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     

In-process estimation of radial immersion angle using cutting force in face milling

In this paper, a on-line estimation method of the radial immersion angle using cutting force is presented. The ratio of cutting forces in feed and cross-feed directions acting on the single tooth at the immersion angle is a function of the immersion angle and the ratio of radial to tangential cutting force. It is found that the ratio of radial to tangential cutting force is not affected by cutting conditions and axial rake angle, which implies that the ratio determined by one preliminary experiment can be used regardless of the cutting conditions for a given tool and workpiece material. Using the measured cutting force during machining and predetermined ratio, the radial immersion ratio is estimated in process. Various experimental results show that the proposed method works within5% error range.     

A generalised model of milling forces

This paper presents the development of a generalised cutting force model for both end-milling and face-milling operations. The model specifies the interaction between workpiece and multiple cutter flutes by the convolution of cutting-edge geometry function with a train of impulses having the period equivalent to tooth spacing. Meanwhile, the effect of radial and axial depths of cut are represented by the modulation of the cutting-edge geometry function with a rectangular window function. This formulation leads to the development of an expression of end/face-milling forces in explicit terms of material properties, tool geometry, cutting parameters and process configuration. The explicitness of the resulting model provides a unique alternative to other studies in the literature commonly based on numerical integrations. The closed-form nature of the cutting force expression can facilitate the planning, optimisation, monitoring, and control of milling operations with complicated tool—work interactions. Experiments were performed over various cutting conditions and results are presented, in verification of the model fidelity, in both the angle and frequency domains.Notation * convolution operator - helix angle of an end mill - _A,_R axial and radial angles of a face mill - angular position of any cutting point in the cylindrical coordinate system - unit area impulse function - ^(i–1)(–T _o) (i–1)th derivative of (–T _o) with respect to - angular position of cutter in the negative Y-direction - _L, lead and inclination angles of a face mill - angular position of any cutting point in the negative Y-direction - ₁, ₂ entry and exit angles - upper limit of cutting edge function in terms of - as defined in equation (10) - A _xk ,A _yk ,A _zk kth harmonics of cutting forces in the X-, Y-, and Z-directions - d _a,d _r axial and radial depth of cut - dA instantaneous cut area - D diameter of cutter - f _o frequency of spindle - f _t,f _r,f _a local cutting forces in the tangential, radial, and axial directions - f _x ,f _y ,f _z local cutting forces in the X-, Y-, and Z-directions - F _x ,F _y ,F _z resultant cutting forces in the angle domain in the X-, Y-, and Z-directions - F as defined in equation (5) - h derivative of height function of cutting edge with respect to - h() height function of one cutting edge with respect to - H height of any cutting point - K _r,K _a radial-to-tangential and axial-to-tangential cutting force ratios - K _t tangential cutting pressure constant - K as defined in equation (6) - p as defined in equation (6) - N number of cutting edges - r() radius function of one cutting edge with respect to - R radius of any cutting point - T cutting engagement time function of any cutting point - T _o cutting engagement time of the cutting point at =0 - T th() tooth sequence function - t _c average cut thickness - t _x feed per tooth - W _A,W _W,W _C amplitude, width and centre of a window function - W(,) unit rectangular window function - y _min,y _max minimum and maximum positions of workpiece in the Y-direction - Z _min,Z _max integration limits in the Z-direction     

The estimation of the diameter error in bar turning: a comparison among three cutting force models

Machining accuracy is considerably affected by the deflection of the machine-tool-workpiece system under the action of the cutting force. A new model to estimate a bar diameter error due to the deflection of the tool, of the workpiece-holder and of the workpiece was defined by the authors, starting from a cutting force model. This work deals with a comparison among the bar diameter errors that are calculated by means of the developed model involving three different cutting force models. The considered cutting force models were the specific cutting resistance, the Kronenberg cutting force and the unified-generalised mechanics of the cutting force model developed by Armarego. The numerical results were compared with those obtained by experimental tests carried out through a parallel lathe. The results show that the Armarego's cutting force model provides values of the force components and, therefore, the values of the resulting bar diameter errors are closest to the experimental ones.Nomenclature a The longitudinal position of the tool, [mm] - a_pn The nominal depth of cut, [mm] - a_p The real depth of cut, [mm] - b The width of area of cut, [mm] - A The tool-workpiece interference area of cut, [mm²] - AB The generalised cutting edge vector - A_r The area of the workpiece cross section, [mm²] - c_s The spindle compliance, [mm/N] - c_t The tailstock compliance, [mm/N] - c_tht The tangential toolholder compliance, [mm/N] - c_thr The radial toolholder compliance, [mm/N] - D The workpiece diameter, [mm] - E The modulus of elasticity, [N/mm²] - f The feed, [mm/r] - F_rad The radial component of the cutting force, [N] - F_feed The feed component of the cutting force, [N] - F_{tan g} The tangential component of the cutting force, [N] - F_i The resultant of F_feed and F_{tan g}, [N] - G The shear modulus, [N/m²] - h The thickness of the area of the cut, [mm] - I The workpiece moment of inertia, [mm⁴] - L The workpiece length, [mm] - P_i The plane containing the inflected curve of the workpiece - P_f The tool assumed working plane - P_n The cutting edge normal plane - P_nG The generalised cutting edge normal plane - P_r The tool reference plane - r_l The chip length ratio - R The workpiece radius, [mm] - R_b The tailstock reaction force, [N] - R_s The spindle reaction force, [N] - S The shape factor - v_c The cutting speed, [mm/min] - v_e The resultant cutting speed, [mm/min] - v_f The feed speed, [mm/min] - v_ch The chip speed, [mm/min] - v_sh The shear speed, [mm/min] - w(z) The total deflection of the workpiece axis, [mm] - w_a The total displacement of the workpiece axis from z reference axis measured in P_i plane, [mm] - (z) The orientation of P_i with respect to F_rad and F_{tan g}, [degree] - The friction angle, [degree] - _n The normal friction angle, [degree] - _nG The generalised normal friction angle, [degree] - The shear factor - _n The normal shear angle, [degree] - _NG The generalised normal shear angle, [degree] - _f The tool side angle, [degree] - _n The tool normal rake angle, [degree] - _nG The generalised tool normal rake, [degree] - _P The tool back angle, [degree] - _c The chip flow angle, [degree] - _cG The generalised chip flow angle, [degree] - _r The tool cutting edge angle, [degree] - _rG The generalised tool cutting edge angle, [degree] - _s1 The tool cutting edge inclination, [degree] - _s2 The inclination of the secondary tool cutting edge [degree] - _sG The generalised tool cutting edge inclination, [degree] - The friction coefficient - The work material shear stress, [MPa] - _r The tool approach angle, [degree] - The approach angle of the secondary cutting edge, [degree]     

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     

Chatter stability analysis for end milling via convolution modelling

This research discusses the methodology of developing a symbolic closed form solution that describes the dynamic stability of multiflute end milling. A solution of this nature facilitates machine tool design, machining parameter planning, process monitoring, diagnostics, and control. This study establishes a compliance feedback model that describes the dynamic behavior of regenerative chatter for multiflute tool-work interaction. The model formulates the machining dynamics based upon the interconnecting relationship of the tool geometry and the machining system compliance. The tool geometry characterises the cutting forces as a function of the process parameters and the material properties, while two independent vibratory modules, the milling tool and the workpiece, represent the machining system compliance. The compliance feedback model allows the development of a corresponding characteristic equation. By investigating the roots of the characteristic equation, this research symbolically expresses the stability of the system as a function of the cutting parameters, the tool geometry, the workpiece geometry, and the vibrational characteristics of the machine tool. Machining experimentation examining the fidelity of the regenerative chatter model is discussed. The dynamic cutting forces, cutting vibration, and surface finish of the machining process confirm the validity of the analytical prediction.Nomenclature b damping coefficient: mass-spring-damper representation - b _e equivalent damping coefficient: mass-spring-damper representation - C compliance element - CWD chip with density function - D diameter of cutter - d _a axial depth of cut - d _r radial depth of cut - average total cutting force - K _r radial specific cutting pressure constant - K _t tangential specific cutting pressure constant - k spring constant - k _e equivalent spring constant - m mass: mass-spring-damper representation - m _e equivalent mass: mass-spring-damper representation - n number of flutes on the cutter - p _x,y elemental cutting forces - P _1,2 elemental cutting force functions - R cutter radius - s Laplace variable - TS tooth sequencing function - chip thickness - t _c average chip thickness - t _x feed per tooth - helix angle - _x actual displacement of cutter tip - unit impulse function - _d damped circular frequency of vibration - damping ratio - spindle speed     

Toroidal versus ball nose and flat bottom end mills

This paper compares the surface roughness along and across the feed directions produced by toroidal, ball nose, and flat bottom end mills. The study is conducted numerically and by cutting tests of aluminium. The results show that the toroidal cutter inherits the merits of the other two cutters; it produces small scallops across the feed direction, and low roughness along the feed direction.Nomenclature h scallop height - R _s radius of curvature of surface - inclination angle - 2a _c cross-feed - 2 subtended angle between the point of contact on the tool profile and the surface - R _a surface roughness - e offset distance of insert from tool axes for toroidal cutter - r _c cutter radius - r _i radius of insert for toroidal cutter - f _t feed per tooth - h _u undercut height - y, , intermediate variables     

Effects of cutting parameters on tool insert wear in end milling of titanium alloy Ti6Al4V

Titanium alloy is a kind of typical hard-to-cut material due to its low thermal conductivity and high strength at elevated temperatures, this contributes to the fast tool wear in the milling of titanium alloys. The influence of cutting conditions on tool wear has been focused on the turning process, and their influence on tool wear in milling process as well as the influence of tool wear on cutting force coefficients has not been investigated comprehensively. To fully understand the tool wear behavior in milling process with inserts, the influence of cutting parameters on tool wear in the milling of titanium alloys Ti6Al4V by using indexable cutters is investigated. The tool wear rate and trends under different feed per tooth, cutting speed, axial depth of cut and radial depth of cut are analyzed. The results show that the feed rate per tooth and the radial depth of cut have a large influence on tool wear in milling Ti6Al4V with coated insert. To reduce tool wear, cutting parameters for coated inserts under experimental cutting conditions are set as: feed rate per tooth less than 0.07 mm, radial depth of cut less than 1.0 mm, and cutting speed sets between 60 and 150 m/min. Investigation on the relationship between tool wear and cutting force coefficients shows that tangential edge constant increases with tool wear and cutter edge chipping can lead to a great variety of tangential cutting force coefficient. The proposed research provides the basic data for evaluating the machinability of milling Ti6Al4V alloy with coated inserts, and the recommend cutting parameters can be immediately applied in practical production.     

A study of the cutting modes in the grooving of tungsten carbide

In this paper, the cutting modes for grooving a tungsten carbide work material are investigated and presented. The grooving tests were carried out on an inclined workpiece surface using a solid CBN tool on a CNC lathe. The experimental results indicated that there was a transition from a ductile mode cutting to a brittle mode cutting in the grooving of tungsten carbide workpiece material as the depth of cut was increased from zero to a critical value. Ductile mode cutting is identified by the machined workpiece surface texture and the material removal ratio f _ab -ratio of the average of the volume of material removed to the volume of the machined groove. Scanning electron microscopy (SEM) observations on the machined workpiece surfaces indicated that there are three cutting modes in the grooving of tungsten carbide as the depth of cut increased: a ductile mode, a semi-brittle mode and a brittle mode. The ductile cutting mode depends on the stress in the cutting region, i.e., whether or not the shear stress in the chip formation region is greater than the critical shear stress for the chip formation ( _slip > _c ), and whether or not the fracture toughness of the work material is larger than the stress intensity factor (K ₁<K _c ). When ( _slip < _c ) and (K₁>K _c ), crack propagation dominates, the chip formation and the cutting mode are brittle.Nomenclature A ₁ , A ₂ A cross-section areas of the ridge - A _V A cross-section area of the groove - A _W The value of A _V subtracted by A ₁+A ₂ - F _X The horizontal force - F _Z The vertical force - K _C The fracture toughness - K _I The stress intensity factor - f _ab The work material removal ratio - f _n The normal cutting force - f _t The tangential cutting force - The inclined angle - _c The critical shear stress for dislocation - _slip The shear stress in chip formation zone     

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     

平底立铣刀在多刃切削时的切削力变化规律研究

为揭示平底立铣刀在多刃铣削时的切削力变化规律,理论推导了多刃切削的水平方向公称切削力的数学表达式,发现这些公称切削力是旋转角的简谐函数,其常数项与同时参与切削的刃数成正比。将切削力表达式的系数做归一化处理,采用仿真方法,得到各常用齿数平底立铣刀在单刃、多刃连续切削时的公称切削力量纲一均值和刀齿频率幅值,结果表明：切削宽度方向的公称切削力均值在多刃切削时显著增大,而其刀齿频率幅值在多刃切削时有时增大,有时减小。开展了4齿平底立铣刀的切削测力试验,试验结果与理论推导和仿真结果相符。研究结果表明：与单刃连续切削相比,多刃切削的切削宽度方向的静态切削力显著增大;多刃切削在水平方向存在着更平稳和更不平稳两种可能;偶数齿铣刀的多刃切削最平稳。研究结论可为铣削加工中优选浸入角参数提供参考。     

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     

Development of web-based machining chip breaking prediction systems

The prediction of chip breaking in machining is an important task of automated manufacturing. A chip breaking predictive model has been developed to predict the chip breaking behaviour in steel turning with grooved tools. The model is based on the chip breaking limits theory. A web-based chip breaking prediction system has been developed and presented in this paper with industrial application examples. With the system, the chip breaking range in steel turning with grooved tools can be predicted under different cutting conditions. The experimental data for turning different steel material over a wide range of feed rates, cutting speeds and tool geometry showed agreements with the model prediction. The user-friendly system is accessible through the Internet for the purposes of cutting condition design and tool selection. Also, the system can easily be extended to contain new cutting tools and new workpiece materials with a small number of cutting tests.Nomenclature f Feed rate (mm/rev) - d Depth of cut (mm) - V Cutting speed (m/min) - f_cr The critical feed rate (mm/rev) - d_cr The critical depth of cut (mm) - r Insert Nose radius (mm) - W_n Insert chip breaking groove width (mm) - Cutting edge angle (deg) - ₀ Insert rake angle (deg) - ₀₁ Insert land rake angle (deg) - b₁ Insert/chip restricted contact length (mm) - _s Insert inclination angle (deg) - h Insert backwall height (mm) - WP Work piece - DB database     

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     

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)     

Cutting force prediction in ball-end milling with inclined feed by means of geometrical analysis

A geometrical model for the analysis of cutting forces in ball-end milling has been presented in a previous work (Tsai CL, Liao YS, J Mater Process Technol 205:24–33, 10), which can be used to analyze cutting forces in vertical or horizontal feed. In this paper, the three-dimensional geometrical analysis is depicted with different interacting relations among cutting edge, undeformed chip and shear zone along nonhorizontal cutting direction, and a general geometrical model of inclined feed in ball-end milling is presented. According to the geometrical analysis, the cutting directions of horizontal, vertical, inclined downward, and inclined upward feed are defined with a feed angle. A general force model is derived, and the three-dimensional cutting forces are predicted. Experiments are conducted to verify the geometric force model. The influences of different feed angle and helix angle on cutting forces in inclined downward and inclined upward feed are discussed and simulated.     

Investigate on milling force of cryogenic cooling processing aluminum honeycomb treated by ice fixation

Aerospace metal honeycomb materials with low stiffness had often the deformation, burr, collapse, and other defects in the mechanical processing. They were attributed to poor fixation method and inapposite cutting force. This paper presented the improvement of fixation way. The hexagonal aluminum honeycomb core material was treated by ice fixation, and the NC milling machine was used for a series of cryogenic machining. Considering the similar structure of fiber-reinforced composite materials, the milling force prediction model of ice fixation aluminum honeycomb was established, considering tool geometry parameters and cutting parameters. Meanwhile, the influence rule on milling force was deduced. The results show that compared with the conventional fixation milling method, the honeycomb processing effect is improved greatly. The machining parameters affect order on milling forces: the cutting depth is the most important, followed by the cutting width, then the spindle speed and the feed. Moreover, too small cutting depth (a_p?=?0.5 mm) will cause insufficient cutting force, while a_p?>?2 mm with higher force will reduce the processing quality of honeycomb. Simultaneously, the honeycomb orientation (θ) has a great influence on processing quality. Using the model, the predicted and measured error values of the feed and main cutting force are all small in θ?<?90°. But, the rate is 33 and 26% for the main cutting force and feed force error in θ?>?90°, respectively, while they all exhibit the smallest error in θ?=?60°. This bigger error mainly is due to unstable cutting force with obtuse angle. In addition, the tool rake angle has little influence on cutting quality in θ?<?90°, but bigger on that in θ?>?90°. Furthermore, the calculation model successfully conforms to the main deformation mechanism and influences parameters of the cutting force in the milling process, and it can accurately predict the cutting force in θ?<?90° and guide the milling process.     

Multiple-objective optimisation of machining operations based on neural networks

Metal cutting plays an important role in manufacturing industries. Optimisation of cutting parameters represents a key component in machining process planning. In this paper, a neural network based approach to multiple-objective optimization of cutting parameters is presented. First, the problem of determining the optimum machining parameters is formulated as a multiple-objective optimization problem. Then, neural networks are proposed to represent manufacturers' preference structures. To demonstrate the procedure and performance of the neural network approach, an illustrative example is discussed in detail.Nomenclature v cutting speed (m/min) - f feed rate per revolution (mm/rev) - d depth of cut per pass (mm) - T _p total operation time per part (min) - T _i set-up time per part (min) - T _c tool change time (min) - T _i idle time per part (min) - C _p cost per part ($) - C _t cost of tool per piece ($) - C _l labor cost per unit time ($/min) - C _o overhead per unit time ($/min) - V volume to be removed per part (mm³) - MRR metal removal rate (mm³/min) - TL tool life (min) - SR surface roughness (m) - H _p arithmetic centre-line average (m) - P cutting power (kW) - F cutting force (kg) - interface temperature (°C)     

Characteristics of ultrasonic vibration-assisted ductile mode cutting of tungsten carbide

In this study, investigations were carried out to evaluate the characteristics of ultrasonic vibration-assisted cutting of tungsten carbide material using a CNC lathe with CBN tool inserts. The cutting forces were measured using a three-component dynamometer, and the machined workpiece surfaces and chip formation were examined using a SEM. The experimental results showed that the radial force F _x was much larger than the tangential force F _z and axial force F _y . The SEM observations on the machined workpiece surfaces and chip formation indicated that the critical condition for ductile mode cutting of tungsten carbide was mainly the maximum undeformed chip thickness when the tool cutting edge radius was fixed, that is, the ductile mode cutting can be achieved when the maximum undeformed chip thickness was smaller than a critical value. Corresponding to the chip formation mode (ductile or brittle), three types of the machined workpiece surfaces were obtained: fracture free surface, semi-fractured surface and fractured surface. It was also found that the cutting speed has no significant effect on the ductile chip formation mode.     

Investigations of flank wear, cutting force, and surface roughness in the machining of Al-6061�CTiB2 in situ metal matrix composites produced by flux-assisted synthesis

This paper presents the results of an experimental investigation on the machinability of in situ Al-6061?CTiB₂ metal matrix composite (MMC) prepared by flux-assisted synthesis. These composites were characterized by scanning electron microscopy, X-ray diffraction, and micro-hardness analysis. The influence of reinforcement ratio of 0, 3, 6, and 9?wt.% of TiB₂ on machinability was examined. The effect of machinability parameters such as cutting speed, feed rate, and depth of cut on flank wear, cutting force and surface roughness were analyzed during turning operations. From the test results, we observe that higher TiB₂ reinforcement ratio produces higher tool wear, surface roughness and minimizes the cutting forces. When machining the in situ MMC with high speed causes rapid tool wear due to generation of high temperature in the machining interface. The rate of flank wear, cutting force, and surface roughness are high when machining with a higher depth of cut. An increase in feed rate increases the flank wear, cutting force and surface roughness.