DE102009015507B4 - Method for measuring a roll angle and roll angle measuring device - Google Patents

Abstract

Method for measuring a roll angle (α), comprising the steps
(a) directing a first light beam (24) onto a first location (36) of a partially cylindrical section (18) of a reflector (12) to form a first reflection light beam (38) which is at a first reflection angle (λ ₁ ). runs,
(b) directing at least one second light beam (26) to a second location (40) of the partially cylindrical section (18) that is different from the first location (36), so that a second reflection light beam (42) is produced, which is at a second reflection angle ( λ ₂ ),
(C) moving the reflector (12) along a linear guide (44) with a guide surface, wherein the first light beam (24) and the second light beam (26) are directed onto the reflector (12), that a change in the roll angle (α ) causes the first reflection angle (λ ₁ ) to increase and the second reflection angle (λ ₂ ) to decrease,
(d) measuring at least one quantity from which a change of the first reflection angle (λ ₁ ) and the second reflection angle (λ ₂ ) can be deduced ...

Description

The The invention relates to a method for measuring a roll angle. According to one second aspect, the invention relates to a roll angle measuring device.

Of the Roll angle, for example, must be measured on machine tools and gives a twist to a lead around the shift direction.

From the DE 199 26 546 C2 For example, a method is known in which a light beam of linearly polarized light is directed from a fixed light source onto the object to be moved. On the object to be moved, an analyzer is arranged, which measures the intensity of the light beam in a predetermined direction of polarization. As the roll angle changes, the angle between polarizer and analyzer changes and the intensity detected by the detector also changes. In this way, the roll angle can be measured. A disadvantage of this method is that this is relatively complex and requires the implementation of particularly qualified personnel.

From the JP 09 054 102 AA are known a roll angle measuring device for a friction force microscope and an associated calibration method in which two light beams are reflected onto a mirrored cylinder jacket surface. From the difference of the reflection angle is closed on the roll angle.

From the DE 36 43 723 A1 For example, a method and an arrangement for optically measuring the roll angle of a moving machine part are known. The document describes the projection of a complete plane onto a mirrored cylinder, so that the roll angle measurement in mutually perpendicular directions of the method is possible in a single construction. The disadvantage of this is the high expenditure on equipment. Due to the necessity of a light plane, the measurement accuracy is also limited.

From the US 6,741,364 B2 For example, a method for determining the roll angle between two relatively movable objects is known, in which a laser beam is directed onto a lens or a prism. The disadvantage of this is that the method is not very suitable for high-precision measurements.

From the US 3,790,284 A an interferometer system for measuring the roll angle is known. Although very high accuracies can be achieved with such a system, the system is not very suitable for measurement under workshop conditions, for example in a machine tool.

Of the Invention is based on the object, the roll angle with a high Accuracy and a simple measurement setup to measure.

The Invention solves the problem in particular by a method according to claim 1. According to a second Aspect dissolves the invention of the problem by a roll angle measuring device for Measuring the roll angle mt the features of claim 5.

Advantageous The invention is that they measure the roll angle with a particularly high accuracy. So it is possible, the partially cylindrical section to manufacture with high accuracy, so that out of the change the reflection angle closed with high accuracy on the roll angle can be. It is also advantageous that the curvature of the partially cylindrical section and a change the roll angle to a big change the reflection angle leads. That increases the accuracy in measuring the roll angle.

It Another advantage is that the roll angle with the invention especially a fold can be measured.

in the The scope of the present description will be below the partially cylindrical section In particular, each section of the reflector understood, the contour characterized in that a curved curve along a generating Route is shifted. This corresponds to the general definition a cylinder, which can be a circular cylinder, but not have to be.

Under the calculation of the roll angle is understood in particular that an absolute value for the roll angle is calculated. Otherwise, only one change of the roll angle determined.

The reflector is understood in particular to mean any component which throws back the light rays. It is preferably a mirror.

Of the first reflection angle is measured, for example, as the angle, which has the first reflection light beam to the first light beam. Cheap is when the first reflection angle in a coordinate system is measured, one axis perpendicular to a direction of displacement the reflector stands. It is advantageous if both reflection angles be measured in a plane defined by them on the one hand is perpendicular to the plane, which the light rays contains and on the other hand includes one of the two light beams.

Prefers becomes the roll angle from a reflection angle difference from the calculated first reflection angle and the second reflection angle. This has the advantage of having an influence on the reflection angle compensate each other. The determination of the roll angle from the Reflection angle difference is therefore particularly accurate and less error prone.

According to the invention Section partially cylindrical. In this case lets out of the change the reflection angle is particularly easy to calculate the roll angle. In principle, however, the section can have any contour, provided they are local in an environment of the first location and the second Local approximated by a parabola can be.

According to one preferred embodiment become the first light beam and the second light beam on the part cylindrical Section directed that at the beginning of the measurement the first reflection angle corresponds to the second reflection angle. It is favorable if the procedure then continued is that the first angle of reflection to the negative of the second Reflection angle corresponds. This way you can be special accurate readings for get the roll angle. It is particularly favorable if both reflection angles preferably are small, so be substantially 0 °.

According to the invention For example, reflector moves along a linear guide with a guide surface, wherein the first light beam and the second light path are preferred be directed to the reflector so that a connecting link passes through the first place and the second place through the guide surface. The leads to, that a tilting of the reflector to the roll angle to be measured causes that the second reflection angle changes in the opposite way as the first reflection angle. In other words, that means the first reflection angle increases, whereas the second reflection angle increases Reflection angle reduced. In this way, errors remain through a mathematical approximation of the partially cylindrical Section as parabolic arise, small, so that the roll angle are calculated very accurately can.

Advantageous is also when the rays of light are directed at the reflector be that the the connecting distance between first place and second place substantially parallel to the generating path of the Contour of Reflek gate runs. Essentially parallel means that small deviations, for example of less than 3 ° tolerable are.

in the Below, the invention will be described with reference to an exemplary embodiment with reference to the attached Drawings closer explained. It shows

1 a schematic view of a roll angle measuring device according to the invention for measuring a roll angle at the beginning of a measurement,

2 a view of the roll angle measuring device according to 1 of the page,

3 the roll angle measuring device according to 1 in case the roll angle has changed,

4 a schematic view of the situation according to 3 for calculating the roll angle,

5 a plan view of the necessary for the calculation of coordinate systems from the direction of the light source and

6 a view of a coordinate system for calculating the roll angle.

1 shows a roll angle measuring device according to the invention 10 that a reflector 12 , a light source 14 and an evaluation unit 16 includes.

The reflector 12 has a part-circular cylindrical section 18 , The part-circular cylindrical section 18 can by a Schmiegekreis 20 be described, for example, has a radius of 10 mm.

The reflector 12 is on a schematically drawn component 22 fastened in a direction of displacement V along an in 2 drawn guide (reference numeral 44 ) can be moved. The light source 14 is arranged so that it remains stationary in such a movement.

The light source 14 is designed to be a first light beam 24 and one in 1 from the first ray of light 24 concealed second light beam 26 on the reflector 12 to judge. The rays of light 24 . 26 are generated for example by light emitting diodes. The light source 14 is part of a measurement unit 28 ,

The measuring unit 28 also includes an angle measuring device 30 that a first protractor 32.1 and a second protractor 32.2 having. The protractors 32.1 . 32.2 are with the evaluation unit 16 via a data cable 34 connected.

2 shows the roll angle measuring device 10 of the page. It can be seen that the first light beam 24 in a first place 36 on the reflector 12 incident, so that a first reflection light beam 38 arises. The second light beam 26 meets in a second place 40 on the reflector 12 and there is a second reflection light beam 42 ,

The first protractor 32.1 is arranged so that it is from the first reflection light beam 38 whereas the second protractor is 32.2 is arranged so that it from the second reflection light beam 42 is taken. For this purpose, it can be provided that the reflector 12 on one of its component 22 facing side is slightly bevelled.

2 also shows schematically a guide 44 , on whose guide surface F the component 22 can be moved guided in the direction V.

3 shows the case that when moving along the guide, the compo nent 22 and thus the reflector 12 tilt by a roll angle α. It thereby change the reflection angle λ ₁ , λ ₂ , by the protractors 32.1 . 32.3 be measured. From these angular changes, as shown below, the roll angle α can be determined. In the following, the angle changes are not denoted as Δλ ₁ , Δλ ₂ , as it would also be possible, but also as λ ₁ , λ ₂ , since the output angles are each set to zero in order to make the calculation clearer.

The in the following Invoices refer to two light beams and thus two Diffuse radiation. Of course it is also possible that more than two beams of light are used, with the roll angle then calculated by averaging the individual results obtained.

4 schematically shows a cross section through the reflector 12 to calculate the roll angle α from that of the protractors 32.1 . 32.1 ( 3 ) to explain measured angles.

The reflector 12 has a surface that is defined or can be approximated as follows in the drawn co-ordinate system: z '= -k x' 2 (1), regardless of y ', that is, the surface of the reflector 12 is simply by translation of the profile according to formula (1) in the direction y 'results.

wieder unabhängig von y', das heißt, n ^' = f(x'). The normal vector n ^ ', | n ^' | = 1, in the first place 36 then results using ∂z '/ ∂x' = -2kx 'according to formula (1)

again independent of y ', that is, n ^ '= f (x').

The reflector 12 with the surface profile according to formula (1) can also be approximated by a section of a cylinder. In this case applies k = 1 2R , (3), where R is the radius of the cylinder in the x'-z 'plane according to 1 is.

4 schematically shows the point of impact r → 1 . at which the first reflection light beam 38 on the first protractor 32.1 meets.

5 shows the coordinate system xyz for the angle measuring system, and the coordinate system x'-y'-z 'of the rotated by the roll angle α (rotation about the z (= z') axis) reflector. These are also the two places r → 1 and r → 2 for the two-point angle measurement of the first reflection light beam 38 and the second reflection light beam 42 located.

Shown are the non-rotated coordinate system xyz for the angle measuring system, as well as the by the roll angle α (rotation about the z (= z ') - axis) rotated reflector with its coordinate system x'-y'-z'. The two coordinate systems can be converted into each other by the following transformation equations:

wobei z₁ und z₂ die z-Koordinaten der Orte 36, 40 (2) sind, welche nicht bekannt sein müssen.The method is based on the difference between angle measurements at the two different locations 36 . 40 on the reflector 12 , please refer 2 , The two places r → 1 and r → 2 for the two-point angle measurement xyz is the protractor in the coordinate system 32.1 . 32.2 fixed and given by the following equations:

where z ₁ and z _{2 are} the z coordinates of the locations 36 . 40 ( 2 ), which need not be known.

In the coordinate system x'-y'-z 'of the reflector rotated by the roll angle α 12 ( 3 ) results in the following coordinates for the places r → 1 ' and r → 2 ' the two-point angle measurement according to the formulas (5a) and (5b):

These follow from the transformation equations (4a) and (4b) between the coordinate systems. The normal vectors n ^ ' 1 and n ^ ' 2 the reflector surface in the places 36 . 40 which are hit by the two measuring beams according to the formulas (6a) and (6b) result (in the coordinate system x'-y'-z 'of the reflector) from (2)

mit der Relation 2sinαcosα = sin2α.The normal vectors can be calculated using the transformation equations ( 4a ) and (4b) are rotated into the coordinate system xyz of the angle measuring system:

with the relation 2sinαcosα = sin2α.

If a measuring beam with a normalized direction vector u ^ is reflected at a surface point of the reflector with the normal vector n ^, the normalized direction vector results u ^ r of the reflected beam according to u ^ r = u ^ - 2 <u ^ n ^> u, (9), where <u ^ n ^> symbolizes the vector product (inner product).

mit dem normiertem Richtungsvektor u ^ der beiden von der Messeinheit 28 ausgehenden Lichtstrahlen 24, 26 von

After reflection of the two of the measuring unit 28 outgoing light rays 24 . 26 (Measuring beams) in the places 36 . 40 (Surface points of the reflector 12 ) with the normal vectors n ^ 1 and n ^ 2 According to (8a) and (8b), the following normalized direction vectors result u ^ 1r respectively. u ^ 2r :

with the normalized direction vector u ^ of the two of the measuring unit 28 outgoing light rays 24 . 26 from

6 shows the coordinate system xyz of the measuring unit 28 with specially defined polar coordinates λ and δ. It applies

there corresponds to λ the Deflection angle of the reflected measuring beam in the x-z plane the horizontal measuring axis of the angle measuring device, δ corresponds to the beam deflection angle perpendicular to this plane.

From the transformation equation ( 12 ), the following relation results for the polar coordinate λ of a beam with normalized directional vector reflected by the reflector u ^ r :

Thus, from the formulas (10a) and (10b) tanλ 1 = (1 - (2krsinα) 2 ) -1 2krsin2α (14a) respectively. tanλ 2 = - (1 - (2krsinα) 2 ) -1 2krsin2α = -tanλ 1 = tan (-λ 1 ) (14b).

This results in the reflection angle difference Δλ = λ ₁ - λ ₂ Δλ = λ 1 - λ 2 = 2arctane [(1 - (2krsinα) 2 ) -1 2krsin2α (15) and finally

The difference Δλ = λ ₁ - λ ₂ eliminates the error influences of the reflector inclination in Pitch (rotation about the x'-axis), which can also be called nodding, and Yaw (rotation about the y'-axis), which also As yaw can be called, almost completely, as well as the influences of translations of the reflector. Thus, the reflection angle difference Δλ = λ ₁ - λ _{2 of} the angular deflections of the reflection light beams 38 . 42 in the xz plane of the horizontal measuring axis of the measuring unit 28 a unique function of the roll angle α of the reflector 12 ,

mit dem Radius R des Zylinders, der die parabolische Reflektoroberfläche approximiert. Für kleine Winkel lα ist die gemessene Differenz λ₁ – λ₂ der Winkelauslenkungen der reflektierten Messstrahlen in der x-z-Ebene der horizontalen Messachse des Winkelmessgeräts also eine Funktion erster Ordnung im Rollwinkel α des Reflektors.With the approximation α << π for small angles, sinα ≈ α and sin2α ≈ 2α follow. With (2krsinα) ² << 1 follows

with the radius R of the cylinder approximating the parabolic reflector surface. For small angles lα, the measured difference λ ₁ -λ _{2 of} the angular deflections of the reflected measuring beams in the xz plane of the horizontal measuring axis of the angle measuring device is thus a function of first order in the roll angle α of the reflector.

• – Kippung des Reflektors in Pitch, β (Rotation um die x'-Achse, Nicken)
• – Kippung des Reflektors in Yaw, γ (Rotation um die y'-Achse, Gieren)
• – laterale Verschiebung Δx des Reflektors in x' und die
• – laterale Verschiebung Δy des Reflektors in y'.

In the following, it is shown that the roll angle α of the reflector 12 can be determined with the present embodiment of the method according to the invention, regardless of additional rotations and translations, as the

• Tilting of the reflector in pitch, β (rotation about the x'-axis, nodding)
• Tilting of the reflector in Yaw, γ (rotation about the y'-axis, yawing)
• Lateral displacement Δx of the reflector in x 'and the
• Lateral displacement Δy of the reflector in y '.

These error influences will be almost complete eliminated.

• – Roll α, Pitch β, Yaw γ: ±1000 aresec
• – laterale Verschiebungen Δx, Δy: ±1 mm
• – Zylinderradius Reflektor R: 1.0 m
• – halber Abstand Messorte r: 15 mm

For this, the beam guidance using raytracing was calculated exactly and the procedure was realized virtually. The following realistic parameters were assumed for the Monte Carlo simulations (variable parameters were equally distributed in the given intervals):

• Roll α, Pitch β, Yaw γ: ± 1000 aresec
• - lateral displacements Δx, Δy: ± 1 mm
• - Cylinder radius reflector R: 1.0 m
• - half distance measuring locations r: 15 mm

at the first two parameter ranges became relatively large values accepted in order to better test the limits of the process.

7 shows the difference between the roll angle α of the reflector given in the virtual experiment and that according to the approximate equation ( 16 ) determined from the simulated measurement data roll angle. For the parameter ranges assumed above, the standard uncertainty u _{α of} the roll angle determination, due to the influences of the additional rotations and translations of the reflector, is only 0.007 aresec. These are therefore irrelevant to the practical realization of the method.

10

Roll angle measuring device

12

reflector

14

light source

16

evaluation

18

section

20

Schmiegekreis

22

component

24

first beam of light

26

second beam of light

28

measuring unit

30

Angle measuring device

32

protractor

34

data cable

36

first place

38

first Diffuse beam

40

second place

42

second Diffuse beam

44

guide

F

guide surface

V

displacement direction

α

roll angle

λ

angle of reflection

Δλ

Reflection angle difference

Claims (8)

Method for measuring a roll angle (α), comprising the steps of (a) directing a first light beam ( 24 ) to a first place ( 36 ) of a partially cylindrical section ( 18 ) of a reflector ( 12 ), so that a first reflection light beam ( 38 ), which extends at a first angle of reflection (λ ₁ ), (b) straightening at least one second light beam ( 26 ) to one from the first place ( 36 ) different second place ( 40 ) of the partially cylindrical section ( 18 ), so that a second reflection light beam ( 42 ), which extends at a second angle of reflection (λ ₂ ), (c) moving the reflector ( 12 ) along a linear guide ( 44 ) with a guide surface, wherein the first light beam ( 24 ) and the second light beam ( 26 ) so on the reflector ( 12 ), that a change of the roll angle (α) causes the first reflection angle (λ ₁ ) to increase and the second reflection angle (λ ₂ ) to decrease, (d) measuring at least one quantity from the one change of the first reflection angle (λ ₁ ) and the second reflection angle (λ ₂ ) can be deduced and (e) calculating the roll angle (α) of the at least one size A method according to claim 1, characterized in that a reflection angle difference (Δλ) from the first reflection angle (λ ₁ ) and the second reflection angle (λ ₂ ) is used as the size. Method according to one of the preceding claims, characterized in that the first light beam ( 24 ) and the second light beam ( 26 ) so on the part cylindrical section ( 18 ), that at the beginning of the measurement the first reflection angle (λ ₁ ) corresponds to the second reflection angle (λ ₂ ). Method according to one of the preceding claims, characterized in that the first light beam ( 24 ) and the second light beam ( 26 ) so on the reflector ( 12 ), that a link through the first location ( 36 ) and the second place ( 40 ) passes through the guide surface. Roll angle measuring device for measuring a roll angle (α), comprising: (a) a reflector ( 12 ), which has a partially cylindrical section ( 18 ), (b) a light source ( 14 ), which is designed to - directing a first light beam ( 24 ) to a first location of the partially cylindrical section ( 18 ), so that a first reflection light beam ( 38 ), which extends at a first angle of reflection (λ ₁ ), and - directing at least one second light beam ( 26 ) to one from the first place ( 36 ) different second place ( 40 ) of the partially cylindrical section ( 18 ), so that a second reflection light beam ( 42 ), which runs at a second angle of reflection (λ ₂ ), (c) a guide ( 44 ) along which the reflector ( 12 ) is movably guided, (d) an angle measuring device for measuring at least one variable from which a change of the first reflection angle (λ ₁ ) and a change of the second reflection angle (λ ₂ ) can be derived, (e) an evaluation unit ( 16 ) which is set up to calculate the roll angle (α) of at least one size, wherein (f) the light source is designed to direct the first light beam ( 24 ) and the second light beam ( 26 ) so on the reflector ( 12 ) that a change in the roll angle (α) causes the first reflection angle (λ ₁ ) to increase and the second reflection angle (λ ₂ ) to decrease. Roll angle measuring device according to claim 5, characterized in that the evaluation unit ( 16 ) is arranged to calculate the roll angle (α) from a reflection angle difference (Δλ) between the first reflection angle (λ ₁ ) and the second reflection angle (λ ₂ ). Roll angle measuring device according to claim 5 or 6, characterized in that the partially cylindrical portion ( 18 ) Partial cylindrical. Roll angle measuring device according to one of claims 5 to 7, characterized in that the light source ( 14 ) is set up so that the first light beam ( 24 ) and the second light beam ( 26 ) the light source ( 14 ) Leave substantially parallel.