Advanced Path Generator for Sculptured Surface Machining

U>pyrigth "" rFAC MOllon Control for Intelligent Autom.lIon Perugla. Ital)'. October 27·29. 1992

ADVANCED PATH GENERATOR FOR SCULPTURED SURFACE MACHINING P.E. ORBAN National Research Council of Canada, Advanced Manufacturing Technology Program, Institute for Mechanical Engineering Ottawa, K 1A OR6 Ontario, Canada

Abstract In the paper a new path generator for sculptured surface machining is proposed. First the task distribution in the free-fonn shaped pan production is analyzed. Existing mathematical methods for surface description are summarized, and the 3- and 5axis tool path generation is reviewed. The stale of the an in sculptured surface machining is assessed, and the initial results of an advanced path generator are presented. Finally the future work is outlined. Keywords computer numerical control. interpolator, sculptured surface machining, tool path generation INTRODUCTION Manufacturing parts with sculptured surfaces has an ever increasing imponance. These pans have to satisfy several requirements beyond their functionalit y, like aesthetics, shape continuity, flow characteristics, etc . The application of such parts where shape and functionality are so closely integrated , is widespread in the aerospace, car and ship building as well as tool and mold making industries. Their usage in various consumer products is also increasing . The advent of commercially available CAD/CAE systems has provided the means for designing sophisticated parts, but producing these pans on existing machining systems is stilI complicated, time consuming and prone to errors. The reasons for the cumbersome part production are mostly historical. Firstly, the design and production of such pans has been fragmented over many work groups and disciplines. This has hindered the efforts to lOOK at the design and production as an integrated process, and emphasis has instead been placed on advancing the individual levels and their interfaces within the production process. Secondly, the basic principles of NC machines and their programming have not changed much since the fifties, when they were originally laid down. NC machines still generate line segments, and arcs in the main planes. Higher order surfaces,must be approximated by primitives that NC machines can execute, usually only by line segments. This limitation of NC controllers defines the level of abstraction of data in the production process. As a result of the low level data abstraction, the data files ID be produced for the NC controller become huge, The paper proposes an improved path generator for NC controllers, designed to move the tool

directly on a sculptured surface , without approximating the shape with line segments. The manufacturing process itself could be simplified by using such a "more intelligent" controller in the production, the individual tasks redistributed more logically, the intennediate data reduced, and the pan quality improved. In other words , the production of parts would be faster and cheaper with beuer quality . SC~DSURFACEPARTPRODUCTION

When the design of a part in the CAD system is completed and the general fabrication process selected, the next step is ID decide on the machining strategy. NC machining is one of the most frequently used method, due to its flexibility , precision and short lead time. In NC machining the tool path for the part has to be defined fust. The machining of a pan can be classified into two steps: the roughing process and the fmishing. Two sets of tool paths are generated to do the machining. The roughing processor generates programs to remove as much excess material as possible from the blank in a simple and efficient way. The fmishing processor generates the tool path for the final contouring of the pans. Tool paths for the machining programs are commonly output in the language called Automatically Programmed Tools (APT). APT is a manufacturing language in which geometry and machining processes can be described [APT -77J. To generate the APT program for the machining, APT requires the tool geometry to be known. The output lOOl path describes the tool end point coordinates. In the next step, the high level APT program gets compiled into the Cuuer Location (CL) file by the APT processor whose main task is to perform

ll- 25

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geometrical calculations related to the tool path generation. The machine tool dependent information is added to the part program at post processing time. Though the NC language is standardized, the physical features and other properties of machine tool systems differ from each other considerably. All pertinent information on the particular machine tool and its controller is contained in the post processor. The output from the post processor is the NC tape, which can be run on the machine tool [IS0-86J . The last step of the whole procedure is the actual machining. The machining includes the setting up of the part and the cutting tools, and running the previously generated NC programs. Setting up the part and the tools is an imponant step; it inherently influences the accuracy of the produced pan. When machining sculptured surfaces, the set up has to be done very accurately to the predetermined values, i.e. to the values that were used for geometrical calculations during the course of the NC tape preparations.

controller just before machining , and the compensation is calculated and applied run-time by the NC controller. Optimally, the production of free-form parts would be best done in a system consisting of three layers : design, manufacturing planning , and machining. For that solution, a machine tool controller would provide the machining layer by understanding surface information and directly generating tool motions. This would lead to an optimal task distribution among the layers, with reduced amount of data. as compared to existing freeform machining practices. In the following sections the mathematics for the tool motion calculation will be summarized; the surface representation and tool path generation. SURFACE REPRESENT A TION A surface in computer aided design is described by a two variable vector-scalar function: r

= x(u,v) i + y(u.v) j

+ z(u.v) k

EVALUATION It can be seen from the above description of the free -form machining process. and experience has shown also. that the process is complicated, time consuming and prone to errors. There are several problems associated with the production process described above. First of all. the system has far too many layers. The information (APT, CL-file . G-code) passed between the layers is in one of the number of variations of a "standard" file format [Ogorek-85J. Difficulty arises as each vendor has their own implementation and interpretation of the various standards. requiring further customized filtering and conversion between the layers. Debugging the production process is difficult. the source of errors is not always obvious. and it is difficult to pin down from which step the error originated. The information in the CL files and NC tape files, which contain the line segment approximation of the machining tool path, is very low level. and hence huge in size. Handling the huge data files is awkward, and usually special techniques have to be applied 10 overcome the limited storage capacity of NC conttollers [Orban-86J . Another deficiency of conventional sculptured surface part production is that tool and part set up values for the machining have to be known in advance, well before the actual machining. There is nothing wrong with selecting the tool type and specifying the fixturing during the machining planning stage (that should be part of the machining planning). but this selection should only be nominal. The actual values should be able to vary, as tools ~ sharpened repeatedly. or insens replaced. and parts fixtured on the machine tool without high precision. The minute deviations from the nominal values should be compenSated for during machining [Van den Berg-88] . This contrasts sharply with conventional, non free-form machining, where 1001 and pan offset values can be entered into the NC

Engineering surfaces are often too complex to be described by a single patch. they are made up of a set of piece wise patches. The patches are connected to each other with the required degree of continuity. A surface patch is described by the following equation:

n m

r(u,v)

= I.

I.

8iJ' Fi(u) Gj(v)

i=Oj=O The surface patch is given in terms of F(u) and G(v) basis functions . For basis functions CAD systems use cubic-spline, Bezier, B-spline, rational B-spline. etc. expressions. The F(u) and G(v ) polynomial functions are independent from each other, and any of the known functions can be used for the surface definition. The 8ij coefficients are the conttol points of the surface patch. These points should form an onhogonal networlc of points. When limiting the u and v parameter values between 0 and 1, the expression of a surface can be converted to the following concise matrix form : r(u,v) = U A P BTV where in case of a third degree surface U = [u 3 u 2 u 1],.VT [v 3 ,,2 v IJ. A and B are the blending matnces. and the P matrix contains the geometric information on the surface patch. A detailed treatment of the mathematics of surface description can be found in the literature [Faux-79. Mortenson-85].

=

TOOL PATII GENERATION Tool path generation is the process, whereby mouon commands are produced to move the tool far metal removal from the pan. As mentioned previously, the metal removal consists of two pans:

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ADV A."'CED PA 111 GE'-"ERA TOR FOR SCliLl'TURED S L'RF ACE

the roughing process and the finishing cut. The roughing process is relatively simple: the tool usually moves along straight lines. The goal is to remove the maximum amount of excess material with each pass. For the final contouring, or finishing cut, the tool has to follow the surface of the free-form shape with the required tolerance. There are several methods to cut a free-form shape on a machine tool [Giessen-86]. Most widely used machining methods are the 3- and 5-axis contouring. In 3-axis contouring the tool follows a general path in three dimensions around the pan. The orientation of the tool axis does not change during machining. As the contact point varies along the tool path during machining, the machining efficiency, accuracy, tolerance and machining time are all effected. Another drawback of 3D machining is that usually several different part set-ups are required to machine the pan fully, because of the limited tool access to the parl. 3D machining employs a ball nose cutter. The tool center point, which is the feature that can be controlled by the NC machine, moves on an offset surface. (Figure 1.)

R

Figure 1.

N(t)

= ru x rv

Iru x r~

Where r(t) is the tool path on the 3D surface, N(t) is the surface normal unit vector, R is the tool radius, and ru, rv are the partial derivatives of r with respect to u and v. Note. that the expression of ro(t) is no longer polynomial. Another way to look at the 3D tool path generation is to consU'Uct fU'St an offset surface at a distance R from the original surface, and then to specify the tool path on the offset surface: ro(u,v) = r(u,v) + N(u,v) R

u

=U(1). v =v(t),

-+ fO(U.V)

Figure 2. As the contact point between the tool and the pan does not change along the tool path, the tool is always CUlling with high efficiency . Also, the number of set-ups is reduced due 10 the extra degrees of freedom of the machine tool. Despite the requirements for more complex machinery, the popularity of 5-axis machining is increasing due to its advantages: higher accuracy, beuer surface finish and reduced machining time [Giessen-86. Milacron-

Pm

The movement of the tool center point can be described as follows :

=r(t) + N(t) R;

The significance of this is, that offset surfaces themselves can easily be approximated by polynomial surfaces. The accuracy of the approximation depends on the differential features of the original surface [Farouki-86]. 5-axis machining eliminates most of the problems associated with 3D machining. The tool is kept in a constant orientation to the part during machining , described by two angles , the tilt angle At, and the lead angle Bt. (Figure 2.)

87]. A five axis machine tool has two additional rotary axes to maintain the constant relation between the tool and the pan. Coordinates for machining are given in a coordinate system auached to the part. These coordinates have to be transformed into the coordinate system of the machine tool. which can be controlled by the Numerical Controller. The machine coordinates can be calculated from the part coordinates as follows [Paul-8l}:

I(t)

ro(t)

!'.1J\CJ-II.',T'\G

=fO(U(1).v(1» =fO(t) n - 27

=T(x.y.z) Rx(a) Ry(~) (Po + pp)

where Pp is a point on the pan given in the pan coordinate system, Pm is the same point in the machine tool coordinate system. and Po is the part offset. Rx and Ry are the rotational and T is the translational transformation matrices. 5-axis machine tools are manufactured with different morphologies. i.e. different kinematic chains with different transformation matrices. (e.g. machine tools with tilting head and a rotary table. or machine tools with rotary tables whose rotational axis do not intersect.)

REVIEW OF EXISTING SOLUIlONS There are many ways to generate trajectories for machining sculptured surfaces. Perhaps the most established is when the trajectories are approximated by line segments. and the calculations are done offline. This is what most CAD/CAM systems do; design modules pennit the creation of surfaces while

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the machining modules can generate the approximating line segment chains for the surface machining. Alternatively. higher degree curves can be generated in the controller itself. Again. this can be done in different ways: doing the approximation of the curves with line segments real-time and executing them. or calculating the direct movements for the curves, doing away with the run-time approximation. These solutions and their variations are employed in existing controllers. Robot controllers were the first to use higher order curves for trajectory generation. The joint coordinates are calculated according to the inverse kinematics of the manipulator [paul-SI] . The joints. which have to move usually according to complex trigonometric functions, are controlled with spline functions. The spline functions approximate the joint trajectories. The end coordinate trajectory is divided up into segments, and at the segment points with the inverse kinematics the individual joint coordinates are calculated. Through these joint coordinates splines are constructed. Using third order splines smooth acceleration of the joints can be achieved fLin-8:~ , Edwall-S2J. Sata el.al . were the first to report on a system machining sculptured surfaces, with a true , realtime , higher degree interpolation method [Sata-SlJ. The "intelligent controller" does 3D machining on Bczier surfaces with ball nose cutters. Their solution is to implement an incremental interpolator that generates third order Bezier curves. The control points of the curve are passed on to the controller for the path generation . The experimental set-up consisted of a V AX IInSO for the basic calculations for the tool path generation and an 8-bit microcomputer doing the real-time calculations driving a conventional 3-axis machine tool with its controller in the Behind Tape Reader (BTR) mode. In '86 the same research group reported on the progress of the project [Haapaniemi-S6J . Keeping the same principles as before. an updated hardware implementation, better user interface and utilities were provided. Researchers at the Computer and Automation Institute in Hungary have been developing and documenting an integrated system since the late seventies [Renner-7S. Varady-82. Hermann-84. Hermann-88J . The system developed is a comprehensive CAD/CAM system with geometric design. machining planning and optional machine tool conuoller modules. One of the options of the system is a CNC conuoller. that generates higher order curves real-time. The controller is the extension of a "conventional" CNC controller. There is a preprocessor added to the system. which interprets the higher order curve descriptions passed to the controller. and approximates them by line segments in real-time. The interpolator of the CNC executes the approximating line segments. thus generating the higher order curves. The 2D operation of the system was demonstra1ed on a lathe machine. The fIrSt commercial offering of the technology. an integrated CAD/CAM system with a CNC controller executing higher order curves. for designing and milling complex surfaces. was offered

by the Swiss FIDES company [EUCLID-S3 . EUCLID-S6J. The EUCLID CAD system is based on Bezier curve and surface representation . The OZELOT postprocessor and controller represents the CAM part of the system. The machining module produces 3-axis tool path for the spedal controller. The geometric features of the surface paLChes and the tool path on those patches are passed to the controller instead of line segments. The authors claim a factor of 5 - 15 reduction in NC program length. 60% programming time savings, including tool path verification and set-up time. The OZELOT controller itself is based on the NUM ATEK 3000 CNC . Duncan and Mall describe a unique method of machining sculptured surfaces [Duncan-S3) . The method is called polyhedral machining . as the surface to be machined is approximated by a multifaceted non -regular polyhedron. The surfaces are represented as one valued functions. z = f(x .y) . which means, that no undercuts can be modeled with the system . The machining is done by touching the surface successively with ball nose cutters of decreasing diameters. similarly to the "pointing" sculpting method human sculptors use. The method inherently includes interference checking. the tool can sink only as deep into the part that none of the facets would be undercut. The original implementation by the authors was an off-line solution . Kochan et al. describe the elements of a system for designing and producing parts with sculptured surfaces [Kochan-83J. The solution proposed is a three layer system. consisting of design. production planning and manufacturing. The authors also suggest an improved data flow in the production by moving the postprocessing functions into the NC conuoller. They also propose technological and geometric input information for the controller. Broomhead and Edkins describe the real-time generation of NC control blocks at the machine 1001 [Broomhead-86) . Their main motivation for the system is the reduction of paper tape (information) passed passed to the controller. The system developed implements 3-axis machining on surfaces described by Bezier-patches. Instead of LOol path increments. the control polygon of the patches are passed to the conuoller. The system implementation includes a microcomputer with a floating point coprocessor feeding a conventional NC conuoller in the BTR mode. Tests have shown tenfold information reduction for the surface machining. Recently the US Government has initiated a project to develop the Next Generation machine/workstation Controller (NGC). which is part of a wider effon to revitalize the US machine tool industry. The program will develop and validate a Specification for an Open System Architecture Standard (SOSAS) for a family of workstationlmachine conuollers. Among others. the NGC will have "advanced schemes of interpolation suc~ . as parabolic and non-uniform B-splines. in addiuon to conventional linear and circular modes" [Bames-91. MOSAIC-90).

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ADVA,\CED PAm GE.'\CRATOR FOR SCCLJ'1l,"REDSliRFACE MACHr\T'G

and gave an initial estimate on the computational efforts required. Work is under way to generate tool path for non uniform rational B-spline surfaces (NURBS). As NURBS are the most general form of parametric surface descriptions. it inherently includes tool path generation for B-spline. Bezier. Coons and other polynomial surfaces. Both the 3-axis and 5-axis versions are considered. As existing speed control schemas control the speed of the tool centre point. resulting in speed variation in the contact point. proper speed control of the path generation also has to be established.

EV ALUA TION OF EXISTING SOLUTIONS Current systems allow for sculptured surface machining. Most of the solutions apply off-line data processing for the tool path generation. This has all the disadvantages of being complex and producing a huge amount of data as discussed earlier. The systems which provide real-time higher order curve generation do it in a pre-processing fashion : the tool path still consists of line segments. and the approximation is done run-time. That means that the functionality of the interpolator has not improved in the controller. except that the task of interpreting the higher order curves has been off-loaded to a preprocessor. The coupling between the preprocessor and the path generator can be tight. in which case the preprocessor is part of the controller. or it could be loosely coupled. where the preprocessor is not part of the controller. and the controller is driven in the "behind tape reader" mode. The systems reviewed. which do run-time higher order curve generation in the controller. are implemented only for 3-axis control ; 5-axis solutions are realized with off-line data processing. Il\'1TIAL RESULTS AND FUTURE WORK Initial simulations of a 5-axis controller based interpolator. that could directly move the tool on a sc ulptured surface . without approximating it with line segments. has been carried out. The surfaces used for the simulation were represented as third order Hermite patches . Figure 3. shows multiple views of the simulated tool path on the surface.

y

Lx /

,or,.i{L ~

z

Lx

CONCLUSION In this paper the state-of-the-art of sculptured surface machining was reviewed and simulation of a real-time path generator module for a Computer Numerical Controller for machining sculptured surfaces was discussed. It was found. that existing machining practices for the free-form shapes are cumbersome and prone to errors mainly due to the approximation of the tool path trajectories by line segments. The need for using line segments are dictated by the features of the NC machines: in general orientation only line segments can be generated. The consequences of this are the huge data files and the numerous steps of information processing required to produce the NC data for the machine tool. The resulting system is too complex. has too many layers. and the functions are distributed far from an optimal way. The large data files and the elaborate processing can easily lead to errors which are difficult to find . Research has been going to develop methods to generate higher order curves in the NC controller itself. Solutions for the problems have only been partially found. Processing is either done off-line. or real-time path generation in the controllers is done only for a subset of the surfaces and only for 3-axis machining. The implementation of these techniques is also evolutionary. building on the previous generation of NC controllers and on their features. and does not have a fresh look at the problems of sculptured surface pan machining and higher order tool path generation on their own. Initial results on a real-time 5-axis tool path generation method were given. Also the future direction of the research 10 develop a more general solution was outlined. together with other problems. related to the real-time path generation for the machining of objects with sculptured surfaces.

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REFERENCES

Figure 3. The simulation was wriuen in FORTRAN and run on a VAX. computer. The generation of the test surfaces and the display of the results was with the aid of the UNIGRAPHICS CAD/CAM system. The data for the surfaces were taken directly from the CAD system's internal data base. The simulations verified the correcmess of the geometric calculations

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