Generalized Modeling of Milling Mechanics and Dynamics: Part I — Helical End Mills

1999 ◽  
Author(s):  
Serafettin Engin ◽  
Yusuf Altintas
Keyword(s):  
Cutting Forces ◽  
Chip Thickness ◽  
Milling Process ◽  
Cutting Edge ◽  
End Mill ◽  
Edge Point ◽  
Stability Lobes ◽  
End Mills ◽  
Helical Flute ◽  
Cutting Point

Abstract Variety of helical end mill geometry is used in industry. Helical cylindrical, helical ball, taper helical ball, bull nosed and special purpose end mills are widely used in aerospace, automotive and die machining industry. While the geometry of each cutter may be different, the mechanics and dynamics of the milling process at each cutting edge point are common. This paper presents a generalized mathematical model of most helical end mills used in industry. The end mill geometry is modeled by helical flutes wrapped around a parametric envelope. The coordinates of a cutting edge point along the parametric helical flute are mathematically expressed. The chip thickness at each cutting point is evaluated by using the true kinematics of milling including the structural vibrations of both cutter and workpiece. By integrating the process along each cutting edge, which is in contact with the workpiece, the cutting forces, vibrations, dimensional surface finish and chatter stability lobes for an arbitrary end mill can be predicted. The predicted and measured cutting forces, surface roughness and stability lobes for ball, helical tapered ball, and bull nosed end mills are provided to illustrate the viability of the proposed generalized end mill analysis.

scholarly journals Mechanics and Dynamics of Serrated End Mills

Manufacturing ◽  
2002 ◽  
Author(s):  
S. Doruk Merdol ◽  
Yusuf Altintas
Keyword(s):  
Time Domain ◽  
Cutting Forces ◽  
Chip Thickness ◽  
Cutting Edge ◽  
Chatter Stability ◽  
Edge Point ◽  
Oblique Cutting ◽  
Edge Geometry ◽  
End Mills ◽  
Chatter Stability Lobes

Mechanics and dynamics of serrated milling cutters are presented in the article. The serrated flute design knots are fitted to a cubic spline, which is then projected on helical flutes. Cutting edge geometry at any point along the serrated flute is represented by its immersion angle and tangent vectors in radial, tangential and helix directions. The chip thickness removed by each cutting edge point is determined by using previously proposed exact kinematics of dynamic milling. The cutting forces are evaluated by orthogonal to oblique cutting mechanics transformation. The experimentally proven model is able to predict the cutting forces and chatter stability lobes in time domain.

Mechanics and Dynamics of Serrated Cylindrical and Tapered End Mills

2004 ◽  
Vol 126 (2) ◽  
pp. 317-326 ◽  
Author(s):  
S. D. Merdol ◽  
Y. Altintas
Keyword(s):  
Cutting Forces ◽  
Chip Thickness ◽  
Cutting Edge ◽  
Chatter Stability ◽  
Edge Point ◽  
Edge Geometry ◽  
Proposed Model ◽  
Chatter Vibrations ◽  
End Mills ◽  
Chatter Stability Lobes

Serrated end mills are effectively used in suppressing chatter vibrations in roughing operations. Mechanics and dynamics of serrated cylindrical and tapered helical end mills are presented in the article. The serrated flute design knots are fitted to a cubic spline, which is then projected on helical flutes. Cutting edge geometry at any point along the serrated flute is represented by its immersion angle and tangent vectors in radial, tangential and helical directions. The chip thickness removed by each cutting edge point is determined by using exact kinematics of dynamic milling. The cutting forces are evaluated by orthogonal to oblique cutting mechanics transformation. The experimentally proven model is able to predict the cutting forces and chatter stability lobes in time domain. It is shown that the proposed model can be used in evaluating the performance of serrated end mills during their stage.

Mechanism of Cutting Force and Surface Generation in Dynamic Milling

1991 ◽  
Vol 113 (2) ◽  
pp. 160-168 ◽  
Author(s):  
D. Montgomery ◽  
Y. Altintas
Keyword(s):  
Cutting Force ◽  
Surface Finish ◽  
Cutting Forces ◽  
Chip Thickness ◽  
Dominant Frequency ◽  
Milling Process ◽  
Cutting Edge ◽  
Surface Generation ◽  
Uncut Chip Thickness ◽  
Improved Model

An improved model of the milling process is presented. The model proposes a method of determining cutting forces in five distinct regions where the cutting edge travels during dynamic milling. Trochoidal motion of the milling cutter is used in determining uncut chip thickness. The kinematics of the cutter and workpiece vibrations are modelled, which identifies the orientation and velocity direction of the cutting edge during dynamic cutting. The model allows the prediction of forces and surface finish under rigid or dynamic cutting conditions. The proposed mechanism of chip thickness, force and surface generation is proven with simulation and experimental results. It is found that when the tooth passing frequency is selected to be an integer ratio of a dominant frequency of tool-workpiece structure in milling imprint of vibrations on the surface finish is avoided.

Modeling and Simulation of Milling Force in Virtual Numerical Control Milling Process

2008 ◽  
Vol 392-394 ◽  
pp. 697-702
Author(s):  
Xiu Lin Sui ◽  
Jia Tai Zhang ◽  
Jiang Hua Ge ◽  
Ya Ping Wang ◽  
H. Yuan
Keyword(s):  
Modeling And Simulation ◽  
Chip Thickness ◽  
Milling Process ◽  
Cutting Edge ◽  
Numerical Control ◽  
Force Model ◽  
End Mill ◽  
Ball End Mill ◽  
Milling Force ◽  
Milling Force Model

A parameter equation based on cutting edge of ball-end mill is set up by analyzing the parameters of ball-end mill influence the milling force in virtual NC milling process. The relationship among elemental cutting force, instantaneous radial chip thickness and cutting edge length is analyzed, and the dynamic milling force of ball-end mill at arbitrary feed direction is established. The milling force parameter model by quadratic regression equation in different cutting conditions is built. Through experiments in NC machining center and using orthogonal combination and principal components analysis, the regression coefficients are calculated. The correctness of milling force model is testified by experiments. All these can provide theoretical basis for physics modeling and simulation of virtual numerical control milling.

Model of the instantaneous undeformed chip thickness in micro-milling based on tooth trajectory

2016 ◽  
Vol 232 (2) ◽  
pp. 226-239 ◽  
Author(s):  
Xiaohong Lu ◽  
Zhenyuan Jia ◽  
Furui Wang ◽  
Guangjun Li ◽  
Likun Si ◽  
...  
Keyword(s):  
Cutting Forces ◽  
Chip Thickness ◽  
Milling Process ◽  
Cutting Edge ◽  
Micro Milling ◽  
Undeformed Chip Thickness ◽  
Single Tooth ◽  
Extended Length ◽  
Manufacturing Errors ◽  
Tooth Cutting

Instantaneous undeformed chip thickness is one of the key parameters in modeling of micro-milling process. Most of the existing instantaneous undeformed chip thickness models in meso-scale cutting process are based on the trochoidal trajectory of the cutting edge, which neglect the influences of cutter installation errors, cutter-holder manufacturing errors, radial runout of the spindle and so forth on the instantaneous undeformed chip thickness. This article investigates the tooth trajectory in micro-milling process. A prediction model of radial runout of cutting edge is built, with consideration of the effects of the extended length of micro-milling cutter and the spindle speed. Considering the effects of cutting-edge trochoidal trajectory, radial runout of cutting edge and the minimum cutting thickness, a novel instantaneous undeformed chip thickness model is proposed, and the phenomenon of single-tooth cutting in micro-milling process is analyzed. Comparisons of cutting forces under different chip thickness models and experimental data indicate that this new model can be used to predict cutting forces.

scholarly journals Cutting Performance of Different Coated Micro End Mills in Machining of Ti-6Al-4V

Micromachines ◽  
2018 ◽  
Vol 9 (11) ◽  
pp. 568 ◽  
Author(s):  
Zhiqiang Liang ◽  
Peng Gao ◽  
Xibin Wang ◽  
Shidi Li ◽  
Tianfeng Zhou ◽  
...  
Keyword(s):  
Tool Wear ◽  
Cutting Edge ◽  
Micro Milling ◽  
End Mill ◽  
Coating Materials ◽  
Edge Chipping ◽  
Workpiece Surface ◽  
Micro End Mill ◽  
End Mills ◽  
Flank Surface

Tool wear is a significant issue for the application of micro end mills. This can be significantly improved by coating materials on tool surfaces. This paper investigates the effects of different coating materials on tool wear in the micro milling of Ti-6Al-4V. A series of cutting experiments were conducted. The tool wear and workpiece surface morphology were investigated by analyzing the wear of the end flank surface and the total cutting edge. It was found that, without coating, serious tool wear and breakage occurred easily during milling. However, AlTiN-based and AlCrN-based coatings could highly reduce cutting edge chipping and flank wear. Specifically, The AlCrN-based coated mill presented less fracture resistance. For TiN coated micro end mill, only slight cutting edge chipping occurred. Compared with other types of tools, the AlTiN-based coated micro end mill could maximize tool life, bringing about an integrated cutting edges with the smallest surface roughness. In short, the AlTiN-based coating material is recommended for the micro end mill in the machining of Ti-6Al-4V.

An accurate instantaneous uncut chip thickness model combining runout effect in micro-milling using cutters with the non-uniform helix and pitch angles

2019 ◽  
Vol 234 (5) ◽  
pp. 859-870 ◽  
Author(s):  
Qiang Guo ◽  
Yan Jiang ◽  
Zhibo Yang ◽  
Fei Yan
Keyword(s):  
Tool Path ◽  
Chip Thickness ◽  
Milling Process ◽  
Machining Process ◽  
Micro Milling ◽  
Cutter Runout ◽  
Model Combining ◽  
Key Factor ◽  
Cutting Point ◽  
Instantaneous Uncut Chip Thickness

As a key factor, the accuracy of the instantaneous undeformed thickness model determines the force-predicting precision and further affects workpiece machining precision in the micro-milling process. The runout with five parameters affects the machining process more significantly compared with macro-milling. Furthermore, modern industry uses cutters with non-uniform pitch and helix angles more and more common for their excellent properties. In this article, an instantaneous undeformed thickness model is presented regarding cutter runout, variable pitch, and helix angles in the micro-milling process. The cutter edge with the cutter runout effect is modeled. Then, the intersecting ellipse between the plane vertical to the spindle axis and the cutter surface which is a cylinder can be gained. Based on this, the points, which are used to remove the material, on the ellipse as well as cutter edges are calculated. The true trochoid trajectory for each cutting point along the tool path is built. Finally, the instantaneous undeformed thickness values are computed using a numerical algorithm. In addition, this article analyzes runout parameters’ effects on the instantaneous undeformed thickness values. After that, helix and pitch angles’ effects on the instantaneous undeformed thickness are studied. Ultimately, the last section verifies the correctness and validity of the instantaneous undeformed thickness model based on the experiment conducted in the literature.

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.

Virtual Five-Axis Flank Milling of Jet Engine Impellers: Part 1 — Mechanics of Five-Axis Flank Milling

2007 ◽  
Author(s):  
W. Ferry ◽  
Y. Altintas
Keyword(s):  
Cutting Force ◽  
Cutting Forces ◽  
Orthogonal Cutting ◽  
Chip Thickness ◽  
Friction Angle ◽  
Flank Milling ◽  
Cutting Force Prediction ◽  
Jet Engine ◽  
End Mills ◽  
Five Axis

Jet engine impeller blades are flank-milled with tapered, helical, ball-end mills on five-axis machining centers. The impellers are made from difficult-to-cut titanium or nickel alloys, and the blades must be machined within tight tolerances. As a consequence, deflections of the tool and flexible workpiece can jeopardize the precision of the impellers during milling. This work is the first of a two part paper on cutting force prediction and feed optimization for the five-axis flank milling of an impeller. In Part I, a mathematical model for predicting cutting forces is presented for five-axis machining with tapered, helical, ball-end mills with variable pitch and serrated flutes. The cutter is divided axially into a number of differential elements, each with its own feed coordinate system due to five-axis motion. At each element, the total velocity due to translation and rotation is split into horizontal and vertical feed components, which are used to calculate total chip thickness along the cutting edge. The cutting forces for each element are calculated by transforming friction angle, shear stress and shear angle from an orthogonal cutting database to the oblique cutting plane. The distributed cutting load is digitally summed to obtain the total forces acting on the cutter and blade. The model can be used for general five-axis flank milling processes, and supports a variety of cutting tools. Predicted cutting force measurements are shown to be in reasonable agreement with those collected during a roughing operation on a prototype integrally bladed rotor (IBR).

Dynamic cutting force prediction for micro end milling considering tool vibrations and run-out

2018 ◽  
Vol 233 (7) ◽  
pp. 2248-2261 ◽  
Author(s):  
Xuewei Zhang ◽  
Tianbiao Yu ◽  
Wanshan Wang
Keyword(s):  
Cutting Force ◽  
Cutting Forces ◽  
End Milling ◽  
Chip Thickness ◽  
Milling Process ◽  
Force Model ◽  
Dynamic Cutting Force ◽  
Micro End Milling ◽  
Tool Vibrations ◽  
End Milling Process

An accurate prediction of cutting forces in the micro end milling, which is affected by many factors, is the basis for increasing the machining productivity and selecting optimal cutting parameters. This paper develops a dynamic cutting force model in the micro end milling taking into account tool vibrations and run-out. The influence of tool run-out is integrated with the trochoidal trajectory of tooth and the size effect of cutting edge radius into the static undeformed chip thickness. Meanwhile, the real-time tool vibrations are obtained from differential motion equations with the measured modal parameters, in which the process damping effect is superposed as feedback on the undeformed chip thickness. The proposed dynamic cutting force model has been experimentally validated in the micro end milling process of the Al6061 workpiece. The tool run-out parameters and cutting forces coefficients can be identified on the basis of the measured cutting forces. Compared with the traditional model without tool vibrations and run-out, the predicted and measured cutting forces in the micro end milling process show closer agreement when considering tool vibrations and run-out.

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