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.
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Journals,
International Journals,
High Impact Journals,
Monthly Journal,
Good quality Journals,
Research,
Research Papers,
Research Article,
Free Journals, Open access Journals,
erpublication.org,
Engineering Journal,
Science Journals,
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
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.
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.
Active Control of Tool Position in the Presence of Nonlinear Cutting Forces i...Waqas Tariq
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 dressing regime parameters in the process of grinding are the most important
enabling factors that need to be determined. In this study, the influences of the dressing
parameters including the depth of dressing cut, the rate of dressing feed and the speed of
grinding wheel on the surface roughness when grinding tablet shape punches by CBN
wheel on CNC milling machine are investigated. Taguchi technique and analysis of
variance (ANOVA) have been applied to identify the impact of dressing regime
parameters on the surface roughness. The results show that the impact level of the cutting
depth (aed), the wheel speed (RPM), the feed rate (Fe) and errors on surface roughness
(Ra) are 52.63%, 28.45%, 6.59% and 12.33% respectively. By analyzing the experimental
results, optimum dressing parameters with the cutting depth of 0.02 mm, the wheel speed
of 1000 rpm and the infeed rate of 400 mm/min have been determined, that allow to get
the best surface roughness
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.
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.
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
Design and Structural Analysis of 3 Axis CNC Milling Machine Tableijtsrd
In the field of Engineering, the solution of many complex problems is great limitless and usually impossible by analytical methods. For high exactness and repeatability, machine tools are used in industrial operation. Normally, several components such as base, knee, saddle, machine table, column and headstock, column are the main parts of the machine tools to get reliable performance. The work piece is held and supported on the machine table. A machine table should be enough rigid and must have good mechanical properties, to obtain a good finished and accurate work piece on a three axis CNC milling machine. A finite element analysis FEA gives a methodical study of failure principle which helps for additional progress of the 3 axis machine tables. In this paper, Static Analysis is performed on machine table to find out stresses generated in table, deformation of the table due to its weight. The finite element analysis is done by making 3D geometry in Solidworks software and analyse by using ANSYS software. The material comparison is shown in table and Grey Cast Iron is more dependable than other materials. Nyein Chan | Than Zaw Oo | Aung Myo San Hlaing "Design and Structural Analysis of 3 Axis CNC Milling Machine Table" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-6 , October 2019, URL: https://www.ijtsrd.com/papers/ijtsrd29197.pdf Paper URL: https://www.ijtsrd.com/engineering/mechanical-engineering/29197/design-and-structural-analysis-of-3-axis-cnc-milling-machine-table/nyein-chan
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
Simulation of Deep-Drawing Process of Large Panelstheijes
The article deals with the analysis of formability of deep-drawing DC06 steel sheets. The aim of the investigations is to verify possibilities of formability of sheet metal with thickness of 0.85 mm. The mechanical parameters of the sheets have been determined in uniaxial tensile and bulge tests. The numerical simulations using AUTOFORM has been carried out for two drawpiece models. Obtained results can be used during the simulation of real forming process.
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
A novel dual point clamper for low-rigidity plate milling with deformation co...eSAT Journals
Abstract
The surface profile accuracy plays a significant role in achieving the overall product’s functional performance, which is seriously impacted by the cutting forces, clamping forces, and residual stresses. Conventionally, many researches about deformation compensation focus on cutting forces and fixture layout and do not consider clamping forces. Actually, clamping forces, which would dynamically change along with the movements of cutting tools, are essential in precision machining process. In this paper, a novel dual-point clamper method with adaptive deformation compensation is proposed to improve the workpieces milling precision. Based on the Generalized Principle of Superposition Method, a mathematical model considering the deflection from both cutting forces and clamping forces has been estimated and compared with the traditional clamping scheme. Both 3D finite element model (FEM) based simulation experiments and experimental case studies are carried out, and their results show good agreement with each other. The deflection computation and prediction from numerical studies indicates the efficiency and correctness of the proposed approach.
Keywords: Compensation; Deformation; Fixture; Milling
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.
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.
Active Control of Tool Position in the Presence of Nonlinear Cutting Forces i...Waqas Tariq
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 dressing regime parameters in the process of grinding are the most important
enabling factors that need to be determined. In this study, the influences of the dressing
parameters including the depth of dressing cut, the rate of dressing feed and the speed of
grinding wheel on the surface roughness when grinding tablet shape punches by CBN
wheel on CNC milling machine are investigated. Taguchi technique and analysis of
variance (ANOVA) have been applied to identify the impact of dressing regime
parameters on the surface roughness. The results show that the impact level of the cutting
depth (aed), the wheel speed (RPM), the feed rate (Fe) and errors on surface roughness
(Ra) are 52.63%, 28.45%, 6.59% and 12.33% respectively. By analyzing the experimental
results, optimum dressing parameters with the cutting depth of 0.02 mm, the wheel speed
of 1000 rpm and the infeed rate of 400 mm/min have been determined, that allow to get
the best surface roughness
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.
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.
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
Design and Structural Analysis of 3 Axis CNC Milling Machine Tableijtsrd
In the field of Engineering, the solution of many complex problems is great limitless and usually impossible by analytical methods. For high exactness and repeatability, machine tools are used in industrial operation. Normally, several components such as base, knee, saddle, machine table, column and headstock, column are the main parts of the machine tools to get reliable performance. The work piece is held and supported on the machine table. A machine table should be enough rigid and must have good mechanical properties, to obtain a good finished and accurate work piece on a three axis CNC milling machine. A finite element analysis FEA gives a methodical study of failure principle which helps for additional progress of the 3 axis machine tables. In this paper, Static Analysis is performed on machine table to find out stresses generated in table, deformation of the table due to its weight. The finite element analysis is done by making 3D geometry in Solidworks software and analyse by using ANSYS software. The material comparison is shown in table and Grey Cast Iron is more dependable than other materials. Nyein Chan | Than Zaw Oo | Aung Myo San Hlaing "Design and Structural Analysis of 3 Axis CNC Milling Machine Table" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-6 , October 2019, URL: https://www.ijtsrd.com/papers/ijtsrd29197.pdf Paper URL: https://www.ijtsrd.com/engineering/mechanical-engineering/29197/design-and-structural-analysis-of-3-axis-cnc-milling-machine-table/nyein-chan
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
Simulation of Deep-Drawing Process of Large Panelstheijes
The article deals with the analysis of formability of deep-drawing DC06 steel sheets. The aim of the investigations is to verify possibilities of formability of sheet metal with thickness of 0.85 mm. The mechanical parameters of the sheets have been determined in uniaxial tensile and bulge tests. The numerical simulations using AUTOFORM has been carried out for two drawpiece models. Obtained results can be used during the simulation of real forming process.
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
A novel dual point clamper for low-rigidity plate milling with deformation co...eSAT Journals
Abstract
The surface profile accuracy plays a significant role in achieving the overall product’s functional performance, which is seriously impacted by the cutting forces, clamping forces, and residual stresses. Conventionally, many researches about deformation compensation focus on cutting forces and fixture layout and do not consider clamping forces. Actually, clamping forces, which would dynamically change along with the movements of cutting tools, are essential in precision machining process. In this paper, a novel dual-point clamper method with adaptive deformation compensation is proposed to improve the workpieces milling precision. Based on the Generalized Principle of Superposition Method, a mathematical model considering the deflection from both cutting forces and clamping forces has been estimated and compared with the traditional clamping scheme. Both 3D finite element model (FEM) based simulation experiments and experimental case studies are carried out, and their results show good agreement with each other. The deflection computation and prediction from numerical studies indicates the efficiency and correctness of the proposed approach.
Keywords: Compensation; Deformation; Fixture; Milling
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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.
NUMERICAL AND EXPERIMENTAL VALIDATION OF CHIP MORPHOLOGYIAEME Publication
The extensive research studies are used to divination the behavior of complex
Metal cutting processes. The cutting parameters such as speed, feed and force play
important role on conform chip morphology. The experimental techniques for
investigation the chip morphology is expensive and time consuming. To overcome
these difficulties Finite element modeling and simulation process are used as effective
tool to divination the effect of cutting variables. In the present study FEA simulation
process model is developed to divination the chip morphology and cutting forces in
turning of Al-6061 with WC tool. Johnson cook material models are considered for
visco-elastic material behavior. The obtained simulation process results are compared
with experimental process results
NUMERICAL AND EXPERIMENTAL VALIDATION OF CHIP MORPHOLOGYIAEME Publication
The extensive research studies are used to divination the behavior of complex
Metal cutting processes. The cutting parameters such as speed, feed and force play
important role on conform chip morphology. The experimental techniques for
investigation the chip morphology is expensive and time consuming. To overcome
these difficulties Finite element modeling and simulation process are used as effective
tool to divination the effect of cutting variables. In the present study FEA simulation
process model is developed to divination the chip morphology and cutting forces in
turning of Al-6061 with WC tool. Johnson cook material models are considered for
visco-elastic material behavior. The obtained simulation process results are compared
with experimental process results
Finite Element Simulation Analysis of Three-Dimensional Cutting Process Based...IJRES Journal
Metal cutting process is a complicated process of plastic deformation and the finite element
method is used to simulate the cutting process. Chip is an important product of the cutting process, it has
important significance to analysis of it's formation process and influence factors in the research of material
processing performance, cutting tool optimization, etc..In this paper, the three-dimensional orthogonal and
oblique cutting models were established based on Johnson-Cook material constitutive models and damage laws.
The formation process of chip was analyzed according to the metal simulation cutting process, the influence of
cutting variables (Cutting depth, Cutting speed, Work piece thickness)on chip was analyzed based on the status
of chip.
Effects of Cutting Tool Parameters on Surface Roughnessirjes
This paper presents of the influence on surface roughness of Co28Cr6Mo medical alloy machined
on a CNC lathe based on cutting parameters (rotational speed, feed rate, depth of cut and nose radius).The
influences of cutting parameters have been presented in graphical form for understanding. To achieve the
minimum surface roughness, the optimum values obtained for rpm, feed rate, depth of cut and nose radius were
respectively, 318 rpm, 0,1 mm/rev, 0,7 mm and 0,8 mm. Maximum surface roughness has been revealed the
values obtained for rpm, feed rate, depth of cut and nose radius were respectively, 318 rpm, 0,25 mm/rev, 0,9
mm and 0,4 mm.
Implementation of Response Surface Methodology for Analysis of Plain Turning ...IJERD Editor
This paper investigates the effect of cutting speed, feed rate and depth of cut on the surface roughness of mild steel material with turning process. The response surface methodology (RSM) was employed in the experiment. The investigated turning parameters were cutting speed (CS) (1150, 850m/min), feed rate (FR) (1 and 0.5 mm/rev) and depth of cut (DOC) (1.0 and 0.5 mm) and no. of cuts(NOC) (2 and 1). The results showed that the interaction between the feed rate and depth of cut, was the primary factor controlling surface roughness. The responses of various factors were plotted using a three-dimensional surface graph. The optimum condition required for minimum surface roughness(SR) include cutting speed of 1150 m/min, feed rate of 1 mm/rev, axial depth of cut of 0.5 mm and no. of cut 1. With this optimum condition, a surface roughness of 0.280μm was obtained. The methodology for above experimentation is presented in this paper along with results and interpretation.
Prediction of surface roughness in high speed machining a comparisoneSAT Publishing House
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
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.
Sheet Metal Micro Forming: Future Research PotentialsIDES Editor
The paper is aimed to discuss some relevant issues
concerning an innovative sheet metal forming technology,
namely Single Point Incremental Forming. The advantages of
this technology are addressed, including its capability to provide
effective answers to some impellent industrial requirements:
process flexibility, strong customer orientation, production of
highly differentiated goods at low industrial costs. As well some
relevant drawbacks are highlighted, mainly as concerns the
level of accuracy permitted by the process. A wide recognition
of the research efforts in this field is presented, taking into
account some general considerations on the difference sources
of shape and dimensional errors, as well as the influence of the
most relevant parameters. Finally, some strategies for error
minimisation are presented and discussed
Similar to Estimation andexperimentalvalidationofcuttingforcesinball endmilling (20)
1. Short Communication
Estimation and experimental validation of cutting forces in ball-end milling
of sculptured surfaces
Yuwen Sun , Fei Ren, Dongming Guo, Zhenyuan Jia
Key Laboratory for Precision and Non-Traditional Machining Technology of the Ministry of Education, Dalian University of Technology, Dalian 116024, China
a r t i c l e i n f o
Article history:
Received 29 April 2009
Received in revised form
31 July 2009
Accepted 31 July 2009
Available online 12 August 2009
Keywords:
Cutting forces
Chip thickness
Sculptured surface machining
Ball-end mill
a b s t r a c t
Chip thickness calculation has a key important effect on the prediction accuracy of accompanied cutting
forces in milling process. This paper presents a mechanistic method for estimating cutting force in ball-
end milling of sculptured surfaces for any cases of toolpaths and varying feedrate by incorporation into a
new chip thickness model. Based on the given cutter location path and feedrate scheduling strategy, the
trace modeling of the cutting edge used to determine the undeformed chip area is resulted from the
relative part-tool motion in milling. Issues, such as the selection of the tooth tip and the computation of
the preceding cutting path for the tooth tip, are also discussed in detail to ensure the accuracy of chip
thickness calculation. Under different chip thicknesses cutting coefficients are regressed with good
agreements to calibrated values. Validation tests are carried out on a sculptured surface with curved
toolpaths under practical cutting conditions. Comparisons of simulated and experimental results show
the effectiveness of the proposed method.
2009 Elsevier Ltd. All rights reserved.
1. Introduction
Ball-end milling is widely used in machining parts with curved
geometries such as die mould, propellers and turbine blades.
Regardless of the emergence of many advanced CAM systems,
machining of complicated surfaces is still identified as a challenge.
This partly contributes to high demand for tolerance, roughness or
productivity of machined parts and partly to the machinability of
difficult-to-cut materials. For this end, cutting force modeling has
become an essential step to understand the behavior of cutting
process and further to ensure the stability of machining system
and the optimization of process parameters.
Some strategies have been addressed for the prediction of
cutting forces. Kim et al. [1] analyzed the relationship between
undeformed chip geometry and the cutter feed inclination angle.
Cutting forces acting on the engaged cutting edge elements were
calculated using an empirical method. Then the resultant cutting
force was calculated by numerical integration of cutting forces
acting on the engaged cutting edge elements. Fontaine et al. [2]
researched the effect of tool–surface inclination on cutting forces
in ball-end milling, and presented a milling force model based on
a thermo-mechanical modeling of oblique cutting. Lazoglu [3]
presented a new mechanistic model, which has the ability to
calculate the workpiece/cutter intersection domain automatically,
for the prediction of cutting forces in ball-end milling. Further-
more, an analytical approach was used to determine the
instantaneous chip load and cutting forces. Lamikiz et al. [4]
estimated the cutting force in inclined surface machining based
on a semi-mechanistic force model. The undeformed chip for the
slope cutting was calculated as the same as the horizontal case by
means of a special reference system, composed by three
directions: feed direction, normal to machining surface and vector
cross-product of both. The coefficients of the semi-mechanistic
force model were obtained from horizontal slot cutting tests with
different cutting conditions. Imani et al. [5] developed a simula-
tion system for ball-end milling. A modified chip model was
represented based on the effect of vertical component of feed on
the chip thickness. And a commercial solid modeler was used to
automatically extract the critical geometric information required
for the physical simulation. Naserian et al. [6] introduced a static
rigid force model to estimate cutting forces of sculptured surface.
In the model, the approximated equation of chip thickness was
derived from the same fundamental basis as in [5]. Most of the
past researches are based on the premise that cutting force is
viewed as a product of a coefficient and undeformed chip
thickness. Some methods have been proposed for calibrating
milling force coefficients by different authors [7–9], and the chip
thickness is basically calculated with the classic approximation
formula tn ¼ fz sin c sin k.
The increasing number of researches [10–20] on simulation of
milling process highlights the importance of cutting force model
for machining process plan and optimization. Undeformed chip
thickness has become a critical factor of affecting the prediction
accuracy of cutting forces. Li et al. [21] found the classical chip
thickness model assumes that the tooth path is circular and thus
lacks accuracy. They developed a new model for the undeformed
ARTICLE IN PRESS
Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/ijmactool
International Journal of Machine Tools Manufacture
0890-6955/$ - see front matter 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijmachtools.2009.07.015
Corresponding author.
E-mail addresses: xiands@dlut.edu.cn (Y. Sun), renfei_dl@yahoo.com.cn (F. Ren).
International Journal of Machine Tools Manufacture 49 (2009) 1238–1244
2. ARTICLE IN PRESS
chip thickness in horizontal milling. A transcendental equation
was then derived to calculate the underformed chip thickness.
Kumanchik and Schmitz [22] also gave an analytic expression for
chip thickness while considering factors such as the cycloidal
motion of teeth, and uneven teeth spacing. In the model, line feed,
tool rotational speed, and radius associated with milling were
combined into a single, non-dimensional parameter. Sai et al. [23]
noted very little work has been done in research of modeling of
chip thickness in circular interpolation. They described a method
for calculating the instantaneous undeformed chip thickness in
face milling case of circular interpolation and it was compared
with the case of linear interpolation.
Serval improvements have been proposed in linear or arc
interpolation for some specificed ball-end milling cases. However,
there are few literaterures on modeling of chip thickness
for curved geometrics, varying feed and toolpath in parameteric
interploation. Despite the influence of factors in real milling,
from theoretical analysis the existing chip thickness models
inevitablely brings errors to the solution in ideal status in milling
freeform surface along curved path with adaptive feed. It is
essential to further improve the prediction accuracy of cutting
forces and algorithms to concrete implementions for sculptured
surface machining. Hence, we present an approach to estimating
cutting forces based on a new undeformed chip thickness model
derived from the relative tool-part motion analysis in milling.
2. Proposed method
The prediction of cutting forces consists of three steps in the
developed force model. First, a new chip thickness model is
proposed by analyzing the relative tool-part motion so that it is
able to handle the combined effects of toolpath pattern, feedrate
schedule and tool geometry. In the second step a special
procedure to Z-map model is applied for efficient extraction of
the engaged cutting edge. At last, differential cutting forces of
each engaged segment are obtained and integrated to determine
the resultant cutting force based on the calibrated cutting force
coefficients.
As shown in Fig. 1, according to the premise that the cutting
force is proportional to undeformed chip area, the tangential (dFt),
radial (dFr), axial (dFa) components of differential cutting force are
modeled as follows:
dFmðyÞ ¼ Km dAðcij; y; kÞ ð1Þ
where m ¼ t, r, a, Km (N/mm2
) denote the calibrated milling force
coefficients, dA can be calculated as
dAðcij; y; kÞ ¼ tnðcij; y; kÞ db ð2Þ
cijðy; zÞ ¼ y þ ði 1Þjc þ bjðzÞ ð2aÞ
jc ¼ 2p=Nf ð2bÞ
bjðzÞ ¼ zj tanði0Þ=R0 ð2cÞ
where zj denotes the z coordinate component of the jth segment of
the cutting edge in Tool Reference System, tn is the undeformed
chip thickness, and db is the height of axial disc segment.
2.1. Undeformed chip thickness calculation
At the moment during the tool-part engagement, as shown in
Fig. 2, the undeformed chip thickness can be calculated with the
following form by finding the intersection point Q between the
path left by the previous cutting edge and line segment CP
perpendicular to the cutter axis C–C and through the current
cutting point P
tn ¼ JQPJ ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðXP XQ Þ2
þ ðYP YQ Þ2
q
ð3Þ
In this manner, two fundamental issues have to be dealt with.
One is the preceding trace modeling of cutting edge. The other is
the intersection computation of the trace with a line segment
defined by the point and related cutter axis vector. Following the
Nomenclature
(oT, x, y, z) Tool Reference System
(oG,X,Y,Z) Globe Reference System
i index of cutting edge
R0 tool radius
y cutter rotational angle
b lag angle
dA undeformed chip area
Kt, Kr, Ka cutting force coefficients
c rotational angle of a point on the cutting edge
dFt, dFr, dFa differential cutting forces in tangential, radial, and
axial directions system
j index of discrete element of cutting edge
i0 nominal helix angle
jc flute spacing angle
Nf number of cutting flute
F feed speed
N rotational speed of spindle
fz feed per tooth
k positioning angle between a point on the flute and
the z-axis in vertical plane
(XQ, YQ, ZQ) position of intersection point Q in globe reference
system
(XP, YP, ZP) position of current cutting point P in globe reference
system
Fig. 1. Geometrical model of ball-end milling process.
Y. Sun et al. / International Journal of Machine Tools Manufacture 49 (2009) 1238–1244 1239
3. ARTICLE IN PRESS
kinematics of the cutter with respect to the workpiece, the
trajectory surface of cutting edge can be derived which naturally
contains the combined effects of feedrate, toolpath patterns
and cutter geometry. The preceding trace at the z-plane is
just the intersection curve of the trajectory surface of the
preceding cutting edge and the plane. Then, the intersection
point is determined using the line segment/curve intersection
algorithm.
2.1.1. Trajectory of cutting edge in milling
Let rCL(u) ¼ {XCL(u),YCL(u),ZCL(u)} be a given cutter location
path along which the cutter performs the rotational and
translational motion. F(u) is the feed velocity of the cutter with
respect to path parameter u. According to the relative tool-part
motion analysis, the kinematic equation of an arbitrary point on
the cutting edge defined in Global Reference System is established
as follows:
rCE
ðtÞ ¼ rCLðuðtÞÞ þ BðyðtÞÞCðzÞ ð4Þ
where rCE
(t) represents the trajectory of the point at the
time moment t; B(y) is the rotation matrix of the cutter with
y ¼ 2pNt. In Tool Reference System, the position of the point is
given by
CðzÞ ¼
RðzÞ sin ði 1Þjc þ
z tan i0
R0
RðzÞ cos ði 1Þjc þ
z tan i0
R0
z
2
6
6
6
6
6
4
3
7
7
7
7
7
5
ð5Þ
where z is the z coordinate component of the point in Tool
Reference System, R(z) is the radius of the section circle of the
cutter at the z-plane perpendicular to the tool axis vector, as
provided in the following form:
RðzÞ ¼ R0 zZR0
RðzÞ ¼ R0
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
z
R0
1
2
s
zoR0
8
:
ð6Þ
To guarantee the synchronization of two motion processes, it is
necessary to derive the relationship between parameter u and
time t. The mathematical formulation is given as
drCLðuÞ
dt
¼
drCL
du
du
dt
¼ FðuÞ
r0
CLðuÞ
jr0
CLðuÞj
ð7Þ
r0
CLðuÞ
du
dt
¼ FðuÞ
r0
CLðuÞ
jr0
CLðuÞj
ð8aÞ
jr0
CLðuÞjdu ¼ FðuÞdt ð8bÞ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðdXCL=duÞ2
þ ðdYCL=duÞ2
þ ðdZCL=duÞ2
q
FðuÞ
du ¼ dt ð8cÞ
2.1.2. Preceding trace for a point on the cutting edge
For a point on the current engaged cutting edge, there are two
necessary and sufficient conditions to determine those points on
the preceding trace: (I) satisfying Eq. (4) and (II) having the same Z
coordinate component as the specified point on the current
engaged cutting edge in Globe Reference System. Based on
Eqs. (4), (8a)–(8c) and Z coordinate component of the engaged
point, a mathematical equation can be derived to describe the
preceding trace for the point P whose coordinate components are
labeled as XP, YP and ZP in Global Reference System.
rPT
P ðt
Þ ¼ rCLðuðt
ÞÞ þ Bðyðt
ÞÞCðzðt
ÞÞ ð9Þ
where rPT
P ðt
Þ represents the preceding trace for P with regard to
parameter t*; z(t*) denotes the z coordinate component of the
point on the preceding trace in Tool Reference System.
zðt
Þ ¼ ZP ZCLðuðt
ÞÞ þ R0 ð10Þ
where ZCL(u(t*)) represents the Z coordinate component of the
cutter location point at t* in Global Reference System; t*A[t0,t], t
denotes the moment when the cutting point P is intersected with
the workpiece.
t0 ¼ t
i
N
ð11Þ
where i* represents the specified number of backward revolutions
of the cutter and satisfies i*A{1, 2, y}.
2.1.3. Intersection point calculation
As shown in Fig. 2, to calculate the undeformed chip thickness,
the intersection point Q between the preceding trace and the line
segment CP must be known first. Let rCE
P be a vector of the point P
intersected with the workpiece at t. rP
CLis the corresponding cutter
location point at the moment. Then the following expression can
be derived to construct the line segment
sðtÞ ¼ tfrP
CL ta½ðrP
CL rCE
P Þ tag þ ð1 tÞrCE
P ð12Þ
where s(t) represents the line segment with regard to t,tA[0,1]; ta
denotes the cutter axis vector and satisfies ta ¼ [0,0,1]T
in 3-axis
milling. Thus, the intersection point is derived as follows:
rPT
P ðt
Þ sðtÞ ¼ 0 ð13Þ
Due to the implicit relationship between t* and t, numerical
approach is needed to solve the equation. In this case, a geometric
transformation is performed on the preceding trace and the line
OG
X
Y
Z
Preceding trace
Current trace
Cutter geometry at the
cutting moment
Z = ZP section plane
C
P
Q
Current cutter axis
tn
Cutting Direction
Fig. 2. Schematic diagram of undeformed chip thickness calculation.
Y. Sun et al. / International Journal of Machine Tools Manufacture 49 (2009) 1238–1244
1240
4. ARTICLE IN PRESS
segment to convert the issue of curve/line segment intersection
into that of determining the root of an equation. Let b be the
vector angle between the direction vector of line segment CP and
the X component of Global Reference System, then
b ¼ cos1 wP rCE
P
jwP rCE
P j
!
ðvXÞ
#
0rbrp ð14Þ
with vX ¼ [0,0,1]T
. Since both preceding trace rPT
P ðtÞ and line
segment s(t̄) are located on the plane perpendicular to the Z-axis
of the Global Reference System in 3-axis milling, the intersection
point can be determined by solving the equation Y^
r
PT
P
¼ 0 with
subject to X^
r
PT
P
rjwP rCE
P j where X^
r
PT
P
and Y^
r
PT
P
are coordinate
components of a point on transformed preceding trace in Global
Reference System
^
r
PT
P ¼ RotðZ; bÞ ðrPT
P rP
CLÞ ð15Þ
with
RotðZ; bÞ ¼
cos ðbÞ sin ðbÞ 0
sin ðbÞ cos ðbÞ 0
0 0 1
2
6
4
3
7
5
where b ¼ b if the point P is in quadrant I; b ¼ bp in
quadrant II; b ¼ pb in quadrant III and b ¼ b in quadrant IV.
The iteration scheme can be used to solve Eq. (13). The
transformed point P and the negative X direction are selected
as starting iteration point and search direction, respectively. In
special cases, more than one intersection points may exist.
The Bezier clipping technology [24] can be used to find all the
intersection points (Q1, Q2, y) and a set of possible undeformed
chip thicknesses are obtained (tn
1
, tn
2
, y). The desired chip
thickness is determined by
tn ¼ mintl
nðl ¼ 1; 2; . . .Þ ð16Þ
2.2. Engaged cutting edge
Z-Map model is used to determine whether a differential
cutter element is intersected with the workpiece at the moment
of machining. The workpiece is meshed into small grids whose
projection into the XoGY plane is square. In general cases,
the engaged cutter element can be achieved according to the
difference between the cutter element and the projection of the
instantaneous workpiece height into the cutter element.
With consideration of adaptive feedrate schedule, varied work-
piece geometry feature and curved toolpath pattern, more
than one cutter element may cut a grid for each tool movement.
In this case, re-computing each projection of instantaneous
workpiece heights into cutter elements is time consuming.
To counteract the situation, in computing the mesh grids can
be viewed as a set of planes. For each mesh grid, the engaged
cutter elements are those not only they are below the related
plane, but also their projections are located into the correspond-
ing squares as shown in Fig. 3. Repeating the process, the lengths
of cutting edges and the workpiece surface topography can be
obtained.
2.3. Cutting force estimation
The tangential, radial and axial cutting forces of each cutter
disk element are calculated with Eq. (1). In Tool Reference System,
components of differential cutting forces are expressed as
ðdFx; dFy; dFzÞT
¼ A ðdFt; dFr; dFaÞT
ð17Þ
where the matrix A is defined as
A ¼
cos ðcÞ sin ðcÞsin ðkÞ sin ðcÞcos ðkÞ
sinðcÞ cosðcÞsinðkÞ cosðcÞcosðkÞ
0 cosðkÞ sinðkÞ
2
6
4
3
7
5
To obtain the resultant force, it is necessary to perform a
numerical integration along the cutting edge engaged in cutting
process. The engagement conditions of differential cutting
elements are used for the estimation of boundaries of the
integration. By summing up the differential cutting forces for all
in-cutting differential cutting elements, the total cutting forces
are finally determined.
2.4. Cutting coefficient calibration
Precondition to acquiring the cutting force is that the cutting
coefficients should be known. For a specified cutter, part material
and cutting conditions, the cutting coefficients can be calibrated
with experimental data. In this work, one planar milling test was
conducted in milling aluminum 2024-T6 with a vertical CNC
milling machine. Cutting parameters are appropriately selected to
ensure single cutting edge engagement during machining so that
it can guarantee the synchronization between measured cutting
forces and those predicted. At a given cutter rotational angles y*,
for each engaged differential cutter element (j ¼ 1, 2, y, q), the
proposed method is used to determine the instantaneous
undeformed chip thickness t*n(j). By means of instantaneous
average chip thickness, t
nis calculated and then used to calibrate
the coefficients with the corresponding measured instantaneous
cutting forces. According to Eqs. (1), (2) and (17), coefficients
oG
X
Y
Z
Meshed work-piece
CL-path
Discrete cutting
points
Points engaged
in cutting Projection of meshed
work-piece
Grids connecting
with incut edge
A
B
C
D
C'
D'
A'
B'
Fig. 3. Illustration of the Z-map model.
Y. Sun et al. / International Journal of Machine Tools Manufacture 49 (2009) 1238–1244 1241
5. ARTICLE IN PRESS
related to t
n can be obtained as follows:
½Ktðy
ÞKrðy
ÞKaðy
ÞT
¼
1
tndb
X
q
j¼1
A
0
@
1
A
1
½FXðy
ÞFY ðy
ÞFZðy
ÞT
ð18Þ
When the cutter rotates to kjc (k ¼ 1, 2, y, Nf), the angular
position of cutting edge is the same as the one at y*. Thus, the
average value of measured cutting forces can be used to reduce
random errors. Repeat the process for different cutter rotational
angles, relationship between cutter coefficients and the unde-
formed chip thickness is subsequently established.
3. Model validation
3.1. Comparison validation
To investigate the differences between the proposed under-
formed chip thickness model and the classical one, three
numerical cases are simulated where the cutter moves along the
given toolpaths with R0 ¼ 12 mm, N ¼ 600 rpm and fz ¼ 0.25 mm
feed per tooth. During the process, undeformed chip thickness of
specified points on the cutting edge is calculated using the two
methods. Position angles k of the points are selected as
k1 ¼ k3 ¼ 57.61 and k2 ¼ 34.21 where the subscript denotes cases
I, II and III, respectively. Errors of the existing method with respect
to the proposed one are illustrated in Fig. 4. From the figure it can
be seen that the error curves show different shapes and
magnitude ranges in the whole range of the rotational angle
cA[0,p] of the specified point. Case I simulates the simplest
cutting process and the error varies following a quasi-sinusoid
curve. In most region of the rotational angle c, the results
calculated by the existing method are larger than the one
calculated by the proposed method, which may be resulted from
the difference between the circular cutting trace used in the
existing method and the real trace generated by the relative tool-
part motion. In terms of varied feed directions, in case III the
distributions of errors dramatically change with respect to case I,
which shows that feed direction plays a vital role in defining
the chip geometry. The combined effects of the feed direction
and the sectional circle radius of the specified point are illustrated
in case II.
Designed toolpath Preceding trace on the plane perpendicular
to cutter axis from specified point
Designed toolpath
Position angle of specified points for
Case I, II and III
Tooth trajectory
Toolpath
Chip thickness in
one tool revolution
Case III
Tooth trajectory
Toolpath
Chip thickness in
one tool revolution
Approximation error patterns
0
-0.08
30 60 120 180
-0.06
0
0.02
0.04
tooth position angle (Deg.)
approximation
error
(mm)
-0.04
-0.02 Case I
Case III
Case II
Eap
tn
ap
tn
pr
Specified points for Case I and III
Specified point for
Case II
z
x
OT
57.6
34.2
G
o
X
Y
Z
Case II
Case III
Equation of the curve:
Tooth trajectory
Toolpath
Chip thickness in
one tool revolution
Case I
Case II
150
90
= -
Fig. 4. Error analysis between the existing and the proposed undeformed chip thickness model.
0 360
-800
-400
0
400
800
1200 Predicted by existing method
Measured
Predicted by proposed method
Cutting rotational angle (Deg.)
Cutting
force
(N)
Fz
Fy
Fx
60 120 180 240 300
Fig. 5. Comparisons of measured cutting forces and predicted cutting forces with
two methods.
Y. Sun et al. / International Journal of Machine Tools Manufacture 49 (2009) 1238–1244
1242
6. ARTICLE IN PRESS
Compared with the existing model, more accurate chip geometry
is derived by the proposed method. To validate this, a standard
horizontal slot cutting experiment is conducted. Measured cutting
forces and predicted cutting forces are shown in Fig. 5. It can be seen
that cutting forces predicted by the proposed method agrees well
with the measured results, and the maximum relative error of peak
cutting forces is less 5%. However, using the existing model, the
relative errors are about 12% and even more. It also shows the
necessity of using the proposed method in sculptured surface
machining for varying feedrate and curved toolpaths.
3.2. Curved surface milling validation
Validation tests are conducted to testify the proposed method
under real machining conditions. During cutting tests, down-
milling process are carried out without coolant. Workpiece
material is aluminum alloy 2024-T6. The spindle speed is set as
1000 rpm and the depth of cut is 1 mm. The cutter is made to
machine along sinusoidal type cutter paths on a curved surface
expressed as
rðu; vÞ ¼ ð125u; 20 cosðpvÞ; 10 sinðpvÞÞ where ðu; v 2 ½0; 1Þ ð19Þ
Fig. 6 shows the measured and predicted force signals for
sculptured surface machining as well as the detailed views of
cutting forces. From the figures of measured cutting forces,
it can be seen that there exist fluctuations of cutting forces
within a relatively low magnitude range, which are mainly
ascribed to the tool run-out, the dynamic characteristics of the
cutting system, possible influences from the adjacent working
machines in real workshop environment, and the uncertain
factors of the piezoelectric dynamometer. Regardless of these
error sources, results obtained from the experiments prove the
validity of the proposed model in different machining cases.
The magnitude and shape of predicted cutting forces have
good agreements with those of measured forces in validation
test, and the relative errors of peak cutting forces are controlled
within 10% in most milling regions. Unlike iso-parametric
path, this kind of wave-like path has obvious change of feed
direction that is helpful in investigating the influence of
feed direction on the prediction accuracy of cutting forces.
From tested results we can see that in some cutting moments
the chip thickness calculated by the proposed method is different
from each other, even under the same cutter rotational angle
and the engagement region of cutting edge and workpiece.
That is to say, except for the local geometry of part and feedrate,
cutting direction also affects the shape and magnitude of cutting
force. The proposed method has the ability to calculate the
difference of the chip thickness under varying machining
conditions.
Machined geometry
Detail
view
of
measured
and
predicted
cutting
forces
Cutting
force
(N)
z
F
y
F
x
F
Measured
Force
Predicted
Force
Cutting
force
(N)
Fig. 6. Measured cutting force, shape and predicted cutting forces, shapes in validation test.
Y. Sun et al. / International Journal of Machine Tools Manufacture 49 (2009) 1238–1244 1243
7. ARTICLE IN PRESS
4. Conclusions
This paper represents a mechanistic approach to estimate
cutting forces in ball-end milling of sculptured surfaces. On the
basis of driving the kinematic trace expression of cutting edge in
machining, an undeformed chip thickness model is established
which is able to handle cases with complex part geometry, varying
feedrate and various toolpath patterns. Cutting coefficients are
calibrated from the proposed chip thickness model. The relation-
ship between the cutting coefficient and the chip thickness is
established, and resultant cutting forces in milling are then
predicted. Comparison validation with the existing method and
curved surface milling experiments on machining aluminum
2024-T6 are reported. It is shown that the predictions of cutting
forces have good agreements with the experimental results, even
though different types of cutter location paths and curved
geometry are applied. Meanwhile, the accuracy improvement of
the proposed method is not accompanied with the obvious
increase of computing time. Although the proposed chip thickness
model is established for ball-end cutter, it can be easily applied to
other type general cutter such as cylindrical milling cutter. The
proposed approach is capable of using in the prediction of cutting
forces in sculptured surface machining with varying feedrate,
depth of cut and geometrically complex toolpath. It is a feasible
alternative especially in some cases that will result in the
imperfection of predicted cutting forces using the classic
undeformed chip thickness. However, mechanistic modelling of
5-axis milling and cutting force-based feedrate schedule have not
been considered currently. They need to be researched further.
Acknowledgements
This research is supported by NSFC (50775023), NCET
(NCET-8-0081) and National Basic Research Program of China
(2005CB724100).
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