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The traction sum for the movement on a longitudinal inclined plane at the

angle will be:( ) ( ) ++= sinGGcosfZfZF 2211maxm (5)

The power sum will be:

11tr3

RR1p3

pp

3me

10

M

10

M

10

M

+

=

[kW] (6)

Figure 1.1 The schemata of the forces and moments which actuate

on a bunkerless combine with semi-trailer

1.2 Self-Propelled Bunkerless Combine with Towed Semi-Trailer

The forces and moments which actuate on the combine are presented in

figure 1.1.

Compared to the previous case, now there appears the traction force Ft .

When the moving speed is constant (v = ct) the equation of the traction sum is:

t22112 FfRfRZ ++= , where (7)( ) 3cr33t fZGfZF == when the unit moves on horizontal plane( 3c )r33t fZcosGfZF == when the unit moves on a longitudinal

inclined plane.

Zc is part of the semi-trailer weight and of the load supported by the towinghoop, respectively:

(8)cr ZZG +3The reaction Z1 will result from the equation of moments related to point B:

( ) ( )( ) ( ) 0hFfrcZcfrbGGcfrLZ ct22c22111 =++++++++

( )( ) ( )cfrL

hFfrcZcfrbGGZ

11

ct22c221 ++

++++= (9)

The reaction Z2

will result from the equation of moments related to point A:

( ) ( ) ( )( ) 0hFfraGGfrfrLZfrLcZ ct112211211c =++++++


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from which:

( )( ) ( )

2211

ct11c112

frfrL

hFfrcLZfraGGZ

+++++++

= (10)

The reaction Z3 will result from the equation of moments related to point C:

( ) 0aGfrLZ 1r313 = , from which:

331

1r3

frL

aGZ

= (11)

The reaction Zc will be calculated from the equation of moments related to

point D:

( 0frbG)frL(Z 331 )r31c = from which:( )

331

331rc

frL

frbGZ

= (12)

We do the checking: rc GZZ =3 (13)That is

( ) ( ) ( )r

331

331r

331

311r

331

1r

331

31r GfrL

frLG

frL

frbaG

frL

aG

frL

frbG=

=

+=

+

where .111 Lba =+The power sum will be:

11tr3

RR1p3

pp

3me

10

M

10

M

10

M

+

=

[kW] (14)

The power at the driving axle must ensure the movement of the combine as a

unit together with the semi-trailer.

The power necessary to tow semi-trailer will be:

3t

t10

vFP

= [kW] (15)

where v is the working speed in m/s.

The working speed ( )= 1vv t (16)where vt is the theoretical speed in m/s and is the slipping.

2. THE COMBINE MOVEMENT ON A TRANSVERSAL INCLINE

AT AN INCLINATION ANGLE 2.1 Self-Propelled Combine Equipped with Bunkers Without Towed Trailer

It is considered that the combine movement on the transversal incline is

rectilinear and it is made at a constant speed (v = ct).

Soil reactions Zd and Zs on combine wheels are determined from the equations

of moments related to points B and A according to the schemata in figure 2.1:

( ) ( ) 02

BcosGGhsinGG

2

BcosVhsinVBZ gvd =++

from which:


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( )

B

2

BcoshsinV

2

BcoshsinGG

Zvg

d

++

++

= (17)

( ) ( ) 02

BcosVhsinV

2

BcosGGhsinGGBZ vgs =++++

from which:

( )

B

2

BcoshsinV

2

BcoshsinGG

Zvg

s

+

= (18)

or

( )

B

hsin2

BcosVhsin

2

BcosGG

Zvg

s

+

+

=

( )

( )

( )( )[ ]++=

++=

=

+

+

+

+

++

++

=+

VGGcosB

2

BcosV2

2

BcosGG2

B

hsin2

BcosV

B

hsin2

BcosGG

B

2BcoshsinV

2BcoshsinGG

ZZ

vg

vg

sd

or ( ) ++=+ cosVcosGGZZ sd (19)

Figure 2.1 The schemata of the forces which actuate on the combine during

its movements on a transversal incline at an inclination angle


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Combine harvesting has a maximal working incline of 120, the movement

direction being identical to the general direction of level curves.

According to the calculation schemata in figure 2.1 the combine overturntowards the base of the incline (round the point A) is possible if Zs = 0 (the stability

limit). So,

( )

B

hsin2BcosVhsin

2BcosGG

Zvg

s

+

+

= =0 (20)

from which it results that:

( ) 0hsin2

BcosVhsin

2

BcosGG vg =

+

+

or

( )

=

+ vg hsin

2

BcosVhsin

2

BcosGG

or

GG

V

hsin2

Bcos

hsin2

Bcos

v

g

+

=

GG

V

htg2

B

htg2

B

v

g

+

=

+

= vg htg2

B

GG

Vhtg

2

B

+

+=

++

GGV

12

BhhGG

Vtg gv

GG

Vhh

GG

V1

2

Btg

vg +

+

+

+= (21)

If hg = hv then:

gh2

Btg = or

gh2

Barctg= (22)

The above relation represents the limit angle in case of overturn when hg = hv .

The condition of maintaining transversal stability to slipping, according to

figure 2.1 is:

- for the front axle (usually driving)1y1 ZY =

- for the back axle, where2y2 ZY = y is the transversal coefficient of

adherence.

sd21 ZZZZ +=+ (23)


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2.2 Self-Propelled Combine without Bunker with Towed trailer

In case of trailer towing, on the bunkerless combine on horizontal plane, there

also actuates the traction force Ft inclined at an angle related to the longitudinalsymmetry axis of the combine. Ft can be decomposed into the following components:

- on the longitudinal direction; cosFt- on the transversal direction. sinFt

The condition of maintaining transversal stability to lateral slipping is:

- for the front axle (usually the driving axle)1y1 ZY =

- for the back axle, where+= sinFZY t2y2 y is the transversal

coefficient of adherence.

Soil reactions Zs and Zd dont change compared to the previous case and the

expression of the limit angle in case of transversal overturn remains the same.

To maintain stability to trailer lateral slipping there must be fulfilled the next

conditions:- for the trailer front axle;r1yr1 ZY =

- for the trailer back axle.r2yr2 ZY =

3. CONCLUSIONS

3.1. For all the studied cases we have determined the stability conditions both

on a horizontal plane and on inclined plane;

3.2. We have determined the power sum both for the solo combine and for the

situation when it tows a semi-trailer;

3.3. The data established by this study are necessary to improve stability,manoeuvrability and maniability.

BIBLIOGRAPHY

1. Dnil I., Neculiasa V.Maini agricole de recoltat, vol. 2, Institutul Politehnic Traian Vuiadin Timioara, Facultatea de Mecanic Agricol, curs litografiat, Timioara, 1987.

2. Dobrescu Constantin Optimizarea parametrilor agregatelor agricole n scopul reduceriiconsumurilor, Redacia de propagand tehnic agricol, Bucureti, 1981.

3. Dobrescu Constantin Studiul sistemic al agregatelor agricole, Redacia de propagandtehnic agricol, Bucureti, 1985.

4. Ninulescu Traian Contribuii la creterea manevrabilitii tractoarelor 4x4 prin utilizarea desoluii constructive noi pentru puntea din fa-tez de doctorat, Universitatea Transilvania din

Braov, 2005;

5. Niescu Gh., Nstsoiu t., Popescu S. Tractoare, Editura Didactic i Pedagogic,Bucureti, 1974;

6. Pisoschi Al.-Gr.Tractoare, automobile i sisteme de propulsie note de curs, Universitatea

din Craiova, Facultatea de Mecanic, Craiova, 2003.

7. Tecuan N., Ionescu E.Tractoare i automobile, Editura Didactici Pedagogic, Bucureti,1982.

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