Helical End Mill Research Articles

Time-averaged and Instantaneous Mechanistic Models using Artificial Force Synthesis in Helical End Milling

This paper aims to develop field-deployable mechanistic milling models with the aid of the Virtual Machining Simulation Environment (VMSE). Stabler's rule and sharp tool hypotheses were adopted. VMSE force components for artificial materials with unit normal (Kn) and friction (Kf) force coefficients were least-squares-fit to experimental values to obtain actual Kn and Kf and then functionally fit to chip thickness h, speed v and normal rake angle α. The new approach was tested with a simple ball end mill tool. Both time-averaged (MMa model) and location-averaged instantaneous (MMi model) force components from a subset of experimental data were used. Physical force components reported by the VMSE with both MMa and MMi for the complete test matrix agreed with their experimental counterparts. MMi significantly expanded the range of h and was identical to MMa in the common range.

Analytical modeling of residual stress in helical end milling of nickel-aluminum bronze

The end milling of nickel-aluminum alloy has been widely applied to the manufacture of seawater applications, while the prediction of residual stress induced by this process is seldom reported. An analytical model of residual stress is proposed, based on mechanical loading and thermal loading during end milling. For the first time, the sequential discontinuous variable mechanical loading feature of end milling is taken into consideration. Also, the analytical model of stress field in the workpiece during cutting is analyzed which is intermediate variable to study residual stress. Model predictions are compared with experimental data and FEM method for cutting forces, cutting temperature, and residual stress.

Effects of geometric parameters of wavy-edge bull-nose helical end-mill on cutting force prediction in end-milling of Inconel 718 under MQL cooling strategy

This paper presents the results of the development of a mechanistic cutting force prediction model for wavy-edge, bull-nose, helical endmill (WEBNHE), which was validated and used to investigate the effects of the geometric parameters of the WEBNHE on the predicted cutting force components and the resultant cutting force. The mechanistic cutting force prediction model was validated by conducting end-milling experiments on Inconel 718 and incorporating the effect of the Minimum Quantity Lubrication (MQL) cooling strategy through experimentally identified six cutting force and edge force coefficients. The geometric parameters investigated in this research were: the wavelength, wave magnitude, axial shift of the linear part, and the helix angle of the wavy cutting edges. These parameters were varied one at a time, and the cutting force components for each variation were predicted using the mechanistic cutting force prediction model. The results show that the predicted and measured cutting force components were in good agreement in magnitude and shape. The cutting force components generated from the end-milling under the MQL cooling strategy were lower than under the emulsion cooling strategy. The magnitudes and shapes of the predicted cutting force components and the resultant cutting force of the WEBNHE were unique (asymmetric) in magnitude and shape compared to those of standard, bull-nose, helical endmill (SBNHE) due to the uniqueness of the wavy-cutting edge geometry.The results also show that the predicted cutting force component in the feed direction Fy is the largest and the most affected by the geometric parameters, followed by Fx. However, Fz is insignificantly affected. It was also observed that the maximum magnitudes and ranges of the cutting force component in the feed direction Fy and the resultant cutting force FR increased with an increase in the wave magnitude and decrease with increase of the wavelength, axial shift, and the helix angle. The wavy cutting edge spends more time in the cutting zone than the standard, helical, cutting edge; this extra time affects the frequency content of the cutting force signals generated by the endmill and improves the end-milling dynamics. Additionally, the distribution of the cutting forces on the wavy cutting edges was not equal due to the asymmetric cutting edge geometry.

Analytical prediction of chatter stability of end milling process using three-dimensional cutting force model

This article presents the dynamic stability issues in helical-end milling using a three-dimensional cutting force model with flexibility consideration in spindle-tool holder-tool unit. Frequency responses of tool-tip are obtained by finite-element modelling of spindle-tool assembly. Assembly level geometrical variations, such as tapered hole in spindle and holder elements as well as multiple steps in spindle shaft, are properly considered during modelling. These tool-tip frequency responses are validated with 3-D finite-element models, where all component flexibilities are included. The three-dimensional cutting force model is employed to generate the expressions for stable depth-of-cut and operating speeds during machining operation, and these outcomes are compared with those obtained from two-dimensional cutting force model. The 3-D stability model is experimentally verified using the cutting tests at the proposed operational parameters. Later, the work concentrates on the analysis of the cutting forces and the vibrations generated in the helical-end milling process at different depths of radial immersions.

Optimization of End Mill Geometry Parameters Based on Oblique Cutting Theory

An optimization method of end mill geometry parameters is presented for minimizing cutting energy. The helical end mill geometry is established at first. Then, the helical flutes are decomposed a set of infinitesimal oblique cutting edges. At every oblique cutting element, the differential cutting energy, which consists of differential shear energy and differential friction energy, is calculated using oblique cutting theory. By integrating the differential cutting energy along each cutting edge in the end mill, the cutting energy can be predicted during end milling. The effects on cutting energy of end mill geometry parameters are analyzed. Finally, the end mill geometry can be optimized in order to minimizing cutting energy.

Stability of Milling Operations With Asymmetric Cutter Dynamics in Rotating Coordinates

High-speed machine tools have parts with both stationary and rotating dynamics. While spindle housing, column, and table have stationary dynamics, rotating parts may have both symmetric (i.e., spindle shaft and tool holder) and asymmetric dynamics (i.e., two-fluted end mill) due to uneven geometry in two principal directions. This paper presents a stability model of dynamic milling operations with combined stationary and rotating dynamics. The stationary modes are superposed to two orthogonal directions in rotating frame by considering the time- and speed-dependent, periodic dynamic milling system. The stability of the system is solved in both frequency and semidiscrete time domain. It is shown that the stability pockets differ significantly when the rotating dynamics of the asymmetric tools are considered. The proposed stability model has been experimentally validated in high-speed milling of an aluminum alloy with a two-fluted, asymmetric helical end mill.

Force prediction models for helical end milling of nickel-aluminium bronze

Nickel-aluminium bronze is used widely in seawater environment. The mechanistic method and analytical method to predict helical end milling force are briefly described and compared. The mechanistic approach is shown to depend on milling force coefficients determined from milling tests. By contrast, the analytical method is based on a predictive machining theory, which regards the workpiece material properties, tool geometry, cutting conditions and types of milling as the input data. Each cutting edge of the helical end cutter is discretized into a series of infinitesimal elements along the cutter axis and the cutting action of which is equivalent to the classical oblique cutting process. Thus, the cutting force components applied on each element can be calculated using a predictive oblique cutting model and the total instantaneous cutting forces are obtained by summing up the forces contributed by all cutting edges. The equation of equivalent plane angle is derivation through coordinate transformation. Experiments on machining nickel-aluminium bronze under different cutting conditions were conducted to validate the proposed model.

Development of a mechanistic cutting force model for wavy-edge bull-nose helical end-milling of inconel 718 under emulsion cooling strategy

This paper presents the results of the development of a mechanistic cutting force model to predict cutting forces in high-speed end-milling of Inconel 718 using a wavy-edge, bull-nose, helical endmill (which hereafter will be abbreviated as WEBNHE). The model incorporates the effects of emulsion cooling strategy into the mechanistic cutting force model through the experimental determination of six specific cutting force and edge force coefficients. The cutting force is predicted as three components (Fx, Fy, and Fz) and the resultant cutting force FR. The mechanistic cutting force model depends on a mathematical model to represent the geometry of this endmill, which is also developed in this research. The mechanistic model also depends on three cutting force coefficients in the tangential, radial, and axial directions (ktc, krc, kac, respectively), and on three edge force coefficients (kte, kre, kae), also in the tangential, radial, and axial directions. These coefficients are determined experimentally in a separate work in which “emulsion” was applied as the cooling strategy. MATLAB codes were developed and used to simulate the developed mathematical and mechanistic cutting force models. Finally, to validate the mechanistic cutting force model, machining experiments were conducted and real cutting force components were measured and compared with the predicted cutting force components. The predicted values agree fairly well with the experimentally measured values in both magnitude and shape. The percentage of the prediction error for the highest peak force magnitudes at 93 rpm were 11.38%, –0.46%, and 11% for the Fx, Fy, and Fz components respectively, while the percentage prediction error for the lowest cutting force magnitudes are 15.25%, 17.84%, and 10% for Fx, Fy, and Fz components respectively. The developed mechanistic cutting force model can be used to investigate the effect of tool geometry and machining parameters on cutting forces, machining power, machine tool vibration, and to simulate the end-milling process to improve machinability and productivity, and also to understand more fully the end-milling process using WEBNHE.

Modeling of cutting forces in end milling based on oblique cutting analysis

A force model is presented to predict cutting forces in end milling. The helical end mill geometry model is established containing the cutting velocities and the cutting forces during the cutting process, which considers the pitch angle and the helix angle of each flute. The helical flutes are decomposed into a set of infinitesimal oblique cutting edges. At every oblique cutting element, the geometric angles and the cutting velocities are expressed in the three-dimensional plane and the differential cutting forces are determined by cutting energy in the effective cutting plane. By integrating the differential cutting forces along each cutting edge, which considers the effect of the feed velocity, the milling forces can be predicted. The proposed model has been verified with various cutting tests using regular end mill and variable helix end mill. The predicted and measured cutting forces are compared to illustrate the viability of the proposed cutting force model in end milling.

Application of a new thick zone model to the cutting mechanics during end-milling

In this paper, a modified Oxley׳s predictive machining theory was utilized to analyze the mechanics of cutting in end milling using helical end mill tools. The milling tool is modeled along its axis as discrete segments. Each segment of the tool is treated as a single point cutter performing oblique cutting with an instantaneous uncut chip thickness determined by angular position and tool run-out. Subsequently, the cutting force and thrust force are calculated based on the instantaneous chip load. The total forces at a given angular position are obtained by summing up forces contributed by every cutting edge segment engaged into cutting. A modified Oxley׳s predictive machining theory was utilized as the foundation to obtain the desired milling force components through the work hardening and temperature dependent flow stress. First of all, Oxley׳s approach was extended by substituting Johnson–Cook constitutive equation by the velocity-modified-temperature dependent power law in order to generalize the applicability of the model for a wider range of work materials. Then, the equidistance thick primary shear zone model has been revised by considering the non-equidistant primary shear zone configuration as a framework to propose a more realistic nonlinear shear strain rate distribution. Finally, several cutting tests have been performed on AISI1045, Al7075 and Ti6Al4V and the predicted cutting forces using the proposed model have been compared with the experimental ones to validate the extended Oxley׳s model.

Prediction of frequency response function (FRF) of asymmetric tools from the analytical coupling of spindle and beam models of holder and tool

The prediction of chatter stability diagrams in milling requires accurate frequency response functions (FRF) at the tool – workpiece contact zone. Traditionally, the most accurate FRFs are best obtained through the experimental modal testing of each tool, which is costly. This paper presents analytical modeling and coupling procedures for spindle–holder–tool assemblies with asymmetric tools. Tools and holders are analytically modeled with continuous Timoshenko beams, while considering variation of the cross section geometry of the fluted sections and helix angle. While each solid part segments with varying geometry are assembled with rigid receptance coupling, the holder–spindle and tool–holder are coupled using contact stiffness and damping. The asymmetric cross sections of the helical end mills cause the variation of FRF as a function of the spindle's angular position. It is experimentally proven that the proposed method can predict the FRFs as the asymmetric tools rotate.

Analysis and Prediction of Micromilling Stability with Variable Tool Geometry

Micromilling can fabricate miniaturized components using micro-end mill at high rotational speeds. The analysis of machining stability in micromilling plays an important role in characterizing the cutting process, estimating the tool life, and optimizing the process. A numerical analysis and experimental method are presented to investigate the chatter stability in micro-end milling process with variable milling tool geometry. The schematic model of micromilling process is constructed and the calculation formula to predict cutting force and displacements is derived. This is followed by a detailed numerical analysis on micromilling forces between helical ball and square end mills through time domain and frequency domain method and the results are compared. Furthermore, a detailed time domain simulation for micro end milling with straight teeth and helical teeth end mill is conducted based on the machine-tool system frequency response function obtained through modal experiment. The forces and displacements are predicted and the simulation result between variable cutter geometry is deeply compared. The simulation results have important significance for the actual milling process.

Discrete-Time Prediction of Chatter Stability, Cutting Forces, and Surface Location Errors in Flexible Milling Systems

This paper presents a discrete-time modeling of dynamic milling systems. End mills with arbitrary geometry are divided into differential elements along the cutter axis. Variable pitch and helix angles, as well as run-outs can be assigned to cutting edges. The structural dynamics of the slender end mills and thin-walled parts are also considered at each differential element at the tool-part contact zone. The cutting forces include static chip removal, ploughing, regenerative vibrations, and process damping components. The dynamic milling system is modeled by a matrix of delay differential equations with periodic coefficients, and solved with an improved semidiscrete-time domain method in modal space. The chatter stability of the system is predicted by checking the eigenvalues of the time-dependent transition matrix which covers the tooth period for regular or spindle periods for variable pitch cutters, respectively. The same equation is also used to predict the process states such as cutting forces, vibrations, and dimensional surface errors at discrete-time domain intervals analytically. The proposed model is experimentally validated in down milling of a workpiece with 5% radial immersion and 30 mm axial depth of cut with a four fluted helical end mill.

Improved dynamic simulation of end-milling process using time series analysis

Milling is a competitive manufacturing process that is widely used in automotive, aerospace, biomechanical and die/mould industries. Due to the complex geometry and intricate mechanics of milling, the realistic simulation of various milling processes is a challenging research task. Accurate simulation of the milling process requires a proper knowledge of its dynamics. In this paper, a method is developed for the accurate prediction of cutting forces and surface texture in the end-milling operation, based on Time Series Analysis (TSA). In the proposed approach, an equivalent damping ratio is defined for the cutting zone, while the damping ratio of the non-cutting zone is determined by experimental modal analysis. Using a correlation sum criterion, the simulation and experimental force signals are compared to anticipate the value of process damping inside the cutting zone, by assessing the variations in correlation dimensions for both signals. The simulation algorithm incorporates the Time Finite Element Analysis (TFEA) for predicting the dynamics of the milling system. It also takes into account the effect of cutter deflections and run out. The feasibility of the proposed algorithm is verified experimentally for the side wall machining of aluminum 7075-T6, using a High Speed Steel (HSS) helical end mill. The implemented model can accurately predict cutting forces and a 3D surface texture for low radial immersion cutting.

Analysis of Cutting Forces and Machining Error in Ball End Milling of Cylindrical Surfaces

Cutting forces and machining error in contouring of concave and convex surfaces using helical ball end mills are theoretically investigated. The cutting forces are evaluated based on the theory of oblique cutting. The machining errors resulting from the tool deflections due to these forces are evaluated at various points of the machined surface. The influence of various cutting conditions and cutting modes on machining error is investigated and discussed.

Milling Force Predicting Modeling and Analysis for Helical Tooth End Mill on Inside Corner

Milling force is an important parameter during machining, which is directly related to the tool deformation, the tool life, the quality of the part surface, cutting heat, etc. In actual production, the cutting force on inside corner is more complex than the linear. For lack of the accurate cutting force information, there is liable to cause over-cut and owes-cut, rough surface, cutter breaking phenomenon. According to the structural characteristics of the corner, the cutting force model is established, which cutting force is further subdivided and the overall prediction accuracy is improved. Effects of different helix angle and forward amount each gear on cutting force. A good agreement is shown between the model simulation and the results of the experimental ones. The research provides a theoretical basis of predicting the cutting force on inside corner, and it is also helpful for further and practice.

A novel mechanics model of parametric helical-end mills for 3D cutting force prediction

Cutting force prediction plays an important role in modern manufacturing systems to effectively design cutters, fixtures, and machine tools. A novel mechanics model of parametric helical-end mills is systematically presented for three-dimensional (3D) cutting force prediction in the article, which is different from mechanistic approach and Oxley’s predictive machining theory in model formulation and shear stress identification process. The single-flute cutting edge and multiflute cutting edge of helical-end mills are modelled according to kinematic analysis with vector algebra. Based on Merchant’s oblique cutting theory, a new mechanics model of 3D cutting force with runout has been developed. Meanwhile, the asynchronous problem between predicted and measured curves is solved by adjusting phase angle to minimize the average deviation. After minimizing the asynchronous phase angle deviation, shear stress can be estimated directly using corresponding peak-to-peak ratio or valley-to-valley ratio of the predicted curves and the measured curves in X- and Y-directions of an arbitrary selected milling test. To assess the feasibility of the general model, over 100 milling experiments of aluminium alloy (7075) using flat-end mills and ball-end mills were conducted, respectively, and numerical tests implemented in time domain on MathWorks platform. The comparative results indicated that the predicted and the measured waveforms were quite satisfied in both pulsation pattern and period.

Computer Simulation of Helical Groove Processing on the Workpiece of End-milling Cutter

The paper describes a method of processing of helical end mills shaped surfaces of straight profile. The authors describe the possibility of processing the contoured surface of the helical cutter with a given profile by means of mathematical and computer modeling.

Mechanics of micro-milling with round edge tools

This paper presents analytical prediction of micro-milling forces from constitutive model of the material and friction coefficient. The chip formation process is predicted with a slip-line field model which considers the strain hardening, strain-rate and temperature effects on the flow stress of the material. The cutting force coefficients are identified from series of slip-line field simulations at a range of cutting edge radii and chip loads. The predicted cutting force coefficients are used to simulate micro-milling forces. The proposed chain of predictive micro-milling model is experimentally proven by conducting brass cutting tests with a 200 μm diameter helical end mill.

Analysis of Cutting Forces in Helical Ball-End Milling Based on Coordinate Conversion

In this work, the prediction and analysis of cutting forces in helical ball-end milling operations is presented. The cutting forces model for helical end-mills is based on the oblique cutting theory and the geometric relations of the ball-end milling process. The helical flutes are divided into small differential oblique cutting edge segments. According to the transformation relationship between the local and global coordinate system of the cutter, the differential cutting force of cutting element is obtained by two coordinate conversions from the orthogonal cutting force. The total cutting force of helical ball-end milling is the sum of the cutting force in whole cutting field of the miller. As a result, the predicted cutting forces show an agreement with the values from the cutting experiments.