scholarly journals THEORETICAL RESEARCH ROLLER FOR SMALL TILLAGE MACHINE

2021 ◽  
pp. 80-85
Author(s):  
Gubeydulla Yunusov ◽  
Aleksey Aleshkin ◽  
Bulat Ziganshin ◽  
Damir Haliullin
Keyword(s):  
Differential Equation ◽  
Kinetic Energy ◽  
Mechanical System ◽  
Degrees Of Freedom ◽  
Rational Design ◽  
Agricultural Sector ◽  
Lagrange Equation ◽  
Equation Of Motion ◽  
Theoretical Research ◽  
Technological Parameters

The efficiency of the agricultural sector, and in particular the production of crop products, to a greater extent depends on the cost of the products obtained, which can be reduced, taking into account the factors affecting the technical, economic and operational indicators. Every year, the demand for small-sized tillage equipment, which is a real assistant for gardeners when working on their backyard plots, is growing. But in order to increase the functionality of the equipment and the quality of soil preparation for sowing, it is necessary to conduct research on the possibility of using various additional working bodies for the walk-behind tractor. The aim of the research is to develop and study the design of an active roller for a walk-behind tractor, which allows high-quality preparation of the soil for sowing. To solve the set tasks, the mechanical system of a slatted-spiral roller for a walk-behind tractor is considered. The number of degrees of freedom, the kinematic connection and the position of the mechanical system in the inertial frame of reference associated with the walk-behind tractor have been determined. Taking into account some assumptions, neglecting the small values of some variables, on the basis of the Lagrange equation of the second kind, a differential equation of motion for generalized coordinates is compiled. To solve the differential equation of motion, the kinetic energy of the system is calculated, which is determined as the sum of the kinetic energies of the frame and the roller. The expression for determining the kinetic energy of the system depends on the axial and centrifugal moments of inertia, mass, angular and linear speeds of the frame and roller. The expressions obtained make it possible to substantiate the main rational design and technological parameters of a slatted-spiral roller for a walk-behind tractor

Invented Forces in Supercell Models

2021 ◽  
Author(s):  
Robert Davies-Jones
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Planetary Boundary Layer ◽  
Degrees Of Freedom ◽  
Wind Profile ◽  
Equation Of Motion ◽  
Force Balance ◽  
Frictional Loss ◽  
Hydrostatic Equation ◽  
Wind Profiles

AbstractThis paper examines methods used in supercell models to maintain a steady, sheared, horizontally uniform environment with a three-force balance in the planetary boundary layer (PBL) and a two-force balance above it. Steady environments are maintained while ignoring the thermal-wind balance that permits large shear above the PBL. The Taylor-Proudman theorem indicates that wind profiles above the PBL must be unidirectional for balanced environments. In principle, supercell models that do not accommodate thermal advection should not support balanced steady environments with veering horizontally uniform winds.Recent methods add a permanent, pervasive, horizontal external force that varies only with height. By adding two more degrees of freedom, this force circumvents the Taylor-Proudman theorem and enables a static, horizontally uniform environment for any wind profile. It succeeds by adding spurious energy in lieu of flow towards low pressure to offset frictional loss of kinetic energy. However, the artificial force has downsides. It decouples the environmental horizontal equation of motion from the hydrostatic equation and the thermodynamics from the dynamics. It cancels environmental friction and the part of the Coriolis force that acts on the environmental wind. Within the storm, its curl can speciously generate significant horizontal vorticity near the ground. Inaccuracies arise in circulations around material circuits because of modifications by the artificial force and resulting miscalculations of parcel trajectories. Doubt is cast on conclusions about tornadogenesis drawn from recent simulations that contain an invented force.

scholarly journals An algorithm for deriving equations of motion of constrained mechanical system

1999 ◽  
Vol 21 (1) ◽  
pp. 36-44 ◽  
Author(s):  
Dinh Van Phong
Keyword(s):  
Differential Equation ◽  
Mechanical System ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Computer Processing

The article deals with the form of equations of motion of mechanical system with constraints. For holozoic systems the number of differential equation is equal to the degrees of freedom, without regard to the number of chosen coordinates. The possibilities of computer processing (symbolical and numerical) are shown. Two simple examples demonstrate the described technique.

Simulation of the process stripping harvester for the collection of oilseed flax seeds

2021 ◽  
pp. 127-135
Keyword(s):  
Numerical Modeling ◽  
Mass Fraction ◽  
Rational Design ◽  
Agricultural Sector ◽  
Rotation Frequency ◽  
Technological Parameters ◽  
Seed Loss ◽  
Loss Index ◽  
Flax Seeds

The article presents the main results of research on the development of a physical and mathematical model of the technological process of collecting flax seeds with a combing header and the justification of the range of its operating parameters based on software simulation and numerical modeling. The process of harvesting agricultural crops, including oil flax, is an important technological operation of their production in the agricultural sector of Ukraine. The positive dynamics of the growth of oil flax production, which is due to the growing demand for seeds in the domestic and foreign markets, requires the intensification of harvesting equipment technological processes. The main reasons for restraining the production of oil flax are the imperfection of the equipment for harvesting and the inconsistency of the quality indicators of work with the established requirements. One of the directions for solving this problem is the technology of harvesting by stripping plants on the standing. Timely harvesting of oil flax seeds in optimal agrotechnical terms (plant condition, weather conditions, weediness, etc.) with minimal losses and contamination of the heap is one of the important scientific tasks of improving harvesting technology. Improving the efficiency of collecting oil flax seeds and, as a result, improving the quality of products requires new approaches to the development and implementation of technical means in progressive technologies. As a result of numerical modeling of the separation process of a heap in a combing header with a curvilinear casing shape, taking into account the physical and mechanical properties of its components, the dependences of the mass fraction of husk and stem particles leaving its area (an indicator of the quality of cleaning the heap from impurities) δh and the fraction of seeds and capsules leaving with seeds (seed loss index) δs from the rotation frequency of the beater-reflector n1 and the stripping drum n2, the position of the transparent zone of the boundary L and its width B. Solving the compromise problem, namely, maximizing the mass fraction of husk and stalk particles leaving the header area (quality indicator cleaning the heap from impurities) δh and minimizing the proportion of seeds and seed boxes leaving the header area (seed loss index) δs Obtained rational design and technological parameters of the combing type header with a curved casing: rotation frequency of the beater-reflector n1 = 782 rpm, combing drum rotation speed n2 = 671 rpm, transparent position zone of the boundaries L = 0.82 m and its width B = 0.45 m. In this case, the mass fraction of husk and stem particles leaving is δh = 42.4%, and the fraction of losses of seeds and capsules with seeds from the header area is in accordance with δs = 2.5%.

SYMBOLIC REPRESENTATION OF FORCED OSCILLATIONS OF BRANCHED MECHANICAL SYSTEMS

2021 ◽  
pp. 118-130
Author(s):  
I.P. Popov ◽  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Mechanical System ◽  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Time Instant ◽  
Forced Oscillations ◽  
Parallel Connections ◽  
Clear Idea ◽  
The Relationship

A calculation of dynamics of a mechanical system with n degrees of freedom, including inert bodies and elastic and damping elements, involves the derivation and integration of a system of n second-order differential equations, which are reduced to a differential equation of 2n order. An increase in the degree of freedom of the mechanical system by one increases the order of the resulting differential equation by two. The solution of higher-order differential equations is rather cumbersome and time-consuming. Integration of equations is proposed to be replaced with rather simpler algebraic methods. A number of relevant theorems that relate both active and reactive parameters of mechanical systems in the series and parallel connection of mechanical power consumers are proved. Using parallel-series and series-parallel connections as an example, the calculation methods for branched mechanical systems with any number of degrees of freedom, based on the use of symbolic or complex representation of forced harmonic oscillations, are shown. The phase relationships determining loading conditions and a possibility of its artificial change are considered. The vector diagrams of the amplitudes of forces, velocities and their components in a complex plane at a zero time instant are presented, which give a complete and clear idea of the relationship between these quantities.

scholarly journals Mechanical and mathematical modeling of the load movement on the thread wound on cylindrical drum with movable axis

2021 ◽  
Vol 102 (2) ◽  
pp. 54-63
Author(s):  
Serhii Podliesnyi ◽  
Mykola Dorokhov ◽  
Oleksandr Stadnyk ◽  
Yurii Yerfort
Keyword(s):  
Mathematical Model ◽  
Mechanical System ◽  
Degrees Of Freedom ◽  
Nonlinear Dynamical Systems ◽  
Lagrange Equation ◽  
Vertical Axis ◽  
Material Point ◽  
Nonlinear Dynamical ◽  
Load Movement ◽  
Angular Coordinates

A mechanical system, where the load in the form of material point is suspended on inextensible thread screwed on the rotating cylindrical drum, but the drum is connected to the boom rotating around fixed horizontal axis is considered. Using the Lagrange equation of the second kind, a mathematical model of the motion of the mechanical system is obtained. The system has three degrees of freedom, two of which are cylindrical. The investigation of the system motion is carried out using computer technology. As a result, the dependences of linear and angular coordinates and velocities in time at different values of the output data for two main modes of the system operation, namely – under the conditions of lifting and lowering the load are obtained. Appropriate graphs are constructed, including the trajectories of the cargo motion. The mathematical model takes into account nonlinearities of the system and allows you to find the amount of tension of the hoisting rope at any time. The analysis showed that vertical oscillations occur twice as fast as horizontal ones. The phase portrait of the generalized coordinate (angle of the rope with the vertical axis) is the focus, which is untwisted when lifting due to nonlinearity in the system, and when the load moves down, the focus, which twists and approaches the mathematical pendulum is obtained. The obtained results can be used in modeling of controlled pendulum motions for different mechanical systems. The methodology and program are recommended to the students and graduate students in terms of learning the principles of construction and analysis of complex nonlinear dynamical systems.

Passivity Based Control of a Cart with Inverted Pendulum

2013 ◽  
Vol 332 ◽  
pp. 339-344 ◽  
Author(s):  
Matthias Jörgl ◽  
Kurt Schlacher ◽  
Hubert Gattringer
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Lyapunov Function ◽  
Mechanical System ◽  
Simple Proof ◽  
Control Strategy ◽  
Inverted Pendulum ◽  
Equation Of Motion ◽  
Control Law ◽  
Passivity Based Control

This paper deals with passivity based control of a cart , which can moves on a skew plain. On the cart a non actuated pendulum is assembled. Therefore, the mechanical system is non-linear, one degree under actuated and instable. The equation of motion is derived by the method of Lagrange. The goal of the control strategy is to stabilize the cart and the upper position of the pendulum. The applied control strategy is called Interconnection Damping Assignment Passivity Based Control (IDA-PBC). This method allows a physical approach with a simple proof of stability having appropriate Lyapunov function on hand. The simple proof of stability is an advantage of this theory. However, the proof of stability is fulfilled, challenging partial differential equation have to be solved to get the control law. Measurements results are presented.

scholarly journals Theoretical researches of threshing and separation processes of bread mass by the threshing-separating device

2020 ◽  
pp. 60-66
Author(s):  
O.M. Hrytsaka
Keyword(s):  
Mathematical Model ◽  
Rational Design ◽  
Theoretical Research ◽  
Design Parameters ◽  
Technological Parameters ◽  
Separation Processes ◽  
Combine Harvester ◽  
Combine Harvesters ◽  
The Mathematical Model ◽  
Grain Losses

Annotation Purpose. Theoretical researches of increase of efficiency of working processes of threshing, separation of grain mass by combine harvesters by improvement and use of a multi-drum design of the threshing-separating device with rational design and technological parameters of work capable to provide necessary agrotechnical requirements. Methods. In theoretical researches the analysis of interaction of the threshing-separating device with grain mass with use of mathematical modeling of processes of threshing of grain, separation of a rough heap and their estimation is carried out. Results. The mathematical model of the mobile multi-drum thresher modernized as a result of change of settings that allowed to increase efficiency of its work is considered; the dependences of quality on the design parameters of the threshing-separating device during the implementation of technological processes of grain harvesting due to the reduction of the total level of injuries and grain losses are obtained. Conclusions. A mathematical model of improvement of the threshing process, separation of grain mass in the threshing gap of the threshing-separating device was developed, which allowed to obtain the dependences of the influence of structural and technological parameters on the level of threshing and separation. It is established that a significant reserve for improving the process of threshing, separation of grain mass is changes in the settings of threshing drums. Keywords: combine harvester, mathematical model, threshing-separating device, theoretical research, grain harvesting, threshing process.

scholarly journals A Finite Element Approach to the Analysis of Rotating Bladed-Disk Assemblies Coupled With Flexible Shaft

1994 ◽  
Author(s):  
Wen Zhang ◽  
Wenliang Wang ◽  
Hao Wang ◽  
Jiong Tang
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Coupled System ◽  
Equation Of Motion ◽  
Coupled Systems ◽  
The Finite Element Method ◽  
Bladed Disk ◽  
Modal Synthesis ◽  
Element Approach ◽  
Final Equation

A method for dynamic analysis of flexible bladed-disk/shaft coupled systems is presented in this paper. Being independant substructures first, the rigid-disk/shaft and each of the bladed-disk assemblies are analyzed separately in a centrifugal force field by means of the finite element method. Then through a modal synthesis approach the equation of motion for the integral system is derived. In the vibration analysis of the rotating bladed-disk substructure, the geometrically nonlinear deformation is taken into account and the rotationally periodic symmetry is utilized to condense the degrees of freedom into one sector. The final equation of motion for the coupled system involves the degrees of freedom of the shaft and those of only one sector of each of the bladed-disks, thereby reducing the computer storage. Some computational and experimental results are given.

scholarly journals Motion Planning for a Mobile Humanoid Manipulator Working in an Industrial Environment

2021 ◽  
Vol 11 (13) ◽  
pp. 6209
Author(s):  
Iwona Pajak ◽  
Grzegorz Pajak
Keyword(s):  
Kinetic Energy ◽  
Collision Avoidance ◽  
Industry 4.0 ◽  
Degrees Of Freedom ◽  
Industrial Environment ◽  
Acceleration Level ◽  
Different Types ◽  
Manipulability Measure ◽  
Robotic Tasks ◽  
Primary Problem

This paper presents the usage of holonomic mobile humanoid manipulators to carry out autonomous tasks in industrial environments, according to the smart factory concept and the Industry 4.0 philosophy. The problem of transporting lengthy objects, taking into account mechanical limitations, the conditions for avoiding collisions, as well as the dexterity of the manipulator arms was considered. The primary problem was divided into three phases, leading to three different types of robotic tasks. In the proposed approach, the pseudoinverse Jacobian method at the acceleration level to solve each of the tasks was used. The redundant degrees of freedom were used to satisfy secondary objectives such as robot kinetic energy, the maximization of the manipulability measure, and the fulfillment mechanical and collision-avoidance limitations. A computer example involving a mobile humanoid manipulator, operating in an industrial environment, illustrated the effectiveness of the proposed method.

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