Modernization of Bodies of Dumping Trailers with Put-On ... · PDF fileModernization of Bodies of Dumping Trailers with ... budgetary study is carried out to Yelets state ... Fig

Comput. Sci. Appl. Volume 1, Number 3, 2014, pp. 139-151 Received: July 24, 2014; Published: September 25, 2014

Computer Science and Applications

www.ethanpublishing.com

Modernization of Bodies of Dumping Trailers with

Put-On Sides and Their Calculation on Durability

Eugene Slivinskii, Sergey Radin and Irina Gridchina

Department of Mechanics and Technological Processes, Yelets State University I.A. Bunin, Yelets, 399770, Russia

Corresponding author: Eugene Slivinskii ([email protected])

Abstract: The materials concerning development of a perspective design of a dumping body of the autotractor trailer supplied put-on sides are presented in the present article, with the folding panels intended for consolidation and transportation of lightweight freights. The proposed technical solution created at the level of the invention, allows to increase operational reliability of a dumping body due to decrease in tension arising in its constructional elements. Analytical researches with development of settlement schemes and method of calculation of a design of a body on static and dynamic durability are conducted, and calculations of power loading of constructional elements the put-on sides of a body of the dumping trailer intended for unpacked transportation of lightweight freights are carried out. Development are recommended, both domestic, and to foreign research and industrial structures in the field of autotractor mechanical engineering for the purpose of their further studying and possible introduction in practice. Key words: Trailer, body, main boards, put-on sides, folding panel, additional support.

1. Introduction

Increase of reliability of agricultural cars is one of

the major tasks of increase of efficiency of agricultural

production in our country. The successful solution of

problems of increase of safe operation and reliability

of cars in work, economy of metal and lightness of

designs probably only on the basis of the theory and

application in practice of design of modern methods

and funds of calculation for durability, wear resistance

and rigidity. One of the major technological processes,

for example, in an agronomical complex are transport

operations on transportation of various freights to

what various trucks and the autotractor trains

consisting of tractors of aggregated with trailers and

semi-trailers are widely applied. The broadest

application is found by tractor transport. As tractors to

transportation of trailers and semi-trailers apply wheel

tractors of a class 0.9 t, such as a tractor four-wheel

T-28X4M-C1 and T-40AM. Wheel tractors of a class

of 1.4 t are the MTZ-52, MTZ-80, YuMZ-6M tractors,

etc. Designs of tractor dumping trailers are also

diverse and generally it is tractor biaxial dumping

trailers of models 2PTS-4-793-01, 2PTS-4-887,

2-PTS-4M, and also heavy-load tractor semi-trailers

of model 3-PTS-12 with a loading capacity of 12.0 t

aggregated with the wheel K-700 tractors, etc. [1-3].

Basis of a design of all tractor trailers is the chassis

which serves for installation on it of a platform and

adaptations. Usually in the package of the chassis are

included: frame, running gear, the traction coupling

device, the brake system, the overturning mechanism

and electric equipment. The frame of the trailer

represents a welded design and consists of two

stamped wing spar connected among themselves

cross-pieces. In a middle part of a frame by means of a

basic arm, the bottom support of the hydroelevator is

welded. When trailers are involved in transportation of

lightweight freights of their platform are supplied with

the put-on sides lateral folding and stationary face

boards having under operating conditions low

Modernization of Bodies of Dumping Trailers with Put-On Sides and Their Calculation on Durability

140

reliability. Usually at all models of autotractor

dumping 2PTS-4 trailers hydroelevators are executed

telescopic type from steel pipes entering each other.

For the purpose of increase of safety of service and

repair of knots and details of the trailers which are in

hard-to-reach spots, they are supplied with safety

racks of platforms. Essential lack of such safety racks

is that they are established manually and in practice

often the service personnel, having forgotten them to

establish, is subject to traumatizing at the expense of a

possible self-omitting of a body because of existence

of possible defects in tractor and trailer hydraulic

systems. Therefore, in practice, ways on creation and

use are found now, first, new technical solutions

connected with strengthening of durability and rigidity

of element base the put-on sides of platforms raising

their operational reliability, and secondly, use of

various devices on a design allowing to mechanize

process establish also dismantle of safety racks

operating in an automatic mode. Considering it the

budgetary study is carried out to Yelets state

University of I.A. Bunin on chair of mechanics and

technological processes throughout a row of years on

the subject “Dynamics, Durability and Reliability of

Transport, Construction and Road and Agricultural

Cars, and also the Industrial Standard and

Non-standard Equipment in Relation to the

Chernozem Region of the Russian Federation” and to

one of its sections researches directed on increase of

reliability of dumping bodies of trailers and to

improvement of working conditions of the service

personnel taken are executed at their operation.

2. Aim of the Research

Considering the above an objective of this

research is

(1) Development perspective designs of a body of

the dumping autotractor trailer created at the level of

the invention and the control supplied with the

mechanism of the folding panels intended for

consolidation of lightweight freights;

(2) Development of settlement schemes and a

calculation procedure on durability of constructional

elements of a body of the dumping trailer supplied

with put-on sides boards and the device carrying out

consolidation of lightweight freight located in it.

allowing to make calculations for determination of

their rational geometrical parameters, and also

calculation of constructive elements of a body on

durability;

(3) Assessment of technical and economic

efficiency of the proposed technical solution for the

purpose of possible introduction of the last in practice.

3. The Research Methodology

It is known [1, 4-9] that at movement of the

autotractor dumping trailers loaded by lightweight

freight, for example, by cotton raw, because of spatial

fluctuations of the last bearing elements of a body

perceive considerable power loading, and cross linear

and angular movements of a body together with in

advance condensed cotton raw located in it have the

greatest impact on such loading. For carrying out

analytical researches power loading of a body of the

trailer 2PTS-4-793A the settlement scheme (Fig. 1)

consisting of the chassis and a body with folding

lateral panels’ opening outside of a body is developed.

On the settlement scheme the trailer is presented in

the form of four mass systems with a specified mass

of mт (the cart with wheels), mк (a frame of the trailer

and its body), mп (own mass of cotton in a body) and

respectively the moments of inertia of Jт, Jk and Jп,

connected among themselves by elastic

communications with constant values of coefficients

linear Ст, С3 and torsion Kк and Кп of roughness from

connections of mass of the trailer with its platform, a

platform with put-on sides boards and the put-on sides

of boards with mass the cotton raw located in a body.

Relative movements of masses are characterized by

the generalized coordinates φк and φп. Vibrational

excitation model performed kinematic coordinate φт,

taking into account fluctuations of the trailer relative


141

to the axis OZ, and features micro roughness profile

ZЛ(t) and Zп(t), causing its displacement relative to the

OХ axis.

For a postcompaction of lightweight freight folding

lateral panels serve in a body of the trailer the put-on

sides of boards which consist (Fig. 1) of the top and

bottom 2 bearing bars connected among themselves

by racks 3. Power loading of each folding lateral panel

is carried out by the concentrated efforts of Рв2, made

from operation of the mechanism of the drive of their

management, and also uniform the distributed loading

of q1, operating on folding panels from the condensed

mass of cotton raw. In the middle part of the lower

timber 2 at Б3 placed additional support with stiffness

coefficient of linear С3, the construction of which is

recognized as the invention SU956328.

Following assumptions were made to develop a

model. Characteristics of a spring suspension bracket

are linear, gaps in kinematic couples are replaced with

equivalent roughness, roughnesses of a micro and

macro profile influence periodically all wheels of the

trailer, and the form and their amplitude changes in

time under the harmonious and impulsive law, the

accepted system of coordinates is located at the level

of the conditional road and moves concerning them

with a constant speed, movement of folding lateral

panels happens without distortions, bars and racks of

folding panels are loaded with the “equivalent”

loading which plane of action is located parallel to

their longitudinal axes.

The developed model and the accepted assumptions

allow to investigate power loading of bearing

elements of folding lateral panels in two directions: as

a result of mechanical consolidation of cotton raw by

them and at their dynamic loading at trailer movement

with cotton already condensed in its body.

We will consider the first task. Put boards of branch

of the parties with folding groups and put boards of

the person of the parties, submit the welded projects

executed in the form of structure, the metal gauze

enclosed in a sheath. Existence of a metal gauze

causes a certain loading of communications of

structure with transfer of the freight distributed at

height by them. As the settlement scheme for the

folding panel the flat rod system (Fig. 2) loaded with

distributed loading with specific pressure of qв and qн,

is chosen, and we consider that change of specific

pressure on height of the panel is subordinated to

linear dependence. We represent each vertical

communication of the folding panel in the form of the

Fig. 1 Calculation scheme of body dumper trailer.


142

Fig. 2 Calculation scheme of panel and rack.

beam loaded with distributed loading of LiqB to Liqн

(Fig. 2), having elastic support with coefficients of

linear Свi and Снi, torsion Квi and Кнi roughness.

Such beam perceives the moment of friction forces

of cotton about the grid, represented in the form of

two concentrated moments:

4B H BTi i i

q qМ L l

4B H BTi i i H

q qМ L l e

(1)

where ев, ен are eccentricity organize vertical

connection to the center of the upper and lower torsion

bars panel; μ—coefficient of friction of cotton raw.

On the basis of Refs. [9, 10-18], values of torsion of

Квi and Кнi roughness are possible to determine by

dependences: 0

0

L

ВiK

G J BКL L

0

0

HHi

K

G J LК

L L

where Lо and Lк are lengths of pieces of Li of the sites

perceiving the single moment, the enclosed on top or

bottom bar of the panel; 0

J is the polar moment of inertia of the area of cross section of a bar.

Values of coefficients of linear roughness Свi and

Снi are defined as

220

3

K

BВi

LL

LEJС

2 20

3 HHi

K

EJ LС

L L

where J is the moment of inertia of the area of cross

section of a bar.

When performing calculations of a tension of the

top and bottom bars of the folding panel (Fig. 3), we

consider that the last at the same time perceive group

of the concentrated torques of М12, ..., М56 and group

of the concentrated horizontal load Рв(н)1, ..., Рв(H)5,

located in sections of an adjunction of intermediate

vertical communications.

At determination of parameters of power loading of

vertical communication (Fig. 2) basic reactions of Rвi,

RHi, are unknown, and the bending moments MBi and

Mиi. For such scheme can be worked out only three

equations of balance:

1

21 ( ) 0

6 3

B Ta Bi Hi Ti Ti Hi

B Hi

М M M M M R l

q qL l

1 1 ( ) 03 6

HB Bi Hi Ti Ti

B HBi i

М M M M M

q qR l L l

(2)

2B H

x i i Bi Hi

q qP L l R R

Fig. 3 The scheme of loading of the upper and lower beams.


143

We will receive the additional fourth equation after

the solution of the differential equation of a bend of

section of the communication loaded with the

moments and external efforts: 22

32

1

( )2 3i

H H Bc Hi

q Z q qd XЕJ R Z L Z

dZ l

(3)

where X—deflections of sections of vertical

communication.

Regional conditions for this equation are, at Z = 0:

,)0(Yi

Hi

C

RX

(0) Hi Ti

Hi

M MdX

dZ K

Having made a number of transformations of Eq.

(2), as a result we will receive system of the algebraic

equations for definition of unknown RHi, RBi, MНi, МВi:

3 23) 1 11

1 11

1 1

1 11

1*

(

6 2

(4 )20

*2 2

(2 ) ( )30 6

HiC Hi Bi Bi C

Hi Bi Hi

c C BiH

Bi Hi C

B Hc Bi cB Ti Ti

Bi Hi c Hi

REJ C C l K EJ ll

C C K

EJ EJ l l Klq

C K EJL l

EJ l K EJ ll EJq M M

C K EJ K

(4)

HiHBBi RqqlL

R )(2

11

BTiHBHi

C

BiBi Mqq

lLR

EJ

KlM

)(62

111

)(6

)2(62

1111

1HB

iHBHi

C

BiHi qq

lLqq

lLRl

EJ

KlM

HTi

BTi

C

Bi MMEJ

Kl 2

21

We will consider now a tension of the bottom bar of

the folding panel which is loaded with group of the

concentrated efforts of RH1 ÷ RH5 and torques of M12 ÷

M56 caused by existence RHi and MHi, determined by

formulas (4), but taken with the return signs. As on

the settlement scheme (Fig. 1) in a middle part of the

bottom bar Б3, support is entered, (such design of a

bar is recognized by SU956328 invention) that when

performing calculation of the bending moments of М12

÷М56 we will consider it as the beam lying on three

support Б2—БЗ—Б2. Then in reference points from

action of forces Р62 and Р63 will arise according to

reaction Rа, Rб and Rв. In this case it is possible to

write down:

Rа + Rб + Rв =

RH1 + RH2 + RH3 + RH4 + RH5

5612М Ra (L1 + L2 + L3) - Rб (L4 + L5 + L6) - RH1

(L2 + L3) - RH2L3 + RH4L4 + RH5 (L4 + L5) = 0 (5)

Y1 (L1 + L2 + L3) = B

B

R

C

where Y1(X)—function of a deflection of sections of a

bar on considered sites.

For the decision of system of Eq. (5), previously we

will work out the equation of the bending moments for

a site Б2—Б3 (Fig. 1):

)()()(

21121112

12

LLXRLXRXRdX

XydEJ HHaH

(6)

As a result of consecutive integration of this

equation, we will receive the equations by definition

of reaction Rа, Rб and RB:

1 2 3 1 2 1 2 3

1 2 33

1 2 3

1 2 3 2 1 2 341 2 3

4 1 2 3 4 5 1 2 3 4 5

( 2 ) (2 2 )112

1( )

6[ ( 2 2 ) ( 2 )

( )

( ) ( )]

H Ha

H

B

HHi H

B

H H

R L L L R L L LR

EJ L L LC L L L

EJR L L L R L L L

C L L L

R L L L L R L L L L L

5 4 4 5 4 5 2 3 2 31 2 3

1[ ( ) ( ) ]a H H H HR R R L R L L R L L R L

L L L

1 2 3 4 5B H H H H H a bR R R R R R R R

The received values of load allow known methods

[6, 8, 10] to calculate М12 ÷ М56 torques, therefore,

and tension in the bottom bar. Calculation of the

moments М12 ÷ М56 for the top bar is similar described

above with that only a difference that the last has no

third intermediate Б3 support.

For calculation on durability of face boards of a

body which are structurally executed as well as

folding panels, we will use the settlement scheme (Fig.

4).

The board is loaded through a grid connecting a

framework with the distributed loading with specific

pressure qув and qун. On average rack С2 further efforts

are transmitted 0.5Рг, caused by work management

mechanism hinged side panels. When performing

calculations on durability of a face board previously

we will establish the parameter of power loading of all

vertical racks of С1 and С2, and then the top bar. For a

rack of C1 (Fig. 4), we will accept the scheme of the

console beam loaded with distributed load of 0.5В1 =

qyB to 0.5В1qун, changing on height linearly. The top


144

Fig. 4 Calculation scheme of the end boards and racks.

support of a beam is executed pliable with coefficients

of rigidity Стс to action of the radial load arising, in a

place of coverage of a rack lateral put-on sides Borg’s

basic arm with the folding panel and Kтс to action of

the bending moments. For simplification we consider

that the rack of C1 is jammed on the main face board

of a platform of a body as the last is executed by the

very rigid.

For determination of coefficient of rigidity of Стс

we consider that the top bar of a board is located the

ends on two hinged support loaded with single

concentrated loading, enclosed in the plane passing

through an axis of a bend of a rack of C2. Using

recommendations [13, 14], for the left rack of C1 we

will write down the following equation:

1 2 32 2

1 2 3

3 ( )

( )

TB

ТС

EJ B B BС

B B B

For determination of coefficient of rigidity of Kts,

we assume that to a piece of the top bar placed

between the next racks of C1 and C2, the single

moment is enclosed. From the action of such a

moment occurs plot twist beam and in this case [11],

1 2

1 2

( )TOBb

TC

GJ B BK

B B

From the accepted settlement scheme (Fig. 4) which

is statically indefinable, unknown basic reactions Rво,

Rно and bending moments Mво and Mно. For definition

of such unknown we will work out the equations: 2

1 10 1 0

2 6 3yB yH

a BO HO

q qB lM M M R l

21 1

1 02 3 6

yB yHB BO HO BO

q qB lM M M R l

and two additional equations following from the

solution of the differential equation of a bend of a rack

of C1:

)62

(2

3

1

2

1

2

2

Zl

qqZqBZR

dZ

YdEJ yByHyH

HOT

(7)

For the solution of Eq. (7), the following regional

conditions are chosen: at Z = 0: ;0)0(

)0( dZ

dYY at

Z = l1: TC

Bi

C

RlY )( 1 , .

)( 1

TC

Bi

K

M

dZ

ldY

As a result of transformations of the equation, we

will receive system of the algebraic equations in a

look 2

1 10 0 0 1

21 1

0 0 0 1

3 40 0 1 1 1

2 30 0 1 1 1

( ),2 6 3

( ),2 3 6

2(4 ),

6 240

(3 ).2 48

YB YHB H H

YB YHB H B

B HYH YB

TC T T

B HYH YB

TC T T

B l q qM M R l

B l q qM M R l

R R l B lq q

C EJ EJ

M R l B lq q

K EJ EJ

(8)

Solving system of Eq. (8) widely known way, we

will receive 311 1

0 3 31 1

1 10 0

2 21 1

0

(6 0.4 )

4(6 ) + (6 0.1 )

( )4

(3 )2 24

YH T TCH

T TC YB T TC

B YH YB H

TCB Hl YH YB

T

q EJ l CB lR

EJ l C q EJ l C

B lR q q R

K l lM R q q

EJ


145

1 10 0 0 1 (2 )

12H B B YB YH

B lM M R l q q (9)

Dependences (9) allow to execute numerical

calculations of tension arising in racks C1. For

calculation of parameters of power loading of average

vertical racks C3, we will use the settlement scheme

shown in Fig. 4. For the accepted settlement scheme

which is statically indefinable, unknown basic

reactions 11 , HB RR and the bending moments 1BM

и 1HM . For definition of these unknown, we will

work out two equations of balance in a look

0)36

(22

21211111

YHYBPГ

HHBa

qqBBl

ePlRMMM

(10)

0)63

(22

211111

YHYB

BPГ

HBB

qqBBlR

ePMMM

(11)

and two additional equations, following from the

decision differential the equations of a bend of a rack: 22

31 212

1

( ) ( )2 2 6 2

YH YH YB Г PT H Г

B B q Z q q P ed YEJ R Z Z Z Z

dZ l

(12)

meeting regional conditions at Z = 0:

0)0(

)0( dZ

dYY and at Z = l1,

1

12

( ) ,B

B

RY l

C 1 1( ) B

TC

dY l M

dZ K .

Having made a number of transformations of Eq.

(12), we will receive the following equations: 31 12

1 1 1 1 2 13 31 1 1 1

6 0.4 )16 ( )

4( 6 ) (6 0.1

T B YHH r P B

B T Yb T B

EJ l C qR P e l C B B l

C l EJ q EJ l C

1121

1 )(4 HYHYBB Rqql

BBR

(13)

21 1 21 1 1 1 (3 )

2 24TC

B H YH YB r pT

K l B BM R l l q q P e

EJ

1 1H BM M R

The removed formulas allow to calculate the load

attached to bearing elements the put-on sides of

boards of a body, therefore, and to define numerical

values of tension arising in them. It is known also [6,

8, 10, 17] that except static components of the efforts

operating on elements the put-on sides of boards of a

body, in the course of the trailer movement, the listed

elements will be subject also to dynamic loading.

Therefore we will consider such task with use of the

settlement scheme shown in Fig. 1.

Taking into account the accepted assumptions on

dynamic model (Fig. 1) of the equation of kinetic and

potential energy will assume an air:

222

22

2222

22322

)()(

)(

)()(

)()(

2

1

ПKTПKTKTT

ПTKП

TKeDKTП

TKПDKTKTKT

JJJ

l

llrm

llrmrm

T

2 21( )

2 K K П ПП K K (14)

Using Lagrange’s equations and a formula (14), we

will receive system of the differential equations in a

look 2

2 2

( )

( ) ( ) ( )K КП K K П П П П T КП

К П П П П П П П П П T П П П

J K J m l J

J m l m l J K m l J

(15)

where 2 2 2( )КП K K П e П K ПJ m l m l l J J .

It is known [15, 16, 18] that spatial fluctuations of

vehicles happen at the expense of a micro and macro

profile of periodically repeating roughnesses or single

impulsive roughnesses of paving. We will determine

(15) dynamic components of the moments attached to

folding lateral panels of a body in case of

overcoming of repeating and impulsive roughnesses

by system.

In case of overcoming by the trailer of the

periodically repeating roughnesses, function of

accelerations of angular fluctuations 2

2

)(dt

dt T

T

, it

can be presented in the simplified look:

1,2

( ) ( )( ) cos

2

nЛ П

T i i HiK

Z t Z tt a t

B

(16)

where 2π П

HH

V

l —circular frequency of repetition of

the longest (length lH) of roughnesses of a conditional

paving;

VП—the speed of movement of the trailer;

ai—amplitudes of harmonicas of accelerations of

kinematic indignation of angular fluctuations of the

trailer;

n—number of the last considered harmonica.

For the subsequent calculations of folding lateral

panels on durability, it is necessary to know sizes of

elastic angular deformations φП. Therefore, accepting

entry conditions zero, in system of Eq. (15), we find

the decision only on the generalized coordinate φП.

Considering that function )(tT registers in the form


146

of a row, for each harmonious component we look for

the system decision in a look ( ) cosKi Ki i Ht a t

( ) cosПi Пi i Ht a t (17)

After substitution of the last functions and their

second derivatives )(tK and )(tП in system (15)

and reductions of all members of the equations on tHcos , we will receive system

2 2 2 2 2 2 2

2 2 2 2 2 2

2 2 2

( ) ( ) ,

( ) ( )

( )

Ki K КП H ПI H П П П i H КП

Ki H П П П Пi П H П П П

i H П П П

a K J i a i J m l a i J

a i J m l a K i m l J

a i m l J

(18)

In the last system of the algebraic equations

unknown are coefficients Kia and Пia . As a result

of the decision of system (18), we will receive the

following expression: 2 2 2 2 2 2

2 2

2 2 2 2 2 4 2 2 2

( )( ) ( )

( ) ( ) ( )K КП H П П П H П П П КП

Пi i H

K КП H П П П П П H П П П

K J i m l J i J m l Ja a i

K J i K i m l J i J m l

(19)

Then the equation of the compelled elastic

fluctuations of mass of cotton raw Пm

in a body

together with folding panels will have an appearance

n

iHПiП tiat

2,1

,cos)( and the maximum value of

the dynamic elastic moment YKM operating on each

folding lateral panel, approximately will be equal

1,2

0.5n

YK П Пii

M K a

(20)

It is known [5, 12, 15] that the most adverse power

effect on elements of lateral folding panels will be

made by harmonicas of those circular frequencies Hi

for which there will correspond big amplitudes Пia .

At resonant angular fluctuations of the trailer such

conditions will be created at approach of a

denominator of a formula (19) to zero, then resonant

frequency will be equal 2

2 2 2

22

2 2 2 2 2

2 2 2 2

( )

2( )( )

( )

4( ) ( )

( )( )

РЕЗ КП П K П П ПH

П П П К K П e K

КП П K П П П

П П П K K П e K

П K

П П П K K П e K

I K K m l Ii

m l I т l m l I

I K K m l I

m l I m I m l I

K K

m l I m l m l I

(21)

Impulsive change of function )(tT is possible in

case of overcoming of single roughnesses of a paving

in the form of holes or ledges, thus the last the

manifestation are characterized by dependence [15],

)()()( 00 TTT ttat where Ta —amplitude of an impulse of angular

acceleration by the cart fullering, caused by shock

interaction of wheels of the trailer with roughness of

the road;

—time of duration of an impulse of acceleration.

For a considered case, accepting entry conditions

the zero ПУ(0) (0) (0) 0KY KY ПУ , the decision

of system (14) it is feasible a method of operational

calculation on one variable. We will enter

designations ( ) ( ); ( ) ( )KY KY ПУ ПУt P t P

then 2 2( ) ( ); ( ) ( )

( ) (1 T

KY KY ПУ ПУ

pT T

i p P t P P

t a e

Thus we will write down the image of system (15)

in a look 2 2 2( )( ) ( )( )

(1 )T

KY K КП ПУ П П П

PТ КП

P K P J P P J m l

а е J

(22)

2 2

2 2

2

( )( )

( ) ( )

(1 )( ).T

KY П П П

ПУ П П П П

PT П П П

P P J m l

P K P m l J

a e m l J

We solve such system of the equations concerning

image function as usual system of the algebraic

equations, as a result we will receive look expression: 2

2 2 2

4 2 2

( ) (1 )

( ) ( )

( )

ТРK П П П Т

ПУ

K КП П П П П

П П П

K m l J а е

K P J K Р т l J

P m l J

(23)

For search of the original of the last function it is

necessary to find roots of a denominator of the Eq.

(23). For this purpose, having equated it to zero, we

will receive

КПППППK

KeПKKПППKП

KeПKKППП

ПППK

JKJlmK

JlmlmJlmKK

JlmlmJlт

уlmKiP

)(

))((411

))((2

)(

2

222

222

2

2,1

According to the theorem of decomposition [13] we

will find the function original YП

:


147

2 2 2

2 2 2 21 2

(1 )( ) ( )( )

( )( )

T

У

PT П П П K КП КП

П

a e m l J K P J J PP

N P P P P

(24)

where ).)(( 222ReПKKППП JlmlmJlmN

We will similarly receive the decision from two

other roots :2ip

2 2 2 2 2 2

2 1 1 2

21 2 2 2 1 1

(0) ( )( )( )

cos cos ( cos cos

T KПУ ПУ

П П П e K

T T

a Kt

m l т l J P P P P

P p t p t p p t p t

(25)

The maximum values тПУ within time Tt are

reached at 1cos 1.0p t and 2cos 1.0p t , and

peak maximum values at Tt at

2)(coscos 11 Ttptp and

2)(coscos 22 Ttptp . Therefore value тПУ

can be written down in a look: 2

2 21 22 2 2 2

2 1 1 2

2 ( )( )

( )т Т П П ППУ K K

а т l JP K P K

N P P P P

(26)

Therefore, the elastic moment arising on bearing

elements of the folding panel of a body of the trailer

from action of mass of cotton raw on it: тПУПY KM (27)

Thus, the total moment arising from action on the

panel of periodically repeating and impulsive loading,

it is possible to present a formula

1,2

0.5n

П тУ УК У П ni П ПУ

i

M М М K a K

(28)

The removed formulas allow to calculate dynamic

components of tension arising in bearing elements the

put-on sides of boards of a body.

For calculation of tension arising in bearing

elements of a body, we will use their geometrical sizes

and power characteristics (Figs. 2-4) [11, 13]:

l1 = 102.0 sm, L = 462.0 sm, le = 50.0 sm, C = 7 pcs,

L1 ÷ L6 = 77.0 sm, eВ = 3.6 sm, eН = 3.2 sm, JХВ = 72.6

sm4, JХН = 66.4 sm4, Jk(П1 ÷ П2)=48.94 sm4 3 3 8

1 2

3 3 3 4

4.0 10 ;5.0 10 ;6.0 10 ;

7.0 10 ;8.0 10 ;9.0 10 ;1.0 10 N

B BP P

Cotton raw weight in a body of the trailer for each

case PB1 and PB2 also got out equal 700, 1,400, 2,100

and 2,800 kgfs.

By a technique [13] numerical values qB and qH are

determined depending on the average specific pressure )(3 Zq C

X , falling on the folding panel of a body (Table 1).

Values of the module of elasticity E of cottons raws,

calculated on dependences [1] for a row PB1 = PB2 =

4.10·103 ÷ 1.0·104 N respectively made: 3 3 3 3

3 3 3 2

4.05 10 ;4.82 10 ;5.58 10 ;6.35 10 ;

7.11 10 ;7.88 10 ;8.64 10 N/m

For calculation of flexural rigidity of sites of the top

and bottom bars CBi and CHi, and also their torsion

rigidity KBi and KHi we will use geometrical

parameters of the folding panel (Table 2).

Practice of operation of the tractor trailer 2

PTS-4-793A [11, 13] shows that the nominal amount

of cotton raw in its body makes 2,100 kgfs.

For such quantity of a raw the following parameters

are characteristic: 3 2 2

2 2

7.11 10 N/m , 8.14 10N/m

2.61 10 N/m

B

H

E q

q

Using dependences (4), we will calculate basic

reactions RB1, RB2, RB3 which are respectively equal

6.07·102, 7.20·102, 8.35·102 N. These reactions allow

Table 1 Results of calculations of the distributed loading of the panel.

Numerical values of parameters of loads of the folding panel

of a body

PB1 = PB2

(N)

3( )CXq Z

(N/m2) qB (N/m2) qH (102 N/m2)

4.0·103 9.04·10 4.08·10 1.66

5.0·103 1.03·102 4.35·10 1.80

6.0·103 1.34·102 6.03·10 2.12

7.0·103 1.59·102 6.70·10 2.38

8.0·103 1.81·102 8.14·10 2.61

9.0·103 2.1·102 9.04·10 2.88

1.0·104 2.26·102 1.02·102 3.09

Table 2 Geometrical parameters of the panel.

Site of

panel

СВ

(N/m)

СН

(104N/m)

КВ

(N·m/rad)

КН

(104N·m/rad)

L1 2.40·105 7.55 1.224·105 9.44

L2 2.40·105 7.55 1.224·105 9.44

L3 9.39·104 2.95 7.65·104 5.90

L4 7.42·104 2.33 6.80·104 5.24


148

on formulas [18]:

1 2 1 2 1 3

12 1 1 1

23 1 1 1

34 1 1 1 2

3(2 2 2 )

( )

(2 2 )

(3 3 2 )

B B iП П B B B B

BB П

Bi B П B

Bi B П B B

LR R R R R R

L

М L P R

M L P R R

M L P R R R

(29)

to define numerical values of the moments M12, M23,

and M34, which sizes respectively made: 5.61·102,

2.21·103 and 2.60·103 N·m.

In a similar way moments М12, М23 and М34 are

calculated. For the bottom bar which does not have the

third support in a point of Б3 (Fig. 1) which

respectively made 2.74·102, 4.77·103 and 5.86·103

N·m. The analysis of the received results shows that

numerical values of the moments of the greatest sizes

in middle parts of the top and bottom bars reach

2.6·103 and 5.86·103 N·m. It is clear, that such

moments will cause considerable tension in bars.

Therefore for unloading of the bottom bar we will

enter an additional support with rigidity close to

rigidity of the Б2 support (Fig. 1). We will make

calculation of values of reactions Ra, RБ and RВ and

also the moments М12, М23 and М34, operating in

sections of the bottom bar of the folding panel: 32 1 2

312 1

323 1 1 2

334 1 2 3

308 (2 2 )1.38 10 N

231 2

( ) 1.77 10 N m

2 ( ) 2.31 10 N m

( ) 2 3.91 10 N m

H H H HBa b

i a H

i a H H

i a H i H i H

R B R R RR R

B

M L R R

M L R R L R

M L R R L R L R

(30)

The analysis of the obtained data testifies that with

introduction of an additional support of the bottom bar

of effort on its ends decrease by 1.14 times in

comparison with a bar without support. However the

additional support perceives considerable efforts. Thus

bending moment in its section in comparison with the

bending moment of a bar in the same section, not

having a support, decreases by 1.52 times. On

numerical values of the moments attached to bars, and

their geometrical characteristics probabilistic values of

the flexural tension (Table 3) are calculated.

It is visible that tension in the top bar not only does

not exceed a limit of fluidity of a material from which

the last is executed on a natural body of the trailer

(steel 25ПС MППTK 260 ), but also is 3.24 times

lower than it.

Therefore for decrease in metal consumption of the

top bar with preservation of its bearing ability it is

recommended to lower the moment of its inertia on

the average by 36% that will allow to save 2.5 kg of

metal on one body.

Considerable tension arises in the bottom bar of the

folding panel (180.86 MPa) therefore it is

recommended to establish the additional support

reducing such tension on the average for 34% in its

middle part. For calculation of face boards on

durability we will use the following basic data:

l1 = 102.0 cm, В1 = В3 = 77.0 cm, В2 = 59.0 cm, eP

= 13.0 cm, Zr = 22.0 cm, JXB = 13.74 cm4, JXС1 = 4.55

cm4, JXС2 = 16.03 cm4, СТС1 = 3.37·105 N/m, СТС2 =

2.29·105 N/m, КТС1 = 7.40·104 N·m/rad, КТС2 =

1.70·105 N·m/rad, Е = 7.11·103 N/m2, qВ = 8.14·10

N/m2, qК = 2.61·102 N/m2.

On dependences (12) reactions and the bending

moments in racks (Fig. 4) are calculated: for a rack С1

- RHO = 2.25·10 N, RBO = 3.0·10 N, MHO = -3.32·10

N·m, MВO = -2.49·10 N·m, for rack С2 - RH1 =

1.83·103 N, RB1 = 1.79·103 N, MH1 = -3.73·10 N·m,

MB1 = -1.03·10 N·m.

For calculation of tension in the top bar of a face

board the last is representable in the form of the beam

placed on support A and Б, and we will determine by

known methods basic reactions of Ra, Rb and bending

moments in sections, M12 and М13, where C1 and C2

racks on dependences are established:

Table 3 Calculated values of tension.

Bar site Top bar

σ (МPа)

Bottom bar

σ (МPа)

Without the

additional

support

With an

additional

support

L1 17.28 84.56 54.32

L2 68.21 147.25 70.98

L3 89.23 180.86 120.6


149

0 1 1 1 2

12 0 1 1 1 0

23 1 2 0 1 2

( )

( )

( )( )

B B Ba b

B a B a

B a B

R B R R B BR R

BM R B R B B R R

M B B R R R B

(31)

As a result of the solution of Eq. (30), the

following values are received: 2 2

12

2 223

1.49 10 N, 1.49 10 N,

1.26 10 N m, 3.48 10 N m

a bR R M

M

According to the obtained data with the help of

geometrical characteristics of the top bar tension

arising on its sites of B1 and B2, which respectively

made 39.9 MPa and 120.0 MPa are calculated.

Tension in the top bar is highest on a site B2 in a zone

of an arrangement of the mechanism of management

of lateral folding panels, however they are lower than

the allowed (steel 25ПС МПаТК 260 ) by 2.1

times. Therefore it is possible to consider that the

section of the top bar with Jx = 13.74 cm4 is nominal.

For calculation of the turning moments of МУК and

М/У, operating on folding lateral panels of the trailer

2PTS-4-793A in the course of its movement on

characteristic roads and off road terrain in field

conditions of tension necessary for calculation arising

in bearing elements of its body, we use the following

basic data:

JП = 98.8 kg·m·s2, JK = 7.988 kg·m·s2, KK =

5.48·107 N·m/rad, KП = 0.187·108 N·m/rad, lП = 0.2

m, тП = 285.0 kgf·s2/m, тК = 99.8 kgf·s2/m, СТ =

1.38·103 N/sm, ВТ = 0.63 m, lП = 1.02 m, lК = 0.5 m,

φ = 0.223 rad, V = 13.85 km/h, τ = 0.7-1.4 s, t =

1.89-2.35 s.

In these parameters of dynamic model (Fig. 1) and

frequency of the compelled fluctuations of system

ranging from 0 to 30 rad/s with an interval 0.5 rad/s

with use of a program complex on the computer

amplitudes of ani and φmПУ are calculated and on Eqs.

(19) and (26), the elastic moments МУК and М/У are

calculated.

The analysis of the obtained data (Table 4) shows

that the greatest moment of МУК, attached to folding

panels, corresponds to frequency 12 rad/s with and

7,400 N·m makes, and at frequencies below 6 and

higher than 15 rad/s with decreases. With the most

characteristic operational frequencies of hook-on

vehicles 6-15 rad/s about arithmetic-mean value Мук =

2,351 N·m.

It is known that at a choice of optimum power

characteristics of the mechanism controls of folding

lateral panels of a body of the trailer 2PTS-4-793A

that the moment Mук, attached to the folding lateral

panel from effect of condensed cotton raw, reaches

6,240.0 N·m. Therefore, the total moment ΣМук,

operating on the panel when overcoming periodically

repeating roughnesses, will be made 2,351.0 + 6,240.0

= 8.75 × 103 N·m, and the coefficient of dynamics will

be equal 1.36. In case of overcoming by the trailer of

impulsive roughness, average value will make М'у =

3,466.9 N·m, summary moment ΣМ'у = 6,400.0 +

3,466.9 = 9,866.9 N·m, thus coefficient of dynamics is

equal 1.55.

Knowing geometrical characteristics of sections of

the bottom and top bars, in view of that the bottom bar

perceives bending moment 2.59 times bigger, than top,

we will define numerical values of dynamic tension in

bars at impact on the panel of the moment Myk =

2,351.0 N·m. Data of calculation are presented in

Table 5.

It is visible (Table 5) that in the presence of an

additional support of the installed folding panel (Fig. 1)

Table 4 Settlement parameters.

ω (rad) ani (10-4 rad) Мук

(N·m) φm

ПУ (rad) М/У (rad)

6 1.2 1,116.0 -1.6·10-4 -2,291.1

7 1.3 1,202.5 -1.8·10-4 -3,333.5

8 1.5 1,387.5 -1.2·10-4 -2,340.5

9 1.8 1,665.5 -2.2·10-5 -423.6

10 2.4 2,220.0 8.9·10-5 1,652.02

11 3.6 3,330.0 1.6·10-4 3,072.4

12 8.0 7,400.0 1.7·10-4 3,279.0

13 4.6 4,255.0 1.1·10-4 2,179.2

14 2.4 2,220.0 1.0·10-5 197.7

15 1.6 1,480.0 -1.0·10-4 -1,872.6

MCP 2,351.0 3,466.9


150

executed on the patent SU956328 on bottom bar,

tension in comparison with a bar of the panel not

having a support of tension is 1.47 times lower.

Technical and economic advantage of the offered

design of a dumping body in comparison with known

technical solutions consists in the following. It is

known that the most important parameter from which

efficiency of use of dumping trailers of the lightweight

freights intended for transportation significantly

depends the mechanization of the labor-intensive

processes directed on exceptions of manual skills of

occupied at works of connected with leveling and

consolidation of lightweight freights in bodies of

trailers is. Therefore the considered design of a body

allows to exclude completely, first, manual skills and

by that to reduce the service personnel, secondly, to

reduce idle time of the trailer being under loading

from 7.5 to 2.5 min and in the third, due to use of a

technical solution according to the patent SU956328

to reduce metal consumption the put-on sides of

boards in comparison with a known design of a body

supplied with put-on sides boards by 5.6%.

4. Results of Research

On the basis of the above it is possible to draw the

following conclusions and offers:

(1) The analysis both domestic, and foreign designs

of autotractor trailers supplied with put-on sides

boards and the lightweight freights intended for

transportation shows that the last possess the essential

shortcoming, consisting, in low reliability of bearing

designs which under operating conditions under action

both static, and dynamic load are subject not only to a

bend, but compression and stretching, Such power

load causes high tension in their bearing elements, as

leads not only to their destruction, but also all the

Table 5 Tension in bars of the folding panel.

Bar МУК (N·m) М/У (N·m) σУК (МPа) σУ (МPа)

Top 907.7 1,338.5 28.01 41.3

Bottom 1,443.3 2,128.4 44.5 65.6

put-on sides of boards as a whole. As a result of the

enterprise operating such equipment incur

considerable labor and financial expenses connected

with repair and restoration the put-on sides of boards

of bodies.

(2) Considering the above at the level of the

invention (SU956328) the technical solution allowing

to raise not only technical but also operational

reliability the put-on sides of boards of a body of the

dumping trailer intended for transportation of

lightweight freights is developed. For establishment of

a tension of such designs and to calculation of rational

parameters for their modernization settlement schemes

and a technique on their justification in conditions

both static, and their dynamic loading are created. So,

the carried-out calculations, in relation to the

autotractor trailer of model 2PTS-4-793A with use of

a technical solution according to the patent SU956328

showed that as a whole tension in the bottom and top

bars of folding panels of a body decreases by 1.47

times and does not exceed strength of a material at

numerical value of coefficient of dynamics equal 1.55.

Therefore, the durability the put-on sides of boards

and in particular with use of an additional support of

their bottom bars of springs will be much higher than

their folding panels, than at a serial sample of the

trailer of the PTS-4-793 model.

In too time the considered design of a body in

comparison with a known serial design of the

PTS-4-793 trailer allows to exclude completely, first,

manual skills and by that to reduce the service

personnel, secondly, to reduce idle time of the trailer

being under loading from 7.5 to 2.5 min and in the

third, due to use of a technical solution according to

the patent SU956328 to reduce metal consumption the

extension of boards in comparison with a known

design of a body supplied with put-on sides boards by

5.6%.

(3) Results of research are recommended to the

domestic and foreign motor transportation enterprises,

the autotractor industry and the scientific and design


151

divisions working in the field of tractor and

automotive industry for studying and the analysis of

offered designs for the purpose of possible further of

their widespread introduction in practice.

References

[1] A.D. Glushhenko, E.V. Slivinskij, Dynamics and Strength of the Transport System for Carrying Light Loads, Fan, Tashkent, 1988, P. 116.

[2] M.S. Vy’sockij, L.I. Dobrax, Z.L. Sirotkin, Automobile and Tractor Trailers, Mashgiz, 1962, p. 161.

[3] V.V. Osingurov, Dump Trucks, Mashgiz, 1952, p. 124. [4] S.P. Markelov, Yu.N. Kry’lov, Modern Designs of Trailers

in the Capitalist Countries, CNIIavtoprom, 1976, p. 118. [5] D.P. Velikanov, Development of trains and their dynamic

qualities, Automotive Industry 2 (1960) 22. [6] S.S. Dmitrichenko, Investigation of the fatigue strength

of tractor-trailers, Tractors and Agricultural Machinery 6 (1986) 16-17.

[7] Ya.X. Zakin, Applied Theory of Motion of Trains, Transport, 1987, p. 286.

[8] A.G. Nazarenko, Dynamics of tractor train and develop methods and apparatus for testing automotive trains fluctuations, Doctor Dissertation, Novosibirsk, 1963, p. 46.

[9] M.I. Zaks, The state of stress at the nodes automobile frames at its torsional, in: Proceedings of NAMI, 1963, pp. 38-60.

[10] V.B. Proskuryakov, Dynamics and Strength of Frames

and Housings of Transport Vehicles, Mashinostroenie,

1972, p. 229.

[11] E.V. Slivinskij, The study of vibrations and force loading

of tractor-trailers 2PTS 4-793A, Candidate Dissertation,

Technical Sciences, SXI, Alma-Ata, 1977, p. 165.

[12] A.D. Glushhenko, Yu.V. Grohovskij, E.V. Slivinskij, The

study of vibrations and force loading of tractor-trailers

2PTS 4-793A, Tractors and Farm Machinery 4 (1980)

8-11.

[13] E.V. Slivinskij, Improving performance trailed vehicles

on the basis of effective scientific and technical solutions,

Doctor Dissertation, GTU, Oryol, 2010, p. 334.

[14] Sh.V. Israilov, Improving performance trailed vehicles on

the basis of effective scientific and technical solutions,

Doctor Dissertation, Technical Sciences, TIIIMSX,

Tashkent, 1967, p. 26.

[15] I.M. Babakov, Theory of Oscillations, Nauka, 2000, p.

159.

[16] E.V. Slivinskij, S.V. Ascaturov, Investigation seal of

cotton in the back of a tractor trailer, Mechanization of

Cotton 6 (1979) 10.

[17] V.I. Feodos’ev, Strength of Materials, Nauka, 1998, p.

544.

[18] Research and Development of Recommendations for

Trailers with Increased Capacity for Transportation of

Cotton, Report VCNTI, No. Gos. Reg. 80047100, Inv. №

0040486, 1983, p.195.

Documents

Modernization of Bodies of Dumping Trailers with Put-On ... · PDF fileModernization of Bodies of Dumping Trailers with ... budgetary study is carried out to Yelets state ... Fig