Methods Of Classical Mechanics Research Articles

Study on working bodies of the soil preparation machine for sowing potatoes

The purpose of the study is to substantiate the parameters of the guide knife and the loosening pointed leg of the machine. The basic principles and methods of classical mechanics, mathematical analysis and statistics were used in this study. Theoretical studies were carried out to determine the parameters of the guide knife and the loosening pointed leg of the machine. It is established that to ensure the required value of the crest height with minimal energy consumption, the height and length of the guide knife should be 8 and 15 cm, respectively, the angle of the knife blade to the horizon - 30º, the longitudinal distance from the toe of the ploughshare body of the knife toe – 13 cm. To ensure the required crumbling of the soil, the width of the pointed loosening paw should be 15 cm.

Study on plowing of cotton soil using two-tier plow

The purpose of the study is to substantiate the parameters of a two-tier plow for plowing soil from under cotton. The basic principles and methods of classical mechanics, mathematical analysis and statistics were used in this study. The effects of the cotton field relief on the tillage and traction resistance of a two-tier plow were studied theoretically and experimentally. Analytical expressions are obtained for determining the uniformity of the course, the load of the bodies and the center of resistance of the plow, depending on its main parameters and the roughness of the relief of the cotton field. It is established that serial two-tier plows, due to the discrepancy between their width of the gripper and the width of the row spacing, do not meet the requirements of agricultural technology: the plowing depth is not stable, the coefficient of variation of the plowing depth reaches 16% for a trailed plow, and for a mounted plow - 25.8%; the transverse direction of the plough the bottom of the furrow turns out to be stepped; the value of the traction resistance changes at each pass of the plow. To improve the quality of plowing fields from under cotton, a new plowing method has been developed, carried out by a two-tier plow, the width of which is a multiple of the width of the row spacing of cotton. The width of the plow bodies is equal to half the width of the row spacing.

Optimalization of Design Parameters of Experimental Installation Concerning Preparation of Liquid Feed Mixtures

The article describes the initial conditions for the development of universal mechanization means for the process of mixing dry and liquid components. The essence of the method is to study the motion of a particle with different constructive and physical properties of the medium. The mathematical model of particle motion is based on theoretical mechanics and hydraulics. In this case, the main purpose of the study is to find the optimal design parameters for the installation. At the beginning, a theoretical analysis of the installation was carried out using the methods of classical mechanics and hydraulics. Experimental studies were carried out in several stages. At the beginning, one-factor experiments were conducted, followed by allocating the main factors and determining their interaction. Then, using the methods of planning the experiment, we obtained the regression equations and further optimized the parameters to summarize the main findings of the article. Modern installations should have versatility in any technological line; for example, an installation is presented that can not only mix, but further transport the mixture like a conventional pump, while providing a dosing device that is necessary for the feeding of dry components. Theoretical studies have been carried out in which the design of the impeller is substantiated at various speeds. Experimental studies to determine the design parameters of the installation are in continuous operation. The degree of homogeneity was Θ = 74%, with β2 = 80 … 100° and βst = 65 … 102°, while the value of the consumption of electrical energy is equal to Eel = 0.265 … 0.28 kWh/t.

The synthesized method based on classical mechanics and finite element for vehicle collision accident reconstruction analysis

ABSTRACT Most of the traditional methods for accident reconstruction are only based on a single theoretical system – either classical mechanics or finite element. In order to compensate for this limitations, the analytic methods of finite element and classical mechanics were synthesized to simulate and reconstruct a vehicular collision and deformation. Using an actual accident case, the finite element simulation models of accident vehicles are constructed, and the simulation experiment is also conducted. During the experiment, there are some analyses about the characteristics of velocity variation, forming process of deformation, state of stress distribution, and law of energy transformation of vehicles, and analyses also including vehicle simulation deformation and actual deformation shapes. It is shown that the synthesized method breaks through the limitations of traditional methods that rely on a single theoretical system. Meanwhile, comparing the finite element simulation deformation with the actual deformation can improve the reliability of accident reconstruction.

Акустический сенсор для оценки состояния производственного оборудования

An important trend in the development of industry is the development of digital models of industrial facilities, the work of which is based on information coming from sensors. This allows you to optimize functionality, predict the technical condition of objects, which is especially important, for example, in the field of metallurgical production, where forced stops are accompanied by huge losses. The sensors themselves are also modeling objects, because they need to adapt to rigid production conditions in which their own shortcomings are manifested, while the correct introduction of corrections for environmental conditions, diagnostics and self-diagnostics, which are impossible without building various types of sensor models, is important. The purpose of the work is to deve¬lop a universal discrete model of an acoustic sensor suitable for receiving and emitting acoustic signals. Methods. The work used methods of classical mechanics and mathematics, vibration theory, generalized functions, distributed systems, and mathematical programming methods were used to provide calculations. Results. The main result is a universal discrete model of a sensor with a working element in the form of a round plate, which by choosing parameters can be transformed into a model of a unidirectional dynamic microphone with a flat membrane or a radiator with a focusing spherical element. It is shown that on the basis of the model it is possible to synthesize narrow-directional radiation diagrams and thereby obtain the necessary spatial selectivity and noise immunity of measurements. Conclusion. Calculations made using the proposed model correspond to the known results of acoustics. Verification of the discrete model using a natural sample showed a high accuracy in determining the resonant frequencies and forms of oscillation of the sensor.

Projective representation of the Galilei group for classical and quantum–classical systems* *Contribution to the special collection ‘Koopman Methods in Classical and Quantum-Classical Mechanics’.

A physically relevant unitary irreducible non-projective representation of the Galilei group is possible in the Koopman–von Neumann formulation of classical mechanics. This classical representation is characterized by the vanishing of the central charge of the Galilei algebra. This is in contrast to the quantum case where the mass plays the role of the central charge. Here we show, by direct construction, that classical mechanics also allows for a projective representation of the Galilei group where the mass is the central charge of the algebra. We extend the result to certain kind of quantum–classical hybrid systems.

Traction resistances of the cotton seeder moulder

The purpose of the study is to determine and analyze the traction resistance of the cotton seeder moulder. The moulder of the cotton seeder consists of a visor, two side dumps and a straight part. The forces acting on the elements of the comb shaper are considered. The basic principles and methods of classical mechanics, mathematical analysis and statistics were used in this study. Analytical dependences for determining the traction resistance of the moulder depending on their design parameters are obtained. It is established that the traction resistance of the moulder movement depends on the physical and mechanical properties of the soil, the depth of its penetration into the soil, the length of the skids, the width of the input edge of the skids and the angles of installation of the side dumps of the moulder. With the optimal parameters of the moulder, the traction resistance of the sowing unit will increase by 0.6-0.8 kN, which practically does not affect the operation of the sowing unit.

Combined machine for preparing the soil for re-sowing crops

The technologies used to prepare the soil from under winter crops for re-sowing consist of numerous soil preparation operations, which lead to loss of moisture, delay in the preparation of the soil for sowing and increase operating costs. The purpose of the research is to develop a combined machine for preparing the soil from under winter crops for sowing repeated crops. The authors developed a combined machine consisting of non-shaft housings, spherical disk batteries and a roller. The basic principles and methods of classical mechanics, mathematical analysis and statistics were used in this study. It is established that the most optimal design scheme of a combined machine is considered to be a scheme consisting of non-shaft housings with crushers, a battery with cut-out spherical disks and a roller. The experimental studies have established that the shaft-free body of the machine with dyes provides high-quality crumbling of the soil with minimal energy consumption. The main parameters of the machine and its technical characteristics are given. It is established that the proposed machine reliably performs the specified technological process and its performance indicators fully meet the requirements. The use of the developed combined machine for non-tillage of the soil and its preparation for sowing of repeated crops makes it possible to reduce operating costs in comparison with the existing technical means for processing each hectare of the field by 53.4 %.

Researching the parameters of the disc plough and its smooth run throughout the tillage depth

The purpose of the study is to substantiate the parameters of a disc plough and to study its uniformity of stroke along working depth. Basic principles and methods of classical mechanics, mathematical analysis and statistics were used in this study. Equality of running disk plough throughout tillage depth is studied theoretically and experimentally. In accordance with the implemented studies, in order for disc plough to operate at the required level on soil with low energy consumption, its operating elements should be installed in the range of 35-40° relative to direction of movement, and 15-18° relative to steep, cross-section between them should be 28-32 cm, and longitudinal distance should be at least 60 cm, and vertical distance from base plane to bottom tie point should be between 62-70 cm in order for disc plough to sink to specified depth and walk evenly at the same depth, as well as to ensure the required transport hole.

Movement of crushed stem particles when they interact with hammers

The purpose of the paper is to study the movement of crushed stem particles when interacting with hammers inside the chopper. The basic principles and methods of classical mechanics, mathematical analysis and statistics were used in this study. An analytical expression is obtained for determining the speed of movement of crushed stem particles when they interact with hammers. It is established that the intensive splitting of the stalks of coarse feed by the rotor hammers is provided at their circumferential speed of 30-35 m/s. The particle velocity from the entrance to the exit from the working chamber gradually increases and is 15-16 m/s. The performance of the crusher depends on the angular velocity and radius of the rotor, as well as on the density and feed rate of the processed material.

Effective Hamiltonians for almost-periodically driven quantum systems* *Contribution to the special collection ‘Koopman methods in classical and quantum-classical mechanics’

We present an effective Hamiltonian theory available for some quasi-periodically driven quantum systems which does not need the knowledge of the Fourier frequencies of the control signal. It could also be available for some chaotically driven quantum systems. It is based on the Koopman approach which generalizes the Floquet approach used with periodically driven systems. We show the properties of the quasi-energy states (eigenvectors of the effective Hamiltonian) as quasi-recurrent states of the quantum system.

The Schwinger action principle for classical systems* *Contribution to the special collection ‘Koopman methods in classical and quantum-classical mechanics’

We use the Schwinger action principle to obtain the equations of motion in the Koopman–von Neumann operational version of classical mechanics. We restrict our analysis to non-dissipative systems. We show that for velocity-independent forces the Schwinger action principle can be interpreted as a variational principle.

Separation of scales: dynamical approximations for composite quantum systems* *Contribution to the special collection ‘Koopman methods in classical and quantum-classical mechanics’

We consider composite quantum-dynamical systems that can be partitioned into weakly interacting subsystems, similar to system–bath type situations. Using a factorized wave function ansatz, we mathematically characterize dynamical scale separation. Specifically, we investigate a coupling régime that is partially flat, i.e. slowly varying with respect to one set of variables, for example, those of the bath. Further, we study the situation where one of the sets of variables is semiclassically scaled and derive a quantum–classical formulation. In both situations, we propose two schemes of dimension reduction: one based on Taylor expansion (collocation) and the other one based on partial averaging (mean-field). We analyze the error for the wave function and for the action of observables, obtaining comparable estimates for both approaches. The present study is the first step towards a general analysis of scale separation in the context of tensorized wavefunction representations.

Effect of the adhesive thickness on butt adhesive joints under torsional loads

Adhesive joints are extensively used in diverse industrial applications, exploiting the improved mechanical performance they offer over classical mechanical joining methods. To effectively design adhesive joints, it is first necessary to determine the mechanical properties of the materials being used (e.g. the adhesives and adherends). In this work, an epoxy based structural adhesive was characterized under tensile and shear loads using butt joints with solid adherends. The tensile tests were performed in a universal tensile machine and the shear tests were carried out in a torsional testing machine that ensures perfect alignment of the specimens and avoids any spurious bending moments, compression and tension loads during the test. The effect of adhesive thickness on the tensile and shear properties of the adhesive was evaluated, showing that under torsional loads there is a significant effect of the adhesive layer thickness on the shear strength and stiffness of the adhesive.

Impulse control of a two-link manipulation robot

A nonlinear problem of controlling the movements of a two-link manipulation robot is considered. The free mechanical system has two first integrals in involution. Methods of classical mechanics are used for analytical integration of the system of nonlinear differential equations. A trajectory connecting the initial and final positions of the two-link manipulation robot in the configuration space is found. Impulse controls at the initial moment of time impart the necessary energy to the robot to enter this trajectory. Impulse controls are also used to damp the speeds of the robot at the end position. In a computer simulation of the proposed procedure for moving the robot, generalized impulse controls are approximated by rectangular impulses.

Substantiation the technology and parameters of the “paraplau” type soil dredger for a two-tier plow

The purpose of the study was to substantiate the technology and parameters of the “paraplau” type soil dredger for a two-tier plow. The basic principles and methods of classical mechanics, mathematical analysis and statistics were used in this study. Sub-tillage loosening of the most compacted layers of the soil of the fields from under the cotton must be carried out in a strip way along the line of the middle of the irrigation furrows between the rows. It is established that for the implementation of strip loosening of the subarable soil layers of fields from under cotton, the width of the two-tier plow should be a multiple of the width of the row spacing. At the same time, for loosening the compacted subsurface layers of the middle of the row spacing of cotton with one working body, the soil dredgers are installed behind each even lower body in the plane of the field edges of the odd bodies. In the case of subtillage loosening of the middle of the row spacing by two soil dredgers with an inclined stand, one soil dredger is installed behind each lower body. An analytical relationship is obtained to justify the relative position of the plow bodies and the soil dredgers, as well as their parameters. Experimental studies have established that the resistivity of a two-tier plow decreases (in comparison with continuous loosening) when the most compacted layers of the middle of the row are loosened with a pointed paw by 17.56%, two soil dredgers with inclined posts by 24.04%, and one soil dredger with an inclined post by 23.24%.

Study on mechanisms of tillage for melon cultivation under the film

The aim of the study is to develop a machine for preparing the soil for sowing melons under a tunnel film. The authors have developed a machine for preparing the soil for sowing melons under a tunnel film, which is equipped with deep-diggers with an inclined stand of the “paraplau” type, a furrow maker and rotary working bodies. A design diagram and a fragment of the machine operation have beak given. The basic principles and methods of classical mechanics, mathematical analysis and statistics were used in this study. Tests have established that the developed machine reliably performs the specified technological process and its performance indicators fully meet the requirements. When using the developed machine for preparing the soil for sowing melons under the film, the direct cost of processing one hectare of area is reduced by 33.4%. The study’s goal is to create a machine that prepares soil for seeding melons under a tunnel film. The authors have created a machine that includes deep-diggers with a “paraplau” style inclined platform, a furrow maker, and rotating working bodies for preparing the soil for planting melons beneath a tunnel film. A design schematic as well as a portion of the machine functioning has been provided. In this work, the fundamental concepts and methodologies of classical mechanics, mathematical analysis, and statistics were employed. The created machine reliably executes the required technical procedure, and its performance indicators completely fulfill the criteria, according to tests. The direct cost of processing one hectare of land is lowered by 33.4 percent when utilizing the developed machine to prepare the soil for growing melons beneath the film.

Intensity of the continuous feed mixing process in the mixer

The physical basis of the mixture formation is analyzed. The study aims to increase the intensity of the process of continuous mixing of feed in the mixer. The basic principles and methods of classical mechanics, mathematical analysis, and statistics were used in this study. The design of the mixer cover in the form of a three-sided box is justified, which eliminates additional resistance to the rotation of the screw due to the impact of the feed masses reflected from the cover. When using a lid in the form of a three-sided box, the mixing quality improves by 4-5% and reaches 93% or more at a capacity of 15 t/h. It is established that the optimal angle of inclination of the reflecting plane of the mixing chamber cover is 31-35° with a screw diameter of 400 mm, the height of the reflecting plane from the screw axis of 350 mm, and a rotation speed of 36.61 s-1. The following indicators of the mixer were determined: the productivity that ensures the mixing quality of more than 90% when mixing green mass and silage with mixed feed - 19 t/h, crushed feed root crops with mixed feed-23 t / h, the speed of the screw - 36.61 s-1.

Dynamics of the movement of the ripping tool for surface tillage

The study aims to analyze the stability of the movement of the ripper tool for surface tillage. The basic principles and methods of classical mechanics, mathematical analysis, and statistics were used in this study. The dynamics of the movement of a ripper tool for surface tillage are considered, depending on the forces acting on it and its design parameters. A computational dynamic model is developed, and an equation describing the angular oscillations of the longitudinal links of the parallelogram ripper mechanism is obtained. It is established that the uniformity of the depth of the cultivator depends on the amplitude and frequency changes of the components of the disturbing force, physical and mechanical properties of the soil, the moment of inertia of the Ripper, the length of the longitudinal links parallelogram mechanism, the forces of the pre-tension pressure springs, and its stiffness. It is established that the required uniformity of the depth of tillage can be achieved by selecting the pre-tension force of the pressure spring and its rigidity. Theoretical and experimental studies have established that the required uniformity of the processing depth with minimal energy consumption of the soil is provided with a pre-tension force of the pressure spring of the ripper attachment mechanism of 350 n, spring stiffness of 40 n / cm, and a speed of 2.0 m/s.

Front-mounted plow for smooth, non-furrow plowing with offsets

The purpose of the study was the development of a front plow with angle clamps, which performs, smooth plowing. The authors have developed an improved front plow with angle clamps. The constructive scheme of the plow has been given. The basic principles and methods of classical mechanics, mathematical analysis and statistics were used in this study. Experimental studies have justified the processing depth within the limits of 10-12. 5 cm and the width of the capture of the angle is within the range of 7.5-10 cm. Economic tests have established that the developed front plow reliably performs the specified technological process and its performance indicators meet agrotechnical requirements. The use of a frontal plow for smooth, plowing provides a reduction in direct costs for processing 1 hectare of area compared to the technical means used by 26.8%.