WO2014044508A1

WO2014044508A1 - Method for orienting a laser sensor in relation to a measurement object

Info

Publication number: WO2014044508A1
Application number: PCT/EP2013/067805
Authority: WO
Inventors: Roland KEMPF; Ulrich Dörr; Norbert Möller; André Mecklenburg
Original assignee: Evonik Litarion Gmbh
Priority date: 2012-09-24
Filing date: 2013-08-28
Publication date: 2014-03-27
Also published as: DE102012217176A1

Abstract

The invention relates to a method for scaling the position and the orientation of at least one laser distance sensor in relation to a calibration body, wherein each laser distance sensor has a laser and a sensor, comprising the following chronological steps A) to C): A) arranging a well-defined calibration body, which has a geometry that is precisely defined at least in some regions, in a measurement set-up comprising the laser distance sensors, wherein the position of the calibration body is precisely defined by arranging the calibration body in the measurement set-up, and coarsely orienting at least one laser distance sensor in relation to the calibration body; B) performing distance measurements of several measurement points or of a continuous course on the surface of the calibration body by means of the laser distance sensor or the laser distance sensors, wherein the calibration body is moved in the measurement setup in relation to the laser distance sensor or the laser distance sensors in order to enable the laser of the laser distance sensor or the lasers of the laser distance sensors to irradiate the various measurement points or the continuous course for the distance measurements; and C) determining the position and the orientation of the at least one laser distance sensor in relation to the calibration body on the basis of the distance measurements and the known geometry and position of the calibration body in the measurement setup. The invention further relates to a method for measuring the thickness of a body or of a coating of a coated body in a measurement setup, wherein at least one laser distance sensor, the position and orientation of which in relation to the calibration body have been determined by means of such a method or which has first been oriented in the measurement setup in relation to a calibration body by means of such a method, is used in the measurement of the thickness of the coating. The invention further relates to a device for performing such methods.

Description

"Method for Aligning a Laser Sensor to a DUT" Description

The invention relates to a method for scaling the position and the orientation of at least one laser distance sensor. The invention also relates to a method for measuring the thickness of a body or the thickness of a coating of a coated body in a measurement setup, wherein at least one laser distance sensor is used in the measurement. Finally, the invention also relates to a device for carrying out such methods.

Laser distance sensors are used, inter alia, when the thickness of a coating is to be measured precisely. In this case, the light reflected from the coating on an object is measured and from this the thickness of the coating is determined.

Such a method is known, for example, from EP 2 031 347 A1, in which the temperature of the object to be coated is also measured during the measurement in order to obtain a more accurate estimate of the thickness of a coating in the case of a thickness measurement.

A method for measuring the coating thickness by means of laser triangulation is known from EP 2 312 267 A1. The measurement is measured before and during or after coating and can be carried out selectively. A similar method is used in DE 103 13 888 A1. In the method, a distance is determined by a laser triangulation method and compared with a reference value in order to be able to estimate the thickness of a coating.

For all these methods, it is important to precisely set the position of the laser for the measurement in order to allow a reliable determination of the layer thicknesses. An error in the positioning affects the accuracy of the layer thickness measurement and therefore leads to errors in the determination of the layer thickness. The aim is to align the position and the orientation of the laser as closely as possible to the object to be measured. The object of the invention is therefore to provide a method for positioning a laser of a laser distance sensor to a coated body to be measured, which is as simple to carry out and leads to the most accurate adjustment and positioning of the laser distance sensor to the object to be measured.

Other tasks not explicitly mentioned arise from the overall context of the following description, examples and claims.

These are solved as well as other tasks which are not explicitly mentioned, but which can be readily deduced or deduced from the contexts discussed herein by way of a method having all the features of patent claim 1 and by a method having all the features of claim 16. Advantageous modifications of the method according to the invention according to claim 1 are provided in the dependent claims 2 to 15 under protection. Likewise, a useful modification of the method according to claim 16 is provided in dependent claim 17 under protection. A solution of the objects of the invention is also provided by an apparatus for implementing such a method according to claim 18. The dependent claims 19 and 20 claim appropriate modifications of the device.

Accordingly, the present invention is accomplished by a method of scaling the position and orientation of at least one laser proximity sensor to a calibration body, each laser distance sensor each having a laser and a sensor comprising the following chronological steps A) through C):

A) arranging a well-defined calibration body with an at least partially precisely defined geometry in a measurement setup comprising the laser distance sensors, wherein the position of the calibration body is precisely defined by arranging the calibration body in the measurement setup, and coarse alignment of at least one laser distance sensor to the calibration body;

B) distance measurements of several measuring points or a continuous course on the surface of the calibration body by the laser distance sensor or the Laser distance sensors, wherein the calibration body is moved in the measurement setup relative to the laser distance sensor or the laser distance sensors to allow the laser of the laser distance sensor or the laser of the laser distance sensors, the irradiation of the different measurement points or the continuous course for the distance measurements; and

C) Determining the position and the orientation of the at least one laser distance sensor to the calibration body based on the distance measurements and the known geometry and position of the calibration body in the measurement setup.

By the method according to the invention, among others, the following advantages can be achieved:

The method is simple to implement and therefore inexpensive to implement. In addition, with the method, a high accuracy of a subsequent measurement can be achieved. It may be sufficient if only the orientation of the laser distance sensor is adjusted.

A scaling of the position and the orientation of at least one laser distance sensor is the same if only the position and the orientation of at least one laser of a laser distance sensor are scaled, if the laser and the sensor of the laser distance sensor are not fixed to one another.

Under a well-defined geometry and storage of the calibration body is understood as high accuracy. Preferably, the dimensions and the mounting of the calibration body can be manufactured to at least 0.5 mm, particularly preferably to at least 0.1 mm, very particularly preferably to at least 0.01 mm. The angles of the surfaces to the axis of rotation and to each other can be made at least to 1 °, preferably to at least 0.1 ° accurate, most preferably to at least 0.01 ° accurate.

It can be inventively provided that the method comprises a step D), D) adjustment of the at least one laser distance sensor based on the thus determined position and orientation of the at least one laser distance sensor to the calibration body, so that a desired position and a desired orientation of the at least one laser distance sensor to the calibration body is desired, wherein step D) after step C).

By performing the adjustment directly after the measurement or between different measurements can be achieved that the evaluation of a subsequent measurement is simplified, without the subsequent measurement would have to be corrected computationally.

A further embodiment of a method according to the invention can provide that the distance measurements are performed on at least five measuring points on the surface of the calibration body by the laser distance sensor or the laser distance sensors are performed.

A higher number of measuring points leads to a smaller error in the subsequent evaluation of the results. At the same time, however, a small number of measuring points accelerate the entire process.

According to a further, particularly preferred embodiment of the invention can be provided that the calibration body is rotatably mounted in the measurement setup and the measurement points are driven by rotating the calibration body in the measurement setup about the axis of rotation or the continuous course is driven by rotating the calibration body in the measurement setup about the axis of rotation , wherein preferably the laser distance sensor or the laser distance sensors is aligned at the rotation axis as a desired orientation or, more preferably, the orientation of the laser distance sensor or the laser distance sensors to the rotation axis with an angle (Γ) of less than 20 °, most preferably at an angle (Γ) less than 5 °.

A rotatable calibration body, in particular a turntable as calibration body, simplifies the entire structure. In addition, the structure can be made much more compact with a rotating calibration body. It can be provided that the angular velocity (co) of the calibration body about the axis of rotation when determining the position and the orientation of the at least one laser distance sensor to the rotatable calibration body is taken into account, in particular in the distance measurement of the continuous course.

By this method, there are possibilities for a simple evaluation of the signal periodic by the rotation.

Furthermore, it can be provided that the angle of rotation (.phi.) Of the calibration body is determined, the time (t) preferably being measured at known angular velocity (co) in order to determine the angle of rotation (.phi.) Of the calibration body, with a marker being particularly preferred the calibration body is measured with the at least one laser distance sensor to determine a full revolution.

As a result, an additional direct measurement of the rotation angle (φ) of the calibration body can be avoided.

Most preferably, it can be provided that a turntable is used as the calibration body, wherein preferably the turntable is inclined against the rotation axis, particularly preferably a tilt angle (δ) between 5 ° and 60 °, very particularly preferably a tilt angle (δ) between 15 ° and 30 ° is inclined.

Due to the inclination or tilting of the turntable increases in a periodic measurement of the swept value range of the signal of the distance measurement. This leads to a better evaluable signal and thus to a more accurate scaling of the orientation and optionally also the position of the at least one laser distance sensor relative to the calibration body.

It can be provided that the tilt angle (δ) of the turntable against the axis of rotation in determining the position and the orientation of the at least one laser distance sensor to the turntable is considered mathematically. By this measure, a further simplification of the calculation of the sought parameters can be achieved. For the scaling of the orientation and the position of a single laser distance sensor, the tilt angle (δ) of the rotary disk relative to the axis of rotation must be known as precisely as possible.

It can also be provided that the laser beam generated by the laser of the at least one laser distance sensor always hits the respectively identical side of the turntable during the distance measurement.

This measure also serves to simplify the arithmetic evaluation for determining the position and orientation of the laser distance sensor.

A particularly preferred embodiment of the invention can provide that the position and the orientation of the at least one laser distance sensor for

Turntable through parameter fits of the equation l _{l =} ⁿ ° ^ ^ ^• | c ₁ | + / _{0 1} determines n ° c _l

or are determined by a Taylor series expansion of this equation, preferably determined by a Fourier analysis of a Taylor series evolution of this equation, where /? the measured values of the at least one laser distance sensor when hitting the turntable, n is the normal vector of the turntable, ie the position vector of the intersection of a surface of the turntable with the axis of rotation, bi the position vector of the virtual intersection of the laser beam with the associated xy plane E _l through the Point di, c _{l of} the in the z-direction normalized to the amount of 1 direction vector of the incident on the turntable laser beam from laser 1 in the direction of increasing measured values and / _{0 1,} the measured value of the laser distance sensor, which

Measuring the point bi would result ..

An evaluation of the above formula with the specified means is mathematically feasible and therefore suitable for calculatory evaluation. It can also be provided that, in the calculation of the data for determining the position and the orientation of the at least one laser distance sensor for the calibration body from a periodic distance measurement, the amplitudes of a fundamental wave (Fi _{, 1} ), in particular the amplitudes of a fundamental wave (Fi, i) and at least the first harmonic (F ₂ , i), wherein preferably the fundamental wave (Fi, i) and / or at least the first harmonic (F ₂ , i) are calculated by a Fourier analysis of the periodic distance measurement, particularly preferred are calculated by a Taylor series expansion and a Fourier analysis of the periodic distance measurement.

The evaluation of a fundamental wave (Fi, i) and at least the first harmonic wave (F ₂ , i) of the periodic signal leads, with high accuracy of the result, to a simple implementability of the method. Details on this can be found in the mathematical derivation of FIGS. 3 to 5 below.

It may be provided that, in the calculation of the fundamental wave (Fi _, i) and / or at least the first harmonic (F ₂ , i), it is assumed that the amplitudes of the fundamental wave (Fi _, i) and / or at least the first harmonic wave ( F _{2 /} i) is greater than or equal to zero.

This assumption also leads to a simplification of the arithmetic evaluation of the signals.

In a very particularly preferred embodiment of the method according to the invention can be provided that the angles i and γι and the amplitudes C _{l of} the representation of the vectors in

Cylindrical coordinates for determining the position and orientation of the at least one laser distance sensor with the equations β _ι = μ _ι - π

be calculated, where μ? the phase of the fundamental wave of Ι _λ (φ) and η _ι the phase angle of the 1st _Harmonic wave of Ι _λ (φ), c _zl = sign (c _zl ) indicates the z-orientation of the laser to the turntable, δ is the tilt angle of the turntable against the rotation axis and F _{1t 1 is} the measured amplitude of the fundamental wave and F ₂ , i is the measured amplitude of the first harmonic.

These formulas, with high accuracy, greatly simplify the formulas for evaluating a signal from a rotating tilted or tilted turntable.

Furthermore, provision can be made for the distance measurements to be carried out using a laser triangulation method and / or for the at least one laser distance sensor to be calibrated in the course of alignment on the basis of the measured data and / or the variables calculated therefrom.

The calibration is particularly preferably carried out by calculating the additive component k, i of the respective measurement signal by / _{0 1} = F _{0 l} - _{2 1} ^■ cos (y _l

Laser triangulation methods are simple and inexpensive to implement and particularly suitable for the implementation of scaling methods according to the invention.

A further development of the invention can provide that the relative position and orientation of at least two laser distance sensors are determined relative to one another, and uncertainties are compensated for by errors in the assessment of the position and geometry of the calibration body.

The relative determination can compensate for errors or uncertainties in the geometry and the bearing of the calibration body.

The objects of the invention are also achieved by a method for measuring the thickness of a body or coating of a coated body in a measurement setup, wherein at least one laser distance sensor is used in the measurement of the thickness whose position and orientation was determined to the calibration body with such a method or which was previously aligned in the measurement setup with such a method against a calibration body.

The advantages of scaling are particularly significant in measuring the thickness of a body or coating of a coated body.

Such methods may preferably also include the following chronological steps:

E) removing the calibration body from the measurement setup;

F) inserting the coated body into a bearing having a known position and orientation to the previously stored calibration body in the measurement setup; and

G) measuring the thickness of a body or its coating by means of the at least one aligned and positioned laser distance sensor and / or measuring the thickness of the one body or its coating, wherein the position and orientation of the at least one laser distance sensor is taken into account mathematically.

As indicated by the alphabetical order of the letters, said steps are carried out in chronological order and according to steps A) to G) of the alignment methods according to the invention.

Further, according to the invention, a step H) may be provided after step G), in which a determination of the thickness of the coating is carried out from the measurement of the thickness of the coated body.

The objects of the invention are also achieved by a device for carrying out such a method, in which the device has at least one laser distance sensor and a bearing for a body to be measured comprises, wherein each laser distance sensor comprises a laser and a sensor, the storage is designed to hold a calibration body with at least partially well-defined surface and the calibration body is defined in the device movable.

It can be provided that the calibration body is rotatably mounted in the device or is storable and the calibration body is rotatable about a defined angle (φ) about an axis of rotation and / or with at least one defined angular velocity (co) is rotatable.

It can be provided in turn that the calibration body is a disc which is inclined against the axis of rotation, preferably tilted by a Verkippungswinkel (δ) between 5 ° and 60 °, more preferably by a Verkippungswinkel (δ) between 15 ° and 30 ° is inclined, most preferably inclined by a tilt angle (δ) between 20 ° to 25 °.

The invention is based on the surprising finding that it is possible to scale the position and orientation of a laser distance sensor or a laser of such a laser distance sensor so accurately by measuring on the surface of a defined calibration body that in a subsequent measurement of a coated body with unknown layer thickness Coating a particularly high accuracy can be achieved, or an improvement in the accuracy can be achieved. The method is relatively simple to perform and easy to implement with the computing power of modern computing systems.

The aim of a measurement setup according to the invention and an evaluation procedure or a method according to the invention is to determine the position and tilt of one or more laser distance sensors relative to a rotation axis defined by the measurement setup. The process is very robust because it does not use the absolute value of the laser distance sensor. In addition, the test setup is characterized by a low height. The position parameters determined in this way can be used in particular for a) aligning one or more laser distance sensors parallel to a rotation axis defined by the measurement setup,

b) align two or more laser sensors parallel to each other, and / or c) to place the laser beams of two counter-rotating laser distance sensors exactly to each other.

Exemplary embodiments of the invention and calculations relating to the invention are explained below with reference to five schematically illustrated figures, without, however, limiting the invention. Showing:

Figure 1 is a schematic side view of a structure for implementing a method according to the invention in a desired position;

Figure 2 is a schematic side view of a structure for implementing a method according to the invention with coarse alignment at the beginning of the process;

FIG. 3 shows a schematic perspective illustration for clarifying the angular relationships in a structure for implementing a method according to the invention in an initial situation;

FIG. 4 shows two schematic side views of a turntable as shown in FIG. 3; and

FIG. 5: a perspective diagram for clarifying the geometric relationships.

FIG. 1 shows a schematic side view of a measurement setup for implementing a method according to the invention in a desired position. The measurement setup comprises a laser distance sensor 2, which has a laser 8 and a sensor 10. The laser 8 and the sensor 10 are arranged at a fixed angle to each other. Above the laser distance sensor 2, a disk is arranged as a calibration body 12 and rotatably supported about a rotation axis z. The axis of rotation z need not be a material axis, as by the drawing is suggested, for example, when the calibration body 12 is held in a rotatable frame.

The laser beam from the laser 8 hits the calibration body 12 in the illustration shown on the underside. But the laser beam could just as well hit the top side of the calibration body 12. As sensors 10, conventional CCD chips with an upstream lens can be used. Such sensors 10 for measuring the reflected laser light are known from laser triangulation methods for determining the layer thickness of a coated body.

In the view shown in Figure 1, the laser 8 is aligned in a desired orientation to the calibration body 12, namely parallel to the axis of rotation z of the calibration body 12. If the laser beam is understood as a vector in the coordinate system of the calibration body 12, this is parallel to the z-axis. With the method according to the invention, the orientation and positioning of the laser distance sensor 2 shown in FIG. 1 is to be achieved for the calibration body 12, or a correction formula can be determined with which the measurement results of the laser distance sensor 2 can be converted so that it matches the measurement result of a correctly aligned laser distance sensor 2 (such as shown in Figure 1) would correspond.

First, the laser distance sensor 2 is only roughly aligned or misaligned in the measurement setup. This arrangement is shown in Figure 2 as a schematic side view. The laser distance sensor 2 is not exactly parallel to the axis of rotation z of the calibration body 12 is arranged but tilted against the z-axis. The aim of the method is to align the laser distance sensor 2 against the calibration body 12 so that the arrangement comes as close as possible to the state shown in Figure 1. Alternatively, the correction formula can also be determined in order to correct the measurement data recorded with the tilted laser distance sensor 2 in such a way that they correspond to the measurement data of a well-aligned laser distance sensor 2 (shown in FIG. 1).

For this purpose, the calibration body 12 is introduced into the measurement setup and rotatably mounted there. With the laser distance sensor 2, several measuring points on the bottom surface of the calibration body 12 was added. For this purpose, the calibration body 12 is rotated in construction. Preferably, not only are discrete measurement points recorded on the surface of the calibration body 12, but a continuous course of the distances of the laser distance sensor 2 from the surface of the rotating calibration body 12 is recorded. With known angular velocity ω and as accurately known geometry of the calibration body 12 information can be obtained from the periodic signal of the laser distance sensor 2, which allow precise conclusions about the arrangement and orientation of the laser 8 and thereby of the laser distance sensor 2 to the calibration body 12. The information thus obtained can be used to adjust the laser distance sensor 2 in order to achieve the desired state in FIG. 1 or to come as close as possible to this. Alternatively, the information thus obtained may be used to calculate the correction formula to correct the measurement data taken with the tilted laser distance sensor 2 to correspond to the measurement data of a well-aligned laser distance sensor 2 (shown in FIG. 1).

In a preferred embodiment, a turntable 12 is rotatably mounted as a calibration body 12 in the measurement setup. The turntable 12 is inclined from the rotation axis z by an angle δ. The turntable 12 is brought into the laser beam of the laser distance sensor 2 and detects the measured values of the distance measurement of the laser 8 to the point of impact of the laser beam on the turntable 12 during its rotation.

Optionally, the absolute angle (or at least its zero crossing) of the rotary disk 12 is measured on the rotation axis z.

From the measurement signal tilting and positioning of the laser 8 and thus of the laser distance sensor 2 to the hub 12 are determined mathematically.

FIG. 3 shows a schematic perspective illustration for clarifying the angular relationships in a structure for implementing a method according to the invention in an initial situation with a roughly adjusted laser 28 of a laser distance sensor. In a real design, the laser beams of the Of course, laser 28 will hit the turntable 32. The displacement of the laser 28 in the xy plane is used here only for a clearer representation of the angular relationships.

For the derivation of the geometric equations and the description of the setting algorithm, the definition of a coordinate system and of variables is necessary.

The z-axis of the Cartesian coordinate system is placed in the axis of rotation of a turntable 32. The turntable 32 is used as a calibration body in the measurement setup. The x- and y-axis is not determined geometrically, but should be based on the adjustment possibilities of the laser sensors. The laser 28 radiates (in this illustration from below) onto the turntable 32.

The position and orientation of the laser sensor are determined by the direction ^{vector c} i of the h F

Laser beam and the piercing point ^u ^ of the laser 28 defined by a plane ⁱ , wherein the plane ^ ^{i is} parallel to the xy plane and the axis of rotation perpendicularly intersects at the point ^, in which the side facing the laser 28 of the rotary disk 32, the axis of rotation, So the z-axis, cuts.

FIG. 4 shows two schematic side views of the turntable 32 according to the illustration according to FIG. 3 in order to be able to vividly discuss the mathematical derivation of a solution according to the invention of the problem.

Within the coordinate system, the position of the rotary disk 32 through the respective relevant intercept on the z-axis (d _zl and d _z2 ) and the

Normal vector n set. Because of the choice of b, b _zl = d _zl . The normal vector n of the rotary disk 32 is tilted or inclined from the z-axis by the angle δ, with 0 <δ <π / 2, so that the angle between the surface of the rotary disk 32 and the x / y-plane is δ. The actual angle of rotation φ of the rotary disk 32 is the angle between the x-axis and the negative gradient of the rotary disk 32 projected into the x / y plane of the footed surface in FIG f cos (<p) sin (<5)

Rotation axis z. According to this definition, the normal vector is parameterized by n sin (<p) sin (<5) cos (<5).

Figure 5 shows a perspective Diagrannnnn to illustrate the geometric relationships. The vectors of a laser beam of a laser (for example of the laser 28 according to FIG. 3) and the vectors and angles used for the calculation are shown in relation to the coordinate system and the laser beam. For a second laser or other lasers, analogue graphs result, which in the following lead to analogous considerations.

For the position b, the following Cartesian coordinates or cylindrical coordinates are used:

The direction of the laser is described by two equivalent vectors: the unit vector c _l pointing in the direction of the first laser beam, namely

Direction of increasing measured values, and ' ^ζ1 ', whose z-component is normalized. These vectors are parameterized as follows:

Then ^{Czl Czl /} l ^Czl

The angle between laser beam and parallels to the axis of rotation is then = arctan (C ₁ ). The parameter ß _x, B _x are out of the measurement at the end, y _x, C _x, determined c _zX, from which all representations of ^ i ^'c i, and thus the position and tilt, the first laser arise.

The following is the geometry and measurement equation derived:

The points on the laser beam of the first laser are parameterized by the associated measured value ^ as follows: p _x (l _x ) = b _x + (l _x -l _ox ) -c _x where ^ ⁰ ' ^{1 is} the measured value at the point ⁼ ^ is.

In addition, all points meet on the side facing the first laser side of the turntable, the equation N ° - referred to herein wherein the sign "°" the dot = 0 (p _x d _x).

At the intersection between the beam of the laser and the turntable both equations are satisfied and one can eliminate the variable P ^ and obtain the following condition for the measured value ^ at the point of intersection: n ° (b _x + (l _x -l _ox ) -c _x -d _x ) = 0

Solving the equation for ^ yields n ° (d _x -b _x )

lo, i

n ° c _x

In the following, a Taylor series development and a Fourier analysis of the measurement signal are carried out in order to obtain easily accessible measurement quantities: To prepare for the Taylor development of the measurement signal of _x , the relation becomes

use. One gets n ° c _x

This equation can already be used according to the invention to calculate the position and orientation of the lasers with respect to one another by means of the distance measurements and the known ones. For this purpose, the equation can be solved mathematically using parameter fits. However, further mathematical simplifications lead to a preferred embodiment of the invention with much simpler calculation.

For this purpose, the definitions of the vectors ^c i and ⁿ are used, taking advantage of the fact that ⁼ ^ ^ζ ΐ · The result is

, - B _x cos ß cos ^ sin ^) sin (jß ₁ ) sin (<p) sin (ö) ^ .2

1 ·

C _x cos (7 _j ) cos (<p) sin (<5) + C _x s (y _x ) sin (<p) sin (<5) + c _zl cos {5)

Now we extend the numerator and denominator with c _zl / cos (<5) and use that c _z ² _l = 1 and the addition theorem cos (β _l ) cos ((p) + sm (β _l ) sm ((p) = cos ((p - and receives

Hereinafter, it is assumed for the Taylor series development that the first laser 28 and the rotation axis z have already been roughly aligned with each other, that is, that

C _x «cot (<5), for example C _x « 1 at δ <π / 4. Then the amount of ε: = c _zX C _x tan (ö) · cos (<p - γ _χ ) in the denominator of _x for every angle φ is much smaller than 1 and a Taylor expansion \ -ε + ε ² -ε ³ + 0 (έ _ι ⁴ ) = (\ -ε) · (\ + 0 (έ ² ))

ε + 1

of the denominator from l _x to ε justified.

With this Taylor expansion k = ki + ("c _z A tan (<5) · cos (<p

(1 + 0 (C _X ² )) ^■ Jüä ² and after dissolving the product terms of the cosine functions l _x = / _{0> 1} + (~ B tan ² (<5) · cos ( _7l - Ä) ^■ (1 + 0 (C ² )) - - · cos (<p - &) · (! + 0 (C ² )) +

From this representation, the Fourier development of _Ι λ (φ) can be in the form of k (<P) = ^F o, i + ^F i, i cos (<p _-μ ι) + _{2> 1} cos (2 <p - η ,) + ... with _u > 0, ₂₁ > 0. In order to obtain always positive amplitudes _u > 0, irrespective of whether the laser beam scans the turntable 32 on the top side or from the underside, the sign of the prefactor, ie -c _zl , may have to be replaced by an angle shifted by π in the argument of cos - Terms are expressed. Thus one obtains μ _ι = β _ι + π · (δ _Λ -ΐ) / 2,

where the Fourier coefficients F _0l , F and _{21 are} _correct except for residual terms of the order 0 {C), 0 (C ² ) or 0 {C). With this preparatory work can now be with knowledge of the tilt angle δ of the hub 32, the z-orientation of the laser 28, that is c _zl = sign (c _zl ), and the first terms of the Fourier series k (<P) = ^F o _, i + ^F i _, i cos (<p - μ _ι ) + _{2> 1} cos (2 <p - η,) + ... the five (nonlinear) equations according to the five unknowns Α ^> 7ι ^> £ Ί ^{> 5ι ι} _m j _{t solve} the following result:

Q = 2 - cot (<5)

B _l = cot (ö) - _n

• cos ^ -A).

From the first four quantities, you can simply use the ones for the determination of the physical setting parameters, for example, l = Q - cos ^),

= ⁵ r ^sin (A) ₅ , which are necessary when using linear tables and tilting tables in the x and y directions.

On the tilt angle δ of the hub 32 can be closed from the storage of the hub 32, which is defined by the measurement setup. The z-orientation of the laser 28 determines whether the turntable 32 is from above or below

F

is irradiated. It should be noted that the constant term of the Fourier series, ie ^0.1 , is not required for this calculation step and thus the measured value may also be offset. With knowledge of all five sizes, each point on the laser beam of the first laser (in the measuring range) can be unambiguously measured

P ^\ (h) ^{~ +} (kh ^{, \} ) ^{'c \} _ZU assign, in particular, the zero point ^ v ^{' Cl} determine in space. For the zero point calibration of the laser, in turn, the offset in the measured value can be determined as the difference between the current measured value and the desired measured value, and the offset can then be taken into account in the evaluation of the later measured values.

In practice, the tilt angle δ is defined and known by the structure of the turntable 32. In the case of an alignment of the laser 28 that is parallel to the z-axis, not even the exact value is necessary: the angle δ scales the

Amplitude value of the normalized tilt C _l and the values derived therefrom c _xl , c _yl , C _l , c _xl , c _yl only. With the alignment of the laser 28 parallel to the z-axis one seeks zeros of such derived quantities, which are independent of the scaling effect of δ.

F F F

The Fourier coefficients ⁰¹ , ^{1 1} , ^{2 1} and the phases μ _ι , η _ι of Ι _γ (φ) can in the

Practice can be gained in different ways, as the following cases show:

1) The measurement signal is measured at previously defined, discrete angular positions (spatial discrete on the turntable 32) and the parameters of Ι _γ (φ), for example, determined by a discrete Fourier transform. According to the invention, continuous measurements are preferred for ease of handling.

2) Instead of the angle-dependent measurement signal Ι _γ (φ), the time signal l _x (t) and the matching angle φ (ί) are measured and from this Ι _γ (φ) and its parameters determined.

3) At possibly unknown, but constant rotational speed ω of the rotary disk 32, a time signal l _x (t) is measured and the times, t ₀ and t _! , two consecutive zero crossings φ (ί ₁ ) = φ (ί ₀ ) = 0. Then can

2π

with the angular velocity co = the angle signal t _l - t ₀ φ (ί) = ω · (ί-ί ₀ ) = 2π ^■ --- be reconstructed. Together with the t _l - t ₀

Time signal l _x (t) can again be determined Ι _γ (φ) and its parameters. A constant angular velocity ω thus leads to a simplification of the calculation of the parameters and is therefore particularly preferred according to the invention.

It is also possible to do without direct angle measurement. Assuming the angle β _l between the laser 28 and the turntable 32 is approximately known, for example, due to a prefabricated measuring attachment. Thus, μ _{ι is} known. A time signal l _x (t) is recorded at a constant rotational speed ω of the rotary disk 32. If then the one laser 8, 28 is already quite well aligned, that is, if C _l << cot (<5), then the fundamental wave dominates the harmonic, that is F »2 F _2l , and it can be very simple successive times t _m0 and t _{ml are} found, in which the signal assumes the maximum. Then

2π

ω =. With the knowledge of the rotational speed ω, the Fourier

Coefficients F _0l , F _ll , F _{2l are determined} from the time signal l _x (t). To the lack of phase angle η to obtain _ι, one first determines times _ί μ1 and _ί η1 at which the maxima of the fundamental wave and the harmonic can be expected, for the so _μ γ = _ω-ί μ1 and η _ι = _2ω-ί η1 applies , Then

2 (ί_ _η -ί Λ 2 (ί ^ -ί Λ τ \ _ί -2μ _ί = 2ω- (ί _ηί -ί _μί ) = 2π - ^ ^μ - and thus η _λ = 2π · - ^ - + 2μ _λ ,

Then all parameters of Ι _γ (φ) are known for the evaluation. For an estimation of the setting accuracy, a construction with the following parameters is considered below by way of example: δ = π / 6 (= 30 °) => tan (<5) = 0.58;

F _xl = 2.5mm;

With respect to F _u , this means that at approximately parallel to the axis of rotation of the

Turntable 12, 32 aligned laser 8, 28, the amplitude of the then approximately sinusoidal distance measurements is 2.5 mm and the Fourier coefficients F _u , F _{2, 1 were determined} with an uncertainty of 1 μιτι.

It applies to the normalized tilt

C _{i = 2} . _C ot (<5) - ^ a setting accuracy of

AQ «2 · cot (ö) ^ = 1,3 - 1 (Γ ³ .

The uncertainty in the angle = arctan (Q) between a laser 8, 28 and a parallel to the axis of rotation z is then at these small values of C _l

ΔΓ = 1 / (1 + Q ² ) · AC _l = 1, 3mrad (= 0.079 °).

For the distance B _{l of} the laser point from the rotation axis z to z height d _A applies

B _l = cot (<5) · F _ll -! - cot (ö) ^■ F _ll

Ί c _x I and thus an inaccuracy of

AB _X «cot (ö) ^■ AF _ul = \, 72 m. In the following, the effects on the uncertainty of a thickness measurement are shown.

The setting accuracy of the laser 8, 28 directly determines the uncertainty of a thickness measurement.

For an estimation we use the above numerical values.

The uncertainty Ad of the measured value in the thickness determination of a plate tilted by a maximum of <5 '= 5 ° in a measuring gap with a positioning accuracy in

Direction of the z-axis of h = 2.5mm by the two setting errors AC _l and

AB _{l of} the laser 8, 28 is then

(Ä - ACi + Aßj- tan S '): 2- W _2tl 0.45 // m.

A second laser (not shown) could provide an analog contribution to refine the measurement. In this case, an alignment of this second laser to the laser 8, 28 take place, to then use both to determine the thickness of the hub and / or their coating.

In order to keep the uncertainty low, the following points should be noted:

1) When setting the position and tilting of the sensors 10, the largest possible angle δ should be selected and the full measuring range should be used as far as possible so that F can be as large as possible. However, this is limited by the real dimensions of the measurement setup, such as the dimensions of the laser distance sensors 2, optionally the thickness of the turntable and the axis of rotation or the diameter of the laser beam. For real constructions with commercially available laser distance sensors 2, an angle δ between 15 ° and 35 ° is particularly preferred since it can be implemented well with these components.

2) The resolution of the laser distance sensors 2 should be as high as possible so that AF and AF _{V are} as small as possible. The resolution of Laser distance sensors 2, for example, be limited by a measurement noise to 1 μηη.

3) In the actual measurement of the object to be measured this should be as little as possible tilted, that is, the angle δ 'be as small as possible, and lie as quiet as possible in the direction of the z-axis, that is h should be as low as possible. An inclination of the object to be measured of 0 ° can preferably be provided.

Two exemplary setting algorithms for methods according to the invention are presented below.

When constructing a suitable measuring device, the restrictions for its use must be taken into account. In particular, care must be taken that the measuring range of the laser distance sensors 2 is both maintained during the measurement, and therefore also very well utilized.

The constructed measuring device is inserted into the beam path of the laser 8, 28.

In order to align a laser 8, 28 with respect to the axis of rotation z, the procedure is as follows:

1) Align axes of laser 8, 28 and axis of rotation z roughly parallel

(=> C _l «cot (<5));

2) measure signal I _x ;

3) Fourier coefficients F _U, F _{2; 1,} and the phases _μ ι, _η ι determined by _Ι γ (φ);

4) position and tilt of the laser 8, 28 by β _ι , γ _ι , 0 _ι , Β _ι determine;

5) determine adjustment parameters of lasers 8, 28;

6) readjust tilt until it is good (usually close to zero against the z axis); and

7) Adjust the position until it is good (until the position corresponds to the desired position). The features of the invention disclosed in the foregoing description, as well as the claims, figures and embodiments may be essential both individually and in any combination for the realization of the invention in its various embodiments.

LIST OF REFERENCE NUMBERS

2 laser distance sensor

8, 28 lasers

10 sensor

12, 32 calibration bodies

Geometric variables δ Tilt angle between turntable (12, 32) and axis of rotation

(Z)

φ angle between projection of the gradient of the turntable (12,

32) in x-y plane and x-axis

n normal vector of the turntable (12, 32) (with positive z-component) d _x position vector of the point of intersection of the first laser

Surface of the turntable (12, 32) with the rotation axis (z) z-component of the position vector ^

E virtual plane perpendicular to the axis of rotation at z height of

Position vector of the virtual intersection of the laser beam (8, 28) with plane ^E ^

i · b _yl , b _zl x, y, z component of the position _vector b

^B l distance of position vector b _x of rotation axis (z)

ßl angle between projection of the position vector b _x in xy-plane and x-axis (= direction of the virtual intersection b _x )

^C l Direction vector of the first laser beam (8, 28) in the direction of increasing measured values

^C x \ ' ^C yl' ^C zl x, y, z component of the direction vector c _x

^C l on | c _zl | normalized direction vector c _x , ie c _x = II \ c _zX \ -c _x

^C x \ ' ^C y \' ^C zl x, y, z component of the normalized direction vector c _x with

c _zl = sign (c _zX )

Amplitude of normalized tilt c _x projected in xy plane

Yl angle between projection of the direction vector c _x in xy-plane and x-axis (= direction of tilting)

T _j = arctan ^) angle between first laser beam (8, 28) and parallel to Rotation axis (z)

X x axis perpendicular to the z axis of the Cartesian

coordinate system

y y axis perpendicular to the z axis and x axis of the Cartesian

coordinate system

z axis of rotation of the calibration body and z-axis of the Cartesian

coordinate system

Measured values and parameters k Measured value of the first laser sensor when hitting the

Turntable (12, 32)

Measured value of the first laser sensor when measuring the point

^F o, i constant term in Fourier evolution of 1 _γ (φ)

^F n amplitude of the fundamental wave of 1 _γ (φ)

^F 2, l amplitude of the 1. Harmonic of 1 _γ (φ)

μ _λ phase angle of the fundamental wave of 1 _γ (φ)

Ii phase position of the 1. Harmonic of 1 _γ (φ)

ω (constant) angular velocity d <p / df of the rotary disc (12, 32)

Claims

claims

1 . Method for scaling the position and orientation of at least one laser distance sensor (2) to a calibration body (12, 32), each laser distance sensor (2) each having a laser (8, 28) and a sensor (10) comprising the following chronological steps A) to C):

A) arranging a well-defined calibration body (12, 32) with an at least partially well-defined geometry in a measurement setup comprising the laser distance sensors (2), wherein the position of the calibration body (12, 32) by arranging the calibration body (12, 32) in the measurement setup is precisely defined, and coarse alignment of at least one laser distance sensor (2) to the calibration body (12, 32);

B) distance measurements of a plurality of measurement points or a continuous course on the surface of the calibration body (12, 32) by the laser distance sensor (2) or the laser distance sensors (2), wherein the calibration body (12, 32) in the measurement setup relative to the laser distance sensor (2) or the laser distance sensors (2) is moved to allow the laser (8, 28) of the laser distance sensor (2) or the lasers (8, 28) of the laser distance sensors (2), the irradiation of the different measurement points or the continuous course for the distance measurements; and

C) Determining the position and the orientation of the at least one laser distance sensor (2) for the calibration body (12, 32) on the basis of the distance measurements and the known geometry and position of the calibration body (12, 32) in the measurement setup.

2. The method of claim 1 comprising step D),

D) adjustment of the at least one laser distance sensor (2) on the basis of the thus determined position and orientation of the at least one laser distance sensor (2) to the calibration body (12, 32), so that a desired Position and a desired orientation of the at least one laser distance sensor (2) to the calibration body (12, 32) is sought,

wherein step D) after step C) takes place.

3. The method according to claim 1 or 2, characterized in that

the distance measurements at at least five measuring points on the surface of the calibration body (12, 32) by the laser distance sensor (2) is performed or the laser distance sensors (2) are performed.

4. The method according to any one of the preceding claims, characterized in that

the calibration body (12, 32) is rotatably mounted in the measurement setup and the measurement points are controlled by rotating the calibration body (12, 32) in the measurement setup about the rotation axis (z) or the continuous course by rotating the calibration body (12, 32) in the measurement setup the axis of rotation (z) is traversed, wherein preferably the laser distance sensor (2) or the laser distance sensors (2) on the rotation axis (z) is aligned as a desired orientation or, particularly preferably, the orientation of the laser distance sensor (2) or the laser distance sensors (2 ) to the axis of rotation (z) with an angle (Γ) of less than 20 °, very particularly preferably with an angle (Γ) of less than 5 °.

5. The method according to claims 4, characterized in that

the angular velocity (co) of the calibration body (12, 32) about the axis of rotation (z) is mathematically taken into account when determining the position and orientation of the at least one laser distance sensor (2) relative to the rotatable calibration body (12, 32), in particular in the distance measurement of the continuous course.

6. The method according to any one of claims 4 or 5, characterized in that the angle of rotation (φ) of the calibration body (12, 32) is determined, wherein preferably the time (t) at known angular velocity (co) is measured in order to determine the angle of rotation (φ) of the calibration body (12, 32), with particular preference a marker on the calibration body (12, 32) is measured with the at least one laser distance sensor (2) to determine a full revolution.

7. The method according to any one of claims 4 to 6, characterized in that as calibrating body (12, 32) a turntable is used, wherein preferably the turntable against the rotation axis (z) is inclined, more preferably by a Verkippungswinkel (δ) between 5 ° and 60 °, most preferably inclined by a tilt angle (δ) between 15 ° and 30 °.

8. The method according to claim 7, characterized in that

the tilt angle (δ) of the turntable against the axis of rotation (z) is taken into account mathematically in determining the position and the orientation of the at least one laser distance sensor (2) to the turntable.

9. The method according to claim 7 or 8, characterized in that

the laser beam generated by the laser (8, 28) of the at least one laser distance sensor (2) always strikes the respective same side of the turntable during the distance measurement.

10. The method according to any one of claims 7 to 9, characterized in that the position and orientation of the at least one laser distance sensor (2) to the hub by Parameterfits the equation l _x = \ + l _{0 l are} determined or with a

Taylor series evolution of this equation can be determined, preferably determined by a Fourier analysis of a Taylor series expansion of this equation, where / _? the measured value of the one laser distance sensor when hitting the turntable (12, 32), n is the normal vector of the turntable (12, 32), ie the position vector of the intersection of the laser facing surface of the turntable with the axis of rotation, bi of the position vectors of the virtual intersection of the first laser beam with the corresponding xy planes E _l through the point di, c _l in the z-direction to the amount of 1 normalized direction vector of the rotary disc (12, 32) incident laser beam of laser (8, 28) in the direction of increasing measured values and h _, i is the measured value of the first laser distance sensor that would result when measuring the point bi.

1 1. Method according to one of the preceding claims, characterized in that

in the calculation of the data for the determination of the position and the orientation of the at least one laser distance sensor (2) for calibration body (12, 32) from a periodic distance measurement, the amplitudes of a fundamental wave (Fi, i), in particular the amplitudes of a fundamental wave (Fi, i ) and at least the first harmonic (F ₂ , i), wherein preferably the fundamental (Fi, i) and / or at least the first harmonic (F ₂ , i) are calculated by a Fourier analysis of the periodic distance measurement preferably be calculated by a Taylor series development and a Fourier analysis of the periodic distance measurement.

12. The method according to claim 1 1, characterized in that

in the calculation of the fundamental wave (Fi _, i) and / or at least the first harmonic wave (F ₂ , i), it is assumed that the amplitudes of the fundamental wave (Fi, i) and / or at least the first harmonic wave (F _2, i) are greater or equal to zero.

13. The method according to any one of claims 7 to 12, characterized in that the angles ßi and γι and the amplitudes Q and ß? for the determination of

Position h sin (A) and the orientation described by the vector

the at least one laser distance sensor (2) with the

equations

β _γ = μ _γ - π - (α _Λ - \) Ι2,

Q = 2 - cot (<5) -

be calculated, where μ? the phase of the fundamental wave of Ι _λ (φ) and η _ι the phase angle of the 1st _Harmonic wave of ^ (φ), c _zl = 5 n (c _zl ) _indicates the z-orientation of the laser (8, 28) to the turntable, δ is the tilt angle of the turntable against the rotation axis (z) and F _{1t 1 is} the measured Amplitude of the fundamental wave and F ₂ , i is the measured amplitude of the first harmonic.

14. The method according to any one of the preceding claims, characterized in that

the distance measurements are carried out with a laser triangulation method and / or that the at least one laser distance sensor (2) is calibrated in the course of the alignment on the basis of the measured data and / or the variables calculated therefrom.

15. The method according to any one of the preceding claims, characterized in that the relative position and orientation of at least two laser distance sensors (2) are determined relative to each other and thereby uncertainties due to errors in the assessment of the position and geometry of the calibration body (12, 32) are compensated.

16. A method for measuring the thickness of a body or a coating of a coated body in a measurement setup, wherein at least one laser distance sensor (2) is used in the measurement of the thickness, its position and orientation to the calibration body (12, 32) with a method according to of the preceding claims was determined or which was previously aligned in the measurement setup with a method according to one of claims 2 to 15 against a calibration body (12, 32).

17. The method according to claim 16, characterized by the chronological steps

E) removing the calibration body (12, 32) from the measurement setup;

F) inserting the body to be measured in a storage, which has a known position and orientation to the previously stored calibration body (12, 32) in the measurement setup; and

G) measuring the thickness of the body or its coating by means of the at least one aligned and positioned laser distance sensor (2) and / or measuring the thickness of the body or its coating, wherein the position and orientation of the at least one laser distance sensor (2) is taken into account mathematically ,

18. A device for carrying out a method according to one of the preceding claims, wherein the device comprises at least one laser distance sensor (2) and a bearing for a body to be measured, wherein the laser distance sensor (2) comprises a laser (8, 28) and a sensor ( 10), the bearing for holding a calibration body (12, 32) is designed with at least regionally well-defined surface and the calibration body (12, 32) is defined in the device movable.

19. The apparatus according to claim 18, characterized in that

the calibration body (12, 32) is rotatably mounted in the device or can be stored and the calibration body (12, 32) is rotatable about defined angles (φ) about an axis of rotation (z) and / or rotatable with at least one defined angular velocity (co) is.

20. The apparatus according to claim 19, characterized in that

the calibration body (12, 32) is a disc which is inclined against the rotation axis (z), preferably tilted by a tilt angle (δ) between 5 ° and 60 °, particularly preferably a tilt angle (δ) between 15 ° and 30 ° °, very particularly preferably inclined by a tilt angle (δ) between 20 ° to 25 °.