Influence of Tooth Errors and Truing Principles of Grinding Wheel Abrasion for Machining Arc Enveloping Worm

2013 ◽  
Vol 652-654 ◽  
pp. 2153-2158
Author(s):  
Wu Ji Jiang ◽  
Jing Wei
Keyword(s):  
Mathematical Model ◽  
Case Studies ◽  
High Precision ◽  
High Performance ◽  
New Method ◽  
Grinding Wheel ◽  
Grinding Process ◽  
The Mathematical Model

Controlling the tooth errors induced by the variation of diameter of grinding wheel is the key problem in the process of ZC1 worm grinding. In this paper, the influence of tooth errors by d1, m and z1 as the grinding wheel diameter changes are analyzed based on the mathematical model of the grinding process. A new mathematical model and truing principle for the grinding wheel of ZC1 worm is presented. The shape grinding wheel truing of ZC1 worm is carried out according to the model. The validity and feasibility of the mathematical model is proved by case studies. The mathematical model presented in this paper provides a new method for reducing the tooth errors of ZC1 worm and it can meet the high-performance and high-precision requirements of ZC1 worm grinding.

Mathematical model for determining the expenditure of cooling and lubricating fluid reaching directly the grinding zone

2018 ◽  
Vol 1 (94) ◽  
pp. 27-34
Author(s):  
W. Stachurski ◽  
J. Sawicki ◽  
K. Krupanek ◽  
S. Midera
Keyword(s):  
Mathematical Model ◽  
Multiple Regression ◽  
Regression Function ◽  
Multiple Regression Equation ◽  
Grinding Wheel ◽  
Grinding Process ◽  
Rake Face ◽  
Rejection Method ◽  
Ansys Cfx ◽  
The Mathematical Model

Purpose: The purpose of this article is to discuss the method of determining the mathematical model used for calculating the amount of emulsion reaching directly the grinding zone during the hob sharpening process. Design/methodology/approach: The mathematical model, in the form of a multiple regression function, was determined based on the acceptance and rejection method. The data for the calculations was obtained by conducting numerical simulations of fluid flow in the Ansys CFX software. Findings: A mathematical model enables calculating the amount of efficient expenditure of emulsion reaching directly the zone of contact between the grinding wheel and workpiece (hob cutter rake face) at various nozzle angle settings and different nominal expenditures of emulsion. The verification of the mathematical relationship confirmed its accuracy. Research limitations/implications: Further research should focus on the other types of grinding process and other types of cooling and lubricating fluids. Practical implications: The mathematical model enables a selection and application in the workshop and industrial practice of various variants of emulsion supply during the grinding of hob cutter rake face. Analysis of the multiple regression equation created on the basis of the acceptance and rejection method also allows predicting changes in the analyzed numerical model. Originality/value: The literature review has shown that no research of this type has been conducted with regard to analyses and optimisation of the grinding process during hob cutter sharpening. The results of this research are a novelty on a worldwide scale.

Grinding Process of Ball End Milling Cutter Flank

2018 ◽  
Vol 764 ◽  
pp. 383-390 ◽  
Author(s):  
Quan Qi Xin ◽  
Tai Yong Wang ◽  
Zhi Qiang Yu ◽  
Hong Yan Hu
Keyword(s):  
Mathematical Model ◽  
End Milling ◽  
Cutting Edge ◽  
Grinding Wheel ◽  
Grinding Process ◽  
Milling Cutter ◽  
Ball End Milling ◽  
Position And Orientation ◽  
The Mathematical Model

In this paper, the mathematical model of "S" - shaped cutting-edge curve is optimized, and the position and orientation of the grinding wheel of the first and second flank of the ball end milling cutter are calculated, The correctness of the algorithm is verified by VERICUT simulation.

Research on Grinding Model of Roller for Manufacturing Involute Spline

2009 ◽  
Vol 416 ◽  
pp. 524-528 ◽  
Author(s):  
Feng Shou Zhang ◽  
Feng Kui Cui ◽  
Chun Mei Li ◽  
Xiao Qiang Wang
Keyword(s):  
Mathematical Model ◽  
Theoretical Basis ◽  
Grinding Force ◽  
Grinding Wheel ◽  
Grinding Process ◽  
Motion Trajectory ◽  
Rolling Experiment ◽  
Grinding Machine ◽  
The Mathematical Model ◽  
Involute Spline

The paper studies the grinding process of cold roller. The shape of grinding wheel, the arc radius of grinding wheel, the motion trajectory of wheel center and the grinding force are analyzed. The mathematical model is established. The cold rolling experiment shows that the analyses and formula deduced in this paper are correct. It provides theoretical basis for designing and manufacturing roller and provides the mathematical guidance for making process parameter and designing grinding machine.

A High Performance Model for Task Allocation in Distributed Computing System Using K-Means Clustering Technique

2018 ◽  
Vol 9 (3) ◽  
pp. 1-23 ◽  
Author(s):  
Harendra Kumar ◽  
Nutan Kumari Chauhan ◽  
Pradeep Kumar Yadav
Keyword(s):  
Mathematical Model ◽  
Distributed Computing ◽  
High Performance ◽  
Computing System ◽  
Performance Model ◽  
Communication Costs ◽  
Clustering Technique ◽  
Proposed Model ◽  
Two Stages ◽  
The Mathematical Model

Tasks allocation is an important step for obtaining high performance in distributed computing system (DCS). This article attempts to develop a mathematical model for allocating the tasks to the processors in order to achieve optimal cost and optimal reliability of the system. The proposed model has been divided into two stages. Stage-I, makes the ‘n' clusters of set of ‘m' tasks by using k-means clustering technique. To use the k-means clustering techniques, the inter-task communication costs have been modified in such a way that highly communicated tasks are clustered together to minimize the communication costs between tasks. Stage-II, allocates the ‘n' clusters of tasks onto ‘n' processors to minimize the system cost. To design the mathematical model, executions costs and inter tasks communication costs have been taken in the form of matrices. To test the performance of the proposed model, many examples are considered from different research papers and results of examples have compared with some existing models.

Mathematical Model and Algorithm of Soy Sauce Quality Evaluation Based on Fuzzy Clustering

2011 ◽  
Vol 55-57 ◽  
pp. 2018-2022
Author(s):  
Yu Feng Li ◽  
Chun Ling Wang
Keyword(s):  
Mathematical Model ◽  
Fuzzy Clustering ◽  
Quality Evaluation ◽  
Soy Sauce ◽  
New Method ◽  
The Mathematical Model

A mathematical model is created, and the algorithm is designed according to the fuzzy clustering. The main indices of the soy sauce samples are detected, and the data are analyzed using fuzzy clustering. As a result, many classes including different soy sauce sample can be obtained, and the quality within the same class is similar. The mathematical model and algorithm provide a method to identification the soy sauce. And in the others, it provides a new method to evaluate the quality of the soy sauce.

scholarly journals MODELING OF HIGH PRECISION POSITIONING SYSTEM / DIDELIO TIKSLUMO PADĖTIES NUSTATYMO SISTEMOS MODELIAVIMAS

2013 ◽  
Vol 5 (6) ◽  
pp. 633-637
Author(s):  
Giedrius Augustinavičius ◽  
Audrius Čereška
Keyword(s):  
Mathematical Model ◽  
High Precision ◽  
Positioning System ◽  
Reduction Mechanism ◽  
Precision Positioning ◽  
Analytical Approaches ◽  
The Mathematical Model ◽  
Architecture Optimization ◽  
Fine Adjustment

This paper presents the modeling of a flexure-based precisionpositioning system for micro-positioning uses. The positioningsystem is featured with monolithic architecture, flexure-basedjoints and ultra fine adjustment screws. Its workspace has beenevaluated via analytical approaches. Reduction mechanism isoptimally designed. The mathematical model of the positioningsystem has been derived, which is verified by resorting to finiteelement analysis (FEA). The established analytical and (FEA)models are helpful for a reliable architecture optimization andperformance improvement of the positioning system. Santrauka Straipsnyje pristatomas didelio tikslumo centravimo ir niveliavimo padėties nustatymo sistemos su besideformuojančiais mechanizmais kūrimas ir modeliavimas. Padėties nustatymo sistema optimizuota Solidworks Simulation programiniu paketu. Centravimo platformų poslinkiams apskaičiuoti sudarytas matematinis modelis, kurio patikimumas buvo patikrintas taikant baigtinių elementų metodą. Sudaryto matematinio modelio ir rezultatų, gautų pritaikius baigtinių elementų metodą, skirtumai buvo mažesni nei 10 %. Pasiūlyta modeliavimo metodika gali būti taikoma kuriant padėties nustatymo sistemas su besideformuojančiais mechanizmais.

Research on Power and Brake Detection Integration of Wheeled Construction Machinery

2014 ◽  
Vol 945-949 ◽  
pp. 2126-2131
Author(s):  
Cong Cong Gong ◽  
Ming Lu ◽  
Hai Feng Ling ◽  
Bo Li
Keyword(s):  
Mathematical Model ◽  
Performance Test ◽  
New Method ◽  
Test Equipment ◽  
Treatment Efficiency ◽  
Large Area ◽  
Construction Machinery ◽  
Test Platform ◽  
Brake Performance ◽  
The Mathematical Model

The power and brake performance of wheeled construction machinery are separately detected on different test equipment in present chassis detection line. A new method is put forward in the veiw of high cost, large area occupied and low treatment efficiency of the traditional line. A DC dynamometer is provided as the power absorbing device and the reverse drag device to combine the two separate platforms in the proposed method, and the mathematical model of DC dynamometer is built based on the principle of chassis performance test. The parameter of dynamometer is determined by calculating, and power and brake detection integration of the wheeled construction machinery is achieved on the integrated test platform.

Research on NC Dressing of Involute Grinding Wheel

2010 ◽  
Vol 455 ◽  
pp. 132-136
Author(s):  
Xiao Zhong Ren ◽  
Ya Hui Wang ◽  
Jian Xin Su
Keyword(s):  
Mathematical Model ◽  
Simulation Experiment ◽  
Grinding Wheel ◽  
Accuracy Index ◽  
Programming Tool ◽  
Involute Gears ◽  
The Mathematical Model

Aiming at the dressing of involute grinding wheel, the mathematical model of involute interpolation is established. Taking the normal tolerance δ as accuracy index, the dense degree of interpolation points can be changed constantly with the change of developable angle increment △θ so that the numbers of interpolation points can meet the requirements not only for interpolating accuracy, but for interpolating efficiency. The wheel dressing software developed by using VC++ as programming tool can be applied for dressing the involute grinding wheel which can be used to grind involute gears with different teeth and modules. The results of simulation experiment verify the feasibility and correctness of the software.

An Immunity-Based Algorithm for Distribution Center Location

2014 ◽  
Vol 971-973 ◽  
pp. 1537-1542
Author(s):  
Chao Ying Wang ◽  
Zhi Neng Liu
Keyword(s):  
Neural Network ◽  
Mathematical Model ◽  
Immune Algorithm ◽  
Distribution Center ◽  
New Method ◽  
Modern Logistics ◽  
Logistics System ◽  
Center Location ◽  
The Mathematical Model ◽  
Distribution Center Location

The distribution center is the bridge connected supply points and demand points, lies in pivotal status in modern logistics system. Firstly, the mathematical model of a distribution center location is established, based on the study of using neural network to solve distribution center location of the previous scholars, a new method is presented as well as the improved immune algorithm. A new affinity formula is designed for immunoselection criteria. Simultaneously, based on the mathematical model and cases, the algorithm is drilled concrete. A case shows that the improved immune algorithm can better solve the problem of the distribution center location.

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