Abstract:
This invention provides a novel tool path planning method for five-axis flank milling by imposing the constraints of curve interpolation on the tool path. The tool motion is described in the form of spline curves during its optimization-driven calculation process, instead of discrete cutter locations in CNC linear interpolation. The coefficients of the curve equations are generated by minimizing accumulated geometrical errors on the machined surface using optimization algorithms. The continuity imposed by the spline motion reduces uneven modifications of cutter locations during the optimization process. The resultant tool path yields superior.

Description:
PRIORITY CLAIM 
       [0001]    This application claims the benefit of the filing date of Taiwan Patent Application No. 102126814, filed Jul. 26, 2013, entitled “FIVE-AXIS FLANK MILLING SYSTEM FOR MACHINING CURVED SURFACE AND TOOLPATH PLANNING METHOD THEREOF,” and the contents of which are hereby incorporated by reference in their entirety. 
       FIELD OF THE INVENTION 
       [0002]    The invention is related to a five-axis flank milling system for machining a curved surface and a tool path planning method thereof, more particularly, related to the system and method utilizing the constraint of curve interpolation in the tool path planning to improve the surface quality of the machined surface. 
       BACKGROUND 
       [0003]    Five-axis milling is an advanced manufacturing technology commonly used for creating complex geometries in the automobile, aerospace, mold-making, and energy industries. It offers higher shaping capability and productivity than traditional three-axis machining does, with two rotational degrees of freedom in the tool motion. Five-axis milling operations are classified into end milling and flank milling according to how the cutter removes stock material. In flank milling, the cutting edges along the cutter peripheral, generally of a cylindrical or conical shape, perform the cutting action. Tool path planning in five-axis flank milling remains challenging. Completely eliminating tool overcut and undercut is highly difficult, if not impossible. In practice, the finished surface is considered acceptable when the amount of geometrical deviations is within a given tolerance. However, effective methods of controlling the deviations are still lacking in five-axis flank machining 
         [0004]    For reducing the geometrical deviations (not considering the errors induced physically such as cutter deflection and tool wear) produced in five-axis flank milling, past studies have proposed numerous tool path planning methods based on optimization schemes. Various optimization methods have been proposed for adjusting cutter locations simultaneously by applying an objective function to minimize the accumulated geometrical deviations of the finished surface. These methods demonstrate the following drawbacks. The computational effieiency is low in a high-dimensional search space corresponding to a large number of cutter locations. In addition, both the tool center point and axis must be modified during the optimization process. Such modifications are particularly observable at the cutter locations around the surface regions of excessive twist. Uneven modifications of the tool motion often result in poor surface roughness on the finished part. 
       SUMMARY OF THE INVENTION 
       [0005]    This invention provides a novel tool path planning method for five-axis flank milling by imposing the constraint of curve interpolation on the tool motion. The tool motion is described in the form of spline curves during its optimization-driven calculation process, instead of individual discrete cutter locations in CNC linear interpolation. The coefficients of the curve equations are generated by minimizing accumulated geometrical errors on the machined surface using optimization algorithms. The number of variables to be determined in the planning process is much lower than that of traditional methods. The computational efficiency of the planning process is thus enhanced. The continuity imposed by the spline motion reduces uneven modifications of cutter locations during the optimization process. The resultant tool path yields superior machining quality on the finished surface. 
         [0006]    Other advantages and features of this invention will be further manifested with the following descriptions and the appended drawings. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0007]      FIG. 1  illustrates a curved surface, a tool path constrained by two spline curves, and a matrix containing the coeffieients of the curve equations in the present invention. 
           [0008]      FIG. 2  illustrates a test surface and a table showing the coordinates of the control points defining the surface. 
           [0009]      FIG. 3  illustrates the convergence curves of the optimization scheme proposed by this invention. 
           [0010]      FIG. 4  illustrates the convergence curves of the optimization scheme proposed by the prior art. 
           [0011]      FIG. 5(   a ) illustrates a tool path constrained by two spline curves and a table showing the coordinates of the control points defining the two curves in the present invention;  FIG. 5(   b ) illustrates the tool path generated by the prior art. 
           [0012]      FIG. 6  illustrates two surfaces machined using traditional and spline-constrained tool paths respectively. 
           [0013]      FIG. 7  illustrates the function blocks in the present invention. 
           [0014]    Table 1 lists the machining parameters in the tool path planning. 
           [0015]    Table 2 shows the parameter setting in the PSO algorithm. 
           [0016]    Table 3 shows the test results generated using different tool path planning methods. 
           [0017]    Table 4 shows the cutting conditions in the finishing cut. 
           [0018]    Table 5 shows the surface roughness estimated from a surface scanner for the surfaces machined by two different tool paths. 
       
    
    
     DETAILED DESCRIPTION 
       [0019]    The present invention discloses a five-axis flank milling system for machining a curved surface and a tool path planning method thereof. It should be noted that the term “CNC interpolation of tool path” means generation of intermediate tool positions between consecutive discrete cutter locations on a CNC machine tool. The term “workpiece” means the part being machined. The term “curved surface” means the surface to be cut on the workpiece. The other publications or patents of the inventor, such as Taiwan patent application number 96147909, could be deemed as a basis to bring this invention in practice. The optimization scheme used in this invention can be existing methods in the prior arts, such as Genetic Algorithm, Particle Swarm Optimization, Ant Colony Optimization, Simulated Annealing, and they will not be described in detail here. 
         [0020]    Generation of a tool path consisting of discrete cutter locations is described first to differentiate the present invention from the prior arts. A cutter location (CL) is defined by the cutter center point and cutter axis. To define each vector requires three variables in 3D space. Thus, specifying a cutter location requires six variables. Assume that a tool path consists of N cutter locations. The solution space becomes 6N-dimensional in the tool path planning of linear interpolation. N is often used as a two-digit number in the machining of a curved surface. Searching for optima in such a highly nonlinear domain is extremely difficult, if not impossible. The computational time is lengthy and the solution quality is occasionally poor; therefore, reducing the number of optimization variables is advantageous. 
         [0021]    A feasible method for reducing the dimensionality in the solution space is to impose a motion pattern and the corresponding constraints while adjusting the cutter locations. More importantly, a continuous motion pattern produces a smooth tool path without creating excessive changes to the cutter locations during the optimization process. The part cut by the constrained tool path should exhibit higher surface quality than that cut by one that is unconstrained. 
         [0022]    As shown in  FIG. 1 , a tool path is defined according to two curves along which the two tool center points move. Assume both curves are represented using a cubic polynomial equation with four coefficients. Each vector coefficient contains 3 variables. Completely describing a tool path of this form requires 24 variables. This number is much smaller than that of the tool path defined according to a set of discrete cutter locations in the prior arts. Fewer variables lead to a lower dimensional solution space when searching for optimal tool paths using a proper optimization scheme. The computational effieiency of the optimization process is thus increased and the solution quality may be improved. As in most previous studies, the objective function applied in the optimization scheme is to minimize the accumulated geometrical deviations on the finished surface. Estimation of the machined geometry is highly nonlinear without a closed-form representation. In this case, the coefficients of the curve equations can be solved by meta-heuristic optimization methods such as Genetic Algorithms, Particle Swarm Optimization, Ant Colony Optimization, or Simulated Annealing. 
         [0023]    Both simulation and real machining tests have been conducted. The comparison between the linear interpolation tool path generated by the prior art and the constrained tool path produced by this invention is shown as follows. Table 1 lists the machining parameters in the comparion test. Table 2 lists the parameter setting in the PSO algorithm. A test ruled surface is defined according to two boundary curves; their control points are shown in  FIG. 2 . Each boundary is specified as a cubic Bézier curve in 3D space. The coordinates of each control point are present by A1 to A4 and B1 to B4. 
         [0024]    The PSO algorithm was conducted five times at the given parameter settings (Tables 1 and 2) to reduce the randomness involved in the search process.  FIG. 3  shows the convergence curves for the best, worst, and average results in 100 iterations. All five runs converged to optimal solutions, although their processes appear slightly different. The PSO algorithm that adjusts the tool path without the motion constraint was also tested under the same conditions.  FIG. 4  shows the corresponding convergence curves. Table 3 lists the final solutions generated using both methods. The optimal tool path constrained by spline curves produces a smaller amount of geometrical deviations than that consisting of independent cutter locations does.  FIGS. 5(   a ) and  5 ( b ) indicate the traditional and constrained tool paths, respectively. The spline tool path needs to be converted into G01 motions because current CNC controllers in five-axis machining do not support the spline interpolation defined by two curves. The converted motion contains 40 cutter locations, which is of the same number of cutter locations in the traditional tool path. 
         [0025]    A cutting experiment was conducted to verify the simulation results. A Deckel-Maho nonoBlock™ five-axis CNC machine tool was used in this experiment. The moving range of the worktable is 780×560×560 mm. The maximal spindle speed is 12000 RPM. The machining operation consists of roughing and finishing cuts. The roughing cut involved using a φ4 ball-ended cylindrical cutter with a total length of 30 mm and a cutting length of 20 mm. This operation enabled removing most stock materials and left a material layer 0.2 mm thick on the design surface, to be removed by the finishing cut. A new tool of the same type as that used in the roughing cut was adopted in the finishing cut to eliminate the influence of tool wear. The cutting conditions in the finishing cut, suggested by the cutter provider, are summarized in Table 4. The cutting length can cover the entire surface along the shorter side and thus the finishing cut requires only one tool path. 
         [0026]    The finished part consists of two surfaces as shown in  FIG. 6 . The geometrical deviations of both surfaces according to the design specifications were measured using the Form Talysurf™ PGI 1250A surface scanner. The stylus of this device moves along predefined trajectories on the surface to be measured. With respect to a reference point, the 3D coordinates can be automatically determined at discrete measurement positions along each trajectory. Nine isoparametric curves were created based on the design surface along the longer side. Each curve contains 280 measurement points of equal increments within the curve parameter along the curve. The measurement results for both surfaces are listed in Table 5. 
         [0027]    This invention provides a five-axis flank milling system using the proposed tool path planning method.  FIG. 7  is a schematic drawing illustrating the function blocks in the invention. In  FIG. 7 , the system  1  includes an interface device  10 , a storage device  20 , a control device  30  and a milling tool properly selected. The interface device  10  provides a data access function. The storage device  20  provides a data storage function for a predetermined machining process. The control device  30  provides controls function for executing the predetermined process. 
         [0028]    In detail, the interface device  10  is a device that acquires the design data of a curved surface and machining instructions from the user. In one embodiment, the interface device  10  is a keyboard of a personal computer, but it is not a limitation. The interface device  10  can be a touch panel, keyboard, card reader, or other similar devices with the data input function. 
         [0029]    In one embodiment, the storage device  20  is a hard disk, but it is not a limitation. The storage device  20  can be volatile, non-volatile memory, or a server connected to the system  1 . 
         [0030]    In one embodiment, the control device  30  is a CPU and control software running on the CPU, but it is not a limitation. The control device  30  can be a CNC controller embedded with control functions. 
         [0031]    The followings describe the predetermined process in the storage device  20  in detail. In step S 1 , the interface device  10  receives a command from the user for decreasing or minimizing the geometrical errors of the curved surface after machining The geometrical errors are the total amount of the overcut errors and the undercut errors. The command is not limited to reducing the total geometrical errors in this invention; it can be to decrease or minimize the overcut errors or the undercut errors. 
         [0032]    In step S 2 , the coefficients of the curve equations that describe the optimal tool path are calculated. It should be note that the two curve equations are of degree 3 in this embodiment. 
         [0033]    In step S 3 , a tool path is generated from the two curve equations. 
         [0034]    In step S 4 , the tool path generated in step S 3  is loaded to the control device  30  for conducting the machining process.