CC BY
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Soliyev Hayitboy Mirzadavlatovicvh, scientific-researcher, Scientific-research, institute of mechanization and electrification of agriculture Republic of Uzbekistan, E-mail: [email protected] Tukhtabayev Mirzokhid Akhmadjanovich, senior scientific-researcher, Scientific-research institute of mechanization and electrification of agriculture Republic of Uzbekistan, E-mail: [email protected]
MATHEMATIC MODEL OF COURSE STABILITY WIDE-COVERAGE SOWING AND CULTIVATOR MACHINE-TRACTOR AGGREGATE
Abstract: in article are brought elaboration mathematic model of course stability wide-coverage machine-tractor aggregate and analytic solution of it. It is described the influenced forces of it when machine-tractor aggregate is moved.
Keywords: course stability, wide-coverage sowing and cultivator aggregate, machine-tractor aggregate, cultivator tractor, row spacing, front and rear wheels, mathematic model, resistance force.
Солиев Хайитбой Мирзадавлатович, научно-исследовательский институт механизации и электрификации сельского хозяйства, научный сотрудник-исследователь. E-mail: [email protected] Тухтабаев Мирзохид Ахмаджанович, научно-исследовательский институт механизации и электрификации сельского хозяйства, старший научный сотрудник-исследователь E-mail: [email protected]
МАТЕМАТИЧЕСКАЯ МОДЕЛЬ КУРСОВОЙ УСТОЙЧИВОСТИ ШИРОКОЗАХВАТНОГО ПОСЕВНОГО И ПРОПАШНОГО-ТРАКТОРНОГО АГРЕГАТА
Аннотация: в статье приведены разработка математическая модель курсовой устойчивости широкозахватного машинно-тракторного агрегата и её аналитическое решение. Опысано параметры широкозахватного машинно-тракторного агрегата.
Ключевые слова: курсовая устойчивость, широкозахватной посевной и пропашной агрегат, машинно-тракторный агрегат, пропашной трактор, междурядья, передние и задние колеса, математическая модель, сила сопротивления.
It is increased efficient in bring up growing the crop that applying the wide-coverage machine-tractor aggregate for the purpose decreasing the working productivity and time spending. Therefore, it is required to research dynamic movement of wide-coverage machine-tractor aggregate. Across and corner vibrations are influenced noticeable to the movement of sowing and row space cultivator aggregate where at horizontal plain. The main reasons to create of vibration aggregates are accidental awakens created from working-body in row space where cultivating, unevenness of cultivating depth are caused to it and diverse of mechanic characteristic in row space. The presence of vibrations on horizontal plain of plunging aggregate is deteriorated quality of realized technologic process, haul way is increased and productivity is decreased. Traction resistance are increased from changing rough terrain than being cultivated row space layer and increased the comparative fuel expense and the work of machine-operator thickness is increased [1]. These vi-
brations the movement stability level. It will deteriorate of movement stability what the tendency is directing at increase of work productivity that owing to increase the seizure of width and working speed of machine-tractor aggregate were existing in now.
It follows that, it is required to investigate conditions of way stability at movement of wide-coverage machine-tractor aggregate.
For making up the differential equation of aggregate movement are based on calculated scheme at Picture-1. It is taken some following limits [2]: a) the aggregate movement is occurred evenly and advanced; b) it is taken the identical equivalent wheel with inflexibility coefficient of changeable wheel, that wheels are fixed on a bridge of tractor; the traction resistance of working-body are depicted form of the sum vector of driving force that brought to center; d) it is taken the small corners of sinus and the tangent are equal to themselves that are expressed in radian but cosinus is equal to one.
Picture-1. Calculated scheme for making up the differencial equation of cultivator aggregate movement [2]: 1, 2 - "equivalent" wheel of the tractor; 3 - symmetric plain of aggregate
We will see the regular and straight-line V movement condition as compared with not moveable ofX, O, Y plains the center of gravity S of aggregate. With the center of gravity of aggregate. We will connect the beginning in rectilinear, advanced moving system ofXOY coordinates. In according with main rectilinear, advanced movement ofaggregate will connect the center ofgravity ofaggregate to the system with rectilinear, advanced moving ofaggregate. The % Dq plain is rigidly connected with a longitudinal axis of the aggregate. It is described as from main rectilinear movement that is turning the plain than XOY plain.
It is accepted the following notes for making a differential equation: TA, TB - across forces of'equivalent" wheels oftractor, kN; MA, MB - moments of'equivalent" wheels oftractor when appearing a friction, kN-m; MDlrt, MD 2,t •••, MDn-hit, MDn,it = MDni - main moments of couple forces where the point is putted, kN-m; SA - rolling resistance force of "equivalent" wheels, kN; FB - driving force of'equivalent" leading wheels oftractor, kN; R - main vector of the working-body resistance forces, kN; p - simple slope corner of the aggregate symmetric plain than the axis Y, rad; x - the slope corner from the aggregate symmetric plain of the main vector which is force resistance; S - the corner between which is putting center of the speed vector and the aggregate symmetric plain, rad; y/A, y/B - corner deformation in friction of tractor tire; D - the force resistance putting center ofworking-body and driving forces.
Differencial equation of aggregate absolute movement:
mXs = E Fix;
mys =E Fiy; (3.1)
Js<f = X Ms (Fi).
Differencial equation of cultivator aggregates are taken following form, if, it takes into consideration of the corners p, , y/B and %:
™Xs =-TA-TB + SA ) - FB ($-VB ) -
-p i + •••+Pn №+(R + R2+•••+Rn )(4-x)
my s = Fb - Sa - (R + R2+-R)
Js$ = aTA - bTB - MA - MB + (M^lf + M,
••• + Mdni f - Mdi,n - Md2,rt-----Mdn,t ) +
+ aSA^A + bFB¥B + d(Pd l + Pd 2 + ••• + P„n) -
d2, If '
- <3.2)
here a = SA u b = SB - the distance from the center of gravity S to the "equivalent" front A and rear B wheels, m;
d = SD - the distance from the center of gravity S to the center D is putted that force resistance, m.
In according to the slipping theory of the tire, the across force (TA ,TB ) ,stabilizing moments (Ma , Mb ) and the deformation of the corner of tire (Aare determined the following formulas
T = cA; M = fy\ y/= kA. here c - the coefficient of across rigidity of tractor tire, kN/m; f - the coefficient of corner rigidity of tractor tire, kN-m/rad; k - the coefficient proportionality between deformations, 1/m; A - across deformation of tire, m;
Declination to the corner x from aggregates' symmetry plain of main vector of force resistance is determined following expression
X = ao5';,
here a0 - characterized coefficient of force parameters (R,Pa) of working-body.
Now, we will determine analytic solution of elaborated mathematic model of course stability wide-coverage sowing and cultivator machine-tractor aggregate by expression (3.2). Rewrite the equation (3.2), it will have the following form:
mxr = F
1'
my s = F2;
Jsj> = M;
(3.3)
here
Fi =-T A -TB - HD +SA(^-VA)-FB(^-VE
-(Pdi + -+Pdn )(<P-M)+(Ri+ R2 + -+Rn M-X); F2 = Fb + (Pdi + Pd 2 + ••• + Pdn) - Sa - R + R2 + -RJ ; M = aTA - bTB - dHd - Ma - MB + (MdUf + Mdu + -
- + MdnJf - MdUt - Md2,rt-----Mdn,rt ) + aSA^A +
+bFs¥B + d(Pdi + Pd 2 +- + Pdn)»-d (Ri + R2 +- + Rn )X From system of equations (3.3) it will determine the sought for dynamic functions xs, ys u (¡) :
-d(R + R2 +■■■ + Rn )x
xs =— F1
m
• 1 c 7s ^ F2 m
6= — M Js
(3.4)
Leading vector function Y = ,ys, rewrite the system equations (3.4) the form of vector:
7 =
-F
m m
1M J
= F или Y = F
(3.5)
The discrete analogy is formed on the base of elaborated mathematic model of course stability wide-coverage sowing and row space cultivator machine-tractor aggregate. To solve investigating dynamic problem are worked out the calculation algorithm [3], instruction to use for from software and numerical algorithm of implementing calculation scheme.
References:
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Tukhtabayev M. A. Applying for wide coverage four wheel machine-tractor aggregate in row-spacing / Modern trends in the development of the agricultural complex: materials of the international scientific-practical conference / p. Salted Zaimishche. FGBNU "PNIAAZ". - Solenoye Zaimishche, - 2016. - P. 1263-1266. Гашенко А. А. Повышение эффективности использования культиваторного агрегата улучшением устойчивости движения дисками-движителями. Автореферат дисс.... канд.техн.наук. - Пенза: ФГОУ ВПО, -2010. -18 с.
Исомиддинов А., Туланов И., Солиев Х., Тухтабаев М. Программное обеспечение для расчета курсовой устойчивости широкозахватного пропашного машинно-тракторного агрегата // Государственное патентное ведомство РУз. Свидельство № DGU 04847. 27.10.2017 г.
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