EP1836454A1 - Method of determining the uncertainty of a coordinate measuring machine - Google Patents

Method of determining the uncertainty of a coordinate measuring machine

Info

Publication number
EP1836454A1
EP1836454A1 EP05818133A EP05818133A EP1836454A1 EP 1836454 A1 EP1836454 A1 EP 1836454A1 EP 05818133 A EP05818133 A EP 05818133A EP 05818133 A EP05818133 A EP 05818133A EP 1836454 A1 EP1836454 A1 EP 1836454A1
Authority
EP
European Patent Office
Prior art keywords
database
phase
uncertainty
modified
data
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Withdrawn
Application number
EP05818133A
Other languages
German (de)
French (fr)
Inventor
Giulio Barbato
Raffaello Levi
Grazia Vicario
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Politecnico di Torino
Original Assignee
Politecnico di Torino Dipartimento di Energetica
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Politecnico di Torino Dipartimento di Energetica filed Critical Politecnico di Torino Dipartimento di Energetica
Publication of EP1836454A1 publication Critical patent/EP1836454A1/en
Withdrawn legal-status Critical Current

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Classifications

    • 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

Definitions

  • the present invention relates to a method for determining the uncertainty of a coordinate measuring machine.
  • coordinate measuring machines comprise a feeler (normally consisting of a ruby sphere) which is moved by actuator devices in a three-dimensional measuring space. Said feeler is placed in contact with a point of the outer surface of the piece to be measured; the machine software is designed to establish a relation between the point of contact and the centre of the feeler the coordinates of which are measured by the machine along its three Cartesian measuring axes, or other reference systems such as polar or cylindrical coordinates. In this way it is possible to identify, by means of trigonometric rotation-translation relations, the position of the point of contact with respect to the machine measuring axes. Alternatively, the coordinates of the point to be measured can be obtained via no-contact procedures. Coordinate measuring machines are characterised, by considerable versatility which, on the one hand, means that they can be used for measuring mechanical parts in all sorts of different shapes, but on the other does not permit the development of a unitary method for determination of the uncertainty on the measuring results obtained.
  • the quality standards require the result of each measurement or test to be accompanied by the corresponding uncertainty which is fundamental to establish relations between the values measured and the prescribed tolerances, as established by the ISO 14253-1 standard.
  • a piece to be measured is arranged in a plurality of different positions in the measuring space and in each of said positions the coordinates and therefore the dimensions of the piece are determined.
  • the values of the respective dimensions (which would be identical in the various positions if there were no uncertainties) are compared with each other to determine the dispersion and, therefore, the corresponding measurement uncertainty.
  • Said procedure is, however, rather complicated, determination is lengthy and laborious and keeps the machine busy throughout the operation.
  • a further complication consists in the need to develop various measuring programs, with different control points, to take into account the uncertainty due to the irregularity in the shape of the element being measured, and combine with measurement of the part some measurements of length samples to take account of any systematic machine errors.
  • a sample machine is used which, in addition to the fact that it must have extremely high-level mechanical and geometric characteristics, must be analysed by means of an in-depth and analytical calibration procedure to identify the primary errors (as known, in a coordinate measuring machine there are twenty-one primary errors) .
  • the measuring uncertainty is obtained by extracting (for example via the Monte Carlo method) from the distributions of the primary errors determined beforehand a group of their possible values with which new possible measuring results are assessed virtually. This virtual procedure is repeated a sufficient number of times to obtain the statistical distribution of each measuring result and therefore its uncertainty.
  • the aim of the present invention is to overcome the above limits so that the normal machines used industrially are able to provide, together with the measuring result, its uncertainty, whatever the measuring task assigned.
  • the proposed method permits determination of the uncertainty associated with each measuring action of a coordinate measuring machine which can be applied at industrial level, i.e. using the results of the normal calibration operations (ISO 10360) and without requiring on the part of the operator the performance of operations other than those necessary for carrying out the measurements.
  • the preceding aim is achieved by the present invention as it relates to a method for determination of the uncertainty of the measuring results obtained with a coordinate measuring machine of the type described in claim 1.
  • figure 1 illustrates the phases of the method of the present invention.
  • figure 2 illustrates a diagram by way of example of the method of the present invention.
  • An elementary action of the measuring machine can be considered the contact with a series of points on the mechanical surface in question, determination of the coordinates of said points and calculation, via the machine's mathematical algorithms, of the characteristic parameters of the surface examined (for example the coordinates of the centre and the radius of a spherical surface) .
  • the proposed invention adds some steps which the machine can perform automatically designed to express the uncertainty of the values calculated for the geometric parameters of the surface in question.
  • Figure 1 illustrates a block diagram which describes the operations of the uncertainty determination method on the geometric parameters determined by the elementary measuring operation of a coordinate measuring machine.
  • the normal action of the machine is described by a block 100 in which each of the steps of a measuring task is initiated, i.e. a set of n data Sl is identified by performing a plurality of successive measurements on n points of a surface of an element measured. For example n sets of three coordinates (xl,yl,zl, x2,y2,z2, . . . xn,yn,zn) can be identified.
  • the subsequent normal action of the machine is described in block 160 and consists in using the Sl data set to calculate one or more parameters P of the element examined
  • the coordinates of the n points Sl identified are sent to a block 200 which carries out a process parallel to the measuring process; in particular the block 200 uses the data provided at the input to define a database on which subsequent processing is performed.
  • block 200 is followed by a block 210 which is designed to modify the structure of the database by means of statistical processing.
  • Block 210 is followed by a block 220 which checks whether the modified database has a data arrangement that can be used for the purpose of the present processing; if not (modified database having non-acceptable data arrangement) , block 220 is followed by a block 230 which discards the modified database and repeats the modification operations from the original database (for said purpose block 230 is followed by block 210) .
  • block 220 calculates the centre of gravity and the variance ⁇ 2 of the data set that forms the modified database; if the shift in the centre of gravity with respect to that of the original Sl data (which indicates that the modified data have greater importance in one of the eccentric positions) or the value of the variance ⁇ 2 is below a threshold value ⁇ 2 lim determined on the basis of the variance of the original Sl data (i.e. in the case of accumulation of the data around the centre of gravity) block 220 is followed by block 230, otherwise block 220 is followed by block 250.
  • a check is therefore performed on the data handled via the Bootstrap or Jackknife method.
  • the Bootstrap method a sequential process is performed via which elements of the database undergo random extraction with re-entry; the modified database obtained via application of the Bootstrap method has the same dimensions (n in the example shown) as the original database.
  • the Jackknife method a sequential process is performed by means of which elements of the database are extracted at random and are not subsequently re- entered; the modified database obtained by application of the Jackknife method has smaller k dimensions (k ⁇ n in the example shown) than the original database.
  • Block 250 uses the information normally available as a result of the calibration operations scheduled by ISO 10360, usually- represented by a maximum machine error. More sophisticated use, which requires the intervention of a more advanced operator, consists in choosing from the error parameters, always provided by the calibration according to ISO 10360, the one(s) most suited to describing the error conditions in the specific measurement task.
  • Block 250 applies to each element of the modified database a value extracted from the rectangular distribution that represents the maximum error or the typical measuring machine error chosen, thus generating a perturbed database SIi; in particular the error value to be added algebraically to each element of the modified database is chosen at random.
  • Block 250 is followed by a block 260 which uses the elements of the perturbed database SIi to calculate one or more parameters P of the element examined (for example coordinates of the centre and radius of a spherical surface) exactly as occurs in the normal machine measuring action in block 160.
  • a block 260 uses the elements of the perturbed database SIi to calculate one or more parameters P of the element examined (for example coordinates of the centre and radius of a spherical surface) exactly as occurs in the normal machine measuring action in block 160.
  • the sequence of operations from block 200 to block 260 is repeated an adequate number of times for a certain parameter or for a certain number of parameters, for example fifty - one hundred times (block 280 subsequent to block 270 in turn subsequent to block 260) , in order to determine (and if necessary represent) the distributions of the values of the parameters P calculated by blocks 200-260 during successive repetitions; on the basis of the distributions obtained, the corresponding confidence intervals, with the risk of error accepted, are determined via the traditional statistical methods (block 300 subsequent to 280) .
  • Said confidence intervals represent the bands of uncertainty to be associated with the values of the parameters P determined by the machine in block 160.
  • the action of the elementary step of the measuring task described in blocks from 100 to 160 for the physical action, has a perfect parallel in the action of assessment of the uncertainty described in the blocks from 200 to 260, hence it 5 is easy to see how it can be applied, step after step, to any measurement task.
  • the selection of a different measurement task for the calculation of a different parameter/different parameters P is indicated by blocks 170 and 270.
  • a sequence is determined that consists in the identification of a piece reference system and, subsequently, the position and geometric parameters of a surface of the piece itself.
  • phase 1 Determination of the piece reference system
  • phase 2 determination of the geometric parameters relative to the surface in question.
  • the first step of phase 1 consists in determining (block 100-1) the coordinates, in RO, of a series of points Sl-I (not indicated in figure 2 to avoid confusion) , 5 positioned on the wall 1 of the piece that represents the coordinated plane Xl, Yl in the Rl piece reference system, and calculating (block 160-1) the geometric parameters, consisting in this case of the directrix cosines of said plane and the coordinates of the centre of gravity of the points measured.
  • the second and third step consist in measuring analogously (blocks 100-2 and 100-3) the points Sl-2 and Sl-3 (indicated in figure 2 by solid circles, since they are measured points) , of faces 2 and 3 representing the other coordinated planes Xl, Zl and Yl,Zl and determining in an orthogonal manner the 5 geometrical parameters already referred to for face 1 (blocks 160-2 and 160-3) of said coordinated planes.
  • a parameter determination operation therefore similar to that of block 160, which can be indicated by the code 160-4, the machine determines the piece reference system Rl.
  • the procedure is based on a limited number of simple operations (blocks 200-280) that can be performed easily and quickly. In this way, the duration of the measurement process is not significantly increased; > it provides determination of the uncertainty which takes account of the main factors involved, including machine error and the effect of irregularities in the shape of the piece.
  • the method of the present invention only uses the results of the measurements performed to determine the geometric parameters (block 100) always available because already required by the normal measurement activities. No measurement repetitions are therefore necessary.

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Length Measuring Devices With Unspecified Measuring Means (AREA)

Abstract

Method for determining the uncertainty of a coordinate measuring machine which combines with every elementary machine operation in a measuring task a parallel operation repeated an adequate number of times aimed at estimating the uncertainty of the geometric parameters determined. The elementary operation of the machine consists of the phases of identifying (100) a set of n data S1 performing a plurality of successive measurements on an element subject to measurement, measuring the coordinates (x1, y1, z1, x2, y2, z2, …,xn, yn, zn) of n points on the surface of the element, and performing at least the calculation/interpolation of a geometric parameter P of the surface of the element examined (160) on the basis of the data measured. The method for estimating the uncertainty is based on an operation parallel to the preceding one consisting of the phases of defining a database (200) using the set S1 of data identified; performing statistical processing (210) on the database generating a modified database; checking (220) whether the modified database has an acceptable data distribution; applying (250) to each element of the modified database an error typical of the measuring machine chosen at random in the field defined by the maximum error, generating a perturbed database; performing at least the calculation (260) of the same geometric parameter P on the basis of the perturbed database; repeating the operations from (210) to (260) an adequate number of times to define the distribution of the results obtained for the parameter P from which, via the usual statistical methods, the uncertainty in measurement of the same geometric parameter P is assessed.

Description

METHOD FOR DETERMINING THE UNCERTAINTY OF A COORDINATE MEASURING MACHINE
TECHNICAL FIELD The present invention relates to a method for determining the uncertainty of a coordinate measuring machine.
BACKGROUND ART
As a rule, coordinate measuring machines comprise a feeler (normally consisting of a ruby sphere) which is moved by actuator devices in a three-dimensional measuring space. Said feeler is placed in contact with a point of the outer surface of the piece to be measured; the machine software is designed to establish a relation between the point of contact and the centre of the feeler the coordinates of which are measured by the machine along its three Cartesian measuring axes, or other reference systems such as polar or cylindrical coordinates. In this way it is possible to identify, by means of trigonometric rotation-translation relations, the position of the point of contact with respect to the machine measuring axes. Alternatively, the coordinates of the point to be measured can be obtained via no-contact procedures. Coordinate measuring machines are characterised, by considerable versatility which, on the one hand, means that they can be used for measuring mechanical parts in all sorts of different shapes, but on the other does not permit the development of a unitary method for determination of the uncertainty on the measuring results obtained.
The quality standards, on the other hand, require the result of each measurement or test to be accompanied by the corresponding uncertainty which is fundamental to establish relations between the values measured and the prescribed tolerances, as established by the ISO 14253-1 standard.
In the state of the art some methods for assessment of uncertainty exist (standards ISO/DTS 15530-2:2004 and ISO/TS 15530-3:2004) but they are excessively laborious due to the experimental work required or due to the characteristics of the machines and equipment involved.
According to a first method of determination of the uncertainty (ISO/DTS 15530-2:2004) , a piece to be measured is arranged in a plurality of different positions in the measuring space and in each of said positions the coordinates and therefore the dimensions of the piece are determined. The values of the respective dimensions (which would be identical in the various positions if there were no uncertainties) are compared with each other to determine the dispersion and, therefore, the corresponding measurement uncertainty. Said procedure is, however, rather complicated, determination is lengthy and laborious and keeps the machine busy throughout the operation. A further complication consists in the need to develop various measuring programs, with different control points, to take into account the uncertainty due to the irregularity in the shape of the element being measured, and combine with measurement of the part some measurements of length samples to take account of any systematic machine errors.
According to a different method of determination of the uncertainty (prerequisite for implementation of the method described in the ISO/TS 15530-3:2004 standard), a sample machine is used which, in addition to the fact that it must have extremely high-level mechanical and geometric characteristics, must be analysed by means of an in-depth and analytical calibration procedure to identify the primary errors (as known, in a coordinate measuring machine there are twenty-one primary errors) .
In this way the measuring uncertainty is obtained by extracting (for example via the Monte Carlo method) from the distributions of the primary errors determined beforehand a group of their possible values with which new possible measuring results are assessed virtually. This virtual procedure is repeated a sufficient number of times to obtain the statistical distribution of each measuring result and therefore its uncertainty.
This procedure, due to the quality characteristics of the machine to which it can be applied and the calibration effort required, can only be used in Calibration Centre laboratories and does not lend itself to industrial application. Its use, described in the ISO/TS 15530-3:2004 standard, consists in dimensionalIy qualifying a specimen of the elements to be measured, so that it can be used as a sample piece, employing the machines installed in the industrial field only for comparison between said sample piece and the pieces produced to be tested. Obviously said application is possible only for testing of mass-produced items, given the cost and time required for calibration of the sample pieces; it cannot be used for testing small product batches or for the development of prototypes.
DISCLOSURE OF INVENTION
The aim of the present invention is to overcome the above limits so that the normal machines used industrially are able to provide, together with the measuring result, its uncertainty, whatever the measuring task assigned. The proposed method permits determination of the uncertainty associated with each measuring action of a coordinate measuring machine which can be applied at industrial level, i.e. using the results of the normal calibration operations (ISO 10360) and without requiring on the part of the operator the performance of operations other than those necessary for carrying out the measurements.
The preceding aim is achieved by the present invention as it relates to a method for determination of the uncertainty of the measuring results obtained with a coordinate measuring machine of the type described in claim 1.
BRIEF DESCRIPTION OF THE DRAWINGS
The invention will now be illustrated with particular reference to the elementary operation performed by a coordinate measuring machine in the successive steps of performance of its measuring task and with reference to the accompanying figures which represent a preferred embodiment in which:
• figure 1 illustrates the phases of the method of the present invention; and
• figure 2 illustrates a diagram by way of example of the method of the present invention.
BEST MODE FOR CARRYING OUT THE INVENTION
An elementary action of the measuring machine can be considered the contact with a series of points on the mechanical surface in question, determination of the coordinates of said points and calculation, via the machine's mathematical algorithms, of the characteristic parameters of the surface examined (for example the coordinates of the centre and the radius of a spherical surface) . The proposed invention adds some steps which the machine can perform automatically designed to express the uncertainty of the values calculated for the geometric parameters of the surface in question.
Figure 1 illustrates a block diagram which describes the operations of the uncertainty determination method on the geometric parameters determined by the elementary measuring operation of a coordinate measuring machine.
The normal action of the machine is described by a block 100 in which each of the steps of a measuring task is initiated, i.e. a set of n data Sl is identified by performing a plurality of successive measurements on n points of a surface of an element measured. For example n sets of three coordinates (xl,yl,zl, x2,y2,z2, . . . xn,yn,zn) can be identified. The subsequent normal action of the machine is described in block 160 and consists in using the Sl data set to calculate one or more parameters P of the element examined
(for example coordinates of the centre and radius of a spherical surface) .
Assessment of uncertainty requires the performance of a series of statistical and control operations. The coordinates of the n points Sl identified are sent to a block 200 which carries out a process parallel to the measuring process; in particular the block 200 uses the data provided at the input to define a database on which subsequent processing is performed. In said regard, block 200 is followed by a block 210 which is designed to modify the structure of the database by means of statistical processing.
In particular, to perform the modification, the process known in literature as "Bootstrap" or the process known in literature as "Jackknife" can be used. Said processes (of known type) will be briefly detailed below.
Block 210 is followed by a block 220 which checks whether the modified database has a data arrangement that can be used for the purpose of the present processing; if not (modified database having non-acceptable data arrangement) , block 220 is followed by a block 230 which discards the modified database and repeats the modification operations from the original database (for said purpose block 230 is followed by block 210) .
If the modified database has an acceptable arrangement, block 220 is followed by block 250. In greater detail, block 220 calculates the centre of gravity and the variance σ2 of the data set that forms the modified database; if the shift in the centre of gravity with respect to that of the original Sl data (which indicates that the modified data have greater importance in one of the eccentric positions) or the value of the variance σ2 is below a threshold value σ2lim determined on the basis of the variance of the original Sl data (i.e. in the case of accumulation of the data around the centre of gravity) block 220 is followed by block 230, otherwise block 220 is followed by block 250. A check is therefore performed on the data handled via the Bootstrap or Jackknife method.
In particular, according to the Bootstrap method a sequential process is performed via which elements of the database undergo random extraction with re-entry; the modified database obtained via application of the Bootstrap method has the same dimensions (n in the example shown) as the original database.
Further details on said method can be found in "An introduction to the Bootstrap", Bradley Efron and Robert J. Tibshirani, ed. Chapman and Hall, London 1993.
Alternatively, according to the Jackknife method, a sequential process is performed by means of which elements of the database are extracted at random and are not subsequently re- entered; the modified database obtained by application of the Jackknife method has smaller k dimensions (k < n in the example shown) than the original database.
Further details on said method can be found in "The Jackknife the Bootstrap and other resampling plans", Bradley Efron, ed. Chapman and Hall, London 1982.
Block 250 uses the information normally available as a result of the calibration operations scheduled by ISO 10360, usually- represented by a maximum machine error. More sophisticated use, which requires the intervention of a more advanced operator, consists in choosing from the error parameters, always provided by the calibration according to ISO 10360, the one(s) most suited to describing the error conditions in the specific measurement task.
Block 250 applies to each element of the modified database a value extracted from the rectangular distribution that represents the maximum error or the typical measuring machine error chosen, thus generating a perturbed database SIi; in particular the error value to be added algebraically to each element of the modified database is chosen at random.
Block 250 is followed by a block 260 which uses the elements of the perturbed database SIi to calculate one or more parameters P of the element examined (for example coordinates of the centre and radius of a spherical surface) exactly as occurs in the normal machine measuring action in block 160.
The sequence of operations from block 200 to block 260 is repeated an adequate number of times for a certain parameter or for a certain number of parameters, for example fifty - one hundred times (block 280 subsequent to block 270 in turn subsequent to block 260) , in order to determine (and if necessary represent) the distributions of the values of the parameters P calculated by blocks 200-260 during successive repetitions; on the basis of the distributions obtained, the corresponding confidence intervals, with the risk of error accepted, are determined via the traditional statistical methods (block 300 subsequent to 280) . Said confidence intervals represent the bands of uncertainty to be associated with the values of the parameters P determined by the machine in block 160. The action of the elementary step of the measuring task, described in blocks from 100 to 160 for the physical action, has a perfect parallel in the action of assessment of the uncertainty described in the blocks from 200 to 260, hence it 5 is easy to see how it can be applied, step after step, to any measurement task. The selection of a different measurement task for the calculation of a different parameter/different parameters P is indicated by blocks 170 and 270.
.0 For example, in figure 2 a sequence is determined that consists in the identification of a piece reference system and, subsequently, the position and geometric parameters of a surface of the piece itself.
L5 The measurement task, normally performed by the machine, can be considered, for the sake of generality, to consist of two phases: phase 1 - Determination of the piece reference system; phase 2 - determination of the geometric parameters relative to the surface in question. 0
For the sake of generality, we start from the RO machine reference system. The first step of phase 1 consists in determining (block 100-1) the coordinates, in RO, of a series of points Sl-I (not indicated in figure 2 to avoid confusion) , 5 positioned on the wall 1 of the piece that represents the coordinated plane Xl, Yl in the Rl piece reference system, and calculating (block 160-1) the geometric parameters, consisting in this case of the directrix cosines of said plane and the coordinates of the centre of gravity of the points measured. 0 The second and third step consist in measuring analogously (blocks 100-2 and 100-3) the points Sl-2 and Sl-3 (indicated in figure 2 by solid circles, since they are measured points) , of faces 2 and 3 representing the other coordinated planes Xl, Zl and Yl,Zl and determining in an orthogonal manner the 5 geometrical parameters already referred to for face 1 (blocks 160-2 and 160-3) of said coordinated planes. With a parameter determination operation, therefore similar to that of block 160, which can be indicated by the code 160-4, the machine determines the piece reference system Rl. We then proceed to phase 2, with a new measurement operation, this time on the surface to be explored, determining the coordinates, in the Rl reference system, of the points Sl-4, again indicated in figure 2 (also by circles since they are points measured, but empty to distinguish them from the piece reference measurement points) felt on the surface being examined. From said points via a parameter determination operation, block 160-5, the parameters of the geometric form examined are assessed, for example the position of the centre and the value of the radius.
For assessment of the measurement uncertainty said sequence must be followed by a successive series of operations as described by the blocks 200 to 260, on the perturbed sets SIi- 1, Sli-2, Sli-3 respectively (all indicated in figure 2 by crosses since they are perturbed points) , with which via the parameter determination operations (blocks 260-1, 260-2, 260-3 and 260-4) the RIi perturbed piece reference system is determined and lastly, by introducing the perturbed coordinates SIi-4 (indicated in figure 2 by solid rhombi) , obtained from points Sl-4, via a last parameter determination operation, which can be indicated parallel to 160-5 as 260-5, the values of the perturbed geometric parameters Pi are obtained. Said values, read in the reference system Rl, highlight the dispersion of the measurement results, and therefore the measurement uncertainty, on the parameters of the surface in question to be assessed.
From what is described above, the advantages of the present invention are clear since:
> it can be easily applied to a measurement phase without extensive programming work;
> the procedure is based on a limited number of simple operations (blocks 200-280) that can be performed easily and quickly. In this way, the duration of the measurement process is not significantly increased; > it provides determination of the uncertainty which takes account of the main factors involved, including machine error and the effect of irregularities in the shape of the piece.
In fact, to determine the uncertainty the method of the present invention only uses the results of the measurements performed to determine the geometric parameters (block 100) always available because already required by the normal measurement activities. No measurement repetitions are therefore necessary.

Claims

1. - Method for determining the uncertainty of a coordinate measuring machine, characterised in that it comprises the following phases:
- using (100) a set of n data Sl identified in the normal operating condition of a coordinate measuring machine performing a plurality of successive measurements on an element subject to measurement, measuring the coordinates (xl,yl,zl, x2,y2,z2,.- xn,yn,zn) of said element;
- defining a data base (200) using the data set identified;
- performing statistical processing (210) on said database generating a modified database; checking (220) whether the modified database has an acceptable data distribution;
- applying (250) to each element of the modified database an error typical of the measuring machine generating a perturbed database;
- performing the interpolation (260) of at least one parameter on the basis of at least one perturbed database; determining the distributions of the values of the parameters P calculated during successive repetitions (280) in order to define confidence intervals that represent the machine's uncertainty bands.
2. - Method as claimed in claim 1, in which said phase of performing statistical processing (210) on said database generating a modified database comprises the phase of subjecting the elements of the database to a "Bootstrap" type process.
3.- Method as claimed in claim l, in which said phase of performing statistical processing (210) on said database generating a modified database comprises the phase of subjecting the elements of the database to a "Jackknife" type process.
4.- Method as claimed in claim 1, in which said verification phase (220) comprises the phase of calculating the variance σ2 of the dataset that forms the modified database, said 5 verification phase comprising furthermore the phase of comparing the variance calculated σ2 with a threshold value σ2lim.
5.- Method as claimed in claim 1, in which said verification
LO phase (220) comprises the phase of calculating the centre of gravity of the elements that form the modified database, said verification phase comprising furthermore the phase of checking that the distance between the centre of gravity calculated with the perturbed data and the one calculated with
15 the data measured does not exceed a limit value.
6.- Method as claimed in claim 1, in which said phase of applying (250) to each element of the modified database an error typical of the measuring machine comprises the phase of 20 selecting at random the maximum error or the error typical of the measuring machine and applying to each element of the modified database the value selected.
I 7.- Method as claimed in claim 1, characterised in that said 25 phases below are repeated (280) for a set number of cycles:
- performing statistical processing (210) ;
- checking (220) whether said modified database has an acceptable data distribution;
- generating (250) a perturbed database; and
30 - performing the interpolation (260) of at least one parameter.
EP05818133A 2004-12-17 2005-12-15 Method of determining the uncertainty of a coordinate measuring machine Withdrawn EP1836454A1 (en)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
ITTO20040886 ITTO20040886A1 (en) 2004-12-17 2004-12-17 METHOD OF DETERMINING THE UNCERTAINTY OF A COORDINATE MEASURING MACHINE
PCT/IB2005/003793 WO2006064352A1 (en) 2004-12-17 2005-12-15 Method for determining the uncertainty of a coordinate measuring machine

Publications (1)

Publication Number Publication Date
EP1836454A1 true EP1836454A1 (en) 2007-09-26

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CN115542237B (en) * 2022-11-29 2023-04-07 北京志翔科技股份有限公司 Uncertainty determination method and device and electronic equipment

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IT1296727B1 (en) * 1997-10-09 1999-07-15 Dea Brown & Sharpe S P A Ora B METHOD OF DETERMINING THE MEASUREMENT UNCERTAINTY OF A COORDINATE MEASURING MACHINE.
JP3821739B2 (en) * 2002-03-22 2006-09-13 株式会社ミツトヨ Measurement data shaping method

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