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Section 6. Mechanics
DOI: http://dx.doi.org/10.20534/ESR-17-3.4-75-77
Matmurodov Farkhod Matkurbonovich, associate professor Tashkent state technical university E-mail: matmurodovfarhod@yandex.com Daminov Oybek Olimovich, is the senior teacher Tashkent state technical university E-mail: ems-tdtu@umail.uz Mirzaabdullayev Jakhongir Bakhtiyarovich, is the senior teacher Tashkent state technical university E-mail: dvs-tgtu@mail.ru Hakimov Zhamshid Oktyamovich, is the senior teacher Tashkent state technical university E-mail: dvs-tgtu@rambler.ru
Mathematical modeling of transfer of the moment from the engine to the executive mechanism
Abstract: Dynamic loading of hubs of motor-transmission and power gears of the traction vehicle are analysed. Made mathematical model of transfer of the moment from the engine to the executive mechanism which allows to learn working conditions of each main knot of the car. The moments of resistance of driving wheels and a shaft of selection of power are analytically defined, taking into account the moment of friction it is elastic the pneumatichydraulic drive.
Keywords: the engine, the executive mechanism, the car, a driving wheel, a powertake-off, a motor and transmission and power gears, the traction vehicle, it is elastic the pneumatichydraulic drive, dynamic loading, the friction moment.
Progress in autotractor building is characterized by continuous increase of requirements as to functional indicators of cars — productivities, universality, rapidity, dynamism, a power saturation, and to consumer — reliability, durability, non-failure operation, noiselessness and small vibroactivity. All indicators of cars depends on quality and loading of their main working hubs.
One of the most important elements of the traction vehicle is the complex of hubs of motor-transmission, or power gears.
Loading of motor and transmission and power gears of the traction vehicle has dynamic character. It is formulated as a result of action of both external, and internal perturbations. Loading of motor and transmission and power gears of the traction vehicle has dynamic character. It is formulated as a result of action of both external, and internal perturbations. Among external fluctuations of traction resistance and engine torque, perturbation from fluctuations of skeleton on the suspender, and also influences from control system are considered as the main. Among internal kinematic and power perturbations from regears engagement, misalignment of shaft, not uniformity of rotation of cardan, deformations and shifts of case shaped parts are considered as the main.
Numerous researches demonstrate that on loading of transfer from internal perturbations decisive impact is exerted by correctness of the choice of its own dynamic characteristics determined by set of elastic and inertial and dissipative parameters of elements [4].
In this regard, more and more the importance is got by problem of purposeful forming at design stage of dynamic characteristics of power gears on the basis of the analysis of influence on their loading of dynamic parameters of elements of transfers and the external and internal loading factors.
In view of the fact that now there are no methods allowing at design stage that is in the conditions of incompleteness of information on dynamic parameters of elements, adequately to consider influence on loading of transfers of internal perturbations, the specified problem has not received the full decision. Meanwhile at design stage there are possibilities of purposeful forming of set of dynamic parameters for ensuring the required loading in elements of transfers of operation. Therefore, creation of the methods allowing to estimate dynamic loading of each element of the power gear at change of parameters and certain ranges is necessary.
Emergence of irregularity of thrust effort, its unsteady character and excessive fluctuation in PTO negatively influences dynamic, fuel and economic and ergonomic indicators of the tractor and transport and machine and tractor unit.
Considering start-off and dispersal, M. M. Schukin in pile to work has defined that elastic communication influences nature of process of start-off and dispersal. The elastic hitch allows the tractor at start-off from the place to make preliminary dispersal within deformation of elastic element. Energy of dispersal is implemented in the
Section 6. Mechanics
form of additional effort on hook. At the same time traction properties and passability of the traction and transport unit increases. At very small rigidity of the traction coupling device or sharp startoff from the place the tractor with elastic hitch is theoretically capable to shift the trailer having weight twice big than the tractor with rigid hitch. Besides, elastic communication in comparison with rigid hitch can provide start-off of the machine and tractor unit from the place at much smaller coefficient of coupling with the soil. For decrease in dynamic shock loads in the course of start-off and the size of slipping of clutch coupling it is necessary to install the elastic damping drive (EDD).
The analysis of the developed mathematical models of machine and tractor units which is carried out by B. P. Fedorov has shown that cardinal way of decrease in dynamic loading of tractor — application of the elastic elements reducing danger of impact on health of the operator of low-frequency fluctuations.
Number of scientists believe that one of ways of improvement of traction and economic indicators of the tractor and transport unit (TTU) at the unsteady loading is creation of such transmission which will allow the engine not to feel influences ofvariable nature of traction efforts in certain conditions.
However use in point of hook of the tractor and trailer of elastic communication — the traction coupling device with the elastic damping element [1, 2] is most acceptable for stabilization of the thrust effort improving operating and ergonomic characteristics of TTU. Use of such device will improve operational properties and as a result — will positively influence productivity and fuel efficiency.
Forming of the machine and tractor unit (MTU) on the basis ofpower saturated tractors has led to development of the truck tractor into the mobile power means (MPM) now [3]. The analysis of MTU on the basis of MPM shows that the "excess" part of power of the tractor engine removed from PTO appears opportunity unitization of the perspective wide and combined farm vehicles. It unitizations allows uses of weight of all MTU for creation of thrust effort that to lower costs of self-movement of tractor and consolidation of the soil with simultaneous increase in productivity of MTU and decrease in specific power consumption of works. At it unitizations appears excessive fluctuations of driving wheels and in PTO.
The exception of adverse effect of alternating load is possible improvement of operational receptions, or improvement of design of the making MTU. One of constructive solutions of partial, or full isolation of the engine from the excessive shifting jerks caused by change of drag torque is application of the transmissions possessing the high damping qualities. In transmission comes two third-party excessive fluctuation, from the moving mechanisms and from external influences. And external influences appears from excessive fluctuations of axis of driving wheels and in PTO.
For removal of excessive fluctuations of axis of driving wheels and PTO the elastic damping drive of different design is usually used. EDD repays excessive fluctuations easier and to provide standard duties of work.
We accept dynamic rated system such view: "engine" - "transmission" - "axis of driving wheels with EDD" - "PTO with EDD" -"the mass of the rotating mechanisms of the unit given to the cardan shaft". Let's model this rated scheme.
Mathematically process of inclusion of friction coupling is described by system of the differential equations of dynamic balance (1) considering position forces (elastic forces) and resistance forces (damping, friction force). The formula for calculation of the moment of friction includes two functional dependences: specific pressure upon friction surfaces, time-dependent, and friction coef-
ficient as function from the relative speed of sliding of the interfaced surfaces. The second and third equations of this system describe power communication between leaders and the conducted parts of friction coupling. Thanks to such option of drawing up mathematical model it is possible to consider nature of change of friction coefficient for different models of friction, and also to consider behavior of system at different laws of change of pressure in the booster of friction coupling.
JA + К (P-p2 ) + ci (Pi-Рг ) = Md
J2p2 + c, (Pi - P2 ) = Mmii J 3p3 + c2 (Рз - P4 ) = Mmi2
JP + К (Рз -<Pl) + C4 (Рз -Pj = M С1)
JpP5 + К ( -ф5 ) + ^ ( - A ) = Ms vk. ± Mup,v.k
JpФе + К ( A - p6 ) + C6 ( P4 - A ) = Mvom ± M udpvom J7p7 + k7 ( P6 - p7 ) + C7 ( Рб - P7 ) = Ms.vrash.m.a.
here Md - the torsion torque developed by the engine; Mmii - moment of drive disk of clutch coupling; Mmi2 - moment of driven disk of clutch; Mr - the moment on transmission; Ms v t - drag torque of driving wheels; Mudps v t - the moment of the elastic damping drive to resistance of driving wheels; Mvom - the moment on PTO; Muipvom - the moment of the elastic damping drive in PTO; Ms msh m a - drag torque of the rotating unit mechanisms.
JMi+К ((- s<Pd 2 )+c i ( + S(Pd i- Ф02- S(Pd 2 ) = Md+SMd
J2S(Pd2 + Ci (Poi + SPdi - Po2 - SPd2 ) = Mmii
JM3 + C2 (Po3 +SPd3 - P04 - SPd4 ) = Mmi2 J4S(Pd4 + К (SPd3 - SPd4 ) + C4 (Po3 + SPd3 - P04 - SPd4 ) = M J5SPd5 + К (SPd4 - SPd5 ) + ^ (Po4 + SPd4 - Po5 - SP ,, ) = Ms.,.L ± M J6SP6 + К (SPd4 - SPd6 ) + c6 (Po4 + SPd4 - P06 - SPd.6 ) = Mvom ± M, J7S(Pd7 + К7 (SPd4 - SPd7 ) + C7 (P06 + SPd6 - Po7 - SPd7 ) = M,vrash.m.a
here Sfdi , Sfd 2 , S<Pd3 , Sfd4 ,SPd 5 ,SPd 6 ,SPd 7 - deviations anglesof rotation from equilibrium state by the form impacts on system of
the variable moment from the engine; Voi , ф02 , Vo3 , Ф04 , VOS ,Vo6, ,Vo7
-angles of rotation, caused by static load.
J M + KS ( -5фs ) + С s (S<P4 -S<P5 ) = Ms.v.t. ± Mudfs.v.t (3 ) JM + k6 (S<4 -S<6 ) + c6 (< - < ) = Ms.m,h.m.,. ± Mudpvom
here 8(pl, S(p2, 8<p,,S(p4, S(p5,8<p6,S(p7 - fluctuations of instant angle of rotation rather equilibrium state.
From fluctuations of turning angles we will pass to fluctuations of the moments into transmissions SMr, resistance of back driving wheels SMsvt, PTO SMvomand resistance of the rotating unit mechanisms SMs.,r„h.m.SMsv.t.= c 5 (S<P4 -§Ps) , SMsv.t.= c S (8Ф4 -8<Ps) , SMs.v.t. = С5 (8<Pl-8(p5); SMrom = С6 (S(Pi-8<p6),SMm = c6 (-8ф6),
SMv0m = С6 ( -Sp6) . (4)
Having substituted the equations (4) in (3) and having transformed the turned-out equations, we will receive, in it value of size
S (p4 does not influence system, we consider their valuesare equal to zero
J5SMiv.t./ c5 +ôMsvth5/ c5 +ÔMsvt = Ms v t ± M,
(2)
udps .v .t udpvom
J6SMvom / c6 + 5Mmmh6 / c6 + SMvo
M
± M.„
(5)
vrash .m .a. udpvo
SMs.v.t, +SMs.v.t A / J S +SMs.v.t c S / JS = Ms.v.t.c J JS ± Mudps, ^ 5 / J 5
SM +SM \/Jt +SM cjJt = M
cj Jf ± Md cj J6
6 J 6 udpvom 6 J 6
(6)
M
M
M
M
ai (S2 + biS + b2 )-b2 (aiS + a2) к 8 , bi (S2 + aiS + a,2)-a,2 (biS + b,2) ' S
(7)
here S =(S2 + atS + a2 )(S2 + btS + b2 ) - (S + b2) ( + a.). a1,a2,b1,b2 - coefficients of dynamic system.
ai = K/ J5 < a2 = C5/ J5 ,b1 = k6 / J6 < b2 = C6/ J6 .
Conclusion. The analysis of dynamic loading of nodes motor and transmission or power gears of the traction vehicle, has given the chance to find the existing problems of elementstraction vehicle.
- mathematically modeling transfer of the moment from the engine to the executive mechanism which allows to learn operating condition of each main nodes of the car. This model will help clerks and designers for creation new designs of TTU and MTU.
- have analytically defined drag torques of driving wheels and shaft of selection of power taking into account the moment of friction it is elastic the pneumatichydraulic drive.
References:
1. Gamayunov A. M. Improvement of dynamics of start-off and dispersal of the tractor and transport unit due to improvement of the elastic damping track-coupling device. The abstract of the thesis for degree of Candidate of Technical Sciences. Saratov, - 2008.
2. Piedmont I. E. Decrease in dynamic loads of the h traction and drive units at the expense of the elastic damping drive of shaft of selection of power. The abstract for degree of Candidate of Technical Sciences. Voronezh, - 1998.
3. Sidorov V. N. Forming of agricultural energy saving machine and tractor units. Bryansk. "Bryansk GCXA", - 1998. - P 41.
4. Shekhovtsov V. V. Improvement of autotractor power gears on the basis of the analysis and synthesis of their dynamic characteristics at design stage. The abstract of the thesis for degree of Candidate of Technical Sciences. - Volgograd, - 2004.
