with five roadwheels than that of the system with eight overlapping roadwheels. The performance parameters of the three track'systems with various initial track tensions at 20% slip on Petawawa Muskeg A are summarized in Tables A-4, A-5 and A-6 of the Appendix. It can be seen from the tables that for the track systems with five and six roadwheels at low initial track tensions, the belly comes into contact with the terrain surface. However, for the track system with eight overlapping wheels, the belly does not come into contact with the terrain even at low initial track tensions.

110

J.Y. WONG

Effects of design parameters on performance on LETE sand The variations of the drawbar pull to weight ratio with slip at various initial track tension to weight ratios for the three track systems over LETE sand are shown in Figs. 22, 23 and 24. It can be seen that on this sandy terrain, the initial track tension has an insignificant effect on tractive performance. For the baseline vehicle with five roadwheels, increasing the value of the initial track tension to weight ratio, To~W, from 0.096 to 0.382 results in an increase of the drawbar pull to weight ratio of only 8.5% at 20% slip. This is primarily due to the fact that the LETE sand was a relatively firm terrain. The increase in initial track tension does not cause a significant increase of the load supported by the track segments between roadwheels, Track

.7 J~ (3]

System N l t h

5 Roadwheels

(LETE Sand)

.6

03 Z

.5

\

.4 O_ £_ no J3

- -

.3

0. 096

0.191

3 L

.2

.1

J

o

20

i

J

40

60

__

Slip Fzo. 22.

- - - -

0,287

. . . .

0. 382

L

.

i

80

100

(%)

Drawbarperformanceofatracksystem withfiveroadwheelsatvariousratiosofinitial t r a c k t e n s i o n t o weighton k E T E s a n d .

Track

System N i t h

6 Roadwheels

(LETE Sand) CO3

83 \

D OL t~ o 3 t~

--

0.

I91

0. 287 .

1

0

.

.

0,382

.

J

i

i

i

i

20

40

60

80

100

S]ip

FIG. 23.

--

(%)

Drawbar performance of a track system with six roadwheels at various ratios of initial track tension to weight on LETE sand.

COMPUTER AIDED ANALYSIS OF TRACKED VEHICLE PERFORMANCE T r a c k System H i t h .7 .c 03

8

111

Roadwheels

(LETE Sand)

.8

O3

-~

.5

\

To/H

EL

.3 J~

3

.2 .I

0

20

48

50

Slip FIG.

24.

8. B9B --

- - 8 . 191

~'--

B. 287

....

8. 382

80

100

(X)

Drawer ~ormance ofatracksystem witheightoverlappingroadwheelsatvarious ratiosofinitialtracktensionto weighton LETEsand.

and hence noticeable improvement in performance. It can also be seen from Figs. 22 and 24 that for the same initial track tension to weight ratio of 0.191, the track system with eight overlapping roadwheels has similar tractive performance to that of the system with five roadwheels. The difference between them in drawbar pull at 20% slip is merely 2.4%. Figures 25 and 26 show the normal pressure distributions under the track system with five roadwheels at initial track tension to weight ratios of 0.096 and 0.287, respectively. It is shown that the effects of initial track tension on pressure distribution under the track on LETE sand are much less significant than they are on Hope Valley snow or Petawawa Muskeg A.

Dr aub ar E c~

U3

0 (2_ *¢

SI

ip=28X

180 280

&e

380

L 480

Q-

580

FIG. 25.

Predicted normal pressure distribution under a track system with five roadwhecls at initial track tension to weight ratio of 0.096 on LETE sand.

112

J.Y. WONG

Dr a w b a r U

S I i p=20~. 0 O--

t00 200

L

H L

[3--

300 400 500

FIG. 26.

Predicted normal pressure distribution under a track system with five roadwheels at initial track tension to weight ratio of 0.287 on LETE sand.

Figure 27 shows a comparison of the effects of initial track tension on drawbar pull at 20% slip for the three track systems. It indicates that on LETE sand the effects of initial track tension on tractive performance are relatively insignificant, compared with those on Hope Valley snow. The effects of initial track tension on tractive efficiency of the three track

LETE

Sand

.51 (Slip:

20%)

c"

/

.4s

/ .//

\

.48 a_

//

L

c~

/

"'/ ,,/

.4g "/

/

- - 5

/

--

Roadwheels

--

G Roadwheels

B Roadwhee

....

.45 .44

FIG. 27.

/ / /

/ /

.47

L

x~ 3

/ i'" //

i

.l Initial

i

.2 Track

i

.3 Tenslon

i

/

.4 Nelght

Is i

.5

A comparison of the effects of initial track tension on drawbar pull at 20% slip for three track systems on LETE sand.

systems are shown in Fig. 28. It is shown that while the initial track tension has some minor effect on the tractive efficiency of the track system with five roadwheels, it has practically no effect on the tractive efficiency of the system with eight overlapping roadwheels. The performance parameters of the three track systems with various initial track tensions at 20% slip on LETE sand are summarized in Tables A-7, A-8 and A-9 of the Appendix.

C O M P U T E R A I D E D A N A L Y S I S OF T R A C K E D V E H I C L E P E R F O R M A N C E

• 805 u c

LETE

Sand

(Slip:

2@%)

113

.B

............. o

-~-%

-

-

t

~.795 W

.79

>

Ro a d w h e e I s

u

Roadwhee I s

L.785 ....

.7B

FIG.

28.

8

.

.I Initial

.

.

.

B Roadtuhee I s

.

.2 .3 .4 Track Tension / Height

.

.5

A comparison of the effects of initial track tension on tractive efficiency at 20% slip for three track systems on LETE sand.

Figures 29, 30 and 31 summarize the effects of initial track tension on external motion resistance coefficient over the three types of terrain for track systems with five roadwheels, six roadwheels, and eight overlapping roadwheels, respectively. It is shown that on LETE sand, the initial track tension and track system configuration have little effect on the external motion resistance. On the other hand, the initial track tension has a significant effect on the external motion resistance of the three track systems on Hope Valley snow. On Petawawa Muskeg A, while the initial track tension has a noticeable effect on the external motion resistance of the track systems with five and six roadwheels, it has little effect on the external motion resistance of the system with eight overlapping wheels.

Track System With S Roaduheels

.2

(Slip:

u

28%)

40 U

'

15

C

I/I

n,

~now

.05 --

Muskeg

¢o

. . . .

c L

o x I.M

@

i

@

.1

Initial FIG. 29.

S~nd

.2 .3 .4 Track Tension / Neight

.5

Effects of initial track tension on external motion resistance of a track system with five roadwheels at 20c~, slip over three types of terrain.

114

J.Y. WONG

+a co

Track

.2

System N i t h (Slip:

(3

4OJ 0 U

G Roaduheels 28%)

.15

O3

U

g

"--

.1

r-v

~.......

~

.05

S

n

--

o

w

--

Muskeg

Sand

. . . .

eL +J

i

0

.I

Initial FIG. 30.

-1-

~

i

i

.4

.5

. . . . . . . . . . . . . . . . . . . . . . . . .

0

.2

Track

.3

Tension

/ Neight

Effects of initial track tension on external motion resistance of a track system with six roadwheels at 20% slip over three types of terrain.

C

Track

.2

System N i t h (Slip:

8 Roaduheels 20%)

o 4-

e

0 U

"

15

0 C ~

.1

- - S n o w

n, .05

--

....

--

Muskeg Sand

c Q.I 0

. . . . . . . . . . . . . . . . . . . . . . . . . . .

0

FIG. 3 I.

.I Initial

.2 .3 .4 Track Tenslon / Ne~ght

.5

Effects of initial track tension on external motion resistance of a track system with eight overlapping roadwheels at 20c~: slip over three types of terrain.

Figures 32, 33 and 34 summarize the effects of initial track tension on drawbar pull over the three types of terrain for track systems with five roadwheels, six roadwheels, and eight overlapping roadwheeis, respectively. It is shown that on LETE sand the initial track tension and track system configuration have little effect on the drawbar performance. On Hope Valley snow and Petawawa Muskeg A, the initial track tension has, in general, a noticeable effect on the drawbar pull of the three track systems. It is interesting to note, however, that on Petawawa Muskeg A the initial track tension has slightly less effect on the drawbar pull of the track system with eight overlapping roadwheels than that of the track systems with five or six roadwheels.

COMPUTER AIDED ANALYSIS OF TRACKED VEHICLE PERFORMANCE

Track

.B

System

With 5 R o a d w h e e l s

( S l i p : 20%)

.C ~n O~ t" I...--.

--

~ . . - - -

. . . . .

..---

. . . . . . . . . .

.4

(i_ ¢. to c~ 3 to

~ S n o w

.2

--

--Muskeg

. . . .

i

l

~0

FIG.32.

.2 Track

.1 Initial

Sand

i

.3 Tension

/

i

.4 Height

.5

Effects of initial track tension on drawbar pull of a track system with five roadwheelsat 20% slip over three types of terrain.

Track

.B

System With 6 Roadwheels (Slip:

20%) /

QI \

J

.4

L - --

Q

. . . .

0

FIG. 33.

Snow --

Muskeg

5end

i

0

.I Initial

.2 .3 Track Tension

.4 / Weight

.5

Effects of initial track tension on drawbar pull of a track system with six roadwheels at 20e~ slip over three types of terrain.

115

116

J.Y. WONG

Track

.8

System With (Slip:

8 Roadwhee]s 20%)

.12

.6 \

.4 n L ..Q 3

Snow

•~

~

--

L

....

0

i

O

FIG. 34.

--

i

.I Initial

i

Muskeg

Sand

L

.2 .3 .4 Track Tension / Nelght

.5

Effects of initial track tension on drawbar pull of a track system with eight overlapping roadwheels at 20% slip over three types of terrain.

Figures 35, 36 and 37 summarize the effects of initial track tension on tractive efficiency over the three types of terrain for the track systems with five roadwheels, six roadwheels, and eight overlapping roadwheels, respectively. It can be seen that on LETE sand, both the initial track tension and track system configuration have little effect on tractive efficiency. The tractive efficiency is more sensitive to the initial track tension than to track system configuration on Petawawa Muskeg A. On Hope Valley snow, both the initial track tension and track system configuration have a significant effect on tractive efficiency.

Track

System

With

(Slip:

o c

5 Roadwheels 20%)

.8

(3

c4LO

>

.4 Snow

(3 Huskeg

L

.2

....

0 0

i

i

i

I

i

.1

.2

,3

.4

.5

Initial FIG. 35.

Sand

Track Tension / Nelght

Effects of initial track tension on tractive efficiency of a track system with five roadwheels at 20°~ slip over three types oi terrain.

COMPUTER AIDED ANALYSIS OF TRACKEDVEHICLE PERFORMANCE Track System N i t h (Slip: u

117

G Roadwheels 20%)

.B

o q-

.6

bJ Q3 >

•4

~

- -

Snow

u

--

--

Muskeg

L •

2

....

i

0@

i

.I Initial

t

Sand

i

i

.3

.5

.4 Track Tension / N e i g h t .2

FIG, 36. Effects of initial tension on tractive efficiency of a tracksystemwithsix roadwheelsat 20% slip over three types of terrain. Track System Nith

1 >, U

c

(Slip:

8 Roadwheels 20%)

.8

u q-

.6

I

> -

O L-

•q

Snow

-

--

--

....

,2

i

@

i

.1

i

.3 Track Tension / .2

Initial

Muskeg Sand

i

.4 14eight

i

.5

FIG. 37. Effects of initial track tension on tractive efficiency of a track system with eight overlapping roadwheels at 20% slip over three types of terrain.

CLOSING REMARKS Among the vehicle design parameters examined in this study, the initial track tension is found to have a significant effect on vehicle performance on highly compressible (soft) terrains, such as the Hope Valley snow and Petawawa Muskeg A used in this study. The effect of initial track tension on tractive performance becomes less pronounced asthe terrain becomes firmer. For instance, on LETE sand, the increase in initial track tension has an insignificant effect on the performance of the three track systems examined in this study. Since an increase in initial track tension will normally cause an increase in the internal mechanical losses and wear in the track-suspension system, the increase in tension as a means of improving performance is justifiable only when operating on highly compressible terrain.

118

J.Y. WONG

For tracked vehicles that are expected to operate over marginal terrains for any significant period of time, a case can be made for the installation of a central track tension regulating system that can be conveniently controlled by the driver. Over normal terrains, the drive r can set the initial track tension at a lower level. When traversing marginal terrains is anticipated, the driver can readily increase the track tension to an appropriate level to improve vehicle mobility. It should be mentioned that the increase of initial track tension will affect the operation of the suspension system. This has to be taken into account when considering the design of the central track tension regulating system. The track system configuration is shown to have a noticeable effect on tractive performance over highly compressible terrain. As the terrain becomes firmer, the effect of track system configuration on performance becomes less significant. It is interesting to note that the improvement in performance achieved by using eight overlapping roadwheels at lower initial track tensions can usually be matched by using five or six roadwheels at higher initial track tensions. Consequently, to improve the mobility of existing tracked vehicles over marginal terrains, the increasing of the initial track tension would appear to be the most cost-effective means. The results of this study have demonstrated the usefulness of the computer simulation model NTVPM-85 in parametric analysis of tracked vehicle performance, as it can quantitatively define the effects of design parameters and terrain conditions on vehicle performance. In comparison with the widely used conventional method based on the nominal ground pressure [5], which is incapable of distinguishing between different track system designs, the computer simulation model NTVPM-85 takes into account the effects of all major design parameters of the vehicle. Thus, it can be an extremely useful tool for the development and design engineer, as well as the procurement manager, in the selection of the most promising design for a given mission and environment. The computer simulation model NTVPM-85 is currently being used to aid tracked vehicle manufacturers in the development and design of new products. While the basic features of the computer simulation model NTVPM°85 have been validated over a range of terrains, additional field tests and correlation studies to further ascertain its versatility and validity over a wider range of operating conditions will be useful. Acknowledgements--The initial development of the computer simulation model for tracked vehicle performance was funded, through contract arrangements, by the Canadian Department of National Defence, during the period between March 1980 and June 1984. Subsequent developments of the computer simulation model NTVPM-85 have been performed under the auspices of Vehicle Systems Development Corporation, Nepean, Ontario, Canada. The parametric studies described in this paper were supported in part by Vehicle Systems Development Corporation and in part by the Natural Sciences and Engineering Research Council of Canada. The contribution of Mr. J. Preston-Thomas to the development of the computer simulation model is appreciated.

REFERENCES [I]

J.Y. WONG, M. GARBERand J. PRESTON-THOMAS,Theoretical prediction and experimental substantiation of the ground pressure distribution and tractive performance of tracked vehicles, Proceedings of the Institution of Mechanical Engineers, Vol. 198, Part D, No. 15, pp. 265-285, 1984. [2] J.Y. WONGand J. PPRES'rON-THOMAS,Parametric analysis of tracked vehicle performance usingan advanced computer simulation model, Proceedings of the Institution of Mechanical Engineers, Vol. 200, Part D, No. 2, pp. 101-114, 1986. [3] M.G. BEKKER, Theory of Land Locomotion. The University of Michigan Press, Michigan (1956). [4] J.Y. WoNG, Theory of Ground Vehicles. John Wiley, New York (1978). Russian edition, Machinostroenie Publishing House, Moscow, U.S.S.R. (1982).

COMPUTER AIDED ANALYSIS OF TRACKED VEHICLE PERFORMANCE [5] [6] [7] [8]

119

J.Y. WONGand J. PRESTON-THOMAS,A comparison between a conventional method and an improved method for predicting tracked vehicle performance, Proceedingsof the 8th International Con/'erenceof lSTVS, Vol. I, Cambridge, U.K. (1984). W. L, HARRISON, Vehicle performance over snow, math-model validation study, Technical Report No. 268, U.S. Army Corps of Engineers, Cold Regions Research and Engineering Laboratory, December 1975. J.Y. WONG, J. R. RADFORTnand J. PRESTON-THOMAS,Some further studies on the mechanical properties of muskeg in relation to vehicle mobility, Journal of Terramechanics 19(2)(1982). J.Y. WONG, An improved method for predicting tracked vehicle performance, Journal of Terramechank's 21(I) (1984).

120

J.Y. WONG

.__ ± ~

•,-:

--

e,i

o

d

,5

~i

0

z

~

~o

.~, ~ = ° " ' :

Z 0

z

~ , ~ e~

~

~

~o..~

",~

o

.~.~ ~ a;

~ ~ ~ ~ ~ :_~ e,

Z i-~,.

<

.8"U

~ - ~ §:_~ ~"u

No

N! s

~=

z

"~.-~

•N ~ ~.~

o ~.=

o N~ -.~ o

L~ e-i e~

8

kN

;>

E

E o

COMPUTER A I D E D ANALYSIS OF TRACKED VEHICLE PERFORMANCE

121

<

<

~

2:

t~

< O

~e

2.~o

• .,

O

< tt~

< <

O c~

QO

t~

<


t~

~e

oee~ < Z < t~ Z <

•~ o ~e t~ e~

~.

,q.

,q.

,q.

< 'q" <

t~

e~

>.

%"

'q"

~1"

122

J.Y. WONG

~.~c <

v,

:E

<

.( {.. z 0

Z ©

{...

< 0

,?,: ~=

=

~E~

t~

~

~"

8

,,=,

~~ ~ 8._u o.-~ =

~"~

~"o

~.u

0

..~ o

P~ {.,.

Z

~4 Z

#. •

~'~

m

"~,

",~ ~0' ~ ' { ~ ' ~

{-

u

0

0

0

COMPUTER AIDED ANALYSIS OF TRACKED VEHICLE PERFORMANCE

Z

-~

.o

,-

.o

tq

tq

Z

l-

hu~ "~

Z 0 .-

~.~

=~ ~ ~o "~

.7: o

O ~t~'~"

< 0

~o

u

oo

m

v

"°

< X

~8.-

<

='~.

m "e l'-

-'~ ~

-~

=-~

"~ ~ ~ . ~ <

-~-~ ~.~ m

< Z

~"~

Z

0

0

0

0

Z

N

~"

ul

~,-~ ~

~u

"~ ~

<

"~.

""

0

~'.~

d

"0 <

~'~

~:,.5 u

~K

d

123

e4

124

J.Y. WONG

o

I.

I.,14

~'~

~I

~ Z ~=

.ooNo

N

,-,

~

~ 8~

~

,

~

,

8"o

0

k ~-

~

-~o ~_~ °~'=

<

~==

m

~i

°~ o

;>

,~;

0

0