Method for the dimensional measurement of workpieces

A method for a dimensional measurement of a workpiece, while taking into account external temperature influences on the workpiece during the measurement, by measuring the temperature of the workpiece before the dimensional measurement and by taking into account a linear thermal expansion by use of a coefficient of thermal expansion of the workpiece, the method comprising the steps of:

• measuring, at a start of a dimensional measurement run, a temperature T.sub.1 of the workpiece at an instant t.sub.1 and recording a relative position of the workpiece in relation to a system of coordinates of a measuring apparatus a first time, wherein the dimensional measurement run is executed by recording a number of scanning points;
• measuring, at an end of the dimensional measurement run, a temperature T.sub.2 of the workpiece at an instant t.sub.2 and recording the relative position of the workpiece in relation to the system of coordinates a second time;
• and
• correcting each individual scanning point of the dimensional measurement run with respect to an instant of measurement in an interval (t.sub.1, t.sub.2), the method further comprising the following steps:
• a) measuring the temperature T.sub.1 of the workpiece and of an ambient temperature T.sub.u at the instant t.sub.i (start of measurement),
• b) determining a workpiece system of coordinates .SIGMA..sub.1 at the instant t.sub.1,
• c) dimensionally measuring the scanning points of the workpiece, and storing the scanning points and the instants of the respective measurements in relation to the starting instant t.sub.1,
• d) measuring the temperature T.sub.2 of the workpiece and of the ambient temperature T.sub.u at the instant t.sub.2 (end of measurement or end of an interval),
• e) determining a workpiece system of coordinates .SIGMA..sub.u at the instant t.sub.2,
• f) calculating a transform .SIGMA..sub.1 .fwdarw..SIGMA..sub.2 with a set-up of a corresponding rotation matrix .sup..PHI. and of a corresponding displacement vector .DELTA..nu.,
• g) parametrization of the rotation matrix .sup..PHI. and of the displacement vector .DELTA..nu. with the temperature,
• h) determining characteristic quantities of a temperature trend according to:
• ##EQU12## with (T.sub.1 -T.sub.u)=temperature difference between workpiece temperature and ambient temperature in the first temperature measurement at the instant t.sub.1 at the start of the dimensional measurement run,
• (T.sub.2 -T.sub.u)=temperature difference between workpiece temperature and ambient temperature in the temperature measurement at the instant t.sub.2 at the end of the dimensional measurement run or of the interval,
• .tau.=fade-out constant of the temperature as a function of time and temperature:
• ##EQU13## i) correcting each scanning point of the dimensional measurement run by performing the following steps:
• aa) calculating a temperature T.sub.t of the workpiece at the instant t of a scan according to:
• ##EQU14## bb) calculating a rotation matrix .sup..PHI. (T.sub.t) and a displacement vector .DELTA..nu. (T.sub.t) for the instant t,
• cc) transforming the scanning point by use of .sup..PHI. (T.sub.t) and .DELTA..nu. (T.sub.t), into a workpiece system of coordinates .SIGMA. valid at the instant t,
• dd) executing a temperature compensation of the scanning point by relating the measured workpiece temperature T.sub.t to 20.degree. Celsius and by relating scanning coordinates to an expansion center at an origin of the workpiece system of coordinates .SIGMA. at the instant t, and
• k) evaluating the scanning points.

A method for a dimensional measurement of a workpiece, while taking into account external temperature influences on the workpiece during the measurement, by measuring the temperature of the workpiece before the dimensional measurement and by taking into account a linear thermal expansion by use of a coefficient of thermal expansion of the workpiece, the method comprising the steps of:

• measuring, at a start of a dimensional measurement run, a temperature T.sub.1 of the workpiece at an instant t.sub.1 and recording a relative position of the workpiece in relation to a system of coordinates of a measuring apparatus a first time, wherein the dimensional measurement run is executed by recording a number of scanning points;
• measuring, at an end of the dimensional measurement run, a temperature T.sub.2 of the workpiece at an instant t.sub.2 and recording the relative position of the workpiece in relation to the system of coordinates a second time;
• and
• correcting each individual scanning point of the dimensional measurement run with respect to an instant of measurement in an interval (t.sub.1, t.sub.2),
• wherein an interval (t.sub.1, T.sub.1 ;
• t.sub.2, T.sub.2) is divided into at least two part intervals,
• the method further comprising the following steps:
• a) measuring the temperature T.sub.1 of the workpiece and of an ambient temperature T.sub.u at the instant t.sub.1 (start of measurement),
• b) determining a workpiece system of coordinates .SIGMA..sub.1 at the instant t.sub.1,
• c) dimensionally measuring the scanning points of the workpiece, and storing the scanning points and the instants of the respective measurements in relation to the starting instant t.sub.1,
• d) measuring the temperature T.sub.2 of the workpiece and of the ambient temperature T.sub.u at the instant t.sub.2 (end of measurement or end of an interval),
• e) determining a workpiece system of coordinates .SIGMA..sub.u at the instant t.sub.2,
• f) calculating a transform .SIGMA..sub.1 .fwdarw..SIGMA..sub.2 with a set-up of a corresponding rotation matrix .sup..PHI. and of a corresponding displacement vector .DELTA..nu.,
• g) parametrization of the rotation matrix .sup..PHI. and of the displacement vector .DELTA..nu. with the temperature,
• h) determining characteristic quantities of a temperature trend according to:
• ##EQU15## with (T.sub.1 -T.sub.u)=temperature difference between workpiece temperature and ambient temperature in the first temperature measurement at the instant t.sub.1 at the start of the dimensional measurement run,
• (T.sub.2 -T.sub.u)=temperature difference between workpiece temperature and ambient temperature in the temperature measurement at the instant t.sub.2 at the end of the dimensional measurement run or of the interval,
• .tau.=fade-out constant of the temperature as a function of time and temperature:
• ##EQU16## i) correcting each scanning point of the dimensional measurement run by performing the following steps:
• aa) calculating a temperature T.sub.t of the workpiece at the instant t of a scan according to:
• ##EQU17## bb) calculating a rotation matrix .sup..PHI. (T.sub.t) and a displacement vector .DELTA. .nu. (T.sub.t) for the instant t,
• cc) transforming the scanning point by use of .sup..PHI. (T.sub.t) and .DELTA..nu. (T.sub.t), into a workpiece system of coordinates .SIGMA..sub.t valid at the instant t,
• dd) executing a temperature compensation of the scanning point by relating the measured workpiece temperature T.sub.t to 20.degree. Celsius and by relating scanning coordinates to an expansion center at an origin of the workpiece system of coordinates .SIGMA..sub.t at the instant t, and
• k) evaluating the scanning points.

A method for a dimensional measurement of a workpiece with a coordinates measuring apparatus while taking into account a thermal change of the workpiece during the measurement, by measuring the temperature of the workpiece before the dimensional measurement and by taking into account a linear thermal expansion by use of a coefficient of thermal expansion of the workpiece, comprising the steps of:

• recording, at a start of a dimensional measurement run, a temperature T.sub.1 of the workpiece at an instant t.sub.1 and recording a first time a relative position of the workpiece in relation to a system of coordinates of a measuring apparatus;
• subsequently executing the dimensional measurement run with a number of scanning points being recorded;
• measuring, at an end of the dimensional measurement run, a temperature T.sub.2 of the workpiece at an instant t.sub.2 and recording a second time the relative position of the workpiece in relation to the system of coordinates;
• correcting each individual scanning point of the dimensional measurement run in relation to the instant of measurement in an interval t.sub.1, t.sub.2 ;
• and executing and evaluating at least one measurement of workpiece temperature and of the workpiece system of coordinates during the dimensional measurement run, within an interval t.sub.1, T.sub.1 ;
• t.sub.2, T.sub.2, in addition to measurements executed before and after the dimensional measurement run;
• wherein the at least one additional measurement of the temperature and of the workpiece system of coordinates is executed during the measurement run at the instant of a measurement of the coordinates of the workpiece.