US20110060542A1 - Method for determining dynamic errors in a measuring machine - Google Patents

Method for determining dynamic errors in a measuring machine Download PDF

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Publication number
US20110060542A1
US20110060542A1 US12/666,855 US66685507A US2011060542A1 US 20110060542 A1 US20110060542 A1 US 20110060542A1 US 66685507 A US66685507 A US 66685507A US 2011060542 A1 US2011060542 A1 US 2011060542A1
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input
measuring machine
mobile element
quantities
output
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US12/666,855
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Inventor
Giampiero Guasco
Giuseppe Menga
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Hexagon Metrology SpA
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Hexagon Metrology SpA
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Assigned to HEXAGON METROLOGY S.P.A. reassignment HEXAGON METROLOGY S.P.A. ASSIGNMENT OF ASSIGNORS INTEREST (SEE DOCUMENT FOR DETAILS). Assignors: GIAMPIERO, GUASCO, GIUSEPPE, MENGA
Publication of US20110060542A1 publication Critical patent/US20110060542A1/en
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G01B21/02—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
    • G01B21/04—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness by measuring coordinates of points
    • G01B21/045—Correction of measurements
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G01B21/02—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
    • G01B21/04—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness by measuring coordinates of points
    • G01B21/042—Calibration or calibration artifacts
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B5/00—Measuring arrangements characterised by the use of mechanical techniques
    • G01B5/004—Measuring arrangements characterised by the use of mechanical techniques for measuring coordinates of points
    • G01B5/008—Measuring arrangements characterised by the use of mechanical techniques for measuring coordinates of points using coordinate measuring machines

Definitions

  • the present invention relates to a method for determining dynamic errors in a measuring machine.
  • a measuring machine with cartesian co-ordinates, of the contact type comprises three slides that are mobile along the respective orthogonal axes and are designed to move a contact sensor in a three-dimensional measurement space. Said measuring machine returns at output the position of the contact sensor with respect to a cartesian reference system, from the measurement of the position of the respective slides. To move the measurement sensor, linear electric motors that impress a force on the moving masses are used.
  • Aim of the present invention is to provide a method for determining dynamic errors in a measuring machine that will enable determination and compensation of the dynamic errors with extreme precision (for example, of the order of the micron).
  • FIG. 1 illustrates, by way of example, a measuring machine, in which the method of the present invention is implemented
  • FIG. 1 a illustrates, in cross-sectional view, a detail of the measuring machine
  • FIGS. 1 b and 1 c illustrate a portion of the machine of FIG. 1 subjected to dynamic deformation
  • FIG. 2 describes the steps of the method according to the present invention
  • FIG. 3 a details some steps of the method
  • FIG. 3 b illustrates the evolution in time of physical quantities involved in the method according to the present invention.
  • the measuring machine (of the portal type) comprises a base 5 provided with a plane resting surface (working surface) 6 , mobile along which is a motor-driven slide 8 , which slides along a first axis (axis Y) of the orthogonal reference system of the working space.
  • the slide 8 is approximately C-shaped and comprises two vertical uprights 8 a , 8 b perpendicular to the resting surface 6 and a top horizontal cross-member 8 c , which extends between the top ends of the vertical uprights 8 a , 8 b.
  • the top cross-member 8 c carries a second slide 10 , which slides along a second axis (axis X), of the orthogonal reference system.
  • the vertical column 12 carries at the bottom the measurement sensor 3 (of a known type).
  • the measuring machine 1 is controlled by an electronic unit (not illustrated) provided with a power section 14 e (represented schematically), which supplies the linear electric motors (not illustrated) that move the slides 8 , 10 and the column 12 for displacement of the measurement sensor 3 along the axes Y, X and Z and hence its positioning in the measurement space.
  • the electronic power unit 14 e supplies to the linear electric motors illustrated above the currents I Y , I X and I Z to bring about the respective displacements of the slides 8 , 10 and of the column 12 .
  • the measuring machine 1 supplies at output—through a software based upon algorithms of a known type—the position xa, ya, za of the measurement sensor 3 in the measurement space, detecting the position of the slides along the respective axes X, Y and Z.
  • the position of the measurement sensor 3 is affected by a position error ex, ey, of a dynamic type with respect to the measured values xa, ya, za, due to the fact that the mechanical structure that supports the measurement sensor 3 (principally the vertical upright 8 a , the cross-member 8 c , and the area of connection between the top end of the vertical upright 8 a and the cross-member 8 c ) undergoes elastic deformation on account of the forces impressed by the electric motors that move the slides 8 and 10 .
  • a position error ex, ey of a dynamic type with respect to the measured values xa, ya, za
  • FIG. 1 b illustrates the deformations caused by the displacement of the slide 8 along the axis Y.
  • Said deformations mainly comprise:
  • FIG. 1 c illustrates, instead, the deformations caused by the displacement of the slide 10 along the axis X.
  • Said deformations mainly comprise:
  • the functions of the two-dimensional position transducer 14 can be performed by the comparison system VM 182 produced by the firm HEIDENHAIN, used for calibration of the machine.
  • a laser sensor 16 which supplies information on the dynamic deformations my, mx that the mechanical structure of the machine 1 undergoes during the movements of the slides 8 and (as regards the deformations, see what was said with reference to FIGS. 1 b and 1 c ).
  • the laser sensor 16 is supported by a vertical post 20 , which extends within a vertical cavity 19 of the upright 8 a and has a first bottom end 20 a rigidly fixed with respect to the slide 8 (and hence not subject to the deformations of the upright 8 a ), and a second top end, which exits from the upright 8 a and carries a laser-emitting device 22 , housed in a first end of an internal cavity 24 of the cross-member 8 c.
  • the laser-emitting device 22 emits a laser beam 26 , which traverses the cavity 24 parallel to the axis X and hits the target 28 set at the opposite end of the cavity 24 .
  • the target 28 is constituted by a position-sensor device (PSD) of a known type, which detects displacements of the laser beam 26 along the two axes Y and Z of the orthogonal reference system according to the deformation of the mechanical structure.
  • PSD position-sensor device
  • measuring machine 1 illustrated above is an example of machine on which the method of the present invention, which can be transferred to measuring machines having a different structure, can find application.
  • the method forming the subject of the present invention comprises an initial step of calibration (block 100 , FIG. 2 ), in which an input-output model M is defined, which describes the dynamic behaviour of the measuring machine 1 (said step is also defined as “model identification”).
  • the input-output model M ( FIG. 3 a ) is multivariable with at input (input u) the currents for supplying the two motors for controlling the respective displacements along the axes X and Y (it has preliminarily been verified that the dynamics due to the displacements of the slide along the axis Z leads to negligible errors), and at output a plurality of response quantities (output quantities y), which comprise the position ya, xa of the measurement sensor 3 obtained from the axes of the machine, the position errors ey, ex introduced by the elasticity of the machine 1 along the axes X and Y, which are measured by means of the two-dimensional position transducer 14 , and the deformations my, mz of the machine measured by the laser sensor 16 .
  • the entire model may be broken down into two models: a first model M 1 , which receives at input the current Iy of the motor corresponding to the axis Y and supplies at output the position ya along the axis Y, as well as position errors ey, ex and measurements of deformation my, mz along the axes Y and Z, and a second model M 2 , altogether equivalent to the model M 1 , which has as input the current 1 x of the motor corresponding to the axis X, and supplies at output the position xa along the axis X, as well as the position errors ey, ex and the measurements of deformation my, mz along the axes Y and Z.
  • the model M 1 has, as input quantity u, the current Iy, and the output quantities y are:
  • A, B, C, D and K are the matrices of the model, in particular,
  • C [ c 11 c 12 c 13 c 14 c 15 c 16 c 21 c 22 c 23 c 24 c 25 c 26 c 31 c 32 c 33 c 34 c 35 c 36 c 41 c 42 c 43 c 44 c 45 c 46 c 51 c 52 c
  • the input quantities u and output quantities y are measured and recorded during a series of work cycles (block 110 ), in which the slide 8 is made to translate along the axis Y, subjecting the machine 1 to an acceleration that causes deformation of the machine itself by dynamic effect. Then, the dynamic input-output model M 1 that describes the elastic behaviour of the machine is identified, setting in relation the input quantities u with the output y quantities.
  • FIG. 3 b A typical example of work cycle, used for identification, is illustrated in FIG. 3 b.
  • the slide 8 of the axis Y with a closed-loop control is made to be follow a path of displacement, which, starting from a stationary condition, has a first step in acceleration, to which there corresponds a ramp at a speed T 1 , a second step at a constant speed, and a third step of deceleration T 2 , until it comes to a stop again.
  • a current cycle characterized by a positive step during acceleration, a reduced value during the stretch at constant speed, and a negative step during deceleration.
  • the input quantities u and output quantities y are sampled, with a sampling step of 500 ⁇ s and stored.
  • the samples of the input quantities and output quantities are supplied to an identification algorithm, which, with a maximum-likelihood approach (for the definition of maximum-likelihood algorithm, reference may be made to the text by Lennart Ljung, entitled “System Identification—Theory for the user”, Prentice Hall; Upper Saddle River, N.J. 1999), applied to an innovative linear model, characterized by a quintuple of matrices A,B,C,D,K, identifies the input-output model M 1 , as described by the system of differential equations appearing above.
  • the model is not constant throughout the working space of the machine, so that different calibration steps are performed similar to the one described above before the entire measurement space is covered.
  • the variability of the model relates to the axes X and Z, so that the working space has been divided into a plurality of sections (for example, nine sections: bottom-left, bottom-centre, bottom-right, centre-left, etc.), in which respective models M 1 a , M 1 b , M 1 c . . . , M 1 n have been defined.
  • M 1 compl which approximates the various models M 1 a , M 1 b , M 1 c , . . . , M 1 n in the three-dimensional measurement space.
  • the matrices A, B, D and K of the various models are substantially constant in the measurement space, whereas only part of the matrix C is modified in the three-dimensional measurement space.
  • the global model M 1 compl consequently comprises the matrices A, B, D and K that do not vary in the measurement space, and a matrix C, having a portion (the rows corresponding to the error signals ex, ey) with variable parameters, which is a function of the co-ordinates of the axes X and Z and hence variable in the measurement space
  • the two-dimensional position transducer 14 is removed.
  • step 100 is then followed by a step 200 , in which, starting from the global model M 1 compl, an estimator filter ⁇ circumflex over (M) ⁇ 1 is designed.
  • model M 1 compl is represented (in the time domain, a similar representation is possible in a discrete way) in the following form:
  • the matrix C 1 comprises the first three rows of the matrix C, and the matrix C 2 the last two rows of the matrix C.
  • the matrix D 1 comprises the first three rows of the matrix D, and the matrix D 2 the last two rows of the matrix D.
  • the estimator filter ⁇ circumflex over (M) ⁇ 1 is designed with robust-filtering techniques of analysis (in this connection, see the text by P. Colaneri, A. Locatelli, J. C. Jeromel, entitled “Control theory and design, a RH2-RH-inf viewpoint”, Academic Press, 1997) on the basis of the global model M 1 compl, previously identified.
  • the estimator makes available the estimation of the dynamic deformations for the instant (t-Delta).
  • Delta is a time delay small enough not to jeopardize the efficiency of the machine in rendering the measurements made readily available, but is sufficiently large to improve the precision of the estimation. Practically, it has been found that a value of Delta equal to a few hundredths of a second is convenient.
  • the estimator filter ⁇ circumflex over (M) ⁇ 1 yields, in response to the values measured of the input u and of the output quantities y (measurements ya along the axis Y and values of deformation my, mz), an estimate z of the error.
  • the estimator filter ⁇ circumflex over (M) ⁇ 1 is represented by the equations
  • the estimator filter ⁇ circumflex over (M) ⁇ 1 supplies at output an estimate of the error of a dynamic type.
  • the matrices of the estimator filter ⁇ circumflex over (M) ⁇ 1 of a linear type are stored and integrated in the machine measurement software for estimation of the unknown error (block 400 ):
  • the signals my, mz generated by the deformation measuring device 16 are not used for definition of the input-output model M 1 and consequently are not made available to the estimator filter ⁇ circumflex over (M) ⁇ 1 .
  • the estimation is based exclusively upon the current of the motors and the position of the slide.
  • the input u comprises the current Iy
  • the output y is made up of:
  • a second variant also envisages the further elimination of the information on the current, so that the model and the estimator are based only upon the measurement of position of the slide.
  • the input of the model is given just by the noise, and the outputs y are the position ya and the errors ex, ey.

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Length Measuring Devices With Unspecified Measuring Means (AREA)
  • Length Measuring Devices By Optical Means (AREA)
  • Instruments For Measurement Of Length By Optical Means (AREA)
  • Measurement Of The Respiration, Hearing Ability, Form, And Blood Characteristics Of Living Organisms (AREA)
  • Spectrometry And Color Measurement (AREA)
  • A Measuring Device Byusing Mechanical Method (AREA)
  • Numerical Control (AREA)
  • Control Of Position Or Direction (AREA)
US12/666,855 2007-06-28 2007-06-28 Method for determining dynamic errors in a measuring machine Abandoned US20110060542A1 (en)

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PCT/IT2007/000465 WO2009001385A1 (fr) 2007-06-28 2007-06-28 Procédé de détermination des erreurs dynamiques dans une machine de mesure

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US12/666,850 Active 2031-01-13 US8908194B2 (en) 2007-06-28 2007-12-27 Compensation of measurement errors due to dynamic deformations in a coordinate measuring machine

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US (2) US20110060542A1 (fr)
EP (2) EP2160565A1 (fr)
JP (1) JP5331802B2 (fr)
KR (1) KR101464148B1 (fr)
CN (2) CN101821582B (fr)
AT (1) ATE497145T1 (fr)
BR (1) BRPI0721773B1 (fr)
DE (1) DE602007012317D1 (fr)
ES (1) ES2359801T5 (fr)
PL (1) PL2167912T5 (fr)
TW (2) TWI468643B (fr)
WO (2) WO2009001385A1 (fr)

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US9459096B2 (en) 2011-07-06 2016-10-04 Hexagon Metrology S.P.A. Method of calibration of a mathematical model of a coordinate measuring machine for the compensation of dynamic errors due to deformation
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