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4
Section 5. Mechanics
Shermukhamedov Abdulaziz Adilkhakovich, Professor, Head of Department of Reliability of Land Transport Systems Tashkent Institute of Design, Construction and Maintenance of Automotive Roads,
E-mail: sheraziz@mail.ru Annakulova Gulsara Kuchkarovna, Academy of Sciences of the Republic of Uzbekistan Mechanics and seismic stability of structures after M. T. Urazbaev Leading Scientific Researcher, Scientific Research Center E-mail: Annaqulova-g@mail.ru Astanov Bekzod Jangiboevich, Junior Scientific Researcher E-mail: bekboy38@mail.ru Umarova Dilrukhsor Fakhriddinovna, Scientific researcher Tashkent Institute of Irrigation and Agricultural Mechanization Engineers
DEFINITION OF KINEMATIC AND DYNAMIC PARAMETERS OF HYDRO-HINGED SYSTEM OF A TRACTOR OF HIGH LOAD-CARRYING CAPACITY
Abstract: In article the kinematics of mounted hydraulic system of energetically saturated tractor with use of a method of the closed vectors is considered. The system consists from flat lever seven links the mechanism with rotating kinematic steams of links and copes the power hydro cylinder informed with a hydro drive of a tractor and the mathematical model of dynamic calculation of tractor mounted hydraulic system of the high load-lifting capacity is offered. The received results qualitatively close describe real process of work of mounted hydraulic system.
Keywords: universal plough tractors, hydro-hinged system, hydraulic cylinders, kinematic, dynamic, method.
Modern universal plough tractors are equipped with The HHS is controlled by a separate-aggregate
diesel engines of increased power. In this regard, the hydraulic drive of a tractor. The HHS of modern en-hydro-hinged system (HHS) of power tractors should ergy universal plough tractors should provide a load-have a high load-carrying capacity. This condition is pro- carrying capacity of 3.0, 3.5 tons, (30 kN, 35 kN) or vided by the use of a lever seven-link mechanism with more. The effective work of the HHS of a tractor es-rotating kinematic pairs of links, which is controlled by a sentially depends on the correct calculation of lifting power cylinder coupled to the hydraulic drive of a tractor. force, the definition of necessary and sufficient number
and types of hydraulic cylinders to be installed, as well as the substantiation of their main parameters. For this purpose it is necessary to carry out dynamic calculation of the HHS. In this paper, the dynamic calculation of the HHS is considered.
Consider the kinematics of the HHS (Fig. 1) and determine the displacement, velocity and acceleration of the angles of its links.
When pressure acts on the piston of hydraulic cylinder, the rod, i. e. the link l2, becomes longer or shorter, as a result, the link l3 rotates by an angle y . Using the well-known technique [1; 2], we write the closure condition of the vectors for AABS (Fig. 1):
The projection on the XOY coordinate axis gives:
[l, cos fa + l, cos fa = l, cos fa
I 1 Vi 2 V2 3 V3 (1)
[lj sin fa +12 sinfa, = 13 sinfa3 Excluding from (1), y3 and y2, respectively, we obtain: li +122 + 2l 12 cos (fa -fa ) = i23,
fa = fa - arccos
^3 - 12 - 12 '
V zti 42 y
l23 + li - 2l1l3 cos(fa -fa ) = l22, fa = fa + arccos
rl2 +12 -12?
2£ ■£
V 1 3 y
Figure 1. Kinematic scheme of the HHS. 2, 3, 5, 6, 9, 10, 12 - are the links of the lever mechanism; 1, 4, 7, 8 - artificially introduced links of the lever mechanism
GM - load weight.
To define the angular velocity the derivative from (1) is taken.
-£1 sinfatt^ -£2 sinfatt>2 + £2 cosfa = -£3 sinfa®,
[£1cos01®1 + £ 2cosfa2®2 + £ 2 sinfa, = £ 3cosfa3®3 As y1 = const, w1 = 0.
Excluding from (2), io2 and w3 respectively, we obtain:
®2 = 7ctg (2 , ®3 = , ■ h . \ .
¡2 /3sin (02 -fa )
(2)
To define the angular acceleration, the derivative from (2) is taken.
| -l2 cos02®22 -12 sin02£2 +l2 cos02 - 2/2 sin02tt>2 +13 cos03®32 + l3 sin03£3 = 0 I-l2 sin02tt>22 +12 cos02£2 + i2 sin02 + 2Z2 cos02tt>2 +13 sin03tt>32 -13 cos03£3 = 0
(3)
Excluding from (3), £2 and £3 respectively, we obtain:
^2 =
\
^ -®22
l2
V 2 y
2l
^g (02 -03 )-"T
+
l3®32
:, £3 =
l2®2
l
l2 2 l2 sin ( -03 ) 3 l3Sin (03 -02 ) l3Sin (03 -02 )
-®3ctg(03 -0) .
Introduce an artificial link 02 C, its length denoted as l4. Its value can be found by calculating the coordinates of points 02 and C.
Define the coordinates of the point C:
X = l2!cos02 j
Yc = l11 + l21 Sin02 j ,
where l31=l3 + l3', ln - is the length of the segment 02 A.
As 02 (0, 0), define: l4 = ^ Xc 2 + Yc 2 = yjl312 cos2 03 + (( +131 sin03)2 .For A02 AC write: 4 + 4 = ¿4.
Projecting this equation on the XOY coordinate axes, we obtain
[^11cos011 + 131cos03 = 14cos04
[£ 11sin011 +131sin03 = 14sin04
Taking into account that fn = 270 from the first equation we define:
(l>
( = arccos —cos(
V ^ 4
To define w4, e4, l4 and l4, we take the derivative from (4) and with w11 = 0, we obtain
-l31 sin03tt>3 = -l4 sin04tt>4 + Z4 cos(4 [l31 cos (3a3 = l4 cos 04®4 +14 sin (4
Excluding from (5) Z4 and w4, respectively, we obtain:
l
S(03 , l4 = l31®3cos (03 .
Next, we take the derivative from (5)
| -l31 cos03®32 -131 sin03£3 = l4 cos(4 - 2Z4 sin04tt>4 -14 cos04®42 -14 sin04£4 [-l31 sin (f)3a32 +131 cos (3£3 = l4 sin (j)4 + 2Z4 cos 04®4 -14 sin 04®42 +14 sin04£4
Excluding from (6) l4 and e4, respectively, we obtain:
£4 = Y £3 cos (03 - 04 ) - I1 « sin ((/»3 - 04 ) - « ,
l4 l4 l4
I4 = ^ - ¿31®32 cos (03 - 04 ) - I31S3 sin (03 - 04 ) . Consider A02 CK: ¿4 + ^ = .
Like the above-mentioned sequence, carrying out the corresponding calculations, we obtain
(4)
(5)
(6)
05 = 04 - arccos
¿26 - ¿4 - ¿5
6_4_5_
2/ •/
V 4 5 y
, 06 = 04 + arccos
¿6 + ¿4 - ¿5
6_4_5
2/ •/
V Z"C6 ^4 y
^ = -m.ksin ( - 04)- ¿4 cos (06 - 04) ^ = -^4/4 sin ( - 04) - ¿4cos (05- fa)
5 l5 sin (06 - 05 ) ' 6 l6Sin (06 - 05 )
(4 - l4 ) c0S (06 ) - (l4 + 24^4 ) Sin (06 - 04 ) - ^5 c0S (06 - 05 ) - ^6
/5 sin (06 -fa )
(4 - l4 ) c0s (05 ) - (l4 + 2h4^4 ) sin (05 - 04 ) - c0s (06 - 05 ) + ^5
l6sin (06 -05 )
=
=
Introduce the artificial links 020: and 01T, and denote them by the numerals 7 and 8, respectively (see Fig. 1). The length of the links is determined by the coordinates of points 02, 01 and T The coordinates of the point T are:
Xr =16,cos06 j
YT = l6isin06 J '
where l61=l6 + l6.
Since the coordinates of the points are
02(0,0),01(X01, Y02), the length of a link 0201 will be:_
l7 =^XO12 + YO12 ,
and the length of a link 01 T:
l8 ^ .
From A0101T we obtain: £7 + £g = £61.
Projecting this equation on XOy coordinate axes, we obtain
U7cos07 + ¿8 cos08 = ¿61 cos06
l¿ 7sin07 + ¿ 8sin08 = ¿ 61 sin06
Excluding from (7) f6, we obtain: 08 = 07 - arccos
Define w8, £8, ¿8 h /8, similar to the link 02 C
/2 _/2 _/2
^61 7 8
2/ •/
V 7 S y
I
s(06 , ¿8 =161®6cos (06 -0j,
(7)
/ / 2/ ^8 = "f ^6 cos (06 -08 )-"f ®6sin (06 -08 )-®8 , /8 /8 /8
l8 = l8®8 - l61®62 cos (06 - 08 ) - l61^6 sin (06 - 0j .
Further, from A01FT we obtain: + = .
Like the above sequence, conducting the appropriate calculations, the following is obtained:
8
= - arccos
r /2 _/2 _/2 ^ O ' ^n
©„ =
_ 8 sin (010 - 08 ) - 4 C0S (010 - 08 ) „ _ sin (09 - 08 ) - 4 C0S (09 - 08 )
®io =■
^9 =
^10 =
19Sin (010 -09 ) ' 10 110Sin (010 -09 )
( - 4 ) C0S (010 - 08 ) - ( + 2/8®8 ) Sin (010 - 08 ) - ^9 C0S (010 ~ 09 ) - <^0
19Sin (010 -09 )
Sin (09 - 08 ) - C0S (010 - 09 ) + ^
( - 4 ) C0S (09 - 08 ) - ( + 28®8 )
110Sin (010 09 )
(Fig. 2) shows the results of numerical calculation of the change in angles, angular velocities and angular accelerationsofthe2,3and6linksoftheHHS.Incalculation, the following values ofthe links are taken: l1 = 0.415 m, l2= =0.447 m, l3 = 0.2 m, l3' = 0.158 m, l3l =1 0.358 m, l5 = 0.599 m, L = 0.49 m, I' = 0.5 m, I = 0.99 m, L = 0.558 m,
'6 '6 '61 '7 '
l9 = 0.61 m, l10 = 0.711 m, l11 = 0.574 m, l12 = 1.22 m, X01 = 0.292 m, Y01 = 0.476m, ^ = -83° = -1.-448 rad, <p7 = 58° = =1.012 rad.
Thus, the obtained dependences of the change in angles, angular velocities and angular accelerations of the links could be used for dynamic calculation of the HHS.
The HHS of a tractor is controlled by a power cylinder connected with the tractor hydraulic drive. The load force of the HHS is calculated by successively defined forces and moments of the force couple in the link joints under given load located at the conditional point (CG) of the kinematic scheme of the mechanism
(Fig. 1).
We will compose the equations of motion by the method of reduced mass and resistance force to a specific link. Let the link of the reduction is a rod of hydraulic cylinder (Fig. 1), i. e. a link l2=l2 (t). Then the dynamics of the hydraulic cylinder is described by the following system of differential equations [1]
d {mdV 2/2 + j dr®22/2)
dl
_ P - Kv2 - Pfrsign v2 - Pf
dP1_ Ec (Q1 - v2F1 )
dt d P2
V, + IF
(8)
__ Ec (v F - Q2 )
dt V02 + ( - /2 )
where
22 mr =Zm(vt/v2) + jt(coi/v2),
i=2
n 2 2
iir =Xm, ( / (2 ) + h (( / (2 ) ,
i=2
Pd = PF - p2F2 ,
n
Pf = X P,v, cos $ / v2 + MiO)l / v2
m
dr -
jdr - are the masses and moments of inertia of the moving parts, driven to the rod of hydraulic cylinder; ly v, œ2 - displacement, velocity and angular velocity of hydraulic cylinder; ke - coefficient of viscous friction; Pfr - coefficient of dry friction; Pd - the driving force acting on the piston of hydraulic cylinder; P - resistance forces driven to the rod of hydraulic cylinder; p]) p2 -pressure in head and discharge cavities of the hydraulic cylinder; F1, F2 - effective areas in head and discharge cavities; V01, V02 - initial volume of fluid in head and discharge cavities; m. - the mass of the i-th link; j. - the moment of inertia of the i-th link about the axis passing through the center of mass; v. - velocity of the center of gravity of the i-th link; œ. - angular velocity of the i-th link; P, M. - the values of the active forces and moments acting on the links; f. - the angle between the directions of forces P. and the velocity v; t. - length of the i-th link.
The coordinates of the center of mass of the considered device can be determined by formula
xc = XG,x, /IG,
Yc =XGiyi /IG \ (9)
i = 2...12
2
c)
Figure 2. The dependence of the change in angles; a) angular velocities b) angular accelerations; c) of the 2, 3 and 6 links of the HHS
The velocity and moment of inertia of the links are determined by the formulas
= la /2, (10)
j = m,
( -Xc)2 + ( -7c)21 , i = 2...12 (11)
where xy - are the coordinates of the center of gravity of the i-th link.
To study the flow of fluid in a pipeline, a model is chosen where the fluid is assumed to be compressible and concentrated in one or two bulks of small length (a system with lumped parameters, taking into account the compliance of hydraulic system elements). In this model, there is a possibility to take into account the compressibility of undissolved air bubbles [3].
pressure and flow rate in the inlet of a pipeline; pout Qouf -pressure and flow rate in the outlet of a pipeline; t - time; p and Ef - the density and the bulk modulus of the fluid;
d , E , E - the diameter, wall thickness and the bulk
pip pip pip '
modulus of pipeline material, respectively; ks - the coefficient of the approximation, its value depending on the relative roughness e of hydraulic lines; Z - the local resistance coefficient; f and l - the area and length of the pipeline; Vf - the volume of fluid in a pipeline; y - the dynamic viscosity of the fluid.
The flow rate through the distributor is determined by the dependence [3]:
" _ (14)
Qp =n
pj p
2 pp-pj/ p
„ d2x „„ dx p£ — + 27,5—— + dt f dt
„ _ J dx ^
+(0,443-^ + 0,5<p)
Vf V dt J
dx
sign ~Jt + p°ut = pn
dp dt
E fàp,pEp,p V Eprpàpip + dpipEf J
Q - Q
V
(12)
(13)
where pp - is the pressure created by the pump, f (y) -the area of flow section, np - flow rate coefficient.
The flow section of the distributor can be approximated by the following characteristic:
0, in t < t
nd.7 (t-t)/(4 (tk -1 )), in t< t < tk, nd 2 / 4, in t > tk
y 7 k
fp (y)=
. dx |1 V > 0 where sign— = <
dt 1-1 V < 0
, p Q - are the
' 1 in, ^-in
where dy - is a conditional passage, t - the lag time, tk - time of full opening of the passage.
Figure 3. Dependences of the change in driving force (Pd) and resistance force (Pc) on the hydraulic cylinder rod versus time
The system of equations (8) - (14), with initial and boundary conditions, is a mathematical model of dynamic calculation of the HHS of a tractor with increased loading capacity. To solve the mathematical model, a computer program was developed in DELPHI algorithmic language.
Figure 3 shows the results of numerical calculation of the change in driving force and resistance force on the rod of the hydraulic cylinder (3rd - link, Fig. 1). In calculation, the following values of links and the initial data are taken: l1 = 0.415 m, l2 = 0.447 m, l3 = 0.2 m,
l3' = 0.158 m, l31 = 0.358 m, l5 = 0.599 m, l6 = 0.49 m, l6' = 0.5 m, l61 = 0.99 m, l7 = 0.558 m, l9 = 0.61 m, l10 = 0.711 m, ln = 0.574 m, l12 = 1.22 m, m2 = 14.2 kg, m3 = 6.98 kg, m5 = 6.84 kg, m6 = 19.1 kg, m9 = 1.52 kg, m10 = 2.14 kg, m12 = 3028.9 kg, P2 = 142 N, P3 = 69.8 N, P5 = 68.4 N, P6 = 191 N, P9 = 15.2 N, P10 = 21.4 N, P12 = 30289 N, t = 0, t = 0.2, tk = 2, pp = 12 MPa, pin = Qin=
= Pout = Q0Mt = l2 = V 2 = W2 = p1= p2 = 0.
Analysis of the graphs shows that when the distributor is switched on with account of delay at t = 0.2
... 0.65 seconds, the driving force sharply increases to about 170 kN, then it decreases to the value which is the resistance force. Further to the value of complete opening of the distributor at t = 0.65 ... 2 seconds, the value of the driving force increases monotonically according to the resistance force. When the value of complete opening of the distributor is reached, the driving force begins to oscillate and eventually decays.
Results of numerical calculation obtained qualitatively closely describe the actual process of the HHS operation.
References:
1. Malikov R. H. Problems of pre-model diagnostics of machine mechanisms. Tashkent: Science, - 1991. - 60 p. (in Russian).
2. Zinoviev V. A. Course of the Theory of mechanisms and machines. - M.: Science, - 1975. - 204 p. (in Russian).
3. Matluk N. F., Avtushko V. P. Dynamics of pneumatic and hydraulic drives for vehicles. - M.: Mechanical engineering, - 1980. - 231 p. (in Russian).
