Feed rate optimization based on cutting force calculations in 3-axis milling of dies and molds with sculptured surfaces

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Int. J. Mach. Tools Manufact. Vol. 34, No. 3. pp. 365-377, 1994. Copyright (~) 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0890-6955/9456.00 + .00

Pergamon

FEED RATE OPTIMIZATION BASED ON CUTTING FORCE CALCULATIONS IN 3-AXIS MILLING OF DIES AND MOLDS WITH SCULPTURED SURFACES ZEKI YAZAR,~ KARL-FRIEDRICH KOCH,:~ TOM MERRICKt a n d TAYLAN ALTANt

(Received 25 November 1992)

Abstract--The use of CAD/CAM systems and NC machine tools for die and mold manufacturing offers considerable advantages over conventional methods, such as reduction in machining time and costs, and improvements in accuracy and reproducibility. However, the selection of cutting tools and machining strategy and parameters, which have a significant impact on overall machining efficiency and process reliability, still depends on the experience of the machinist or the NC programmer. Based on these considerations, this study had two major objectives: (a) develop a method for estimating the cutting forces in 3-axis milling so that the NC programmer can "'optimize" the machining parameters; and (b) establish the "best" rough milling strategy to reduce machining time and cost. This paper concentrates on the first objective, namely on optimizing the feed rate to improve machining efficiency in end milling. By simulating the end milling process and predicting the cutting force in 3-axis milling of sculptured surfaces, an approach and the associated computer program have been developed to optimize the feed rate, already at the NC programming stage. The calculated cutting force, which includes the overall net effect of all process variables, is used as a feedback variable to adjust the feed rate. The method also allows the NC programmer to visualize cutting forces in a CATIA CAD/CAM environment.

NOMENCLATURE axial depth of cut (mm) back engagement of cut (radial width) (mm) nominal width of cut (in directions parallel to tool edge) (mm) b nominal width of cut for an incremental cutting edge element on the cutter surface of a Ab miLlling cutter (ram) C~, C,~, C~. factors for approximating the effects of different rake angles on the cutting forces factors for approximating the effects of different cutting edge inclination angles on the C~, C,~, Cp~ cutting forces C~.h, C,~b, Cp~h factors for approximating the effects of the width of land wear on the cutting forces feed (ram) f adjusted feed rate (mm/min) foot programmed feed rate (mm/min) fpre. F resultant cutting force (N) cutting forces in cutting, thrust and passive directions, respectively (N) Fc, F , , F o force constraint for a specific tool-workpiece material combination used for feed rate Fj~m optimization (N) highest of the maximum cutting forces at specified points on a single cutter path (N) Fmax force range factor for feed rate optimization FORRNG nominal thickness of cut (mm) h k.L~, k . . . krL~ specific forces of the Kienzle equation in cutting, thrust and passive directions (N/ mm 2) l-m., 1-ml, l-rap the exponents for cutting, thrust and passive forces, respectively (as functions of the nominal thickness of cut) spindle speed (rev/min) N override factor for feed rate optimization OVRD start and end point of the cutter tip point for a linear cutter path PI, 1"2 corner radius of a single point cutting tool (mm) re Vc cutting speed (m/min) width of land wear on the cutting edge (0.1 mm) VB height of material in cut on the cylindrical section of the cutter (mm) Zcyl clearance angles of the main and the side cutting edges, respectively (degree) Or, Otn wedge angle of the main cutting edge (degree) aa ap

tEngineering Research Center for Net Shape Manufacturing, The Ohio State University, Columbus, Ohio, U.S.A. *Fraunhofer-Institute for Production Technology, Aachen, F.R.G. 365

366

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Z. YAZAR et al. rake angle of the cutting edge (degree) value of the rake angle of a milling cutter, which is assumed to be constant on the entire cutting edge (degree) corner angle of a single point cutting tool (degree) angle between two consecutive nodes on the sphere of a ball end cutter/specification of relative distance between two nodes for all cutters tool cutting edge angle (degree) cutting edge inclination angle (degree) helix angle of end mill (degree) 1. INTRODUCTION

REDUCTION of product lead times (Concept to Customer), higher demands for quality, the need for cutting costs, and globalization of world markets require continuous improvements in manufacturing. In this context, productive use of CAD/CAM systems and NC/CNC machines is essential for remaining competitive in the die and mold manufacturing industry. Many commercial CAD/CAM systems enable the designer to generate a computer model of a part and the part programmer to determine NC tool paths using the same geometric model stored in the system. These systems have a variety of features to create, modify and manage the design and NC data, as well as facilitate their use with powerful interactive graphic interfaces. Nevertheless, the transition from design idea to finished part, from CAD to CAM, cannot be realized automatically. The user (NC programmer) still needs considerable interaction with the system to generate a more or less optimized tool path with the appropriate machining data (feed rate, spindle speed, etc.) and strategy [1]. During 3-axis milling of a die surface, the geometric interference between the cutter and the workpiece changes, continuously influencing the cutting force and tool deflections. The use of cutters with a high length-to-diameter ratio, which is often necessary to machining of small corner radii and deep pockets encountered in dies and molds, aggravates this phenomenon. To avoid broken cutting tools or unacceptable tolerances in critical parts of the 3D sculptured surfaces, the NC programmer tends to be conservative, normally by reducing the feed rate. As a result, most of the material is removed by using uneconomically low feed rates, leading to longer machining times and higher costs [2]. For efficient machining, CAD/CAM tools are needed that can support part programmers in determining the cutting conditions, machining parameters and strategy. Towards achieving this objective, Koch et al. developed at ERC/NSM, a computer program that optimizes the feed rate, as a function of the estimated cutting forces [2]. 2. FEED RATE OPTIMIZATION IN 3-AXIS MILLING

The feed rate is one of the major parameters that affects the process efficiency and reliability in machining. Usually the process variables such as feed rate and depth of cut are specified by the part programmer or the NC/CNC machine tool operator based on experience, handbooks, or tables of tool/machine tool manufacturers. Commercial CAD/CAM systems, now being used in many die and mold making shops, usually do not support the user in determining those machining parameters, although metal cutting has been studied extensively and several predictive models have been developed. It is difficult to predict an optimum feed rate when preparing an NC program for machining sculptured surfaces, while avoiding chatter, instability, excessive tool deflection, and possible tool breakage. A solution to this problem would be to adjust or optimize the machining parameters to variations that occur during the process. Thus, extensive work has been done in the area of adaptive control, where the cutting conditions are monitored in-process using various sensors (e.g. acoustic emission sensors), and the feed rate is controlled automatically based on a transfer function usually relating the feed rate to the cutting force [3-5]. However, adaptive control may not be always practical in end milling of 3D sculptured surfaces, where the variations of cutting conditions are characterized by

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rapid changes in the cutting force (compared to slot and face milling with relatively constant cutter-workpiece penetration, rigid tools and high material removal rates). Consequently the response times of adaptive controls and spindle speeds (mass inertia) are often too large for controlling the feed rate adequately [2]. Estimating an optimum feed rate already at the part programming stage would certainly reduce 'Lhe time and cost required for program verification and modification, and insure operation reliability and process efficiency. In order to achieve this goal, the cutting force must be estimated with an acceptable accuracy, based on the simulation of the 3D milling process. A few approaches found in the literature use the volume of material removed as feedback [6] or the machine tool horse power as constraint [7] to regulate the feed rate. The cutting force, as a single parameter for describing the net effect of all input variables, is an optimal quantity for use as a feedback from the simulated process for feed rate optimization. Consequently, it was necessary to develop a cutting force model, which is capable of simulating 3-axis milling of 3D sculptured surfaces with frequently used cutters such as fiat end and ball end mills. This model must be reasonably accurate and require moderate amounts of computing time to perform calculations. In addition, technological data must be available for different cutter/workpiece combinations used in the model. 2.1. The E R C / N S M program for cutting force calculation [2] 2.1.1. The geometry model. For estimating the cutting force, the ERC/NSM program, developed by Koch et al., uses a geometry model to describe the workpiece surface at each instant of the machining process [2]. Thus, the workpiece surface geometry, gener~Lted by the cutter motion between two cutter locations can be modified. Several studies [8-10] and some commercial CAD~CAM systems use solid modellers based on CSG (constructive solid geometry) models for NC path simulation and verification due to the simplicity of algorithms for generating machined volumes with Boolean operations. But this method needs enormous internal calculations that restrict its practical use. The ERC/NSM program is based on a geometry model used by Roeders [11], which represents the surface of a die or mold with a 2-dimensional array of points (Fig. 1). The basic idea i,; to specify an equidistant grid with small distances in the x - y plane of the workpiece. Then the sculptured die surface can be described as a lattice just by storing the z-value at each point of the grid in a 2-dimensional array. For any x - y point in between, the height can be approximated by locally interpolating the z-values of the four neighbouring points. The major advantage of this geometric model is that the mathematical effort, necessary for describing the part surface, is independent of the number of NC paths processed.

Die for a turbine blade

Detail of a machined surface

FIG. 1. Lattice geometries with different specifications [2].

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The modification of workpiece geometry, i.e. the simulation of material removal, merely consists of checking the z-value of the lattice points. If this value is higher than the surface of the tool path calculated from the tool geometry, then the height of these points is reduced to the surface of the cutter path, i.e. the surface generated by the cutter. The distance, between the initial (before cutting) and the final (after cutting) z-values, is used for describing the actual chip volume. The program can simulate the material removal by cutting with ball end and flat end mills. The lattice size depends on the availability of computational power and storage capacity. By defining different initial distances between the lattice points, the model can easily be adapted to represent a local portion of the surface geometry with high accuracy or the entire geometry of the die with reduced accuracy. Since just one z-value for each x - y lattice point can be stored, the geometry model is not capable of representing undercuts (which may be needed in 5-axis milling) and vertical walls. For a good description of the workpiece surface, it is recommended to select the distance between the lattice points to be less than one-tenth of the cutter diameter used. 2.1.2. The force model. The ERC/NSM program uses a so-called "Instantaneous Force Model" (for a classification of force models, see Ref. [12]) for cutting force calculations in 3-axis milling with ball end and flat end cutters. This model was selected instead of the more accurate but complex and computation-intensive methods, since it was necessary to perform the required force calculations at a large number of cutter locations. In this model, the instantaneous force is calculated on incremental sections of the helical cutting edge. Thus, the edge of the milling cutter is divided into a set of connected, elemental single point cutting tools (Fig. 2). To calculate the cutting force, it is necessary to identify the tooth elements actively engaged in cutting for a given cutter orientation. Further, it is necessary to determine the fundamental tool geometry, depth of cut and width of cut for each element to obtain the elemental force components from the classical orthogonal cutting analysis. The ERC/NSM program uses Kienzle's force model, for which a data bank is maintained at the Technical Ball-end cutter (here: no inner diameter) z

Flat-end cutter (here: with inner diameter) Z

i

:yl

FIG. 2. Geometricalrepresentation of a cutting edge with a set of nodes [2]. Symbolsare explained in the Nomenclature.

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University of Aachen, F.R.G. for different workpiece materials used in the industry. Kienzle's force model [13], like other empirical force models, is directly related to cutting and thrust forces, F~ and Ft. Using the nomenclature given in Fig. 3, the forces in the cutting, tlhrust and passive directions can be calculated with expanded Kienzle equations as:

(1) (2) (3)

F¢ = b • kcl., " h (1''~) " C~.v • C~;, • C~vb Ft = b • ktt.1 " h (1-''') • Cry • Ctx • Ctvb Fp = b .kpl.1 • h(1-mp )" Cp.v • Cpx" Cpv b .

In their basic forms, equations (1)-(3) were derived from the empirically determined dependence of the cutting force, Fc, on the cross-sectional area of the cut (ap × f or b x h) in turning experiments [14]. The specific cutting forces k¢l.1, k t l A and kpH are related to the cross-sectional area of the cut b × h = 1 mm, and largely dependent on the tool, material and cutting conditions. The exponents (1-me), ( l - r o t ) and (l-rap) are related to the nominal width of cut (Fc/b) and characterize the cutting force behavior of a workpiece-tool combination for different thicknesses of cut. In turning experiments, conducted at the Technical University of Aachen, F.R.G. [ 14], differences were observed between experiments and simulations. Thus, additional parameters, especially concerning the cutting tool geometry, were taken into account through additional factors, which led to expanded Kienzle equations (1)-(3). The factors Cxx are entered into the equations to incorporate the condensed effect of different rake angles % cutting edge inclinations h and widths of land wear, VB, observed in the experiments. In the present model and within a certain feed range, the cutting force decreases with increasing cutting velocity, v~, in a hyperbolic form, assuming there is no buildup edge (BUE) formation [14]. The data base, maintained at the University of Aachen, contains constants (specific forces and factors) only for one cutting speed for HSS cutters, and for three speeds for carbide cutters. Also the constants are only valid for a certain feed range, from 0.1 to 1.0 mm. On the other hand the applicability of the Kienzle equation has been demonstrated through comparisons with experimental data [15, 16]. A verification example, given in Ref. [2], shows that for measured forces in x-y directions the simulation results are satisfactory and display a good match with the experiments given in Ref. [17].

Geometrical nomenclature

~

Area of cut

Force nomenclature Ot

Fro. 3. Description of geometry and force for single point cutting tools [2]. Symbols are explained in the Nomenclature.

370

Z. YAZARet

al.

2.2. The feed rate optimization program (FEDOPT) The lattice geometry and force models, used in the ERC/NSM program, are independent from a specific CAD~CAM system. Using these models, the feed rate optimization program (FEDOPT) was developed as a stand-alone code. It is written in FORTRAN 77 and compiled with VS FORTRAN, which runs on IBM 4381. The interface with a CAD/CAM system or an NC programming system is the cutter location file (CLFILE). CLFILE has an internationally standardized format and is generated by most of the CAD/CAM systems as a machine tool-independent neutral file. Figure 4 shows the process flow for generating optimized paths using the feed rate optimization program. A CLFILE can be generated by a CAD/CAM system, or by a dedicated NC programming system. Having the CLFILE, the NC programmer normally runs the postprocessor for the machine tool, on which he plans to machine his part, to generate the NC data (G-Codes) for that specific machine tool-NC/CNC controller combination. The FEDOPT program gives the user the option to optimize the feed rate. By running FEDOPT, the user can generate a CLFILE with adjusted feed rates based on force calculations and then go through the same process with the postprocessor. Since the CLFILE format is standardized, FEDOPT can easily be implemented and used in different CAD~CAM environments. Figure 4 also shows the three data files (or data bases) that are required to run FEDOPT, as well as the output files for visualizing the calculated forces in CATIA. Implementing the functions of the CATIA Graphics Interactive Interface (GII) as part of the ERC/NSM program, the F3MCAT module [2] enables the user to visualize the machined surface (based on the lattice geometry model) and the calculated forces on the CATIA screen. 2.2.1. Input data for the simulation and optimization of the milling process. For the simulation of the machining process, calculation of the cutting forces and optimization Technical drawing

CAI)/('AM System (CATIA)

NC

CLFILE

~

System

p,,~m~

~

NCdata

or user input FEDOPT

DATA FEDINFO

D ~

I

~

DATA TOOLS

~

DATA FORCE

DA'TA | I" ~ ] 1 DATA F3MFORI ~

F3MCAT

OutputFiles

for Force Visualization

Force Data Visualization for CATIA

FIG. 4. The process flow for generating optimized NC tool paths using the feed rate optimization program FEDOPT.

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of the feed rate, the NC data are needed. These data, e.g. cutter locations, feed rates, spindle speeds and tool changes, are extracted from CLFILE as the main input file. In addition, for cutting force calculation and feed rate optimization, F E D O P T needs information on tool and workpiece material and the corresponding empirical constants. These data are organized in three files (or data bases), namely DATA TOOLS, D A T A F O R C E and D A T A FSPECS, as discussed below. 2.2.1.1. Tools data file (DA TA TOOLS). The tool data, including tool type, material, diameter, length, number of cutting edges, rake angle, helix angle, and land wear of the total as the force constraint Flim, a r e retrieved from a tools data file called D A T A TOOLS. For the present implementation, the limiting forces for each tool were obtained from the NC milling simulations and force calculations of the ERC/NSM program. For a specific tool (tool geometry and tool material) and workpiece material (here AISI 1034 medium carbon steel), the maximum recommended depth of cut in slot milling was selected from the tables given in Ref. [16] to have the highest acceptable load on that tool. Feed :rates and cutting speeds were set according to the same source. Then force calculatiorLs were made for a slotting application at five points and the highest value was selected as the force constraint for feed rate regulation. The best method for obtaining the constraining force for a given tool and workpiece material is to measure the force directly during the milling operation for a test part with recommended machining parameters for maximum load. This task will be carried out in the near future. In the present work, data for only one workpiece material were used and the Eli m value was put into the DATA TOOLS file. However, for practical implementation, a relational data base structure, containing data for various workpiece and tool materials, would be appropriate. The present version of the program gives no warning in case of an inconsistency between the data retrieved and the tool data used in the "CUTTER" CLFILE statement. A consistency check could easily be added. Also, it would be good practice to maintain a tool,; data base for all the tools used in a machine shop. This would be useful also for other purposes like process planning or shop floor management. 2.2.1.2. Data fi,!e for force calculation constants (DATA FORCE). This data file ( D A T A FORCE) contains the constants for the Kienzle equations, used for force calculation [14], i.e. specific forces and Kienzle exponents in three directions, namely the cutting, feed and passive directions. From the constants obtained for various materials, tools, cutter geometries and spindle speeds stored in this file, FEDOPT retrieves the me,st appropriate set of six constants for the expanded Kienzle equation. The source of these data [14, 18] is subject to copyright. In this study, data for the workpiece material 1034 medium carbon steel were used. The file contained the specific forces and forces for the expanded Kienzle equation for carbide and high speed steel (HSS) end mills. For carbide tools the influence of cutting speed on the force calculation constants was considered by entering different values obtained for three cutting speeds. 2.2.1.3. Specifications data file (DATA FSPECS). This data file contains specifications for the simulation of the cutting process and includes the definition of the dimensions, origin, height, inclination angle of the lattice, e.g. distance between two force calculations, paramelers for calculation density, and feed rate optimization. Unlike the previous two data files (or data bases), which are updated and maintained independently from the individual runs of the FEDOPT program, the file FSPECS is specific for each simulation and optimization. Each time the user runs the FEDOPT program, he can change the values stored in this file to observe different sections of the part geometry and optimize the associated tool paths, try out different workpiece materials, make in-depth calculations for a specific cutter and cutter location, determine the density of force calculation, and specify the accuracy of iterations for feed rate optimization. The user has also the option to enter all these values interactively through dialogue with the system.

372

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2.2.2. Feed rate optimization. FEDOPT uses the calculated cutting force as feedback from the machining process to adjust the feed rate. Figure 5 shows the block diagram of this optimization algorithm in a form similar to a single-loop feedback control system. The feed rate programmed by the NC programmer, fprg, is the reference input to the system. The cutting force feedback is generated by using the lattice geometry model and Kienzle force model. The program starts processing the cutter paths after positioning moves of the cutter in RAPID mode (G00 mode in NC data). It checks also whether initial tool, spindle speed and feed rate are defined. Then for each NC pass (cutter tool path), i.e. APT GOTO or FROM statement (or CLFILE Class 5000 instruction) the cutting force is calculated at intervals specified by the user according to the penetration and force calculation algorithms mentioned earlier in section 2.1. The lattice geometry is modified for a given linear cutter path to simulate the material removal. Also output data are generated for lattice and force data visualization depending on the user specifications. After the resultant forces are calculated at selected intervals for a specific cutter path, the highest of these forces is fed back to adjust the feed rate. Then this maximum resultant force Fmax is compared with the force constraint Fir, of that specific tool-workpiece combination. If the calculated force is greater than the force constraint, the feed rate is reduced by multiplying the programmed value by an override factor, OVRD. Then the forces are calculated again for that cutter path with the new feed rate. For forces less than the constraining force the feed rate is increased to improve the machining efficiency, i.e. reduce the cutting time. Force calculations made by the ERC/NSM program with different feed rates showed a linear relationship between the resultant cutting force and the feed rate, which is due to the form of the Kienzle equations. Although there is no simple relationship between these two variables (cutting force and feed rate), modifying the feed rate,

PLEN~..~

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', , ~ , ~

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/'

Linear NC Cutter Path PI-P2 (e.g. APT GOTO/P2 statement or CLFILE Class 5000 comma

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Force calculation points

programmed feed ratc /prg

CFORCE,M LAT Process Simulation and Forcc Calculation

OVRD x Fprg

adjusted feed rate fc,pt ~.

Fm.x Feed Rate Regulation OPTFED

FIG. 5.

Block diagram of feed rate optimization based on force calculations (FL • • • F.: calculated maximum forces at intervals; Fmax: highest of the maximum forces; PLENF: distance between two force calculations:; OVRD: override factor for feed rate; CFORCE, MLAT, OPTFED: subroutines for cutting force calculation, lattice modification, and feed rate regulation, respectively).

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373

based on a linear relationship between the cutting force and the feed rate, gives reasonable results as a first approximation [4]. Thus, the adjusted feed rate, foot, is calculated from: fopt= OVRD x fprg, where OVRD =

glim/gma

x .

(4)

The calculation of cutting forces and the adjustment of the feed rate are carried out iteratively. This iteration is controlled by a force range factor, FORRNG, which is specified by the user. By using this factor, the user can determine how close the calculated force~; would be to the force constraint. In other words he/she indirectly determines the number of force calculation-feed rate iterations necessary for the optimization. For example, if FORRNG is equal to 0.1, then the iteration will be stopped for a calculated resultant force, Fmax, where 0.9 × Elim < Fmax < Eli m. After the iterations the adjusted feed rate, calculated for a specific cutter path, f o p t is written in CLFILE before that cutter motion instruction. Thus, a new CLFILE containing cutte:r paths with optimized feed rates is created as a result of processing with FEDOPT. 2.2.3. Output data and visualization in CA TIA. The main output of FEDOPT is a new CLFILE with adjusted feed rates. FEDOPT enables the user also to visualize the lattice geometry and the calculated cutting forces in the CATIA system environment. For that purpose it generates the necessary files (see Fig. 4) for the visualization module F3MCAT of the ERC/NSM program [2]. Depending on user specifications, up to three different output files are created for force data visualization in CATIA. The lattice data, representing the whole or a part of the workpiece geometry, are stored in the DATA F3MLAT file. This file is useful for simulating material removal, i.e. displaying the machined surface, for example with scallops for a ball end mill. However, the display quality depends on the resolution of the lattice, and is restricted by its dimensions. Two output files can be generated for cutting force visualization. DATA F3MFOR contains the major data for all cutter locations where force calculations are conducted. For each calculation point, the data consist of the NC tool number, the coordinates of the cutter loc~ttion, the feed vector and the force vectors for maximum and minimum cutting force values on the whole cutter. FEDOPT uses this file to enable the user to detect critical areas of the machining process via force overviews. However, FEDOPT automatically regulates the feed rate so that at no force calculation point do the resultant maximum forces exceed the given force constraint FnimFor obtaining more detailed information about the cutting forces, chip load on the edges and other variables as a function of time, an output file, D A T A F3MFOR1, can be created. This file contains data for only one cutter location. It enables the user to generate 2D diagrams of CATIA (in DRAW mode) showing the cutting forces as a function of time and rotation angle, or showing the apportionment of chip thicknesses or cutting forces along one cutting edge for several rotation angles (see Ref. [2] for more details). Based on the ,data in the mentioned output files, F3MCAT (Fig. 4) basically makes use of the graphics interactive interface (GII) of CATIA for application programming. With GII it is possible to integrate user defined functions (here the visualization functions) in the CATIA environment. The functions may access the CATIA data base and use a standard CATIA user interface, like menus, prompts/dialogue, function box, etc. 3. APPLICATION OF FEDOPT

The FEDOPT program was used to part, which was programmed by using MILL-ROUGH function. Two cutters cutting the first layer on the stock, and HTH 34~3-F

simulate the rough machining of an example the layer (z-planes) strategy of CATIA NC were used: a 2½" diameter flat end mill for a ½" diameter fiat end mill for the rest of the

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roughing. Figure 6 shows the lattice simulating the material removal, i.e. the rough machined part, generated by FEDOPT and displayed by the F3MCAT function in CATIA. In the simulation, the tool material was HSS, and the workpiece material was AISI 1034 medium carbon steel. The lattice dimensions were 228 × 228 with 1 mm step sizes in the x- and y-directions. The thickness of the raw block was 55.5 mm. The dimensions of the stored lattice for visualization in CATIA were 28 × 28 with 8 mm step size. The force calculations were made at intervals of 15 mm. On IBM 4381 hardware, the running time for the feed rate optimization program, FEDOPT, was under 30 min for both cases with the specifications given above.

3.1. Case I: use of F E D O P T by an inexperienced programmer The turbo charger cover was machined from wood and wax on an OKADA 3-axis milling machine at the ERC/NSM facilities. Assuming that an inexperienced programmer tries to machine the same part from 1034 steel, this case shows how FEDOPT can be helpful in selecting a proper feed rate without endangering the tool and the process. Thus, FEDOPT is useful in training inexperienced NC programmers. Figure 7 shows only the cutting forces calculated for the 2½" tool, since the display of all of the forces (including the forces for the ½"tool) would result in a very confusing image. The forces calculated at user specified intervals were displayed as vectors. It can also be noticed from Fig. 7 that the forces were not calculated unless the cutter was completely inside the material, i.e. the lattice representing the workpiece. In Table 1 and Fig. 7, it is seen that the maximum forces, Fmax for the 2½" cutter before the feed rate optimization were nearly constant for the displayed force calculation points, and they were far smaller than the force constraint, Flim, for that tool. But for the ½" cutter, since the cutting parameters, i.e. depth of cut aa, spindle speed N and feed rate fprg, were chosen similar to those of cutting wax, they exceeded the force constraint, which would probably result in tool breakage. Table 1 also shows the adjusted feed rates, fopt and calculated forces, Fmax, after the feed rate optimization. FEDOPT reduced the feed rates for the ½" end mill, so that the forces were then below

I

Fro. 6. Lattice geometry generated by FEDOPT and displayed by F3MCCAT in CATIA representing the rough machined turbo charger cover.

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FiG. 7. Cutting forces calculated for rough machining of the turbo charger cover displayed as vectors for the 2~" flat end mill before feed rate optimization (Case I). TABLE 1. CUTTING ~.?ARAMETERS AND CALCULATED FORCES USING F E D O P T

FOR ROUGH MACHINING OF TURBO

CHARGER COVER (CASE I ) t

Cutter 2½"-flat end ½"-fiat end

at,

N

for,

F.,.x

f,,o~

Fm.x

F,,,

(mm)

(rpm)

(mm/min)

(N)

(mm/min)

(N)

(N)

6.7 4.35-6.85

800 1200

480 480

6300 2600-4700

1410 80-160

15,370 1050-1150

15,800 1150

~Total machining timc: bcfore feed rate optimization. 88 min; after feed rate optimization, 271 min.

the critical limit. They were also above 90% of the force constraint Flim, since the force range factor F O R R N G was selected as 0.1. After optimization, the calculated forces for the 2½" end mill were higher owing to the increased fi.~ed rate for a better machining efficiency. For the ½" tool, the total machining time increased considerably after the optimization with F E D O P T because before the optimization the cutting parameters were selected improperly. Thus, for this case, F E D O P T was useful mainly in improving the process reliability. 3.2. Case 11: use o f F E D O P T by an experienced programmer As a second case, let us assume that the NC programmer used machining data tables from a handbook, e.g. Ref. [16]. Also let us assume that, like many other programmers, he tended to be'. conservative in choosing the cutting parameters to prevent excessive tool wear and possible tool breakage. The cutting parameters selected can be seen in Table 2. In this case, F E D O P T TABLE 2. CU'Iq'ING PARAMETERS AND CALCULATED FORCES USING

FEDOPT

FOR ROUGH MACHINING OF TURBO

CHARGER COVER(CASE II)'t"

Cutter 2½"-flat end ½"-fiat end

a~

N

fpr~

Fm~,x

Lp,

Fm~x

F,~m

(ram)

(rpm)

(mm/min)

(N)

(mm/min)

(N)

(N)

6.7 4.2.5-6.85

600 800

60 30

1150 320-550

1320 40-120

14,570 1050-1130

15,800 1150

tTotal machining time: before feed rate optimization, 1366 rain: after feed rate optimization, 933 min.

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increased the feed rate for both cutters, i.e. 2½" and ½" flat end mills, so that there was a significant reduction, approximately 30%, in machining time. Comparing the results, especially the changes in the cutting forces and the machining times, it is seen that FEDOPT supports the user in determining feed rates that would not damage the tools, and also not cause unnecessarily long machining times. However, since the feed rate adjustment is based on force calculations, the proper selection of other basic cutting parameters like depth of cut and spindle speed are still important for improving machining efficiency. This can be seen from a comparison of the total machining times in both cases (Cases I and II) after the feed rate optimization of the same NC cutter path for the rough machining of the turbo charger cover. 4. SUMMARY AND RECOMMENDATIONS

In this study, an approach and the associated computer program FEDOPT are presented for improving the process reliability and efficiency in 3-axis milling of sculptured surfaces encountered in dies and molds by optimizing the feed rate. In FEDOPT, the process simulation and the force calculations are based on a lattice geometry model and an empirical force model developed by Kienzle. The geometry model allows the calculation of penetration between the workpiece and two types of cutters, i.e. ball end and flat end mills. The initial workpiece geometry for milling simulation is limited to a raw block, which may also have an inclined top plane. Force calculation equations include constants determined in machining experiments at the Technical University of Aachen for several tool and workpiece materials, and made available in data bases that are subject to copyright. Although the force model is derived from turning experiments, it can also be applied to milling operations. For the feed rate regulation, FEDOPT uses a force constraint for each tool-workpiece combination. The major criterion for optimization is minimum machining time. Thus, the feed rate is increased if the calculated maximum forces are below the given constraint, and reduced if they are over. The override factor used to regulate the feed rate is calculated assuming a linear relationship between cutting forces and feed rate. Thus, FEDOPT automatically adjusts the feed rate starting with an initially programmed feed rate and a given force constraint. FEDOPT may be used: (a) in determining proper machining parameters without much machining experience and in providing a training tool; and (b) to improve the machining efficiency by selecting a relatively high feed rate while maintaining process reliability. There are several possibilities for expanding this study and using FEDOPT in a production environment.

4.1. Improvement of the geometry and force models The lattice geometry model is restricted to a certain geometry, allowing the user to investigate forces in rough machining from a die block. By making the necessary modifications in the program, it is possible to define the rough machined part as the initial geometry (lattice) to calculate forces and regulate feed rate for finishing operations. The force model can also be improved to calculate the machining forces while the cutter is not entirely inside the workpiece material.

4.2. Verification of the force model There is a need for a more complete verification of the force model. Additional experiments are necessary for setting the correct force constraints for each tool-workpiece material combination instead of deriving them from simulations. 4.3. Optimization criteria Besides the minimum machining time, maximum tool life is also an essential criterion influencing the overall production costs. Thus, in future work, this criterion should also be included in the optimization.

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4.4. Process planning The results of this work can be integrated with other studies being conducted at the ERC/NSM or elsewhere for improving machining efficiency in an expert system environment. It may be possible to develop a process planning system for machining dies and molds with sculptured surfaces, similar to the system described in Ref. [19]. REFERENCES [1] Z. YAZAR,T. IVIERRICKand T. ALTAN, Feed rate optimization based on cutting force calculations in 3axis milling of sculptured surfaces, Report no. ERC/NSM-D-92-35, Engineering Research Center for Net Shape Manufacturing (ERC/NSM), Ohio State University (1992). [2] K.-F. KOCH, B. LILLY, E. KROPPand T. ALTAN,Development of a CAE-module for calculating cutting forces in 3-axi,; milling of sculptured surfaces in die manufacturing, Report No. ERC/NSM-D-90-43, Engineering Research Center for Net Shape Manufacturing, Ohio State University (1990). [3] A. ASA! and T. TSURUHASHI,Development of die-cutting feed rate control system, JSAE Rev. 9, 77-82 (1988). [4] B. K. FUSSEL and K. SRINIVASAN,On-line identification of end milling process parameters, Trans. ASME, J. Engng Ind. I l l , 322-330 (1989). [5] J. F. KAHLES,Machinability data requirements for advanced machining systems, Ann. CIRP36, 523-529 (1987). [6] CGTech VERICUT News Vol. 1, Issue 1. CGTech, Irvine, California (1992). [7] W. J. ZDEBLICKand L. J. HAWKISS, Machinability data base for end mill application, CASA SME Technical Paper MS81-184, SME 1981 International Tool and Manufacturing Engineering Conference, Detroit, Michigan (1981). [8] S. TAKATA,M. D. TSAI, M. INUI and T. SATA,A cutting simulation system for machinability evaluation using a workpiece model, Ann. CIRP 38, 417-420 (1989). [9] Y. ALTINTASand A. SPENCE, End milling force algorithms for CAD systems, Ann. CIRP 40, 31-34 (1991). [10] M. F. DEWAELE, C. H. MENQ and T. ALTAN, Numerical control milling simulation and part program verification using constructive solid geometry, Report no. ERC/NSM-D-89-12, Engineering Research Center for Net Shape Manufacturing, Ohio State University (1989). [11] J. ROEDERS, Simulation of the cutting conditions in milling with ball end mills and arbitrary cutter goemetries (in German), Dissertation, RWTH Aachen (Technical University), F.R.G. [12] S. SMITrland J. TLUSTY,An overview of modeling and simulation of the milling process, Trans. ASME, J. Engng Ind. 113, 169-175 (1991). [13] O. KIENZLE, Prediction of Forces and Power in Machine Tools for Metal-cutting (in German), pp. 299-305. VDI.Z 94, Duesseldorf (1952). [14] W. KOENIG,K ESSEL and L. WlrrE, Specific Cutting Force Data for Metal-Cutting (in German). Verlag Stahleisen GmbH, Duesseldorf (1982). [15] K.-D. BOUZAKISand G. METHENITIS,Determination of the values of the technological parameters which are used to describe the time course of cutting force components in milling, Ann. CIRP 34, 141-144 (1985). [16] Machining Data Handbook Vols 1 and 2, 3rd edition. Machinability Data Center, Metcut Research Associates Inc., Cincinnati, Ohio (1980). [17] V. HANN, Kinematics of end milling (in German), Ph.D. Dissertation, RWTH Aachen (Technical University), F.R.G. [18] W. EVERSHEIN, W. KOENIGet al. Computer aided planning and optimization of cutting data, -time and -costs, Ann. CIRP 30, 409-412 (1981). [19] B. E. BARKOCYand W. J. ZDEBLICK,A knowledge based system for machining and operation planning, CASA/SME paper MS84-716, also presented at the AUTOFACT Conference, Anaheim, California (1984).