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.

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.

Force tracking control of grinding end effector based on backstepping + PID

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Shijie Dai ◽  
Shining Li ◽  
Wenbin Ji ◽  
Zhenlin Sun ◽  
Yufeng Zhao
Keyword(s):  
Mathematical Model ◽  
Linear System ◽  
Control Strategy ◽  
Grinding Force ◽  
Constant Force ◽  
End Effector ◽  
Content Type ◽  
Modeling And Analysis ◽  
The Mathematical Model ◽  
Automobile Wheel

Purpose This study aims to realize the constant force grinding of automobile wheel hub. Design/methodology/approach A force control strategy of backstepping + proportion integration differentiation (PID) is proposed. The grinding end effector is installed on the flange of the robot. The robot controls the position and posture of the grinding end actuator and the grinding end actuator controls the grinding force output. First, the modeling and analysis of the grinding end effector are carried out, and then the backstepping + PID method is adopted to control the grinding end effector to track the expected grinding force. Finally, the feasibility of the proposed method is verified by simulation and experiment. Findings The simulation and experimental results show that the backstepping + PID strategy can track the expected force quickly, and improve the dynamic response performance of the system and the quality of grinding and polishing of automobile wheel hub. Research limitations/implications The mathematical model is based on the pneumatic system and ideal gas, and ignores the influence of friction in the working process of the cylinder, so the mathematical model proposed in this study has certain limitations. A new control strategy is proposed, which is not only used to control the grinding force of automobile wheels, but also promotes the development of industrial control. Social implications The automatic constant force grinding of automobile wheel hub is realized, and the manpower is liberated. Originality/value First, the modeling and analysis of the grinding end effector are carried out, and then the backstepping + PID method is adopted to control the grinding end effector to track the expected grinding force. The nonlinear model of the system is controlled by backstepping method, and in the process, the linear system composed of errors is obtained, and then the linear system is controlled by PID to realize the combination of backstepping and PID control.

Nonlinear dynamic analysis of a Stockbridge damper

2019 ◽  
Vol 46 (9) ◽  
pp. 828-835
Author(s):  
Nilson Barbieri ◽  
Marlon Elias Marchi ◽  
Marcos José Mannala ◽  
Renato Barbieri ◽  
Lucas de Sant’Anna Vitor Barbieri ◽  
...  
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Nonlinear Dynamic Analysis ◽  
Nonlinear Behavior ◽  
Vibration Data ◽  
Electric Transmission Line ◽  
Good Concordance ◽  
Tip Mass ◽  
The Mathematical Model ◽  
Stockbridge Damper

The purpose of this work is to validate a nonlinear mathematical model (finite element method) for dynamic simulation of Stockbridge dampers of electric transmission line cables. To obtain the mathematical model, a nonlinear cantilever beam with a tip mass was used. The mathematical model incorporates a nonlinear stiffness matrix of the element due to the nonlinear curvature effect of the beam. To validate the mathematical model, the numerical results were compared with experimental data obtained on a machine adapted from cam test. Five different circular cam profiles with eccentricities of 0.25, 0.5, 0.75, 1.25, and 1.5 mm were used. Vibration data were collected through three accelerometers arranged along the sample. A good concordance was found between the numerical and experimental data. The same behavior was observed in tests of another Stockbridge damper excited by a shaker. The nonlinear behavior of the system was evidenced.

The Solution Design of Hobbing Worm Milling Cutters Face Teeth Undercut

2018 ◽  
Vol 919 ◽  
pp. 59-67
Author(s):  
Aneta Milsimerová
Keyword(s):  
Mathematical Model ◽  
Negative Impact ◽  
Helix Angle ◽  
Grinding Wheel ◽  
Wheel Surface ◽  
Teeth Grinding ◽  
Complex Operation ◽  
The Face ◽  
Solution Design

Face teeth grinding of special tools, as hobing worm milling cutters are, is the shape and cinematically complex operation with the respect to achieving the necessary accuracy and resultant shape geometry. The grinding wheel shape, it ́s size and the control helix angle of hobing worm are the primary factors which are compelling the ground groove accuracy during the face teeth sharpening process. Inappropriately selected combination of these parameters causes undercut of this surface and the negative impact on required accuracy. The main aim of the solution is to find a variable and to create a parametric mathematical model to calculate appropriate grinding wheel shape according to the input factors – hobing worm and grinding wheel parameters which affects this issue. This system will be used to create the initial grinding wheel surface and a helix groove undercut calculation program. The graphical part of this programme will be the next benefit.

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.

The Influence of the Grinding Force to the Material Removal Rate in the Heavy Load Honing

2011 ◽  
Vol 63-64 ◽  
pp. 719-722
Author(s):  
Jian Ye Guo ◽  
Chao Yu ◽  
Guang Qi Cai
Keyword(s):  
Mathematical Model ◽  
Material Removal Rate ◽  
Material Removal ◽  
Removal Rate ◽  
Grinding Force ◽  
Processing Technology ◽  
Heavy Load ◽  
Theoretical Significance ◽  
The Mathematical Model ◽  
The Relationship

This paper took the grinding force in the heavy load honing as the object to research, it mainly analyzed the influence of the grinding force to the material removal rate. First the mathematical model of grinding force was established from starting with the honing pressure. Then the mathematical model of material removal rate was established according to the relationship between material removal volume and honing pressure. Finally the influence of the honing pressure to the material removal rate was analyzed with the aid of software. The results of this paper have important theoretical significance to optimize the processing technology of heavy load honing and further enhance the machining precision and the honing efficiency.

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.

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