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
  • G01B21/042—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 invention relates to a method and an arrangement for calibrating
• a calibration object e.g. a Kalibrierkugel
• a sensor generates sensor signals that correspond to a deflection of the stylus when probing. From the sensor signals and from information about the location of each touched
• Probe point calibration parameter of the sensor are determined.
• CMMs tactile CMMs
• the measurement object is usually placed on a measurement table or using another suitable support or holder.
• the sensor with the probe element attached thereto is brought into a suitable position relative to the measurement object for the purpose of touching the surface of the measurement object.
• the sensor In this relative position of the stylus, which carries the probe element at its free end, deflected against a base of the sensor.
• the sensor may be configured to be three linear
• the measurement signal of a sensor is proportional to the value of the displacement (displacement and / or rotation) which the measurement signal is to reproduce.
• the dependence of the sensor signal on the deflection is not linear. It is Therefore, it has already been proposed to determine by calibration parameters of the sensor, which correspond to the nonlinearities. In the calibrated region, the actual deflection is then calculated from the measurement signals using these calibration parameters of the sensor.
• the calibration device can be designed so that it does not itself contribute significantly to the error of the calibration.
• a special device may be designed so that frictional forces do not or only insignificantly contribute to a calibration error.
• such a special device may be designed so that frictional forces do not or only insignificantly contribute to a calibration error.
• the calibrated range may be much larger than the range of displacements that can occur when using the sensor on a CMM. In the field of application, the calibration may therefore have inaccuracies. To avoid this, the calibration must be carried out specifically for a calibration range that also occurs in practice.
• different CMMs may require different ranges of calibration because of the different degrees of freedom of movement and also because of differences in the design of different CMMs.
• a very accurate calibration before the first use of a sensor in most cases is not sufficient for the entire life of the sensor. Over time, the characteristics of the sensor may change, e.g. by fatigue of materials or by shocks. The calibration of the sensor must therefore at least at longer intervals or after certain events, such as. a push, be repeated.
• the invention relates to the calibration of sensors on the CMM, to which the respective sensor is used for the measurement of measurement objects.
• the calibration range ie the range of deflections occurring during the calibration, is limited in many cases by the stylus specially attached to the sensor and also by the calibration standard used (eg calibration ball).
• the calibration ball can not be reached on all sides of the probe element.
• CMM In addition, increasingly used in practice CMM, the moving parts are not air-bearing, but are mechanically stored. In particular, a rolling bearing is increasingly used. Such CMM contribute to a considerable extent
• a method for calibrating a measuring sensor which has a stylus with a tip for contacting a workpiece. The method determines a sensor calibration matrix that
• a calibration object is scanned at a first sensor deflection to first
• the calibration object is at a second
• Sensor deflection scanned to obtain second machine data The first and second machine data are used to obtain a pure sensor calibration matrix in which possible machine errors are substantially eliminated.
• the sensor matrix is determined numerically based on the assumption that the distance between the first and second machine position data is known. As already mentioned, the expense of such a calibration of the sensor taking into account the positions of the machine during the deflection, ie during the touchdown, is high.
• a reference measurement object with known properties is provided.
• a plurality of reference measurement values are acquired at the reference measurement object and calibration data are determined from the reference measurement values and the known properties, wherein the calibration data include a first number of polynomial coefficients that are designed to be non-linear measurement errors of the coordinate measuring machine based on at least one of them
• the first number of polynomial coefficients is reduced to a lesser second number in an iterative process, wherein a plurality of pairs of polynomial coefficients is formed, and wherein one each
• Polynomial coefficient of a pair is eliminated when a statistical dependence between the polynomial coefficients of the pair is greater than a defined one
• Threshold As a result, it is possible to prevent good correction results from being obtained at the points in the calibrated region that were actually measured during calibration due to an excessive number of polynomial coefficients, but that considerable calibration errors can occur at other points.
• a basic idea of the present invention is to arrange not only one, but more than one stylus on the sensor to be calibrated, wherein the longitudinal axes of the styli extend in different directions.
• Each of the styli has at its free end a probe element, such as a probe ball, a Tastzylinder or Tastkegel, so that the calibration object can be touched from different directions.
• the calibration range is extended, since different deflections can be generated when probing from different directions than when using a single stylus.
• a sensor that measures the displacement along a straight axis is only calibrated in a direction along the axis when the calibration object is only touched from above with a single stylus because the longitudinal axis of the stylus extends from top to bottom and therefore a probing of the Calibration object from below is not possible.
• the styli have a rectilinear shaft, at the free end of the probe element is attached.
• the longitudinal axis of the stylus is clearly defined by the longitudinal axis of the shaft, i. defined by the axis, which extends approximately in the middle of the shaft and extends to the probe element.
• the longitudinal axis is defined by the central axis of the shaft profile in the region in front of the projection of the probe element.
• a longitudinal axis are defined by an axis is selected, wherein upon displacement of the shaft and the probe element in the direction of the longitudinal axis with respect to all possible displacement directions lowest possible penetration is achieved in a cylindrical bore, wherein the cylindrical bore has a diameter equal to the largest width of the probe element in a direction perpendicular to the longitudinal axis.
• the longitudinal axis is e.g. defined by the fact that it extends in the direction in which the stylus, the maximum range for probing surface points of a measured object with the
• Tastelement has. It is assumed that rotationally symmetric areas of the surface of the test object, ie the specific shape of the measurement object should not limit the range in that protruding parts or angled surface areas hinder the probing in a particular direction.
• the surface is usually touched from a direction perpendicular to the surface of the calibration sphere, with the probing generally not taking place in the direction of the longitudinal axis of the stylus (but can also take place).
• the plurality of (at least two pieces) feeler pins which are deflectably arranged on the sensor via a common carrier, are used successively in the calibration proposed here for probing the surface of the calibration object.
• first a number of surface points are scanned with a first one of the styli thus connected. Thereafter, surface points are probed with a second one of the styli, etc., due to the connection of the styli, which may be considered to be approximately rigid (except for possible small deflections caused by the probing force), the interconnected styli are deflected together, though only the probe touches a surface point of the calibration standard on one of the styli. Therefore, the measuring devices of the sensor react with the same deflection in the same way, regardless of which stylus touches a surface point and therefore causes the deflection.
• the common carrier of Tastriche can be realized in different ways.
• the styli may be parts of a so-called star stylus in which, starting from a connection point, styli extend with their shafts in different directions.
• the common carrier in this case may e.g. the shaft of one of the styli, from which the shafts of the other styli extend.
• styli extend from a plate in different directions. In this case, the plate is the carrier.
• the senor has receptacles for receiving a plurality of individual styli, which extend in different directions.
• the area of the sensor with the recordings forms the common carrier.
• this case is not preferred because the connection between the individual styli and the sensor in this case is not completely reproducible, but in principle tolerances are possible.
• tolerances are also possible in the case that a common carrier, which is firmly and permanently connected to the individual Tastwaken, attached to the sensor. In this case, however, the tolerance occurs in common with respect to all the styli.
• the calibration parameters of the sensor are in a common
• Equations that are considered in the optimization calculation In addition to the calibration parameters of the sensor, parameters of the individual styli are included in the individual equations. With a sufficient number of measuring points and
• Calibration parameters are determined (as preferred) in the same optimization calculation simultaneously with the sensor parameters.
• the sensor parameters are preferably linearization parameters, i. by parameters that describe the deviation between a linear sensor characteristic (sensor signal as a function of the deflection) and the actual sensor characteristic.
• the sensor parameters in all residual equations considered in the optimization calculation are simultaneously varied in the same way to determine the result of the optimization.
• the calibration parameters of the individual styli are varied only in the individual equations that were set up for measuring points of the stylus.
• not only two styli are used, which are connected to each other via the common carrier, but at least three styli, wherein the longitudinal axes of the styli preferably in the three directions of coordinate axes a Cartesian coordinate system, which can be defined with respect to the styli.
• Particularly preferred is the use of five styli, which are connected to each other as a star stylus.
• two pairs of styli each extend with their longitudinal axes in the same direction.
• the fifth stylus extends with its longitudinal axis in pairs perpendicular to the longitudinal axes of the other four styli.
• Such an arrangement has the advantage that in particular a calibration ball can be touched on almost all surface points, with the exception of the points at which the calibration ball is connected to its holder.
• Calibration object is probed with a mounted on the coordinate measuring stylus at several probing points, wherein a sensor generates sensor signals corresponding to a deflection of the stylus when probing, wherein from the
• Antastorgans calibration parameters of the sensor are determined, wherein for touching one after the other at least two styli are used, which are jointly deflected relative to the sensor and the stylus longitudinal axes are oriented in different directions, with probing points of the calibration object with the at least two
• Taststab be touched, the Tastdifte are deflected when touching the calibration object relative to the sensor, each using the sensor generates the sensor signals corresponding to a deflection of the Tastrich when touched, and wherein the sensor signals and information about the location of in each case with one of the styli touched probing point in a common for the Tastriche optimization calculation the calibration parameters of the sensor can be determined.
• the “measured values” of the sensors are measured values of the deflection that arises when one of the styli is touched.
• information about the location of the probing point probed with the styli includes the case that this location indirectly over various other information in the common
• the position vector can enter the sphere center of a calibration sphere, and the location of the detection point can be taken into account by using the sphere radius of the calibration sphere become. The place of the touch point does not have to be at the beginning of the
• Optimization calculation can be eliminated or determined as the result of the optimization calculation, if a sufficient number of measured values of the sensors were recorded. For example, can for the same place of a touch point at different
• Deflections are measured so that the location can be determined.
• the sensor parameters in particular the linearization parameters, may be e.g. stored in a data memory of the control of the CMM.
• the sensor parameters are associated with the sensor and can also be used in the operation of the CMM with the sensor and other styli arranged thereon. The reason for this is that they are the result of a calibration with several different parameters
• aligned styli are.
• an averaging over the different measurement conditions when using the various styli is performed in the optimization calculation.
• an averaging over the location of the sensor carrier takes place during the probing with the various styli.
• Linearization parameters can be determined in a wide range of deflections and are largely independent of the characteristics of the Tastriche used in the calibration. Also the error influences of the CMM become by the
• the sensor parameters are available in the long term for the operation of the CMM. At most, at longer intervals or when special events occur (such as a hard impact by striking a stylus mounted on the sensor against an obstacle), the calibration of the sensor can be repeated. Compared to the individual calibration of the sensor with different individual
• Stylus probes are needed for determining the sensor parameters of fewer sensor readings. From the sensor's point of view, a measurement point can be considered as the totality of the sensor's measured displacement signals. Each measuring point therefore corresponds to a touched surface point at a certain deflection and therefore a certain measuring force.
• measuring points are recorded while the stylus is moved along the surface of the calibration object, different relative velocities of the stylus and the scanned surface can also influence the measured values of the sensor.
• each measuring force at each scanning speed for each of the interconnected feeler pins it is not necessary to apply each measuring force at each scanning speed for each of the interconnected feeler pins, at least not for equally scanned surface areas of the calibration object as for separate calibration measurements with non-connected feeler pins. Nevertheless, a larger surface area of the calibration object can be touched overall with the various feeler pins, which corresponds to a larger calibration range with respect to the deflections occurring during the calibration. This avoids that subregions of the possible space of deflections during calibration do not occur and measurements of DUTs in these areas in the
• Sensor parameter set are determined in which the error of the CMM is further reduced.
• the method and the arrangement are also suitable for determining at least one calibration parameter of a joint device, by means of which the at least two feeler pins are attached to the coordinate measuring machine.
• one side of the hinge device is attached eg to one arm of the coordinate measuring machine or to another, preferably movable, part of the coordinate measuring machine and the other side of the hinge device is connected to the stylus arrangement.
• the Tastrichan Mr is preferably connected via the sensor with the hinge device.
• the sensor may also be integrated in the articulation device.
• the hinge device allows a rotational movement and / or pivoting movement of the Tastrichan Aunt relative to a base of the coordinate measuring machine and in particular relative to the arm of the coordinate measuring machine.
• it may be in the hinge device to a so-called rotary / pivot joint, which allows rotation or pivoting movements about two different axes of rotation, the orientation is in particular perpendicular to each other.
• a vertical alignment of the two axes does not necessarily mean that the two axes actually intersect at right angles. Rather, the two axes can be skewed, but can by parallel displacement of an axis an imaginary
• the sensor parameters are not just in one for the
• the calibration according to the invention does not preclude the preparation of the
• the sensor with individual styli a portion of the sensor parameters is calibrated using the single stylus. This may only be necessary with a small number of sensor parameters.
• the other sensor parameters can be determined solely from the joint optimization calculation for the results of calibration with the interconnected styli. For example, there are sensors without Tarriervorraum, the differences in the weight of the at the
• Sensor parameters or may be e.g. a few of the sensor parameters (the parameter or parameters depending on the weight of the stylus or stylus assembly) are calibrated by probing a calibration object with the single stylus. The same applies if, instead of the arrangement with at least two styli, under the use of the sensor parameters were determined, a different arrangement of styli should be used. Then, at least part of the sensor parameters can be determined using the other arrangement by probing a calibration object.
• Fig. 2 is a plan view of a stylus whose ausgestaltetes as a probe ball
• Probe touches the surface of a test object, eg a calibration standard
• Fig. 3 shows a sensor with a single attached thereto stylus and a
• Fig. 4 is a two-dimensional diagram, wherein the coordinate plane of the
• Fig. 5 shows the sensor of Fig. 3, but with a star stylus with a total of five
• Stylus is attached to the sensor so that the calibration ball can be touched from all sides
• Fig. 6 is a diagram as in Fig. 4, but according to the possibilities of probing of FIG. 5, a larger calibration range is located, and
• Fig. 7 shows a sensor attached thereto stylus, wherein the movement of the
• Tastriches relative to a base of the sensor has two rotational degrees of freedom and a linear degree of freedom of movement.
• the illustrated in Fig. 1 coordinate measuring machine (CMM) 1 1 in gantry design has a measuring table 1, on the columns 2, 3 in the Z direction of a Cartesian
• Coordinate system are arranged movable.
• the columns 2, 3 together with a cross member 4, a portal of the CMM 11.
• the cross member 4 is at its
• the cross member 4 is combined with a cross slide 7, which is air-bearing along the cross member 4 in the X direction of the Cartesian coordinate system movable.
• the current position of the cross slide 7 relative to the cross member 4 can be determined by a scale division 6.
• the movement of the cross member 4 in the X direction is driven by a further electric motor.
• the cross slide can also be supported by roller bearings, which can result in larger measurement errors in coordinate determination and calibration.
• a movable sleeve in the vertical direction 8 is mounted, which at its lower end via a mounting device 10 with a sensor 5 for the
• the sensor 5 may also be referred to as a probe
• the sensor 5 includes in a housing measuring means for measuring deflections of a stylus relative to a sensor base 9.
• the sensor 5 is detachably mounted on the sleeve 8. Down on the sensor 5, a stylus 12 is attached.
• the quill 8 can be driven by a further electric motor relative to the
• Cross slide 7 are moved in the Y direction of the Cartesian coordinate system. Due to the total of four electric motors, the sensor 5 and thus also the stylus 12 can therefore be moved to any point below the cross member 4 and above the measuring table 1, which lies in the gap defined by the columns 2, 3.
• FIG. 2 shows a plan view of a stylus 65 with a shaft 66 and a probe ball 64 fastened to the end of the shaft.
• the shaft 66 extends approximately vertically downwards from above the image plane to the stylus ball 64.
• the Tastkugel 64 is attached.
• the probe ball 64 exerts a probing force f on the measurement object. Therefore, the shaft 66 is slightly curved in its longitudinal direction. The curvature itself can not be seen in FIG. The strength of the curvature of the
• Shank 66 depends on the rigidity of the stylus 65, which is substantially equal to the stiffness of the shaft 66.
• Stiffness can be determined from measurement signals of the sensor to which the stylus 65 is attached.
• the measuring systems of the sensor measure the deflection of the stylus, which is caused by the opposing force of the probing force.
• the deflection is z. B. a pivoting of the Tastrichansatzes about a pivot axis, which is located in the region in which the stylus 65 is attached to the sensor device, or which is located in the region of the sensor device.
• the deflection is reversible and is counteracted by an elastic restoring force, e.g. the force of a spring parallelogram causes. If the spring constant or
• the opposing force can be calculated from the deflection of the probing force.
• the position of the stylus 65 in the region in which it is connected to the sensor, or at least the position of the axis of rotation is known, can Calibration also the deflection can be determined.
• the rigidity of the stylus in this case is the calibration parameter which determines the relationship between the for
• Coordinate measuring determined, it can be calculated from the stiffness.
• FIG. 3 shows a sensor 70 with a housing in which the measuring devices of the sensor 70 are accommodated.
• a stylus 65 is mounted, wherein the shaft 66 of the stylus 65 extends in the representation of the figure with its longitudinal axis vertically downwards. Accordingly, at the lower free end of the shaft 66, the probe element is fixed, here a Tastkugel 64.
• the stylus 65 is deflected relative to the sensor 70, as indicated by a second representation of the stylus in Fig. 3. However, a deflection is different than shown in Fig. 3
• Measuring object occur.
• the measuring devices of the sensor 70 measure the deflection.
• a Kalibrierkugel 71 which is held by a holder 73, it is indicated in Fig. 3 that the sensor can be calibrated with the attached thereto stylus 65 on the Kalibrierkugel 71.
• a plurality of points on the surface of the calibration ball 71 are scanned with the probe ball 64. It is also possible that not only individual points on the surface of the Kalibrierkugel 71 are touched by moving the probe ball 64 and back moving back the Tastkugel 64 away from the surface, but that the surface of the Kalibrierkugel 71 is scanned.
• FIG. 4 schematically shows the calibration range which corresponds to that shown in FIG.
• the calibration area is a range of excursions in the coordinate system of the sensor 70. Two of the three coordinate axes of this
• Coordinate system are shown in Fig. 4.
• the calibration area is semicircular. If the third coordinate axis v of the sensor, which runs perpendicular to both coordinate axes u, w shown in FIG. 4, would also be shown, the calibration region would be a hemisphere in the half-space above the plane, which is spanned by the coordinate axes u, v. This means that the probe ball 64 can not touch the calibration ball 71 below its equatorial line. The equatorial line runs in the plane spanned by the coordinate axes u, v.
• a preferred embodiment of the invention is shown.
• a star stylus 75 with a total of five styli 64a-64e is shown.
• the probe ball 64e is relative to the sensor 70 approximately at the same position as the probe ball of the individual stylus 65 in Fig. 3.
• the longitudinal axes of the styli 64a 64d are oriented with their longitudinal axes perpendicular to the longitudinal axis of the stylus 64e.
• the longitudinal axes of the styli 64a, 64b are aligned flush with each other in the same direction, but the styli of the styli 64a, 64b lie opposite each other at the free ends of the shafts of the styli 64a, 64b.
• the lengths of the feeler pins ie in particular their shanks, have different lengths.
• the lengths of the feeler pins ie in particular their shanks.
• the lengths of the feeler pins have different lengths.
• the compliances for example in the form of a compliance matrix, can be included in the equations describing the position of the probed point on the surface of the measurement object as a function of the sensor signals.
• the sensor 70 is shown with the attached button 75 twice, which corresponds to different positions in the coordinate system of the CMM.
• the coordinate measuring machine is able to move the sensor into the two positions shown in FIG. 5 and to move it into a plurality of further positions.
• In the upper position shown in Fig. 5 can by a vertical
• Movement of the sensor 70 down a point immediately above the surface of the Kalibrierkugel 71 are touched with the stylus 64 a. This is shown by an arrow running from top to bottom.
• a point on the surface of the calibration ball 71 which lies opposite the first-mentioned point and thus lies directly below the lower pole of the calibration ball 71, can be detected by a vertical movement of the sensor 70 be touched on top of the stylus 64b. This is indicated by an arrow pointing upwards.
• Fig. 6 shows the corresponding diagram in the coordinate system of the sensor 70 as in Fig. 4.
• the measuring range is in this case, however, a circle.
• the calibration area would be a ball, since the calibration ball can be touched from all sides.
• the small surface area at which the calibration ball is connected to its holder 73 is neglected.
• Fig. 7 shows an example of a sensor attached thereto stylus 12. On a bracket 78, the z. Example, by a housing (not shown in Fig. 7) of the sensor or by a fastening for attaching the sensor to an arm of a
• Coordinate measuring device or is realized on a quill, two leaf springs 72, 79, mounted, which are arranged at a distance from one another and parallel to each other. At the opposite ends of the bracket 78, the leaf springs 72, 79 with a Platform 74 connected. The holder 78 forms a sensor base, relative to which the stylus 12 is deflectable.
• the angled in this embodiment stylus 12 is mounted in the center of the platform 74 on the underside of the platform 74.
• the y-axis extends in the center line between the two leaf springs 72, 79.
• the part of the shaft 13 of the stylus 12, which is fixed to the platform 74, extends in the z-direction.
• the platform and thus the stylus 12 thereby performs a rotation about a parallel to the x-axis extending axis of rotation, which can be described by a superposition of a rotation about the x-axis and a linear displacement in the z-direction.
• a rotation of the platform about the y-axis is possible when the attached to the platform 74 end of the leaf spring 79 moves upward and the end of the leaf spring 72 moves simultaneously down or vice versa.
• the force vector f and the deflection vector a are shown schematically. Their directions do not coincide, since the elasticity or rigidity of the sensor with the stylus 12 attached thereto is direction-dependent. In particular, a rotation about the z-axis is blocked, d. H. not possible. Also locked is a linear movement in the y-direction.
• the example shows that even with buttons with rotational degrees of freedom of motion only transmitters (the measuring devices) can be used, which detect a linear motion.
• the measuring devices 16 ', 17', 18 ' are connected via signal lines with a
• Detection device 41 connected, for example, is a computer that may be part of the control of the CMM.
• Detection device 41 is a computer that may be part of the control of the CMM.
• an optimization calculation is described, in which both linearization parameters of the sensor and calibration parameters of the feeler pins are determined from the measurement points of a sensor. The optimization calculation is carried out, for example, by the determination device 41 illustrated in FIG. 7.
• the senor has three individual transducers which each generate a measurement signal which depends on the deflection of the stylus with respect to one spatial direction in the coordinate system of the sensor.
• the measurement signal of each transmitter is approximately linear to the displacement of the stylus in the respective spatial direction relative to the sensor base.
• a measurement signal vector s (si, s 2 , s 3 ) contains as components the measurement signals Si, s 2 , s 3 (whose assigned spatial directions need not be aligned orthogonal to one another, but in particular those used in FIGS. 4 and 6 Measuring signals u, v, w can be) of the three transducers.
• the conversion of the measuring signal vector s into a three-dimensional measured variable in the usual way selected Euclidean space is carried out by a coordinate transformation with the signal transformation matrix A and by adding an offset vector p 0 in the space of the measured variable p.
• Signal transformation matrix can be called a probe matrix. It is a 3 * 3 matrix, ie it has nine coefficients.
• p A s + p 0 (1)
• the polynomial coefficients c can be determined by an optimization calculation from the
• Measurement points of the sensor from calibration measurements are determined, for example, be determined by a method of minimizing error squares.
• CMM Coordinate Measuring Machine
• the linearization parameters cij and the 13 unknown stylus parameters ⁇ A, p 0 , d T ⁇ become measurement points of one Calibration determined with nTast styli.
• nTast is the number of styli used in calibration
• n is the run index to designate a stylus.
• d T is the Tastkugel prepared by the linearization parameters cij and the 13 unknown stylus parameters ⁇ A, p 0 , d T ⁇ become measurement points of one Calibration determined with nTast styli.
• nTast is the number of styli used in calibration
• n is the run index to designate a stylus.
• a ball equation can be used as the objective function in the optimization calculation, with the sum of the calibration ball diameter and
• Tastkugel Asmesser is determined. In order to determine the probe ball parameter, the calibration ball diameter can then be deducted from the ball diameter.
• the parameters are determined in a common optimization calculation from all measuring points of the sensor.
• the calibration ball is touched on a sufficient number of surface points, with all styli for the probing be used, m is the index of the measurement points.
• nMess measuring points are recorded, where nMess is an integer.
• Several measuring points can be recorded at each surface point, eg by recording measured values of the sensor at different deflections.
• the calibration is usually as Gaussian best-fit routine with the aim of minimizing the sum of least squares of the normal deviations
• the stylus parameters ie the button offset position vector p 0, n , the
• the distance function contained in equations (5) of the equation system is linearized and a linear overdetermined result is obtained
• the objective function Q1 (Equation 4) of this overdetermined equation system can be improved in an iterative optimization calculation, for example with the Householder method (or another suitable mathematical method), until the parameter changes are sufficiently small as the iteration continues.
• both the calibration parameters relevant per stylus and the parameters (coefficients) of the linearization polynomials are determined in an invoice.

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