The Modulation of Chatter Vibrations

1969 ◽  
Vol 91 (3) ◽  
pp. 673-677 ◽  
Author(s):  
R. A. Thompson
Keyword(s):  
Mathematical Model ◽  
Vibrational Frequency ◽  
Machining Process ◽  
Experimental Investigations ◽  
Characteristic Frequencies ◽  
Chatter Vibrations ◽  
Machining Chatter

The results of several experimental investigations concerning the nature of machining chatter are discussed. They indicate that chatter vibrations are generally amplitude modulated and that the chatter frequency may or may not vary from the free vibrational frequency of the chattering component. Of the several results considered each is explained in terms of an extension of the empirically derived lag equation for the machining process of Doi and Kato whereby the characteristic frequencies of the lag equation are determined. The fact that the frequency related phenomena of several independent tests are confirmed by the lag equation, which was not derived from frequency considerations, seems to justify it as a valid mathematical model for the machining process.

Mathematical Modelling the Process of Cup Wheel Precision Grinding of Rotating Concave Paraboloid

2016 ◽  
Vol 693 ◽  
pp. 837-842
Author(s):  
Fu Yi Xia ◽  
Li Ming Xu ◽  
De Jin Hu
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Abrasive Particle ◽  
Influence Factors ◽  
Machining Process ◽  
Quadric Surface ◽  
Precision Grinding ◽  
Cup Wheel ◽  
The Mathematical Model ◽  
Trajectory Equation

A novel principle of cup wheel grinding of rotating concave quadric surface was proposed. The mathematical model of machining process was established to prove the feasibility of precision grinding of rotating concave paraboloid based on the introduced principle. The conditions of non-interference grinding of concave paraboloid were mathematically derived. The processing range and its influence factors were discussed. The trajectory equation of abrasive particle was concluded. Finally, the math expressions of numerical controlled parameters was put forward in the process of grinding of the concave paraboloid.

scholarly journals The Role of Cell Motility in Metastatic Cell Dominance Phenomenon: Analysis by a Mathematical Model

2000 ◽  
Vol 3 (1) ◽  
pp. 63-77 ◽  
Author(s):  
A. V. Kolobov ◽  
A. A. Polezhaev ◽  
G. I. Solyanik
Keyword(s):  
Mathematical Model ◽  
Cell Motility ◽  
Threshold Value ◽  
Experimental Investigations ◽  
Metastatic Cell ◽  
Metastatic Cells ◽  
Motile Cells ◽  
Cell Subpopulations ◽  
Cell Motion ◽  
Slow Growing

Metastasis is the outcome of several selective sequential steps where one of the first and necessary steps is the progressive overgrowth or dominance of a small number of metastatic cells in a tumour. In spite of numerous experimental investigations concerning the growth advantage of metastatic cells, the mechanisms resulting in their dominance are still unknown. Metastatic cell overgrowth occurs even if doubling time of the metastatic subpopulation is shorter than that of all others subpopulations in a heterogeneous tumour. In order to examine the hypothesis that under conditions of competition of cell subpopulations for common substrata cell motility of the slow-growing subpopulation can result in its dominance in a heterogeneous tumour, a mathematical model of heterogeneous tumour growth is suggested. The model describes two cell subpopulations which can grow with different rates and transform into the resting state depending on the concentration of the substrate consumed by both subpopulations. The slow-growing subpopulation is assumed to be motile. In numerical simulations it is shown that this subpopulation is able to overgrow the other one. The dominance phenomenon (resulting from random cell motion) depends on the motility coefficient in a threshold manner: in a heterogeneous tumour the slow-dividing motile subpopulation is able to overgrow its non-motile counterparts if its motility coefficient exceeds a certain threshold value. Computations demonstrate independence of the motile cells overgrowth from the initial tumour composition.

Novel Direct Model for Machining Regenerative Chatter

2016 ◽  
Author(s):  
Aaron Lalley ◽  
Mark Bedillion
Keyword(s):  
Simulation Model ◽  
Machining Process ◽  
Direct Simulation ◽  
Regenerative Chatter ◽  
Stability Lobe ◽  
Direct Model ◽  
Machining Chatter ◽  
The Stability ◽  
Time Information ◽  
New Time

Regenerative machining chatter or resonance in the machining process has traditionally been modeled with the stability lobe approach. This paper presents a new time based direct simulation model and compares it with traditional stability lobe modeling. The direct model has the ability to discriminate directional and time information, resulting in a number of advantages over frequency-based stability lobe analysis.

Performance Enhancement of Pneumatic Vibration Isolators Using Self-Tuning PID Feedback and Time-Delay-Control (TDC)-Based Feedforward Scheme

2018 ◽  
Author(s):  
Jin-Wei Liang ◽  
Hung-Yi Chen ◽  
Lyu-Cyuan Zeng
Keyword(s):  
Mathematical Model ◽  
Performance Enhancement ◽  
Control Method ◽  
Hybrid Control ◽  
Model Performance ◽  
Experimental Investigations ◽  
Isolation System ◽  
Control Scheme ◽  
Self Tuning ◽  
Hybrid Control Scheme

A hybrid control scheme that combines a self-tuning PID-feedback loop and TDC-based feedforward scheme is proposed in this study to cope with an active pneumatic vibration isolator. In order to establish an effective TDC feedforward control a reliable mathematical model of the pneumatic isolator is required and developed firstly. Numerical and experimental investigations on the validity of the mathematical model are performed. It is found that although slight discrepancy exists between predicted and observed behaviors of the system, the overall model performance is acceptable. The resultant model is then applied in the design of the TDC feedforward scheme. A neuro-based adaptive PID control is integrated with the TDC feedforward algorithm to form the hybrid control. Numerical and experimental isolation tests are carried out to examine the suppression performances of the proposed hybrid control scheme. The results show that the proposed hybrid control method outperforms solely TDC feedforward while the latter outperforms the passive isolation system. Moreover, the proposed hybrid control scheme can suppress the vibration near the system’s resonance.

Influence of a delamination on Lamb wave excitation by a nearby piezoelectric transducer

2020 ◽  
pp. 1045389X2091997 ◽  
Author(s):  
Alisa N Shpak ◽  
Mikhail V Golub ◽  
Inka Mueller ◽  
Artem Eremin ◽  
Jens Kathol ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Piezoelectric Transducer ◽  
Lamb Wave ◽  
Lamb Waves ◽  
Boundary Integral ◽  
Experimental Investigations ◽  
Wave Excitation ◽  
Damage Scenarios ◽  
Active Sensor ◽  
Piezoelectric Wafer

This article presents the results of theoretical and experimental investigations of characteristic changes of Lamb wave excitation and scattering by a strip-like horizontal delamination in a layered elastic waveguide for Lamb waves induced by a piezoelectric wafer active sensor. The boundary integral equation method is used to describe wave propagation in an infinite layered waveguide with a delamination, while the frequency domain spectral element method is employed to model the dynamic behaviour of the piezoelectric wafer active sensor, which allows to simulate debonding between the piezoelectric wafer active sensor and the waveguide. Experimental investigations of the dynamic interaction of the piezoelectric wafer active sensor with a layered plate containing a horizontal delamination is conducted for several damage scenarios, showing a good agreement with the results obtained using the developed mathematical model. The obtained mathematical model is employed to analyse alteration of the piezo-induced Lamb waves including modes’ decomposition due to delamination. The conversion and/or conservation of the Lamb waves on account of a delamination is investigated. The electro-mechanical impedance of the piezoelectric transducer and the stress intensity factors of a delamination are analysed in dependence on the delamination location.

scholarly journals Modeling of Pressure Drop During Refrigerant Condensation in Pipe Minichannels

2017 ◽  
Vol 38 (4) ◽  
pp. 15-28 ◽  
Author(s):  
Małgorzata Sikora ◽  
Tadeusz Bohdal
Keyword(s):  
Mathematical Model ◽  
Pressure Drop ◽  
Computer Modeling ◽  
Experimental Verification ◽  
Flow Resistance ◽  
Experimental Results ◽  
Experimental Investigations ◽  
Flow Conditions ◽  
Conservation Equations ◽  
Mathematical And Computer Modeling

Abstract Investigations of refrigerant condensation in pipe minichannels are very challenging and complicated issue. Due to the multitude of influences very important is mathematical and computer modeling. Its allows for performing calculations for many different refrigerants under different flow conditions. A large number of experimental results published in the literature allows for experimental verification of correctness of the models. In this work is presented a mathematical model for calculation of flow resistance during condensation of refrigerants in the pipe minichannel. The model was developed in environment based on conservation equations. The results of calculations were verified by authors own experimental investigations results.

Design, Development & Experimental Investigation of Electro-Discharge Diamond Surface Grinding of Ti-6Al-4V

2011 ◽  
Vol 418-420 ◽  
pp. 1478-1481 ◽  
Author(s):  
Manoj Modi ◽  
Gopal Agarwal
Keyword(s):  
Removal Rate ◽  
Surface Grinding ◽  
Machining Process ◽  
Diamond Surface ◽  
Experimental Investigations ◽  
Grinding Wheel ◽  
Hybrid Machining ◽  
Hard Materials ◽  
Hybrid Machining Process ◽  
Pulse On Time

Abstract: Ti-6Al-4V are used extensively in aerospace, medical, marine and surgical implants etc. but it is hard to machine. Machining of advanced difficult-to-machine very hard materials (Ti-6Al-4V, composites and ceramics) is a big challenge. By conventional machining processes, their machining is not only costly but results in poor surface finish and shorter tool life. To meet these challenges, new hybrid machining process (HMP) has been developed. This article is focused on hybrid machining process comprising of conventional surface grinding along with electro-discharge machining between the periphery of metal bonded diamond grinding wheel and flat rectangular shape workpiece. This process has the advantage of shaping advance engineering materials and difficult-to- machine very hard materials. The experimental investigations of various input parameters like wheel RPM, duty factor, current and pulse on-time on material removal rate of Ti-6Al-4V in EDDSG process have been reported here on newly self designed & fabricated set up. Keywords: Electro-Discharge Diamond Surface Grinding (EDDSG), Hybrid Machining Process (HMP), Ti-6Al-4V.

Analysis of Cutting Technologies for Lightweight Frame Components

2006 ◽  
Vol 10 ◽  
pp. 121-132 ◽  
Author(s):  
Klaus Weinert ◽  
Sven Grünert ◽  
Michael Kersting
Keyword(s):  
Finite Element ◽  
Metal Cutting ◽  
Thermal Stresses ◽  
Machining Process ◽  
Frame Structure ◽  
Experimental Investigations ◽  
Promising Alternative ◽  
Thin Walled ◽  
Process Strategy ◽  
Conventional Drilling

Most technical components applied in industrial practice are subjected to metal cutting operations during their production process. However, this leads to undesirable thermal and mechanical loads affecting the machined workpiece, which can result in an impairment of its serviceability. Due to their small wall thickness lightweight hollow profiles are highly susceptible to the inevitable machining loads and thermal stresses during drilling processes. For the virtual optimization of the machining process and in order to ensure a suitable process strategy, a finite element simulation of cutting operations for thin-walled light metal profiles is conducted. Due to the flexibility within creating drill holes of different diameters without tool changes circular milling represents a promising alternative to the application of conventional drilling tools for variable process strategies to handle batch sizes down to one piece efficiently. Hence, this article gives an insight into the investigations regarding the modeling concepts of the mechanical and thermal loads induced into the thin-walled lightweight frame structure during the circular milling process. Furthermore, process reliability aspects as well as the correlation of the calculated and the measured results will be discussed on the basis of experimental investigations. Finally, this article compares Finite Element Analysis aspects of circular milling processes with conventional drilling processes.

scholarly journals A New Mathematical Model for Flank Wear Prediction Using Functional Data Analysis Methodology

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Sonja Jozić ◽  
Branimir Lela ◽  
Dražen Bajić
Keyword(s):  
Mathematical Model ◽  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Flank Wear ◽  
End Milling ◽  
Cutting Parameters ◽  
Machining Process ◽  
Wear Prediction ◽  
Analysis Methodology

This paper presents a new approach improving the reliability of flank wear prediction during the end milling process. In the present work, prediction of flank wear has been achieved by using cutting parameters and force signals as the sensitive carriers of information about the machining process. A series of experiments were conducted to establish the relationship between flank wear and cutting force components as well as the cutting parameters such as cutting speed, feed per tooth, and radial depth of cut. In order to be able to predict flank wear a new linear regression mathematical model has been developed by utilizing functional data analysis methodology. Regression coefficients of the model are in the form of time dependent functions that have been determined through the use of functional data analysis methodology. The mathematical model has been developed by means of applied cutting parameters and measured cutting forces components during the end milling of workpiece made of 42CrMo4 steel. The efficiency and flexibility of the developed model have been verified by comparing it with the separate experimental data set.

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