General mathematical model for investigation of hobs suitable for generating cylindrical and conical worms, worm gears and face gear generators

2004 ◽  
pp. 124-181
Author(s):  
Illés Dudás
Keyword(s):  
Mathematical Model ◽  
Face Gear ◽  
Worm Gears ◽  
General Mathematical Model

The Generation Principle and Mathematical Models of Double-Enveloping Internal Gear Pairs

2015 ◽  
Author(s):  
Xuan Li ◽  
Bingkui Chen ◽  
Yawen Wang ◽  
Guohua Sun ◽  
Teik C. Lim
Keyword(s):  
Mathematical Model ◽  
Load Capacity ◽  
Geometrical Shape ◽  
Gear Pair ◽  
Numerical Examples ◽  
Proposed Model ◽  
General Mathematical Model ◽  
Meshing Characteristics ◽  
Internal Gear ◽  
Tooth Pair

In this paper, the planar double-enveloping method is presented for the generation of tooth profiles of the internal gear pair for various applications, such as gerotors and gear reducers. The main characteristic of this method is the existence of double contact between one tooth pair such that the sealing property, the load capacity and the transmission precision can be significantly improved as compared to the conventional configuration by the single-enveloping theory. Firstly, the generation principle of the planar double-enveloping method is introduced. Based on the coordinate transformation and the envelope theory, the general mathematical model of the double-enveloping internal gear pair is presented. By using this model, users can directly design different geometrical shape profiles to obtain a double-enveloping internal gear pair with better meshing characteristics. Secondly, to validate the effectiveness of the proposed model, specific mathematical formulations of three double-enveloping internal gear pairs which apply circular, parabolic and elliptical curves as the generating curves are given. The equations of tooth profiles and meshing are derived and the composition of tooth profiles is analyzed. Finally, numerical examples are provided for an illustration.

scholarly journals DETERMINING THE FORCES OF INTERACTION OF MAIN GEOKHODS SYSTEMS WITH GEO-ENVIRONMENT AND WITH EACH OTHER

2018 ◽  
pp. 23-30
Author(s):  
V. Yu. Beglyakov ◽  
V. V. Aksenov ◽  
I. K. Kostinets ◽  
A. A. Khoreshok
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Interaction Process ◽  
Generalized Model ◽  
Machine Elements ◽  
General Mathematical Model ◽  
Mine Workings ◽  
Modular Principles ◽  
Sufficient Strength

The processes occurring during the geodetic excavation of underground excavations are characterized by the interaction of the elements of the geokhod with each other and with the geo-environment. The interaction process can be investigated in mathematical modeling, solving the problems of justifying the parameters of the drives and interacting forces, ensuring sufficient strength of the machine elements and the bearing capacity of the contour array. The proposed block-modular principles of constructing a mathematical model allow solving particular problems of the system and its individual elements. From the solution of particular problems, it is now necessary to proceed to the solution of the generalized model, using equivalent loads and reduced total moments (forces). The construction of a generalized model requires a number of assumptions, but its solution will reveal the interaction between the elements of the geokhod and the geo-environment, which is very relevant.As an example, the solution of a particular problem is given-the determination of the value of the forces arising from the interaction of the blade of an external engine with the medium.A list of assumptions is formulated that allow us to describe a general mathematical model of the interaction between the geo-environment and the geokhod, as well as the processes occurring during geodetic excavation of mine workings.

General Mathematical Model of Multi-Arm Cooperating Robots With Elastic Interconnection at the Contact

1997 ◽  
Vol 119 (4) ◽  
pp. 707-717 ◽  
Author(s):  
Milovan Z˘ivanovic´ ◽  
Miomir Vukobratovic´
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Dynamic Environment ◽  
Six Degrees Of Freedom ◽  
General Mathematical Model ◽  
Cooperating Robots ◽  
Six Degree Of Freedom ◽  
Physical Phenomena ◽  
First Time ◽  
Object Dynamic

The procedure of modeling and the complete general form mathematical model of manipulators with six degrees of freedom in cooperative work are presented in the paper, together with the solution of undefiniteness problem with respect to force distribution. For the first time, a system of active spatial six-degree-of-freedom mechanisms elastically interconnected with the object (dynamic environment) is modeled. The reason for the emergence of the undefiniteness problem with respect to force is explained and the procedure for solving this problem given. Unlike the approaches given in the available literature, the undefiniteness problem with respect to force is solved in accordance with physical phenomena. The modeling procedure is illustrated by a simplified example.

Real-Time Multi-Body Software for HIL Simulations

2010 ◽  
Author(s):  
Paolo Righettini ◽  
Alberto Oldani
Keyword(s):  
Mathematical Model ◽  
Embedded Systems ◽  
Design Process ◽  
Hardware In The Loop ◽  
Real Behavior ◽  
Hardware Component ◽  
General Mathematical Model ◽  
The Subject ◽  
Complex Mechanical Systems ◽  
Multi Body

The Hardware in the Loop simulation is an useful instrument to simulate complex mechanical systems in which the subject of the test is an hardware component. The results of the simulation, closer to the real behavior of the system, are the main advantage of this approach. This application is often used during the design process to test components of a complex mechanical system before the development of the prototype (e.g. embedded systems). The literature examples show, in general, mathematical model finalized to the application. The objective of this work is focused on the development of a generic Multi-Body software for HIL applications. Some simulations examples, the dynamic of a slider-crank and of a McPherson suspension, are presented at the end of the paper.

Study on Microcomputer Inverse Time Over-Current Protection Algorithm of Underground Low-Voltage Power-System

2011 ◽  
Vol 143-144 ◽  
pp. 8-13 ◽  
Author(s):  
Jun Ying Zhao ◽  
Xing He Ma ◽  
Li Jia ◽  
Gen Xian Zhang
Keyword(s):  
Mathematical Model ◽  
Power System ◽  
Taylor Expansion ◽  
Low Voltage ◽  
Expansion Method ◽  
Time Algorithm ◽  
Look Up Table ◽  
General Mathematical Model

Analysis of general mathematical model and the traditional anti-time algorithm of over-current protection for microcomputer based on the algorithm proposes look-up table and Taylor expansion. To solve the problem of c=0.02 of general anti-time in microcomputer is difficult to implement directly. This paper chooses the Taylor expansion method and selects the general anti-time and thermal over-load (no storage) anti-time for experiment. The experiment proves that the Taylor expansion method can achieve exactly the characteristics of microprocessor-based inverse time.

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