This work presents a practical approach to the control of tool’s position, in orthogonal cutting, in the presence nonlinear dynamic cutting forces. The controller is Linear Quadratic Gaussian (LQG) type constructed from an augmented model of both, tool-actuator dynamics, and a nonlinear dynamic model relating tool displacement to cutting forces. The latter model is obtained using black-box system identification of experimental orthogonal cutting data in which tool displacement is the input and cutting force is the output. The controller is evaluated and its performance is demonstrated
The simulation analysis of tool flank wear based on cutting forceeSAT Journals
Abstract In the process of cutting, cutting tool wear has an important influence on the surface quality of the work piece, therefore, it is of great significance for the research of tool wear detection. In this paper, this work focuses on researching relationship between cutting force and tool flank wear. In different experiment conditions, the consistency of the results of simulation and experiment results was obtained through the comparative analysis between the two. It is a complex problem that cutting tool wear and measuring process and not easy to get the accurate ideal results by experiment, the simulation experiment has the characteristics of simple and easy to operate and the result is diminutively influenced by complex factors, therefore, it is the primary method to carry out this work by simulation experiment .In this paper, it is mainly investigated into the simulation analysis of the tool flank wear. The specific content of the simulation experiment is explaining the causation for the tool flank wear through the analysis of the temperature field at the tip and obtaining the data of cutting force in different tool flank wear(10,100,200,300um). The empirical cutting force model was established through multiple regression analysis and the tool flank wear prediction model was reversed and gained by analysis of the results of simulation experiments. Keywords: Tool Flank Wear; Cutting Force; Simulation
This document presents a method for estimating cutting forces in ball-end milling of sculptured surfaces. The method involves developing a new chip thickness model based on analyzing the relative tool-part motion to account for toolpath patterns, varying feedrates, and tool geometry. Using the new chip thickness model, differential cutting forces are calculated for each engaged cutting edge segment and integrated to determine the resultant cutting force. The method is validated through experiments on a sculptured surface with curved toolpaths under various cutting conditions, showing the effectiveness of the proposed force estimation approach.
Optimizing Material removal rate and surface roughness using Taguchi techniqueroymeister007
The objective of this advanced design project is to obtain an optimal setting of turning parameters (Cutting speed, Feed and Depth of Cut), which results in an optimal value of material removal rate (MRR) while machining a cylindrical bar made of mild steel. In our study, an attempt has been made to generate a model to predict material removal rate using Regression Technique. Also an attempt has been made to optimize the process parameters using Taguchi Technique. A three level orthogonal array L9 was selected to satisfy the minimum number of experiment conditions for the factors and levels presented in this project.
Tool Wear measurement of great apprehension in
machining industries and it effects the surface quality, dimensional
accuracy and production cost of the materials components. In the
present study twenty seven experiments were conducted as per 3
parameter 3 level full factorial design for turning operation of a
mild steel specimen with high speed steel (HSS) cutting tool. An
experimental investigation on cutting tool wear and a mathematical
model for tool wear estimation is reported in this paper and SN
Ratio calculation was made and an optimized combination was
determined.
IRJET-Experimental Study on Spring Back Phenomenon in Sheet Metal V- Die BendingIRJET Journal
This document presents an experimental study on the spring back phenomenon in sheet metal V-die bending. The study investigates how factors like angle, sheet thickness, and varying width cross-section affect the amount of spring back that occurs in CRC-D steel sheets. Experiments were conducted using a design of experiments approach based on response surface methodology. 20 bending experiments were performed according to the experimental design matrix. The results show that spring back decreases with increasing angle and first increases then decreases with increasing thickness. Spring back also increases linearly with increasing width. A regression model was developed to predict spring back based on the experimental results.
The document discusses research on integrating geometric and mechanistic models for cutting process simulation and feedrate optimization in five-axis milling of free-form surfaces. It presents a method for extracting cutter-workpiece engagement geometry from CAD/CAM toolpaths to be used as input for a discrete mechanistic force prediction model. Experimental validation showed good agreement between simulated and measured cutting forces. The integrated modeling approach uses geometric simulation to dynamically update the workpiece model and determine cutter contact areas, while the mechanistic model estimates forces to calculate optimal feedrates within constraints of part quality, tool life, and machine limitations.
General stiffness model for five-axis CNC machiningIJRES Journal
Five-axis CNC machining has become an important method for processing thin-walled parts. However, compared with the traditional three-axis machine system, the tool path planning becomes more difficult especially in high-speed and accuracy machining process. In this paper, taking into consideration the rigidity establishes a general stiffness model in order to increase the surface quality, restrain the chatter of the machine and provide a reference for tool path planning. The model considerate the comprehensive impact of the tool posture, tool overhang length, transmission axis of the machine and the parts, in which the finite element method and the principal of virtual-work are applied.
The simulation analysis of tool flank wear based on cutting forceeSAT Journals
Abstract In the process of cutting, cutting tool wear has an important influence on the surface quality of the work piece, therefore, it is of great significance for the research of tool wear detection. In this paper, this work focuses on researching relationship between cutting force and tool flank wear. In different experiment conditions, the consistency of the results of simulation and experiment results was obtained through the comparative analysis between the two. It is a complex problem that cutting tool wear and measuring process and not easy to get the accurate ideal results by experiment, the simulation experiment has the characteristics of simple and easy to operate and the result is diminutively influenced by complex factors, therefore, it is the primary method to carry out this work by simulation experiment .In this paper, it is mainly investigated into the simulation analysis of the tool flank wear. The specific content of the simulation experiment is explaining the causation for the tool flank wear through the analysis of the temperature field at the tip and obtaining the data of cutting force in different tool flank wear(10,100,200,300um). The empirical cutting force model was established through multiple regression analysis and the tool flank wear prediction model was reversed and gained by analysis of the results of simulation experiments. Keywords: Tool Flank Wear; Cutting Force; Simulation
This document presents a method for estimating cutting forces in ball-end milling of sculptured surfaces. The method involves developing a new chip thickness model based on analyzing the relative tool-part motion to account for toolpath patterns, varying feedrates, and tool geometry. Using the new chip thickness model, differential cutting forces are calculated for each engaged cutting edge segment and integrated to determine the resultant cutting force. The method is validated through experiments on a sculptured surface with curved toolpaths under various cutting conditions, showing the effectiveness of the proposed force estimation approach.
Optimizing Material removal rate and surface roughness using Taguchi techniqueroymeister007
The objective of this advanced design project is to obtain an optimal setting of turning parameters (Cutting speed, Feed and Depth of Cut), which results in an optimal value of material removal rate (MRR) while machining a cylindrical bar made of mild steel. In our study, an attempt has been made to generate a model to predict material removal rate using Regression Technique. Also an attempt has been made to optimize the process parameters using Taguchi Technique. A three level orthogonal array L9 was selected to satisfy the minimum number of experiment conditions for the factors and levels presented in this project.
Tool Wear measurement of great apprehension in
machining industries and it effects the surface quality, dimensional
accuracy and production cost of the materials components. In the
present study twenty seven experiments were conducted as per 3
parameter 3 level full factorial design for turning operation of a
mild steel specimen with high speed steel (HSS) cutting tool. An
experimental investigation on cutting tool wear and a mathematical
model for tool wear estimation is reported in this paper and SN
Ratio calculation was made and an optimized combination was
determined.
IRJET-Experimental Study on Spring Back Phenomenon in Sheet Metal V- Die BendingIRJET Journal
This document presents an experimental study on the spring back phenomenon in sheet metal V-die bending. The study investigates how factors like angle, sheet thickness, and varying width cross-section affect the amount of spring back that occurs in CRC-D steel sheets. Experiments were conducted using a design of experiments approach based on response surface methodology. 20 bending experiments were performed according to the experimental design matrix. The results show that spring back decreases with increasing angle and first increases then decreases with increasing thickness. Spring back also increases linearly with increasing width. A regression model was developed to predict spring back based on the experimental results.
The document discusses research on integrating geometric and mechanistic models for cutting process simulation and feedrate optimization in five-axis milling of free-form surfaces. It presents a method for extracting cutter-workpiece engagement geometry from CAD/CAM toolpaths to be used as input for a discrete mechanistic force prediction model. Experimental validation showed good agreement between simulated and measured cutting forces. The integrated modeling approach uses geometric simulation to dynamically update the workpiece model and determine cutter contact areas, while the mechanistic model estimates forces to calculate optimal feedrates within constraints of part quality, tool life, and machine limitations.
General stiffness model for five-axis CNC machiningIJRES Journal
Five-axis CNC machining has become an important method for processing thin-walled parts. However, compared with the traditional three-axis machine system, the tool path planning becomes more difficult especially in high-speed and accuracy machining process. In this paper, taking into consideration the rigidity establishes a general stiffness model in order to increase the surface quality, restrain the chatter of the machine and provide a reference for tool path planning. The model considerate the comprehensive impact of the tool posture, tool overhang length, transmission axis of the machine and the parts, in which the finite element method and the principal of virtual-work are applied.
IRJET- Determining the Effect of Cutting Parameters in CNC TurningIRJET Journal
This document discusses a study that aims to determine the effect of cutting parameters in CNC turning. The study analyzes the effects of spindle speed, feed rate, depth of cut, and material type on surface roughness and material removal rate during CNC turning operations. Experiments were designed using Taguchi's orthogonal array and analyzed using ANOVA. The results showed that spindle speed and feed rate significantly affect surface roughness, while depth of cut significantly affects material removal rate. Optimal parameters were identified for minimum surface roughness and maximum material removal rate.
IRJET- ANN Modeling for Prediction of Cutting Force Component during Orthogon...IRJET Journal
This document describes research using an artificial neural network model to predict cutting force during orthogonal turning. The researchers developed a MATLAB interface to estimate the effects of cutting parameters like speed, feed rate, and depth of cut on cutting force. They conducted turning experiments on mild steel and measured cutting forces. This experimental data was used to train an ANN model with cutting parameters as inputs and measured cutting forces as outputs. The trained ANN model could then predict cutting forces based on given cutting parameter values, providing a way to estimate experimental results without additional physical tests. Evaluation showed the ANN model provided precise predictions of how cutting parameters influence cutting force.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
IRJET- Multi-Response Parametric Optimization During Turning of En-31 Bar usi...IRJET Journal
The document discusses using the Grey Relational Analysis (GRA) method to optimize multiple responses during turning of EN-31 steel bar. GRA was used to determine the best process parameters to simultaneously maximize material removal rate and minimize surface roughness. An experiment was conducted using a CNC lathe with varying cutting speed, feed rate, and depth of cut. Response values for material removal rate and surface roughness were measured and a GRA coefficient was calculated for each experimental condition. The condition with the highest GRA coefficient ranking would provide the optimal settings to meet the goals of high productivity and quality.
Parametric Analysis and Optimization of Turning Operation by Using Taguchi Ap...IJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
International Journal of Modern Engineering Research (IJMER) covers all the fields of engineering and science: Electrical Engineering, Mechanical Engineering, Civil Engineering, Chemical Engineering, Computer Engineering, Agricultural Engineering, Aerospace Engineering, Thermodynamics, Structural Engineering, Control Engineering, Robotics, Mechatronics, Fluid Mechanics, Nanotechnology, Simulators, Web-based Learning, Remote Laboratories, Engineering Design Methods, Education Research, Students' Satisfaction and Motivation, Global Projects, and Assessment…. And many more.
Experimental study of Effect of Cutting Parameters on Cutting Force in Turnin...AM Publications
This document summarizes an experimental study on the effect of cutting parameters on cutting force during the turning process. Experiments were conducted on a lathe to study the influence of cutting speed, feed rate, and depth of cut on cutting force and surface roughness. Analysis of variance (ANOVA) found that depth of cut and the interaction between feed and depth of cut significantly affected cutting force. Feed rate, and the interaction between speed and feed most influenced surface roughness. Regression models were developed for cutting force and surface roughness based on the experimental results.
Medición de los parámetros "twist" de rugosidad, nuevos requerimientos de medición en la industria automotriz. Jenoptik a incorporado la metodología y evaluación de este parámetro en nuestros software.
This summary provides the key points about a study on simulating machining deformation and experiments for thin-walled titanium alloy parts:
1) A finite element simulation was conducted to analyze deformation regularity and cutting force variations for milling thin-walled titanium alloy parts with a ball-end milling cutter.
2) Experiments were also performed to machine thin-walled parts and measure cutting forces, which validated the accuracy of the cutting force model developed based on the simulations.
3) Both the simulation and experimental results showed good agreement and provided an effective basis for further control of machining deformation in thin-wall titanium alloy parts.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Optimization of input parameters of cnc turning operation for the given compIAEME Publication
This document summarizes a study that used Taguchi methods to optimize cutting parameters (spindle speed, feed rate, depth of cut) for CNC turning of an aluminum alloy component. The goals were to minimize surface roughness and dimensional variation. An L9 orthogonal array experiment was conducted, varying the three parameters at three levels each. Surface roughness and dimensional tolerance measurements were used as quality metrics. Analysis found that spindle speed most impacts dimensional variation while feed rate most influences surface roughness. The optimal combination of cutting parameters was identified to improve both surface roughness and dimensional tolerance.
This document summarizes a study that used Taguchi experimental design to optimize process parameters for friction stir welding of aluminum alloy 6063. Experiments varied tool rotational speed, welding speed, and axial force. Tensile testing found the highest strength (92 MPa) at a rotational speed of 1400 rpm, welding speed of 1.2 mm/sec, and axial force of 7 KN. Welding speed had the greatest influence on strength. Analysis of variance identified statistically significant parameters affecting strength. The optimal parameters achieved a joint efficiency of 70%.
EXPERIMENTAL STUDY OF TURNING OPERATION AND OPTIMIZATION OF MRR AND SURFACE R...AM Publications
In this research work turning operation is performed on AISI 1020 mild steel. Here we conducted experiments by taking Cutting Speed, Feed Rate & Depth of cut as process parameters and got the optimized value of MRR & SR. An L9 orthogonal array, the signal-to-noise (S/N) ratio are employed to the study the performance characteristics in the turning using WNMG332RP carbide insert with a nose radius of 0.8mm. Taguchi method is used to optimize surface roughness and material removal rate (MRR) during machining operation on CNC turning. The experimental result shows that on increasing depth of cut and feed the combined S/N ratio increases while on increasing cutting speed the combined S/N ratio decreases. It results that cutting speed is most significantly influences the Surface roughness followed by feed and in case of MRR, depth of cut is the most significant parameter followed by cutting speed .While the combination of both is most significantly affected by the depth of cut followed by the feed.
This document analyzes turning parameters to minimize surface roughness when turning AISI 1040 steel using the Taguchi method. 27 experiments were conducted varying cutting speed, feed rate, and depth of cut. The results found that depth of cut had the most significant impact on lowering surface roughness, followed by feed rate. Cutting speed had the least effect. The Taguchi method showed that interactions between feed rate and depth of cut also influenced surface roughness. The analysis identified the optimal cutting conditions to achieve the lowest surface roughness.
Application of taguchi method and anova in optimization of cuttingIAEME Publication
The document describes a study that used Taguchi methods and analysis of variance (ANOVA) to optimize cutting parameters for material removal rate (MRR) and surface roughness during turning of mild steel. Experiments were conducted varying spindle speed, depth of cut, and feed rate as cutting parameters. ANOVA results showed that spindle speed had the greatest influence on MRR, while feed rate most significantly impacted surface roughness. Taguchi analysis indicated spindle speed provided the largest variation in MRR and feed rate produced the greatest variation in surface roughness. The optimal cutting parameters for maximum MRR and minimum surface roughness were determined.
The document discusses surface error compensation in high-speed machining of thin-walled structures. It begins with an introduction to the importance of machining thin-walled parts in the aerospace industry and the problem of surface errors caused by workpiece deflection during cutting. It then describes the development of a predictive cutting force model and validation through experiments. Next, it covers using the force model input for deformation analysis in ANSYS software. Finally, it discusses how an error compensation strategy will be developed using NC simulation software to improve machining accuracy for thin-walled components.
IRJET- Optimization of Machining Parameters for Turning on CNC Machine of Sta...IRJET Journal
This document discusses an experimental investigation into optimizing machining parameters for turning stainless steel 316 on a CNC machine. Taguchi methods were used to determine the optimal levels for cutting speed, feed rate, and depth of cut. Eighteen experiments were conducted using an L18 orthogonal array with different combinations of the parameters. The results found that depth of cut and feed rate significantly affected material removal rate and surface roughness, while cutting speed did not have a significant impact. Analysis of variance (ANOVA) identified depth of cut as the most influential factor. Optimization found the maximum material removal rate occurred at high cutting speeds, low feed rates, and high depth of cuts.
Artificial Neural Network Modeling and Analysis of EN24 &EN36 Using CNC Milli...ijiert bestjournal
Metal cutting is one of the most significant manufa cturing processes in the area of material removal. It is Block it is defined metal cutting as the removal of metal chips from a work piece in order to obtain a finished product with de sired attributes of size,shape,and surface roughness.The imperative objective of the science o f metal cutting is the solution of practical problems associated with the efficient and precise removal of metal from work piece. It has been recognized that the reliable quantitative pred ictions of the various technological performance measures,preferably in the form of equ ations,are essential to develop optimization strategies for selecting cutting condi tions in process planning. In this thesis experiments has to be conducted to improve the surf ace finish quality of a work piece by using carbide tips. The type is bull nose tip. A se ries of experiments have to be done by varying the milling parameters spindle speed,feed rate and depth of cut and modeling is done by ANN. and Analysis is done by ANSYS.
Experimental Investigation and Parametric Analysis of Surface Roughness in C...IJMER
The manufacturing industries are very much concerned about the quality of their products.
They are focused on producing high quality products in time at minimum cost. Surface finish is one of the
crucial performance parameters that have to be controlled within suitable limits for a particular process.
Surface roughness of machined components has received serious attention of Researchers for many years.
It has been an important design feature and quality measure in machining process. There are a large
number of parameters which affect the surface roughness. These include cutting tool variables, work
piece material variables, cutting conditions etc. Therefore, prediction or monitoring of the surface
roughness of machined components has been challenging and unexplored area of research
The present work is therefore in a direction to integrate effect of various parameters which effect the
surface roughness. Experiments were carried out with the help of factorial method of design of
experiment (DOE) approach to study the impact of turning parameters on the roughness of turned
surfaces. A mathematical model was formulated to predict the effect of machining parameters on surface
roughness of a machined work piece. Model was validated with the experimental data and the reported
data of other researchers. Further parametric investigations were carried out to predict the effect of
various parameters on the surface research
it & Economic Performance a Critical Review of the Empirical DataWaqas Tariq
The present study undertakes a critical review of the research around the multi-significant issue of the correlation between the IT investments and the economic performance to both micro and macroeconomic level. The aim of this study is to shed light on the interaction of IT with the economy, at corporate, industry and national level and document it¢ s contribution to productivity and therefore to economic growth. My conclusion is that there is a positive effect of IT investments to both the above economic indicators in all aspects, but is something that needs further research so as to find a more clear and risk adjusted relation.
Planning in Markov Stochastic Task DomainsWaqas Tariq
In decision theoretic planning, a challenge for Markov decision processes (MDPs) and partially observable Markov decision processes (POMDPs) is, many problem domains contain big state spaces and complex tasks, which will result in poor solution performance. We develop a task analysis and modeling (TAM) approach, in which the (PO)MDP model is separated into a task view and an action view. In the task view, TAM models the problem domain using a task equivalence model, with task-dependent abstract states and observations. We provide a learning algorithm to obtain the parameter values of task equivalence models. We present three typical examples to explain the TAM approach. Experimental results indicate our approach can greatly improve the computational capacity of task planning in Markov stochastic domains.
IRJET- Determining the Effect of Cutting Parameters in CNC TurningIRJET Journal
This document discusses a study that aims to determine the effect of cutting parameters in CNC turning. The study analyzes the effects of spindle speed, feed rate, depth of cut, and material type on surface roughness and material removal rate during CNC turning operations. Experiments were designed using Taguchi's orthogonal array and analyzed using ANOVA. The results showed that spindle speed and feed rate significantly affect surface roughness, while depth of cut significantly affects material removal rate. Optimal parameters were identified for minimum surface roughness and maximum material removal rate.
IRJET- ANN Modeling for Prediction of Cutting Force Component during Orthogon...IRJET Journal
This document describes research using an artificial neural network model to predict cutting force during orthogonal turning. The researchers developed a MATLAB interface to estimate the effects of cutting parameters like speed, feed rate, and depth of cut on cutting force. They conducted turning experiments on mild steel and measured cutting forces. This experimental data was used to train an ANN model with cutting parameters as inputs and measured cutting forces as outputs. The trained ANN model could then predict cutting forces based on given cutting parameter values, providing a way to estimate experimental results without additional physical tests. Evaluation showed the ANN model provided precise predictions of how cutting parameters influence cutting force.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
IRJET- Multi-Response Parametric Optimization During Turning of En-31 Bar usi...IRJET Journal
The document discusses using the Grey Relational Analysis (GRA) method to optimize multiple responses during turning of EN-31 steel bar. GRA was used to determine the best process parameters to simultaneously maximize material removal rate and minimize surface roughness. An experiment was conducted using a CNC lathe with varying cutting speed, feed rate, and depth of cut. Response values for material removal rate and surface roughness were measured and a GRA coefficient was calculated for each experimental condition. The condition with the highest GRA coefficient ranking would provide the optimal settings to meet the goals of high productivity and quality.
Parametric Analysis and Optimization of Turning Operation by Using Taguchi Ap...IJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
International Journal of Modern Engineering Research (IJMER) covers all the fields of engineering and science: Electrical Engineering, Mechanical Engineering, Civil Engineering, Chemical Engineering, Computer Engineering, Agricultural Engineering, Aerospace Engineering, Thermodynamics, Structural Engineering, Control Engineering, Robotics, Mechatronics, Fluid Mechanics, Nanotechnology, Simulators, Web-based Learning, Remote Laboratories, Engineering Design Methods, Education Research, Students' Satisfaction and Motivation, Global Projects, and Assessment…. And many more.
Experimental study of Effect of Cutting Parameters on Cutting Force in Turnin...AM Publications
This document summarizes an experimental study on the effect of cutting parameters on cutting force during the turning process. Experiments were conducted on a lathe to study the influence of cutting speed, feed rate, and depth of cut on cutting force and surface roughness. Analysis of variance (ANOVA) found that depth of cut and the interaction between feed and depth of cut significantly affected cutting force. Feed rate, and the interaction between speed and feed most influenced surface roughness. Regression models were developed for cutting force and surface roughness based on the experimental results.
Medición de los parámetros "twist" de rugosidad, nuevos requerimientos de medición en la industria automotriz. Jenoptik a incorporado la metodología y evaluación de este parámetro en nuestros software.
This summary provides the key points about a study on simulating machining deformation and experiments for thin-walled titanium alloy parts:
1) A finite element simulation was conducted to analyze deformation regularity and cutting force variations for milling thin-walled titanium alloy parts with a ball-end milling cutter.
2) Experiments were also performed to machine thin-walled parts and measure cutting forces, which validated the accuracy of the cutting force model developed based on the simulations.
3) Both the simulation and experimental results showed good agreement and provided an effective basis for further control of machining deformation in thin-wall titanium alloy parts.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Optimization of input parameters of cnc turning operation for the given compIAEME Publication
This document summarizes a study that used Taguchi methods to optimize cutting parameters (spindle speed, feed rate, depth of cut) for CNC turning of an aluminum alloy component. The goals were to minimize surface roughness and dimensional variation. An L9 orthogonal array experiment was conducted, varying the three parameters at three levels each. Surface roughness and dimensional tolerance measurements were used as quality metrics. Analysis found that spindle speed most impacts dimensional variation while feed rate most influences surface roughness. The optimal combination of cutting parameters was identified to improve both surface roughness and dimensional tolerance.
This document summarizes a study that used Taguchi experimental design to optimize process parameters for friction stir welding of aluminum alloy 6063. Experiments varied tool rotational speed, welding speed, and axial force. Tensile testing found the highest strength (92 MPa) at a rotational speed of 1400 rpm, welding speed of 1.2 mm/sec, and axial force of 7 KN. Welding speed had the greatest influence on strength. Analysis of variance identified statistically significant parameters affecting strength. The optimal parameters achieved a joint efficiency of 70%.
EXPERIMENTAL STUDY OF TURNING OPERATION AND OPTIMIZATION OF MRR AND SURFACE R...AM Publications
In this research work turning operation is performed on AISI 1020 mild steel. Here we conducted experiments by taking Cutting Speed, Feed Rate & Depth of cut as process parameters and got the optimized value of MRR & SR. An L9 orthogonal array, the signal-to-noise (S/N) ratio are employed to the study the performance characteristics in the turning using WNMG332RP carbide insert with a nose radius of 0.8mm. Taguchi method is used to optimize surface roughness and material removal rate (MRR) during machining operation on CNC turning. The experimental result shows that on increasing depth of cut and feed the combined S/N ratio increases while on increasing cutting speed the combined S/N ratio decreases. It results that cutting speed is most significantly influences the Surface roughness followed by feed and in case of MRR, depth of cut is the most significant parameter followed by cutting speed .While the combination of both is most significantly affected by the depth of cut followed by the feed.
This document analyzes turning parameters to minimize surface roughness when turning AISI 1040 steel using the Taguchi method. 27 experiments were conducted varying cutting speed, feed rate, and depth of cut. The results found that depth of cut had the most significant impact on lowering surface roughness, followed by feed rate. Cutting speed had the least effect. The Taguchi method showed that interactions between feed rate and depth of cut also influenced surface roughness. The analysis identified the optimal cutting conditions to achieve the lowest surface roughness.
Application of taguchi method and anova in optimization of cuttingIAEME Publication
The document describes a study that used Taguchi methods and analysis of variance (ANOVA) to optimize cutting parameters for material removal rate (MRR) and surface roughness during turning of mild steel. Experiments were conducted varying spindle speed, depth of cut, and feed rate as cutting parameters. ANOVA results showed that spindle speed had the greatest influence on MRR, while feed rate most significantly impacted surface roughness. Taguchi analysis indicated spindle speed provided the largest variation in MRR and feed rate produced the greatest variation in surface roughness. The optimal cutting parameters for maximum MRR and minimum surface roughness were determined.
The document discusses surface error compensation in high-speed machining of thin-walled structures. It begins with an introduction to the importance of machining thin-walled parts in the aerospace industry and the problem of surface errors caused by workpiece deflection during cutting. It then describes the development of a predictive cutting force model and validation through experiments. Next, it covers using the force model input for deformation analysis in ANSYS software. Finally, it discusses how an error compensation strategy will be developed using NC simulation software to improve machining accuracy for thin-walled components.
IRJET- Optimization of Machining Parameters for Turning on CNC Machine of Sta...IRJET Journal
This document discusses an experimental investigation into optimizing machining parameters for turning stainless steel 316 on a CNC machine. Taguchi methods were used to determine the optimal levels for cutting speed, feed rate, and depth of cut. Eighteen experiments were conducted using an L18 orthogonal array with different combinations of the parameters. The results found that depth of cut and feed rate significantly affected material removal rate and surface roughness, while cutting speed did not have a significant impact. Analysis of variance (ANOVA) identified depth of cut as the most influential factor. Optimization found the maximum material removal rate occurred at high cutting speeds, low feed rates, and high depth of cuts.
Artificial Neural Network Modeling and Analysis of EN24 &EN36 Using CNC Milli...ijiert bestjournal
Metal cutting is one of the most significant manufa cturing processes in the area of material removal. It is Block it is defined metal cutting as the removal of metal chips from a work piece in order to obtain a finished product with de sired attributes of size,shape,and surface roughness.The imperative objective of the science o f metal cutting is the solution of practical problems associated with the efficient and precise removal of metal from work piece. It has been recognized that the reliable quantitative pred ictions of the various technological performance measures,preferably in the form of equ ations,are essential to develop optimization strategies for selecting cutting condi tions in process planning. In this thesis experiments has to be conducted to improve the surf ace finish quality of a work piece by using carbide tips. The type is bull nose tip. A se ries of experiments have to be done by varying the milling parameters spindle speed,feed rate and depth of cut and modeling is done by ANN. and Analysis is done by ANSYS.
Experimental Investigation and Parametric Analysis of Surface Roughness in C...IJMER
The manufacturing industries are very much concerned about the quality of their products.
They are focused on producing high quality products in time at minimum cost. Surface finish is one of the
crucial performance parameters that have to be controlled within suitable limits for a particular process.
Surface roughness of machined components has received serious attention of Researchers for many years.
It has been an important design feature and quality measure in machining process. There are a large
number of parameters which affect the surface roughness. These include cutting tool variables, work
piece material variables, cutting conditions etc. Therefore, prediction or monitoring of the surface
roughness of machined components has been challenging and unexplored area of research
The present work is therefore in a direction to integrate effect of various parameters which effect the
surface roughness. Experiments were carried out with the help of factorial method of design of
experiment (DOE) approach to study the impact of turning parameters on the roughness of turned
surfaces. A mathematical model was formulated to predict the effect of machining parameters on surface
roughness of a machined work piece. Model was validated with the experimental data and the reported
data of other researchers. Further parametric investigations were carried out to predict the effect of
various parameters on the surface research
it & Economic Performance a Critical Review of the Empirical DataWaqas Tariq
The present study undertakes a critical review of the research around the multi-significant issue of the correlation between the IT investments and the economic performance to both micro and macroeconomic level. The aim of this study is to shed light on the interaction of IT with the economy, at corporate, industry and national level and document it¢ s contribution to productivity and therefore to economic growth. My conclusion is that there is a positive effect of IT investments to both the above economic indicators in all aspects, but is something that needs further research so as to find a more clear and risk adjusted relation.
Planning in Markov Stochastic Task DomainsWaqas Tariq
In decision theoretic planning, a challenge for Markov decision processes (MDPs) and partially observable Markov decision processes (POMDPs) is, many problem domains contain big state spaces and complex tasks, which will result in poor solution performance. We develop a task analysis and modeling (TAM) approach, in which the (PO)MDP model is separated into a task view and an action view. In the task view, TAM models the problem domain using a task equivalence model, with task-dependent abstract states and observations. We provide a learning algorithm to obtain the parameter values of task equivalence models. We present three typical examples to explain the TAM approach. Experimental results indicate our approach can greatly improve the computational capacity of task planning in Markov stochastic domains.
Reading digital comic on mobile phone is demanding now. Rather that create a new mobile comic content, adaptation of existing digital comic web portal is valuable. In this paper, we proposed an automatic e-comic mobile content adaptation method for automatically create mobile comic content from existing digital comic website portal. Automatic e-comic content adaptation is based on our comic frame extraction method combine with additional process to extract comic balloon and text from digital comic page. The proposed method work as a content adaptation intermediary proxy server application, while generating a Comic XML file as an input source for mobile phone to render a specific mobile comic contents. Our proposed method is an effective and efficient method for real time implementation of reading e-comic comparing to other methods. Experimental results show that our proposed method has 100% accuracy of flat comic frame extraction, 91.48% accuracy of non-flat comic frame extraction, and about 90% processing time faster than previous method.
Audio Art Authentication and Classification with Wavelet StatisticsWaqas Tariq
An experimental computation technique for audio art authentication is presented. Specifically, the computational techniques used by painting/drawings art authentication are transformed from twodimensional (image) into one-dimensional (audio) methods. The statistical model consists of first and higher-order wavelet statistics. Classification is performed with a multi-dimensional scaled 3D visual model. The results from the analyses of music/silence discrimination, audio art authentication, genre classification, and audio fingerprinting are demonstrated.
Data mining visualization to support biochemical markers for liver fibrosis i...Waqas Tariq
The reference diagnostic test to detect fibrosis is liver biopsy (LB), a procedure subject to various limitations, including risk of patient injury and sampling error. FibroTest (FT) and ActiTest (AT) are biochemical markers (noninvasive tests) used in determining the level of fibrosis and the degree of necroinflammatory activity in the liver. The objective of this work is to discover the differences in the temporal patterns between noninvasive tests and liver biopsy by visualization tools, which made it easier to understand the relations of the complicated rules. This Study ware focused on the major serum fibrosis markers (FT/AT). The test uses a combination of serum biochemical markers with visualization technique to evaluate whether biochemical markers can be used to estimate the stage of liver fibrosis and necro-inflammatory activity in the liver.
A Method to Provide Accessibility for Visual Components to Vision ImpairedWaqas Tariq
Non-textual graphical information (line graphs, bar charts, pie charts, etc.) are increasingly pervasive in digital scientific literatures and business reports which enabling readers to easily acquire the nature of the underlying information [1]. These graphical components are commonly used to present data in an easy-to interpret way. Graphs are frequently used in economics, mathematics and other scientific subjects. In general term data visualization techniques are useless for blind people. Being unable to access graphical information easily is a major obstacle to blind people in pursuing a scientific study and careers [2].This paper suggests a method to extract implicit information of Bar chart, Pie chart, Line chart and math’s graph components of an electronic document and present them to vision impaired users in audio format. The goal is to provide simple to use, efficient, and available presentation schemes for non textual which can help vision impaired users in comprehending form without needing any further devices or equipments. A software application has been developed based on this research. The output of application is a textual summary of the graphic including the core content of the hypothesized intended message of the graphic designer. The textual summary of the graphic is then conveyed to the user by Text to Speech software .The benefit of this approach is automatic providing the user with the message and knowledge that one would gain from viewing the chart.
A Simple Integrative Solution For Simultaneous Localization And MappingWaqas Tariq
Simultaneous Localization and Mapping is a method used to find the location of a mobile robot while at the same time build a constructive map of its surrounding environment. This paper gives a brief description about a simple integrative SLAM technique using a Laser Range Finder (LRF) and Odometry data, primarily for indoor environments. In this project, a solution for the SLAM problem was implemented on a differential drive mobile robot equipped with a SICK laser scanner.
One of the fundamental issues in computer science is ordering a list of items. Although there is a number of sorting algorithms, sorting problem has attracted a great deal of research, because efficient sorting is important to optimize the use of other algorithms. This paper presents a new sorting algorithm (Index Sort) which runs based on the previously sorted elements.. This algorithm was analyzed, implemented and tested and the results are promising for a random data.
From TION-EMO Theory To A New Beginning Of Artificial EmotionsWaqas Tariq
This document summarizes Rafael Navia's Tion-Emo Theory (TET), which proposes a new system for building artificial emotions. The TET involves three "objects" that represent different regions - the intellectual object in the intellectual region, the social object in the semi-intellectual region, and the self-object in the non-intellectual region. Connecting these objects allows for the formation of a self-sustaining emotional system, with the self-object regulating emotional energy and censorship systems. The TET draws from studies of animal behavior, evolutionary robotics, and neuroscience to provide a framework grounded in biological principles for developing artificial emotions.
Mathematical Derivation of Annuity Interest Rate and its ApplicationWaqas Tariq
A fundamental task in business for investor or borrower is to know the interest rate of an annuity. In this type of problem, the size of each periodic payment(R), the term(n), and the amount(Sn) or the present value of the annuity(An) are usually given. However, a direct equation representing the Annuity Interest Rate(i) is not available, since an approximate value of the Annuity Interest Rate is obtained by interpolation method based on table showing (Sn/R) values. This paper emphasizes the real time computational problem for Annuity interest rate. It has therefore been important to derive an equation for computing the Annuity Interest rate. The evaluation of error analysis has been discussed. The new algorithm saved computational energy by approximately 99.9% than that of the tabulated one.
Decision Tree Classifiers to determine the patient’s Post-operative Recovery ...Waqas Tariq
Machine Learning aims to generate classifying expressions simple enough to be understood easily by the human. There are many machine learning approaches available for classification. Among which decision tree learning is one of the most popular classification algorithms. In this paper we propose a systematic approach based on decision tree which is used to automatically determine the patient’s post–operative recovery status. Decision Tree structures are constructed, using data mining methods and then are used to classify discharge decisions.
Design and Implementation of Sliding Mode Algorithm: Applied to Robot Manipul...Waqas Tariq
Refer to the research, review of sliding mode controller is introduced and application to robot manipulator has proposed in order to design high performance nonlinear controller in the presence of uncertainties. Regarding to the positive points in sliding mode controller, fuzzy logic controller and adaptive method, the output in most of research have improved. Each method by adding to the previous algorithm has covered negative points. Obviously robot manipulator is nonlinear, and a number of parameters are uncertain, this research focuses on comparison between sliding mode algorithm which analyzed by many researcher. Sliding mode controller (SMC) is one of the nonlinear robust controllers which it can be used in uncertainty nonlinear dynamic systems. This nonlinear controller has two challenges namely nonlinear dynamic equivalent part and chattering phenomenon. A review of sliding mode controller for robot manipulator will be investigated in this research.
Computer Assisted System for Enhancing the Application of Ergonomics in Manuf...Waqas Tariq
The current paper focuses on the need and a plan for the development of a Computer Assisted Interactive and Intelligent Ergonomics System which, through a user friendly consulting mode presents the guidelines and formalized procedures for the application of ergonomics knowledge and data in manufacturing organizations. The system is expected to allow a production engineer or supervisor or even a worker with minimal ergonomics knowledge, to understand, analyze and find solutions to problems related to industrial ergonomics. A survey which is conducted in this regard is also described in this paper and through the out come of the survey it is shown that the poor acceptance and application of ergonomics is due to lack of exposure to ergonomics knowledge and non-availability of ergonomics knowledge in a suitable form for its application in manufacturing systems. 10
Design of A Spell Corrector For Hausa LanguageWaqas Tariq
In this article, a spell corrector has been designed for the Hausa language which is the second most spoken language in Africa and do not yet have processing tools. This study is a contribution to the automatic processing of the Hausa language. We used existing techniques for other languages and adapted them to the special case of the Hausa language. The corrector designed operates essentially on Mijinguini’s dictionary and characteristics of the Hausa alphabet. After a brief review on spell checking and spell correcting techniques and the state of art in the Hausa language processing, we opted for the data structures trie and hash table to represent the dictionary. The edit distance and the specificities of the Hausa alphabet have been used to detect and correct spelling errors. The implementation of the spell corrector has been made on a special editor developed for that purpose (LyTexEditor) but also as an extension (add-on) for OpenOffice.org. A comparison was made on the performance of the two data structures used.
Multi User Detection in CDMA System Using Linear and Non Linear DetectorWaqas Tariq
DS-Code division multiple access is considered as the third generation of cellular mobile used in interim standard 95(IS-95) [1]and it is currently being standardized for universal mobile telecommunication systems (UMTS). CDMA offers attractive features, such as frequency reuse, soft handoff, increased capacity, and multipath combating. In a CDMA system, several users simultaneously transmit information over a common channel using pre-assigned codes. The conventional single user detector consists of a bank of filters matched to the spreading codes. This detector suffers from two problems. First, multiple access interference (MAI) produced by the other co-channel users is a significant limitation to the capacity of this detector. The second problem is the near-far effect which occurs when the relative received power of interfering signals becomes larger. A potential solution is multi-user detection which exploits the information of signals of interfering users. In the present study performance of various linear detectors like matched filter detector, MMSE detector, and adaptive LMS detector are studied. These are the linear detectors that operate linearly on the received signal statistics and are suboptimal detectors. The matched filter bank is the conventional detector and offers the simplest way of demodulating CDMA signals .The detector resulting from the MMSE (minimum mean square error) criterion shows better performance over the conventional one for low SNR value. Adaptive LMS is employed to enhance the BER performance in MUD application.Several factors motivated the research to apply neural network as multi-user detector. NN are nonlinear classifier in addition to being adaptive and computationally efficient. The performance of two layer perceptron neural network using BP learning rule is used for multi-user detection of CDMA signals in AWGN channels. The neural network detectors show improvement of BER in the comparative analysis done in the present work. and offers further research scope for solving multi-user detection problems in CDMA application.
A Business Review of E-Retailing in IndiaWaqas Tariq
Abstract As a professor in computer science I am very much interested in training my students in e-Commerce and prepared myself for an in depth research in this area and to present a quick journal about e-Retailing concepts / framework, how an organization can start e-Retailing business quickly? Its Pro’s & Con’s, how to make the e-Retailing venture successful? How retailers should plan / experience to achieve varying success by leveraging the internet technology? How to incorporate traditional retails practices with Internet technology? And strive for success in India. How internet is used by users and its use for online shopping. It serves a s a best article for all the readers across the globe. Keywords: E-Retailing in India, e-tailing, E commerce, Online store, retail, e business
An Efficient Hybrid Successive Markov Model for Predicting Web User Usage Beh...Waqas Tariq
With the continued growth and proliferation of Web services and Web based information systems, the volumes of user data have reached astronomical proportions. Analyzing such data using Web Usage Mining can help to determine the visiting interests or needs of the web user. As web log is incremental in nature, it becomes a crucial issue to predict exactly the ways how users browse websites. It is necessary for web miners to use predictive mining techniques to filter the unwanted categories for reducing the operational scope. The first-order Markov model has low accuracy in achieving right predictions, which is why extensions to higher order models are necessary. All higher order Markov model holds the promise of achieving higher prediction accuracies, improved coverage than any single-order Markov model but holds high state space complexity. Hence a Hybrid Markov Model is required to improve the operation performance and prediction accuracy significantly. The present paper introduces An Efficient Hybrid Successive Markov Prediction Model, HSMP. The HSMP model is initially predicts the possible wanted categories using Relevance factor, which can be used to infer the users’ browsing behavior between web categories. Then predict the pages in predicted categories using techniques for intelligently combining different order Markov models so that the resulting model has low state complexity, improved prediction accuracy and retains the coverage of the all higher order Markov model. These techniques eliminates low support states, evaluates the probability distribution and estimates the error associated with each state without affecting the overall accuracy as well as protection of the resulting model. To validate the proposed prediction model, several experiments were conducted and results proven this are claimed in this paper.
A Robotic Prototype System for Child MonitoringWaqas Tariq
This document describes a robotic prototype system for child monitoring. The system consists of a Khepera robot, host computer, and circuits to trigger lights and alarms. The robot uses image processing to find and follow a baby prop (Lego blocks) in a testing area with obstacles. It can detect when the baby enters danger zones and activate the circuits. Experimental testing showed the robot could successfully find and track the baby prop while avoiding obstacles in scenarios of increasing complexity. The system provides a starting point for developing mobile robotic child monitoring in the home.
Prediction of surface roughness in high speed machining a comparisoneSAT Publishing House
This document compares three techniques for predicting surface roughness (Ra) in high speed machining operations: Response Surface Methodology (RSM), Artificial Neural Network (ANN), and Adaptive Neuro-Fuzzy Inference System (ANFIS). Experiments were conducted using different cutting speeds and feeds to measure surface roughness and tool vibrations. RSM, ANN, and ANFIS models were developed using the experimental data to predict surface roughness based on the input parameters of cutting speed, feed rate, and vibration. The predicted values from each technique were compared to the actual experimental values and to each other to determine which technique most accurately modeled and predicted surface roughness.
IRJET- Static Analysis of Cutting Tool using Finite Element ApproachIRJET Journal
This document summarizes a study that used finite element analysis to examine the static stress on a single point cutting tool under different tool geometry parameters. A CAD model of the cutting tool and workpiece was created in ANSYS. The tool's total deformation and von Mises stress were calculated for variations in relief angle, back rake angle, and chip formation. The results showed that increasing the relief angle and back rake angle decreased tool stress levels significantly. A positive back rake angle helped move chips away from the workpiece and led to easier material shearing over compression. Continuous chip formation with a positive rake angle also helped maintain tool safety during hard material cutting. In conclusion, a positive rake angle is preferred for machining
IRJET- Accuracy Enhancement of CNC Turning by Linear Positioning Error Co...IRJET Journal
This document presents a study that aims to improve the accuracy of CNC turning machines through a simple and low-cost method for identifying and compensating for linear positioning errors. The method involves machining test parts on the CNC lathe and then precisely measuring the parts using a coordinate measuring machine to determine positioning errors in the lathe's X and Z axes. Mathematical models of the errors are developed and used to edit the lathe's part program code to reconstruct the tool paths and compensate for the identified errors, improving machining accuracy.
In this study, a control strategy is presented to control the position and the feed rate of a table of a milling
machine powered by three-phase induction motor, when machining pieces constituted by different types of
materials: steel, brass and nylon. For development of the control strategy, the vector control technique was
applied to drive the three-phase induction machines. The estimation of the electromagnetic torque of the
motor was used to determine the machining feed rate for each type of material. The speed control was
developed using fuzzy logic Takagi-Sugeno (TS) model and the estimation of the electromagnetic torque
using the artificial neural network (ANN) of the least mean square (LMS) algorithm type. The induction
motor was fed by a three-phase voltage inverter hardware driven by a digital signal processor (DSP).
Experimental results are presented.
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
Theoretical work submitted to the Journal should be original in its motivation or modeling structure. Empirical analysis should be based on a theoretical framework and should be capable of replication. It is expected that all materials required for replication (including computer programs and data sets) should be available upon request to the authors.
tcStatistical and regression analysis of vibration of carbon steel cutting to...ijmech
Machining is a convoluted process in which many variables can deleterious the desired results. Among them, cutting tool vibration is the most decisive phenomenon which influences dimensional precision of the components machined, functional behavior of the machine tools and life of the cutting tool. In a machining operation, cutting speed, depth of cut and the tool feed rate principally influence cutting tool vibrations. In this paper, effects of cutting speed, feed rate and depth of cut on cutting tool vibration in both the directions, i.e. axial and tangential are investigated by the statistical methods of signal to noise ratio
(SNR), analysis of variance (ANOVA) and regression analysis. Experiments have been conducted using the L9 orthogonal array in the centre lathe machine. Carbon steel was selected as cutting tool materials to conduct the experiments. From experimental results, the amplitude of vibration of the cutting tool was ascertaining for each machining performance criteria. The significance and percentage contribution of each parameter were determined by Analysis of variance (ANOVA).It has been observed that cutting speed has a maximum contribution on cutting tool vibration in both the directions. Variation of the vibration of cutting tool with machining parameters was mathematically modeled by using the regression analysis
method. The predicted value from the developed model and experimental values are found to be very close
to each other justifying the significance of the model. Confirmation runs demonstrates that the optimized result and the values obtained through regression analysis are within the prescribed limit
Research Inventy : International Journal of Engineering and Science is publis...researchinventy
This document presents a new analytical method for identifying stability lobes in high-speed machining of thin ribs. It describes developing a stability lobe diagram that shows the relationship between axial depth of cut and spindle speed, with lobe number as a parameter. The method involves using experimental modal analysis to determine dynamic characteristics of the machine-tool system and then using mathematical equations to simulate the real and imaginary parts of the frequency response function. This allows predicting stable and unstable machining regions. The document outlines the specific steps of the proposed method and shows examples of simulating the frequency response function and stability lobes using Mathcad software. It concludes that the method can predict stability lobes considering workpiece flexibility and that future work will incorporate experimental validation.
IRJET-Optimization of Geometrical Parameters of Single Point Cutting Tool to ...IRJET Journal
The document discusses optimizing the geometrical parameters of a single point cutting tool to reduce stress and vibration during turning operations. Modal and harmonic analyses were performed to determine the tool's natural frequency range of 11384Hz to 45322Hz. Optimization found the minimum stress and vibration occurred with a horizontal and vertical cross-sectional dimension of 18.2mm, a back rack angle of 10.88°, side rack angle of 10.88°, end relief angle of 9.06°, end cutting angle of 27.2°, and side cutting edge angle of 13.6°. The optimal parameters can help reduce tool wear and extend the life of single point cutting tools.
This document summarizes a research study that used the firefly algorithm to optimize machining parameters (cutting speed, feed rate, and depth of cut) in CNC turning operations. Pilot experiments were conducted on a CNC lathe to machine stainless steel using different tools and cutting parameters. Empirical relationships were developed to relate machining time to the cutting parameters based on the experimental data. The firefly algorithm was then applied to determine the optimal cutting parameters that minimize machining time for given operations and surface finish requirements. The results showed that the firefly algorithm was effective at solving this parameter optimization problem.
Static and Dynamic Characteristics Analysis of Three Coordinates manipulator ...IJRES Journal
The paper studied the static and dynamic characteristics of the three coordinates manipulator which
was used in reliability test system for low voltage electrical apparatus. The deformation cloud diagram and
stress cloud diagram were obtained by using the finite element analysis software Ansys Workbench to carry out
the static analysis, and the result showed that the mechanism satisfied the rigidity and the intensity request. The
modal analysis of the mechanism which got the natural frequencies and the corresponding mode shapes of the
first 8 order and compared the resonance frequency of the actual work environment was carried out. The random
vibration analysis of the mechanism wad carried out on the basis of modal analysis, which got the acceleration
response in the direction of x、y、z and the equivalent stress cloud diagram of the mechanism. According to the
results of analysis, the vibration control of the body should be applied to reduce the random vibration response
value.
On account of cutting gadget holder preoccupation, cutting force affects the
dimensional precision. The troublesome of equipment holder redirection is attempted
routinely in a course of action of building surface things, and to accomplish this point
uninvolved strategy can be utilized. In this unassuming work, a refreshed hypothetical
momentous cutting force appear for end getting ready is open, utilizing confined part
approach. The model be committed to variable data sources, pick the kind of the end
procedure holder, in the event that it is straight or discontinuous. The cutting
parameters are given for getting a perfect preparing instrument redirection dispersing
and rehash an area examination. The expansion results demonstrate that the
instrument evading impacts the dimensional precision of the completed part. The
essential structures of pulled back technique for distraction mask of mechanical
frameworks are quickly exhibited. It depends upon the hypothesis of dynamic
redirection. For handling forces and gadget holder redirection, two sorts of instability
show yields are shown identifying with cutting force parameters
Effects of the Cutting Conditions and Vibration on the Surface Roughness of E...IRJET Journal
The document presents the results of a study investigating the influence of cutting parameters (spindle speed, axial depth of cut, feed rate) and machining vibration on surface roughness in an end milling process of aluminum alloy. Regression analysis was used to establish mathematical models for predicting surface roughness under various cutting conditions. The results show that accounting for machining vibration in the model improves the correlation between predicted and measured surface roughness values compared to a model using only cutting parameters. This suggests vibration greatly influences cutting quality and is an important parameter for prediction models.
This document discusses a modified approach for indirectly measuring cutting forces during face milling processes. It presents a method for estimating cutting forces based on measuring the current of feed drive servomotors using Fanuc SERVOGUIDE software. Models are developed relating feed motor current to cutting forces based on cutting geometry. Experimental results found the estimated cutting forces using this indirect method agreed to within 10% of values measured directly using a dynamometer under similar cutting conditions, proving this to be a reasonably accurate and economical alternative approach.
Modeling and Simulation of Nonlinear Friction in XY AC Servo Table Thuan Truongvan
This document summarizes a study that models and simulates nonlinear friction in an XY servo table. The study proposes a new partition friction model that separately models static friction and dynamic friction. Static friction is modeled using a Kelvin chain model that represents the friction surface as a viscoelastic material. Dynamic friction is modeled using a LuGre model. Parameters for the models are estimated from experiments. Simulations show the new partition model provides better tracking accuracy compared to using just a static Stribeck model, particularly around velocity reversals, by better reflecting static friction characteristics.
Analysis of Vibration of Radial Drilling Machine Structure Using Finite Eleme...IRJET Journal
1. The study analyzes the vibration of a radial drilling machine structure using finite element analysis. The natural frequencies and mode shapes of the structure are determined.
2. A finite element model is created to represent the machine structure as frame elements. The first three natural frequencies are identified as 35.68Hz, 52.24Hz, and 318.7Hz.
3. The first three vibration mode shapes are described, showing the displacement patterns of different parts of the structure at each natural frequency.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Modeling and Optimization of Surface roughness and Machining Induced Vibratio...theijes
This paper presents the machining induced vibration and surface roughness modeled, predicted and optimized as functions of the cutting tool overhang, feed rate and cutting speed during hard and high speed turning of 41Cr4 alloy structural steel on an engine lathe machine with a carbide tool. The response surface methodology, based on central composite design of experiment was adopted, and analysis facilitated by using the Design Expert 9 software to generate and validate the models, predict the effect of the process variables on the response variables as well as obtain the optimum setting of the process variables that would minimize the response variables. Quadratic regression models were suggested as best fit for the measured machining induced vibration and surface roughness data. All the model terms of the machining induced vibration are significant with exception of the square term of the tool overhang. Whereas, all those of the surface roughness are significant with exception of the linear term of the tool overhang. The optimum setting of the cutting tool overhang at 57.8784 mm, feed rate at 0.15 mm/rev and the cutting speed at 328.507 rev/min minimized the machining induced vibration to a value of 0.18 mm/s2 , and the surface roughness to a value of 4.399 µmm with desirability of 0.822. Within the selected experimental design limits, the obtained response surface models can be used to accurately predict and optimize the machining induced vibration and surface roughness as functions of the tool overhang, feed rate and cutting speed during hard turning of 41Cr4 alloy structural steel.
Identification of dynamic rigidity for high speed spindles supported on ball ...eSAT Journals
Abstract The widespread use of high-speed machining in recent decades has led to a significant area of research on issues that limit its productivity. Regenerative chatter is a well‐known machining problem that results in unstable cutting process, leads to the poor surface quality, reduced material removal rate and damage on the machine tool itself. The main requirement for the stability of system dynamics is the information of tool tip frequency response functions (FRF’s).The present work considered a coupled model of spindle-bearing system by using the angular contact ball bearing forces on stability of machining. Using Timoshenko beam element formulation, the spindle unit is analyzed by including the gyroscopic and centrifugal terms and the bearing contact forces are arrived from Hertzian contact theory. Then, the model is used for studying the effects of viscous damping to obtain the tool point FRF for the dynamic spindle. Index Terms: Spindle dynamics, Stability, High speed effects, Bearing contact forces, Hertzian contact theory, Finite element modeling.
Similar to Active Control of Tool Position in the Presence of Nonlinear Cutting Forces in Orthogonal Cutting (20)
The Use of Java Swing’s Components to Develop a WidgetWaqas Tariq
Widget is a kind of application provides a single service such as a map, news feed, simple clock, battery-life indicators, etc. This kind of interactive software object has been developed to facilitate user interface (UI) design. A user interface (UI) function may be implemented using different widgets with the same function. In this article, we present the widget as a platform that is generally used in various applications, such as in desktop, web browser, and mobile phone. We also describe a visual menu of Java Swing’s components that will be used to establish widget. It will assume that we have successfully compiled and run a program that uses Swing components.
3D Human Hand Posture Reconstruction Using a Single 2D ImageWaqas Tariq
Passive sensing of the 3D geometric posture of the human hand has been studied extensively over the past decade. However, these research efforts have been hampered by the computational complexity caused by inverse kinematics and 3D reconstruction. In this paper, our objective focuses on 3D hand posture estimation based on a single 2D image with aim of robotic applications. We introduce the human hand model with 27 degrees of freedom (DOFs) and analyze some of its constraints to reduce the DOFs without any significant degradation of performance. A novel algorithm to estimate the 3D hand posture from eight 2D projected feature points is proposed. Experimental results using real images confirm that our algorithm gives good estimates of the 3D hand pose. Keywords: 3D hand posture estimation; Model-based approach; Gesture recognition; human- computer interface; machine vision.
Camera as Mouse and Keyboard for Handicap Person with Troubleshooting Ability...Waqas Tariq
Camera mouse has been widely used for handicap person to interact with computer. The utmost important of the use of camera mouse is must be able to replace all roles of typical mouse and keyboard. It must be able to provide all mouse click events and keyboard functions (include all shortcut keys) when it is used by handicap person. Also, the use of camera mouse must allow users troubleshooting by themselves. Moreover, it must be able to eliminate neck fatigue effect when it is used during long period. In this paper, we propose camera mouse system with timer as left click event and blinking as right click event. Also, we modify original screen keyboard layout by add two additional buttons (button “drag/ drop” is used to do drag and drop of mouse events and another button is used to call task manager (for troubleshooting)) and change behavior of CTRL, ALT, SHIFT, and CAPS LOCK keys in order to provide shortcut keys of keyboard. Also, we develop recovery method which allows users go from camera and then come back again in order to eliminate neck fatigue effect. The experiments which involve several users have been done in our laboratory. The results show that the use of our camera mouse able to allow users do typing, left and right click events, drag and drop events, and troubleshooting without hand. By implement this system, handicap person can use computer more comfortable and reduce the dryness of eyes.
A Proposed Web Accessibility Framework for the Arab DisabledWaqas Tariq
The Web is providing unprecedented access to information and interaction for people with disabilities. This paper presents a Web accessibility framework which offers the ease of the Web accessing for the disabled Arab users and facilitates their lifelong learning as well. The proposed framework system provides the disabled Arab user with an easy means of access using their mother language so they don’t have to overcome the barrier of learning the target-spoken language. This framework is based on analyzing the web page meta-language, extracting its content and reformulating it in a suitable format for the disabled users. The basic objective of this framework is supporting the equal rights of the Arab disabled people for their access to the education and training with non disabled people. Key Words : Arabic Moon code, Arabic Sign Language, Deaf, Deaf-blind, E-learning Interactivity, Moon code, Web accessibility , Web framework , Web System, WWW.
Real Time Blinking Detection Based on Gabor FilterWaqas Tariq
The document proposes a new method for real-time blinking detection based on Gabor filters. It begins by reviewing existing methods and their limitations in dealing with noise, variations in eye shape, and blinking speed. The proposed method uses a Gabor filter to extract the top and bottom arcs of the eye from an image. It then measures the distance between these arcs and compares it to a threshold: a distance below the threshold indicates a closed eye, while a distance above indicates an open eye. The document claims this Gabor filter-based approach is robust to noise, variations in eye shape and blinking speed. It presents experimental results showing the method can accurately detect blinking across different users.
Computer Input with Human Eyes-Only Using Two Purkinje Images Which Works in ...Waqas Tariq
A method for computer input with human eyes-only using two Purkinje images which works in a real time basis without calibration is proposed. Experimental results shows that cornea curvature can be estimated by using two light sources derived Purkinje images so that no calibration for reducing person-to-person difference of cornea curvature. It is found that the proposed system allows usersf movements of 30 degrees in roll direction and 15 degrees in pitch direction utilizing detected face attitude which is derived from the face plane consisting three feature points on the face, two eyes and nose or mouth. Also it is found that the proposed system does work in a real time basis.
Toward a More Robust Usability concept with Perceived Enjoyment in the contex...Waqas Tariq
Mobile multimedia service is relatively new but has quickly dominated people¡¯s lives, especially among young people. To explain this popularity, this study applies and modifies the Technology Acceptance Model (TAM) to propose a research model and conduct an empirical study. The goal of study is to examine the role of Perceived Enjoyment (PE) and what determinants can contribute to PE in the context of using mobile multimedia service. The result indicates that PE is influencing on Perceived Usefulness (PU) and Perceived Ease of Use (PEOU) and directly Behavior Intention (BI). Aesthetics and flow are key determinants to explain Perceived Enjoyment (PE) in mobile multimedia usage.
Collaborative Learning of Organisational KnolwedgeWaqas Tariq
This paper presents recent research into methods used in Australian Indigenous Knowledge sharing and looks at how these can support the creation of suitable collaborative envi- ronments for timely organisational learning. The protocols and practices as used today and in the past by Indigenous communities are presented and discussed in relation to their relevance to a personalised system of knowledge sharing in modern organisational cultures. This research focuses on user models, knowledge acquisition and integration of data for constructivist learning in a networked repository of or- ganisational knowledge. The data collected in the repository is searched to provide collections of up-to-date and relevant material for training in a work environment. The aim is to improve knowledge collection and sharing in a team envi- ronment. This knowledge can then be collated into a story or workflow that represents the present knowledge in the organisation.
Our research aims to propose a global approach for specification, design and verification of context awareness Human Computer Interface (HCI). This is a Model Based Design approach (MBD). This methodology describes the ubiquitous environment by ontologies. OWL is the standard used for this purpose. The specification and modeling of Human-Computer Interaction are based on Petri nets (PN). This raises the question of representation of Petri nets with XML. We use for this purpose, the standard of modeling PNML. In this paper, we propose an extension of this standard for specification, generation and verification of HCI. This extension is a methodological approach for the construction of PNML with Petri nets. The design principle uses the concept of composition of elementary structures of Petri nets as PNML Modular. The objective is to obtain a valid interface through verification of properties of elementary Petri nets represented with PNML.
Development of Sign Signal Translation System Based on Altera’s FPGA DE2 BoardWaqas Tariq
The main aim of this paper is to build a system that is capable of detecting and recognizing the hand gesture in an image captured by using a camera. The system is built based on Altera’s FPGA DE2 board, which contains a Nios II soft core processor. Image processing techniques and a simple but effective algorithm are implemented to achieve this purpose. Image processing techniques are used to smooth the image in order to ease the subsequent processes in translating the hand sign signal. The algorithm is built for translating the numerical hand sign signal and the result are displayed on the seven segment display. Altera’s Quartus II, SOPC Builder and Nios II EDS software are used to construct the system. By using SOPC Builder, the related components on the DE2 board can be interconnected easily and orderly compared to traditional method that requires lengthy source code and time consuming. Quartus II is used to compile and download the design to the DE2 board. Then, under Nios II EDS, C programming language is used to code the hand sign translation algorithm. Being able to recognize the hand sign signal from images can helps human in controlling a robot and other applications which require only a simple set of instructions provided a CMOS sensor is included in the system.
An overview on Advanced Research Works on Brain-Computer InterfaceWaqas Tariq
A brain–computer interface (BCI) is a proficient result in the research field of human- computer synergy, where direct articulation between brain and an external device occurs resulting in augmenting, assisting and repairing human cognitive. Advanced works like generating brain-computer interface switch technologies for intermittent (or asynchronous) control in natural environments or developing brain-computer interface by Fuzzy logic Systems or by implementing wavelet theory to drive its efficacies are still going on and some useful results has also been found out. The requirements to develop this brain machine interface is also growing day by day i.e. like neuropsychological rehabilitation, emotion control, etc. An overview on the control theory and some advanced works on the field of brain machine interface are shown in this paper.
Exploring the Relationship Between Mobile Phone and Senior Citizens: A Malays...Waqas Tariq
There is growing ageing phenomena with the rise of ageing population throughout the world. According to the World Health Organization (2002), the growing ageing population indicates 694 million, or 223% is expected for people aged 60 and over, since 1970 and 2025.The growth is especially significant in some advanced countries such as North America, Japan, Italy, Germany, United Kingdom and so forth. This growing older adult population has significantly impact the social-culture, lifestyle, healthcare system, economy, infrastructure and government policy of a nation. However, there are limited research studies on the perception and usage of a mobile phone and its service for senior citizens in a developing nation like Malaysia. This paper explores the relationship between mobile phones and senior citizens in Malaysia from the perspective of a developing country. We conducted an exploratory study using contextual interviews with 5 senior citizens of how they perceive their mobile phones. This paper reveals 4 interesting themes from this preliminary study, in addition to the findings of the desirable mobile requirements for local senior citizens with respect of health, safety and communication purposes. The findings of this study bring interesting insight to local telecommunication industries as a whole, and will also serve as groundwork for more in-depth study in the future.
Principles of Good Screen Design in WebsitesWaqas Tariq
Visual techniques for proper arrangement of the elements on the user screen have helped the designers to make the screen look good and attractive. Several visual techniques emphasize the arrangement and ordering of the screen elements based on particular criteria for best appearance of the screen. This paper investigates few significant visual techniques in various web user interfaces and showcases the results for better understanding and their presence.
This document discusses the progress of virtual teams in Albania. It provides context on virtual teams and how they differ from traditional teams in their reliance on technology for communication across distances. The document then examines the use of virtual teams in Albania, noting the growing infrastructure and technology usage that enables virtual collaboration. It highlights some virtual team examples in Albanian government and academic projects.
Cognitive Approach Towards the Maintenance of Web-Sites Through Quality Evalu...Waqas Tariq
It is a well established fact that the Web-Applications require frequent maintenance because of cutting– edge business competitions. The authors have worked on quality evaluation of web-site of Indian ecommerce domain. As a result of that work they have made a quality-wise ranking of these sites. According to their work and also the survey done by various other groups Futurebazaar web-site is considered to be one of the best Indian e-shopping sites. In this research paper the authors are assessing the maintenance of the same site by incorporating the problems incurred during this evaluation. This exercise gives a real world maintainability problem of web-sites. This work will give a clear picture of all the quality metrics which are directly or indirectly related with the maintainability of the web-site.
USEFul: A Framework to Mainstream Web Site Usability through Automated Evalua...Waqas Tariq
A paradox has been observed whereby web site usability is proven to be an essential element in a web site, yet at the same time there exist an abundance of web pages with poor usability. This discrepancy is the result of limitations that are currently preventing web developers in the commercial sector from producing usable web sites. In this paper we propose a framework whose objective is to alleviate this problem by automating certain aspects of the usability evaluation process. Mainstreaming comes as a result of automation, therefore enabling a non-expert in the field of usability to conduct the evaluation. This results in reducing the costs associated with such evaluation. Additionally, the framework allows the flexibility of adding, modifying or deleting guidelines without altering the code that references them since the guidelines and the code are two separate components. A comparison of the evaluation results carried out using the framework against published evaluations of web sites carried out by web site usability professionals reveals that the framework is able to automatically identify the majority of usability violations. Due to the consistency with which it evaluates, it identified additional guideline-related violations that were not identified by the human evaluators.
Robot Arm Utilized Having Meal Support System Based on Computer Input by Huma...Waqas Tariq
A robot arm utilized having meal support system based on computer input by human eyes only is proposed. The proposed system is developed for handicap/disabled persons as well as elderly persons and tested with able persons with several shapes and size of eyes under a variety of illumination conditions. The test results with normal persons show the proposed system does work well for selection of the desired foods and for retrieve the foods as appropriate as usersf requirements. It is found that the proposed system is 21% much faster than the manually controlled robotics.
Dynamic Construction of Telugu Speech Corpus for Voice Enabled Text EditorWaqas Tariq
In recent decades speech interactive systems have gained increasing importance. Performance of an ASR system mainly depends on the availability of large corpus of speech. The conventional method of building a large vocabulary speech recognizer for any language uses a top-down approach to speech. This approach requires large speech corpus with sentence or phoneme level transcription of the speech utterances. The transcriptions must also include different speech order so that the recognizer can build models for all the sounds present. But, for Telugu language, because of its complex nature, a very large, well annotated speech database is very difficult to build. It is very difficult, if not impossible, to cover all the words of any Indian language, where each word may have thousands and millions of word forms. A significant part of grammar that is handled by syntax in English (and other similar languages) is handled within morphology in Telugu. Phrases including several words (that is, tokens) in English would be mapped on to a single word in Telugu.Telugu language is phonetic in nature in addition to rich in morphology. That is why the speech technology developed for English cannot be applied to Telugu language. This paper highlights the work carried out in an attempt to build a voice enabled text editor with capability of automatic term suggestion. Main claim of the paper is the recognition enhancement process developed by us for suitability of highly inflecting, rich morphological languages. This method results in increased speech recognition accuracy with very much reduction in corpus size. It also adapts Telugu words to the database dynamically, resulting in growth of the corpus.
An Improved Approach for Word Ambiguity RemovalWaqas Tariq
Word ambiguity removal is a task of removing ambiguity from a word, i.e. correct sense of word is identified from ambiguous sentences. This paper describes a model that uses Part of Speech tagger and three categories for word sense disambiguation (WSD). Human Computer Interaction is very needful to improve interactions between users and computers. For this, the Supervised and Unsupervised methods are combined. The WSD algorithm is used to find the efficient and accurate sense of a word based on domain information. The accuracy of this work is evaluated with the aim of finding best suitable domain of word. Keywords: Human Computer Interaction, Supervised Training, Unsupervised Learning, Word Ambiguity, Word sense disambiguation
Parameters Optimization for Improving ASR Performance in Adverse Real World N...Waqas Tariq
From the existing research it has been observed that many techniques and methodologies are available for performing every step of Automatic Speech Recognition (ASR) system, but the performance (Minimization of Word Error Recognition-WER and Maximization of Word Accuracy Rate- WAR) of the methodology is not dependent on the only technique applied in that method. The research work indicates that, performance mainly depends on the category of the noise, the level of the noise and the variable size of the window, frame, frame overlap etc is considered in the existing methods. The main aim of the work presented in this paper is to use variable size of parameters like window size, frame size and frame overlap percentage to observe the performance of algorithms for various categories of noise with different levels and also train the system for all size of parameters and category of real world noisy environment to improve the performance of the speech recognition system. This paper presents the results of Signal-to-Noise Ratio (SNR) and Accuracy test by applying variable size of parameters. It is observed that, it is really very hard to evaluate test results and decide parameter size for ASR performance improvement for its resultant optimization. Hence, this study further suggests the feasible and optimum parameter size using Fuzzy Inference System (FIS) for enhancing resultant accuracy in adverse real world noisy environmental conditions. This work will be helpful to give discriminative training of ubiquitous ASR system for better Human Computer Interaction (HCI). Keywords: ASR Performance, ASR Parameters Optimization, Multi-Environmental Training, Fuzzy Inference System for ASR, ubiquitous ASR system, Human Computer Interaction (HCI)
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
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Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
How to Setup Warehouse & Location in Odoo 17 InventoryCeline George
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
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There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
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Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
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How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
Active Control of Tool Position in the Presence of Nonlinear Cutting Forces in Orthogonal Cutting
1. A.H. El-Sinawi
International Journal of Robotics and Automation (IJRA), Volume (2) : Issue (3) : 2011 157
Active Control of Tool Position in the Presence of Nonlinear Cutting Forces
in Orthogonal Cutting
A.H. El-Sinawi aelsinawi@aus.edu
Mechanical Engineering department
American University of Sharjah,
Sharjah, UAE PO Box 26666
Abstract
This work presents a practical approach to the control of tool’s position, in orthogonal cutting, in
the presence nonlinear dynamic cutting forces. The controller is Linear Quadratic Gaussian
(LQG) type constructed from an augmented model of both, tool-actuator dynamics, and a
nonlinear dynamic model relating tool displacement to cutting forces. The latter model is obtained
using black-box system identification of experimental orthogonal cutting data in which tool
displacement is the input and cutting force is the output. The controller is evaluated and its
performance is demonstrated.
Key words: LQG, Nonlinear ARX Model, Orthogonal Cutting, Active Control, Nonlinear Cutting
Force
1. INTRODUCTION
Performance of machining processes is assessed by dimensional and geometrical accuracy as
well as the surface texture of the part. Factors such as cutting force, workpiece vibration,
machine-tool vibration, process instability, tool wear and thermal deformation deteriorate this
performance. Recent interest in high speed-machining and high manufacturing efficiency requires
faster, higher bandwidth actuation, and controllers that are more robust. Besides determining
part functional behavior, the surface texture also plays a key role in the area of manufacturing
process control [1]. The basis for using surface texture as means of process control is derived
from the fact that a slight change in the manufacturing process manifests itself as a
corresponding change in the resulting surface geometry. The roughness, waviness, lay, and flaws
constitute the texture of the workpiece surface [2]. Surface texture of the work-piece is highly
dependent on tool position during cutting which in turn is affected by cutting dynamics. Therefore
extensive research work has been done on modeling and analysis of tool work-piece interaction
and the dynamics of the cutting process. Altintas [3] have presented a cutting force model as a
function of regenerative chip thickness, cutting speed, and the velocity and acceleration terms of
the vibrations. In their work, amplitude and frequency of inner and outer vibration waves are
generated on the chip by an instrumented fast tool servo powered by a piezo actuator. They
established a model in which the coefficients of dynamic cutting forces are identified and used in
analyzing the effect of cutting speed, tool wear, vibration frequency and wavelength on the
chatter stability of a turning process. Ikua [4] have studied the cutting force generated in ball end
milling and presented a model for the radial and tangential forces as a function of depth of cut,
and other factors related to the geometry of the tool and workpeices.
Researchers have tried to establish quantitative relations between the surface finish and the
cutting parameters of the depth of cut, feed, and cutting speed using methods such as, among
others, wavelength decomposition surface roughness, wavelet analysis, and tool vibration [4-9].
The cutter–workpiece interaction forces are assumed to cause relative displacement between the
cutter and the work piece, which influence the surface generation mechanism. Analytical,
experimental and mechanistic methods were used to predict the interaction forces. The analytical
methods focused on establishing a relationship between the cutting force and the instantaneous
uncut chip cross – section [10, 11] and the non – linear mechanisms [12, 13]. The analytical
models were not capable of predicting the dynamic forces accurately due to the secondary non –
2. A.H. El-Sinawi
International Journal of Robotics and Automation (IJRA), Volume (2) : Issue (3) : 2011 158
linear effects that stems from the tool/workpiece interaction. The experimental methods include
static, dynamic and time–series methods. The static methods are assumed based on linear
assumptions and linear cutting conditions [14]. The dynamic methods replaced the static methods
and the cutting process is assumed to be a combination of two independent actions namely, the
wave cutting action and the wave removing action [15]. The time-series method was formulated
to identify the dynamic cutting force coefficients as well as the transfer functions of the three
dimensional dynamic cutting process directly from operating data [16]. The mechanistic modeling
methods view the machining process as a combination of the chip load/cutting force relationship,
cutting – tool geometry, machining conditions and tool /work – piece displacement due to cutting
forces. The workpiece dynamic behavior is constructed using either the distributed – parameter
[17], or the lumped – parameter approaches [18]. Few researchers investigated the dynamic
effect of the tool holder. Shawky and Elbestawi [19] concluded that the effect of tangential force is
insignificant and no model of the tool holder is needed in that direction. Their experimental work
showed that modeling the tool by a second order system in each axis provides significant
approximation of the dynamic behavior of a single point tool during cutting [19].
Control of machining process includes three levels of control that one might encounter in a
controller for machining process, namely they are the servo control, the process control [20] and
the supervisory control [21]. In the servo control process, the motion of the cutting tool is taken
relative to that of the workpiece. The process control level is used to control the cutting forces and
tool wear to maintain high production rates and good part quality. The highest level of control is
the supervisory control and it directly measures product related variables, such as part
dimensions and surface finish. Different approaches are used to correct for machining errors by
means of dynamic error compensation. More recently, Tian et al. [22] have presented a
methodology for modeling and control of a high precision flexure-based mechanism for ultra-
precision turning operation based on the position control of an auxiliary precision mechanism
utilized on the turret of the conventional lathe to implement nanometer level infeed. El-Sinawi [23]
has presented an optimal control method for controlling the tool position in orthogonal cutting in
both feed are radial directions. Moradi et al. , [24] have presented a robust control method for
Orthogonal turning process in the process was modeled as a single degree of freedom model that
includes the effect of tool flank wear with a control input of the system being force applied to the
tool provided by a piezo-actuator. Huang et al. [25] have presented a tool wear detection based
on cutting force monitoring.
In this work, a control scheme for the purpose of improving surface texture of turned surfaces
through control of tool position in the presence of nonlinear cutting force is developed.
Improvement of surface quality is achieved via active positioning of the tool or cutter through the
attenuation of cutting forces effect on the tool in both radial and tangential directions. The process
is assumed to be stochastic due to both process and measurement noise. Experimental force-
displacement data is used to construct a nonlinear dynamic model of dynamic cutting forces.
Various nonlinear models are constructed using system identification techniques including ARX,
nonlinear ARX, and Hammerstein-Wiener techniques [26]. The best nonlinear model obtained
that closely fits experimental data, is then linearized and constructed in state-space form to later
utilize in the Linear Quadratic Gaussian Controller. Simulation results will be used to verify the
effectiveness of the proposed modeling and control approach, and to enhance current
understanding of the mechanisms responsible for generating both stochastic and deterministic
components of the surface texture. Simulation work of the proposed modeling and control
techniques will be based on actual parameters for actuators and the cutting process data, which
is readily available in the literature [27].
2. MODEL DEVELOPMENT
Force-displacement data obtained from experimental cutting of a 6061 Aluminum workpiece
using a carbide tool with
o
0 rake angle and
o
7 clearance angle, depth of cut of 0.4 mm, feed of
0.050 mm/rev, and spindle speed: 2200 rev/min, are shown in Figures 1 and 2, have been used
to construct a force displacement model using black-box system identification.
3. A.H. El-Sinawi
International Journal of Robotics and Automation (IJRA), Volume (2) : Issue (3) : 2011 159
Four dynamic models with tool displacement as input and cutting force as output are constructed
are indentified and compared as shown in Figure 3. In reference to Figure 3, the first model
identified as LinMod1, is a linear ARX model of the form
)()1(.....)1()()(......)2()1()( 2121 tetxbtxbtxbtfatfatfatf ccccccc +−−++−+=−++−+−+ µτ µτ (1)
Where cc xf , are the cutting force and tool displacement in the corresponding direction,
respectively. )1(),...,1()(),(),..,2()1( −−−+−−+− µτ txtxtxtftftf cccccc are delayed
input and output variables called regressors. Linear ARX model predicts the output cf as a
weighted sum of its regressors. τ is the number of past output terms while µ is the number of
past input terms used to predict the current output cf and )(te is a white noise sequence.
The second and third models identified as LinMod3 and LinMod4 are constructed as follows;
LinMod3 is constructed using Predictive Error Minimization or PEM with various constraints on
the order or number of states of the state-space model. This method yields a discrete time-
domain state-space dynamic model of the form,
)()()()(),()()()( tetDutCxtytKetButAxTstx ++=++=+ (2)
In which x are the states, y is output, DKCBA ,,,, represent dynamics, input output,
disturbance and feed through matrices, respectively [28].
Narx1 model is constructed using Nonlinear ARX model which is an extension of ARX model
given in Equation (1) except that the input –output mapping is nonlinear and of the form;
.....)),1(),(),....,2(),1(()( −−−= txtxtftfFtf ccccn (3)
Where nf is the output and F is a nonlinear mapping function, such as Wavelet network, Tree
partition, etc…, [29].
Nhw1 model shown in Figure 3, is constructed using Hammerstein-Wiener model; see [Yucai
Zhu, 2002 and Lennart Ljung, 1999] for further details. It is clear from Figure 3 that the Narx1 has
the best fit to experimental data with 99.9% fit.
2.1 Linearization of the Nonlinear ARX Model
The nonlinear model that best fits input-output data is clearly the nonlinear ARX model mapped
with a single-layer sigmoid function. The nonlinear mapping of input-output data is shown in
Figure 4, with
))(()()( rvQgdrvLvF −++−= (4)
v is a vector of the regressors. drvL +− )( is the output of the linear block shown in Figure 4, d
is a scalar offset, ))(( rvQg − is the output of the nonlinear function block, and Q is a projection
matrix and r is the mean of regressors ( v ). Function )(vg expressed as
))(()(
1
∑=
−=
n
k
kkk vvg ξβφα with ( ) 1
1)(
−
+= s
esφ is the nonlinearity estimator of the sigmoid
function type. kβ is a row vector such that )( kk v ξβ − is a scalar, s is the Laplace variable and
n is the number of sigmoid network units. The model obtained by this approach is of the form
given in Equation 3 with ,4=τ and 4=µ .
Step response of the models obtained for both forces in the radial ( xf ) and tangential ( yf )
directions is shown in Figures 5 and 6, respectively. The step response shows the steady state
4. A.H. El-Sinawi
International Journal of Robotics and Automation (IJRA), Volume (2) : Issue (3) : 2011 160
values of both functions which are later on used in linearzing the model. See Appendix A for
linearization details.
Linearized state-space model of the radial force is;
crrrrx
crrrrr
xDtXCf
xBtXAtX
+=
+=
)(
)()(&
(5)
Where )(tXr
& are the states of the radial force model, rrrr DCBA ,,, are dynamic, input, output
and feed through matrices, respectively. crx xf , are radial cutting force and radial tool
displacement, respectively. The same procedure is carried out for the tangential cutting force
model which yields;
ctttty
cttttt
xDtXCf
xBtXAtX
+=
+=
)(
)()(&
(6)
2.2 Modeling of the Machining Process
Figure7 shows the difference between tool post (passive) and proposed active tool fixture that will
allow for implementation of the proposed controller. Figure (7.a) shows the conventional tool post
rigidly attached to the machine tool structure, while Figure (7.b) shows the active tool holder
platform equipped with two actuators placed between the tool and the machine tool structure.
This will allow the control force to provide necessary manipulation of the tool to maintain a
constant depth of cut.
During cutting, the tool is perturbed form nominal depth of cut by two inputs namely; the dynamic
cutting forces in both radial and tangential directions, in addition to process noise )(tw .
State-space model of the tool-actuator assembly in the radial direction can be represented as;
arcrrcrcr
arcrrcrr
FDxCY
FBxAx
+=
+=&
(7)
Such that,
[ ] 0,01,1
0
,
10
==
=
−−
= crcrcracaccr DC
m
B
m
b
m
kA ,
where rx is vector of the tool states, namely, displacement and velocity. m is the mass of the
tool and its mount, acac bk , are the elastic stiffness and damping coefficients of the actuator,
respectively. acac bk , can be obtained by an FR test of the tool-actuator assembly. Notice that,
the same procedure can be carried out for the tangential direction since both actuators are
orthogonal.
Refer to [23, 27] for more information on the model development.
3. CONTROL STRATEGY AND THE CONTROLLER DESIGN
The control strategy will be centered on reducing the amplitude of the tool' dynamic displacement
to zero for the purpose of maintaining a constant depth of cut and subsequently, a smooth
surface texture of the workpiece. This requires minimization of the error between the desired and
the actual position of the tool. The desired or nominal tool position is the one yielding a constant
depth of cut. However, the existence of the dynamic cutting forces perturbs the tool form its
5. A.H. El-Sinawi
International Journal of Robotics and Automation (IJRA), Volume (2) : Issue (3) : 2011 161
nominal position and thus, varies the depth of cut causing subsequent deterioration in surface
texture. Attenuating the effect of the cutting force on the tool’s position, the error in the tool
position will be minimized. This can be achieved by reacting on the tool with an equal but
opposite forces through proper actuation. This task is difficult due to (a) existence of process and
measurement noise and (b) nonlinearity of the dynamic cutting forces. To overcome these
difficulties, the controller must be able to estimate the force needed to minimize the error in the
tool position from noisy process using measurement data contaminated with noise. In addition to
that, the controller has to track and manipulate the position of the tool effectively in the presence
of nonlinear dynamic cutting forces. Added to all of the above, the controller has to maintain high
stability and performance under various disturbance characteristics. To do so, the controller has
to be constructed based on a model that takes into account the dynamics of the tool-actuator
system as well as the cutting force dynamics. Therefore, The plant used for this purpose is a
combination (i.e., augmentation) of the dynamic cutting forces and tool-actuator dynamics in both
radial and tangential directions. The first step in designing the proposed active controller, is the
design of the LQG estimator and regulator gains eL and RK , respectively. The analysis
presented here is in state-space such that the augmented system depicted by Equations (5), and
(6) is;
=
rcrr
cr
a
ACB
A
A
0
(8)
=
crr
cr
a
DB
B
B (9)
[ ]rcrra CCDC = (10)
[ ]crra DDD = (11)
where the matrices Aa, Ba, Ca, and Da are respectively, the dynamic, input, output, and direct
transmission matrices of the augmented system. The four matrices in the foregoing are used to
design the LQG estimator and regulator gain matrices eL and RK , such that,
[ ]
[ ]
[ ]
[ ]
=
=
rR
crR
R
re
cre
e
K
K
K
L
L
L , (12)
This augmentation is necessary to incorporate the cutting force dynamics in the process of
determining the optimal estimator and regulator gains. Equation 12 shows that eL and RK are
both partitioned in two parts each where cr[] corrects crx (i.e., tool-actuator model states) and r[]
corrects rX (i.e., cutting force states). The LQG (virtual model of the system) should be subjected
to all inputs that the actual plant is subjected to, including the control force. Figure 8 shows the
control scheme implementation in the radial direction. Further details on construction of the
controller are found in [30].
4. NUMERICAL EXAMPLE
Force-displacement results obtained from experimental cutting of a 6061 Aluminum workpiece
using a carbide tool with
o
0 rake angle and
o
7 clearance angle, depth of cut of 0.4 mm, feed of
0.050 mm/rev, and spindle speed: 2200 rev/min, shown in Figures 1 and 2, are used to construct
a force-displacement model using black-box system identification. Linearized State-space model
obtained by Nonlinear ARX modeling, presented here in canonical form is;
6. A.H. El-Sinawi
International Journal of Robotics and Automation (IJRA), Volume (2) : Issue (3) : 2011 162
[ ] [ ] crrx
crrr
xtXf
xtXtX
0)(460.7213.8-153.9266.2-1500
0
0
0
1024
)(
00.500
0010
0002
0.4435-0.56510.7-1.145
)(
+×=
+
=&
ETREMA actuator with peak-to-peak excursion of m6
1050 −
× is utilized as the active
manipulator of the tool. The Actuator’s elastic stiffness and damping used in this study were taken
as follows (El-Sinawi et al. 2005): m =0.53 kg for the tool-actuator assembly.
6
106.14 ×=ack N/m, and 10=acb kg /s. The cutting process noise )(tw is assumed to have a
zero mean, and variation of ± 10% of the cutting force, while measurement noise )(tv is also
assumed to be random with zero mean, and variation of ± 10% of measurement values. Notice
that the small values of )(tw and )(tv makes the linearization valid in the vicinity of nominal
trajectory of the system.
5. RESULTS AND ANALYSIS
To implement the proposed control strategy, experimental force-displacement data shown in
Figures 1 and 2 is utilized to construct a transfer function relating the tool’s displacement as input
to cutting force as output. The data is obtained from Altintas [3] and Matlab® System
identification toolbox is used for the purpose of identifying the best transfer function that relates
the input to the output. Figure 3 shows various algorithms implemented by the system
identification process along with the percentage of match to the experimental input-output data.
The figure shows that a transfer function obtained using Narx identification algorithm has a
99.99% match to experimental data. The model obtained from System identification data have the
structure shown in Figure 4. Similar approach is used to obtain a transfer function for the input-
output data in the feed direction. Step responses of radial and feed transfer function models
obtained by System identification are shown in Figures 5 and 6. Latter figures show that both
models are lightly damped with damping of approximately 0.5 % and 1 % for the radial and feed
directions, respectively. Such light damping should not pose a problem since the damping can be
increased using proper feedback control. With the tool’s Displacement-Force model in both radial
and feed directions are available, the tool is mounted on two orthogonal actuators intended to
manipulate the tool’s position in corresponding directions using proper control force as estimated
by the controller. Transfer functions of the Identified models are augmented with the actuators
models to obtain the suitable LQG controller gains Namely, eL and RK . During actual
implementation of the controller, measurements of the tool position are compared to the
estimates of the tool’s position and the difference (i.e. error) is fed back through the estimator
gain ( eL ) to adjust the controller model and thus, improve estimates of the tool’s position. The
estimated position is then fed through the actuator’s transfer function to produce the negative
actuation force needed to maintain a constant depth of cut (i.e., zero tool displacement). The
negative force provided by the actuator is only estimate of the external cutting force that perturbs
the tool from its nominal position. Force estimates depend mainly on the values weighting
matrices Q and R needed to minimize the performance index (J) of the LQG [31]. In general,
choosing a larger value of Q compared to R implies the demand for high controller performance.
On the Other hand, larger value of R implies minimal control energy. In this work, the process
model obtained by the system identification is fairly accurate which allows for large Q. However,
the limitation on the actuator force (approximately 500 N) and excursion (50 micrometer) poses a
limit on the values of Q and R. In such application, the important factor that determines the
performance vs. control energy is main the ratio of Q/R rather than the individual values of each.
7. A.H. El-Sinawi
International Journal of Robotics and Automation (IJRA), Volume (2) : Issue (3) : 2011 163
In this application the ratio chosen for Q/R is 2. Assuming only 10% process and measurement
noise, Figures 9 and 10 show that the proposed control technique has managed to reduce the
tools dynamic displacement by approximately 40%. These results are reasonable only if the
cutting process remains stable (i.e., no occurrence of chatter) and all factors that are not
considered in the model remain unchanged; such factors include tool wear, temperature, micro-
hardness variation of the workpiece and workpiece dynamics. Figures 11 and 12 show the control
force exerted by the actuator on the tool is well within the capability of the actuator. It should be
noted that the identified model will be affected by changes of depth of cut, cutting speed feed-rate
and tool wear. Adaptive implementation of the proposed process is possible where the
displacement-force transfer function identification is continuously updated as the cutting process
progresses. However, the accuracy of the identified model can be a serious drawback of the
control technique proposed by this work.
6. CONCLUSIONS
In this research work, active control of an orthogonal cutting process is presented. Nonlinear
dynamic cutting force model is generated from actual machining data obtained in both radial and
tangential directions. An LQG based controller is developed based on an augmented model of
both tool-actuator dynamics and a linearized model of the dynamic cutting force. The control
objective is to eliminate the tool’s dynamic displacement and maintain a constant depth of cut.
Simulation results have shown that the proposed control strategy has managed to significantly
reduce the dynamic displacement of the tool with minimal force and calculations efforts even in
the presence of significant randomness in the process and measurement as well as the
nonlinearity of the cutting force. Experimental study is undergoing to verify the integrity of the
controller in real time applications.
ACKNOWLEDGEMENT
Author acknowledges the support of the American University of Sharjah
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[28]. M. Farina and L. Piroddi. “An iterative algorithm for simulation error based identification
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FIGURE 1: Sample of experimental dynamic cutting forces in (a) radial and (b) tangential
directions.
10. A.H. El-Sinawi
International Journal of Robotics and Automation (IJRA), Volume (2) : Issue (3) : 2011 166
FIGURE 2: Tool displacement in the radial direction measurements during orthogonal cutting
FIGURE 3: Nonlinear models constructed from experimental results
11. A.H. El-Sinawi
International Journal of Robotics and Automation (IJRA), Volume (2) : Issue (3) : 2011 167
FIGURE 4: Nonlinear ARX model structure
FIGURE 5: Step response of the radial force model xf
12. A.H. El-Sinawi
International Journal of Robotics and Automation (IJRA), Volume (2) : Issue (3) : 2011 168
FIGURE 6: Step response of the tangential force model yf
FIGURE 7: (a) Conventional machine tool, (b) machine tool retrofitted with two actuators
transducer for cutter manipulation. v(t) measurements noise.
13. A.H. El-Sinawi
International Journal of Robotics and Automation (IJRA), Volume (2) : Issue (3) : 2011 169
FIGURE 8: Controller implementation in the radial direction (i.e., x-direction)
FIGURE 9: tool dynamic displacement in the radial direction
14. A.H. El-Sinawi
International Journal of Robotics and Automation (IJRA), Volume (2) : Issue (3) : 2011 170
FIGURE 10: tool dynamic displacement in the tangential direction
FIGURE 11: Control force in radial direction
15. A.H. El-Sinawi
International Journal of Robotics and Automation (IJRA), Volume (2) : Issue (3) : 2011 171
FIGURE 12: Control force in the feed direction
16. A.H. El-Sinawi
International Journal of Robotics and Automation (IJRA), Volume (2) : Issue (3) : 2011 172
Appendix A: Linearization of a Nonlinear system [29]
Common use of time-varying linear systems is related to linearization of nonlinear systems
around a certain “nominal” trajectory. Therefore, for a nonlinear system described by
)())(),(())(()(
)())(),(())(),((()1(
tvtutxmtxhty
twtutxrtutxftx
+=
+=+
a.1
Assuming that the disturbance terms )(tw and )(tv are white and small, with the nominal and
disturbance-free )0)(,0)(( ≡≡ tvtw behavior of the system corresponds to an input sequence
)(*
tu and corresponding trajectory )(*
tx . Neglecting nonlinear terms, the differences,
)()()(
))(()()(
)()()(
*
*
*
tututu
txhtyty
txtxtx
−=∆
−=∆
−=∆
Are then subjected to
)()()()(
)()()()()()1(
tvtxtHty
twtutGtxtFtx
+∆=∆
+∆+∆=+∆
a.2
Such that,
)(
)()(,
)(),(
),()(,
)(),(
),()( *****
tx
xh
x
tH
tutx
uxf
u
tG
tutx
uxf
x
tF
∂
∂
=
∂
∂
=
∂
∂
=
In view of the assumption of small disturbances, the cross terms with disturbance. The terms
)(tw and )(tv in Eq. a.2 above are white disturbances with the following covariance properties:
))(),(()()())(),(()(
))(),(()()())(),(()()()(
))(),(()()())(),(()()()(
****
12
****
2
****
1
tutxmtvtwEtutxrtR
tutxmtvtvEtutxmtvtvEtR
tutxrtwtwEtutxrtwtwEtR
TT
TTT
TTT
=
==
==
a.3
The model is now linear in the vicinity of nominal trajectory.