IND62 TIM CALIBRATION OF FREE-FORM STANDARD AND THEIR APPLICATIONS FOR IN-PROCESS MEASUREMENT ON MACHINE TOOLS VÍT ZELENÝ, IVANA LINKEOVÁ, PAVEL SKALNÍK (LENGTH MEASUREMENT DEPARTMENT) 5th November 2014 TIM Workshop NPL Teddington UK 1
CMM AND CNC CMM Elastic contact of tactile probe and the measured surface CNC Rigid contact of machine tool and the manufactured surface 5th November 2014 TIM Workshop NPL Teddington UK 2
CMM AND CNC CMM 1. Measurement of dimensions 2. Definition of a positon 3. Shape determination 4. Surface quality CNC 1. Definition of a position 2. Measurement of dimensions 3. Shape determination 4. Surface quality y z x 5th November 2014 TIM Workshop NPL Teddington UK 3
KINEMATIC SCHEME MODEL OF CMM MODEL OF CNC MACHINE TOOL 5th November 2014 TIM Workshop NPL Teddington UK 4
CMM AND CNC CALIBRATION DETERMINATION OF 21 GEOMETRICAL ERRORS 12 GEOMETRICAL ERRORS OF ROTARY TABLES TEMPERATURE ERRORS CALIBRATED CMM CALIBRATED CNC Corrections MPE E = 1,3 + 1,5L MEASUREMENT UNCERTAINTY POSITIONING UNCERTAINTY 5th November 2014 TIM Workshop NPL Teddington UK 5
COORDINATE SYSTEM DETERMINATION OF COORDINATE SYSTEM AND TRANSFORMATIONS CARTESIAN CYLINDRICAL SPHERICAL PARAMETRIC z x S x z S z S y S y β v x S z S S(u,v) y S x β z S x S u v z S(u,v) α y S y x S x α u z S z v β S(u,v) y S y x u α y x S, y S, z S x u, v = R cos u x u, v = R cos u sin v u, v y u, v = R sin u y u, v = R sin u sin v z u, v = v z u, v = R cos v 5th November 2014 TIM Workshop NPL Teddington UK 6
COORDINATE SYSTEM x NATURAL y z CURVE C u = x u, y u, z u TANGENT VECTOR t u = C u BINORMAL VECTOR b u = C u C u PRINCIPAL NORMAL VECTOR n u = b u t u CMM GLOBAL COORDINATE SYSTEM CNC GLOBAL COORDINATE SYSTEM WORKPIECE LOCAL COORDINATE SYSTEM 5th November 2014 TIM Workshop NPL Teddington UK 7
WORKPIECE COORDINATE SYSTEM PLANE LINE POINT (3 2 1) FIDUCIAL ELEMENTS (SPHERES) 5th November 2014 TIM Workshop NPL Teddington UK 8
FREE-FORM STANDARD DESIGN MATHEMATICAL MODEL NURBS REPRESENTATION NonUniform B-Spline STEP, IGES format CAD MODEL TRIANGULAR MESH Exact representation of free-form surface Exact representation of free-form surface Approximate representation of free-form surface 5th November 2014 TIM Workshop NPL Teddington UK 9
FF-MS HYPERBOLIC PARABOLOID MATHEMATICAL MODEL z f x, y z x, y x y EXPLICIT SURFACE VECTOR EQUATION S u, v u, v, u v PARAMETRIC EQUATIONS x y z u, v u u, v v u, v u v CAD MODEL CAD MODEL TRIANGULAR MESH 5th November 2014 TIM Workshop NPL Teddington UK 10
FF-MS HYPERBOLIC PARABOLOID FREE-FORM SURFACE INTERPRETATION FREE-FORM SURFACE TWO SYSTEMS OF 3D LINES TWO SYSTEMS OF 3D PARABOLAS SYSTEM OF 3D HYPERBOLA 5th November 2014 TIM Workshop NPL Teddington UK 11
FF-MS HYPERBOLIC PARABOLOID 3D LINE LOCATED ON FREE-FORM SURFACE LINE IS NOT AN INTERSECTION OF TWO PLANES LINE IS A SET OF POINTS VARIOUS DIRECTION OF NORMAL VECTOR AT EACH POINT 5th November 2014 TIM Workshop NPL Teddington UK 12
FF-MS HYPERBOLIC PARABOLOID CALIBRATION ON SIP CMM 5th November 2014 TIM Workshop NPL Teddington UK 13
FF-MS HYPERBOLIC PARABOLOID Graphical result of calibration 5000 points complete mesh 5th November 2014 TIM Workshop NPL Teddington UK 14
Graphical result of calibration 354 points in defined grid lines, parabolas, hyperbolas 5th November 2014 TIM Workshop NPL Teddington UK 15
FF-MS HYPERBOLIC PARABOLOID 5th November 2014 TIM Workshop NPL Teddington UK 16
FF-MS HYPERBOLIC PARABOLOID LOCAL COORDINATE SYSTEM DEFINITION Fiducial elements alignment PLANE LINE POINT (3 2 1) FIDUCIAL ELEMENTS (SPHERES) RPS (REFERENCE POINT SYSTEM) 6 POINTS ON TWO PERPENDICULAR LINES 5th November 2014 TIM Workshop NPL Teddington UK 17
FF-MS APPLICATION IN IN-PROCESS MEASUREMENT ON MACHINE TOOLS Local coordinate system determination 1. Determination of coordinate system by means of fiducial elements (hemispheres) 2. Improvement of coordinate system by means of 3D line 3. Measurement of points along 3D line located on free-form surface Points along 3D line are measured with respect to the free-form surface (various direction of normal vectors) 5th November 2014 TIM Workshop NPL Teddington UK 18
FF-MS APPLICATION IN IN-PROCESS MEASUREMENT ON MACHINE TOOLS 3D LINE = INTERSECTION OF HYPERBOLIC PARABOLOID AND PLANE PARALLEL TO COORDINATE PLANES Parallel to (x, z) plane Parallel to (y, z) plane Intersections are 3D lines 5th November 2014 TIM Workshop NPL Teddington UK 19
FF-MS APPLICATION IN IN-PROCESS MEASUREMENT ON MACHINE TOOLS 3D LINE = INTERSECTION OF HYPERBOLIC PARABOLOID AND PLANE PARALLEL TO COORDINATE PLANES Non-parallel to (x, z) plane Intersection is 3D curve (not 3D line) 5th November 2014 TIM Workshop NPL Teddington UK 20
FF-MS APPLICATION IN IN-PROCESS MEASUREMENT ON MACHINE TOOLS Non-parallel to (x, z) plane Wrong coordinate system determination y y O O x x 5th November 2014 TIM Workshop NPL Teddington UK 21
Measurement on Werth machine with laser scanner probe 5th November 2014 TIM Workshop NPL Teddington UK 22
SURFACE ROUGHNESS SURFACE ROUGHNESS MEASURED ALONG 3D LINES 5th November 2014 TIM Workshop NPL Teddington UK 23
SURFACE ROUGHNESS SURFACE ROUGHNESS MEASURED ALONG 3D LINES 5th November 2014 TIM Workshop NPL Teddington UK 24
FF-MS HYPERBOLIC PARABOLOID MEASUREMENT ON CNC TACTILE SYSTEM RENISHAW 5th November 2014 TIM Workshop NPL Teddington UK 25
FF-MS HYPERBOLIC PARABOLOID MEASUREMENT ON CNC TACTILE SYSTEM RENISHAW 5th November 2014 TIM Workshop NPL Teddington UK 26
FF-MS HYPERBOLIC PARABOLOID MEASUREMENT ON CNC TACTILE SYSTEM RENISHAW 5th November 2014 TIM Workshop NPL Teddington UK 27
MEASUREMENT ON MACHINE TOOL 5th November 2014 TIM Workshop NPL Teddington UK 28
MEASUREMENT ON MACHINE TOOL 5th November 2014 TIM Workshop NPL Teddington UK 29
MEASUREMENT ON MACHINE TOOL 5th November 2014 TIM Workshop NPL Teddington UK 30
FF-MS HYPERBOLIC PARABOLOID MEASUREMENT OF FF-MS ON MACHINE TOOL 1. Measurement of fiducial spheres to determine the local coordinate system 2. Measurement of points along lines 3. Measurement of points along parabolas 4. Measurement of points along hyperbolas 5th November 2014 TIM Workshop NPL Teddington UK 31
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MEASUREMENTS Measured deviations on reference CMM SIP Measured deviations on machine tool 5th November 2014 TIM Workshop NPL Teddington UK 33
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Evaluation according to the usage of En criterium for comparison evaluation gives us a feedback about uncertainty of measurement of machine tool: 95% of measured values is in range of: ± 0,0015mm These measurements shows us the capability of free-form measurements on a machine tool. 5th November 2014 TIM Workshop NPL Teddington UK 35
MANUFACTURING/MEASUREMENT UNCERTAINTY En criterion applied in CNC in-process measurement E n = X R X L U R 2 + U L 2 1 PILOT = CMM TESTED LABORATORY = CNC X R reference value measured on CMM X L measured value on a tested CNC machine U R reference measurement uncertainty of CMM U L measurement uncertainty of a tested CNC machine 5th November 2014 TIM Workshop NPL Teddington UK 36
MANUFACTURING/MEASUREMENT UNCERTAINTY En criterion applied in CNC in-process measurement E n = X R X L U R 2 + U L 2, E n 1 PILOT = CMM TESTED LABORATORY = CNC X R reference value measured on CMM X L measured value on a tested CNC machine U R reference measurement uncertainty of CMM U L measurement uncertainty of a tested CNC machine UNKNOWN VALUE 5th November 2014 TIM Workshop NPL Teddington UK 37
INTERLABORATORY COMPARISON Empirical criterion Interlaboratory comparison E n criterion X L U L U R U R 2 X R U R U R 2 X R U L X L X R E n = X R X L U R 2 + U L 2, E n 1 U R 2 U R 2 U R X R X L U R U L X L U L X R pilot reference value X L measured value in tested laboratory U R pilot reference measurement uncertainty U L measurement uncertainty of tested laboratory 5th November 2014 TIM Workshop NPL Teddington UK 38
MATHEMATICS AND GEOMETRY OF E n Solution of E n = 1 with respect to U L X R X L U R 2 + U L 2 = 1 U L = ± X R X L 2 U R 2 (only plus is considered in practice) Graphical representation: curves of intersection X L is less than X R X L is greater than X R U L = X R X L 2 U R 2 E n = 1 X L < X R U L = X R X L 2 U R 2 E n = 1 X L > X R X L is equal to X R U L = X R X L 2 U R 2 E n = 0 X L = X R 5th November 2014 TIM Workshop NPL Teddington UK 39
En CRITERION En criterion applied in CNC in-process measurement E n = X R X L U R 2 + U L 2, E n 1 Application of E n criterion when evaluating interlaboratory comparison between CMM (pilot) and CNC (laboratory) provides: A feedback about measurement uncertainty of machine tool (e.g. for 95 % of all measured values U L of CNC is 0.0015 mm). Analysis of residual geometrical errors of CNC based on bestfit transformation (6 degrees of freedom => necessary translations and rotations). 5th November 2014 TIM Workshop NPL Teddington UK 40
TEMPERATURE MONITORING SYSTEM OF HOLES FOR TEMPERATURE SENSORS The temperature will be monitored in the cooperation with the CMI Temperatre department and influence of temperature changes on the free-form surface will be investigated 5th November 2014 TIM Workshop NPL Teddington UK 41
FREE-FORM TRACEABILITY SCHEME FREE-FORM STANDARD IS THE LAST MEMBER OF TRACEABILITY CHAIN 5th November 2014 TIM Workshop NPL Teddington UK 42
CONCLUSION DESIGN the design of FF-MS standard satisfies the geometricalmathematical approach z x, y x y MANUFACTURING the FF-MS standard has been manufactured from steel ČSN 17243, AISI 303 CALIBRATION CMM SIP with maximum permissible error 0.8 + 1.3L µm TRACEABILITY application of E n criterion to provide the traceability in free-form manufacturing 5th November 2014 TIM Workshop NPL Teddington UK 43
CONCLUSION The FF artefact is the last member in the line and should be the umbrella for the CNC machine s testing. Designing, measuring and evaluating the measurement of a general shape is a set of very complicated phenomena, approaches and aspects. Using the En criterion is one of the possible procedures towards finding the measurement uncertainty on CNC machines, and to estimate the uncertainty during the production of such machines. The traceability diagram shows that the uncertainty of the calibrated artefact is higher than the end gauge, for example. On the other hand, the large number of dimensions which are contained in it by default, support the FF artefact. Additional characteristics such as roughness and shape change as a function of temperature top off the whole rating of the CNC machine during the production of such a shape-demanding workpiece. 5th November 2014 TIM Workshop NPL Teddington UK 44
THANK YOU FOR YOUR ATTENTION 5th November 2014 TIM Workshop NPL Teddington UK 45
MATHEMATICAL X CAD MODEL Mathematical model of free-form surface is always exact representation of free-form surface. CAD model of free-form surface can be exact or approximate representation of the original shape. Exact representation of CAD model is for example step or iges file. This is a text file where all geometrical entities are described by definition data necessary to the construction of mathematical model. No simplifying of the original smooth geometry caused when exchanging the data by means of step or iges file. However, in the case of triangular mesh using, the free-form surface is represented by a set of triangles. This is represented by stl file, for example. This is an approximation of the original smooth surface by means of polygonal mesh. The accuracy of polygonal mesh is given by requirements applied when generating the triangular mesh for example definition of minimum allowed angle between two polygons, maximum allowed distance of vertex of polygonal mesh from the original smooth surface, etc. 5th November 2014 TIM Workshop NPL Teddington UK 46