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     

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     

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)     

A modified evolutionary programming for flow shop scheduling

In order to avoid premature convergence and to balance the exploration and exploitation abilities of simple evolutionary programming, this paper proposes a Modified Evolutionary Programming (MEP) for flow shop scheduling. Firstly, multiple populations are designed to perform a parallel search with random initialisation in divided solution spaces. Secondly, multiple mutation operators are designed to enhance the search templates. Thirdly, selection with a probabilistic updating strategy based on an annealing schedule like simulated annealing is applied to avoid the dependence on fitness functions and to avoid being trapped in a local optimum. Lastly, a re-assignment strategy for individuals is designed for every sub-population to fuse information and enhance population diversity. Simulation results based on some flow shop scheduling benchmarks show that the MEP is superior to the simple evolutionary programming and the well-known NEH constructive method. In addition, the MEP is general and can be applied for any classes of optimisation problems by suitable adjustment.Nomenclature n number of jobs - m number of machines - p_ij processing time of job i on machine j - C_max makespan - P_size size of population - t, t₀ temperature, initial temperature - k iteration number - difference of the objective values - C_b, C_w makespan of the best and worst initial solutions - p_r initial acceptance probability - temperature decrease rate - L₁ Evolution generation number for sub-population - L₂ Running number for re-assignment operator     

European sea bass gill pathology after exposure to cadmium and terbuthylazine: expert versus fractal analysis

The objective of this study was to compare expert versus fractal analysis as new methods to evaluate branchial lamellar pathology in European sea bass Dicentrarchus labrax (Linnaeus, 1758) experimentally exposed to cadmium and to terbuthylazine. In particular, guided expert quantitative and fractal analysis were performed on selected images from semithin sections to test possible differences according to exposure class (unexposed, cadmium exposed, or terbuthylazine exposed) and the discrimination power of the two methods. With respect to guided expert quantitative analysis, the following elementary pathological features were assessed according to pre‐determined cover classes: ‘epithelial lifting’, ‘epithelial shrinkage’, ‘epithelial swelling’, ‘pillar cells coarctation’, ‘pillar cells detachment’, ‘channels fusion’, ‘chloride cells swelling’ and ‘chloride cells invasion’. Considering fractal analysis, D_B (box dimension), D_M (mass dimension), (mean fractal dimension) as fractal dimensions and lacunarity from D_M and scan types were calculated both from the outlined and skeletonized (one pixel wide lines) images. Despite significant differences among experimental classes, only expert analysis provided good discrimination with correct classification of 91.7 % of the original cases, and of 87.5 % of the cross‐validated cases, with a sensitivity of 95.45 % and 91.3 %, respectively, and a specificity of 75 % in both cases. Guided expert quantitative analysis appears to be a reliable method to objectively characterize fish gill pathology and may represent a powerful tool in environmental biomonitoring to ensure proper standardization and reproducibility. Though fractal analysis did not equal the discrimination power of the expert method, it certainly warrants further study to evaluate local variations in complexity or possible multiple scaling rules.     

Ants colony algorithm approach for multi-objective optimisation of surface grinding operations

An ant colony based optimisation procedure has been developed to optimise grinding conditions, viz. wheel speed, workpiece speed, depth of dressing and lead of dressing, using a multi-objective function model with a weighted approach for the surface grinding process. The procedure evaluates the production cost and production rate for the optimum grinding condition, subjected to constraints such as thermal damage, wheel wear parameters, machine tool stiffness and surface finish. The results are compared with Genetic Algorithm (GA) and Quadratic Programming (QP) techniques.Nomenclature a _p down feed of grinding (mm/pass) - a _w total thickness of cut (mm) - A _o initial wear flat-area percentage (%) - b _e empty width of grinding (mm) - b _s width of wheel (mm) - b _w width of workpiece (mm) - B _k positive definite approximation of the Hessian - doc depth of dressing (mm) - c _d cost of dressing ($) - c _s cost of wheel per mm³ ($/mm³) - CT total production cost ($/pc) - CT ^* expected production cost limit ($/pc) - d _g grind size (mm) - D _e diameter of wheel (mm) - f _b cross feed rate (mm/pass) - G grinding ratio - k _a constant dependent on coolant and wheel grind type - k _u wear constant (mm^-1) - k _c cutting stiffness (N/mm) - k _m static machine stiffness (N/mm) - k _s wheel wear stiffness (N/mm) - L lead of dressing (mm/rev) - L _e empty length of grinding (mm) - L _w length of workpiece (mm) - M _c cost per hour labour and administration ($/h) - N _d total number of pieces to be grouped during the life of dressing (pc) - N _t batch size of workpieces (pc) - N _td total number of workpieces to be grouped during the life of dressing (pc) - P number of workpieces loaded on the table (pc) - R _a surface roughness (µm) - R _a* surface finish limit during rough grinding (µm) - R _c workpiece hardness (Rockwell hardness number) - R _em dynamic machine characteristics - S _d distance of wheel idling (mm) - S _p number of spark out grinding (pass) - t _sh time of adjusting machine tool (min) - t _i time of loading and unloading workpiece (min) - T _ave average chip thickness during grinding (µm) - U specific grinding energy (J/mm) - U ^* critical specific grinding energy (J/mm³) - V _r speed of wheel idling (mm/min) - V _s wheel speed (m/min) - V _w workpiece speed (m/min) - VOL wheel bond percentage (%) - WRP workpiece removal parameter (mm³/min-N) - WRP ^* workpiece removal parameter limit (mm³/min-N) - WWP wheel wear parameter (mm³/min-N) - W _i weighting factor, 0W _i1 (W ₁+W ₂+W ₃=1)     

Identification of yield stress and plastic hardening parameters from a spherical indentation test

Assuming plastic hardening of metals are specified by the stress–strain curve in the form , the material parameters σ₀, k and m are identified from spherical indentation tests by measuring compliance moduli in loading and unloading of the load–penetration curve. The curve P(h_p) is analytically described by a two term expression, each with different exponents. Here, ε_p and h_p denote the plastic strain and permanent penetration. The proposed identification method is illustrated by specific examples including numerical and physical identification tests.     

Precision inspection system for aircraft parts having very thin features based on CAD/CAI integration

In this paper, a precision inspection technique using CAD/CAI integration is proposed for parts having very thin and sharply curved features. The technique begins with feature reconstruction of turbine blades which have combined geometry, such as splines, and thin small radius circles. The alignment procedures consists of two phases — rough and fine phases: the rough phase alignment is based on the conventional 6 points probing on the clear cut surfaces, and the fine phase alignment is based on the initial measurement of the curved parts using the least-squares technique based on iterative measurement feedback. For the analysis of profile tolerance of parts, the actual measured points are obtained by finding the closest points on the CAD geometry by the subdivision technique developed. The Tschebyscheff norm is applied iteratively, giving an accurate profile tolerance. The inspection technique developed is applied to practical blade manufacturing, and has demonstrated good performance.Nomenclature r _i (u),r _j (u) 3D vector curve representing theith,jth curve segment for spline - u, parameters in [0, 1] representing curve - P _i ,P _i+1 ith, (i+1)th control points on the spline curve along the airfoil direction - Q _j ,Q _j+1 jth, (j+1)th control points on the spline curve along the vertical direction - W _i ratio of chord length to the previous chord length on the spline curve - C(Cx, Cy) centre coordinate of the edge circle - _o, initial angle and range angle of the edge circle - N _jp ,N normal vector on the surface patch formed byP _i ,P _i+1,Q _j ,Q _j+1 control points - A ₁ toA ₆ 6 probing points for the rough phase alignment - A ₁ toA₆ contact points at the clear cut surface corresponding to theA ₁ toA ₆ - X(a _x,b _x,c _x),Y(a _y,b _y,c _y),Z(a _z,b _z,c _z) base vectors for CAD coordinate system with respect to the CCM coordinate system - O (O _x,O _y,O _z) origin of the workpiece in the CMM coordinate system - D measurement target points of the workpiece - r probe radius - M coordinate measurement target points in the CMM coordinate system - DM direction vector of the measurement target points in the CMM coordinate system - T ₁ transformation matrix of 4×4 for the rough phase alignment - T ₂ transformation matrix of 4×4 for the fine phase alignment - MM, MM _i measured data of the measurement target points - Lp Tschebyscheff norm of powerP     

A methodology for assessing manufacturing cost due to tolerance of aerodynamic surface features on turbofan nacelles

A component of the direct operating cost of aircraft is that associated with the manufacturing cost. This affects depreciation, interest, insurance and maintenance charges. By relaxing the requirements for aerodynamic surface smoothness the manufacturing cost can be reduced at the expense of an increase in drag and corresponding fuel costs. This work is part of a study to examine this multidisciplinary problem. Only isolated turbofan nacelles are considered. The costs associated with assigning different tolerance levels to the feature dimensions on nacelles are assessed. A statistical procedure is employed to estimate the cost-tolerance relationship for eleven features involving gaps, steps, surface profile and fastener flushness. This procedure requires actual manufacturing and cost source data. A knowledge of the cost-tolerance relationships is useful in a concurrent engineering context. It will allow aerodynamicists to optimise surface smoothness in consultation with production engineers, thus achieving the best compromise between cost and drag.Nomenclature A ₁ statistic distribution area to the left ofL ₁ - A _u statistic distribution area to the right ofL _u - C manufacturing cost (£/piece) - C _a assembly process manufacturing cost (£/piece) - C _c cost per concession (£/concession) - C _ci interface component edgei manufacturing cost (£/piece) - C _i interface manufacturing cost (£/piece) - C _lmh labour man hour cost (£/piece) - C _ma management cost (£/piece) - C _mh man hour cost (£/h) - C _mmh management man hour cost (£/piece) - C _nr non-recurrent cost (£/piece) (cost of all the jigs and tools used in the assembly process divided by the number of units produced) - C _rd redeployment cost (£/piece) - C _smh skilled worker man hour cost (£/h) - C _su support cost (£/piece) - C _sumh support man hour cost (£/h) - C _usmh unskilled worker man hour cost (£/h) - C ₀ initial manufacturing cost (£/piece) - d _tma t _ma parameter - d _{N c} N _c parameter - d _{O f} O _f parameter - d _{t r} t _r parameter - d _{t rd} t _rd parameter - d _{t su} t _su parameter - E _i interface edgei - F _i featurei - G interface gap (mm) - G _n interface gap normal to air flow (mm) - G _p interface gap parallel to air flow (mm) - L _ef production line loss of efficiency factor due to redeployment - L ₁ dimension lower specified limit (mm) - L _u dimension upper specified limit (mm) - M mean - N dimension nominal value (mm) - N _c number of concessions (concession/piece) - O _f worker overtime fraction - P surface profile deviation (mm) - R _on ratio between the worker overtime and the normal man hour cost - S interface step or fastener flushness (mm) - standard deviation - S _n interface step normal to air flow (mm) - S _p interface step parallel to air flow (mm) - T manufacturing tolerance (mm) - T _a assembly process manufacturing tolerance (mm) - t _bw basic work time (hour/piece) - T _ci interface component edgei manuacturing tolerance (mm) - T _i interface tolerance (mm) - t _ma management time (hour/piece) - T _p performance tolerance - t _r rework time (h/piece) - t _rd worker redeployment time to other production line stations different to the usual one (h/piece) - t _su support time of the methods, quality and design departments to the line (h/piece) - T _t tolerance threshold between skilled and unskilled worker employment (mm) - T ₀ initial manufacturing tolerance (mm)     

Computer-aided analysis of the forging process

This paper presents computer simulation of the forging process using the finite volume method (FVM). The process of forging is highly non-linear, where both large deformations and continuously changing boundary conditions occur. In most practical cases, the initial billet shape is relatively simple, but the final shape of the end product is often geometrically complex, to the extent that it is commonly obtained using multiple forming stages.Examples of the numerical simulation of the forged pieces provided were created using Msc/SuperForge computer code. The main results of the analysis are deformed shape, temperature, pressure, effective plastic strain, effective stress and forces acting on the die.Nomenclature C material constant - M strain rate hardening exponent - N strain hardening exponent - S coefficient of the microstructure - T temperature - u _i velocity component - x _j Cartesian coordinates - ̄ effective strain tensor - effective strain rate - ̇ proportionality factor in flow rules - _ij Cauchy stress tensor - _i deviator stress tensor - ̄ effective stress tensor - _y flow stress     

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     

Determination of stretch-bendability of sheet metals

Today's sheet-metal forming industry relies mostly on experience-based methods for finding the forming limits which assure successful forming processes. Such methods are inefficient and there is an obvious need for cost-effective knowledge-based computer-aided techniques.In this paper, a mathematical model for the stretch-bending processes is introduced. The model is capable of performing all calculations necessary to determine the effect of material properties on the process parameters such as forming loads, product geometry, springback, and residual stresses. From this model, the significance of various material parameters from productivity, ease of fabrication, and tool design viewpoints can be evaluated. This should contribute to the development and optimum use of sheet materials with improved properties.Notation c,d distances on the cross-section of the beam, m - h depth of the cross-section of the beam, m - K,n material constants in the power law equation: =K ⁿ - M bending moment, Nm - M _e maximum elastic bending moment, Nm - m non-dimensional bending moment,M./M _e - N axial tensile force, N - N _e maximum elastic tensile force, N - n _r non-dimensional axial force,N/N _e - non-dimensional parameter,c/(h ₂) - non-dimensional parameter,d/(h ₂) - effective stress, MPa - effective strain     

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     

Spindle deflections in high-speed machine tools — Modelling and simulation

This research attempts to develop spindle deflection error models for high-speed machining systems. A model for determining total spindle deflection at the tool-end is presented. The model incorporates spindle bearing characteristics, shifts in ball contact angles, and centrifugal force and gyroscopic moment effects at high speeds. It uses the transfer matrix method to determine the total deflections at the tool-end based upon the point contact deformations at the individual balls of an angular contact ball-bearing assembly. A simulator is also developed for simulating spindle end deflections for various spindle rotational speeds. The results of the simulation show contact angle variations and peak deflections at particular spindle rotational speeds. Important research issues are also presented.Nomenclature AF final position, inner raceway groove centre - RF initial position, inner raceway groove centre - W final position of ball centre - V initial position of ball centre - D ball diameter, mm - r _o inner raceway groove radius, mm - r _i inner raceway groove radius, mm - M gyroscopic moment, N-mm - FO r _o/D - FI r _i/D - P bearing pitch diameter, mm - K _o outer race load-deflection constant, N/mm^1.5 - K _i inner race load-deflection constant, N/mm^1.5 - CF centrifugal force, N - J mass moment of inertia, N.mm² - l length of spindle, mm - E modulus of elasticity, N/mm² - I moment of inertia of spindle, mm⁴ - Y deflection of spindle alongy-direction, mm - z deflection of spindle alongz-direction, mm - M moment at spindle end, N.mm - V shear force at spindle end, N - m spindle mass, kg - material density - _o outer race contact angle - _i inner race contact angle - nominal contact angle - _i inner race deformation - _o outer race deformation - angle between ball centre of rotation and the horizontal - mis-alignment (in degrees) of shaft assembly measured in a plane perpendicular to shaft axis (x-direction) - W1 ball and raceway angular raceway velocity ratio for outer raceway control - W2 ball orbital and angular raceway velocity ratio for rotating inner raceway and outer raceway control - circumferential ball position - raceway control 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     

A PID-type fuzzy controller model for machine control applications

This paper introduces a PID-like fuzzy controller model, which consists of only five fuzzy rules. Each fuzzy rule is designed to carry out a single control task. A self-learning procedure is used to determine the input scale factor for auto-tuning the system. A new performance criterion is suggested as an object function for the auto-tuning procedure. The features of this fuzzy controller, used in position control applications, are demonstrated by the simulation results of two different types of plants — a d.c. motor and an inverted pendulum.Nomenclature adjusting parameter of AIAE - C _I integral control constant in ruleR _I - C _L leading control constant in ruleR _zn andR _zp - C _P proportional control constant in ruleR _P andR _N - D _ZE domain of membership function _ZE - K _a adaptive adjusting constant ofC _L - K _H adjusting parameter for high-border of dynamic domain space - K _L adjusting parameter for low-border of dynamic domain space - P _R ramp input command - P _S step input command - S _de scaling factor for input variable de(change of error) - S _e scaling factor for input variablee(error) - S _o controller output scaling factor - U _max maximum output limit of fuzzy controller     

Loading strategies for a class of just-in-time manufacturing system

In this paper, based on the group technology and the just-in-time manufacturing concepts, two loading models for optimal utilisation of the processing capabilities of an integrated manufacturing system consisting of a set of heterogeneous workstations are developed. These loading models are developed to integrate and utilise the available information from both the bill of materials and the process plans. The objective functions for these models are: the maximum tardiness and the makespan. In these models, the production quantity of each customer order for any part or product always equals its corresponding demand quantity; each part requires a finite number of aggregated stages of operation; job splitting is allowed; and the processing priorities of all the jobs during the planning time horizon are specified based on a desirable dispatching rule. The proposed mathematical programming models are fixed charge problems which are solved by compatible mixed integer programming algorithms. Finally, to provide additional decision-making capabilities, based on these models and their corresponding solution algorithms, a compatible decision support system is suggested.Notation l(1 toL) the product index - t(1 toN) the component (e.g., job type) index - i(1 toN) the job type priority index - j(1 toM) the workstation index - r(1 toR) the processing stage priority index - k(1 toK) the due date priority index - J _i,j,r,k the job with the job type priority indexi of the customer with the processing stage priority indexr and the due date priority indexk which has to be processed at the workstationj - L _i,r,k the number of units of the job with the job type priority indexi of the customer with processing stage priority indexr and the due date priority indexk (e.g. demand quantities) - t _i,j,r the required time to perform the processing stage priority indexr of each unit of the job with the job type priority indexi at the workstationj - D _i,r,k the due date of the job with the job type priority indexi of the customer with the processing stage priority indexr and the due date priority indexk - s _i,j,r the required time for setting up the workstationj for processing the job with the processing stage priority indexr, and the job type priority indexi - X _i,j,r,k the number of units of the job with job type priority indexi of the customer with the processing stage priority indexr, and the due date priority indexk to be produced at the workstationj - l _i,j,r,k the idle time at the workstationj prior to processing the job with the job type priority indexi and the processing stage priority indexr with the due date priority indexk - V the maximum tardiness - W the makespan of the operation - Y _i,j,r,k=1 ifX _i,j,r,k>0 - Y _i,j,r,k=0 ifX _i,j,r,k=0 - _i,j,r,k a sufficiently large constant (e.g. _i,j,r,kL _i,r,k)     

Aspects of scanning microdensitometry: II. Spot size,focus and resolution

In scanning microdensitometry increasing the size of the measuring spot, or throwing the specimen out of focus, decreases the apparent integrated absorbance A_pE_p of a discrete specimen. Both experimental observations and elementary geometrical theory (i.e. ignoring diffraction effects) show that with moderate spot sizes the relative error in A_pE_p is greater with small objects or objects of high absorbance, and that with a given object the absolute error is approximately proportional to the spot diameter (round spot) or spot width (square spot). From the observed apparent integrated absorbances AE₁ and AE₂ obtained using measuring spots of width s₁ and s₂ respectively, the true integrated absorbance AE₀ corresponding to zero spot size can therefore be calculated from the approximate expression which reduces to With very large spot sizes, or with the specimen grossly out of focus, the apparent integrated absorbance of a specimen of radius R and transmittance I_t tends theoretically to a limit: A_pE_p = 0.4343πR² (I-I_t). Provided the true absorbance of the specimen does not exceed about 0.5 at any point, the true integrated absorbance could in principle be estimated with less than 3% error from the expression but in practice A_pE_p can probably not be measured with sufficient accuracy. In scanning measurements of apparent specimen area, the results depend both on the threshold absorbance used and the size of the flying spot. With low thresholds the apparent area of the specimen at first increases and later decreases, as the spot size is increased or as the focus is changed.     

Accuracy and strength of a joint loaded by suddenly applied torque

The influence of the required quality (fit and degree of accuracy) of prismatic joints to achieve guaranteed clearance was a speciality of experienced designers. The problem becomes quite complicated owing to stresses arising in the joint elements during torque transmission under dynamic loading.In this paper a widely used prismatic joint with a hexagonal cross-section is considered. A dynamic loading, generated by a spring mechanism is applied. D'Alambert's principle was employed in solving the kinesthetic problem.The paper presents equations for the dynamic coefficient, the angle of clearance, _i and the maximum tangential stress. It is pointed out that torque-loaded elements cannot be produced from rolled stock, obtained from drawings.The presented graphs permit selection of the steel grade in accordance with the fit and the degree of accuracy of the joint and with the permissible torsional stress.The proposed procedures may be used for computer-aided design of torque-transmitting prismatic splines, key joints and torsion mechanisms.Nomenclature d ₁ diameter of hole (see Fig. 1) - d _max D _n + es maximum limit of shaft size - d _min D _n + is minimum limit of shaft size - D _max D _n + ES maximum limit of hole size - D _min D _n + EI minimum limit of hole size - D _n nominal size of the hole and of shaft - ES, es upper deviation of hole and shaft - EI, ei lower deviation of hole and shaft - F area of hexagon - G modulus of transverse elasticity - (see Fig. 1) - I _p polar moment of intertia - polar moment of inertia of hexagon - polar moment of inertia of circle - K dynamic coefficient - l length of shaft - m number of polygon sides - M _d torque under dynamic loading - M _s torque under static loading - S _i clearance - S _max = ES-ei maximum clearance of joint - S _min = EI-es minimum clearance of joint - T tolerance - W section modulus of torsion - W _c circle section modulus of torsion - W _h hexagon section modulus of torsion - (see Fig. 1) - maximum tangential stress under dynamic loading - maximum tangential stress under static loading - _d twist angle under dynamic loading - _i angular displacement - _s twist angle under static loading     

Optimal concurrent tolerance based on the grey optimal approach

A new method for optimal concurrent process tolerance is proposed. Information related to process planning is used during the structure design stage of a product. The functional tolerances of the assembly of a product are considered process tolerances. A nonlinear optimal concurrent process tolerance model has been established to minimize the total manufacturing cost with different weight factors for the operations of the product. The constraints include concurrent process tolerance chains, the standard coefficient of process tolerance, and the economical maximum tolerance of the machine tools. In order to obtain optimal process tolerances, a new approach based on grey difference degree is presented in this paper. This approach takes the sequence consisting of the optimal value of every objective as the standard sequence, and that consisting of the actual values as the objective sequence. Thus, grey difference degree is calculated and used as the objective of the function. Finally, a practical example is introduced to demonstrate the effectiveness of the proposed method.Nomenclature Y ₀ standard sequence - Y ₀(k) k-th component of the standard sequence - Y _i objective sequence - Y _i (k) k-th component of the objective sequences - (k) the grey correlation coefficient of Y _i relative toY ₀ at point k - y _i the i-th required tolerance specification of assembly structure - TX design tolerance vector of assembly structure - r _u the total number of relative process steps for u-th part - T _uv v-th relative process tolerance vector of u-th part - _uv selection coefficient of process sequence - w _uv the weight coefficient of the process tolerance T _uv - C _uv manufacturing cost of the process tolerance T _uv - C _uv ^* the ideal value of C _uv - z _uv the standard normal transform coefficient relative to process tolerance T _uv - _uv the standard deviation of T _uv