MATHEMATICAL MODEL FOR CHIP GEOMETRY CALCULATION IN FIVE-AXIS MILLING

2015 ◽  
Vol 77 (23) ◽  
Author(s):  
Hendriko Hendriko
Keyword(s):  
Coordinate System ◽  
Inclination Angle ◽  
Mapping Technique ◽  
Depth Of Cut ◽  
Work Piece ◽  
Primary Input ◽  
Proposed Model ◽  
Engagement Angle ◽  
Scheduling Method ◽  
Five Axis

This paper presents the method to calculate the geometries of instantaneous chip in five-axis milling. The inclination angle changes in between two consecutive CC-points were taken into account in the calculation. In the first stage, the engagement angle, the axial depth of cut and cut width were determined through the mapping technique. The engagement point of the Work piece Coordinate System (WCS) was mapped to a Tool Coordinate System (TCS). In the second stage, the engagement angle and depth of cut, which were defined in the first stage were then used as a primary input to obtain the cut thickness and cut width. Two simulation tests have been presented to verify the ability of the proposed model to predict the cut geometry. The first tests revealed that the inclination angle makes the size of the cut thickness and cut width fluctuate. The cut width increased when the tool inclination angle increased. For the cut thickness, its magnitude was influenced by two effects, the orientation effect and the tooth path effect. The final result was a compromise between these two effects. In the second simulation test, the proposed model was successfully implemented to support the feedrate scheduling method.

Geometric Modeling of Cutter/Workpiece Engagements in 3-Axis Milling Using Polyhedral Models

2007 ◽  
Author(s):  
Eyyup Aras ◽  
Derek Yip-Hoi
Keyword(s):  
Cutting Forces ◽  
Geometric Modeling ◽  
Tool Path ◽  
Cutting Tool ◽  
Milling Process ◽  
Mapping Technique ◽  
Depth Of Cut ◽  
Modeling Methodology ◽  
Machining System ◽  
Engagement Angle

Modeling the milling process requires cutter/workpiece engagement (CWE) geometry in order to predict cutting forces. The calculation of these engagements is challenging due to the complicated and changing intersection geometry that occurs between the cutter and the in-process workpiece. This geometry defines the instantaneous intersection boundary between the cutting tool and the in-process workpiece at each location along a tool path. This paper presents components of a robust and efficient geometric modeling methodology for finding CWEs generated during 3-axis machining of surfaces using a range of different types of cutting tool geometries. A mapping technique has been developed that transforms a polyhedral model of the removal volume from Euclidean space to a parametric space defined by location along the tool path, engagement angle and the depth-of-cut. As a result, intersection operations are reduced to first order plane-plane intersections. This approach reduces the complexity of the cutter/workpiece intersections and also eliminates robustness problems found in standard polyhedral modeling and improves accuracy over the Z-buffer technique. The CWEs extracted from this method are used as input to a force prediction model that determines the cutting forces experienced during the milling operation. The reported method has been implemented and tested using a combination of commercial applications. This paper highlights ongoing collaborative research into developing a Virtual Machining System.

Analytical Cut Geometry Prediction for Free Form Surface During Semi-Finish Milling

2013 ◽  
Author(s):  
Hendriko ◽  
Emmanuel Duc ◽  
Gandjar Kiswanto
Keyword(s):  
Computational Time ◽  
Free Form ◽  
Depth Of Cut ◽  
Solid Model ◽  
Workpiece Surface ◽  
Engagement Angle ◽  
Rough Milling ◽  
Five Axis ◽  
Toroidal Cutter

In five-axis milling, determination of continuously changing Cutter Workpiece Engagement (CWE) is still a challenge. Solid model and discrete model are the most common method used to predict the engagement region. However, both methods are suffering with the long computational time. This paper presents an analytical method to define CWE of toroidal cutter during semi-finishing of sculpture part. The workpiece from 2.5D rough milling is represented by a number of blocks. The length of cut at every engagement angle can be determined by calculating the outermost engagement point called upper CWE point. This point was determined by first assumed that the workpiece surface is flat. A recalculation for CWE correction is then performed for the engagement occurred in two workpiece blocks. The method called Z-boundary and X-boundary are employed to obtain the upper CWE point when the engagement occurred on toroidal side. Meanwhile Cylinder-boundary method was used when the engagement occurred on the cylinder side. The developed model was examined to ensure its accuracy. A sculptured surface part was tested by comparing the depth of cut generated by the simulation developed and the depth of cut measured by Unigraphic. The result indicates that the proposed method is very accurate. Moreover, due to the method is analytically, and hence it is efficient in term of calculation time.

Geometric Modeling of Cutter/Workpiece Engagements in Three-Axis Milling Using Polyhedral Representations

2008 ◽  
Vol 8 (3) ◽  
Author(s):  
Eyyup Aras ◽  
Derek Yip-Hoi
Keyword(s):  
Cutting Forces ◽  
Geometric Modeling ◽  
Tool Path ◽  
Cutting Tool ◽  
Milling Process ◽  
Mapping Technique ◽  
Depth Of Cut ◽  
Modeling Methodology ◽  
Machining System ◽  
Engagement Angle

Modeling the milling process requires cutter/workpiece engagement (CWE) geometry in order to predict cutting forces. The calculation of these engagements is challenging due to the complicated and changing intersection geometry that occurs between the cutter and the in-process workpiece. This geometry defines the instantaneous intersection boundary between the cutting tool and the in-process workpiece at each location along a tool path. This paper presents components of a robust and efficient geometric modeling methodology for finding CWEs generated during three-axis machining of surfaces using a range of different types of cutting tool geometries. A mapping technique has been developed that transforms a polyhedral model of the removal volume from the Euclidean space to a parametric space defined by the location along the tool path, the engagement angle, and the depth of cut. As a result, intersection operations are reduced to first order plane-plane intersections. This approach reduces the complexity of the cutter/workpiece intersections and also eliminates robustness problems found in standard polyhedral modeling and improves accuracy over the Z-buffer technique. The CWEs extracted from this method are used as input to a force prediction model that determines the cutting forces experienced during the milling operation. The reported method has been implemented and tested using a combination of commercial applications. This paper highlights ongoing collaborative research into developing a virtual machining system.

Micro-Ball Endmilling of Tungsten Carbide for Micro-Molding and Prototyping Applications

2012 ◽  
Vol 516 ◽  
pp. 591-594 ◽  
Author(s):  
Muhammad Arif ◽  
Mustafizur Rahman ◽  
Yoke San Wong ◽  
Kui Liu
Keyword(s):  
Tungsten Carbide ◽  
Inclination Angle ◽  
Surface Finish ◽  
End Milling ◽  
Depth Of Cut ◽  
Work Piece ◽  
Machining Parameters ◽  
Cutting Mechanism ◽  
High Quality ◽  
Ball End Milling

This paper presents micro-ball end milling of tungsten carbide using a CBN cutter to investigate its capability for machining slots for micro-moulds. Crack-free slots were machined at different axial depths of cut by inclining the work piece surface at different angles to the spindle axes to study the influence of these machining parameters on the cutting mechanism and surface finish. The experimental results show that up to 150 µm deep slots can be finished efficiently on tungsten carbide work pieces without leaving any fracture marks. It was identified that the chip disposal ability of micro-ball end milling reduced with increase in axial depth of cut. The cutting action was more efficient in up milling cuts compared to that in down milling when machining a slot. The inclination of the work piece proved propitious for machining slots with high-quality finish on tungsten carbide work pieces and a larger inclination angle also facilitated chip disposal.

MATHEMATICAL APPROACH AND GENERAL FORMULATION FOR ERROR SYNTHESIS MODELING OF MULTI-AXIS SYSTEM

2010 ◽  
Vol 24 (15n16) ◽  
pp. 2737-2742 ◽  
Author(s):  
DONG-MOK LEE ◽  
SEUNG-HAN YANG
Keyword(s):  
Machine Tools ◽  
Geometric Model ◽  
Mathematical Formulation ◽  
Kinematic Chain ◽  
Work Piece ◽  
Kinematic Chains ◽  
Proposed Model ◽  
Local Coordinates ◽  
Error Terms ◽  
Five Axis

Improving position accuracy of multi-axis machine tools is widely researched. The best known and widely used parametric approach models the direct kinematics of the work-piece and tool kinematic chain and use error synthesis modeling composed of homogeneous transform matrix (HTM). With respect to five axis machine tools, the increase in the number of axis and consideration of different configuration make computation of error matrices difficult and result in long error equations. In addition it becomes difficult to interpret the physical meaning of error terms in these equations. This work presents a mathematical formulation of error synthesis modeling for multi-axis system with the general joint series. This formula can be applied to all possible configurations. The geometric model for an arbitrary joint is defined which is applicable to either prismatic or rotary joint. The error synthesis model for any configuration can be computed from the kinematic chains of a series of arbitrary joints. The proposed model consists of combination of error components of each local axis. Hence it is intuitive and easy to understand the effect of origin offset of local coordinates and squareness error with reference to the measurement coordinate.

Calculation of Effective Ground Depth of Cut by Means of Grinding Process Model

2011 ◽  
Vol 496 ◽  
pp. 7-12 ◽  
Author(s):  
Takazo Yamada ◽  
Michael N. Morgan ◽  
Hwa Soo Lee ◽  
Kohichi Miura
Keyword(s):  
Process Model ◽  
Ground Surface ◽  
Depth Of Cut ◽  
Grinding Wheel ◽  
Grinding Process ◽  
Wheel Wear ◽  
Elastic Deformations ◽  
Proposed Model ◽  
Effective Depth ◽  
Grinding Machine

In order to obtain the effective depth of cut on the ground surface, a new grinding process model taking into account thermal expansions of the grinding wheel and the workpiece, elastic deformations of the grinding machine, the grinding wheel and the workpiece and the wheel wear was proposed. Using proposed model, the effective depth of cut was calculated using measured results of the applied depth of cut and the normal grinding force.

Modeling and Optimization of Vibration Amplitude in Turning of Ti-6Al-4V Using Response Surface Methodology

2012 ◽  
Vol 217-219 ◽  
pp. 1567-1570
Author(s):  
A.K.M. Nurul Amin ◽  
Muammer Din Arif ◽  
Syidatul Akma Sulaiman
Keyword(s):  
Response Surface Methodology ◽  
Response Surface ◽  
Vibration Amplitude ◽  
Desirability Function ◽  
Cutting Speed ◽  
Vibration Sensor ◽  
Experimental Investigations ◽  
Depth Of Cut ◽  
Work Piece ◽  
Inferior Surface

Chatter is detrimental to turning operations and leads to inferior surface topography, reduced productivity, dimensional accuracy, and shortened tool life. Avoidance of chatter has mostly been through reliance on heuristics such as: limiting material removal rates or selecting low spindle speeds and shallow depth of cuts. But, modern industries demand increased output and not steady operational limits. Various research efforts have therefore focused on developing mathematical models for chatter formation. However, as yet there is no existent model that meets all experimental verification. This research employed a novel technique based on the synergy of statistical modeling and experimental investigations in order to develop an effective empirical mathematical model for chatter amplitude and to subsequently find optimal machining conditions. Ti-6Al-4V, Titanium alloy, was used as the work-piece due to its increased popularity in applications related to aerospace, automotive, nuclear, medical, marine etc. A sequence of 15 experimental runs was conducted based on a small Central Composite Design (CCD) model in Response Surface Methodology (RSM). The primary (independent) parameters were: cutting speed, feed, and depth of cut. The tool overhang was kept constant at 70 mm. An engine lathe (Harrison M390) was employed for turning purposes. The data acquisition system comprised a vibration sensor (accelerometer) and a signal conditioning unit. The resultant vibrations were analyzed using the DASYLab 5.6 software. The best model was found to be quadratic which had a confidence level of 95% (ANOVA) and insignificant Lack of Fit (LOF) in Fit and Summary analyses. Desirability Function (DF) approach predicted minimum vibration amplitude of 0.0276 Volts and overlay plots identified two preferred machining regimes for optimal vibration amplitude.

Experimental Determination of Optimal Speeds for Alloy Steels in Plane Turning

2008 ◽  
Author(s):  
T. Srikanth ◽  
V. Kamala
Keyword(s):  
Surface Roughness ◽  
Force Measurement ◽  
Cutting Speed ◽  
Vital Role ◽  
The Other ◽  
Depth Of Cut ◽  
Work Piece ◽  
Material Interface ◽  
Alloy Steels

In machining, speeds play vital role. The operator should know exactly the speed at which machining should be performed to get the required surface finish. In this paper, an attempt is made to determine the optimal cutting speed for machining of alloy steels. Three work piece materials having different hardness are taken and machined using a round nose tool with a coated tip. The tool dynamometer is attached to the tool post for force measurement. Turning operation on the work piece is performed on lathe at four different speeds, keeping the feed and depth of cut constant. Cutting forces acting on the tool, temperature at the tool and material interface are recorded. Power consumed being determined by a wattmeter and surface roughness values are measured. The same procedure is repeated for the other two work-pieces materials and optimal speeds for machining are determined for the three specimens. The results obtained are compared with the theoretical values and found to be very close.

scholarly journals The cutting behavior of cortical bone in different bone osten cutting angles and depths of cut

2021 ◽  
Author(s):  
Yuanqiang Luo ◽  
Yinghui Ren ◽  
Yang Shu ◽  
Cong Mao ◽  
Zhixiong Zhou ◽  
...  
Keyword(s):  
Fracture Toughness ◽  
Cutting Force ◽  
Cortical Bone ◽  
Depth Of Cut ◽  
Cutting Angle ◽  
Small Depth ◽  
Proposed Model ◽  
Cutting Processes ◽  
The Impact ◽  
Cutting Path

Abstract Cortical bones are semi-brittle and anisotropic, this brings the challenge to suppress vibration and avoid undesired fracture in precise cutting processes in surgeries. In this paper, we proposed a novel analytical model to represent cutting processes of cortical bones, and we used to evaluate cutting forces and fracture toughness, and investigate the formations of chips and cracks under varying bone osteon cutting angles and depths. To validate the proposed model, the experiments are conducted on orthogonal cuttings over cortical bones to investigate the impact of bone osteon cutting angle and depth on cutting force, crack initialization and growth, and fracture toughness of cortical bone microstructure. The experimental results highly agreed with the prediction by the proposed model in sense that (1) curly, serrated, grainy and powdery chips were formed when the cutting angle was set as 0°, 60°, 90°, and 120°, respectively. (2) Bone materials were removed dominantly by shearing at a small depth of cut from 10 to 50 µm, and by a mixture of pealing, shearing, and bending at a large depth of cut over 100 µm at different cutting orientations. Moreover, it was found that a cutting path along the direction of crack initialization and propagation benefited to suppress the fluctuation of cutting force thus reduce the vibration. The presented model has theoretical and practical significance in optimizing cutting tools and operational parameters in surgeries.

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