Mathematical Modeling and Modifying of Turntable’s Angle for 5/12 Automatic Numerical Controlling Bending Hoop Machine

2011 ◽  
Vol 189-193 ◽  
pp. 1955-1959
Author(s):  
Xiao Hong Zhang ◽  
Guo Fu Yin
Keyword(s):  
Mathematical Model ◽  
Rotation Angle ◽  
Bending Moment ◽  
Numerical Control ◽  
Bending Test ◽  
Spring Back ◽  
Plastic Bending ◽  
Elastic Plastic ◽  
The Mathematical Model ◽  
Nc Bending

Aiming at 5/12 full-automatic numerical control (NC) bending hoop machine, the paper analyzed the elastic-plastic bending deformation with the knowledge of elastic-plastic bending principle, theoretically mechanics and spring-back, and deduced the relationship of bending moment and curvature ratio, and built the mathematical model between bending hoop turntable’s rotation angle and stirrups angle considering the spring-back deformation. Then the different spring-back angles under two types of stirrups diameter, Φ=8 mm and Φ=10 mm, are measured. The mathematical model of turntable’s rotation angle and stirrup’s angle for 5/12 automatic NC bending hoop machine is modified according to the analysis of bending test data.

Analysis of Polar Positioning System in Laser Device for Glass Engraving

2009 ◽  
Vol 147-149 ◽  
pp. 107-112 ◽  
Author(s):  
Roman Trochimczuk ◽  
Marek Gawrysiak
Keyword(s):  
Mathematical Model ◽  
Rotation Angle ◽  
Positioning System ◽  
Laser Device ◽  
Output Data ◽  
Cartesian Coordinates ◽  
Object Structure ◽  
Mechanical Parts ◽  
The Mathematical Model ◽  
Discretization Process

In the work the new concept of polar positioning system, alternative for Cartesian one, is presented. The mathematical model which allows calculation of the rotation angle of polar positioning system is considered. The Cartesian coordinates of formed points of object structure, received after discretization process of object are the inputs data to calculation. Output data however are rotation angles i.e. both working arm and rotation table angles. The influence of the stiffness of mechanical parts on the precision of instrument positioning and productivity of the presented polar device is defined.

scholarly journals Research on the model of Human-Robot football professional skills competition

2018 ◽  
Vol 246 ◽  
pp. 03019
Author(s):  
Yong Ding ◽  
Jiefang Liu
Keyword(s):  
Mathematical Model ◽  
Humanoid Robot ◽  
Rotation Angle ◽  
Research Direction ◽  
Linear Motion ◽  
Professional Skill ◽  
Professional Skills ◽  
Robot Soccer ◽  
Door Frame ◽  
The Mathematical Model

In this paper, the robot (humanoid robot) soccer activity is decomposed according to the process of Human-Robot football professional skill competition. This paper analyzes the shooting problem of robot in the forward range and outside the range of the door frame, applies it to the rotation angle of robot foot, and gives the mathematical model of linear motion through the force of the center of the ball. Then, the further research direction are discussed.

A Method for Calculating the Amount of the Deflection and Force-Energy Parameters for Copper-Clad Steel Tube in the Process of Straightening

2013 ◽  
Vol 477-478 ◽  
pp. 137-140
Author(s):  
Liang Yu Xia ◽  
Dong Ming Sun ◽  
Gui Rong Kang ◽  
Jian Sun
Keyword(s):  
Mathematical Model ◽  
Engineering Application ◽  
Bending Moment ◽  
Scientific Basis ◽  
Steel Tube ◽  
Elastic Plastic ◽  
Energy Parameters ◽  
Continuous Bending ◽  
Clad Steel ◽  
The Relationship

Based on Roller Straightening Theory and Elastic-Plastic Beam Research, A Appropriate Mathematical Model of Straightening has Set up.The Author Regards the Tube as a Continuous Bending Beam and Discuss in Detail the Relationship between the Straightening Force and the Bending Moment. Calculating the Amount of Deflection for Tube. in this way ,it Provided a Scientific Basis for the Copper-Clad Steel Tube Straightening Parameter Set and Engineering Application.

Plastic-Rigid Analysis of Long Beams Under Transverse Impact Loading

1952 ◽  
Vol 19 (4) ◽  
pp. 465-470
Author(s):  
M. F. Conroy
Keyword(s):  
Impact Loading ◽  
Bending Moment ◽  
Large Strains ◽  
Transverse Impact ◽  
Plastic Bending ◽  
Elastic Plastic ◽  
Straight Line ◽  
Probable Form ◽  
Constant Yield ◽  
Elastic Strains

Abstract The object of this paper is to set forth the results of an investigation of the behavior of long beams under transverse, constant-velocity impact loading, when a plastic-rigid type of analysis is adopted. It was expected that such an analysis would be satisfactory for problems involving large strains, and easier to evaluate than the corresponding elastic-plastic solution. Consideration is first given to the case of ideal plasticity. Elastic strains are neglected and the material of the beam is assumed to flow plastically at a constant yield limit. In this case expressions for the bending moment, shear force, curvature and deflection distributions along the beam are obtained analytically for any given impact velocity. The manner in which the solution for a beam having an elastic-ideally plastic bending moment-curvature relationship converges to the plastic-rigid solution, as EI increases, is discussed. Consideration is next given to the case of work-hardening where the material is assumed to obey a plastic-rigid bending moment-curvature relationship consisting of a straight line with nonzero slope. Unfortunately, difficulty arises in finding a solution analytically in this case. However, by considering the solution for a beam having the corresponding elastic-plastic bending moment-curvature relationship and a large EI-value, some speculation as to the probable form of the solution may be made.

Machine Bed Support with Sliding Surface for Improving the Motion Accuracy

2016 ◽  
Vol 10 (3) ◽  
pp. 447-454 ◽  
Author(s):  
Yusaku Shirahama ◽  
◽  
Ryuta Sato ◽  
Yusuke Takasuka ◽  
Hidenori Nakatsuji ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Machine Tool ◽  
Frequency Response ◽  
High Speed ◽  
Numerical Control ◽  
Sliding Surface ◽  
Response Curves ◽  
Support Mechanism ◽  
Speed Tracking ◽  
The Mathematical Model

The purpose of this study is to develop a new machine bed support mechanism for reducing the vibration generated during the high-speed tracking motion of numerical control machine tools. In order to achieve this, the frequency response and motion trajectory of a machine tool with the proposed machine bed, which has a sliding surface, are measured and compared with that of the conventional support. Based on the modal analysis of the machine tool structure, a mathematical model representing the influence of the machine bed characteristics on the vibration is also developed. The model consists of a bed, saddle, table, column, and spindle head. Every component has three degrees of freedom for each of the translational and rotational axes. In order to evaluate the characteristics of the machine bed, the mathematical model determines the stiffness and damping along the X-, Y-, and Z-axis between the bed and the ground. The frequency response curves simulated by using the mathematical model are compared with that of the measured ones. From the results of the experiments and simulations, it is confirmed that the vibration generated during high-speed tracking motions can be reduced by using the proposed machine bed with a sliding surface.

Study on the Turing of Toric Spectacle Lens by Use of Slow Tool Servo Method

2011 ◽  
Vol 52-54 ◽  
pp. 1526-1531 ◽  
Author(s):  
Min Kang ◽  
Xing Sheng Wang ◽  
Yong Yang ◽  
Xu Zheng
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Numerical Control ◽  
Experimental Setup ◽  
Numerical Control System ◽  
Spectacle Lens ◽  
Slow Tool Servo ◽  
The Mathematical Model

To solve the difficulties in machining toric spectacle lens, the turning method with slow tool servo was discussed. First, the experimental setup was developed, which have X-axis, Z-axis and C-axis, and the movement of the three axes can be simultaneously controlled by numerical control system. Then, the mathematical model of toric was established, and its machining model was analyzed and simulated. Finally, the machining experiments were carried in the experimental setup. The experiments showed that the turning method based on slow tool servo can meet the requirements for machining the toric spectacle lens.

A Laser Projection Device for Locating Points on the Plane Object

2012 ◽  
Vol 190-191 ◽  
pp. 1094-1098
Author(s):  
He Ding ◽  
Jian Fei Ouyang ◽  
Xiang Ma ◽  
Yong Gang Yan
Keyword(s):  
Mathematical Model ◽  
Image Processing ◽  
Digital Image Processing ◽  
Rotation Angle ◽  
Control Unit ◽  
Stepper Motor ◽  
Two Dimensional ◽  
Laser Pointer ◽  
Projection Device ◽  
The Mathematical Model

Digital image processing technology can extract the main feature of an image. In order to achieve the interaction between virtual points and plane objects, we propose the equipment for indicating points on the plane object using laser projection. We designed the equipment with a bracket, stepper motor, two-dimensional turntable, PC control unit, and a laser pointer. Next, we analyzed the mathematical model of the equipment and developed an algorithm for solving the motor rotation angle. Finally, we verified our design with an image. Here, we develop a system that can control a laser projection to a specified location by adjusting coordinates of virtual points on a computer.

Some theoretical considerations relating to strain concentration in elastic-plastic bending of beams

1968 ◽  
Vol 3 (4) ◽  
pp. 304-312 ◽  
Author(s):  
M Radomski ◽  
D J White
Keyword(s):  
Strain Hardening ◽  
Numerical Solutions ◽  
Bending Moment ◽  
Rate Of Change ◽  
Plastic Bending ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Rate Of Increase ◽  
Plastic Zones ◽  
Elastic Perfectly Plastic

Theoretical derivations are presented for the relations between maximum deflection and the corresponding maximum strain for some simple beams subject to elastic-plastic bending. Both elastic-perfectly plastic and arbitrary stress-strain relations are considered. Where possible, explicit analytical solutions are given, but where this is not possible numerical solutions are obtained by means of computer programmes. The calculations show that in elastic-perfectly plastic material short plastic zones may develop and cause large strains in the beam even though the deflection corresponding to first yield is not greatly exceeded. On the other hand, strain hardening elongates the plastic zones, so producing a more favourable strain distribution along the length of the beam than would exist without it. The more pronounced the strain-hardening characteristic, i.e. the greater the rate of increase of stress with strain, the less concentrated will be the strains. The mode of loading is important in that the higher the rate of change of bending moment, in the region of ihe maximum bending moment, the more concentrated will be the local strains.

Simulation of the Mathematical Model for Lathe Tool Cutter

2010 ◽  
Vol 156-157 ◽  
pp. 1297-1300
Author(s):  
Xue Bin Liu ◽  
Wei Zhao ◽  
Su Chang Ma ◽  
Chong Ning Li
Keyword(s):  
Mathematical Model ◽  
Machine Tool ◽  
Virtual Environment ◽  
Simulation Software ◽  
Numerical Control ◽  
Nc Machine Tool ◽  
Nc Machine ◽  
The Mathematical Model ◽  
Lathe Tool

The numerical controlling simulation of process indicates a mapping of NC machine tool in the virtual environment, and it includes the technique of manufacture, the theories of NC machine tool, CAD, CAM, and the technique of modeling and simulating. The people can apperceive the virtual environment of 3D simulated model developed by computers, carry the NC process of parts in virtual condition before the true doing when we design or alter a project, inspect the exactitude and justification of NC program, evaluate and optimize the project of process. Thereby the intention, abridging the time of developing products, depressing the cost of manufacture, advancing the quality of products and the efficiency of Production, can be finally achieved. With the rapid development of NC technique and computer graphical technology and the extensive application of computer, NC simulation technology provide an effective tool in order to validate the NC machining program and forecast the machine process. The main purpose of this dissertation is to derive the mathematical model and to simulate the lathe tool cutter. In order to enhance the operating efficiency and the demonstration quality of the numerical control lathe simulation software, the analysis has compared a kind of shape about lathe tool cutter-- PARALLELOGRAM, has established the cutter forms, thus inferred the mathematical model of the numerical control lathe simulation on the lathe tool cutter. The cutter is display in the DELPHI software development platform based on the environments of GLSence using this derived mathematical model.

scholarly journals Mathematical modeling of the grain trajectory in the workspace of the sheller with rotating decks

2020 ◽  
Vol 17 ◽  
pp. 00093 ◽  
Author(s):  
Ravil Ibyatov ◽  
Andrey Dmitriev ◽  
Bulat Ziganshin ◽  
Damir Khaliullin ◽  
Alsu Zinnatullina
Keyword(s):  
Mathematical Model ◽  
Rotation Angle ◽  
Angular Rotation ◽  
Disk Rotation ◽  
Working Space ◽  
Cereal Grain ◽  
The Moment ◽  
The Right ◽  
The Impact ◽  
The Mathematical Model

The purpose of the work is to determine the possibility of controlling the operation of cereal grain husks by changing the angular rotation speed of the disk (rotor) and deck to provide optimal conditions for peeling (removal of the flower shell from the grain). For this purpose, the movement of grain in the working space of the husk between the disk and the rotating deck is considered. The mathematical model of grain movement in the working space of the husk, taking into account the real aerodynamics of the rotating air flow, where the efficiency of peeling is determined by the speed and direction of the grain flight, is presented. To study the nature of the influence of structural and regime parameters of the desiccant on the efficiency of work, on the basis of the obtained mathematical model, numerical calculations and graphical dependences are made. On the basis of the analysis of the received graphs it is revealed that the direction of the grain impact on the deck is strongly influenced by the direction of the grain velocity vector at the moment of its tearing from the disk edge and the deck rotation angle speed. At the same time, the right angle impact of the grain can be achieved at low speeds of the deck rotation, and the speed of the grain during the impact is mainly determined by the speed of the disk rotation and practically does not depend on the speed of the deck rotation.

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