Toothed Belt-Load Distribution

1983 ◽  
Vol 105 (3) ◽  
pp. 339-347 ◽  
Author(s):  
M. R. Naji ◽  
K. M. Marshek
Keyword(s):  
Mathematical Model ◽  
Friction Force ◽  
Coefficient Of Friction ◽  
Material Properties ◽  
Load Distribution ◽  
Experimental Results ◽  
Spring Constant ◽  
Pitch Difference ◽  
Toothed Belt ◽  
The Mathematical Model

A mathematical model was developed to study the effect on belt load distribution of belt material properties, pitch variations, friction force, and pulley rotation. Results are presented which show the influence on load distribution of pitch difference, tight side tension, slack side tension, belt tooth spring constant, and coefficient of friction, for the belt on stationary, driver, and driven pulleys. Data from the mathematical model compared well with experimental results available in the literature.

Simulation of oscillatory processes in the MVSTUDIUM package

2022 ◽  
Vol 14 (4) ◽  
pp. 139-148
Author(s):  
Aleksandr Poluektov ◽  
Konstantin Zolnikov ◽  
V. Antsiferova
Keyword(s):  
Mathematical Model ◽  
Friction Force ◽  
Computer Models ◽  
3D Models ◽  
Oscillatory Process ◽  
Suspension Point ◽  
Factors Affecting ◽  
2D And 3D ◽  
The Mathematical Model ◽  
Oscillatory Processes

The mathematical model and algorithms of oscillatory movements are considered. Various factors affecting the oscillatory process are considered. Oscillatory movements are constructed in the MVSTUDIUM modeling environment. The schemes of three computer models demonstrating oscillatory processes are determined: a model of a pendulum with a non-movable suspension point, a model of a pushing pendulum with friction force and a model of a breaking pendulum. Classes are being built to execute models with embedded properties, as well as with the ability to export the created classes to other models, and embed classes created by the program developer into the model. Creation of 2D and 3D models of oscillatory processes, an experiment behavior map and a virtual stand.

Mathematical Modeling of Electrochemical Deburring

2010 ◽  
Vol 126-128 ◽  
pp. 545-550 ◽  
Author(s):  
Wen Ji Xu ◽  
W. Wang ◽  
Xu Yue Wang ◽  
Gui Bing Pang
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Influencing Factors ◽  
Applied Voltage ◽  
Experimental Results ◽  
Electrode Gap ◽  
Workpiece Material ◽  
Burr Height ◽  
Object A ◽  
The Mathematical Model

The drilling burr is taken as the research object. A mathematical model of electrochemical deburring (ECD) is established and the effects of main influencing factors, such as inter-electrode gap, applied voltage and deburring time, on burr height have been analyzed. The results show that the deburring time increases with the increase of initial burr height, inter-electrode gap, with the decrease of volume of electrochemical equivalent of the workpiece material, conductivity of electrolyte and applied voltage. The deburring time for various burr heights can be predicted by the mathematical model. The calculated results obtained from the mathematical model are approximately consistent with the experimental results. The results show that initial burr height h0=0.722mm is removed, and the fillet radius R=0.211mm is obtained.

scholarly journals Developing an Analytical Model and Computing Tool for Optimizing Lapping Operations of Flat Objects Made of Alloyed Steels

Materials ◽  
2020 ◽  
Vol 13 (6) ◽  
pp. 1343 ◽  
Author(s):  
Tudor Deaconescu ◽  
Andrea Deaconescu
Keyword(s):  
Mathematical Model ◽  
Surface Roughness ◽  
Material Properties ◽  
Depth Of Cut ◽  
Operation Optimization ◽  
Abrasive Grains ◽  
Finishing Process ◽  
Real World Applications ◽  
The Mathematical Model

Lapping is a finishing process where loose abrasive grains contained in a slurry are pressed against a workpiece to reduce its surface roughness. To perform a lapping operation, the user needs to set the values of the respective lapping conditions (e.g., pressure, depth of cut, the rotational speed of the pressing lap plate, and alike) based on some material properties of the workpiece, abrasive grains, and slurry, as well as on the desired surface roughness. Therefore, a mathematical model is needed that establishes the relationships among the abovementioned parameters. The mathematical model can be used to develop a lapping operation optimization system, as well. To this date, such a model and system are not available mainly because the relationships among lapping conditions, material properties of abrasive grains and slurry, and surface roughness are difficult to establish. This study solves this problem. It presents a mathematical model establishing the required relationships. It also presents a system developed based on the mathematical model. In addition, the efficacy of the system is also shown using a case study. This study thus helps systematize lapping operations in regard to real-world applications.

Shaping Law and Motion Design in NC-ECM under Effect of Twiste Angle

2011 ◽  
Vol 128-129 ◽  
pp. 1010-1014
Author(s):  
Rui Wu ◽  
Dan Wen Zhang ◽  
Juan Sun
Keyword(s):  
Mathematical Model ◽  
Electrochemical Machining ◽  
Experimental Results ◽  
Working Face ◽  
Relationship Of ◽  
The Mathematical Model ◽  
The Relationship ◽  
Motion Design

The twiste angle has a great effect on shaping law and stability of Numerical Controlled Electrochemical Machining (NC-ECM) process. In order to avoid the disadvantages caused by twiste angle, a methode of study shaping law by dispersing cathode working face in NC-ECM was proposed, and a mathematical model of the shaping law with the effects of twiste angle has been established in this paper. The mathematical model disclosed the relationship of twiste angle β, feeding velocity vf and thickness of removal material h in NC-ECM. Theoretical and experimental results show the the mathematical model of shaping law described in this paper can be considered as a useful reference and is helpful for the analysis of the NC-ECM and general ECM process.

scholarly journals Experimental Study of the Forces and Parameters for the Opening of Incisions Inside Ocular Cavity

2020 ◽  
Author(s):  
Victor Olenin Ramírez-Beltrán ◽  
Luis Adrian Zuninga Avilés ◽  
Rosa Maria Valdovinos-Rosas ◽  
Jose Javier Reyes-Lagos ◽  
Giorgio Mackenzie Cruz-Martínez
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Experimental Study ◽  
Linear Relationship ◽  
Elastic Material ◽  
Experimental Results ◽  
Orbital Cavity ◽  
Experimental Procedure ◽  
The Mathematical Model

The experimental results of forces and efforts derived from the opening of incisions in the orbital cavity in a pig’s head are presented in this article. The different areas of the incision openings are related to the needs at the incision procedure for a dacryocystorhinostomy. In terms of the experimental procedure, an origin and a plane are defined so as to allow the location of the opening of the incision. The incisions are retracted along an axis of said origin. This procedure has been based on the mathematical model developed for this work, which consists of a procedure for determining the behavior of an incision when a force is applied to retract the skin. The experimental data obtained, suggests the existence of an almost linear relationship between the increment of resistance in relation to the time obtained for each opening, the same of which is deemed to be consistent with the behavior of an elastic material.

Modeling and Calibration of Grid Structured Light Based 3-D Vision Inspection

1999 ◽  
Vol 122 (4) ◽  
pp. 734-738 ◽  
Author(s):  
Guangjun Zhang ◽  
Liqun Ma
Keyword(s):  
Mathematical Model ◽  
Coordinate System ◽  
Structured Light ◽  
Calibration Method ◽  
Experimental Results ◽  
Image Feature ◽  
Feature Analysis ◽  
Calibration Process ◽  
Vision Inspection ◽  
The Mathematical Model

The principle of structured light 3-D vision is introduced, and using projective and perspective transformations, the mathematical model of grid structured light based 3-D vision inspection is established in homogeneous coordinate system in this paper. Based on the image feature analysis of grid structured light, a calibration method of grid structured light based 3-D vision inspection is proposed, and experimental results are also presented. This method is easy, efficient and fast to carry out. It simplifies the calibration process while guaranteeing its accuracy. [S1087-1357(00)00703-6]

scholarly journals Mathematical model of energy efficiency in internal spur gears

2019 ◽  
Vol 23 (Suppl. 5) ◽  
pp. 1801-1813
Author(s):  
Predrag Dobratic ◽  
Mileta Ristivojevic ◽  
Bozidar Rosic ◽  
Radivoje Mitrovic ◽  
Dragan Trifkovic
Keyword(s):  
Mathematical Model ◽  
Load Distribution ◽  
Energy Losses ◽  
Spur Gears ◽  
Contact Ratio ◽  
Cylindrical Gear ◽  
Heating Effects ◽  
Effective Efficiency ◽  
The Impact ◽  
The Mathematical Model

The impact of geometric parameters of teeth and lubricating oils to the efficiency of involute internal spur gears, when the transverse contact ratio is 2 < ?? ?3, has been analyzed in this paper. The mathematical model and computer program for determining the current and the effective value of the efficiency have been developed. The influence of the character of load distribution and energy losses due to heating effects during the meshing period is included in the factor of load distribution. The results of computer simulation are given in the form of a diagram of the current values of the efficiency during the meshing period. Also, the values of effective efficiency for the considered cylindrical gear pairs have been calculated.

Study of the Mathematical Model for Online Predicting Mix Mooney Viscosity on the Rubber Open Mill

2013 ◽  
Vol 561 ◽  
pp. 54-58
Author(s):  
Xian Kui Zeng ◽  
Chang He Yang ◽  
Ze Shuai Song ◽  
Shu Hong Zhao
Keyword(s):  
Mathematical Model ◽  
Low Temperature ◽  
The Self ◽  
Experimental Results ◽  
Mooney Viscosity ◽  
The Mathematical Model ◽  
Predictive Effect

According to studying the mechanism of open mill mixing in low temperature and its intelligent mixing theory, based on the analysis of the experimental results getting from the self-developed XK-160E type open mill, we established a mathematical model for predicting the mix Mooney viscosity. The inspection and verification of mathematical model results showed that the predicted Mooney viscosity was very close to the practical value indicating a good predictive effect．

Component Tests and Simulation of Advanced Buckling Restrained Braces

2006 ◽  
Author(s):  
C. S. Tsai ◽  
Wen-Shin Chen ◽  
Bo-Jen Chen
Keyword(s):  
Mathematical Model ◽  
Civil Engineering ◽  
Numerical Results ◽  
Experimental Results ◽  
Maximum Compression ◽  
Maximum Tension ◽  
Buckling Restrained Braces ◽  
The Mathematical Model

Recently, the earthquake proof technology has been acknowledged to be able to ensure the safety of the structures effectively during earthquakes. In this paper, two advanced buckling restrained braces (BRBs) that include multi-curved reinforced BRB and simplified reinforced BRB are presented. These two braces not only improve the disadvantages of traditional buckling restrained braces but also are more economic than the traditional ones. In order to understand the behaviors of advanced buckling restrained braces, the component tests of the advanced buckling restrained braces were carried out in the Department of Civil Engineering, Feng Chia University, Taichung, Taiwan. The experimental results illustrate that the behaviors of the advanced buckling restrained braces were very stable, as well as the maximum tension forces are close to the maximum compression forces. Furthermore, the Wen’s model in an increment form was utilized to simulate the behaviors of the advanced buckling restrained braces under cyclic loadings. The comparison between the experimental and numerical results shows that the mathematical model could simulate the behaviors of the advanced BRBs well.

scholarly journals Study on Rock-Breaking Depth and Damage Area under Particle Jet Impact

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Fushen Ren ◽  
Tiancheng Fang ◽  
Xiaoze Cheng
Keyword(s):  
Mathematical Model ◽  
Impact Velocity ◽  
Particle Diameter ◽  
Rock Breaking ◽  
Water Jet ◽  
Experimental Results ◽  
Damage Area ◽  
Jet Impact ◽  
Mathematical Calculation ◽  
The Mathematical Model

Particle jet impact drilling technology is an efficient method which mainly uses high-velocity particles to break rock. As the important criterion for evaluating rock-breaking effect, rock-breaking depth and damage area were studied in this paper. Firstly, a particle jet impact rock-breaking test device was developed, and laboratory experiments have been carried out. Then, based on the spherical cavity expansion theory, the mathematical model of rock-breaking depth and damage area under particle jet impact was established. Afterward, the effect of water-jet impact velocity, impact angle, and particle diameter on rock-breaking depth and damage area was analyzed by comparing experimental results and mathematical calculation. The results show that rock-breaking depth and damage area would increase with increase of water-jet impact velocity and decrease slightly with increase of particle diameter. And the combination of 8° and 20° is recommended for nozzle layout. The experimental results and mathematical calculation are basically consistent, which could verify the correctness of the mathematical model. The study has significance for development and application of particle jet impact rock-breaking technology and perfection of theoretical research.

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