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Технологии. Машины и оборудование
DOI: 10.12737/111991 УДК 630*377.44
МОДЕЛЬ РАСЧЕТА НАГРУЖЕННОСТИ ЭЛЕМЕНТОВ ТРАНСМИССИИ ПРИ УПРАВЛЯЕМОМ КРИВОЛИНЕЙНОМ ДВИЖЕНИИ ГУСЕНИЧНОЙ ЛЕСОЗАГОТОВИТЕЛЬНОЙ МАШИНЫ
кандидат технических наук, доцент В. Е. Клубничкин1 кандидат технических наук, доцент Е. Е. Клубничкин1 доктор технических наук, профессор В. И. Запруднов1 кандидат технических наук, доцент Л. Д. Бухтояров2 кандидат технических наук С. В. Малюков2 кандидат технических наук Д. Ю. Дручинин2 1 - ФГБОУ ВПО «Московский государственный университет леса», г. Москва, Российская Федерация
2 - ФГБОУ ВО «Воронежский государственный лесотехнический университет имени Г.Ф. Морозова», Воронеж, Российская Федерация
Выполнение задачи, поставленной в стратегии развития лесного комплекса Российской Федерации до 2020 года по увеличению заготовок древесины до 294 млн м3 в год, невозможно без оснащения лесозаготовительных предприятий комплексом машин и оборудования, обеспечивающих эффективную заготовку древесины, в том числе в сложных природных условиях, которые преобладают на большинстве лесных площадей (слабонесущие грунты, сильно переувлажненная местность, глубокий снежный покров и т.д.). На переувлажненных лесосеках, крутых склонах, при глубоком снеге, там, где многоярусный лес, в пересеченной местности с изобилием препятствий в виде пней, камней и поваленных деревьев, где проходимость и сила тяги колесных машин недостаточны, целесообразно использование гусеничных машин. На обледенелых поверхностях преимущества гусеничного движителя еще более значительны. В данной статье предлагается модель нагруженности элементов трансмиссий при управляемом криволинейном движении гусеничной лесозаготовительной машины. В основу этой модели положена оценка влияния внешних и внутренних факторов, воздействующих на нагруженность трансмиссий гусеничных лесозаготовительных машин, модель взаимодействия элементов опорной поверхности гусениц лесозаготовительной машины с грунтом. Основные нагрузки в трансмиссии возникают в результате внешнего воздействия со стороны опорной поверхности при движении машины. Траки гусеничной ленты взаимодействуют с опорной поверхностью и передают усилия на ведущие звездочки. В основу модели расчета нагруженности элементов трансмиссии при управляемом криволинейном движении гусеничной лесозаготовительной машины была положена ранее полученная модель взаимодействия элементов опорной поверхности гусениц лесозаготовительной машины с грунтом.
Ключевые слова: лесозаготовительная машина; движение; ходовая система; грунт; опорная поверхность; модель; элемент; гусеница.
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MODEL ТО CALCULATE LOADING OF TRANSMISSION ELEMENTS AT CONTROLLED CURVILINEAR MOTION OF THE TRACKED TIMBER HARVESTING
MACHINE
Ph.D. in Engineering, Associate Professor V. E. Klubnichkin1 Ph.D. in Engineering, Associate Professor E. E. Klubnichkin1 DSc in Engineering, Professor V. I. Zaprudnov1 Ph.D. in Engineering, Associate Professor L. D. Bukhtoyarov2 Ph.D. in Engineering S. V. Malyukov2 Ph.D. in Engineering D. Y. Druchinin2
1 - Federal State Budget Education Institution of Higher Professional Education «Moscow State
Forest University», Moscow, Russian Federation
2 - Federal State Budget Education Institution of Higher Education «Voronezh State University of Forestry and Technologies named after G.F. Morozov», Voronezh, Russian Federation
Abstract
It is impossible to accomplish the task set by the development strategy of the timber complex of the Russian Federation until 2020 to increase timber harvesting up to 294 min. m3. without providing the timber harvesting enterprises with a complex of machines and equipment ensuring efficient timber harvesting, including in the severe weather conditions which prevail in most forest areas (weak soil, heavily waterlogged area, deep snow, etc.). It is advisable to use tracked machines on the waterlogged cutting areas, steep slopes, in deep snow, multi-storeyed wood, cross-country full of obstacles in the form of stubs, stones and fallen trees, where the performance and traction power of the wheeled vehicles are insufficient. The advantage of the tracked running gear is even more evident on the ice surface. This paper offers a model of loading of the transmission elements at controlled curvilinear motion of the tracked timber harvesting machine. This model is based on evaluation of the effect of the external and internal factors on the loading of the tracked machine transmission. The main loads in the transmission result from the external action of the ground contacting area during the vehicle movement. The caterpillar band tracks interact with the ground contacting area and translate force to the track drive sprockets. As a basis of a model to calculate loading of transmission elements at controlled curvilinear motion of the tracked timber harvesting machine was taken model of interaction between elements of the timber harvesting machine track ground contacting area.
Keywords: harvester; motion; propel system; soil; bearing surface; model; element; track.
It is impossible to accomplish the task set by the development strategy of the timber complex of the Russian Federation until 2020 to increase timber harvesting up to 294 min. cu.m, without providing the timber harvesting enterprises with a complex of machines and
equipment ensuring efficient timber harvesting, including in the severe weather conditions which prevail in most forest areas (weak soil, heavily waterlogged area, deep snow, etc.) [11, 12].
It is advisable to use tracked machines
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on the waterlogged cutting areas, steep slopes, in deep snow, multi-storeyed wood, crosscountry full of obstacles in the form of stubs, stones and fallen trees, where the performance and traction power of the wheeled vehicles are insufficient. The advantage of the tracked running gear is even more evident on the ice surface [2, 5, 8, 10].
This paper offers a model of loading of the transmission elements at controlled curvilinear motion of the tracked timber harvesting machine. This model is based on evaluation of the effect of the external and internal factors on the loading of the tracked machine transmission. The main loading is caused by the external action from the ground contacting area at interaction with the track links.
Work [3] presents a model of interaction between elements of the timber harvesting machine track ground contacting area, which was taken as a basis of a model to calculate loading of transmission elements at controlled curvilinear motion of the tracked timber harvesting machine.
Let us suppose the track is loaded with force Q (normal track-on-soil load) which is normal to its surface. When the track travels relative to the soil, this causes a response force that we mark as R. This force is proportional to the normal load:
R= R Q. (i)
The proportionality factor R is called a factor of the track-soil interaction.
Let us call the hodograph of force R at Q= 1 the hodograph of the track-soil interaction coefficient R .
The results of experiments [1, 5, 7, 8, 9] showed that this hodograph practically has the shape of ellipsis and may be described in the
following equation:
R
Rx'Ry
• sin2 a + ц2 • cos2 a
(2)
where Rx , ^ У is a value of the coefficient of the track-soil interaction at (separate) travel of the track by value <7 in longitudinal and lateral directions; Ct is an angle between direction of the track displacement and longitudinal axis of the tracked timber harvesting machine.
Let us record expressions for elementary forces acting from the soil on the element of the ground contacting area of the leading track.
Basing on the expresions (1) we can record:
dR, = -r(x) -q2(x)-dx, (3)
where q2(x) - is a load from the weight of the tracked timber harvesting machine per unit of the length of the track ground contacting area. Sign "minus" is because the forces acting on the element of the ground contacting area are opposite to the velocity of travel of this element relative to the soil.
For the longitudinal and lateral components of the elementary response force dR^
we can record the following expressions:
dP2 = dR2-cos a;
dS2=dR2• sin a;
(4)
or
(5)
dS2 = -r(x) ■ q2(x) • sin a • dx, where
cosa=vx2/v;bc; sma = Vy2IV“bc. (6)
Using expressions (2) and (6), we record the formulas (5) in the following form:
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dP2 = q2(x)- Mx2 ' My2 ■Vx2-dx; (7)
ЫЛ+&-V;2
s. & 11 q2(x)-~ Mx2 ' My2 ЫЛ+Ар2 ■Vy2-dx. (8)
The value of velocity VX2 does not clearly depend on the position of the element along the length of the track ground contacting area and traveltime parameters of turn, while the value of velocity Vy2 is a function of traveltime parameters of the curvilinear motion of the tracked timber harvesting machine. Considering the above, dependencies (7) and (8) can be presented in the following form:
Mx2 ' My2
dl\ = -q2(x) dS2=~q2{x)
\jMv2 ' Kx2 Mx2 ' ■*)
Mx2 ' My2
r-Vx2-dx;
y/dy2-K22+dx2-®2(X-X)2
Hence
p2=-\ qi(x)-
^2 = -f <h(x)-
Mx2 ' My2
P;2-K2 + A-°>4x-*f
■Vx2-dx\
Mx2 ' My2
■a>-(x~x)-dx,
(9)
(10)
(И)
(12)
where
K=h-td! 2.
k ~h+td/2',
The elementary moment of cornering resistance determined by the track-soil interaction, relative to the center-of-mass of the tracked timber harvesting machine shall be calculated by the following formula
dM2 =x-dS2.
Then we obtain the following expression for the moment of cornering resistance:
к'
M2=-\ 92(X)'
ln
Similar for the retreating track:
V
№x2 * №y2
p<=- ] 41,1
n
$i =-J ?iW-
Mxl ■ My,
^уг-Ух21 + Ц2х1-со2(х-х)2
■ со ■ (X - x) ■ x ■ dx.
■vxi~dx;
Mx, ■ My,
l'
V
Ml =-} qx{x)-
■sjMy • ,u: ■(■> (x x):
Mx 1' Myl
■<x>-(x-x)-dx,
■ со ■ (X - x) ■ x ■ dx.
(13)
(14)
(15)
(16)
/; ^My,-V2 + y2xl-co2(x-x)2
In formulas (11) - (16) the law of load distribution along the length of the track ground contacting
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area does not depend on the traveltime parameters of the track-soil interaction. All other values are determined by the nature of track elements-to-soil interaction. With the given law of track elements-to-soil
interaction Uc(?x). forces P2, S2 and the cornering resistance moment M2 are determined by slipping
velocity VX2 and longitudinal displacement of the center-of-tum X , and forces Pi, Si and moment Mi, by slipping velocity Vx/ and longitudinal displacement of the center-of-tum, respectively.
For the controlled curvilinear motion, we can assume that normal responses of the support rollers to the soil are concentrated. This assumption was proved experimentally [1, 4, 6, 7, 9]. Considering the above, we can record the following expressions:
A = -I<22i-
7
У 2
■V.,
(17)
^ = -Za,-
Pxl'Pyl
4v2yi-K+A-(°2(,x-h)2
■yA\
(18)
y=y1+y2 = -£a
n
-IG:
Pxl ■ Myl
■■=' " Jp2yi-K\ + pli-®2(x-h)
Px2 ' Py2
■co-(X-h)-
(19)
m=m1+m2 = -YjQ1
i=1 V^2'Fx2+^2-® (X~h)
Pxl ■ Pyl
-Z0
Px2 ' Py2
а-(Х~1,У,
■a-ix-h)-1,-
(20)
i=1 ^ ^Р2у2-К22+Р2х2-®2(Х-1г)2
®-(x~h)-h-
where n is the number of support rollers on one side of the machine;
Qt is a normal load from /-nd roller on the soil;
i is the roller's number counted from the bow of the tracked timber harvesting machine to the aft; h is a distance between the center-of-mass of the tracked timber harvesting machine to the center of the /-nd support roller.
The equation system of the controlled curvilinear motion of the tracked timber harvesting machine has the following form [4, 6]:
m-'s = [(Pj + P2) - (Pj + P2)] • cos /3 - (Sl + S2) ■ sin /3;
Jz • ^(s) • 5 +• s2 + /3 j = (M„ -MR -Mc);
V2
m----= -[(P1+P2)-(P1 +P2)]-sin/3-(P1 +P2)-cos/3.
Pc
(21)
In accordance with this system it is necessary to determine the laws of distribution of the normal
loads on the ground contacting area Q and expressions for the motion resistance forces R/ and P2.
When moving over the non-deforming soil the analytical expressions for forces Ri and P2 can
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be pretty exactly recorded in the following form:
(22)
- (23)
where frp is a coefficient of motion resistance of the tracked timber harvesting machine.
All forces acting on the tracked timber harvesting machine can be reduced to two resultants directed along and across the longitudinal axis of the machine and applied to its center-of-mass. Under these forces the normal loads from the rollers on the soil are re-distributed (Fig. 1, 2).
Assuming that under the action of the above forces the deformation of the flexible elements of the cushioning system is insignificant and within those deformations the stiffness of the flexible elements can be taken constant, let us find out the law of distribution of the normal loads on the track ground contacting area using the following expressions:
Fig. 1. Re-distribution of normal loads on the track ground contacting area under the axial forces
Fig. 2. Re-distribution of normal loads on the track ground contacting area under the cross forces
Qh 'dfir- (24)
Qu=Pm+Cr5f,n (25)
where 0?/, Qu are normal load on the ground contacting area from /'-nd roller of the leading and retreating tracks, respectively;
Pot is a static load from the /'-nd roller on the ground contacting area;
Cj is stiffness of suspension of the /-nd roller around its static position;
is additional from axial and cross
forces, relative travel of the /'-nd roller.
For additional travels we can record:
3/у=-1г(р-В/2-в; (26)
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Sf2i=-lr(p+B/2-6, (27)
where ^ is an angle of axial tilt of the body; в is an angle of cross tilt of the body; Let us substitute (26), (27) to (24), (25)
On =I1H ~сг •(-<P+Ct-B/2-&, (28)
Ou=1m-crlr(P-crB/2-^ (29)
Then,
Qi = = ±p„-'Lcr/r(P+
7=1 7=1 7=1
„ (30)
+£c,-B/2-0;
7=1
a =Sa=2A-2>-
7=1 7=1 7=1
„ (31)
crB/2-e.
7=1
Let us formulate an equation of moments of active forces and response forces relative to the center-of-mass of the tracked timber harvesting machine in the cross plane
f(ZGa-Sa]-^e=o, (32)
^ V *=1 1=1 j
where hc is a distance from the center-of-mass of the machine to the ground contacting area.
Let us substitute (30), (31) to equation
(32) and solve it relative to ^
П
52-2><
(33)
7=1
Let us formulate an equation of moments of active forces and response forces relative to the center-of-mass of the tracked timber harvesting machine in the axis plane
■/,=*■*■ (34)
7=1
7=1
Let us substitute (30), (31) to equation (34)
ixv+lx-/,-
7=1
7=1
-l-(p-Ycrl=X-hc.
7=1
In this equation
S^207 ^7+=0-
(35)
7=1
7=1
Then,
<P = -
X-h
7=1
(36)
(37)
Let us substitute expressions (33) and (37) to equations (28) and (29):
027 - P20i +
X-h-Cr l Y -h- c.
C l l
в-Ъ
(38)
„ _ X-h -c •/ Y-h -c
a=p,o,+—^ (39)
2 ■!>,■/’ B-Y^c,
7=1 7=1
If we assume that the stifihess of all flexible elements of the cushioning system is equal, then
027 - Р2Ш +
X-h-l Y-h
2-B!
Bn
(40)
a
Pm +
x-K-h
n
2-B!
7=1
r-K.
Bn ’
(41)
Thus, all forces included into equation of system (21) become defined. Now we use the expression for those forces and represent the system of equations of the controlled motion of the tracked timber harvesting machine in the final form.
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т-
dV
dt
-Z&,
Их2’Иу2
Jvb-Ki+Mrt-n'-iX-I,)
^2-za,
AVPyl
-fim-G + C,n) ]-cos/3-
Vxl’Vyl
У q, -=____________________________
sJm^i ■K+A-^-ix-iy r<o<X-h)-
J., -
-la,
•1
V1
Их2-Ну2
m
* “V^V^2+^v®2-a-/,) (
-Za,
«•a-/,)
Pc
sin j6;
K2-XQ,-
Ихги
У 1
ч ’=‘ ' VaVF,2+P22'®2-a-/,)2 " ‘=1 ‘ yl^yl-K
'Ki-
-Лт-G + Gn)-sin/3 -
Mxl-Myl
^Qu Va2i -Fn+p,2i -®2 -a-a2
■«•a-o-
-Za
Vx2-t*y2
> ‘ VaVF,22+p22-®2-a-a2
т-ю-а-о
cos /?;
Г PA: .
.Л
Jz ------5 + k(P) -5 + P =
V Ps
■Za
j
Vxl'Vyl
Aft2 ' Afy2
-Za,
- ^a4-^+a4-®2-(p-/,):
2 ic2 , ,,2 „2
V^2 A /
•-+lza,
^2 +
'=' “VaVFn+ar®2-a-o; 2 v-> 21 VaVaz+apV®2-^-/)
Л
Их2'Му2
Mx-0 +
-Za
AAti' Af,i
A
yIti-K]+Krv2 -(x-1,Y
^®a-a
A' . n \ D
-|Za,-Za, I ■ fdm '~z-
(42)
4\
Conclusion
The obtained system of equations defines the possibility of motion of the tracked timber harvesting machine in the preset mode and along the preset trajectory. Those equations can form the basis of calculation of loading of the transmission elements at the controlled curvilinear motion of the machine. The analysis of this system of equations indeed demonstrates that at the given laws of
track-soil interaction M:(^x)and №у(&у) the forces acting in the plane of the ground contacting areas of the tracked timber harvesting machine are defined by the controlled parameters of turn: motion velocity and trajectory curvature. Adding a computed model of transmission to this mathematical model of the controlled curvilinear motion of the tracked timber harvesting machine gives a mathematical model to calculate loading of the transmission elements.
Библиографический список
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Сведения об авторах
Клубничкин Владислав Евгеньевич - доцент кафедры колесных и гусеничных машин, ФЕБОУ ВПО «Московский государственный университет леса», кандидат технических наук, доцент, г. Москва, Российская Федерация; e-mail: vklubnichkin@mgul.ac.ru.
Клубничкин Евгений Евгеньевич - доцент кафедры колесных и гусеничных машин, ФЕБОУ ВПО «Московский государственный университет леса», кандидат технических наук, доцент, г. Москва, Российская Федерация; e-mail: klubnichkin@mgul.ac.ru.
Запруднов Вячеслав Ильич - заведующий кафедрой геодезии и строительного дела, ФЕБОУ ВПО «Московский государственный университет леса», доктор технических наук, профессор, г. Москва, Российская Федерация; e-mail: zaprudnov@mgul.ac.ru.
Бухтояров Леонид Дмитриевич - заведующий кафедрой лесной промышленности, метрологии, стандартизации и сертификации, ФЕБОУ ВО «Воронежский государственный лесотехнический университет имени Е.Ф. Морозова», кандидат технических наук, доцент, г. Воронеж, Российская Федерация; e-mail: vglta-mlx@yandex.ru.
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Малюков Сергей Владимирович - старший преподаватель кафедры механизации лесного хозяйства и проектирования машин, ФГБОУ ВО «Воронежский государственный лесотехнический университет имени Г.Ф. Морозова», кандидат технических наук, г. Воронеж, Российская Федерация; e-mail: maljukov-sergejj@rambler.ru.
Дручинин Денис Юрьевич - старший преподаватель кафедры механизации лесного хозяйства и проектирования машин, ФГБОУ ВО «Воронежский государственный лесотехнический университет имени Г.Ф. Морозова», кандидат технических наук, г. Воронеж, Российская Федерация; e-mail: druchinin.denis@rambler.ru.
Information about authors
Klubnichkin Vladislav Evgenyevich - Associate Professor of Wheeled and Tracked Vehicles department, FSBEI HPE «Moscow State Forest University», Ph.D. in Engineering, Associate Professor, Moscow, Russian Federation; e-mail: vklubnichkin@mgul.ac.ru.
Klubnichkin Eugeny Evgenyevich - Associate Professor of Wheeled and Tracked Vehicles department, FSBEI HPE «Moscow State Forest University», Ph.D. in Engineering, Associate Professor, Moscow, Russian Federation; e-mail: klubnichkin@mgul.ac.ru.
Zaprudnov Vyacheslav Ilyich - Head of the Department of Geodesy and Construction, FSBEI HPE «Moscow State Forest University», DSc in Engineering, Professor, Moscow, Russian Federation; e-mail: zaprudnov@mgul.ac.ru.
Bukhtoyarov Leonid Dmitrievich - Head of Department of Forest Industries, metrology, standardization and certification, FSBEI HE «Voronezh State University of Forestry and Technologies named after G.F. Morozov», Ph.D. in Engineering, Associate Professor, Voronezh, Russian Federation; e-mail: vglta-mlx@yandex.ru.
Malyukov Sergey Vladimirovich - Senior Lecturer Department of Forestry Mechanization and Machine Design, FSBEI HE «Voronezh State University of Forestry and Technologies named after G.F. Morozov», PhD in Engineering, Voronezh, Russian Federation; e-mail: maljukov-sergejj@rambler.ru.
Druchinin Denis Yuryevich - Senior Lecturer Department of Forestry Mechanization and Machine Design, FSBEI HE «Voronezh State University of Forestry and Technologies named after G.F. Morozov», PhD in Engineering, Voronezh, Russian Federation; e-mail: druchinin.denis@rambler.ru.
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