Test Piece for 5-axis Machining Centers

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1 Test Piece for 5-axis Machining Centers S. Bossoni, W. Knapp, K. Wegener Institute of Machine Tools and Manufacturing, ETH Zurich, Switzerland, and inspire AG für mechatronische Produktionssysteme und Fertigungstechnik, Zurich, Switzerland Abstract The only standardized test piece for simultaneous 5-axis machining is defined in NAS 979 which does not specify detailed setup conditions. In this paper, the influence of test piece parameters and location (position and orientation in the machine coordinate system) on the movements of the machine axes is analyzed for simultaneous 5-axis milling applications. To conclude recommendations of parameter sets are presented and the influence of geometric machine errors is shown for one specific machining center. Keywords: Machine; Test piece; 5-axis machining 1 INTRODUCTION More and more 5-axis machine tools are used in industry, but today a standardized test piece for 5-axis machine tools, directly applicable to different machine tool designs, is still missing. The Aerospace Industries Association of America, Inc. (AIA) published a National Aerospace Standard (NAS) describing uniform cutting tests about 40 years ago [1]. It includes a profile cone frustum cutting test that can be performed to verify accuracies of five combined axes of motion (three linear and two rotary) for five axis machines under finishing conditions. The description in [1] is well suited for profiler machines common in the aerospace sector addressed by the standard. For such configurations, the description requires a simultaneous 5-axis movement without any further definition of the setup. On the contrary, for other types of machine designs, the setting conditions have to be defined more precisely in order to require a simultaneous 5-axis movement and to enable comparability. Moreover, no research has been found about the effects of individual geometric machine errors on such test piece geometry. The prediction and compensation of geometric machine errors of 5-axis machining centers on the geometry of a cone frustum test piece is described in [2]. 2 TOOL PATH REQUIRED FOR A CONE GEOMETRY When analyzing a required movement of a 5-axis machine a series of tool positions and directions have to be analyzed. For the case of a tool path for a cone geometry, the set of tool directions describe also a cone. The type and position of this cone depends on the cone geometry, the position of the workpiece and on the milling strategy. For end milling the cone formed by the tool directions is parallel to the cone of the workpiece at a distance of the tool radius from the workpiece (same cone angle α). The analysis presented in this work is focused on simultaneous end milling test pieces on a machining center with a tilting rotary table setup. More specific a machine with a t-(c)-z-y-b-x-b-c-w kinematic chain (structure code according to [3]) is used as an example. In this structure code, the upper case letters stand for the machine axes according to ISO 841 [4]. An upper case letter in brackets indicates an axis without positioning control. The lower case letters represent: tool (t), bed (b), and workpiece (w). Figure 1: Example of a right circular cone (α = 30 ) inclined by an angle β = 20 with the two frames Σ 0 and Σ The Proceedings of MTTRF 2009 Annual Meeting 235

2 2.1 Parameters of an inclined right circular cone The form of a right circular cone is defined only by the cone angle α (also referred to as half apex angle). The position and orientation in a specific frame can be defined either by definition of the position of the apex A and the direction of the cone axis or by definition of a circular section of the cone with the center M, the radius r and the direction of the cone axis towards the apex. When analyzing the cone describing the tool path it makes sense to use the circular base represented by the nominal tool positions instead of the apex. For the definition of a point P on the perimeter of the cone (representing a point of the tool path), a radial angle of the cone φ is needed. The orientation of a cone depends on the inclination angle β (wedge angle). The cone is inclined relative to a frame Σ 1 with the angle β around Y 1 (Y-direction of frame Σ 1 that coincides with Y 0, according to figure 1). The coordinates of a point 1 P in frame Σ 1 result according to figure 1 in: 1 r cos β cos φ P = rsin φ r sin β cos φ 2.2 Movement of rotational axes The movements of the rotational axes of a 5-axis machine, required to manufacture a cone geometry, depend only on the cone form (angle α) and the inclination of the cone axis relative to the nominal direction of the rotational axis of the machine nearest to the workpiece (seen in the kinematic chain). The movement of the rotary axes of all 5-axis machining centers with a serial kinematic setup with two orthogonal rotary axes is the same for a given combination of cone angle α and inclination angle β. In case of the analyzed tilting rotary table machine setup the inclination angle β is used to describe the angle between the C-axis (rotary table axis) and the cone axis. Therefore, the Z-axis of frame Σ 1 is defined to be parallel to the nominal direction of the axis C of the rotary table. The orientation of frame Σ 1 relative to the angle C of the rotary table only has an influence on the starting angle of the rotary table. This is of reduced importance since the rotary table has an unlimited angular range and therefore an arbitrary point of origin. The zero of the C-axis is defined to be equal to the zero of the radial cone angle φ. The translational position of the cone has only an influence on the movement of the linear axes Required angles of the tilting axis B The origin of the angle B of the tilting axis (B = 0 ) is defined to be the position of the axis B where the axis C is parallel to the direction Z 1. The angle of the tilting axis B corresponds to the angle between the tool direction and the direction of the rotary table axis C. This must be the angle between a slant s and the Z-axis of frame Σ 1 (see figure 1) which can be expressed as: B = arccos cos αcos β + sin αsin βcos φ (2) ( ) (1) Two important facts can be concluded from equation (2): The sign of the angle B is not defined. The extreme values of the angle of the tilting axis B for a given cone and setup (α and β are constant) are at φ = 0 and φ = 180. This means that the extreme values of the tilting axis B are in the XZ-plane of frame Σ Required angles of the rotary table C The rotary table needs to turn the slant into the plane perpendicular to the tilting axis. The angle C of the rotary table can be derived when analyzing the projection of the cone in the plane of the rotary table (plane perpendicular to the axis of the rotary table, which corresponds to the XY-plane of frame Σ 1 ). The angle C equals the angle between the projection of the height of the cone (in this case in positive X-direction of frame Σ 1 ) and the projection of the slant (see figure 1). Equation (3) results for the angle C. sin φ C = arctan (3) cos β cos φ sin β cot α For the interpretation of the resulting movements of the rotational axes of the machine, three situations are distinguished: α > β, α = β, α < β. 2.3 Cone angle α larger than inclination angle β For α > β the projection of the apex A into the XY-plane of frame Σ 1 is inside the projection of the base as shown in figure 1. Therefore, the range of the angle C of the rotary table is from 0 to 360 since it depends on the direction of the projection of the slants in the XY-plane of frame Σ 1. The minimal displacement of the tilting axis B min results to be the difference between the cone angle α and the inclination angle β whereas the maximal displacement of the tilting axis B max is equal to the sum of α and β. Therefore the range of the tilting axis is equal to twice the inclination angle β and independent of the cone angle α (except for special setups with α = β where the range of the tilting axis B can be up to four times the inclination angle β). Generally for α > β the tilting axis B has a reversal but the rotary axis C has no reversal. 2.4 Cone angle α equal to inclination angle β If the cone angle α is equal to the inclination angle β the slant at φ = 0 is parallel to the Z-direction Z 1 of frame Σ 1 and the projection of the apex A into the XY-plane of frame Σ 1 is on the projection of the base. Since the angle B of the tilting axis corresponds to the angle between a slant of the cone and the direction Z 1, B must be zero for φ = 0 for α = β (tool axis parallel to C). The angle C of the rotary table is not defined if the projection of the slant in the XY-plane of frame Σ 1 has no length. Therefore the angle C for φ = 0 depends on the angles C for φ close to 0. The limit of the angle C for the radial cone angle approaching 0 differs by 180, depending on the direction of approach The Proceedings of MTTRF 2009 Annual Meeting

3 ' Z 1 Y 1 = Y 0 Z 1 Z 0 Z 0 A A C X 1 X 1 A Y 1 X 1 X 0 Figure 2: Example of a configuration with α < β for the geometrical analysis of the range of the angles of the rotary table C 2.5 Cone angle α smaller than inclination angle β For α < β the projection of the apex A into the XY-plane of frame Σ 1 is outside the projection of the base as shown in figure 2. The range ΔC of the angles of the rotary table are equal to the angle between the two tangents to the ellipse of the projection of the tool path into the XY-plane of frame Σ 1 trough the projection of the apex A into the XY-plane of frame Σ 1. Therefore ΔC must be smaller than 180 for α < β. The minimum range ΔC of the angle of the rotary table is twice the cone angle α. This is the case if the inclination angle β is 90. A general expression of the range ΔC of the angle of the rotary table is: 1 ( an ) Δ C = 2arctan cos β tan arccos(t α cot β ) 2.6 Recommended angular parameters The range of the rotary axes should be the same on all types of machines in order to have a fair comparison. Therefore, the cone angle α and the inclination angle β are recommended to be the same, independent of the machine design. In order to have a full rotation of the rotary axis C, the cone angle α has to be larger than the inclination angle β. The test piece should be applicable on machines with a range of the tilting axis of 90 or more. The range needed during the simultaneous movement for the cone geometry is chosen to be 2/3 of the minimal range of 90, which is 60. This is obtained with an inclination angle β of 30. The range of the tilting axis is selected to be centered between 0 and 90. For an inclination angle β = 30 a cone angle of α = 45 results. 3 MOVEMENT OF LINEAR AXES The movement of the linear axes of 5-axis machines can be divided into a component needed for the relative translational displacement of the tool and a second component, which is needed in order to change the tool direction. This second compensational component consists of the linear displacement of the rotary axes in order to change the tool direction without changing the location of the tool center point (TCP). It is proportional to the distance between the rotational axes and the TCP. (4) 3.1 Tilting rotary table For the analysis of the movement of the linear machine axes of 5-axis machines with both rotational axes on the work piece side (tilting rotary table), the position of the workpiece relative to the crossing of the two rotary axes is relevant. A third frame Σ 2 is introduced according to figure 3. It is attached to the rotary table with its origin O 2 at the nominal crossing of the rotary table axis C with the tilting axis B. A Point 2 P in frame Σ 2 results through translation according to: 2 1 x cos cos + 0 r β φ x0 P = P+ y = rsin φ + y 0 0 z sin cos + 0 r β φ z0 In order to obtain the machine coordinates M P the rotations of the two workpiece sided rotary axes have to be taken into account to yield: P = R R M 2 tilt table P cos B 0 sin B cos C sin C 0 = sin cos 0 sin B 0 cos B O 2 Z 2 X 2 Y 2 x 0 y0 2 C C P O 1 β Z 1 z 0 A Z 0 (5) (6) Figure 3: Example of a right circular cone (α = 30 ) inclined by an angle β = 20 in frame Σ 2 with the frames Σ 0 and Σ 1. X 0 Y 1 X The Proceedings of MTTRF 2009 Annual Meeting 237

4 The expression of equation (6) as a function of the cone parameters with the radial angle φ (instead of the angles of the rotary axes) becomes very complex. Instead, some special configurations and setups are mentioned: If the apex A of the cone formed by the tool directions coincides with the crossing of the two rotary axes of the machine, no movement of the linear axes is required. (2- axis movement) If the cone axis crosses the point O 2 (figure 3, crossing of the axes B and C), the Z-axis of the machine has no movement (4-axis movement) The range of the Y-axis (axis parallel to the tilting axis) corresponds to twice the distance of the apex A from the C-axis. If the cone axes crosses the C-axis (y 0 = 0) the movement of the machine axes have a symmetry to the XZ-plane of frame Σ 2 (see figure 3). 4 PROPOSED SIZE AND SETUP FOR A SPECIFIC MACHINE DESIGN For a given machine design the size and position of the test piece is limited by the ranges of the machine axes and by collisions. To avoid collisions the test piece is recommended to be placed within the surface of the work piece pallet on the rotary table (r Table = 100 mm diameter for the analyzed vertical machining center). Since the test goal of the test piece is to show the relevant geometric errors of the machine no unnecessary machine dynamics is wanted for the movement. Therefore, the lateral displacement y 0 is recommended to be zero to avoid dynamics of the linear axes due to an asymmetric movement. The diameter of the cone limits the range of the linear axes because with an increase of the diameter, the cone has to be positioned closer to the crossing of the two rotary axes (point O 2 in figure 3). In order to be still well manageable (fixation, measurement) the diameter of the tool path is proposed to be 80 mm. The movement of the linear axis parallel to the tilting axis (Y-axis) is not influenced by the motion of the tilting axis B. Thus, it only needs a range over the dimensions of the surface of the work piece pallet. The other two axes (X and Z) need a larger range of movement for the compensational movements. Therefore, the range of the linear axes should be larger for the X- and Z-axis than for the Y-axis. This can be reached by placing the cone at a negative distance x 0 = - r Table + r TCP cosβ = mm and at a maximal height above the tilting axis B. For the given ranges a height z 0 = 150 mm is chosen in order to stay within the limits of the ranges of the X- and Z-axes. The resulting movement of the machine axes is shown in figure 4 as a function of the radial angle φ. To give a better idea of the path of the TCP, figure 5 shows the path relative to the machine frame. 5 INFLUENCE OF GEOMETRIC MACHINE ERRORS For the simulation of the geometric errors and identifying the resulting test piece errors, three basic steps are carried out [5, 6]: 1. Transform points of the work piece geometry into the nominal kinematic model of the machine. 2. Transform points back into the work piece coordinate system with a general kinematic model containing all potential geometric errors. 3. Identify the resulting cone form: 238 a. Least squares plane and circle through the actual coordinates of the points. b. Cone axis through center of least squares circle normal to least squares plane. Least squares circle evaluation of the distances of points from cone axis in direction normal to the cone surface results in a measure for the cone form deviation. X M, Y M, Z M [mm] X M B C Y M φ [ ] Figure 4: Positions of the machine axes as a function of the radial cone angle φ (α = 45, β = 30, r = 40mm, x 0 = -65.4mm, y 0 = 0, z 0 = 150mm) Z M z 0 x 0 Z 1 Z 2 X 0-50 X 2 0 X M Y 150 M -50 Figure 5: Illustration of the cone position in the machine coordinate system when the TCP is at the bottom position of the cone (φ = 0). The red curve corresponds to the path of the TCP in the machine coordinate system and represents the movement of the machine axes The Proceedings of MTTRF 2009 Annual Meeting Z 0 X 1 Z M Y B, C [ ]

5 The effect of an individual error depends on the error magnitude and on the direction of the error. The component of the direction of the error in the sensitive direction (i.e. normal to the cone surface) affects the form of the cone. However, only changing effects can be seen as a form deviation since constant effects just change the cone angle or the cone position. When analyzing the components of the normal directions (n x, n y, n z ) of the cone surface in the machine frame as a function of the radial cone angle φ, the following points can be seen: n x : the component of the unit length normal direction of the cone surface in X-direction is always positive and has a length between 1 and 0.7. n y : the component of the unit length normal direction of the cone surface in Y-direction has a length between -0.7 and 0.7 n z : the normal direction of the cone surface has no component in Z-direction since it corresponds to the tool direction (length = 0). An example of a typical cone form deviation due to a constant error acting in X-direction, as well as in Y-direction is shown in figure Geometric errors with negligible influence on the form of an end milled cone surface on a machine with the tilting rotary table: Nomenclature of errors follows [7]. Vertical straightness error motions EZX, EZY, Z positioning error EZZ, Z zero position Z0Z, radial error motion EZB: geometric machine errors acting only in tooldirection (Z) have no influence on an end milled cone surface (nor on any end milled surface on a machine tool with tilting rotary table) Hysteresis of C positioning ECC hyst : the axis of the rotary table has no reversal point for setups with cone angles α larger than the inclination angle β. Therefore, the hysteresis of the positioning error of the rotary table cannot have any influence. If an analysis of the influence of ECC hyst on the cone form is desired, a setup with α < β needs to be chosen. Z tilt error motions EAZ, EBZ are rotations of the tool axis around the TCP, which have a negligible influence on the cone form for a small cone height of 5 mm. Y yaw error motion ECY and Z roll error motion ECZ are rotations around the tool axis and have no additional influence on the workpiece geometry (additional to straightness error motions). Squareness of B to X axis C0B: influence negligible because B max and B min are reached at Y M = 0, thus the sensitive direction is in X and not in Y. C tilt error motions EAC, EBC and B tilt error motion ECB: no additional influence to radial error motion of the axis C, respectively B for small cone heights. 5.2 Direct measurement of the 5-axis movement for a cone geometry In different publications [2, 8] the measurement of the deviations of a 5-axis movement for a cone geometry with a double ball bar (DBB) measuring device is presented. It should be noted that the results of a measurement setup with the DBB square to the cone axis does not represent the errors of the cone form because errors parallel to the cone surface are also measured as form errors. For a more realistic representation of the form error, the DBB should be set up perpendicular to the cone surface. This way also collision problems are avoided [8]. On a machine with tilting rotary table, an alternative would be to use an R-Test [9] and to position the precision sphere at the apex of the cone. In any case, the measurement cannot replace the cutting of a test piece but it is very well suited for a study of parameter influence, such as changing contouring feed. 6 CONCLUSION A test piece for 5-axis machining centers has been presented and the influence of the test piece and the setup parameters are analyzed. The following points can be concluded: The required movements of the rotary machine axes are the same for all machine tools with two orthogonal rotary axes (independent of the machine design and the translatory position of the test piece) A combination of a cone angle α = 45 and an inclination angle β = 30 represents a recommendable test piece setup for machines with a tilting axis with a range of at least 90 and a second rotary axis with an unlimited range. For machines with different ranges of the linear axes the Figure 6: Typical form error due to a constant geometric error acting in X-direction (a), e.g. X-position of B-axis, and in Y- direction (b), e.g. Y-position of the axis C. (blue: result with positive error value, red: result with negative error value) The Proceedings of MTTRF 2009 Annual Meeting 239

6 procedure how to decide on the angular parameters to be chosen was shown, a procedure that is also applicable for conical ball bar tests. The influence of the translatory position of the test piece on the movement of the linear axes has been shown for the most complex machine design (tilting rotary table machine). A recommended setup has been shown for a specific machine. The presented test piece is a good way to test the performance of a 5-axis machine for the specific milling strategy (end milling). If another milling strategy (e.g. face or ball nose end milling) is of interest, the same analysis has to be carried out for a test piece manufactured with the other milling strategy since then the influence of the geometric machine errors of the test piece errors changes. REFERENCES [1] NAS 979, 1969, Uniform Cutting Tests - NAS Series Metal Cutting Specification. Aerospace Industries Association of America, Inc. [2] Uddin, M. S.; Ibaraki, S.; Matsubara, A., Matsushita, T., Prediction and compensation of machining geometric errors of five-axis machining centers with kinematic errors, Precision Engineering, 2009, 33, [3] ISO/WD , 2008, Test conditions for machining centres Part 6: Accuracy of feeds, speeds, and interpolations. working document ISO/TC 39/SC 2/WG3 N123. [4] ISO 841, 2001, Industrial automation systems and integration - Numerical control of machines - Coordinate system and motion nomenclature. [5] Bringmann B., 2007, Improving Geometric Calibration Methods for Multi-axes Machining Centers by Examining Error Interdependencies Effects, 2/664. Fortschritt-Berichte VDI, Düsseldorf. [6] Bringmann B., Besuchet J.P., and Rohr L., 2008, Systematic evaluation of calibration methods. Annals of the CIRP 57/1: [7] ISO 230-1, 1996, Test Code for Machine Tools Part 1: Geometric Accuracy of Machines Operating Under No-Load or Finishing Conditions. [8] Matano K., Ihara Y., 2007, Ball bar measurement of five-axis conical movement. 8th International Conference and Exhibition on Laser Metrology, Machine Tool, CMM & Robotic Performance, Lamdamap. [9] Weikert S, Knapp W., 2004, R-Test: A New Device for Accuracy Measurements on Five Axis Machine Tools. Annals of the CIRP 53/1: The Proceedings of MTTRF 2009 Annual Meeting

7 MTTRF 2008 Test piece for 5-axis machining centers S. Bossoni, K. Wegener IWF ETH Zurich, Switzerland, and inspire AG, Zurich, Switzerland Outline Existing test pieces for 5-axis milling and their deficiencies Requirements for test piece Definition of test piece Movements of rotational axes and of linear axes Suggested test parameters Influence of geometric machine tool errors Summary 1 Existing Test Pieces for milling The Proceedings of MTTRF 2009 Annual Meeting 241

8 Deficiencies of the state of the art Standardized test piece for a 5-axis machine tool, directly applicable to different machine tool designs, is still missing. No detailed analysis of the adequacy of a cone geometry and possible combinations with other elements on a test piece has been published. Effects of geometric machine errors on such test pieces have not been shown. Publications with different variations of test pieces can be found in literature but no reasons are given for the selected parameters. Influence of different parameters (test piece + setup) is not understood yet. 3 5-axis milling machines The Proceedings of MTTRF 2009 Annual Meeting

9 Goals and requirements of the test piece The ideal test piece for acceptance tests of 5-axis machining should have the following features: easy and fast to manufacture easy and fast to measure easy to evaluate measuring results Set up in a way that it must be manufactured using 5 simultaneous axes on different types of 5-axis machining centers. Give comparable and quantitative results. Show the influence of the machine and not of the tool and the tool setup. Show the influence of errors relevant for the analyzed manufacturing strategy (e.g. end milling) with sufficient sensitivity. 5 Geometry of test piece For simultaneous 5-axis motion: normal and tangent vectors not all parallel to each other Possible geometries: sphere cone toroid Cone best because: only geometry that can be generated with straight lines can be manufactured with one closed movement with end mill easy and fast to measure and evaluate measuring results The Proceedings of MTTRF 2009 Annual Meeting 243

10 General transformation for 5-axis machines 7 Movement of linear machine axes Compensational movement of linear machine axes: Movements of the linear axes needed in order to change the relative orientation between tool and workpiece without changing the relative position of the tool centre point between tool and workpiece. Depends on configuration of rotary axes Offset of the rotary axes from the TCP: workpiece sided rotary axes: depends on position of TCP first tool sided rotary axis: constant second tool sided rotary axis: function of angle of first rotary axis Most complex for tilting rotary table because both rotary axes are workpiece sided The Proceedings of MTTRF 2009 Annual Meeting

11 Inclined right circular cone Set of tool directions for manufacturing of cone also describe a cone 9 Ranges of the angle C of the rotary table The Proceedings of MTTRF 2009 Annual Meeting 245

12 Angle C of rotary table depending on relation of α and β 11 Range of angle C for α< β The Proceedings of MTTRF 2009 Annual Meeting

13 Movements of rotary machine axes for α=β 13 Recommended angular parameters for all machine setups The Proceedings of MTTRF 2009 Annual Meeting 247

14 Proposed test piece parameters for machine example (slide 9) 15 Positions of machine axes The Proceedings of MTTRF 2009 Annual Meeting

15 Positions of machine axes (animation) 17 Radial representation of positions of machine axes The Proceedings of MTTRF 2009 Annual Meeting 249

16 Geometric errors of machines component errors: 6 for each machine axis location errors 3 per linear axis 5 per rotary axis 6 location errors are set zero for machine frame total of 43 geometric errors for 5-axis machine without the working spindle 19 2 types of resulting error forms Type 1: top-bottom B0Z B0C X0X X0C EXX lin EBX lin EYY lin EAY lin ECC lin Type 2: asymmetric C0Y EBY lin A0Z A0B A0C Y0Y ECX lin EAX lin The Proceedings of MTTRF 2009 Annual Meeting

17 Effects of location errors 21 Effects of 1000 random combinations of errors The Proceedings of MTTRF 2009 Annual Meeting 251

18 Summary of geometric evaluation Test piece for a 5-axis machine tool, directly applicable to different machine tool designs. Influence of parameters analyzed for any machining center with three orthogonal linear axes and two orthogonal rotary axes. Proposed test piece parameters are deduced from the analysis. Effects of geometric machine errors on test piece have been shown. Novel visualization forms presented. Influence of different parameters is understood. 23 Application for Mori Seiki NMV 5000 (project) Geometric errors of machine. Simulation of test piece for measured geometric errors. Machining of test piece. Variations (e.g. feed, position, orientation) with conical circular test, R-test The Proceedings of MTTRF 2009 Annual Meeting

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