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Chap 6 mapping geometric and thermal errors in a turning center 6.1 introduction ● Ph.D. thesis of a researcher in NIST(미국표준 연구소) ('85 Purdue) - First in error mapping (a function of position and temperature) - Error compensation algorithm based on S/W ⇒ compensating geometric and thermal errors ● “A general methodology for machine tool accuracy enhancement” by Dr. Alkan Donmez of the NIST 6.1 introduction ● machine tool: 2 axis turning center ("Superslant“ lathe) 6.1 introduction ● slanted bed to remove chips easily ● 8 tools mounted on a turret - upper turret: outside surface cutting - lower turret: end surface cutting 6.1 introduction 6.1 introduction ● spindle (connected to bed) - revolute joint ● carriage (connected to bed) - sliding joint ● cross-slide (connected to carriage) - sliding joint ● turret (connected to cross-slide) - revolute joint ● cutting tool (connected to turret) - fixed ● workpiece (connected to spindle) - fixed 6.3 machine tool metrology ● error at toolpoint is represented by combination of errors in machine elements ● all errors measured or predicted (for all positions and temperature) ⇒ error compensation at the tool tip is possible ● various errors as functions of position and temperature construct error map by measuring errors at position and temperature 6.3 machine tool metrology ● reversal error (ex, hysteresis) can be obtained (ex, backlash) For each axis, - in one direction, table is moved and error is measured - in the other direction, same procedure 6.3 machine tool metrology ● when measurement interval is selected, measurement position is set as a (even number) multiple of lead ⇒ periodic error can be separated ● to remove the effect of temperature in periodic error determination for small interval (1-2 times of lead) separate experiment assume the same periodic error in entire range Preliminary temperature test ● temperature rise during operation (temperature change at several parts) Preliminary temperature test ● error measurement is needed in order to find out the effect of temperature on errors ● warm-up: reciprocating the slide ● temperature measurement position (near heat sources): bearing housing, slide way, motor, bed, fixture, environment 4 groups of errors ● linear displacement error ⇒ length change ● angular error ⇒ angle change ● straightness, parallelism, squareness ● spindle thermal drift error linear displacement error ● linear error along moving axis of machine element cause: geometric incorrectness ● ball screw - Lead error: distance variation per 1 rotation - misalignment (between rotating shaft and center axis): error occurs perpendicular to moving axis - Geometric inhomogeneous: machining error in ball screw - coupling error between feedback unit and ball screw ● laser interferometer measurement is desirable angular errors ● cause: geometric incorrectness in slide, misalignment during assembling machine structural elements yaw Y Z turret X tool roll pitc h angular errors ● roll and pitch errors are in nonsensitive direction (depending on machine tools) ● yaw error is important (sensitive direction, making the tool move in radial direction) ● laser interferometer (or autocollimator) is normally used straightness ● translational error in two directions perpendicular to Z (moving axis) Y Z X ● non-contact capacitance sensor, and precision test arbor are used (laser interferometer is hard to mount because of allowable space and size of optical device) straightness ● test arbor is attached to spindle -Sensor attached to carriage moves with carriage, and measure the gap between sensor and arbor ● measurement contains straightness error, test arbor non-straightness, and misalignment - reversal technique is used to remove arbor profile error - misalignment can be removed by deleting best- fit line slope parallelism ● parallelism between Z motion and center axis of the spindle ● procedure - Two measurements at two positions along test arbor difference/distance parallelism ● to measure parallelism without other errors affecting measurement two sensors 0 ° and 180° (top and bottom of artifact) are used probe 1 spindle artifac t probe 2 parallelism ● with small spindle rotation (in order for spindle error motion small) - Measuring distance = 12" -512 points per 1 rotation ⇒ best-fit circle is determined ri R n - R: radius of the best-fit circle - ri: sensor output at angle i - n: number of data parallelism ● To remove straightness error of the shaft, two sensors (0° and 180 °) are used best-fit circle is determined from two outputs ● parallelism error ( R21 R11 ) ( R22 R12 ) p 2z ( R21 R11 ) ( R12 R22 ) z z 2 parallelism R11: least square radius at position 1 and sensor 1 R21: least square radius at position 2 and sensor 1 R12: least square radius at position 1 and sensor 2 R22: least square radius at position 2 and sensor 2 z: distance from sensors 1 and 2 orthogonality ● To measure straightness of X motion wrt the Z direction, and orthogonality between x axis and spindle center line, one more test arbor is used. (7" diameter, lapped flat surface) ● reversal technique cannot be used because of machine ⇒ surface should be calibrated 0 C ross- slide ex straightness X Z orthogonality ● In order to remove arbor misalignment and squareness error, - As cross-slide moves against test arbor surface, measurement is done at the interval - Repeat measurement with spindle rotated 180 ° Orthogonality and Z straightness of X motion can be determined orthogonality m1 ( x) z ( x) e( x) m2 ( x) z ( x) e( x) m1(x): 1st measurement m2(x): 2nd measurement (spindle at 180 °) dz: Z straightness of X motion e(x): arbor squareness and misalignment error z ( x) (m1 ( x) m2 ( x)) / 2 ● orthogonality can be calculated from best-fit line slope averaged from m1 (x) and m2 (x) 6.3.4 spindle thermal drift ● thermal drift: distance between two bodies changes due to temperature change (internal or external heat sources) ● 3 components of spindle thermal drift - axial thermal drift: spindle deformation in the Z direction - radial thermal drift: perpendicular to Z and deformation in sensitive direction - tilt thermal drift: spindle’s tilting motion in X-Z plane 6.3.4 spindle thermal drift ● capacitance sensor and precision test arbor are sued ● investigate position and orientation of spindle wrt time ● positions of temperature measurement: sensitive to temperature change 6.3.4 spindle thermal drift ● operate spindle for 8 hours at constant speed - temperature, spindle thermal drifts in radial and axial direction at every 10 minutes - stop after 8 hours, and same measurement is repeated during cooling ● to remove roundness error of test arbor, and fundamental spindle error motion, measure at the same spindle angle ● tilt is determined radial displacement difference/distance between two sensors 6.4 calibration measurement results ● given condition of Superslant - lead of the screw = 0.2" - travel range = 13" (carriage, Z axis), 3.4" (cross-slide, X axis) - measuring interval = 1" (carriage), 0.2" (cross- slide) ● interval = multiple of lead periodic error is separated ● periodic error is obtained for 0.4"(2 times of lead) with 0.002“ of interval (200 points) 6.4 calibration measurement results carriage (Z) linear displacement error ● initial backlash of 200min ⇒ different backlash due to nonlinear lead screw ● backlash compensation⇒ calibrations different for forward and reverse directions ● home position change (drift) ⇒ home position is unstable ⇒ limit switch is needed ● geometric error due to state ⇒ as warm-up, error curve slope changes carriage (Z) linear displacement error ● best positions for temp measurement (sensitive position) : - bearing housing at ends of ball screw - ballnut assembly carriage (Z) linear displacement error ● 2 parameter nonlinear least square regression analysis for position and temperature ⇒ fails ● error behavior wrt temperature at each position (Z axis: 1", X axis: 0.2") is analyzed ⇒ temperature is only parameter z ( z ) a0 a1T a2T 2 a3T 3 a4T 4 carriage (Z) linear displacement error carriage (Z) linear displacement error ● 12 sets of 5 coefficients for each position is necessary to map linear displacement performance of the carriage ● interpolation scheme is used to determine error between two positions ● prediction of periodic displacement error is required to determine accurate Z position ⇒ determined from 0.02" interval experiment carriage (Z) linear displacement error ● to determine periodic error (without temperature effect) ⇒ measurement is conducted for small range (0.4") (assuming homogeneous periodic error in all range) carriage (Z) linear displacement error ● net error motion data and fitted curve per one revolution carriage (Z) linear displacement error ● forward 'z ( z ) 3.19 0.164 cos(31.4 z ) 3.54sin(31.4 z ) 301z 1694 z 2 z: incremental nominal position ● reverse 'z ( z ) 15.1 6.45cos(31.4 z ) 4.42sin(31.4 z ) 1209 z 5953 z 2 carriage (Z) linear displacement error ● sinusoidal interpolation procedure based on superposition can be applied to find the periodic error at any point ● when combined with thermal error, the total linear displacement error for the carriage is obtained ⇒ same procedure applied to cross-slide carriage yaw error ● 1 stage yaw error of carriage cross-slide assembly was measured when the machine was at its home position (machine gradually warmed up from cold state) ● 2 stage yaw error can be determined as a function of distance (as cross-slide and carriage are away from home position) carriage yaw error carriage yaw error carriage yaw error ● depending on direction analyzed separately ● effect of temperature on yaw erroris constant over carriage motion one parameter(z) regression forward: y ( z ) 15.1 2.64 z 0.109 z 0.00397 z 2 3 backward: y ( z ) 16.3 ...z 3 ● applied to cross-slidesimilarly X straightness of the Z motion X straightness of the Z motion ● sample raw data from two probes ⇒ X direction straightness of carriage as a function of Z ⇒ linear regression analysis to calculate best fit line ● temperature effect is not significant ● irregular curve least square curve fitting does not give satisfactory correlation ⇒ look-up table X straightness of the Z motion X straightness of the Z motion ● to determine parallelism error between carriage motion and spindle shaft average line, best fit circle is calculated (two probes at 0 and 180) temperature effect is small ⇒ average -14 mrad ⇒ constant value is used to error compensation orthogonality ● best fit line slope (squareness between cross- slide and spindle axis) 0 345 7.34T 0.0512T 2 spindle radial and tilt thermal drift ● data was obtained using two probes mounted 8” apart along the test arbor - Difference between the radial displacements measured by two probes divided by the distance tilt - Using this value, the pure radial displacement at the spindle nose was also calculated ● noise occurs due to spindle error motion ⇒ amplified by tilt ● radial thermal drift is more complicated (temperature and rotating speed influence) 6.6 real-time implementation of the error compensation system ● error of each element depending on temperature and position ⇒ HTM ⇒ error vector at machining point ⇒ error compensation signal to the controller⇒ accuracy improves ● error compensation algorithm ⇒ into micro computer 6.6 real-time implementation of the error compensation system ● HTM 1 Z ( z ) Y ( z ) a X ( z ) ( z) 1 X ( z ) b Y ( z ) R Tnerr Z Y ( z ) X ( z ) 1 c Z ( z) 0 0 0 1 6.6 real-time implementation of the error compensation system ● position command signal is calculated - Compare command with position feedback - for speed control, velocity feedback is monitored or speed feedback signal is determined from position feedback signal ● real-time error compensation system: put error compensation signal to position servo loop 6.6 real-time implementation of the error compensation system ● To calculate error, 3 independent variables (position, direction, temperature) ● error calculated is sent to machine controller Cutting tests ● real time error compensation is constructed cutting tests is conducted at unsteady state (error compensation effect is to be found) - With or without error compensation system ● significant precision improvement in diameter and length (up to 20 times)