The movement of the system "tractor - transport-technological machine of variable mass" is considered in the context of the movement of the center of mass of the system, given the equality of the internal forces of this system among themselves. Using the obtained dependences, it is possible to determine the effect of changes in the acceleration of the centre of mass of the transporttechnological unit with variable mass on the load of the tractor's transmission parts. The tractor control algorithm is synthesized in the rational area of transmission elements loading and a program for its implementation in the field is developed. The developed application is an information system, the purpose of which is to inform the operator of the presence of stress in the transmission`s elements of the tractor, which cause it overloading and, therefore, reduce the resource of its parts. If the strength condition for fatigue failure is not met, the operator of the transport-technological unit is offered to change the driving mode to reduce the load on the transmission elements.
Transport Service System that combines transportation technologies, transport-technological units and organization of technological works is one of the most important components of the agricultural system. Improvement of the Transport Service System is possible using modern information control and diagnostic systems that reduce the probability of error due to the human factor. A number of works are devoted to these problems. The paper [1] considers problems pertaining to operational diagnosis of transport facility operator (driver), describes a basis algorithm of physiological operator’s charCopyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). acteristics with the purpose to control his activity during non-standard situations. Introduction of a system activity with use of modern satellite technologies allows to lower transportation costs, to increase efficiency of use of agricultural machinery is considered in the work [2].
The issue of designing the machine tractor movement trajectory is relevant today because its optimization significantly reduces the transport costs [3]. Comparative study of the usability of directional commands for two different conceptions of agricultural machinery is conducted in the work [4]. The clarification of the normal reactions distribution between the axles allows to choose more rational forces distribution between the axles. It has a significant impact on the stability against skidding and the wheeled tractor braking effectiveness. [5] The dependence of the influence of vertical accelerations on the dynamic loads on the axle of the tractor front and rear axles is determined in the article [6].
However, research on the use of tractors on the transport and technological agricultural operations were identified unsolved problems, which include: dynamics of a variable mass aggregate, energy saving [7], formation of system properties of the unit elements [8]. The general principles of forming the time to failure due to deviations from the nominal values of external perturbations do not justified [9, 10]. The problem of dynamics of transport-technological unit with variable mass is not solved in terms of their energy efficiency and performance [11]. 2
The acceleration of the centre of mass as a quantity forms the energy of the movement of the unit The movement of the system "tractor - transport-technological machine of variable mass" can be considered in the context of the movement of the centre of mass of the system, given the equality of the internal forces of this system among themselves.
Then, it can said that the movement of the centre of mass of the given system at each
moment of time is equivalent to the movement of a material point with a mass equal to
the mass of the system at a given moment of time, which is affected by a force equal to
the resulting forces applied to the system:
d m vc
dt
F ,
(
Multiplying equation (
dt
Opening the brackets and taking out the quasistatic mass beyond the differential sign, got: m dvc dScon m dvc dSvar FdScon FdSvar .
dt dt Considering that dAcon FdScon , and dAvar FdSvar , it can be written: dAcon m dvc dScon ;
dt dAvar m dvc dSvar .
dt where ∆m - changes in weight of the transport-technological unit.
The value Acon m aunit Sunit determined by dependence (
Value Avar m ac Sc - the work spent by the unit on moving Sc the center of mass of the unit with acceleration ac as a result of changes in its mass.
Thus, it can be argued that there is a direct proportion link between the work expended by the unit, and the acceleration of the center of mass. Therefore, using known definition of safety margin and accepting aunit → 0, it can be obtained the condition of fatigue strength of transmission`s parts, taking into account the acceleration of the center of mass ac at a certain displacement Sc ac l W 2 K 2 Kd2 21 1
p F 3, 4 G J p munit Sc K2 21 K2 21 .
Using the obtained dependence, it is possible to determine the effect of changes in
the acceleration of the centre of mass of the transport-technological unit with variable
mass on the load of the tractor's transmission parts.
(
Ensuring the fatigue strength of transmission elements, taking into account the energy losses of the unit The strength of materials under impact loads variables characterized fatigue curve. It presents the link between the highest values of variable cyclic stress in a material a and the number of cycles these stresses N to destruction.
When building the dependence of the number of cycles of alternating strength in the material of the part to destruction from changing them amplitudes in logarithmic coordinates lg a lg N , the fatigue curve is represented like a broken line, the left branch of which is inclined to the abscissa axis at an angle, and the right branch is conventionally assumed horizontal due to its small inclination in reality and propagation to such a large number of load change cycles, which is assumed to be rare due to the limited service life of the tractor's transmission.
The common form of the fatigue curves for various materials and samples allowed us to use their analytical expression and compare the characteristics of fatigue strength not by comparing the curves as a whole, but by comparing individual numerical indicators.
Stepped dependency is the most common analytical description of a fatigue curve: where A – constant.
For the discrete repeatability of stress cycles in the part material, the mathematical expression of the linear accumulation of fatigue damage has the form: where ni - is the number of cycles with the amplitude of the i-th level, during the process; Ni - the number of cycles with amplitude of the i-th level, with continuous action of which the material is destroyed; r - the number of strength levels, covers the entire range of changes during the process; L - indicator of damage.
According to this cumulative hypothesis, destruction in the material occurs when L = 1. However, numerous experimental researches show that the indicator of damage L during breakage is different from 1. Moreover, formula (8) becomes: The value a depends mainly on the material of the part and partially on the parameters of the spectrum of stress amplitudes. In this regard, for calculating the equivalent stress, the condition for summing the damaging effects of various cycles, while maintaining am N A, r i1 Ni n
i L, r i1 Ni n i a.
(7) (8) (9) linearity, is attributed to a certain calculated fatigue curve that differs from the initial degree in terms of degree m.
When calculating the absolute durability of accounting for such an amendment is very significant. When calculating the comparative durability, the spread of the indicator a in the usual range for steels (0,8 ... 1,4) leads to small differences in the degree of the calculated fatigue curve from the real one.
Thus, it can concluded that the use of relator in comparative calculations does not give large errors even when the parameters of the specter amplitude of the compared modes will differ significantly.
We introduce two modes of transmission elements loading: for the movement of a transport-technological unit of constant and variable masses. Then, for the moment when the accumulated damage in the metal is equal, we get:
Lcons Lvar , and taking into account expression (8) it can be can written: rcons ni cons
rvar ni var . i1 Ni i1 Ni Since the calculation of the transmission elements loading is carried out according to the stresses, which are defined in accordance with the law of fatigue failure, for cycles of any level, it can be written: where σ-1 – the endurance limit.
Then and from the expression (11): ami N m1 N , i 0
m 1 N ,
Ni 0
a i rcons ni cons m i1 1
a i cons N0
rvar ni var
m i1 1
a i cons N0 .
Taking into account the fact that, for a given part, the values σ-1 and N0 are independent of the load conditions, expression (14) takes the form: (10) (11) (12) (13) (14) Let the transport-technological unit carry out the technological process with a certain value of the expended work A, and the work to a comparable degree of damage to the material is equal A*.
Then the number of cycles of each observed level until the moment of comparison on the compared operating modes of the transport-technological unit can be expressed through the results of experimental studies in the form: rcons rvar ni cons ami ni var ami . i1 i1
*
Acons , ni cons nicons Acons
*
Avar ni var nivar Avar (16) (17) (18) (19) (20) (21) The resulting expression can be considered as the coefficient of equivalence of the work spent on moving the transport-technological unit with constant and variable masses.
Denoting it by the letter ke, will get: The given stress of the steady state σnp, equivalent to that in the unsteady mode, is determined from the dependence of the form: where the dash indicates that the corresponding value obtained on the basis of realized process.
Substitute (17) in (16):
Ac*ons rcons nicons ami Av*ar rvar nivar ami .
Acons i1 Avar i1 Then the ratio of work on these modes:
* Acons
* Avar
rcons Acons nicons ami i1 rvar Avar nivar ami i1
.
Acons ke Av*ar .
* np 1 m a
1 .m im ni .
N0 i Then, the safety margin can be determined from an equation of the form: n np To test of the transport-technological unit with variable mass based on the KhTZ-17221 tractor as part of an aggregate with a machine for applying liquid organic fertilizers MZHT-10, the experimental researches of the overload signaling device of the tractor's transmission unit were carried out, developed on the Android platform. The developed application is an information system, the purpose of which is to inform the operator of the presence of stress in the transmission`s elements of the tractor, which cause it overloading and, therefore, reduce the resource of its parts. The main application window consists of four main zones (Fig. 1). The top part of the main application window is a menu for adjusting the view of the transmission`s elements and the selection of the constituent elements of a transporttechnological unit with the variable mass. When the model of tractor and agricultural machine are selected, the program independently, using the existing database, generates mass-geometric indicators of the transport-technological unit for the future calculations.
The second (middle) part of the main application window displays the load distribution in the transmission`s elements. Because of the smartphones architecture, the visualization of transmission elements is a set of frame-by-frame animation of load redistribution.
Second (middle) part the main window the programs are designed for visualization distribution load elements transmission installation. Given features architecture smartphones visualization elements transmission is a set of time-lapse animation redistribution loaded.
The third part of the main application window displays basic information about the values of stresses caused by the torque in the transmission elements, and the value of the cycles to fatigue failure.
Moreover, if the stress value exceeds the permissible limits, and the value of the residual number of cycles is critical, the fourth part of the main application window (information panel) changes its color from green (see Fig. 1) to orange (Fig. 2), and the inscription “Continue to work on this gear ”is replaced by the inscription“ Need to change gear ”(see Fig. 2).
Fig. 2. General view of the application window for controlling the transport-technological unit
with variable mass when the transmission is overloaded The developed application uses input data from its own database (the mass of the transport-technological unit, transmission ratios and engine characteristics), as well as acceleration of the centre of gravity along three coordinate axes.
To attract the operator`s attention, when the elements of the transmission are overloaded and the operation mode needs to be changed, an audio signal is given, and it turns off only after the transmission loading mode returns to rational.
According to the results of a comprehensive analysis of the energy losses of the transport-technological unit with the variable mass, when performing the technological process, the concept of a systematic approach is substantiated, which is the scientific novelty of the study, increasing the operability of the unit, which, unlike the known ones, is based on the proved statement, ensuring a minimum of energy losses on oscillatory the motion of the center of mass.
The tractor control algorithm is synthesized in the rational area of transmission elements loading and a program for its implementation in the field is developed. The principle of the application is based on the algorithm and use an acceleration sensor built into the phone. Because the application is designed on an open operating system Android, it can be said that it is available for almost all existing smart phones.
The main condition for the correct functioning of the program is the location of the phone so that at least one of the axes of its accelerometer coincides with the direction of movement of the transport-technological unit with the variable mass.
Obtained results can be extended and used on other types of vehicles. In the future, it is planned to expand the amount of source data for the application, which will increase the accuracy in determining the optimal modes of operation. 7. Shulyak, M. Selecting a rational operation mode of mobile power unit using measuring and control complex. CEUR Workshop Proceedings, vol. 1, 141-151 (2019). 8. Podrigalo, M. Stability of Wheel Tractors during Braking. SAE Technical Paper vol. 201901-2142, (2019). 9. Bauchau, O. Parallel computation approaches for flexible multibody dynamics simulations.
Journal of the Franklin institute, vol. 347, 53-68 (2001). 10. Hernandez, W. Improving the response of a rollover sensor placed in a car under performance tests by using optimal signal processing techniques. IEEE International Symposium on Industrial Electronics, 2803–2808 (2006). 11. Zahariev, E. Stabilization of multiple constraints in multibody dynamics using optimization and a pseudo-inverse matrix. Mathematical and Computer Modelling of Dynamical Systems, vol. 9, 417-435 (2003).