The mathematical model of the abrasion of a grinding wheel

1977 ◽  
Vol 17 (3) ◽  
pp. 163-170
Author(s):  
Yu.I. Mokin
Keyword(s):  
Mathematical Model ◽  
Grinding Wheel ◽  
The Mathematical Model

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.

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.

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 Cam Contour Error of Grinding Machining

2014 ◽  
Vol 620 ◽  
pp. 199-204
Author(s):  
Xiu Mei Chen ◽  
Qiu Shi Han ◽  
Bao Ying Peng
Keyword(s):  
Mathematical Model ◽  
Servo System ◽  
Linear Motor ◽  
Motor Drives ◽  
Position Error ◽  
Contour Error ◽  
Grinding Wheel ◽  
The Mathematical Model ◽  
The Relationship ◽  
The Way

In order to obtain higher cam quality, the research on the cam contour error is studied. The cam is machined in the way of X-C biaxial linkage motions. The linear motor drives the grinding wheel mechanism to get the motion of X axis, and the motion of C axis is the rotating of cam driven by the torque motor. Because of the servo-system-lag of the two axes, the cam contour error is formed in the X-C biaxial linkage motions. Moreover, the following position error of X axis and C axis is not same as the cam contour error. The relationship between axis following position error and cam contour error is studied. The mathematical model of cam contour error is constructed, the relationship between the cam contour error and the following position error are obtained. At last, the conclusion which the cam contour error can be controlled is made, although the following position error exists at the same time. To design the contour error controller for higher quality cam is based on the above conclusion.

A Designing and Generating Method for Grinding Relief Surfaces of a Dual-Cone Double-Enveloping Hourglass Worm Gear Hob

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Chengjie Rui ◽  
Haitao Li ◽  
Jie Yang ◽  
Wenjun Wei ◽  
Xuezhu Dong
Keyword(s):  
Mathematical Model ◽  
Worm Gear ◽  
Double Cone ◽  
Grinding Wheel ◽  
Dual Cone ◽  
Generating Method ◽  
Motion Parameters ◽  
Grinding Machine ◽  
The Mathematical Model

Land widths and relief angles of a dual-cone double-enveloping hourglass worm gear hob are important factors that influence the life and the hobbing performance of the hob. Both of them are obtained by generating relief surfaces of the hob. Due to the reason that all teeth of this type of hob have different profiles with each other, all of the relief surfaces are difficult to generate for keeping all cutting teeth with uniformed relief angles and uniformed land widths. For the purpose that land widths and relief angles could be machined precisely, this paper puts forward a designing and generating method for grinding the relief surfaces. The relief surfaces are ground using the same double-cone grinding wheel as grinding the helical surfaces of the worm. Based on the theory of gearing, the mathematical model for grinding relief surfaces is built. Motion parameters when grinding the different points of the land edges on different teeth of the hob are solved. A generating simulation is built by putting those motion parameters into a four-axis hourglass worm-grinding machine. The results of the simulation show that the relief surfaces can be ground continuously and the land widths and the relief angles meet the requirements.

Research on the Mathematical Model of Helical Groove of the End Mill Based on the Grinding Wheel Attitude

2013 ◽  
Vol 589-590 ◽  
pp. 416-420 ◽  
Author(s):  
Xian Feng Zhao ◽  
Lin He ◽  
Hong Yan Shi
Keyword(s):  
Mathematical Model ◽  
Differential Geometry ◽  
Relative Motion ◽  
3D Model ◽  
Rake Angle ◽  
Grinding Wheel ◽  
End Mill ◽  
Helical Groove ◽  
The Mathematical Model ◽  
Main Factor

This paper presents the mathematical model of helical groove of the end mill according to the differential geometry and meshing principle based on the grinding wheel attitude. The profile of the helical groove can be precisely calculated using a given wheel attitude and the relative motion between the workpiece and the grinding wheel.The relation between the grinding wheel attitude and the rake angle can be obtained through adjusting the grinding wheel attitude angle.And the accurate 3D model of helical groove was generated in the SolidWorks.The research shows that the grinding wheel attitude is the main factor that affects the rake angle of end mill.There is a linear relationship between the rake angle and the grinding wheel attitude. The smooth and accurate 3D model of helical groove lay the foundation for studying the cutting performance and dynamic characteristics of end mill.

A Novel Error Detection and Compensation Method of Hourglass Worm Gear Hob

2012 ◽  
Author(s):  
Q. Y. Shu ◽  
Q. Y. Qiu ◽  
P. E. Feng ◽  
L. Cao
Keyword(s):  
Mathematical Model ◽  
Error Detection ◽  
Worm Gear ◽  
Grinding Wheel ◽  
Gear Pair ◽  
Manufacturing Error ◽  
Optical Projection ◽  
Lubrication Condition ◽  
The Mathematical Model ◽  
Detecting Method

The double enveloping hourglass worm gear pair is a type of transmission, which has many traits, such as more teeth in mesh for transmission, higher contact quality, better lubrication condition and so on. Therefore, it has higher efficiency of transmission, stronger bearing capacity and longer work life. But the manufacturing difficulty of the worm gear hob has limited its popularization and application. Unlike the traditional worm gear hob which can use the principle of optical projection to detect the hob shaft section and compare with its mathematical model, currently, there is no standard mathematical model to detect the shaft section of hourglass worm gear hob. Hence, the accuracy of hourglass worm gear hob can’t be guaranteed during manufacturing process, and the accuracy of hourglass worm gear can’t be guaranteed too. Thus, the transmission performance of the manufactured double enveloping hourglass worm gear pair will be affected. The paper puts forward a novel detection method for hourglass worm gear hob on the basis of the detecting method for traditional worm gear hob and established the mathematical model of the shaft section of hourglass worm gear hob. The manufacturing error of hourglass worm gear hob can be obtained through such detection. The paper also points out that the error is mainly produced during the grinding of hob teeth, because the grinding wheel is worn out and the blank hob is thermally deformed. At last, a method for error compensation is advanced during the process of hob grinding. The paper presents a test to verify the feasibility of this method and the test result shows that the manufacturing error of hourglass worm gear hob is reduced from 30.15μm to 10.3μm.

Dynamic Model of Oscillation-Assisted Cylindrical Plunge Grinding With Chatter

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Witold Pawłowski
Keyword(s):  
Mathematical Model ◽  
Frequency Response Function ◽  
Nonlinear Behavior ◽  
Grinding Force ◽  
Grinding Wheel ◽  
Wheel Surface ◽  
Plunge Grinding ◽  
Excited Vibration ◽  
Dynamical Properties ◽  
The Mathematical Model

In this paper, the mathematical model of the oscillation-assisted cylindrical plunge grinding process has been presented. In this model, the dynamical properties of the grinder, self-excited vibration (regenerative chatter), and nonlinear behavior of the grinding force have been taken into consideration. This mathematical model has been applied to analyze both formation and development of chatter on the workpiece and the grinding wheel surface during oscillation-assisted cylindrical plunge grinding. The frequency response function (FRF), describing dynamical properties of the grinder, has been determined by means of modal experiment. The model has been implemented in matlab-simulink environment in order to perform simulations. The results of the simulations confirmed the antiregenerative properties of the oscillations of the workpiece rotational movement during cylindrical plunge grinding.

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.

Sign in / Sign up

Export Citation Format

Share Document