scholarly journals A Mathematical Model of a Differential Drive with a Limited Gear Ratio

2021 ◽  
Vol 54 ◽  
pp. 699-711
Author(s):  
Andrey Efimov ◽  
Oleg Polushkin ◽  
Sergey Kireev ◽  
Marina Korchagina
Keyword(s):  
Mathematical Model ◽  
Gear Ratio ◽  
Differential Drive

Mobility and Energy Efficiency of Military Tactical Vehicle With Hybrid-Electric Driveline System

2014 ◽  
Author(s):  
Vladimir V. Vantsevich ◽  
Jesse R. Paldan ◽  
Jeremy P. Gray
Keyword(s):  
Mathematical Model ◽  
Eddy Current ◽  
Hybrid Electric Vehicle ◽  
Operation Mode ◽  
Planetary Gear ◽  
Electrical Current ◽  
Gear Ratio ◽  
Front Axle ◽  
Tactical Vehicle ◽  
Hybrid Electric

In this paper, a technical concept is described for a power transmitting unit to control the split of power between the drive axles of a 4×4 hybrid-electric vehicle. This new power transmitting unit uses a planetary gear set and eddy current brake to provide a continuously variable gear ratio that can be integrated into the vehicle driveline between the transfer case and front axle. The paper details the electrical and mechanical characteristics of the device, including its operation mode, its mathematical model built from the equations of the planetary gear set and eddy current brake, the optimization equation by which the device will be controlled to improve vehicle slip efficiency, as well as its torque and electrical current usage. Computer simulations are performed on a mathematical model of a 4×4 military truck using the power transmitting unit in conjunction with a series hybrid-electric configuration transmission.

scholarly journals MODELING OF THE MANAGEMENT SYSTEM OF A FULL-DRIVE FOUR-WHEEL AGRICULTURAL MOBILE ROBOT

2019 ◽  
Vol 4 (5) ◽  
pp. 147-154
Author(s):  
Т. Круглова ◽  
Tat'yana Kruglova ◽  
А. Власов ◽  
A. Vlasov
Keyword(s):  
Mathematical Model ◽  
Mobile Robot ◽  
High Precision ◽  
Management System ◽  
Mobile Platform ◽  
Control Algorithms ◽  
Modern Trend ◽  
Precision Control ◽  
Differential Drive ◽  
State Trajectory

Widespread robotization is a modern trend in the development of agriculture. Currently, various designs of robots are being actively implemented. They are aimed to replace a human when performing various tasks. Most of these robots are wheeled mobile platform, for which it is necessary to ensure high maneuverability and accuracy of control. This problem can be solved by developing optimal high-precision control algorithms, for the study of which it is advisable to use a mathematical model of a mobile agricultural robot. This article presents the results of modeling the movement of a four-wheel mobile robot with a differential drive that moves across a rectangular field along a “snake state” trajectory that is optimal by speed

Model Predictive Control of a Differential-Drive Mobile Robot

2018 ◽  
Vol 10 (1) ◽  
pp. 20-41
Author(s):  
Samir Bouzoualegh ◽  
El-Hadi Guechi ◽  
Ridha Kelaiaia
Keyword(s):  
Mathematical Model ◽  
Model Predictive Control ◽  
Mobile Robot ◽  
Predictive Control ◽  
Control Law ◽  
Input Output ◽  
Linearization Technique ◽  
Differential Drive ◽  
Predictive Controller ◽  
Simulation Results

Abstract This paper presents a model predictive control (MPC) for a differential-drive mobile robot (DDMR) based on the dynamic model. The robot’s mathematical model is nonlinear, which is why an input–output linearization technique is used, and, based on the obtained linear model, an MPC was developed. The predictive control law gains were acquired by minimizing a quadratic criterion. In addition, to enable better tuning of the obtained predictive controller gains, torques and settling time graphs were used. To show the efficiency of the proposed approach, some simulation results are provided.

Meshing analysis of a gear with a ring-involute gear

2003 ◽  
Vol 217 (12) ◽  
pp. 1287-1299 ◽  
Author(s):  
S-C Yang
Keyword(s):  
Mathematical Model ◽  
Stress Analysis ◽  
Geometric Model ◽  
Gear Ratio ◽  
Geometric Modelling ◽  
Numerical Example ◽  
Involute Gear ◽  
The Family ◽  
New Type ◽  
Kinematic Errors

The surface of a gear with ring-involute teeth generated by a rack cutter with ring-involute teeth is a new type of gear. This paper describes a method developed from gear theory for deriving a pinion and a gear with ring-involute teeth. A gear with ring-involute teeth is regarded as an envelope to the family of rack cutter surfaces when the pinion and gear rotate for a cycle. Using a developed mathematical model, the investigation on the undercutting analysis of the proposed gear is studied. Here the kinematic errors are investigated according to the obtained geometric modelling of the designed gear meshing when assembly errors were present. Stress analysis for the proposed gear was performed. Finally, a numerical example is presented to demonstrate the geometric model of a gear with ring-involute teeth and a gear ratio of 3:2.

A mathematical model of a worm mechanism generated by a conical cutter

2009 ◽  
Vol 224 (8) ◽  
pp. 1707-1716 ◽  
Author(s):  
S-C Yang
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Stress Analysis ◽  
Geometric Model ◽  
Gear Ratio ◽  
Worm Gear ◽  
Von Mises Stress ◽  
The Family ◽  
Gear Mechanism ◽  
Von Mises

In this article, an imaginary conical cutter was used to determine the geometric models of the worm—gear mechanism including a worm and a gear. Mathematical models of the worm and the gear were derived using an imaginary conical cutter and gear theory. Based on the geometric relations between the worm and conical cutter surfaces and between the gear and conical cutter surfaces, the worm and the gear were regarded as an envelope to the family of conical cutter surfaces when they rotated for one cycle. Using the developed mathematical model, the stress analysis of the proposed mechanism was examined. The results show that the von Mises stress and volume of the proposed worm and gear were smaller than those of the conventional worm—gear mechanism. Lastly, a numerical example was used to illustrate the geometric model of a gear and a worm with a gear ratio of 30:1.

A Hybrid-Electric Power Transmitting Unit for 4x4 Vehicle Applications: Modeling and Simulation

2014 ◽  
Author(s):  
Vladimir V. Vantsevich ◽  
Jesse R. Paldan ◽  
Jeremy P. Gray
Keyword(s):  
Mathematical Model ◽  
Electric Power ◽  
Eddy Current ◽  
Hybrid Electric Vehicle ◽  
Planetary Gear ◽  
Electrical Current ◽  
Gear Ratio ◽  
Front Axle ◽  
Mechatronic Systems ◽  
Hybrid Electric

In this paper, a technical concept is described for a hybrid-electric power transmitting unit (HE-PTU) to control the split of power between the drive axles of a 4×4 hybrid-electric vehicle. This new power transmitting unit is a mechatronic systems by its design and uses a planetary gear set and eddy current brake to provide a continuously variable (dynamic) gear ratio that can be integrated into the vehicle driveline between the transfer case and front axle. The paper details the electrical and mechanical characteristics of the device, including its various operation modes, its mathematical model built from the equations of the planetary gear set and eddy current brake, an optimization condition by which the device will be controlled to improve vehicle energy efficiency, as well as its torque and electrical current usage. Computer simulations are performed on a mathematical model of a 4×4 military truck using the power transmitting unit in conjunction with a series hybrid-electric configuration transmission.

Modeling of the Meshing of Trochoidal Profiles With Clearances

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Lozica Ivanović ◽  
Goran Devedžić ◽  
Saša Ćuković ◽  
Nenad Mirić
Keyword(s):  
Mathematical Model ◽  
Gear Ratio ◽  
Geometrical Parameters ◽  
Circular Arc ◽  
Numerical Examples ◽  
Gerotor Pumps ◽  
General Mathematical Model ◽  
Height Change ◽  
Gear Profile ◽  
Profile Development

This paper explains development of the general mathematical model of trochoidal gearing that can be applied for gerotor pumps and cyclo reducers. The model analyzes geometry and physics of the gearing pair in trochoidal pump where the outer gear has one tooth more than the inner gear. The inner gear profile is described by peritrochoid equidistance and the outer gear profile by circular arc. Mathematical model of gearing with clearances is based on the principle of an ideal profile development. Minimum clearance height between teeth profiles in relation to instantaneous gear ratio is determined. The influence of gear profile geometrical parameters on gearing process, clearance height change, and pulsation of drive moment is analyzed and presented in numerical examples. Obtained results can be used for the design of the trochoidal gearing where accurate and silent operation is required.

Proposal of a radially differential type magnetic-geared motor

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Kazuaki Takahara ◽  
Katsuhiro Hirata ◽  
Noboru Niguchi ◽  
Hironori Suzuki ◽  
Hajime Ukaji
Keyword(s):  
Mathematical Model ◽  
Gear Ratio ◽  
Conventional Model ◽  
Content Type ◽  
Operational Principle ◽  
Proposed Model ◽  
Differential Type ◽  
Conventional Models ◽  
The Relationship ◽  
Maximum Transmission

Purpose This paper aims to propose a new magnetic-geared motor (MGM) which can easily increase the gear ratio up to approximately several hundred. The operational principle is described, and the relationship between the maximum transmission torques of each layer of the differential harmonic magnetic gear is investigated using a mathematical model and finite element method (FEM). Design/methodology/approach The operational principle and maximum transmission torque are described using a mathematical model. The FEM is used to investigate the operational principle and torque characteristics. Findings As the proposed model can realize a larger gear ratio than the conventional model, the torque constant can be approximately 100 times as large as that of the conventional model. Research limitations/implications The proposed and conventional models have the same shape stator, and it is not optimized. Originality/value The relationship between the maximum transmission torques of each layer is described, and this helps the design of a differential type MGM.

Studies on Epitrochoid Gear for Cycloid Drives

2003 ◽  
Vol 19 (2) ◽  
pp. 271-278 ◽  
Author(s):  
Shinn-Liang Chang
Keyword(s):  
Mathematical Model ◽  
Differential Geometry ◽  
Service Life ◽  
High Efficiency ◽  
Gear Ratio ◽  
Low Noise ◽  
Force Transmission ◽  
Compact Size ◽  
Tooth Number ◽  
Computerized Simulation

ABSTRACTCycloid drives are widely used in the industries because of their excellent characteristics, namely, high gear ratio, smooth transmission, compact size, high efficiency, low noise and long service life. In this paper, a mathematical model of an epitrochoid gear for a cycloid drive with a small tooth number difference has been proposed. Computerized simulation of the generated epitrochoid gear has also been developed. In this paper, the pressure angle, which has an important role in the analysis of cycloid drives as it influences the direction and magnitude of force transmission in gears, is derived based on the theory of differential geometry. The rack cutter profile, which is the fundamental tooth profile of a hob cutter, which in turn is the main manufacturing process of epitrochoid gear, has been obtained based on the theory of gearing. It is anticipated that the results from this paper will be beneficial to the design, analysis and manufacture of cycloid drives.

Mathematical model of hit phenomena and its application to movie advertisement

2008 ◽  
Author(s):  
Ishii Akira ◽  
Yoshida Narihiko ◽  
Hayashi Takafumi ◽  
Umemura Sanae ◽  
Nakagawa Takeshi
Keyword(s):  
Mathematical Model
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