Patent Application: US-201213984634-A

Abstract:
the invention relates to a method of toolpath generation and cutting parameters optimization for high speed milling of a convex pocket , wherein said method comprises a first sub - method of generating a toolpath and a second sub - method of generating optimized chatfree cutting parameters using a genetic algorithm wherein the first sub - method generates milling toolpaths that minimize the radial depth of cut variations as well as the curvature change variations while avoiding leftover material at the corners , wherein said toolpaths automatically avoid self - intersecting features encountered during the offsetting of pocket boundary such that the said toolpaths result in reduction in milling time for a given maximum acceptable radial depth of cut and wherein said second sub - method allows the free choice of cutting parameters and optimizes the milling time and wherein the optimization method incorporates relevant milling constraints as milling stability constraint , cutting forces , machine - tool and cutting tool capabilities .

Description:
the present invention will be better understood from a detailed description of embodiments and from the drawings which show : fig2 illustrates the cutting parameters required for pocket milling ; fig3 illustrates an example of change in radial depth of cut along the toolpath ; fig4 illustrates an example of a stability lobe diagram ; fig5 ( b ) illustrates toolpath according to the invention ; fig6 illustrates an example of pocket boundary and corresponding signed distance function of the pocket boundary ; fig7 illustrates the slot pass and the generation of signed distance function according to slot pass ; fig8 ( a ) illustrates a non - conformed toolpath and fig8 ( b ) illustrates a conformed toolpath ; fig1 illustrates the offsetting until it reaches the boundary confirmed pass ; fig1 ( a ) and 11 ( b ) illustrate the change in data structure ; fig1 illustrates the complete toolpath along with regular stepover passes and corner lopping passes fig1 illustrates a flow chart to generate an initial population of chromosome ; fig1 illustrates a flow chart for creating a new generation from a previous population ; fig2 illustrates an iteration loop for genetic algorithm analysis . fig2 illustrates an example of the pocket ( all dimensions are in mm ) fig2 illustrates an example of the frfs in feed and normal to feed direction fig2 illustrates an example of complete toolpaths according to the present invention . ( i ) inputs : parametric form of pocket boundary , tool radius and stepover for the complete toolpath generation are used as inputs in the method for toolpath generation . ( ii ) using the parametric form of pocket boundary , the arbitrary convex pocket boundary is initialized to signed distance function using fast marching method [ dhanik , 2010 ] cited hereunder , this publication being incorporated by reference in its entirety in the present application . this involves the domain of interest to be divided into rectangular grid points based on user specified grid distance . the grid points close to boundary within the length of one grid distance are initialized by travelling along the closed boundary . using these grid points value as the known value , the partial differential equation is solved for distance value at neighboring unknown grid points are calculated . in this manner , the distance values of the unknown grid points are carried out until no grid point with unknown value is left . the output of this method is a matrix [ pocket_boundary ] of grid points . an example of this approach is given in fig6 . toolpath at various levels can be extracted as the contour of the zero level set of signed distance function depending upon the radius of tool and the stepover distance . the toolpath matrix corresponding to the conforming to the boundary can be calculated as [ boundary_conformed_pass ]=[ pocket_boundary ]− tool_radius ( iii ) next a contour is extracted as a slot milling pass from the top of signed distance function . assuming this contour as a boundary , signed distance function of this boundary is again calculated using fast marching method [ dhanik , 2010 ] as shown as an example in fig7 . it is stored as [ first_pass ]. an iterative method is then devised to extract other successive contours as shown in next steps . ( iv ) set local variable i = 1 and set [ current_pass ]=[ first_pass ] ( v ) extract the zero level contour from [ current_pass ] using the contour program and saved it as modified_tool_path ( i ). ( vi ) set i = i + 1 . ( vii ) check for the intersection between the two signed distance functions , [ boundary_conformed_pass ] and [ current_pass ]. the intersection condition specifies whether the toolpath is exceeding the pocket boundary , in such case it is needed to make the new toolpath to conform to the boundary of pocket . with the signed distance function this could be simply checked by a boolean operation . first , calculate min ([ boundary_conformed_pass ],[ current_pass ]) and subtract it with [ current_pass ]. if the result produces a matrix with zero value at each data point , it means there is no intersection of the two signed distance functions , otherwise there is an interaction . if there is no intersection , go to step ( viii ) otherwise , go to step ( ix ). ( viii ) [ current_pass ]=[ current_pass ]+ step_over . use the contour program to extract the zero level boundary and store it as modified_tool_path ( i ). go to step ( vi ). ( ix ) in this step , [ current_pass ] is modified to conform to [ boundary_conformed_pass ]. again , the signed distance boolean operations are utilized to make quick calculations . [ current_pass ]= min ([ current_pass ], [ boundary_conformed_pass ]) gives the modified toolpath . as shown in fig8 , the modified_tool_path ( i ) is crossing the zero level contour of [ boundary_conformed_pass ] i . e . last_pass . overwrite modified_tool_path ( i ) by the zero level contour of [ current_pass ] ( the modified toolpath for conforming to boundary pass ) extracted by the contour program . ( x ) the tool can move along the modified_tool_path ( i ) but this will introduce a lot of idle sections ( idle sections refers to cutting toolpaths involving no actual cutting action ) in the toolpath , due to the fact that the inevitable boundary conformed pass ( the zero level boundary of [ boundary_conformed_pass ]). note , however that the final shape of the pocket could be achieved . the corner points of the modified_tool_path ( i ) denoted by points in fig8 ( b ) are determined simply by identifying the common points between the modified_tool_path ( i ) and the zero level boundary of [ boundary_conformed_pass ], they are the intersection points between the modified toolpath and the last pass ( pocket boundary ). set level_cp = 1 and go to step ( xi ). ( xi ) if variable level_cp = 1 , an array is initialized to store the ordered list of coordinates of the corner points ( for example , point a , b , c . . . h in fig8 ( b )) and their level which is the respective toolpath in the corner points . the dimension of the array is set based on the number of pairs of corner points . this information is stored as corner_points ( pair , level_cp ). the data structure of this level is shown in fig9 . each pair of points indicated by ( i_p , i_q ) can be accessed by calling the pair and level number corner_points ( pair , level_cp ) or [ i_p , i_q ]= corner_points ( pair , level_cp ). note with reference to fig8 , i_p and i_q could be a , b , . . . h . ( xii ) if variable level_cp = 1 , skip this step , otherwise store the points by checking that the intersection points are filled directly below the appropriate pair of points . ( xiii ) this step is used to determine whether there is a need of further looping around a particular corner . [ current_pass ] is offset by a distance step_over as : [ current_pass ]=[ current_pass ]+ step_over . calculate min ([ boundary_conformed_pass ],[ current_pass ]) and subtract from [ current_pass ]. if the result produces a matrix with zero value at each data points , it means there is no intersection and go to step ( xiv ). otherwise , set i = i + 1 and set [ current_pass ]= min ([ boundary_conformed_pass ], [ current_pass ]), further create modified_tool_path ( i ) as the zero level contour of the modified [ current_pass ]. increment the level of corner_points matrix as level_cp = level_cp + 1 , and go to step ( xii ). ( xiv ) at this stage , all the uniform stepover without breaching the pocket boundary have already been determined . it is shown in fig1 with the black lines “ uniform stepover passes ”. the output is modified_tool_path ( i ) where i ∈ ( 1 , n ) where n refers to the number of passes , signed distance matrix [ boundary_conformed_pass ], and corner_points . ( xv ) corner looping section ( see fig1 and 12 ): assuming the tool starts at some arbitrary point istart situated on the last_pass ( zero level contour of [ boundary_conformed_pass ]), the tool travels to the point i_p 1 and then instead of following the points of the last_pass , the tool follows the loop 1 until i_q 1 . loop 1 is the set of points in the modified_tool_path ( n - level_cp ) between point i_p 1 and i_q 1 . after that the machine tool comes back to the initial point i_p 1 and the process continues . here , two points should be clarified before developing the details of the algorithm first , the point istart can be chosen as an arbitrary point on the ordered point set of last_pass in the middle of two corners . secondly , for a given istart , the position of the istart is first determined in comparison to the corner looping pair of corner_points ( level_cp = 1 ). for example , it is determined that point istart lies between which of the two corner pairs ab , cd , ef and gh in fig8 ( b ). the data structure of corner_points is then modified such that pair 1 refers to the corner pair it will approach first and pain is the last visited corner . this concept is shown in fig1 and 12 . modifying the data structure in this way will help in handling the corner ( xvi ) set local variable i_loop = 1 ( i_loop refers to a pair number ), j_loop = 1 ( refers to the level ), set path_start = istart , initialize an array cl_point as an empty array . ( xvii ) extract point [ i_p , i_q ]= corner_points ( pair i_loop , level j_loop ), if [ i_p , i_q ] is not empty matrix , go to next step . otherwise , there are no more corners left for looping , hence go to step ( h ). ( xviii ) starting from the path_start store last_pass points till the first point i_p to cl_point in append mode . ( square shaped points in fig1 ). ( xix ) append cl_point to include the loop 1 points . this is done by selecting the points of modified_tool_path ( n - level_cp + i_loop − 1 ) between points i_p and i_q . some extra points are also added beyond i_q just for illustration purposes in fig1 . thus , the tool returns from the point i_r to i_p . the points of the modified_tool_path ( n - level_cp ) between i_q and i_r are also appended in cl_point . ( xx ) for the returning path , as the interpolation between two points is assumed linear , the point referring to the end point of interpolation is appended to the list , which is point i_p . set path_start as i_p . ( xxi ) set j_loop = j_loop + 1 and [ i_p , i_q ]= corner_points ( pair i_loop , level j_loop ), if [ i_p , i_q ] is not empty matrix , go to step ( xviii ), otherwise go to next step . ( xxii ) set i_loop = i_loop + 1 , and j_loop = 1 , check first that i_loop ≦ maximum number of pairs ( i . e . number of columns of corner_points matrix ). if yes , go to step ( xvii ), otherwise go to step ( xxiii ) ( xxiii ) follow last_pass from path_start to istart and store the points in cl_point by appending the list . ( xxiv ) the regular passes and the corner looping passes determined from the above method are combined in a manner as shown in fig1 which summarizes the method for determining the toolpath according to the present invention . for a given set of input parameters as described in fig1 which illustrates the overall method of the invention in a block diagram , the abovementioned method “ method for toolpath generation ” utilizes three parameters namely tool radius , stepover and parametric form of pocket geometry and thus generates the corresponding toolpath . for a given input set of parameters , the parametric form of pocket geometry and the tool radius remain same during whole optimization phase , but the value of stepover ( radial depth of cut ) is provided by the method for chatter free optimization described hereunder . for each new value of stepover the corresponding toolpath is generated by the above described method and toolpath length is calculated . the toolpath length value is then returned to the method for chatter free optimization described hereunder . accordingly , both sub - methods are linked together in the more general method of the present invention , as described herein . complete system architecture for the minimization of pocket milling is presented in fig1 . the details of the system are explained in the following paragraphs . 1 . for a given set of inputs cutting parameters , ranges ( search space ) of cutting parameters are defined . for example , radial depth of cut ( a e ) range lies between 0 to tool diameter ( d ), axial depth of cut ( a p ) lies between 0 to minimum of ( cutting length of tool or depth of the pocket ). spindle speed ( n ) and feed rate ( f t ) ranges are selected from the machine tool system specifications or can be specified by the user . 2 . to start with , cutting parameters are randomly coded in a single chromosome ( an array ) with binary bit string composed of zeros ( 0 ) and ones ( 1 ). each cutting parameter is assigned with fixed number of bits see the reference [ rai et al . 2009 ] incorporated by reference in its entirety in the present application . an example of chromosome with bit size 6 per cutting parameter is presented in fig1 . as illustrated in fig1 , each cutting parameter is a quarter segment of coded binary string and represents a percentage value of the range of the parameters and is presented by : y is the decoded value of the respected segment . x is the mapped value of the cutting parameter xmin and xmax are the upper and lower bounds of the cutting parameter respectively . for example the spindle speed range is 10000 - 20000 rpm and decoded value of the spindle speed is 53 ( conversion of ‘ 110101 ’ to decimal point ). the mapped value of the spindle speed will be 18412 rpm . 3 . an initial population is created by generating random chromosomes . the feasibility of each chromosome is checked with various constraints such as machine tool system ( machine tool / spindle / tool - holder / cutting tool ) stability , cutting tool constraints like allowable cutting tool deflection and breaking strength , machine tool constraints like power and torque limits a feasible chromosome is one which respects all the constraints and is also a solution of the optimization problem which may or may not be the optimal . for each feasible chromosome the toolpath is generated using “ method for toolpath generation ” disclosed above . the corresponding toolpath length is calculated . based on all cutting parameters total machining time is calculated . the minimization problem (“ pocket milling time ”) is converted to maximization problem (“ fitness value ”) and the fitness value ( f ) for a given chromosome is equated by : here t mac represented the pocket milling time in seconds , d p is the depth of the pocket in mm , a p is the axial depth of cut in mm , ceil is the round - up function , l toolpath is the length of the generated toolpath at one axial level in mm , f t is the feed rate in mm / flute , n is the number of flutes of the cutting tool and n is the spindle speed in rpm . the steps involved for creating the initial population for ga analysis are presented in fig1 as an iterative process . 4 . after creating the initial population , a new generation ( the next population ) is produced using ga operators namely reproduction , crossover and mutation . the steps involved for creating the generation are presented in fig1 . the ga operators used in the developed method are explained in following paragraphs : reproduction : reproduction selects the above - average chromosome from the current population and makes the mating pool in a probabilistic manner . the i th chromosome in the population is selected with probability proportional to its fitness value , f i . the probability p i for selecting the i th chromosome is given by here n is the population size . a roulette wheel selection is used as a reproduction operator . a roulette wheel is created and divided into slots equal to the number of chromosomes in the population . the width of the slot is proportional to the fitness value of the chromosome . for example , roulette wheel for five chromosomes is given in fig1 . the slot width of first chromosome is calculated by 25 /( 25 + 5 + 40 + 10 + 20 ) and so on for each other chromosome . thought it is clear from the roulette wheel selection that chromosomes with higher fitness values have greater chances of being selected for the mating pool than the chromosomes with a lesser fitness value but to ensure better chromosomes from previous population should not be lost during the reproduction , elitism may also be implemented in the method . in elitism a fixed number of chromosomes ( with better fitness ) are picked from the previous population and transferred as such in the next generation ( new population ). crossover : once the roulette wheel is created , two different chromosomes ( also called parents ) are selected to generate two offsprings ( also called children ). the multi - point crossover operator is used in the present work . a predefined crossover probability is set for ga analysis ( usually a high value , 60 - 100 %). an example of crossover operator used for the analysis is shown in fig1 . parents p 1 and p 2 are selected for the crossover and the crossover site is found by generating a random number from 1 to 5 . multi - point crossover with random crossover site “ 3 ” ( just an example ) is shown in fig1 . the p 1 and p 2 are interchanged with their alleles ( 0 and 1 ) between crossover sites to give birth to the resulted offsprings , o 1 and o 2 . mutation : to prevent the ga solution to fall in a local optimal value , a mutation operator is used . a predefined mutation probability is set for ga analysis ( usually a small value , 0 . 1 - 20 %). during mutation the allele of the gene is interchanged ; this means zero ( 0 ) is changed with one ( 1 ) and vice versa . for a given chromosome each gene ( each bit has an independent chance , with the mutation probability , to mutate ) is given a chance for mutation . the mutation operator used for the developed model is shown in fig2 . only feasible mutated offsprings are taken in the next generation for further analysis , the feasible offspring being defined as the feasible chromosome above in the present description . using all the ga operators , a next generation ( new population ) is produced . ga analysis is an iterative loop and it will continue till the predefined number of generations is reached . the predefined number of generations is selected based upon convergence of the optimal solution . the steps involved are presented in fig2 . the best chromosome in the final generation is the optimal solution . optimal cutting parameters and corresponding toolpath using the radial depth of cut from the optimal cutting parameters are the outputs of the developed optimization system for pocket milling of course , the present invention is not limited to the embodiments described above which are non - limiting examples . one may use variant and equivalents means or steps within the frame and scope of the present invention . 1 . an example pocket dimensions are presented in fig2 . 2 . the specifications of the cutting tool are given in table 1 . where ktc , krc and kac are the cutting coefficients contributed by the shearing action whereas kte , kre and kae are the edge coefficients in tangential , radial and axial directions respectively ( see reference altintas 2000 ). 4 . frequency response function ( frf ) of machine tool / spindle / tool holder / cutting tool system at tool tip in the feed and normal to feed direction is generally measured using hammer testing . the real and imaginary part of frfs in feed and normal to feed direction are presented in fig2 . 5 . the maximum spindle speed of the machine tool is 30000 rpm , axis accelerations up to 5 m / s2 and feed speeds up to 50 m / min . the rated power of the spindle is 12 kw . 1 . various ga operators are defined based on optimization problem : for example : population size : 20 , crossover probability : 90 %, mutation probability : 10 %, no of generations : 100 . spindle speed ( 10000 - 30000 rpm ) and feed rate ( 0 . 1 mm / flute - 0 . 2 mm / flute ) are selected . axial depth of cut : 0 - 25 mm [ 0 - min ( cutting length of the tool , pocket depth )], radial depth of cut : 0 - 16 mm ( selected from cutting tool diameter ). 3 . the randomly created set of cutting parameters is represented in the form of chromosome as shown in fig1 . feasibility of the chromosomes is checked with various constraints calculated based on defined inputs . for each feasible chromosome the toolpath is generated using the developed “ method for toolpath generation ”. fitness value of the objective function is calculated . initial population is created using algorithm proposed in fig1 . 4 . the next generation ( the new population ) is generated using various ga operators namely , reproduction , crossover and mutation as shown in fig1 . the global optimal solution is selected after 100 generations . for this optimization problem the near optimal cutting parameters are presented below : spindle speed = 24000 rpm , feed rate = 0 . 15 mm / flute , axial depth of cut = 5 mm ( 5 axial levels ), radial depth of cut = 12 . 5 mm an example of complete toolpath is shown in fig2 . of course , all the examples and values given above are only for illustrative purposes and should not be construed in a limiting manner . different embodiments of the invention may be combined together according to circumstances . in addition , other embodiments , values and applications may be envisaged within the spirit and scope of the present invention , for example by using equivalent means or other values . altintas , y . and budak , e ., analytical prediction of stability lobes in milling , cirp annals — manufacturing technology , 44 , 3567 - 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