Analysis of force patterns and tool life in milling operations

The paper describes the practical effects of the operating parameters in the milling operation. Experiments have been conducted to measure cutting force and tool life under dry conditions. Based on the experimental results, three mathematical models have been developed: Force, TLife and Force/TLife. Further analyses have been conducted on the cutting force patterns: seasonal pattern and nonlinear trend. A process optimisation that is based on the minimum production cost has been applied to relate Force model, TLife model and machinability criteria, such as power consumption, cutting parameters and surface roughness.Nomenclature C _w cost of workpiece ($) - C _s set-up cost ($) - C _m machining cost ($) - C _o overhead cost ($) - C _r tool replacement cost ($) - C _t tool cost ($) - D diameter of the cutter (inch) - d depth of cut per pass (inch) - d ₀ required depth (inch) - e _t random error attth sample - F cutting force (N) - f feedrate (ipm) - L length of workpiece (inch) - N spindle speed (r.p.m.) - n number of teeth - P power of the motor (h.p.) - R surface roughness (µm) - R _e real part of a complex function - T tool life (min) - t sample number - t _m machining time (s) - t ₀ overhead time (s) - t _r tool replacement time (s) - t _s set-up time (s) - U _i unit cost of itemi ($/unit)v - v cutting speed (i.p.m.)     

Computer-aided selection of optimum machining parameters in multipass turning

In this paper a model and the interactive program system MECCANO2 for multiple criteria selection of optimal machining conditions in multipass turning is presented. Optimisation is done for the most important machining conditions: cutting speed, feed and depth of cut, with respect to combinations of the criteria, minimum unit production cost, minimum unit production time and minimum number of passes. The user can specify values of model parameters, criterion weights and desired tool life. MECCANO2 provides graphical presentation of results which makes it very suitable for application in an educational environment.Nomenclature a _min,a _max minimum and maximum depth of cut for chipbreaking [mm] - a _w maximum stock to be machined [mm] - C _a, _a, _a coefficient and exponents in the axial cutting force equation - C _r, _r, _r coefficient and exponents in the radial cutting force equation - C _T, , , coefficient and exponents in the tool life equation - C _v, _v, _v coefficient and exponents in the tangential cutting force equation - D _w maximum permissible radial deflection of workpiece [mm] - F _a axial cutting force [N] - F _b design load on bearings [N] - F _c clamping force [N] - F _k ^/* minimum value of criterionk, k=1, ...,n, when considered separately - f _m rotational flexibility of the workpiece at the point where the cutting force is applied [mm Nm^–1] - f _r radial flexibility of the workpiece at the point where the cutting force is applied [mm N^–1] - F _r radial cutting force [N] - F _tmax maximum allowed tangential force to prevent tool breakage [N] - F _v tangential cutting force [N] - k slope angle of the line defining the minimum feed as a function of depth of cut [mm] - l length of workpiece in the chuck [mm] - L length of workpiece from the chuck [mm] - L _c insert cutting edge length [mm] - M _g cost of jigs, fixtures, etc. [$] - M _o cost of labour and overheads [$/min] - M _u tool cost per cutting edge [$] - n number of criteria considered simultaneously - N _q, N_p minimum and maximum spindle speed [rev/min] - N _s batch size - N _z spindle speed for maximum power [rev/min] - P _a maximum power at the point where the power-speed characteristic curve changes (constant power range) [kW] - R tool nose radius [mm] - r workpiece radius at the cutting point [mm] - r _c workpiece radius in the chuck [mm] - s _min,s _max minimum and maximum feed for chipbreaking [mm] - T tool life [min] - T _a process adjusting time [min] - T _b loading and unloading time [min] - T _d tool change time [min] - T _des desired tool life [min] - T _h total set-up time [min] - T _t machining time [min] - V _rt speed of rapid traverse [m/min] - W volume of material to be removed [mm³] - W _k weight of criterionk, k=1, ...,n - x=[x ₁,x ₂,x ₃ ] ^T vector of decision variables - x ₁ cutting speed [m/min] - x ₂ feed [mm/rev] - x ₃ depth of cut [mm] - approach angle [rad] - _a coefficient of friction in axial direction between workpiece and chuck - _c coefficient of friction in circumferential direction between workpiece and chuck     

Alternative optimisation strategies and CAM software for multipass rough turning operations

The development of constrained optimisation analyses and strategies for selecting optimum cutting conditions in multipass rough turning operations based on minimum time per component criterion is outlined and discussed. It is shown that a combination of theoretical economic trends of single and multipass turning as well as numerical search methods are needed to arrive at the optimum solution. Numerical case studies supported the developed solution strategies and demonstrated the economic superiority of multipass strategies over single pass. Alternative approximate multipass optimisation strategies involving equal depth of cut per pass, single pass optimisation strategies and limited search techniques have also been developed and compared with the rigorous optimisation strategies. The approximate strategies have been shown to be useful, preferably for on-line applications such as canned cycles on CNC machine controllers, but recourse to the rigorous multipass strategies should be regarded as the reference for use in assessing alternative approximate strategies or for CAM support usage.Nomenclature d _i depth of cut for theith pass - d _opt optimum depth of cut - d _T total depth of cut to be removed - D _i workpiece diameter before theith pass - D _o,D _m initial and final workpiece diameter (afterm passes) - f _i feed for theith pass - f _max,f _min machine tool maximum and minimum feed - f _opt optimum cutting feed - f _sj, V_sj available feed and speed steps in a conventional machine tool - f _sgl, f_rec optimum and handbook recommended single pass cutting feeds - F _pmax maximum permissible cutting force - L workpiece length of cut - m continuous number of passes - m _H next higher integer number of passes from a givenm - m _HW upper limit to the optimum integer number of passesm _opt - m _L next lower integer number of passes from a givenm - m _LW lower limit to the optimum integer number of passesm _opt - m _o optimum (continuous) number of passes - m _opt optimum integer number of passes - N _a machine tool critical rotational speed whenP _a=P _max - N _max,N _min machine tool maximum and minimum rotational speed - n,n ₁,n ₂,K speed, feed and depth of cut exponents and constant in the extended Taylor's tool-life equation - P _a,P _max machine tool low speed and maximum power constraints - T _i tool-life using the cutting conditions for theith pass - T _L loading and unloading time per component - T _R tool replacement time - T _s tool resetting time per pass - T _T production time per component - T _TDi multi-passT _T equation with workpiece diameter effect - T _TDm, T_TDo multi-passT _T equations with constant diameterD _m andD _o, respectively - T _Topt overall optimum time per component - T _Tsgl optimum time per component for single pass turning - T _{T2re c} handbook recommended time per component - V _i cutting speed for theith pass - V _max,V _min machine tool maximum and minimum cutting speed - V _sgl,V _rec optimum and handbook recommended single pass cutting speeds - V _opt optimum cutting speed - a, E, W empirical constants in theP _a/F _pmax/P _max equations - , , feed, depth and speed exponents inF _pmax andP _max equations     

CO2 laser cutting of stained glass

This paper covers the CO₂ laser cutting of stained glass using a Ferranti MF400 CNC laser cutting machine. The report examines the various laser cutting parameters required to generate a cut surface in glass which will require minimal post-treatment to be carried out, and also investigates the degree of geometrical intricacy that can be attempted, together with the associated limitations, in cutting 2D glass components. The experimental procedure used to obtain the necessary information for a preliminary database on the laser cutting of stained glass is also detailed. Finally, the implications and applications of the investigative work are examined for commercial situations through construction of a simple 2D test artefact.Notation f pulse frequency (Hz) - k thermal conductivity (W/mK) - P laser beam power (W) - Pl pulse duration (10^–5 s) - Pr pulse ratio - Ps pulse separation (10^–5 s) - P shield gas pressure (bar) - R _a surface roughness (m) - t _s substrate thickness (mm) - V cutting speed (mm/min) - V _opt optimum cutting speed (mm/min) - w kcrf width (mm) - angle of deviation (deg.) - wavelength (m) - d perforation depth (mm)     

Prediction of tool failure rate in turning hardened steels

This paper presents a stochastic model for predicting the tool failure rate in turning hardened steel with ceramic tools. This model is based on the assumption that gradual wear, chemical wear, and premature failure (i.e. chipping and breakage) are the main causes of ending the tool life. A statistical distribution is assumed for each cause of tool failure. General equations for representing tool-life distribution, reliability function, and failure rate are then derived. The assumed distributions are then verified experimentally. From the experimental results, the coefficients of these equations are determined. Further, the rate of failure is used as a characteristic signature for qualitative performance evaluation. The results obtained show that the predicted rate of ceramic tool failure is 20% (in the first few seconds of machining) and it increases with an increase in cutting speeds. These results indicate that there will always be a risk that the tool will fail at a very early stage of cutting. Such a possibility should not be overlooked when developing proper tool replacement strategies. Finally, the results also give the tool manufacturers information which can be used to modify the quality control procedures in order to broaden the use of ceramic tools.Nomenclature c constant - ch chamfer width of the tool, mm - d depth of cut, mm - h _i hardness value at theith location on the workpiece during machining - h mean ofh ₁,h ₂,h ₃, ...,h _nn - n hardness mean location - m Meyer exponent determined experimentally to define the nonlinear relation between the cutting force and the ratioh _i/h - f feedrate, mm rev^–1 - f(t) probability density function of tool failure - f ₁(t) probability density function of tool failure due to breakage caused by tool quality - f ₂(t) probability density function of tool failure due to breakage caused by workpiece condition - f ₃(t) probability density function of tool failure due to tool chipping caused by chemical wear - f ₄(t) probability density function of tool failure due to flank wear - f ₅(t) probability density function of tool failure due to crater wear - O() error - t cutting time, min - x ₁,x ₂,...,x _n independent variables - A _i instantaneous area of contact between the tool and the workpiece - C ₁ chip load, which can be determined as a function of the cutting conditions and tool geometry - K _I crater wear index - K _T maximum depth of crater wear on tool face, mm - K _M crater centre distance, mm - N number of failures - P(t) probability function of tool failure - P _j(t) corresponding probability of failure, such that 1j5 - R tool nose radius, mm - R(t) reliability function - R _j(t) corresponding reliability function, such that 1j5 - T _V estimate of tool life for a set value of average flank wear (V _B ^* ) - T _K estimate of tool life for a set value of maximum depth of crater wear (K _T ^* ) - V cutting speed, m/min - V _B average tool wear, mm - Z(t) instantaneous failure rate or hazard function - ₃ shape parameter in the Weibull probability density function - rake angle - ₃ scale parameter in the Weibull probability density function, min - failure rate of the cutting tool - mean of a logarithmic normal distribution function - standard deviation of a logarithmic normal distribution function - tool wear function - time corresponding to the occurrence of tool failure - (.) standard logarithmic normal distribution function     

Determining cutting speeds for the CO2 laser machining of decorative ceramic tile

This paper presents a comparison of theoretically predicted optimum cutting speeds for decorative ceramic tile with experimentally derived data. Four well-established theoretical analyses are considered and applied to the laser cutting of ceramic tile, i.e. Rosenthal's moving point heat-source model, and the heat-balance approaches of Powell, Steen and Chryssolouris. The theoretical results are subsequently compared and contrasted with actual cutting data taken from an existing laser machining database. Empirical models developed by the author are described which have been successfully used to predict cutting speeds for various thicknesses of ceramic tile.Notation A absorptivity - a thermal diffusivity (m²/s) - C specific heat (J/kgK) - d cutting depth (mm) - E _cut specific cutting energy (J/kg) - k thermal conductivity (W/mK) - J laser beam intensity (W/ m²) - L latent heat of vaporisation (J/kg) - l length of cut (mm) - n coordinate normal to cutting front - P laser power (W) - P _b laser power not interacting with the cutting front (W) - q heat input (J/s) - R radial distance (mm) - r beam radius (mm) - s substrate thickness (mm) - S _crit critical substrate thickness (mm) - T temperature (°C) - T _o ambient temperature (°C) - T _p peak temperature (°C) - T _s temperature at top surface (°C) - t time (s) - V cutting speed (mm/min) - V _opt optimum cutting speed (mm/min) - w kerf width (mm) - X, Y, Z coordinate location - x, y, z coordinate distance (mm) - conductive loss function - radiative loss function - convective loss function - angle between -coordinate andx-coordinate (rad) - coordinate parallel to bottom surface - angle of inclination of control surface w. r. t.X-axis (rad) - coupling coefficient - translated coordinate distance (mm) - density (kg/m³) - angle of inclination of control surface w.r.t.Y-axis (rad)     

Temperature measurement in orthogonal metal cutting

Orthogonal cutting experiments were carried out on steel at different feedrates and cutting speeds. During these experiments the chip temperatures were measured using an infrared camera. The applied technique allows us to determine the chip temperature distribution at the free side of the chip. From this distribution the shear plane temperature at the top of the chip as well as the uniform chip temperature can be found. A finite-difference model was developed to compute the interfacial temperature between chip and tool, using the temperature distribution measured at the top of the chip.Nomenclature contact length with sticking friction behaviour [m] - c specific heat [J kg^–1 K^–1] - contact length with sliding friction behaviour [m] - F _P feed force [N] - F _V main cutting force [N] - h undeformed chip thickness [m] - h _c deformed chip thickness [m] - i,j denote nodal position - k thermal conductivity [W m^–2 K^–1] - L chip-tool contact length [m] - p defines time—space grid, Eq. (11) [s m^–2] - Q _C heat rate entering chip per unit width due to friction at the rake face [W m^–1] - Q _T total heat rate due to friction at the rake face [W m^–1] - Q _% percentage of the friction energy that enters the chip - q ₀ peak value ofq(x) [W m^–2] - q _e heat rate by radiation [W] - q(x) heat flux entering chip [W m^–2] - t time [s] - T temperature [K] - T _C uniform chip temperature [°C] - T _max maximum chip—tool temperature [°C] - T _mean mean chip—tool temperature [°C] - T _S measured shear plane temperature [°C] - x,y Cartesian coordinates [m] - V cutting speed [m s^–1] - V _C chip speed [m/s] - rake angle - ,, control volume lumped thermal diffusivity [m² s^–1] - emmittance for radiation - exponent, Eq. (3) - density [kg m^–3] - Stefan-Boltzmann constant [W m^–2 K⁴] - (x) shear stress distribution [N m^–2] - shear angle     

General geometric modelling approach for machining process simulation

Machining process simulation systems can be used to verify NC (numerically controlled) programs as well as to optimise the machining phase of the production. These systems contribute towards improving the reliability and efficiency of the process as well as the quality of the final product. Such systems are particularly needed by industries dealing with complex cutting operations, where the generation of NC code represents a very complex and error-prone task. A major impediment to implementing these systems is the lack of a general and accurate geometric method for extracting the required geometric information. In this paper, a novel approach to performing this task is presented. It uses a general and accurate representation of the part shape, removed material, and cutting edges, and can be used for any machining process. Solid models are used to represent the part and removed material volume. Bezier curves (in 3D space) are used to represent cutting edges. It is shown that by intersecting the removed material volume with the Bezier curves, in-cut segments of the tool cutting edges can be extracted. Using these segments, instantaneous cutting forces as well as any other process parameters can be evaluated. It is also shown that by using B-rep (Boundary representation) polyhedral models for representing solids, and cubic Bezier curves for representing cutting edges, efficient, generic procedures for geometric simulation can be implemented. The procedure is demonstrated and verified experimentally for the case of ball end-milling. A very good agreement was found between simulated cutting forces and their experimental counterparts. This proves the validity of the new approach.Notation cx ₃,cx ₂,cx ₁,cx ₀ parameters of cubic polynomialx(t) - cy ₃,cy ₂,cy ₁,cy ₀ parameters of cubic polynomialy(t) - cz ₃,cz ₂,cz ₁,cz ₀ parameters of cubic polynomialz(t) - bx _i ,by _i ,bz _i x-,y-, andz-coordinates of ith control point, respectively - b _i ith control point - R tool radius (m) - angular position of point on cutting edge measured from positivex-axis in case of flat end mill (°) - helix angle of cutting edge on flat end mill (°) - A, B, C, D parameters of the equation of a plane - td _i ,tu _i lower end and upper end of theith in-cut segment (before updating) - n number of in-cut segments (before updating) - td _j ,tu _j lower end and upper end of theith in-cut segment (after updating) - m number of in-cut segments (after updating) - dF _t , dF _r tangential and radial components of the infinitesimal cutting force (N) - K _t ,K _r empirical constants in tangential force and radial force equations (N/m²) - b thickness of axial infinitesimal element of cutting edge (m) - h instantaneous chip thickness of axial infinitesimal element of cutting edge (m) - _s shear strength of workpiece (N/m²) - dA _c cross-section area of undeformed chip on the infinitesimal element of cutting edge (m²) - shear angle (°) - _e effective rake angle (°) - friction angle (°) - or (t) angular position of point on cutting edge of ball nose of ball end mill (rad) - u _j , d _j lower end and upper end ofjth in-cut segment (rad) - t parameter     

Fast evaluation of cutting forces in milling, applying no approximate models

A new method for fast evaluation of cutting forces in milling is introduced and tested experimentally. Unlike all existing procedures, which include the use of cutting models and approximate assumptions, in this method, the elementary functions of the cutting force are obtained from measured values only.The basic force functions for the whole feed range are acquired from one experiment using a single-tooth full-diameter (slot) milling, applying a specially developed procedure. The milling experiment is conducted under low-impact conditions, enabling accurate measurement and convenient signal processing. The basic force functions are then integrated and superimposed, using known procedures, to combine the total force in any multitooth milling combination. In this work the method is explained and tested experimentally.The suggested method enables a reliable evaluation of the cutting forces, while demanding minimal experimental work, the method applies to cutters having complicated edge geometry, and to high speed milling.Nomenclature a radial depth of cut 0<a<D - feed per tooth ratio 0<1 - d axial depth of cut - D cutter diameter - a/D radial depth ratio - cutter rotation angle - cutter rotation angle [6] - F _x,y,z() instantaneous edge cutting forces in fixture coordinates - F _t,r,z() instantaneous edge cutting forces in tool coordinates - F _x,y,z ^* F_t,r,z tool cutting force components on a multitooth cutter - h instantaneous chip thickness [6] - h* equivalent edge coefficient [6] - r ₁,r ₂ tangential radial ratio coefficient [6] - K _T tangential specific cutting force [4] - K _R radial specific cutting force [4] - N number of teeth - R _r resolution reduction factor - t instantaneous chip thickness - S ₁,S feed per tooth     

Drill and clamping interface in high-performance drilling

The behaviour of a drill and a clamping unit was investigated in high-performance drilling. Some clamping units were characterised experimentally. In a series of experiments, the free-rotating drill behaviour, and the drilling events were investigated under high-performance conditions. A non-rotating measurement system, including proper procedures for signal processing, enabled the presentation of all measured values in terms and coordinates of the rotating tool. This led to a better understanding of the first-contact event, the penetration and the full drilling phases, as well as the influence of the clamping unit under different cutting conditions.Notation F impulse test exciting force [N] - Fz drilling axial force [N] - F _x F _y drilling lateral force components [N] - F _T drilling table speed (mm min^–1) - L drill overhang - T drilling torque [Nm] - X, Y, Z world coordinates [mm] - X _T,Y _T,Z _T rotating tool coordinates [mm] - _L hole location error [mm] - drill diameter [mm] - rotating angle [°] - R drill end circular movement fadius in world coordinates [mm] - X, Y drill end deflection in world coordinates [mm] - X _T, Y _T drill end deflection in world coordinates [mm] =2R