Modeling of Ball-End Milling Forces With Cutter Axis Inclination

1999 ◽  
Vol 122 (1) ◽  
pp. 3-11 ◽  
Author(s):  
Ismail Lazoglu ◽  
Steven Y. Liang
Keyword(s):  
End Milling ◽  
Chip Thickness ◽  
Helix Angle ◽  
Force Model ◽  
Ball End Mill ◽  
Ball End Milling ◽  
Model Predictions ◽  
Milling Forces ◽  
Analytical Force Model ◽  
Convolution Method

In the machining of sculpture surfaces with ball-end mill, the cutter axis or workpiece is often inclined to generate an admissible orientation. This paper primarily presents an enhanced cutting force model for ball-end milling with cutter axis inclination. It involves the kinematic reasoning of cutting edge geometry, local helix angle and average chip thickness followed by the analysis of effects of axis inclination in the contact zone between cutter and workpiece. Thereupon, development of the analytical force model for inclined-axis machining is achieved using cutter angle domain convolution method. Experimental evaluation of the model is discussed, and experimental results and model predictions under various cutting conditions are compared in the frequency as well as in the angular domain. [S1087-1357(00)70601-0]

Voxel Based Cutting Force Simulation of Ball End Milling Considering Cutting Edge Around Center Web

2018 ◽  
Author(s):  
Isamu Nishida ◽  
Takaya Nakamura ◽  
Ryuta Sato ◽  
Keiichi Shirase
Keyword(s):  
Cutting Force ◽  
End Milling ◽  
Chip Thickness ◽  
Previous Method ◽  
Cutting Edge ◽  
Force Model ◽  
End Mill ◽  
Uncut Chip Thickness ◽  
Ball End Mill ◽  
Tool Rotation

A new method, which accurately predicts cutting force in ball end milling considering cutting edge around center web, has been proposed. The new method accurately calculates the uncut chip thickness, which is required to estimate the cutting force by the instantaneous rigid force model. In the instantaneous rigid force model, the uncut chip thickness is generally calculated on the cutting edge in each minute disk element piled up along the tool axis. However, the orientation of tool cutting edge of ball end mill is different from that of square end mill. Therefore, for the ball end mill, the uncut chip thickness cannot be calculated accurately in the minute disk element, especially around the center web. Then, this study proposes a method to calculate the uncut chip thickness along the vector connecting the center of the ball and the cutting edge. The proposed method can reduce the estimation error of the uncut chip thickness especially around the center web compared with the previous method. Our study also realizes to calculate the uncut chip thickness discretely by using voxel model and detecting the removal voxels in each minute tool rotation angle, in which the relative relationship between a cutting edge and a workpiece, which changes dynamically during tool rotation. A cutting experiment with the ball end mill was conducted in order to validate the proposed method. The results showed that the error between the measured and predicted cutting forces can be reduced by the proposed method compared with the previous method.

Research on Feedrate Optimization Based on Cutting Force Model with Double Effect for the Ball-End Milling

2011 ◽  
Vol 291-294 ◽  
pp. 2965-2969
Author(s):  
Yu Jun Cai ◽  
Hua Shen ◽  
Tie Li Qi
Keyword(s):  
Cutting Force ◽  
End Milling ◽  
Double Effect ◽  
Machining Process ◽  
Force Model ◽  
Optimization Strategy ◽  
Cutting Force Model ◽  
Ball End Mill ◽  
Ball End Milling ◽  
Feedrate Optimization

A new cutting force model of ball-end mill with double effect is developed through analysing the machining process by using differential geometry. The cutting force model is needed to be revised for the component force in Z direction because of the offset to the actual results. The cutting force and the ball-end milling force coefficients can be given with numerical method. A feedrate optimization strategy is also proposed based on the developed cutting force model and tested effectively.

Prediction of Ball End Milling Forces

1996 ◽  
Vol 118 (1) ◽  
pp. 95-103 ◽  
Author(s):  
G. Yu¨cesan ◽  
Y. Altıntas¸
Keyword(s):  
Cutting Forces ◽  
End Milling ◽  
Chip Thickness ◽  
Cutting Conditions ◽  
Analytic Representation ◽  
Rake Face ◽  
Uncut Chip Thickness ◽  
Ball End Milling ◽  
Helical Flute ◽  
Milling Forces

Mechanics of milling with ball ended helical cutters are modeled. The model is based on the analytic representation of ball shaped helical flute geometry, and its rake and clearance surfaces. It is assumed that friction and pressure loads on the rake face are proportional to the uncut chip thickness area. The load on the flank contact face is concentrated on the in cut portion of the cutting edge. The pressure and friction coefficients are identified from a set of slot ball end milling tests at different feeds and axial depth of cuts, and are used to predict the cutting forces for various cutting conditions. The experimentally verified model accurately predicts the cutting forces in three Cartesian directions.

A Mechanistic Cutting Force Model for 3D Ball-end Milling

2000 ◽  
Vol 123 (1) ◽  
pp. 23-29 ◽  
Author(s):  
Hsi-Yung Feng ◽  
Ning Su
Keyword(s):  
Cutting Force ◽  
Cutting Forces ◽  
End Milling ◽  
Chip Thickness ◽  
Milling Process ◽  
Force Model ◽  
Cutting Force Model ◽  
Ball End Milling ◽  
End Milling Process ◽  
Force Relationship

This paper presents an improved mechanistic cutting force model for the ball-end milling process. The objective is to accurately model the cutting forces for nonhorizontal and cross-feed cutter movements in 3D finishing ball-end milling. Main features of the model include: (1) a robust cut geometry identification method to establish the complicated engaged area on the cutter; (2) a generalized algorithm to determine the undeformed chip thickness for each engaged cutting edge element; and (3) a comprehensive empirical chip-force relationship to characterize nonhorizontal cutting mechanics. Experimental results have shown that the present model gives excellent predictions of cutting forces in 3D ball-end milling.

scholarly journals Modeling and Estimation of Cutting Forces in Ball Helical Milling Process

2021 ◽  
Author(s):  
Haiyan Wang ◽  
Kexin Tao ◽  
Tian Jin
Keyword(s):  
Cutting Force ◽  
End Milling ◽  
Spherical Surface ◽  
Research Result ◽  
Chip Thickness ◽  
Milling Process ◽  
Helical Milling ◽  
Force Model ◽  
Cutting Force Model ◽  
Milling Forces

Abstract Milling forces play an important role in the milling process and are generally calculated by the mechanistic or numerical methods, reliable model of cutting force is very important for the simulation of milling process, which has big scientific significance to further improve machining quality. Ball helical milling technology is used to make holes based on the cutting principle of helical milling using ball end cutter, due to the influence of spherical surface machining characteristic, the modeling of cutting force in ball helical milling is difficult. Therefore, the main purpose of this paper is to first establish an analytical cutting force model in the ball helical milling process. Considering cutting characteristics in the axial feed, the kinematics of ball helical milling is first presented, then the chip thickness distribution in different directions along the cutting edges are predicted. Furthermore, based on the characteristics of helical milling technology and geometry shape of ball end mill and the classical mechanical cutting force model, through the study on the ball-end milling mechanics, a new relatively accurate theoretical cutting force model is established. At the same time, cutting force coefficients are identified through instantaneous force method according to the Ti-alloy experimental research result. Finally, higher simulation precision of cutting force model in ball helical milling process is received.

Cutting Force Prediction of Ball End Milling Based on Fully Voxel Representation of Cutting Edge and Instantaneous Workpiece Shape

2017 ◽  
Author(s):  
Isamu Nishida ◽  
Ryuma Okumura ◽  
Ryuta Sato ◽  
Keiichi Shirase
Keyword(s):  
Cutting Force ◽  
End Milling ◽  
Chip Thickness ◽  
Cutting Edge ◽  
Surface Shape ◽  
Uncut Chip Thickness ◽  
Ball End Milling ◽  
Voxel Model ◽  
Voxel Representation ◽  
Milling Forces

A new cutting force simulator has been developed to predict cutting force in ball end milling. This new simulator discretely calculates uncut chip thickness based on a fully voxel representation of the cutting edge and instantaneous workpiece shape. Previously, a workpiece voxel model was used to calculate uncut chip thickness under a complex change of workpiece shape. Using a workpiece voxel model, uncut chip thickness is detected by extracting the voxels removed per cutting edge tooth for the amount of material fed into the cutting edge. However, it is difficult to define the complicated shape of a cutting edge using the workpiece voxel model; the shape of the cutting edge must be defined by a mathematical expression. It is also difficult to model the voxels removed by the cutting edge when the tool posture is non-uniformly changed. We therefore propose a new method to detect uncut chip thickness, one in which both the cutting edge and the instantaneous workpiece shape are fully represented by a voxel model. Our proposed method precisely detects uncut chip thickness at minute tool rotational angles, making it possible to detect the uncut chip thickness between the complex surface shape of the workpiece and the particular shape of the cutting edge. To validate the effectiveness of our proposed method, experimental 5-axis milling tests using a ball end mill were conducted. Estimated milling forces for several tool postures were found to be in good agreement with the measured milling forces. Results from the experimental 5-axis milling validate the effectiveness of our proposed method.

Estimation of in-process cutting constants in ball-end milling

2003 ◽  
Vol 217 (1) ◽  
pp. 45-56 ◽  
Author(s):  
C M Zheng ◽  
J -J Junz Wang
Keyword(s):  
Cutting Forces ◽  
End Milling ◽  
Estimation Methods ◽  
Force Model ◽  
Average Force ◽  
Ball End Milling ◽  
Source Signal ◽  
Matrix Expression ◽  
Milling Forces ◽  
Milling Force Model

Two methods are presented for the estimation of tangential, radial and axial cutting coefficients for the shearing and ploughing mechanisms from a single set of cutting forces in ball-end milling. These estimation methods are based upon the invertibility of the analytical milling force model, which considers both the shearing and the ploughing mechanisms by incorporating their respective cutting constants in the local force model. The periodic milling forces are established as the convolution integral of the differential local cutting forces and their Fourier coefficients are derived and expressed in a matrix expression as a linear function of the unknown cutting constants in terms of cutting conditions and cutter geometry. This linear expression thus leads to a systematic formulation of the estimation methods allowing the six unknown cutting constants to be determined from the measured milling forces. The first method uses the first harmonic forces as the source signal while the second method extracts the six cutting constants from the average force as well as the first harmonics. Limitations of both estimation methods are discussed. The consistency and accuracy of the estimated cutting constants are confirmed by the experimental results.

Mechanistic Modeling of the Ball End Milling Process for Multi-Axis Machining of Free-Form Surfaces

2000 ◽  
Vol 123 (3) ◽  
pp. 369-379 ◽  
Author(s):  
Rixin Zhu ◽  
Shiv G. Kapoor ◽  
Richard E. DeVor
Keyword(s):  
End Milling ◽  
Chip Thickness ◽  
Mechanistic Modeling ◽  
Free Form ◽  
Surface Geometry ◽  
Workpiece Surface ◽  
Ball End Milling ◽  
Modeling Approach ◽  
Free Form Surfaces ◽  
Cutting Point

A mechanistic modeling approach to predicting cutting forces is developed for multi-axis ball end milling of free-form surfaces. The workpiece surface is represented by discretized point vectors. The modeling approach employs the cutting edge profile in either analytical or measured form. The engaged cut geometry is determined by classification of the elemental cutting point positions with respect to the workpiece surface. The chip load model determines the undeformed chip thickness distribution along the cutting edges with consideration of various process faults. Given a 5-axis tool path in a cutter location file, shape driving profiles are generated and piecewise ruled surfaces are used to construct the tool swept envelope. The tool swept envelope is then used to update the workpiece surface geometry employing the Z-map method. A series of 3-axis and 5-axis surface machining tests on Ti6A14V were conducted to validate the model. The model shows good computational efficiency, and the force predictions are found in good agreement with the measured data.

Analytical Convolution Model of Cutting Forces in 3-D Ball End Milling

2001 ◽  
Author(s):  
Richard Y. Chiou ◽  
Bing Zhao
Keyword(s):  
Cutting Force ◽  
Frequency Domain ◽  
Cutting Forces ◽  
End Milling ◽  
Force Model ◽  
Three Dimensional Model ◽  
Calculation Algorithm ◽  
Ball End Milling ◽  
Convolution Model ◽  
Force Calculation

Abstract This paper presents an analytical convolution model of dynamic cutting forces in ball end milling of 3-D plane surfaces. The model takes into account the instantaneous slope on a sculptured surface to establish the chip geometry in cutting force calculation algorithm. A three-dimensional model of cutting forces in ball end milling is presented in terms of material properties, cutting parameters, machining configuration, and tool/work geometry. Based on the relationship of the local cutting force, chip load and engaged boundary, the total cutting force model is established via the angle domain convolution integration of the local forces in the feed, cross feed, axial direction, and inclination angle. The convolution integral leads to a periodic function of cutting forces in the angle domain and an explicit expression of the dynamic cutting force components in the frequency domain. Following the theoretical analysis, experimental study is discussed to illustrate the implementation procedure for force identification, and frequency domain data are presented to verify the analytical results.

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