scholarly journals MODELING AND ANALYSIS OF PARAMETRIC OPTIMIZATION OF THE MASS OF A CLOSED PLANETARY MECHANISM FORMED BY TWO SIMPLE PLANETARY MECHANISMS OF JAMES

2021 ◽  
pp. 56-70
Author(s):  
Vladimir Matusevich ◽  
Jurij Sharaban ◽  
Aleksandr Shehov
Keyword(s):  
Parametric Optimization ◽  
Bending Strength ◽  
Design Constraints ◽  
Modeling And Analysis ◽  
Dimensionless Function ◽  
Gear Wheels ◽  
Differential Properties ◽  
The Mathematical Model ◽  
The Given ◽  
Planetary Mechanism

The mathematical model of estimation of a design mass of the closed planetary mechanism formed from two simple planetary mechanisms of James (mechanism of type ), taking into account their structural diagrams and design constraints, determined by the conditions of contact and bending strengths of external gearing of sun gears and satellites, is offered. A model is a dimensionless function (analogue of mass) of two variables – transmission relations of simple planetary mechanisms, and set of numerical parameters. As parameters of analogue of mass coefficients are chosen, characterizing the models of mass of gear wheels and carriers, structural and strength limitations of the external gearing of simple planetary mechanisms of the type , and also structure of these mechanisms. In the program Mathcad differential properties of the offered model and influence on position of minimum of analogue of mass are investigational depending on the numerical values of his parameters. Documents of the Mathcad program are presented that implement computer modeling of algorithms for parametric optimization of mass closed planetary mechanism, where the function of the analogue of the mass of the given mechanism is used as the objective function. A comparative analysis of minimizing the design mass of two kinematic schemes of planetary mechanisms is considered – closed planetary mechanism and in-line planetary of the type . Keywords: simple planetary mechanism of James, simple planetary mechanism type ; closed planetary mechanism; in-line planetary mechanism; mass of closed planetary mechanism; contact strength of gearing; bending strength of gearing; parametric optimization; parametric optimization of mass of planetary mechanism

scholarly journals ПАРАМЕТРИЧЕСКАЯ ОПТИМИЗАЦИЯ ПО КРИТЕРИЮ ОБЪЕМА ДВУХСТУПЕНЧАТОГО ПЛАНЕТАРНОГО МЕХАНИЗМА ТИПА AI–II

2019 ◽  
pp. 92-102
Author(s):  
Владимир Анатольевич Матусевич ◽  
Юрий Владимирович Шарабан ◽  
Александр Владимирович Шехов
Keyword(s):  
Objective Functions ◽  
Parametric Function ◽  
Planetary Gears ◽  
Optimization Task ◽  
Parametric Functions ◽  
Analysis Of Function ◽  
Differential Properties ◽  
The Mathematical Model ◽  
Optimal Designing ◽  
Planetary Mechanism

The task of parametric optimization on the criterion of total volume is considered for the two-stage planetary mechanism of type AI–II. The objective function of optimization is built as a sum of two dimensionless parametric functions of volume (analogs of volume) of the separate stages of planetary mechanism of type AI–II. Construction of analogs of volume of simple planetary mechanisms of type AI and II, corresponding the first and second to the stages of planetary mechanism of type AI–II, it is based on their presentation as conditional disks. Thus the volume of the conditional disk is equivalent to the volume of a simple planetary mechanism. The mathematical model of analogs of the volume is built taking into account the terms of the durability of the toothed hooking of the sun gear and planetary gears of simple planetary mechanism, and also taking into account an area possible his transmission relation. Considering terms of contact and bending durability of the toothed hooking, get the analogs of volume at a calculation on contact and bending to durability. Depending on the condition of durability (contact or bending) and type of simple planetary mechanism the analog of his volume appears as a parametric function of corresponding parameters of his kinematics diagram. As parameters transmission relation attitude of simple planetary mechanism, parameters of bringing a mechanism over, toward a conditional disk, and also the relation of reference diameters of planetary gears of the mechanism is chosen. An analysis over of influence of each is brought of parameters of the function of analog of volume on the pattern of behavior to it. On the basis of this analysis of function of analogs of volume of the stages of planetary mechanism of type AI–II appear as parametric functions of the guided parameters. For the simple planetary mechanism of type AI one guided parameter is chosen, namely transmission relation of mechanism. For the guided parameters of function of analog of volume for the simple planetary mechanism of type II a transmission relation and relation of reference diameters of planetary gears of mechanism are chosen, i.e. two guided parameters. Offered approach for the decision of optimization task, based on research of differential properties of objective functions of volume (analogs of volume) of the separate stages of planetary mechanism of type AI–II. It is given the example of the optimal designing of construction of minimum volume of planetary mechanism of type AI–II.

Force tracking control of grinding end effector based on backstepping + PID

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Shijie Dai ◽  
Shining Li ◽  
Wenbin Ji ◽  
Zhenlin Sun ◽  
Yufeng Zhao
Keyword(s):  
Mathematical Model ◽  
Linear System ◽  
Control Strategy ◽  
Grinding Force ◽  
Constant Force ◽  
End Effector ◽  
Content Type ◽  
Modeling And Analysis ◽  
The Mathematical Model ◽  
Automobile Wheel

Purpose This study aims to realize the constant force grinding of automobile wheel hub. Design/methodology/approach A force control strategy of backstepping + proportion integration differentiation (PID) is proposed. The grinding end effector is installed on the flange of the robot. The robot controls the position and posture of the grinding end actuator and the grinding end actuator controls the grinding force output. First, the modeling and analysis of the grinding end effector are carried out, and then the backstepping + PID method is adopted to control the grinding end effector to track the expected grinding force. Finally, the feasibility of the proposed method is verified by simulation and experiment. Findings The simulation and experimental results show that the backstepping + PID strategy can track the expected force quickly, and improve the dynamic response performance of the system and the quality of grinding and polishing of automobile wheel hub. Research limitations/implications The mathematical model is based on the pneumatic system and ideal gas, and ignores the influence of friction in the working process of the cylinder, so the mathematical model proposed in this study has certain limitations. A new control strategy is proposed, which is not only used to control the grinding force of automobile wheels, but also promotes the development of industrial control. Social implications The automatic constant force grinding of automobile wheel hub is realized, and the manpower is liberated. Originality/value First, the modeling and analysis of the grinding end effector are carried out, and then the backstepping + PID method is adopted to control the grinding end effector to track the expected grinding force. The nonlinear model of the system is controlled by backstepping method, and in the process, the linear system composed of errors is obtained, and then the linear system is controlled by PID to realize the combination of backstepping and PID control.

Bond Graph Modeling and Analysis of HEV System Based on Ravigneaux Planetary Mechanism

2013 ◽  
Vol 724-725 ◽  
pp. 1402-1408
Author(s):  
Li He Xi ◽  
Hong Wei Chen ◽  
Xin Zhang
Keyword(s):  
Bond Graph ◽  
Structural Form ◽  
Graph Models ◽  
Modeling And Analysis ◽  
Electric System ◽  
Operating Modes ◽  
Graph Modeling ◽  
Time Requirements ◽  
Bond Graph Modeling ◽  
Planetary Mechanism

The bond graph method is used to analyse and model dynamics of hybrid electric system based on Ravigneaux Planetary Mechanism. Bond graph models are built in different structural form, general equations of torque and speed are derived, and operating modes achieved in different structural form are in consideration. At the same time, requirements of control system in different operating modes are illustrated and analysed, which help lay the foundations for modeling and simulation of HEV system based on Ravigneaux Planetary Mechanism.

scholarly journals Mathematical modeling of physical processes in the complex for testing of induction machines

2018 ◽  
Vol 239 ◽  
pp. 01055 ◽  
Author(s):  
Viktor Kharlamov ◽  
Denis Popov
Keyword(s):  
Mathematical Model ◽  
Frequency Converter ◽  
Electrical Energy ◽  
Induction Machines ◽  
Test Scheme ◽  
Load Testing ◽  
Variable Parameters ◽  
Asynchronous Machines ◽  
The Mathematical Model ◽  
The Given

The paper is devoted to the simulation of the test complex designed for energy-efficient load testing of induction machines by the method of mutual load with the exchange of electrical energy through the network. It is noted that for other similar test schemes, the mathematical model will have a slightly different form, but it will be identical in terms of asynchronous machines, network and frequency converter. The compiled mathematical model of the test complex allows studying the variable parameters of the system in all elements of the test scheme in static and dynamic modes of operation as well. The synthesized mathematical model can be used to determine the parameters of the equipment in the designed test complexes if the parameters of the test and load machines are known. The results of simulation of the test complex for the given parameters of the test and load induction machines are obtained.

scholarly journals Mathematical Modeling and Analysis of Multirobot Cooperative Hunting Behaviors

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Yong Song ◽  
Yibin Li ◽  
Caihong Li ◽  
Xin Ma
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Numerical Solutions ◽  
Rate Equations ◽  
Ratio Analysis ◽  
Hunting Behavior ◽  
Modeling And Analysis ◽  
Cooperative Hunting ◽  
Model Equations ◽  
The Mathematical Model

This paper presents a mathematical model of multirobot cooperative hunting behavior. Multiple robots try to search for and surround a prey. When a robot detects a prey it forms a following team. When another “searching” robot detects the same prey, the robots form a new following team. Until four robots have detected the same prey, the prey disappears from the simulation and the robots return to searching for other prey. If a following team fails to be joined by another robot within a certain time limit the team is disbanded and the robots return to searching state. The mathematical model is formulated by a set of rate equations. The evolution of robot collective hunting behaviors represents the transition between different states of robots. The complex collective hunting behavior emerges through local interaction. The paper presents numerical solutions to normalized versions of the model equations and provides both a steady state and a collaboration ratio analysis. The value of the delay time is shown through mathematical modeling to be a strong factor in the performance of the system as well as the relative numbers of the searching robots and the prey.

Mathematical model of the artificial muscle with two actuators

2020 ◽  
pp. 095440622094156
Author(s):  
Ljubinko B Kevac ◽  
Mirjana M Filipovic ◽  
Ana M Djuric
Keyword(s):  
Mathematical Model ◽  
Control Structure ◽  
Artificial Muscle ◽  
Parallel Robot ◽  
Simulation Results ◽  
Proportional Derivative Controller ◽  
Definition Of ◽  
The Mathematical Model ◽  
The Given ◽  
Very High

Characteristic construction of cable-suspended parallel robot of artificial muscle, which presents an artificial forearm, is analyzed and synthesized. Novel results were achieved and presented. Results presented in this paper were initially driven to recognize and mathematically define undefined geometric relations of the artificial forearm since it was found that they strongly affect the dynamic response of this system. It gets more complicated when one has more complex system, which uses more artificial muscle subsystems, since these subsystems couple and system becomes more unstable. Unmodeled or insufficiently modeled dynamics can strongly affect the system’s instability. Because of that, the construction of this system and its new mathematical model are defined and presented in this paper. Generally, it can be said that the analysis of geometry of selected mechanism is the first step and very important step to establish the structural stability of these systems. This system is driven with two actuators, which need to work in a coordinated fashion. The aim of this paper is to show the importance of the geometry of this solution, which then strongly affects the system’s kinematics and dynamics. To determine the complexity of this system, it was presumed that system has rigid cables. Idea is to show the importance of good defined geometry of the system, which gives good basis for the definition of mathematical model of the system. Novel program package AMCO, artificial muscle contribution, was defined for the validation of the mathematical model of the system and for choice of its parameters. Sensitivity of the system to certain parameters is very high and hence analysis of this system needs to be done with a lot of caution. Some parameters are very influential on the possible implementation of the given task of the system. Only after choosing the parameters and checking the system through certain simulation results, control structure can be defined. In this paper, proportional–derivative controller was chosen.

scholarly journals Optimal Design of Piezoelectric Cantilevered Actuators for Charge-Based Self-Sensing Applications

Sensors ◽  
2019 ◽  
Vol 19 (11) ◽  
pp. 2582 ◽  
Author(s):  
Joël Bafumba Liseli ◽  
Joël Agnus ◽  
Philippe Lutz ◽  
Micky Rakotondrabe
Keyword(s):  
Objective Function ◽  
Geometrical Parameters ◽  
Optimization Approach ◽  
Element Analysis ◽  
Modeling And Analysis ◽  
Multi Objective ◽  
Sensing Applications ◽  
Piezoelectric Cantilever ◽  
Space Saving ◽  
The Given

Charge-based Self-Sensing Actuation (SSA) is a cost and space-saving method for accurate piezoelectric based-actuator positioning. However, the performance of its implementation resides in the choice of its geometry and the properties of the constituent materials. This paper intends to analyze the charge-based SSA’s performances dependence on the aforementioned parameters and properties for a piezoelectric cantilever. A model is established for this type of Piezoelectric Actuator (PEA), and a multi-objective function is defined. The multi-objective function consists of the weighted actuator and sensor objective functions of the PEA. The analytical optimization approach introduced herein aims to assess the evolution of the defined multi-objective function across a defined set of geometrical parameters and material properties and highlights the existence of a subset of solutions for an optimal charge-based SSA’s implementation. The commercially-available finite element analysis software, COMSOL Multiphysics, is used on the parametric model of the given structure to validate the analytical model. Then, experiments are conducted to corroborate the numerical and analytical modeling and analysis.

Identification of the Cutting Forces Coefficients via Milling Process Simulation

2011 ◽  
Author(s):  
Sergey A. Voronov ◽  
Igor A. Kiselev ◽  
Maxim G. Yakovlev
Keyword(s):  
Cutting Forces ◽  
Chip Thickness ◽  
Element Model ◽  
Optimization Method ◽  
Milling Process ◽  
Force Model ◽  
Processed Material ◽  
A New Technique ◽  
The Mathematical Model ◽  
The Given

The paper is devoted to the description of a new technique (numerical and experimental) identification of the dependences between cutting forces and instantaneous chip thickness. It is required to measure only the cutting forces versus cutting conditions. Experimentally, for the given pair the processed material – the tool, coefficients of the cutting forces model are calculated by means of the optimization method (Nelder-Mead algorithm). The mathematical model of the milling process developed by authors on each step of the Nelder-Mead method is used for the process numerical simulation under given coefficients of the cutting force model. The elaborated numerical modeling algorithm allows investigating the dynamics and the kinematics of the milling process. The dynamic model of the tool, the algorithm of geometrical modeling of the instantaneous chip thickness, the finite element model of the detail are embedded into the whole model of the milling process.

Wind-driven land-yacht robot mathematical modeling and verification

2016 ◽  
Vol 43 (1) ◽  
pp. 77-90 ◽  
Author(s):  
Jiqing Chen ◽  
Shaorong Xie ◽  
Jun Luo ◽  
Hengyu Li
Keyword(s):  
Mathematical Model ◽  
Experimental Tests ◽  
Outer Planet ◽  
Mechanism Analysis ◽  
Content Type ◽  
The Antarctic ◽  
The Mathematical Model ◽  
The Given ◽  
Practical Implications ◽  
Wind Resources

Purpose – The purpose of this paper was to solve the shortage of carrying energy in probing robot and make full use of wind resources in the Antarctic expedition by designing a four-wheel land-yacht. Land-yacht is a new kind of mobile robot powered by the wind using a sail. The mathematical model and trajectory of the land-yacht are presented in this paper. Design/methodology/approach – The mechanism analysis method and experimental modeling method are used to establish a dual-input and dual-output mathematical model for the motion of land-yacht. First, the land-yacht’s model structure is obtained by using mechanism analysis. Then, the models of steering gear, servomotors and force of wing sail are analyzed and validated. Finally, the motion of land-yacht is simulated according to the mathematical model. Findings – The mathematical model is used to analyze linear motion and steering motion. Compared with the simulation results and the actual experimental tests, the feasibility and reliability of the proposed land-yacht modeling are verified. It can travel according to the given signal. Practical implications – This land-yacht can be used in the Antarctic, outer planet or for harsh environment exploration. Originality/value – A land-yacht is designed, and the contribution of this research is the development of a mathematical model for land-yacht robot. It provides a theoretical basis for analysis of the land-yacht’s motion.

scholarly journals Development of the methods of calculation of the electrical installations working operation in case of quality supply disturbance

2020 ◽  
Vol 7 (3) ◽  
pp. 140-155
Author(s):  
Ismael Saeed ◽  
◽  
Azad Mohammed
Keyword(s):  
Electrical Equipment ◽  
Equation System ◽  
Fault Current ◽  
Modes Of Operation ◽  
Operating Modes ◽  
Longitudinal Asymmetry ◽  
Methods Of Calculation ◽  
Short Circuits ◽  
The Mathematical Model ◽  
The Given

This paper proposes a method of calculating of asymmetrical modes of operation of electrical installations where simple and adequate loads equivalent circuits are available with working electrical equipment. So the mathematical model of equation system is derived as universal way for calculating the systems operating modes when it is subjected to a disturbance due to asymmetry. With the help of the obtained model we can calculate different cases of symmetry disturbances, all types of short circuits, between phase short circuits, any type of longitudinal asymmetry, open circuits when there is a resistance for the fault current at the place of damage In the given method, specific types of asymmetry are considered as particular cases and easily calculated from the generalized formula, which is essentially reduces the calculation and allows us to consider cases of asymmetry of any complexity. Therefore this method is offered as a basic for calculation of asymmetry when the system is subjected to a disturbance.

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