A STUDY OF CUTTER PATH IN HIGH SPEED ROUGH MILLING OF POCKETS. PART I: MODELLING AND PERFORMANCE EVALUATION. 1. INTRODUCTION

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1 page 1 high speed rough milling, cutter path, pockets, spline interpolation, Luca GIORLEO* Michelangelo GIULIANI** Gaetano Massimo PITTALÁ* Massimo RUBERTO*** A STUDY OF CUTTER PATH IN HIGH SPEED ROUGH MILLING OF POCKETS. PART I: MODELLING AND PERFORMANCE EVALUATION. Abstract - Large aeronautical parts, such as wing ribs, involve a volume of metal removed up to 9-95 % of initial weight, particularly pocket milling takes 6-7% of the total cycle time, so this operation plays an important role in the cost definition of the final product. Since typical materials in aircraft frames are aluminium alloys, High Speed Machining technology is convenient and more frequently used, also for rough operation. Using modern production systems cutting velocity and feedrate are relatively high also in rough machining. It is important to determine cutter path and position vs time law in order to allow the lowest machining time and to control machine dynamic conditions. In this paper linear trajectory and cubic spline trajectory are compared in terms of execution time during high speed rough machining of pockets; in this part the comparison is numerical. The results indicate time saving using spline interpolation and the influence of feedrate and acceleration profile about above cutter paths. This is important information to select best cut condition and machining performance. 1. INTRODUCTION Aircraft parts, with particular reference to frames and ribs, require a large number of machining operations with chip removal rates up to 95%. For this reason HSM technology is getting typical with feedrate requirements up to 6 8 m/min; even if typically smooth on the external surfaces, frames and ribs require also large pocketing machine operation sets (see Fig. 1), so accelerations up to 3g are needed too. It is clear that new generation CNC machines have to fulfil high speed kinematical requirements but at same time CNC machines have to afford high frequency harmonics due to fast direction changes and discontinuities. In the past spline interpolation techniques have been mainly used to substitute or integrate CAD system for profile definition, for example connecting a set of sampled point. But interpolation techniques can be used to provide smooth tool path in order to avoid mechanical vibration dangerous for machine safety, not only in order to * Dipartimento di Meccanica, Politecnico di Milano, Via Bonardi 9, 133, Milan, Italy ** Laboratorio MUSP, Strada Statale 1, Località Le Mose, 9, Piacenza, Italy *** Dipartimento di Ingegneria dei Materiali e della Produzione, Facoltà di Ingegneria, Università degli Studi di Napoli Federico II, P.le Tecchio, 8, 815 Naples, Italy

2 page guarantee profile accuracy: if natural modes of mechanical parts and control system are excited both failure and trajectory errors can occur. This approach has been proposed for open architecture machine tools ([1], [5] and [6]), since it is difficult or impossible to handle proprietary CNC. Y. Altintas and K. Erkorkmaz [] have developed a quintic spline algorithm in order to achieve jerk limited trajectory interpolation. The algorithm proposed works for a real time interpolation procedure and provides smooth profiles, saving the system from mechanical damages. Fig. 1. Example of Aircraft Rib Other authors [7] suggest some trajectory reconstruction techniques used to reduce arc-chord errors in spline interpolation. Notice that these fundamental works can be assumed as mainly dealing with finishing operations, since they aim to a smooth and accurate tool path. In this paper it has been investigated the possibility to reduce the cycle execution time using interpolation technique in rough machining with particular attention to pocket milling operations; notice that the recalled removal rate applies for 3% to finishing and to 7% to rough machining. According to the approach here proposed a typical greek profile (see Fig. ) used to define a pocket operation has been here substituted by an interpolated trajectory: each linear branch of the greek profile has been subdivided with a cosine low (Tchebitchev) shown in Fig. 3. Notice that for sharp corners definition some specific algorithms can be adopted [8]. In case of rough machining can be useful to use the above mentioned approach once fixed an appropriate spacing. A set of points can be obtained sampling the basic greek profile; using a chord length abscissa as synchronization parameter the points projected on the machine axis define x = x(s) and y = y(s) coordinate curves; the points can be interpolated, for example using cubic or quintic splines obtaining a smooth tool path once the coordinate curves are combined to rebuild a new trajectory. The errors so induced can be neglected again, the reconstructed tool path allows an high average feedrate in cycle if compared to a basic greek profile that alternatively need to perform zero feedrate at corner points on each axis drive. Since the interest is here focused in time saving the procedure can work off line, postprocessing the basic APT file generated by CAM system.

3 page y (mm) Fig.. Example of greek profile y (mm) Fig. 3. Example of cosine or Tchebitchev discretization law. SPLINE INTERPOLATION IN MILLING OPERATION Spline interpolation consists of piecewise polynomial functions connections; classical polynomial interpolation links several points (roots of polynomial); an oscillatory behaviour and a consequent poor quality approximation arise as the number of points increases. This problem can be eliminated clustering points in piecewise polynomial curves and so limiting the number of connecting points, typically 4 6; then a polynomial of third or fifth order is obtained and some joint condition must be set. In this paper cubic spline are used, but similar results can be reached using fifth order curves. However for rough machining accuracy is less important than for finishing operations, so it is useful just to control the acceleration in order to reduce machining time, even if jerk control can provide a smoother

4 page 4 tool path too; as higher order derivatives continuity is achieved a lower levels of vibration is induced. The expression of cubic spline is: S( x) = c + c ( x x ) + c ( x x ) + c ( x x 3 1, j, j j 3, j j 4, j j) (1) Where S(x) is a defined in the [a, b] interval, subdivided in n segments; the conditions to be imposed for coefficients computing are: c i, j 1. Interpolation condition S(x j ) = y j (j=, 1,... n).. Tangency and curvature continuity in n- points. Appropriate boundary conditions are necessary to complete the definition of coefficients, for example natural spline condition [4]; in this way a tridiagonal linear system of equations is defined, and its solution can be obtained with Thomas algorithm [4]. Considering a single moving axis, curve 1 in Fig. 4 represents theoretical time law for a linear displacement s, i.e. the ideal set up obtained assigning the value of acceleration (a). With successive integrations velocity (v) and displacement vs time graphs can be obtained; in this way jerk (j) should be unlimited, but in real cases jerk assumes an oscillatory behaviour because of limited impulse and of dissipative phenomena so disturbs to the control law with the risk of integrity of components occur. For this reason control laws with continuous acceleration and limited jerk are typically suggested for rough machining, while continuous jerk is adopted for finishing. If jerk is piecewise linear and so limited, the acceleration is a linear function and the velocity is parabolic (curve 3 in Fig. 5); this produces an increase of machining time respect to limited acceleration case (curve, Fig. 4). If tool path consists of rapid and continuous changes of direction, effectiveness of linear time law reduces since curvature bounds maximum values of feedrate as detailed in next section; once a curvilinear abscissa is fixed tool path kinematical parameters depend both on time and space variables. Notice that trajectory can someway be handled for rough machining, while finishing do not allow this freedom. The use of interpolation function can be suggested: as the matter of fact cubic trajectory involves continuous curvature, acceleration and a piecewise limited jerk, while a quintic trajectory provides a continuous jerk. Notice that a basic linear piecewise interpolation (i.e. a greek profile) corresponds to a piecewise linear acceleration profile, so it can be supposed being the most effective in time saving; since limited values of jerk in real applications occur, the resulting acceleration cannot be impulsive. According to what explained for rough machining, cubic spline represents a matching point for time saving and vibration control requirements if compared respectively to higher order trajectories and to linear laws. c i, j

5 page 5 Fig. 4. Example of controlled velocity trajectory Fig. 5. Example of controlled acceleration trajectory 3. MODELLING In this section the performance of linear interpolation and cubic spline are compared when applied for modelling pocket rough machining; the first aim is to evaluate the effectiveness of trajectory handling even if in a conservative way. The reference operation is shown in Fig. 6: it has been considered a greek tool path with different time laws. Then a cubic spline path is searched in order to reduce machining time. The basic pocket is x mm and a mm diameter and three cuts tool is assumed; so the reference machining parameters here adopted are: 1. Cutting velocity 18 m/min (n = 3 rpm).. Feedrate of 18 m/min (.3 m/s, tooth feedrate =. mm). 3. Maximum acceleration of 6 m/s (.6 g) Y (mm) X (mm) Fig. 6. Reference path greek profile

6 page GREEK PATH The operation starts in the point x = 11 mm, y = 11 mm. The first set of kinematical parameters assigned in each branch is (ballistic): 1. Initial velocity is v i =.3 m/s, assumed equal to the maximum allowable ( v MAX ).. The acceleration a is constant equal to the maximum allowable (a MAX ). Considering for examples x axis drive it follows that: t t s s a = v = v s = v t 1 1 t t t s s s a = a v = a ( t t ) + v MAX 1 F 1 F MAX MAX 1 1 s = vmax t amax ( t t1) MAX MAX () Where v (t=) = v MAX, v (t F ) = m/s, s () = m, s( t1) = s1 and s (t F ) is the length of section; the condition t =t F indicates that the tool is at a corner point. The predicted execution times is 7.8 s; in this case assumptions imply that the tool starts impulsively, so an unlimited power should be needed. The tool stops at final position in a decelerated motion, according to the assigned conditions (). In the following cases a trapezoidal time law is assigned in order to fix more realistic assumptions; the time law is subdivided into three parts using the previous kinematical parameter set: amaxt 1. t t1 s s1 a = amax v = amaxt s = amax t 1. t1 t t s1 s s a = v = vmax s = vmaxt+ vmax t (3) 1 3. t t t s s s a = a v = a ( t t ) F F max max F s a ( t t ) max F = + where s(t 1 ) = s 1, s( t ) = s and s(t F ) = s F. In order to evaluate the acceleration influence a different case with same feedrate of.3 m/s and 1g acceleration is computed. Same comparison has been performed considering a different value of feedrate v =.15 m/s. A brief summary of results is shown below: s F

7 page 7 I - Linear Interpolation (Ballistic) II - Linear Interpolation (Trapezoidal) Tab. 1: Summary of results III - Linear Interpolation (Trapezoidal) IV - Linear Interpolation (Trapezoidal) V - Linear Interpolation (Trapezoidal) a max (m/s ) v max (m/s) Time (s) The ballistic profile is very conservative as an ideal limit; the trapezoidal profile can be considered similarly conservative even if closer to a real condition. Anyway they provide reference values for successive considerations. These results hold once fixed pocket geometry and tool diameter; particularly as tool path branches become smaller, higher acceleration values are needed to reach maximum feedrate. 3. CUBIC SPLINE PATH Cubic spline can be adopted to define the tool path instead of the piecewise linear greek profile. A set of points is obtained sampling the reference path; the points projected on the machine axis are interpolated using a cubic spline once fixed an abscissa s. Combining the resulting coordinate curves x = x(s) and y=y(s) a new trajectory can be rebuild; notice that a chord length abscissa has been defined fixing an approximation. Considering as interpolation set the corner points of basic path, the cubic spline interpolation gives the result in Fig. 7.. y (mm) Fig. 7. Cubic spline interpolation with one section one section cubic spline interpolation Pocket

8 page 8 The tool exceeds the dimension of pocket, so it is impossible to realize a path without collision on limits of the work piece. So basic profile can be subdivided in equally spaced sections (for example five), as shown below (Fig. 8) y (mm) Fig. 8. Equally spaced discretization Selecting these interpolation points the cubic spline interpolation computed is shown in Fig y (mm) Fig. 9. Cubic spline interpolation using equally spaced interpolation points Considering a mm machining tolerance, this tool path involves collisions too, as shown in Fig. 1.

9 page Fig. 1. x coordinate curve using cubic spline interpolation with equally spaced discretization s (mm) Then the basic profile has been subdivided in five parts using a cosine law (or Tchebitchev law), obtaining the set shown in Fig y (mm) Fig. 11. Discretization of reference path using cosine law (five sections) 1. A comparison between equally spaced and cosine law discretization is shown in Fig.

10 page y (mm) Cosine Law Equally Spaced Fig. 1. Comparison between cubic spline interpolation using different discretization laws The tool path obtained using a cosine law respects the imposed tolerance (Fig. 13) s (mm) Fig. 13. x coordinate curve using cubic spline interpolation with cosine law discretization Considering x coordinate and a constant feedrate v =.3 m/s, so that dv/dt follows that for each branch:, it dx dx ds dx = = v dt ds dt ds d x d x ds dx = v+ dt ds dt ds d x d x = () v = a x t dt ds dv/ dt (4)

11 page 11 The x acceleration depends on velocity and curvature; the curvature kx = similarly ky = d y ds are shown in Fig. 14. d x ds and 8 k (1/m) 7 6 x curvature y curvature s (mm) Fig. 14. Curvature for five sections cubic spline interpolation for each axis (cosine law) In order to reduce curvature values corner points are eliminated (Fig. 15). For example, the new path is shown in Fig. 16. The maximum value of curvature reduces to 5% y (mm) Fig. 15. Cosine law discretization eliminating corner points

12 page y (mm) Fig. 16. Cubic spline trajectory with five sections without corner points. In this case, the tool path involves collision once fixed a mm machining tolerance; further discretization laws have been tested with seven and nine sections for each branch in order to cluster point on the corners; collision has been avoided considering in both cases. The following table shows that the curvature decreases using five sections cubic spline and maximum value occurs considering corner points. Collision is checked fixing mm machining allowance. Seven sections interpolation complies with geometry requirements even if with higher curvature values. Corner Without corner Tab.. Summary of results Spine Type k m Collision 1 ( ) MAX Five sections 77 No Seven sections 15 No Nine sections 5 No Five sections 365 Yes Seven sections 71 No Nine sections 117 No The estimated execution time has been obtained considering d x d x d x = v = a () x t am AX. When v a MAX the feedrate v has been limited to satisfy dt ds ds the previous relation and its own maximum allowable value. Anyway feedrate variation has been considered impulsive in each numerical test. The summary of results is shown in Tab. 3 and Tab. 4.

13 page 13 Tab. 3. Summary of results, first part Linear Linear Interpolatio interpolation n (trapezoidal velocity) (Ballistic) Cubic spline interpolation without corner 5 sections Cubic spline Interpolation with corner 5 sections Max Acceleration (m/s ) Max Velocity (m/s) Collision No No Yes No Total time (s) Ballistic (%) trapezoidal velocity (%) Tab. 4. Summary of results, second part Cubic spline interpolation with corner 7 sections Cubic spline interpolation without corner 7 sections Cubic spline interpolation with corner 9 sections Cubic spline interpolation without corner 9 sections Max Acceleration (m/s ) Max Velocity (m/s) Collision No No No No Total time (s) ballistic (%) trapezoidal velocity (%) Cubic spline interpolation save about 4.5 % machining time at least if compared to the linear interpolation with ballistic profile. As referred to a trapezoidal profile time saving is 5.9%. Cubic spline interpolation without corner using 7 sections allows the lowest execution time compared to ballistic path (indicated with ballistic) and to trapezoidal velocity profile (indicated with trapezoidal velocity). 4. CONCLUSIONS Spline interpolation has been adopted for tool path smoothing with effective results in surface finishing; in this work a spline interpolation approach has been evaluated in order to handle rough machining tool path with the aim of machining time saving and vibration reduction. As shown before, cubic spline can fit different needs of smoothing tool path and time saving if applied in rough machining operations. In this case once fixed the tolerance on part surfaces some deviation from the basic path can be allowed; in this manner corner point and their neighbours are smoothed avoiding both higher curvature and feedrate limitations. The numerical evaluation performed shows lower curvature values can be obtained handling the basic greek tool path: each branch can be sampled using a cosine spacing, then corner points are eliminated in order to define the set of points to be interpolated. The results assume a certain interest considering that the procedure here proposed has been conservatively compared to an ideal tool path definition and better

14 page 14 results occur when kinematical parameters get into typical High Speed Machining range. Time spent in basic greek profile execution has been computed considering both ballistic and trapezoidal velocity profile as references; even if these simple assumptions are quite conservative spline handling of tool path provides an appreciable time saving that increases according to maximum allowable acceleration. Thomas algorithm has been here adopted to solve the linear system to definition of spline coefficients; considering rough machining some deviation from assigned tool path is allowable; even though the procedure works offline, iterative methods can be adopted in order to save computing time in case of a large number of operations. From a numerical point of view an optimization algorithm of time dependent kinematical parameters according to trajectory should be evaluated in order to introduce a more effective procedure although considering industrial applications, simple limited acceleration or limited jerk profile are usually adopted; using ISO NC tape it is not possible to affect setup or kinematical parameters and user defined parameters consists of a limited set and features in proprietary CNC. REFERENCES [1] ALTINTAS Y., NEWELL N., ITO M., Hierarchical open architecture multi processor CNC system for motion and process control, ASME Prod. Eng. Div. Publ. PED, Manufacturing Science and Engineering, 1993, Vol. 64, pp [] ERKORKMAZ K., ALTINTAS Y., High speed CNC system design. Part I: jerk limited trajectory generation and quintic spline interpolation, International Journal of Machine Tools and Manufacturing, 1, Vol. 41, pp [3] ERKORKMAZ K., ALTINTAS Y., High speed CNC system design. Part III: high speed tracking and contouring control of feed drives, International Journal of Machine Tools and Manufacturing, 1, Vol. 41, pp [4] PRESS W.H., TEUKOLSKY S.A., VETTERLING W.T., FLANNERY B.P., Numerical Recipes in Fortran - The Art of Scientific Computing, 199, Cambridge University Press. [5] ROBER S.J., SHIN Y.C., Modeling and control of CNC machines using a PC-based open architecture controller, Mechatronics, 1995, Vol. 5, No. 4, pp [6] WANG F.-C., WRIGHT P.K., Open architecture controllers for machine tools. Part: a real time quintic spline interpolator, Journal of Manufacturing Science and Engineering, 1998, Vol. 1, No., pp [7] WANG F.-C., YANG C.H., Nearly arc-length parameterized quintic-spline interpolation for precision machining, Computer-Aided Design, 1993, Vol. 5, No. 5, pp [8] WECK M., YE G., Sharp corner tracking using IKF control strategy, CIRP Annals, 199, Vol. 39, No. 1, pp

15 page 1 high speed rough milling, pockets, spline interpolation, experimental evaluation Michelangelo GIULIANI* Michele MONNO** Gaetano Massimo PITTALÁ** A STUDY OF CUTTER PATH IN HIGH SPEED ROUGH MILLING OF POCKETS. PART II: EXPERIMENTAL EVALUATION IN MILLING CENTRE AND OPEN ARCHITECTURE ROBOT Abstract - Considering large aeronautical parts, such as wing ribs, a volume up to 9-95 % of the initial weight is removed. Particularly pocket milling takes 6-7% of the total cycle time, so this operation plays an important role in the cost definition of the final product. Since typical materials in aircraft frames are aluminium alloys, High Speed Machining technology is convenient and more frequently used, also for rough operation. Using modern production systems cutting velocity and feedrate are relatively high also in rough machining. Main features of linear trajectory and cubic spline trajectory have been numerically evaluated in part I of this paper. In the second part tool paths have been experimentally tested in terms of machining time considering high speed rough machining of pockets; a comparison between linear interpolation and cubic spline has been performed using CNC systems and an open architecture revolute robot. 1. INTRODUCTION Aircraft parts, with particular reference to frames and ribs, require a large number of machining operations with chip removal rates up to 95%; for this reason HSM technology is getting typical with feedrate requirements up to 6 8 m/min; even if typically smooth on the external surfaces, frames and ribs require large pocketing machine operation sets (see Fig.1), so accelerations up to 3g are needed too. It is clear that new generation CNC machines have to fulfil high speed kinematical requirements, but at same time CNC machines have to afford high frequency harmonics due to fast direction changes and discontinuities. In the first part of this work a numerical evaluation of cubic spline interpolation has been performed in order to apply this feature to rough machining with the aim to reduce machining time. This has been done neglecting accuracy problems that can be easily superseded choosing and appropriate sampling strategy if needed. Interpolation approach can be useful since higher feedrate values along the path can be maintained; a smoother tool path can provide a damage saving for machine too []. * Laboratorio MUSP, Strada Statale 1 Località Le Mose, 9 Piacenza, Italy ** Dipartimento di Meccanica, Politecnico di Milano, Via Bonardi 9, 133, Milan, Italy

16 page The experimental test have been performed using different equipments; this approach has been suggested by the need of verifying the state of the art of spline feature in modern CNC machines and in order to overcome the limits of a specific equipment. First of all experimental testing have been performed using a machine equipped without a cubic spline interpolation functionality on CNC; it has been tested a set of different discretization laws obtained handling the basic tool path. Then a CNC machine equipped with spline interpolation functionality has been used. Finally an open architecture revolute robot with has been modified in order to simulate a milling operation with spline interpolation features; the open architecture has been here adopted ([1], [5] and [7]), because it is very difficult or impossible to handle proprietary CNC. The basic set of points defining a greek profile (Fig. 3) has been handled first adding points in each branch according to a cosine law and eliminating corners, then applying a spline operator in order to obtain a C continuous curve (Fig. 4). In this paper cubic spline interpolation is analyzed, but higher order polynomial can be applied with comparable results in terms of time saving. Y. Altintas and K. Erkorkmaz [] have developed a quintic spline algorithm in order to achieve jerk limited trajectories; this allows smoother profiles too but following this approach is an offline procedure more computational work is needed as mentioned in part I of this work Y (mm) X (mm) Fig. 1. Example of greek profile y (mm) Fig.. Example of cubic spline profile

17 page 3 As regards existing industrial application a similar approach consists in adding a small radius to each corner point of the given greek profile so that feedrate do not reduce to zero when direction changes [6]; the radius value is usually.5 1. mm. In this case, even if some time saving can be obtained the tool path is C 1, and then induced vibration can not be avoided.. CNC EXPERIMENTAL FACILITIES The tests have been performed using an open architecture revolute robot and two different CNC machining centers. The revolute robot linear displacements are obtained as resultants of three axis rotations due to inverse kinematical equations integration; the system is equipped with brushless motors and harmonic drives acting for polar axis digital drives, encoder and resolve complete the list of loop control devices mounted on. The motion control is performed using the NI PCI-7344 axis control module [4] and its own software installed on a PC. The robot is capable of 1g acceleration and.3 m/s feedrate. The key features of CNC machines used are: 1. Siemens Sinumerik 84D CNC equipped on.7 g acceleration and m/min feedrate machine tool.. FIDIA C CNC equipped on.8 g acceleration and 6 m/min feedrate machine tool. 3. TEST ON CNC MACHINE TOOL In this section the results of cutter paths tested using CNC machine are presented; preliminary tests have been performed on a machine tool equipped with Fidia C CN that does not support spline interpolation. The assigned greek profile is shown in Fig. 3; the basic greek path has been handled substituting it with a linear piecewise trajectory, connecting the points obtained on cubic spline computed offline; the connecting points are assigned on tool path according to a cosine law is linear. The set of points to be connected is computed offline, then a typical ISO file contains a sequence of coordinates (G1).

18 page 4 14 y (mm) Fig. 3. Tool path analyzed Linear piecewise decomposition without corner points allows a certain time saving as shown in Fig. 4 and Fig. 5. Using higher feedrate five sections decomposition of the path allows a further improvement compared to a seven sections one sections without corner 5 sections without corner 5 sections with corner 7 sections with corner. Difference (%) Feedrate (mm/min) Fig. 4. Difference from greek profile of decomposed curve.

19 page 5 15, Difference (%) 1, 5,, Feedrate (mm/min) -5, -1, 5 and 7 sections without corner 5 and 7 sections with corner 5 sections with and without points 7 sectionss with and without points Fig. 5. Comparison between decomposed curve with and without corner Another set of experimental testing has been performed using Siemens Sinumerik 84D digital CNC equipped with cubic spline interpolation (CSPLINE command); the procedure works on line once the set of points to be interpolated have been off line assigned in ISO file. The cosine law used to provide the set of points to be interpolated is shown in Fig. 6; the results of experiments for a 3x3 mm pocket and for a 15x15 mm are shown in respectively in Tab.1 and Tab y (mm) Fig. 6. Trajectory discretized for 3x3 mm pocket Trajectory discretized Pocket Boundary

20 page 6 Tab. 1. Results of experiments for 3x3 mm pocket Execution Time Feedrate (mm/min) Linear Interpolatio n Spline Interpolation (s) % 447 s 397 s 5 s s 114 s 33 s s 14 s 8 s 1. Tab.. Results of experiments for 15x15 mm pocket Execution Time Feedrate (mm/min) Linear Interpolatio n Spline Interpolation (s) % 5 s 1 s 4 s s 81 s 9 s s 8 s 8 s 5.9 Other tests are performed using G64 Sinumerik functionality; this allows rounding the corner points with radius of.5 mm. The results: Tab. 3. Execution time saving with spline interpolation compared G64 functionality. Feedrate (mm/min) 3x3 15x15 6% 6% % 5% 18 % 4% Notice that kinematical parameters are obtained by limited acceleration profile (.7g) set as CNC environment variables. The plots of these parameters are not reported since the needed I/O features are not available on Sinumerik 84D. 4. TEST ON REVOLUTE ROBOT In this section the results obtained by revolute robot tool path testing are shown; the applied parameters are: 1. Linear interpolation, with v MAX =,115 m/s, a MAX = 1 m/s (Fig. 7). Cubic spline interpolation with v MAX =,115 m/s, a MAX = 1 m/s (Fig. 11).

21 page 7 Fig. 7. Linear interpolation with v MAX =,115 m/s, a MAX = 1 m/s In Fig. 7, the error due to mechanical performance of the robot is shown: the assigned trajectory is not accurately reproduced because of structural limitation of the robot and backleash; it was originally designed for pick and place operation and then it has been modified in order to follow a given path with a user defined interpolation law. X and Z coordinates have been tracked (Fig. 8 for linear interpolation and Fig. 1 for cubic spline interpolation for X direction. It is similar for Z direction.). Fig. 8. X coordinate curve in linear interpolation with v MAX =,115 m/s, a MAX = 1 m/s All kinematical parameters can be obtained thanks to the open architecture; a limited acceleration profile 1g has been adopted. X velocity is plotted in Fig. 9 for linear interpolation; same for cubic spline interpolation in Fig. 13. Finally, X acceleration is shown in Fig. 1 for linear interpolation while spline values are reported in Fig. 14. Fig. 9. X velocity in linear interpolation with v MAX =,115 m/s, a MAX = 1 m/s Fig. 1. X acceleration in linear interpolation with v MAX =,115 m/s, a MAX = 1 m/s

22 page 8 Fig. 11. Spline interpolation with v MAX =,115 m/s, a MAX = 1 m/s Fig. 1. X coordinate curve in spline interpolation with v MAX =,115 m/s, a MAX = 1 m/s Fig. 13. X Velocity in spline interpolation with v MAX =,115 m/s, a MAX = 1 m/s Fig. 14. X acceleration in spline interpolation with v MAX =,115 m/s, a MAX = 1 m/s

23 page 9 The results are shown in table below: Tab. 4: summary of results Linear Interpolatio n Spline Interpolatio n % (1g) Actual Max Acceleration (m/s ) % Actual Max Velocity (m/s) % Curvature (1/mm),3 - Time (s) % 4. CONCLUSIONS In this paper, considering pocket milling operation, the results of spline interpolation strategies testing are shown; the basic idea is to make an offline substitution of a given greek profile with a new tool path that allows execution time saving; this can be done avoiding corner points and high curvature zones so that spline interpolation well fits, giving at the same time an induced vibration reduction. In the first part of the paper time saving due to spline interpolation has been numerically evaluated in order of 7%, making some assumptions on kinematical parameters; then an experimental campaign has been performed considering the following cases: 1. The greek profile has been substituted by a segment piecewise path obtained by a set of points belonging to a spline smoothed curve; the point are linearly connected using G1 function on a Fidia C CNC machine tool.. The greek profile has been substituted by a cubic spline tool path obtained using Siemens Sinumerik 84D; moreover another alternative tool path has been obtained adding a small radius at each corner point, using CNC functionalities; 3. The greek profile has been substituted by a cubic spline tool path obtained using an open architecture revolute robot. The different strategies are based on offline handling of basic tool path; in the first case time saving is limited and mostly linked to elimination of corner points in tool paths; in the second case time saving can be appreciated even if the control of the kinematical parameters is not possible because of proprietary CNC. Even if accuracy is not mandatory for rough machining, using an adequate cosine law distribution the error on part can be controlled. The used revolute robot is governed by an open architecture; it has been originally designed for pick and place operation and it demonstrates to be affected by driver effectiveness. Even if higher values of acceleration and feedrate have been set up, during the testing operation it was not possible to reach such level of performance due to delay of drivers; moreover the basic revolute architecture due to signal delays and mechanical weakness magnify the trajectory deformation. Anyway, the open architecture testing shows that substituting the basic greek profile with a spline tool path the reduction of curvature and the consequent feedrate increment are comparable to what estimated in the first part of the work.

24 page 1 Briefly, the fundamental results obtained with spline interpolation are shown in Tab. 5. Tab. 5. Summary of final results for different pocket dimension CNC CNC CNC CNC Robot Siemens Siemens Siemens Siemens x 3x3 3x3 15x15 15x15 Max Velocity (m/s) Max Acceleration (m/s ) Time Saving (%) The experiments confirm the time saving using cubic spline interpolation functionality in order 1 % compared to linear tool path. The results are confirmed both using equipped in some modern CNC and using an open architecture control robot, where different time law and different spline interpolation path have been performed. More algorithms can be are easily developed with PC open architecture machines, thus creating the basis for future works. REFERENCES [1] ALTINTAS Y., NEWELL N., ITO M., Hierarchical open architecture multi processor CNC system for motion and process control, ASME Prod. Eng. Div. Publ. PED, Manufacturing Science and Engineering, 1993, Vol. 64, pp [] ERKORKMAZ K., ALTINTAS Y., High speed CNC system design. Part I: jerk limited trajectory generation and quintic spline interpolation, International Journal of Machine Tools and Manufacturing, 1, Vol. 41, pp [3] ERKORKMAZ K., ALTINTAS Y., High speed CNC system design. Part III: high speed tracking and contouring control of feed drives, International Journal of Machine Tools and Manufacturing, 1, Vol. 41, pp [4] NATIONAL INSTRUMENTS, NI-Motion User Manual, 7/6. [5] ROBER S.J., SHIN Y.C., Modeling and control of CNC machines using a PC-based open architecture controller, Mechatronics, 1995, Vol. 5, No. 4, pp [6] SIEMENS SINUMERIK 84D sl/ 84 Di sl/84d/84di/81d, Job planning Programming manual, 3/6 Edition. [7] WANG F.-C., WRIGHT P.K., Open architecture controllers for machine tools. Part: a real time quintic spline interpolator, Journal of Manufacturing Science and Engineering, 1998, Vol. 1, No., pp