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)     

Determining the Surface Electrostatic Potential Ψ s of a Dielectric-Bordering Semiconductor Using the Method of Ψ s "/Ψ s Diagrams

A quantitative approach to determining the integration constant _s0(V _{g 0}) in an expression relating the semiconductor surface potential _s to the voltage V _g applied to the metal–insulator–semiconductor (MIS) structure and its quasi-static capacitance–voltage characteristic C _v(V _g) (normalized to the dielectric capacitance) is described. The method is based on the analysis of experimental functions _s ^"( _s ), where _s ^" = d _s /dV _g, and the same functions calculated for an ideal MIS structure. The obtained function _s (V _g) is a rather exact and complete characteristic of electron properties of the MIS-structure phase boundary (the integrated interface state density, flat-band voltage V _FB, sign and density of the dielectric fixed charge, and variations of these parameters under the action of various factors). Using the example of a particular n-Si MIS structure, it is shown that the method of _s ^"/ _s diagrams ensures a noticeable (up to 0.93 eV) widening of the Si gap sounding region and observation (by the value of the V _FB shift) of very small ( 1 × 10⁷ cm^–2) variations in the charge density at the Si/SiO₂ phase boundary.     

Lubricant thickness effects on friction between Pd(100) surfaces

Friction measurements have been made between pairs of Pd(100) surfaces prepared in vacuum with adsorbed n-octane films ranging in thickness from 0 to 20 monolayers on each surface. These measurements have been made at lattice misorientation angles of 0° and 45°. Both sets of measurements reveal friction anisotropy at all except the highest n-octane coverages. The friction coefficient drops with increasing n-octane coverage until it reaches a limiting value of _s 0.4. The static friction coefficient reveals a different dependence on n-octane coverage than has been observed for alcohols. The friction coefficient decreases more slowly with increasing n-octane coverage than for increasing alcohol coverage.     

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     

Eddy-Current Studies of Aging Processes in N26T3 Metastable Austenite Steel

In the N26T3 austenite steel, the eddy-current parameter f ₀ has been measured after one aging cycle at temperatures of 700 and 650°C, and after two aging cycles, one of them at the same temperature and the second at 600 and 550°C. The two-stage aging is conducted by two schemes: (1) preliminary aging at 700 or 650°C, transfer of samples without cooling to the room temperature into a furnace heated to 600 or 550°C, then isothermal aging and cooling to room temperature T _r; (2) the same operations as in the first scheme, but the samples are cooled to T _r after the preliminary aging. The eddy-current parameter f ₀ measured at T _r increases with time after aging at 700 and 600°C owing to isothermal martensite transformation. After the two-stage aging, the isothermal martensite transformation at T _r still takes place, but it is stabilized, i.e., the parameter f ₀ drops with time. The stabilization of the austenite is the more pronounced, the lower the temperature of the second stage of aging, and it is stronger after the two-stage aging by the second scheme.     

Determining Generation–Recombination Characteristics of a Semiconductor–Dielectric Interface from the Current Kinetics of Surface Minority Carrier Generation

Conditions for the one-to-one characterization of the generation (G _s) and surface recombination (R _s) rates of minority charge carriers (MCCs) in a metal–oxide–semiconductor (MOS) structure (in the case of strong nonequilibrium depletion) by the MCC surface generation current (I(t)) flowing in an external circuit of this structure are revealed. These conditions are the following: (1) the generation current I is independent of the time t (until the structure enters an equilibrium state) and the voltage V _{g 0} corresponding to the initial nonequilibrium depletion and (2) the duration of current steps I(V _{g 0}) = const and, consequently, the equilibrium surface charge increase with increasing V _{g 0}. The observed kinetics of the MCC generation current for the MCCs induced in an n-Si MOS structure at 293 K experimentally confirms the realization of these conditions. The values of the generation and recombination rates G _s = 2.84 × 10¹⁰ cm^–2s^–1 and R _s = 6.82 cm s^–1 obtained from current levels I(V _{g 0}) = const are typical of high-quality Si MOS structure. Additionally measured capacitance–voltage characteristics were used to determine the interface state density at the Si/SiO₂ contact near the middle of the Si gap (N _ss(E) 6.4 × 10¹⁰ cm^–2eV^–1), which allowed the estimation of the effective capture cross section of these states _eff 1.4 × 10^–16 cm².     

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     

A Study of Cellular Decay in Austenite Alloys Using an Applied Eddy-Current Transducer

The eddy-current parameter f ₀ of the N36K10T3 invar has been studied in the range of aging temperatures from 600 to 900°C. The maximal drop in f ₀ has been observed at the temperature T _ag = 800°C, and the drop in this parameter was the larger, the longer the aging process. The drop in this parameter is caused by the cellular decay process in the solid solution, which depletes the austenite of nickel and titanium. The parameter f ₀ increases notably (from 4 to 46 kHz) when crystals of lowtemperature martensite (-phase) are generated in samples of the N26T3 steel with 100% cellular decay. This high value (f ₀ = 46 kHz) persists at T _ag < 400°C and drops by a factor of 4.5 over the interval 400 < T _ag < 600°C because the ferromagnetic -phase transforms to the paramagnetic phase-hardened austenite ( _ph). Aging of the phase-hardened austenite in the steel with cellular decay at T _ag = 700°C increases the parameter f ₀ by a factor of two (from 10 to 20 kHz) because the ferromagnetic -phase is generated when the aged phase-hardened austenite transforms to the martensite (_ph ) as a result of cooling the steel from the aging to room temperature.     

Effect of niobium interlayer on high-temperature sliding friction and wear of silver films on alumina

In this study, we investigated the effect of a thin Nb bonding layer (15–20 nm thick) on the high-temperature sliding friction and wear performance of Ag films ( 1.5 m thick) produced on -alumina (Al₂O₃) substrates by ion-beam assisted deposition (IBAD). The friction coefficients of Al₂O₃ balls against the Ag-coated Al₂O₃ flats were 0.32 to 0.5 as opposed to 0.8 to 1.1 against the uncoated flats. Furthermore, these Ag films reduced the wear rates of Al₂O₃ balls by factors of 25 to 2000, depending on test temperature. Wear of Ag-coated Al₂O₃ flats was hard to measure after tests at temperatures up to 400°C. At much higher temperatures (e.g., 600°C), these Ag films (without a Nb layer) were removed from the sliding surfaces and lost their effectiveness; however, Ag films with the Nb bonding layer remained intact on the sliding surfaces of the Al₂O₃ substrates even at 600°C and continued to impart low friction and low wear.     

Effect of temperature on tribological performance of a silicon nitride ball material with a linear perfluoropolyalkylether

The effect of temperature in rolling contact performance of a hot isostatically pressed (HIP) silicon nitride ball material with a linear perfluoropolyalkylether (PFPAE) was studied using a ball-on-rod type rolling contact fatigue tester. The test temperature ranged from ambient to 343°C for a period of 24 h at a stress of 5.5 GPa using thin dense chrome (TDC)-coated T-15 bearing races. The lubricant and its decomposition products, specifically acid fluoride and acids, attacked Si₃N₄ balls at all test temperatures resulting in corrosion pitting. The presence of metal fluoride on all the Si₃N₄, transferred from the races, was detected by X-ray photon spectroscopy (XPS). The thickness of the oxide layer formed on the balls, as determined by Auger electron spectroscopy (AES) increased with temperature. The changes in physical properties of post-test lubricant showed that the lubricant was stable at temperatures up to 288°C. The change in viscosity was constant up to 288°C and with a significant change above 288°C. The FTIR analysis of 316 and 343°C post-test lubricant showed the presence of carboxylic acid. The total acid number (TAN) increased linearly up to 288°C and accelerated at 316 and 343°C. The study indicates that the use of Si₃N₄ balls with a linear PFPAE results in an incompetent tribo system.     

Desorption Kinetics of Polyether Lubricants from Surfaces

Desorption or evaporation is one of the mechanisms for loss of perfluoropolyalkylether (PFPE) lubricants from the surfaces of data storage media. One approach to minimizing PFPE loss to desorption is the use of lubricants with increasing molecular weight or increasing average chain length. In order to understand the effects of chain length on the lubricant evaporation kinetics we have studied the desorption kinetics of monolayer films of oligomeric ethers with varying chain length adsorbed on the surface of graphite. The desorption pre-exponents, v, and desorption barriers, E _des , have been measured for poly(ethylene glycol) dimethyl ethers, CH₃O(CH₂CH₂O) _m CH₃, with m=1,2,3,4,8 and 10. These are models for the PFPE known as Fomblin Z, which has a structure CF₃O(CF₂CF₂O) _x (CF₂O) _y CF₃. The results show that the desorption pre-exponents are independent of chain length and have an average value of v=10^18.7±0.3 s^–1. The E _des for the poly(ethylene glycol) dimethyl ethers vary non-linearly with chain length and can be fit with a power law expression of the form E _des =a+bN , where N is the total number of atoms in the oligomer backbone (N=3m+3) and the scaling exponent has a value of 1/2. This non-linear dependence of E _des on chain length has also been observed in recent studies of the desorption kinetics of straight chain alkanes from graphite. A desorption mechanism is described that explains the non-linearity of E _des for the poly(ethylene glycol) dimethyl ethers. The implication for the lifetime of lubricants on data storage media is that the long chain PFPE lubricants desorb more rapidly than one might expect based on simple linear scaling of the E _des of lower molecular weight PFPEs.     

Burr detection by using vision image

In this paper, a practical force model for the deburring process is first presented. It will be shown that the force model is more general than Kazerooni's model and it is suitable for both upcut and down-cut grinding. In terms of this force model, an algorithm of burr detection by using a 2D vision image is proposed. In the burr detection algorithm, the relevant data of burrs, such as frequency, cross-section area, and height are simplified so that they are functions of the burr contour only. Then, a fast tracking method of the burr contour (BCTM) is developed to obtain the contour data. Experiments show that the BCTM of this passive (i.e. without lighting) image system can be as fast as 18.2 Hz and its precision is 0.02 mm, so online burr detection and control by using the vision sensor is feasible.Nomenclature A _burr cross-section area of the burr - A _chamfer cross-section area of the chamfer - A _n proportional factor - A _work cross section area in the contact zone while deburringA _work=A _burr+A _chamfer - w cutting width - w _root thickness of the root of the burr - a depth of cut - a _root burr heighta _root=a(w _root) - C ₁ static cutting edge density - D equivalent wheel diameter - d _s wheel diameter - d _w workpiece diameterD=d _w d _s/(d _w±d _s)D=d _s andd _w for the deburring process - F _h horizontal grinding force - F _v vertical grinding force - F _n normal grinding force - F _t tangential grinding force - F _n(K) normal grinding force of the Kazerooni's model - F _t(K) tangential grinding force of the Kazerooni's model - F _o threshold thrust force - f _burr burr frequency - f _n normal grinding force per active grain - f _t tangential grinding force per active grain - f _r first resonant frequency of the robot - f _tool resonant frequency of the end-effector at the normal direction - exponential constant for describing the edge distribution = [(1 +n) + (1 –n)]/2 = (1 +n)/2 for = 0 [21] - K proportional factor of the force model of the grinding processK =A _n ^1–n / - K ₀ specific contact force per contact length - K ₁ specific chip formation force per contact length - V _s wheel speed - V _w workpiece speed - _w metal-removal parameter - K ₂ specific metal-removal parameter per wheel speedK ₂ = _w/V _s - K _c specific chip formation force per area - K _f specific friction force per area - k constant for the parabolic burr - k ₁,k ₂,k ₃,k ₄ constants for the circular burr - L contact width between the wheel and the workpieceL is equal to the chamfer's hypotenuse length, orL=w _root when there is no chamfer - l contact length - l _k contact length between the wheel and the workpiece - m exponential constant for describing the edge shape 0m1m=1 for the deburring process [21] - N _dyn number of engaged cutting edges per wheel surface - n exponential constant for describing the cutting process 0n1n=1 for the pure chip formation process andn=0 for the pure friction process [22] - average contact pressure - p exponential constant for describing the relationship between the static cutting edge and the wheel surface depth 1p2p=1 for linear case [21] - Q magnitude of the individual chip cross-section in the contact zone - r radius of the circular burr - Z _w metal-removal rate - ,, exponential constants for describing the edge distribution [21] = (p –m)/(p + 1) = 0 form = 1,p = 1 =p/(p) + 1 = 1/2 forp = 1 = (1 –n) = 1n/2 for = 1/2 - actual contact area between the wheel and the workpiece - coefficient of the sliding friction - variable of the contact angle - _k maximum contact angle - _m mean rotating angle - _t half of the tip angle of the grains - ratio of tangential chip formation force to the normal chip formation force. Usuihideji has pointed out that = /(4tan_t) [29]     

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     

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     

An economic design for variable sampling interval MA control charts

Most of the studies done on the economic design of control charts focus on a fixed-sampling interval (FSI); however, it has been discovered that variable-sampling-interval (VSI) control charts are substantially quicker in detecting shifts in the process than FSI control charts due to a higher frequency in the sampling rate when a sample statistic shows some indication of a process change. In this paper, an economic design for a VSI moving average (MA) control chart is proposed. The results of a numerical example adopted from an actual case indicate that the loss cost of VSI MA control charts is consistently lower than that of the FSI scheme.Design variables n Sampling size for each moving plot - h_a Subsequent sampling interval when preceding sample mean is located at sub-control region I_a, a=1,2,..., - Number of different sampling-interval lengths, 2 - k_a Threshold limit expressed in units of - k₁ Control limit expressed in units of Parameters related to assignable cause µ₀ Target mean - True-process standard deviation - Magnitude of an assignable cause expressed in units of - Occurrence rate of an assignable cause per unit timeCost and technical parameters D Average time taken to find and repair an assignable cause after detection - e Time for a sample to be taken, transmitted to laboratory, and results phoned back to process control room - M Income reduction when =₀+ - T Average cost of looking for an assignable cause when a false alarm occurs - W Average cost of looking for and repairing an assignable cause when one does exist - F_c Fixed cost per subgroup of sampling, inspecting, evaluating and plotting - V_c Variable cost per subgroup of sampling, inspecting, evaluating and plotting     

Surface diffusion and flow activation energies of perfluoropolyalkylether

Surface diffusion of perfluoropolyalkylether (PFPE) Fomblin Z15 and Fomblin Zdol (hydroxyl terminated PFPE) on silicon wafers was investigated over the temperature range of 25 to 50°C using scanning microellipsometry. Zdol exhibits a much lower mobility and a distinctly different thickness profile as compared to Z15. The activation energy for surface diffusion of Zdol is higher than that of Z15, reflecting the stronger affinity of its hydroxyl end groups for the substrate. The viscosity flow activation energy E ^* is compared with that of surface diffusion E _d ^* yielding E _d ^* E ^* for Z15, and E _d ^* 1.5E ^* for ZOn leave from Korea Insitute of Science and Technology, PO Box 131, Cheongryang, Seoul, Korea 305-701.     

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     

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     

An Average Flow Model for Couple Stress Fluids

The interactions of surface roughness and flow rheology of couple stress fluids on thin film lubrication problems are modeled. The generalized average Reynolds equation as well as the flow factors is derived. The effects of couple stress parameters (l), the standard derivation of surface roughness ( _i ), the Peklenik number ( _i), and the roughness orientation angle ( _i) on the flow factors ( ^p _ij , ^s _ij) are discussed. In results, the related Reynolds-type equations and flow factors for Newtonian fluids, power-law non-Newtonian fluids, mixtures of Newtonian and power-law non-Newtonian fluids, and couple stress fluids are tabulated.     

Non-constant parameter NC tool path generation on sculptured surfaces

An algorithm for three-axis NC tool path generation on sculptured surfaces is presented. Non-constant parameter tool contact curves are defined on the part by intersecting parallel planes with the part model surface. Four essential elements of this algorithm are introduced: initial chordal approximation, true machining error calculation, direct gouge elimination, and non-constant parameter tool pass interval adjustment. A software implementation of this algorithm produces graphical output depicting the tool path superimposed over the part surface, and it outputs cutter location (CL) data for further post-processing. Several applications examples are presented to demonstrate the capabilities of the algorithm. The results of this technique are compared to those generated from a commercially available computer-aided manufacturing program, and indicate that equivalent accuracy is obtained with many fewer CL points.Notation C cutting curve - C ¹ cutting curve tangent - CC ₀,CC ₁, ... cutter contact points - d chordal deviation - /_ABC triangle - w incremental step in parameterw - ABC angle - a small quantity - l chord length - n _s ,n _p , ... normal vectors - P, P _r ,P _c ,P ₁ ,P ₂ , ... space point - Q parametric equation of a surface - R radius of a ball-end milling tool - TC ₀,TC ₁, ... tool center points - u, v, u _s ,u _c ,w, t parameters - angle - curvature - h cusp height - T machining tolerance