Method for estimation of torsion angles of silent blocks in the cleaning drive mechanism of a grain harvester

Authors: Kotov A.V., Krol D. G., Ph. D. in Phys. And Math., Assoc. Prof.

This article is a translation of the original work of the same name, which was written in Russian and published in a peer-reviewed journal. I decided to prepare and publish its English version for several reasons. First, science and engineering thinking have no language barriers. Publishing a translation is a step towards drawing attention to my research from a wider audience, including foreign colleagues, engineers and researchers who may find the proposed method useful. Second, publishing the article in English helps increase the visibility of the blog itself in foreign search engines. This means that my developments and findings are more likely to reach those who truly need them. I am open to discussion, feedback and professional dialogue with anyone who finds the topic of my research relevant. I will be glad if this material proves useful beyond the Russian-speaking audience.

Introduction. Grain cleaning is one of the most important stages of a combine harvester's operation, during which, under the action of a fan and vibration, the final separation of grain from the grain heap, unthreshed ears, and other impurities occurs. The functional efficiency of the entire system largely depends on the cleaning drive mechanism, whose kinematics determine the nature of the oscillatory motion of all working links and the associated sieves. The rather high oscillation frequency of the links, combined with the significant mass-inertial characteristics of the sieves (including the technological mass of the harvested crop), allows this mechanism to be classified as a key source of dynamic load on the combine harvester frame. To reduce this dynamic load, silent blocks (elastic hinges) are traditionally used in the joints of the cleaning drive mechanism. These elements are rubber-metal (sometimes with a polyurethane insert) hinges which, due to the elasticity of the elastic element, perform the function of damping vibrations and also ensure the mobility of the connected links, but within a very limited range of twist angle. Figure 1 shows the cleaning system of a combine harvester with the installation locations of silent blocks in the cleaning drive mechanism highlighted.

1 – fan; 2 – cleaning drive mechanism; 3 – straw walker; 4 – upper sieve; 5 – lower sieve
Figure 1 – Cleaning system of a combine harvester

The service life of silent blocks is largely determined by their correct choice based on the permissible twist angle, as well as the applied maximum radial load. Quantitative assessment of these characteristics of silent blocks under operating conditions is quite difficult today. Therefore, in practice, these parameters are calculated at the preliminary design stage using appropriate mathematical or virtual models.

Despite the wide variety of designs of cleaning systems for combine harvesters, including the kinematic schemes of the drive mechanism, the modeling of these systems is quite fully represented in the scientific literature. Works are known related to the study of the kinematics of the cleaning drive mechanism [1 - 3], the calculation of its force loading [2, 4], solving the balancing problem [5, 6], modeling the movement of air and technological mass [7 - 9], as well as virtual testing in a software package for dynamic analysis of rigid body systems [10]. However, the issue of the methodology for calculating the twist angles of silent blocks using these models has still not received due attention [11].

Incorrect selection of a silent block leads to gradual failures in the operation of the cleaning drive mechanism, an increase in dynamic loads and, as a consequence, equipment downtime, which is unacceptable under the tight deadlines of the harvest campaign. In this regard, the operational assessment of the operating parameters of silent blocks (primarily the twist angles) at the stage of mathematical modeling of the cleaning drive mechanism of a combine harvester is an urgent scientific and practical task. Its solution will allow, in a timely manner, even at the design stage, to adjust the kinematic scheme to optimize the characteristics of the unit and prevent possible operational failures in the operation of the cleaning system.

Objective and problem statement. To propose a method for the operational assessment of the twist angles of silent blocks in the cleaning drive mechanism of a combine harvester. The proposed approach makes it possible, even at the stage of preliminary design and virtual testing, to quantitatively assess the deformation load of silent blocks, which is a necessary condition for ensuring their reliability, as well as the stable flow of the entire technological cleaning process. To achieve this goal, an appropriate mathematical model of the cleaning drive mechanism of the combine harvester was developed, analytical dependencies and an algorithm were proposed for the quantitative assessment of the permissible values of the twist angles of silent blocks using an appropriate coefficient.

Materials and methods. In developing the mathematical model of the cleaning drive mechanism, the coordinate transformation method in an invariant basis was used, applying the theory of complex numbers. The main parameters of the twist angles of the mechanism's silent blocks were calculated through the argument of the complex number vector.

Main part. The cleaning drive mechanism of the KZS-1218 "PALESSE GS12" combine harvester manufactured by JSC "Gomselmash" was chosen as the object of study. This mechanism is a spatial structure, symmetrical with respect to its longitudinal plane, which, with a number of assumptions, can be reduced to a plane design scheme, the kinematic scheme of which is shown in Figure 2. The driving link is crank AB, which, through connecting rod BC, sets all the remaining links of the mechanism into oscillatory motion. The straw walker and sieves (not shown in Figure 2) are attached to the links of the cleaning drive mechanism and oscillate in antiphase to move and clean the incoming technological mass.

Figure 2 – Kinematic diagram of the cleaning drive mechanism of a combine harvester

When developing the mathematical model of the cleaning drive mechanism of the combine harvester under consideration, the coordinate transformation method in an invariant basis was used with the application of the theory of complex numbers [12, 13], and the analytical description of the kinematics was carried out in the sequence outlined in the work [1]. The use of the apparatus of the theory of complex numbers in the kinematic analysis of the cleaning drive mechanism of a combine harvester was chosen not by chance, because compared to classical methods, this method has a number of significant advantages: a minimum number of analytical expressions, the use of only elementary operations of addition, subtraction and multiplication, as well as quick access to the angular parameters of the mechanism links. All this made it possible to elegantly describe the kinematics of the considered lever mechanism.

The mechanism under consideration has one degree of freedom, therefore the position of all its characteristic points is uniquely determined by the angle φ of rotation of the input link – crank AB relative to the real axis of the complex plane. This angle is taken as the generalized coordinate. When constructing the mathematical model, the origin of the coordinate system of the complex plane (Re, Im – global abscissa and ordinate axis, respectively) is placed at the fixed support A, and the coordinates of the fixed supports and the dimensions of the links are taken as input parameters.

As a result of mathematical modeling, the kinematics of the considered cleaning drive mechanism of the combine harvester was described using the theory of complex numbers and the radius vectors of all characteristic points as a function of the generalized coordinate were obtained (the underscore is used to denote the complex number vector):

As the results of the study [13] showed, mathematical models of planar lever mechanisms built using the mathematical apparatus of complex numbers make it possible to quite efficiently find all the angular characteristics of the links (angle of inclination, analogues of angular velocity and acceleration) through the argument of a complex number, which in general form can be represented as:

where ri – radius vector of the i-th link of the lever mechanism, represented as a complex number.

Using this property, we will show a method for the operational assessment of the magnitude of the twist angles of silent blocks in the hinges of links (e.g., at point K) and support hinges (e.g., at point L) of the cleaning drive mechanism of a combine harvester, using the design schemes shown in Figure 3.

a                                                                    b
a – silent block in the hinge of links; b – silent block in the support hinge
Figure 3 – Design schemes for assessing the twist angle of silent blocks in hinges

First, consider the silent block in the hinge connecting links KL and KJ. The angles of inclination of these links to the real axis of the local coordinate system of the complex plane (Re*, Im* – local abscissa and ordinate axis, respectively) are found as (see Figure 3, a):

where KL and KJ are the direction vectors of the corresponding links, represented as complex numbers.

The absolute difference of the obtained angles will give the function of the change in the twist angle of the silent block in hinge K depending on the change in the generalized coordinate:

The angle of inclination of the link, calculated via the argument of the complex number vector, can be positive or negative depending on its direction relative to the real axis of the complex plane. If the rotation angle is measured counterclockwise (see Figure 3), the angle will be positive; if clockwise, it will be negative. This circumstance explains the presence of the difference sign in expression (1), while the use of the modulus accounts for the commutativity property for subtracted angular quantities.

The graph of function (1) is a sinusoid (see Figure 4, a), which has a phase shift and two extrema corresponding to the two extreme positions of the driving link (crank), which limit the maximum twist angles of the silent blocks. An important parameter affecting the durability of silent blocks is their twisting speed. Figure 4, b shows the graphical dependence of the analogue of the angular velocity of the twist angle on the generalized coordinate ωqK(φ):

By setting expression (2) to zero and solving the resulting equation numerically (for example, using the PTC MathCAD mathematical package), one can find the crank rotation angles for the two extreme positions:

Using the obtained values, we find the minimum and maximum values of the silent block twist angle in hinge K:

Additional parameters of the twist angle of the silent block, such as the range, amplitude and average value, can be calculated as:

The final evaluation of the silent block twist angle is conveniently performed using the resulting utilization factor of the permissible twist angle:

where [α] is the permissible twist angle for the pre-selected standard size of the silent block according to reference data, rad.

a

b

a – twist angle; b – analogue of the angular velocity of the twist angle
Figure 4 – Graph of the angular parameters variation for the silent block in hinge K of the mechanism

Expression (3) allows for a visual graphical evaluation of the twist angles of all silent blocks of the cleaning drive mechanism on a single graph (hodograph). If the twist angle coefficient does not exceed a value of 1, then the selected silent block satisfies the condition for providing the required twist angle. If the value exceeds 1, then it is necessary to select the next standard size of the silent block or make changes to the kinematic scheme of the cleaning drive mechanism to tighten the twist angles in the hinge being analyzed.

By analogy with the above expressions, the twist angle in the support hinge L (see Figure 3, b) can be calculated. In this case, the twist angle function of the silent block in the hinge is calculated directly, without using expression (1):

The subsequent procedure will be similar to the calculation for the twist angle of the silent block in hinge K, connecting two links, and will not be presented in this work.

Hodographs of the change in twist angles of silent blocks in the hinges of the links of the cleaning drive mechanism of the combine harvester KZS-1218 "PALESSE GS12" are shown in Figure 5, a, and in the support hinges – in Figure 5, b.

a                                                                        b
a – calculation results for the hinges of the links; b – calculation results for the support hinges
Figure 5 – Hodographs of the change in the twist angle coefficient of silent blocks in the hinges of the cleaning drive mechanism

As can be seen from the results of the presented calculation, in all hinges of the cleaning drive mechanism of the combine harvester, the utilization factor of the permissible silent block twist angle does not exceed a value of 1 (it lies inside the unshaded area) with a permissible twist angle of the selected silent block [α] = 9.5°. It should also be noted that the obtained graphs of the change in the twist angle coefficient are symmetrical with respect to a straight line located at an angle that corresponds to the installation angle of the silent blocks in the mechanism (see Figure 5). This straight line is located perpendicular to the line passing through the maximum values of the twist angles at the extreme positions of the cleaning drive mechanism.

The above-described algorithm for the analytical assessment of the twist angles of the silent blocks of the cleaning drive mechanism of a combine harvester can be represented as a block diagram, shown in Figure 6.

Figure 6 – Block diagram of the algorithm for estimating twist angles in a silent block

The above method requires further refinement for the case when the kinematic diagram of the mechanism shows a coincidence of rotational kinematic pairs (hinges), for example, C and C1 (see Figure 2). In this case, it is necessary to introduce a base link, with respect to which we will determine the actual twist angles. For our case, link CF can be taken as such a link. Then, in hinge C we will determine the twist angle of link CD relative to link CF, and in hinge C1 we will determine the twist angle of link C1B relative to link CF.

Conclusion. The proposed method made it possible to analytically carry out an operational quantitative assessment of the twist angles of the silent blocks of the cleaning drive mechanism using the mathematical apparatus of the theory of complex numbers through the argument of a complex number vector. The method is universal, does not depend on the kinematic scheme of the cleaning drive mechanism and can be successfully applied to any flat lever mechanisms requiring an appropriate assessment of twist angles in the hinges. The implementation of the proposed calculation algorithm according to the block diagram is not particularly difficult for modern mathematical packages capable of operating with complex numbers.

References

1. Kotov, A. V. Primenenie vektornogo analiza dlya optimizatsii mekhanizma privoda sistemy ochistki zerna zernouborochnogo kombayna pri ego proektirovanii / A. V. Kotov, Yu. V. Chuprynin // Mekhanika mashin, mekhanizmov i materialov. – 2009. № 2(7). – S. 43-48.

2. Kinematicheskiy i silovoy analiz dvukhstannoy ochistki zernouborochnogo kombayna / D. A. Dubovik, V. I. Pribyl'skiy, A. A. Novikov, A. N. Vyrskiy // Problemy mashinostroeniya i nadezhnosti mashin. – 2019. – № 6. – S. 78–90. DOI: 10.1134/S023571191906004X

3. Badretdinov, I., Mudarisov, S., Lukmanov, R., Permyakov, V., Ibragimov, R., Nasyrov, R. Mathematical modeling and research of the work of the grain combine harvester cleaning system // Computers and Electronics in Agriculture. – 2019, 165, 104966. DOI: 10.1016/j.compag.2019.104966

4. Obosnovanie vybora silovogo metoda snizheniya dinamicheskoy nagruzhennosti privoda sistemy ochistki zernouborochnogo kombayna tipa "POLES'E" / L. I. Boyko, N. L. Rakova, T. V. Boyko, A. S. Vorobey // Agropanorama. – 2016. – № 5(117). – S. 9-14.

5. Klimovich, O. V. Eksperimental'nye issledovaniya rekuperativnogo privoda sistemy ochistki zernovogo vorokha kombayna / O. V. Klimovich, T. V. Boyko // Agropanorama. – 2011. – № 6(88). – S. 11-14.

6. Boyko, L. I. Mekhanika privodov koleblyushchikhsya rabochikh organov mashin / L. I. Boyko. — Minsk: OOO «Medzhik Buk», 2003. — 240 s.

7. Kalinovskiy, A. A. Raschetnaya otsenka vliyaniya dvizheniya reshet na aerodinamicheskie potoki v sisteme ochistki zernouborochnogo kombayna / A. A. Kalinovskiy // Mekhanika mashin, mekhanizmov i materialov. – 2024. – № 4(69). – S. 97-104. DOI: 10.46864/1995-0470-2024-4-69-97-104

8. Sorochenko, S. F. Sistema ochistki zernouborochnogo kombayna dlya raboty na sklonakh: monografiya / S. F. Sorochenko. – Barnaul : AltGTU, 2023. – 148 s.

9. Zhao, Z., Yang, X., Zhang, G. Analysis and optimization test of operation process of cleaning device of corn seed harvester. INMATEH-Agricultural Engineering, 2022. – P. 211–220. DOI: 10.35633/inmateh-68-21

10. Kotov, A. V. Proektirovanie i issledovanie mekhanizma ochistki zernouborochnogo kombayna pri pomoshchi paketa ADAMS / A. V. Kotov, Yu. V. Chuprynin, A. A. Dyuzhev // Traktory, avtomobili, mobil'nye energeticheskie sredstva: problemy i perspektivy razvitiya: doklady Mezhdunar. nauch.-tekhn. konf., posvyashch. 80-letiyu so dnya rozhdeniya d.t.n., prof. Skotnikova V. A., Minsk, 11–14 fevralya 2009 g. / redkol. : A. V. Kuz'mitskiy [i dr.] – Minsk : BGATU, 2009. – S. 165-171.

11. Analiz kinematiki mekhanizma sistemy ochistki rotornogo zernouborochnogo kombayna / D. V. Dzhasov, O. V. Pryadko, N. V. Inozemtseva, M. O. Pryadko // Innovatsionnye tekhnologii v agropromyshlennom komplekse – segodnya i zavtra : sb. nauch. statey 7-y mezhdunar. nauch.-praktich. konf. : v 2 ch., Gomel', 17 noyabrya 2023 g. / NTSTK OAO «Gomsel'mash». – Gomel', 2023. – S. 74-79.

12. Kotov, A. V. Kinematicheskiy i silovoy analiz mekhanizma pod"ema naklonnoy kamery zernouborochnogo kombayna s primeneniem teorii kompleksnykh chisel / A. V. Kotov, D. G. Krol' // Konstruirovanie, ispol'zovanie i nadezhnost' mashin sel'skokhozyaystvennogo naznacheniya : sbornik nauchnykh rabot. – 2025. – № 1(24). – S. 40-48.

13. Kotov, A. V. Sposob i programmnaya realizatsiya kinematicheskogo analiza kulisnogo mekhanizma / A. V. Kotov, D. G. Krol' // Mekhanika mashin, mekhanizmov i materialov. – 2025. – № 4(73). – S. 25-30. DOI: 10.46864/1995-0470-2025-4-73-25-30

14. Baran, I. A. K voprosu o povyshenii proizvoditel'nosti sistemy ochistki samokhodnogo zernouborochnogo kombayna / I. A. Baran, V. B. Popov // Vestnik Gomel'skogo gosudarstvennogo tekhnicheskogo universiteta im. P.O. Sukhogo. – 2023. – № 1(92). – S. 20-30.

Any citation of the text, use of theses or illustrations from this article is permitted only with a mandatory link to the original source. Please respect copyright and intellectual property.

To cite this work:

Котов, А. В. Способ оценки углов закручивания сайлентблоков в механизме привода очистки зерноуборочного комбайна / А. В. Котов, Д. Г. Кроль // Вестник Полоцкого государственного университета. Серия В. Промышленность. Прикладные науки. – 2026. – № 2(54). – С. 7-13. – DOI: https://doi.org/10.52928/2070-1616-2026-54-2-7-13.

Kotov A. V., Krol D. G. Sposob ocenki uglov zakruchivaniya sajlentblokov v mekhanizme privoda ochistki zernouborochnogo kombajna [Method for estimation of torsion angles of silent blocks in the cleaning drive mechanism of a grain harvester]. Vestnik Polockogo gosudarstvennogo universiteta. Seriya V. Promyshlennost'. Prikladnye nauki [Bulletin of Polotsk State University. Series B. Industry. Applied sciences], 2026, no. 2(54), pp. 7-13. DOI: https://doi.org/10.52928/2070-1616-2026-54-2-7-13 (in Russ.).

Link to the original work in *.pdf format