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Разработка алгоритма работы системы динамической стабилизации для колесного трактора 4a4 с индивидуальным ТЭП в режиме вспашки на склоне..pdf

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#7 [652] 2014
??? 629.33
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??? ????????? ???????? 4�? ?????????????? ???
? ?????? ??????? ?? ??????
?.?. ????????, ?.?. ???????
???? ??. ?.?. ???????, 105005, ??????, ?????????? ?????????, 2-? ?????????? ??., ?. 5, ???. 1.
Developing an algorithm for the dynamic stabilization
of 4�wheel tractors with individual
technical-and-economic indices when plowing on slopes
M.M. Zhileykin, E.V. Yagubova
Bauman Moscow State Technical University, building 1, 2-nd Baumanskaya str., 5, 105005, Moscow, Russian Federation.
e-mail: jileykin_m@mail.ru, yagubova.evg@yandex.ru
??? ?????? ?? ???????? ??????? ?????????? ???????? ?????????? ? ?????????? ???????????? ???????? ???????-?????????? ????????? (???). ??? ???? ????? ????? ??????? ???? ?????????? ?????????????? ????, ? ????? ????????? ???????? ???? ??
??????. ?????????? ????????? ?????? ?????? ???????????? ???????????? ????????
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?? ?????????? ??? ????????. ???????? ?????????????? ?????? ????????????? ????????????? ??????????, ?? ??????????? ???????? ????????, ??? ???????? ??????????
?????????? ????????? ???????????? ????????? ? ?????????????? ???????? ????????
?? ??????? ??????? ????????.
???????? ?????: ???????? ???????, ?????????? ????????, ?????, ???????? ? ??????????? ????????????, ???????????? ????????????, ????????????, ?????????????????
???????? ????????.
Working on slopes can reduce longitudinal and transverse stability of vehicles and tractors. In
this case, the elastic pneumatic tires can slip, and the tractor can start sliding down the slope.
This paper presents algorithms for the course and trajectory dynamic stabilization of a wheel
tractor on a cross slope. The algorithms imply distributing the torque between the drive wheels
as well as steering the driven wheels. The laws for detecting a skid of the rear or front axles of the
tractor are described both for rectilinear and curvilinear motion. The techniques for adjusting
the values of the torque and correcting the deviation angle of the longitudinal axis of the tractor from the direction of its motion are presented. A quantitative analysis of the effectiveness
of the developed algorithms is performed. It is found that the most efficient approach involves
both steering the wheels and adjusting the torque on the drive wheels of the tractor.
Keywords: wheel tractor, slope, course and trajectory stability, dynamic stabilization, steering,
torque distribution.
#7 [652] 2014
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??? Vx, Vy ????????? ????? ??????????????
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#7 [652] 2014
2)�??? sign (Q? ? Q?) sign (Q1) < 0, ?? ???????
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????? ?????????? ?? ????????????? ??????????
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???? ???????? tg燪? (??. ???. 1), ? ????? ????????????? ???????? ???????? ????? ???? tg燪?. ???????? ???????????? ??? ????? ?????????????? ???
????????? ???? ?????, ?, ??????, ? ?? ?????????.
???????? tg燪? ??????????? ?? ???????
????? a/L ? 0,5, ?.�. ????? ??????? ????????
????????? ????????? ????, ????? ? = 0,5(?n ? ?1).
????? ??????? ???????????, ??? ? ~ (?n ? ?1). ?????????????, ?? ???????? ????????? ? ? ????????
?????????? ????? ?????? ? ???, ????? ??????-
tg燪? = Vy/Vx,
??? Vx, Vy ? ???????? ??????? ???????? ??????
???? ???????? ?? ??? ????????? ??????? ?????????.
???????? tg燪? ?????????????? ?? ???????
????? L ? ???? ????????; a ? ?????????? ?? ?????? ???? ???????? ?? ???????? ???; Q1?? ? ??????? ???? ???????? ???????? (?????? ? ???????)
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?????? ???? ?????????? ?????? ?? ?????????
???????:
1)�??? sign (Q? ? Q?) sign (Q1) > 0, ?? ???????
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#7 [652] 2014
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(1)
??? L ? ???? ????????; ? ? ????? ????????.
|Q1?? | ? 3�,
(2)
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|b| = | Q? ? Q? | ? 3�,
(3)
?? ???? ???????? ?????? ?????????? ??????????
?? ??? ??????? ?????? (???. 4).
??????? ????????? ???????, ??????? ??????
???? ?????????? ?? i-? ??????? ????????????????
??? ??????????? ???????? i-?? ?????? ? ????????????? ??????? ????????? ???i, ????????????
??????????:
???. 3. ????? ???? ?????????? ????????:
?? ? ???????? ????????; ?? ? ????????????????
?????? ???????? (????????, ???????? ???????
?????????? V = 10 ??/?). ?????
???i = V/r???.(5)
????? r??? ? ??????????? ?????? ??????? ??????
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(???. 3).
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61
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??? ?i ? ?????????? ??????? ???????? ????????
i-?? ??????. ? ???? ?????? ?????????? ????????????? ????????? ??????? M?? ? ??????? ?????????? ??? ????????. ??? ?????????? ??????? (6)
???????? M?? ??????????? ?? ???????
(7)
??? ?????????? ??????? ??????????????
????????????????, ?????????????? ?? ???. 5, ??????? ????????? ???????????:
1) ???????? ?????? ????????? ???????????? ????????? Mmax;
2) ???????? ?????? ????????? ???????
??????????????? ???????????????? (???????????
?? ???????????? ????????) Nmax;
N???max?h = M???i????i,(4)
??? N???max ? ???????????? ???????? ?????????;
h� ??????? ????????????? ???????? ?????????
(??????? ?????? �??� [0;1]); M???i ? ????????
?????? i-?? ?????????.
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? ???????????? ?????? ?? ???????? ????????, ??
??????? ???????????? ?? ??? ???? ?????????-
???. 4. ????????????? ???????? ??? ??????????
??????
62 ???????? ?????? ??????? ?????????. ??????????????
#7 [652] 2014
???? ? < 0, ?? ??????? ?????? ?????????? ?
??????? ?????? ????? ? ??????? ??????? ??????????? ?? ????????
???. 5. ?????????????? ???????? ????????????????,
??????????? ? ???????? ???????? ?????????:
1 ? h1 = 1; 2 ? h2 = 0,75 h1; 3 ? h3 = 0,5 h1; 4 ? h4 = 0,25 h1
3) ??????? ???????? ???????? ?????? ?????????? ???????????? ????????? w??max (??????????? ?? ??????????? ????????? ????????
????????).
???? ??????? (2) ???????????, ? ??????? (3)
?? ??????????? (???. 6), ?? ???????? ??????
?????????????????? ????? ???????? ????????
????????? ???????. ???? ? > 0, ?? ???????
?????? ?????????? ? ??????? ??????? ?????.
??????? ????????? ??????? ??? ??????? ?????
??????? ? ?????? ?????? ???????????? ?? ????????? ????????:
(8)
??? hCDC ? ???? ????????? ???????, ??????????
? ??????? ???? ????? ????????, ?? ??????? ?????????? ?????? ???????. ???????? ???????????
hCDC ????????? ????.
???. 6. ????????????? ???????? ? ??????
????????????? ??????
(9)
????????????? ????????. ???? ??????? (2)
?? ???????????, ????? ??????? ???????? ?????????????. ??? ????, ???? ?? ???????????
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sign�(Q? ? Q?) sign�(Q1cp).
???? sign�(Q? ? Q?) sign�(Q1cp) > 0, ?? ??????????????? ??????????? ?????? ???????? ???.
?�??? ?????? ???????? ?????? ?????????????????? ????? ???????? ???????? ????? ???????,
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??????? ???????? (?? ????????? ? ??????????? ????????) ????? (???. 7). ??????? ????????
???????? ??? ????? ??????????? ???.?? ? ???????? ???.???? ?????? ???????? ??????????????
????????? ???????:
(10)
???? sign�(Q? ? Q?) sign�(Q1cp) < 0, ?? ??????????????? ??????????? ?????? ?????? ???. ? ????
?????? ???????? ?????? ??????????????????
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??????? ?????? ?????????? ? ??????? ??????? ??????????? (?? ????????? ? ???????????
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???. 7. ????????????? ???????? ? ??????
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#7 [652] 2014
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????????? ?????????? [8].
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?? ????????????? ?? ??????? ????????????? ???
????????????? ???????, ??????? ?? ????????????
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???? ????????? ?? ?????????? ? ????????? ?????????????????? ??????? ????????????? (???).
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?????? ???????????? ? ????? ????????? ????????? ?????????? ? ???????? ?????? ?? ?????????
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????, ?????? ???????? ?????? ????????? ??????????, ???????????? ???? ?????????, ????????
?????????? [9?11].
??????? ????????? ????????? ??????????
??????? ?? ????????? ?????. ??????? ??????????
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??????? ?????????????? ??????? ??????????,
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??????, ????? ?????????????? ? ????????? ?????????? ??????????, ??????????? ??? ????????? ?????? ?????????? ? ???????? [12].
63
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??????????????? ??????????:
?1 ? ?????? ???????? ????? ??????????? ?????????????? ? ???????????? ???????? ?????????
|b| = | Q? ? Q? |;
?2 ? ?????? ???????? ????????? ????????
????? ??????????? ?????????????? ? ???????????? ???????? ????????? | b? | .
?????? ???? ???????? ?????????? Y: ????????? ???????? ???????? ?? ??????? hCDC =
= Tmin/Tmax. ??????, ??? ???????? ??????????
Y ?????????? ? ????????? [0; 1]. ????? Tmin ?
??????????? ???????? ?????? ?? ???????
??????; Tmax ? ???????????? ???????? ??????
?? ??????? ??????.
? ???????? ?????? ???????? ????? ????????
?????????????? ?? ???????, ? ??????? ????????????? ????? ? ?????????? ???????. ??????
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????? ??????????? ????????????? ? ??????????????? ?? ??????. ???? ? ?????????? ??????????
?????? ??????? ????? ???????????, ??? ??????
????????? ????? ??????? ??????? ???????,
?????????? ???????? ????????? ?? ??????? ?
????????? ?????. ???????? ????????? ??????
????????? ????????? ? ?????? [12].
??????????? ???????? ??????? ?????????????? ??? ??????? ? ???????? ???????????????
??????????. ???????? ??????? ?????????????? ??? ??????? ??????????????? ??????????
?1 ? ?????? ???????? ????? ??????????? ?????????????? ? ???????????? ???????? ?????????,
??????? ??????????????? ????? ???????: ??????
???????, ??????? ???????, ??????? ???????.
?? ??????????? ??????? ?????? ?????? ??????? ??????? ??????????????? (???. 9, ?).
??????????? ??????? ???? ???????? ???????
?????????????? ??? ??????? ?????????? ?2
(???.��) ? ???????? ?????????? Y (???. 9, ?).
??????? ? ???????? ????????? ???????????
??????. ??????????? ???????? ?????? ?????????? ????????????? ???????, ???????????
??????????????? ?????????? [12]. ????????????
????? ?????? ????????? ????????? ????????
???????, ??????????? ? ?????? ??????.
???????? ????????????? ??????? ??????? ??
??????????? (????? ?????) ? ??????????? (?????
???). ?????????? ????? ????????? ????? ?????
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??????? ???????? ??????
??? ???????? ?????????? Y
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????????? ????????
???. 9. ??????? ??????????????:
? ? X1; ? ? X2; ? ? Y; 1 ? ?????? ???????;
2 ? ??????? ???????; 3 ? ??????? ???????
???????. ? ???? ?????? ??? ???????????? ??????????? ?????????? ?????? ? ??? ???. ????? ???????????? ??? ?????????? ?????? ?????? ?????? ?.
??????? ?????????? ????????? ??????? ?????????? ???????? ?????????? ??????? ? ?????????????? ?? ??? ?????: ????????? ? ??????????.
????? ???????????? ???????? ????????? ??????????? ?????? ??????? [12]. ?????? ?????????
??????? ???????? ????????? ???????:
???? ?1 = ??????? ??????? ? ?2 = ???????
???????, ?? Y = ?????? ???????.
?????? ????? ???????? ?????? ???????? ?
???????.
????????? ??????????????. ?? ?????????
????? ?????????? ??????????? ??????? ?? ???????? ???????? ???????? ???????? Y ????????
???????? ????????????? ????????? ? ???????
????????? ????????. ??? ???????? ??????????
??????????????? (??????????? ??????????).
????? ????????? ?????????????? ?? ?????? ?????? ??????? [12]. ?????? ??????? ???????? ???. 10.
???????????? ????????????? ?????? ?????????? ???????????? ???????? ?????????
????????. ? ????? ????????????? ????????????? ?????? ?????????? ???????????? ???????? ???????? ????????? 4�? ??????????????
??? ???? ????????? ????????????? ???????????? ??????? ????????????? ???????????????
?????????????. ????????? ???????? ?????????????? ?????? ???????? ????????, ? ????? ??
???????? ??????????? ????????? ? ??????? [13,
14]. ?????? ??????????? ? ????? ?????????????
????????????? Matlab Simulink. ? ????? ??????????????? ??????????????
?????????? ????????? ????????
????????????????
??????????, ?:
?? 1-? ??? ?? ??*, ? . . . . . . . . . . . . . . . . . . . . . . . �75
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?????????? ????? ??, ??�2, Jz . . . . . . . . . . . . . ��3
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?????), ?, Ga . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . � 000
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???????????? ????? . . . . . . . . . . . . . . . . . . . . . . �0
??????? ????? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . �
???????????? ???????? ?????? Mmax ?????????
??? 1300 ??/???, ?�:
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* ?? ? ????? ???????.
#7 [652] 2014
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??????????? ???????? ?? ?????? ? ????? 15�
??? ??????? ? ????????????? ??????????????
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?????????? ?s max = 0,4. ??? ???????? �??????
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?????????????? ?????????? ??????????????? ???????? �??????� ?? ???????? 10�?/?.
???????? ??????? ????????????????? ?????????? ?????????? 27,5 ???. ?????????? ????????
????????????? ??? ?????????? ?????? ??????????? ?? ?????? ???????????? 0,6.
???????????? ????????????? ??????????? ???
????????? ????????? ?????????? ????????????:
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???? ????????????????? ???????? ???????? ??
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?? ??? Y2 ? ??????????? ??????? ?????????).
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?????????? ??? ????????????? ????????? (????????????, ???????? ???????????????? ???????
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??????? ????????? ?????? ?? ?????????? ???????????? ???????? ?????????? ?????????? y2.
??? ????? ???????????????? ???????????
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????? ?????????? ?? ???????
(12)
??? ???Ycontr ? ???????????????????? ?????????? ?????????? y2 ?? ???? ??? ????????, ?????
???????? ???????, ????????? ???????????????
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??????????? ?????? ??????????? ??? ?????? ????????? ???????????? ????????? ? ?????????????????? ???????? ???????? ?? ??????? (???. 11).
???. 11. ?????????? ???????? ????????? ???????? ?? ?????? ??? ???????? ? ?????? ???????
??? ????????? ?????????? ?????????? ????????????:
? ? ??? ??????????; ? ? ????????????; ? ? ????????????????? ???????? ????????;
? ? ???????????? + ????????????????? ???????? ????????
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?? ???? ????????????????? ????????
???????? ?? ????????? ??????? . . . . . . . . . . . . . . . �,4
???????????? + ???????? ????????????????
??????? ?? ???? ????????????????? ????????
???????? ?? ????????? ??????? . . . . . . . . . . . . . . . �,6
??????
1. ?????????? ???????? ?????????????????
???????? ???????? ????? ???????? ????????
???????? 4�? ?????????????? ??????? ????-
??????????
#7 [652] 2014
???????????, ?????????????? ?????????
???????? ? ??????????? ???????????? ? ??????
??????? ?? ??????.
2. ?????????? ???????? ???????????????
????????? ????? ???????? ??????????? ?????
(????????????) ???????? 4�? ??????????????
??????? ???????????????, ??????????????
????????? ???????? ? ??????????? ???????????? ? ?????? ??????? ?? ??????.
3. ???????? ????????????? ?????????????
???????????, ??? ??? ????????? ???????? 4�?
?????????????? ??????? ??????????????? ???????? ???????????? ???????? ????????? ????????????, ??????????? ? ?????????? ???????????? + ???????? ???????????????? ???????
?? ???? ????????????????? ???????? ????????
?? ????????? ???????, ?????????????? ????????? ????????????? ???????????? ?????????? ??
81,6�%. ?????? ?? ?????????? ??????? ?? ????
?????????? ?? ??????????? ??????????? ????
(53,4?75,3).
[1] ?????? ?.?. ????????? ???????????????? ??????? ???????? ????????? ?? ???? ????????? ?? ???????? ???????????? ?? ???????. ???????. ????. ... ????. ????. ????. ?????????-??????, 1991. 18 ?.�
[2] ?????? ?.?., ???????? ?.?., ?????? ?.?. ?????? ???????? ??????? ????? ???????????
??????? ????????????. ??????, ???????????????, 2007. 336 ?.
[3] ?????????? ?.?., ???????? ?.?., ??????? ?.?., ???????? ?.?. ???????? ???????? ???
?????? ?? ???????. ??????, ??????????????, 1978. 248 ?.
[4] ?????? ?.?., ?????? ?.?., ????? ?.?., ???????? ?.?. ???????????? ????????? ????????
? ????????. ???????? ? ?????????????, 2011, ?. 8, ?. 18?21.
[5] ????? ?.?. ?????? ???????? ?????????????? ???????? ?????. ??????, ???-?? ????
??. ?.?. ???????, 2010. 391 ?.
[6] ??????? ?.?. ?????? ???????????? ???????? ?????????? ???????????. ??????, ??????????????, 1978. 216 ?.
[7] ???????? ?.?. ????????????? ? ???????????? ??????????. ??????, ??????????????,
1971. 416 ?.
[8] ???????? ?.?., ??????? ?.?., ???????? ?.?. ?????????? ???????????? ?????? ?????????? ???????????? ???????? ??????????????? ? ???????? ?????????? ??????????.
????? ? ???????????, 2013, ???. 7. URL: http://technomag.edu.ru/doc/567714.html doi: 10.7463/0713.0567714 (???? ?????????
05 ?????? 2014).
[9] Ahmadi I. Development of a tractor dynamic stability index calculator utilizing some tractor
specifications. Turkish Journal of Agriculture and Forestry, Tubitak. 2013, vol. 37, pp. 203?211,
doi: 10.3906/tar-1103-19.
[10] Ding N., Taheri S. Application of recursive least square algorithm on estimation of vehicle
sideslip angle and road friction. Mathematical Problems in Engineering, Hindawi Publishing
Corporation. 2010, vol. 2010, no. 541809, pp. 1?18, doi: 1155/2010/541809.
[11] Villella M.G. Nonlinear modeling and control of automobiles with dynamic wheel-road friction
and wheel torque inputs. School of Electrical and Computer Engineering, Georgia Institute
of Technology, Atlanta, Georgia, USA, 2004, pp. 1?86. URL: https://smartech.gatech.edu/bitstream/handle/1853/5198/Villella_Matthew_G_200405_
ms.pdf (accessed 15 April 2014).
#7 [652] 2014
???????? ?????? ??????? ?????????. ?????????????? 67
[12] ?????? ?.?. ?????????????? ???????? ?????? ?????????? MATLAB. ??????, ???????
????? ? ???????, 2007. 288 ?.
[13] ?????? ?.?., ????? ?.?. ??????????? ??????????????? ??????????????? ???????????
?????????? ?????. ??????, ???-?? ???? ??. ?.?. ???????, 2010. 184 ?.
[14] ?????? ?.?., ???????? ?.?., ??????? ?.?. ?????????????? ?????? ??????????????
???????? ?????????? ? ???????? ???????? 8�??? ????????? ???????? ??????????
?????????. ?????? ???, 2009, ?. 2, c. 34?40.
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specifications. Turkish Journal of Agriculture and Forestry, Tubitak. 2013, vol. 37, pp. 203?211,
doi: 10.3906/tar-1103-19.
[10] Ding N., Taheri S. Application of recursive least square algorithm on estimation of vehicle
sideslip angle and road friction. Mathematical Problems in Engineering, Hindawi Publishing
Corporation. 2010, vol. 2010, no. 541809, pp. 1?18, doi: 1155/2010/541809.
[11] Villella M.G. Nonlinear modeling and control of automobiles with dynamic wheel-road friction
and wheel torque inputs. School of Electrical and Computer Engineering, Georgia Institute of
Technology, Atlanta, Georgia, USA, 2004, pp. 1?86. Available at: https://smartech.gatech.edu/bitstream/handle/1853/5198/Villella_
Matthew_G_200405_ms.pdf (accessed 15 April 2014).
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gusenichnykh mashin [Integrated cushioning highly mobile articulated tracked vehicle].
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[14] Kotiev G.O., Chernyshev N.V., Gorelov V.A. Matematicheskaia model? krivolineinogo dvizheniia
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?????? ????????? ? ???????? 28.04.2014
68 ???????? ?????? ??????? ?????????. ??????????????
#7 [652] 2014
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Information about the authors
???????? ?????? ?????????? (??????) ? ??????
??????????? ????, ????????? ??????? �??????? ??????�.
???? ??. ?.?. ??????? (105005, ??????, ?????????? ?????????, 2-? ?????????? ??., ?. 5, ???. 1, e-mail: jileykin_m@mail.ru).
ZHILEYKIN Mikhail Mikhaylovich (Moscow) ? Dr. Sc. (Eng.),
Professor of 玏heeled Vehicles� Department. Bauman Moscow State Technical University (BMSTU, building 1, 2-nd Baumanskaya str., 5, 105005, Moscow, Russian Federation, e-mail:
jileykin_m@mail.ru).
??????? ??????? ???????????? (??????) ? ????????
??????? �??????? ??????�. ???? ??. ?.?. ???????
(105005, ??????, ?????????? ?????????, 2-? ??????????
??., ?. 5, ???. 1, e-mail: yagubova.evg@yandex.ru).
YAGUBOVA Evgeniya Vyacheslavovna (Moscow) ? PostGraduate of 玏heeled Vehicles� Department. Bauman Moscow State Technical University (BMSTU, building 1, 2-nd Baumanskaya str., 5, 105005, Moscow, Russian Federation, e-mail:
yagubova.evg@yandex.ru).
? ???????????? ???? ??. ?.?. ???????
????? ? ???? ??????????
?.?. ??????
�????? ?? ????????????
????????? ???????????�
????? ???????? ?? ?????? ????????????, ??????????? ??????? ????? ? ? ???????????; ???? ????? ????? ????????? ????????? ?????????, ????????? ????????? ??????? ?????? ??????????
�?????????????? ?????� ???? ??. ?.?. ???????.
??????????????? ???????????? ?????? ? ?????????? ??????
??????????????????? ???????; ???????? ??????? ? ????????????
???????????????? ?????????? ? ????????? ??????????? ???????: ?????????? ?????????, ???? ????????? ?? ????? ????????
???????????? ?????????? ???????? ??????????? ??????? ??
?????? ?????? ??????????? ?????????? ???? (? ????????????
??????????).
?? ?????? ?????????????? ?????, ????????????? ?????????
? ?.?. ????????????, ????????? ??????? ??????????? (??????
?? ??????? ???????????) ????? ????????? ??????????? ??????�
???????? ???????? (?????????? ??????? ? ???????? ?????) ???
????????? ???????? ????????????????? ????????. ??? ???? ??????????????? ?????????? ????????? ???????????? (?????�
??????????) ???????.
??? ???????? ??????-???????????? ???????? ? ????? ????????? ??????? ????????, ??? ???????????????? ?????????????? ???? ?????????????? ?? ???????? ????????? ??????????
???????. ?????????? ??????????? ???????, ??? ?? ??? ? ????????????, ??????????? ???????????? ???????????? ??????? ???????????. ?????????? ?????????????? ?????????? ??????????
????????????.
?? ???????? ???????????? ???????????:
105005, ??????, 2-? ?????????? ??., ?. 5, ???. 1.
???.: +7 499 263-60-45, ????: +7 499 261-45-97;
press@bmstu.ru;
www.baumanpress.ru
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