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.

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.

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.

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).

Influence of Reground Tool Sharpness on Micro-Cutting Process

2010 ◽  
Vol 37-38 ◽  
pp. 550-553
Author(s):  
Xin Li Tian ◽  
Zhao Li ◽  
Xiu Jian Tang ◽  
Fang Guo ◽  
Ai Bing Yu
Keyword(s):  
Cutting Forces ◽  
Orthogonal Cutting ◽  
Cutting Tools ◽  
Chip Thickness ◽  
Cutting Edge ◽  
Cutting Process ◽  
Micro Cutting ◽  
Temperature Distributions ◽  
Edge Radius ◽  
1045 Steel

Tool edge radius has obvious influences on micro-cutting process. It considers the ratio of the cutting edge radius and the uncut chip thickness as the relative tool sharpness (RST). FEM simulations of orthogonal cutting processes were studied with dynamics explicit ALE method. AISI 1045 steel was chosen for workpiece, and cemented carbide was chosen for cutting tool. Sixteen cutting edges with different RTS values were chosen for analysis. Cutting forces and temperature distributions were calculated for carbide cutting tools with these RTS values. Cutting edge with a small RTS obtains large cutting forces. Ploughing force tend to sharply increase when the RTS of the cutting edge is small. Cutting edge with a reasonable RTS reduces the heat generation and presents reasonable temperature distributions, which is beneficial to cutting life. The force and temperature distributions demonstrate that there is a reasonable RTS range for the cutting edge.

scholarly journals A Mathematical Modeling to Predict the Cutting Forces in Microdrilling

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Haoqiang Zhang ◽  
Xibin Wang ◽  
Siqin Pang
Keyword(s):  
Mathematical Modeling ◽  
Cutting Forces ◽  
Chip Thickness ◽  
Cutting Edge ◽  
Force Model ◽  
Cutting Mechanism ◽  
Line Field ◽  
Slip Line Field ◽  
Cutting Model ◽  
Secondary Cutting

In microdrilling, because of lower feed, the microdrill cutting edge radius is comparable to the chip thickness. The cutting edges therefore should be regarded as rounded edges, which results in a more complex cutting mechanism. Because of this, the macrodrilling thrust modeling is not suitable for microdrilling. In this paper, a mathematical modeling to predict microdrilling thrust is developed, and the geometric characteristics of microdrill were considered in force models. The thrust is modeled in three parts: major cutting edges, secondary cutting edge, and indentation zone. Based on slip-line field theory, the major cutting edges and secondary cutting edge are divided into elements, and the elemental forces are determined by an oblique cutting model and an orthogonal model, respectively. The thrust modeling of the major cutting edges and second cutting edge includes two different kinds of processes: shearing and ploughing. The indentation zone is modeled as a rigid wedge. The force model is verified by comparing the predicted forces and the measured cutting forces.

Analytical Chatter Stability of Milling With Rotating Cutter Dynamics at Process Damping Speeds

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
M. Eynian ◽  
Y. Altintas
Keyword(s):  
Chip Thickness ◽  
Prediction Method ◽  
Vibration Velocity ◽  
Chatter Stability ◽  
Process Damping ◽  
End Mills ◽  
Nyquist Stability ◽  
Matrix Differential ◽  
The Stability ◽  
Delay Matrix

This paper presents a chatter stability prediction method for milling flexible workpiece with end mills having asymmetric structural dynamics. The dynamic chip thickness regenerated by the vibrations of the rotating cutter and the fixed workpiece is transformed into the principle modal directions of the rotating tool. The process damping is modeled as a linear function of vibration velocity. The dynamics of the milling system is modeled by a time delay matrix differential equation with time varying directional factors and speed dependent elements. The periodic directional factors are averaged over a spindle period, and the stability of the resulting time invariant but speed dependent characteristic equation of the system is investigated using the Nyquist stability criterion. The stability model is verified with time domain numerical simulations and milling experiments.

scholarly journals METHOD FOR CALCULATING CUTTING FORCES BY MODELING CAD WITH A SYSTEM OF GEOMETRIC CUTTING PARAMETERS WITH RADIAL MILLS

2021 ◽  
pp. 50-57
Author(s):  
Alexander Leshchenko
Keyword(s):  
Cutting Forces ◽  
Tool Path ◽  
Cutting Parameters ◽  
Cutting Edge ◽  
Software Module ◽  
Power Characteristics ◽  
Cad System ◽  
Shaping Process ◽  
End Mills ◽  
Processing Zone

The accuracy of processing surfaces of a complex profile largely depends on the selected processing strategy, which will allow creating the same, within certain limits, power characteristics of the shaping process at the intervals of the programmed tool path. In this case, it becomes possible to include tuning modules in programs for CNC machines that form vector values of corrections in certain areas, as reactors for elastic deformations of the cutting process. Therefore, it is especially important to know the modulus and direction of the resulting cutting force vector, which does not necessarily coincide with the feed direction. The purpose of this work is to build a method for calculating cutting forces by modeling the geometric parameters of a cut with a CAD system, a cutter with a nonlinear generatrix. Solid modeling of the process is based on the Boolean operations of "intersection" and "subtraction" of 3D objects: the teeth of a radius cutter with a helical cutting edge and a workpiece "moving" at a feed rate. The tool for the implementation of this method is a software module created on the basis of API functions, the input data for which are: a 3D tool and a workpiece, the equation of the trajectory of its movement and the parameters of the infeed movement. Targeting API properties, the application makes it possible to simulate various trajectories, helical or trochoidal, when machining complex surfaces. In the future, it is possible to take into account the plastic deformation processes in the chip formation zone in the model by connecting external modules. In the course of the conducted research on milling with radial end mills with a helical cutting edge, when two or more teeth are within the arc of contact, it was determined by 3D modeling how much thickness and width the layer cuts off each of the teeth during the feed per revolution. Consequently, in the process of shaping, normal and tangential cutting forces, which are different in direction and modulus, are present as a function of the angle of rotation of the cutter. Therefore, the concept of "circumferential force on the cutter", accepted in the theory of cutting, as a certain constant component of the process, can introduce an error when considering the causes of the excitation mechanism of vibrations of different nature that arise in the processing zone.

scholarly journals Effect of Cutting Edge Geometry on Cutting Forces when Drilling Inconel 718

2017 ◽  
Vol 17 (1) ◽  
pp. 24-29 ◽  
Author(s):  
Milan Daňa ◽  
Miroslav Zetek ◽  
Václav Schorník
Keyword(s):  
Cutting Forces ◽  
Inconel 718 ◽  
Cutting Edge ◽  
Edge Geometry

Development of Micro Milling Machine and Experimental Study on Meso Scale Milling

2007 ◽  
Author(s):  
Chengfeng Li ◽  
Xinmin Lai ◽  
Hongtao Li ◽  
Linfa Peng ◽  
Jun Ni
Keyword(s):  
Chip Formation ◽  
Cutting Forces ◽  
High Speed ◽  
End Milling ◽  
Three Dimensional ◽  
Chip Thickness ◽  
Cutting Edge ◽  
Micro Milling ◽  
Milling Machine ◽  
Meso Scale

This paper develops a three-axis micro milling machine for manufacturing meso-scale components and products. This machine utilizes high-speed miniature spindle to obtain appropriate cutting velocities, and three precision linear stages with 50 nm feed resolution to supply the relative motion. The PMAC2 controller is used to control three axes simultaneously, and a piezoelectric dynamometer is mounted on the X-Y stages to measure three-dimensional cutting forces for the real-time measurement and feedback. More than 200 cutting experiments of end milling operations are performed on the developed machine. When the machined feature ranges at meso scale, the characteristics and phenomena in milling process will heavily differ from those of conventional scale milling due to the size effects. The critical differences at meso scale arise from the breakdown of the assumptions of negligible edge radius effects. The roundness of cutting edge and the runout of spindle have a crucial impact on the chip formation process and the characteristics of cutting forces. The roundness of cutting edge also induces the existence of the minimum chip thickness and the intermittency of the chip formation at a low feed per tooth.

Prediction of Cutting Forces of Solid End Mills With Differential Helix Angles: A Numerical Approach

2016 ◽  
Author(s):  
Hans-Henrik Westermann ◽  
Benjamin Thorenz ◽  
Robert Müller ◽  
Rolf Steinhilper
Keyword(s):  
Mathematical Model ◽  
Cutting Forces ◽  
Numerical Approach ◽  
Edge Length ◽  
Cutting Edge ◽  
Milling Operations ◽  
Variable Helix ◽  
Constant State ◽  
End Mills ◽  
The Mathematical Model

Solid end mills with multi-section cutting edges and variable helix angles are available for application. New types of solid end mills for low energy consumption have recently been developed. These so-called Low Power Cutting (LPC)-Tools are characterized by differential helix angles. Compared to solid end mills with variable helix angles, the new differential helix angles change their pitch continuously over the cutting edge length. Due to this fact the cutting conditions are not in a constant state during the revolution of the cutting tool. Existing mathematical approaches for the calculation of cutting forces only consider constant helix angles in milling operations. This paper describes an approach for the prediction of cutting forces for differential helix angles. The developed mathematical model is based on geometrical considerations. Due to a continuously changing pitch over the cutting edge length a numerical approach for the mathematical model is chosen.

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