WO2008071426A1

WO2008071426A1 - Method and device for the self-calibration of circle segments

Info

Publication number: WO2008071426A1
Application number: PCT/EP2007/010928
Authority: WO
Inventors: Reinhard Probst
Original assignee: BUNDESREPUBLIK DEUTSCHLAND, vertr. d. d. BUNDESMINISTERIUM Für WIRTSCHAFT UND TECHNOLOGIE, dieses vert. d. d. PRÄSIDENTEN DER PHYSIKALISCH-TECHNISCHEN BUNDESANSTALT
Priority date: 2006-12-14
Filing date: 2007-12-13
Publication date: 2008-06-19
Also published as: DE102006059491B3

Abstract

The invention relates to a self-calibration of a circle segment (1, 6) for measuring the angle of a rotatably mounted object, in which the circle segment (1, 6) is divided into a number N of uniform graduation intervals (7), which self-calibration can be carried out with little effort in the installed state of the object and is characterized by the following steps: a) the circle segment (1, 6) is factorized into a first and a second circle subsegment to form the integer factors R and S which have no common divider, where N = R*S; b) a graduation deviation difference dk is determined for each graduation interval (7); c) the d4 are transformed from the space domain into the frequency domain with respect to the first circle subsegment; d) these are used to calculate transformation coefficients F'nl,kl for graduation deviations fk with respect to the first circle subsegment; e) the F'nl,kl are transformed from the space domain into the frequency domain with respect to the second circle subsegment, thus obtaining transformation coefficients Fn0,nl for the graduation deviations fk with respect to the circle segment (1, 6); f) the Fn0,nl are transformed from the frequency domain into the space domain, thus obtaining the graduation deviations fk.

Description

Method and device for self-calibration of subcircuits

The invention relates to a method for the self-calibration of pitch circles for the angular measurement of an object rotatably mounted about an axis, in which the pitch circle is divided into a number N of substantially uniform pitch intervals.

Furthermore, the invention relates to a device for self-calibration of pitch circles for the angular measurement of an object rotatably mounted about an axis.

Subcircles are angle specimens in which a circle is divided equally and measurably into a defined number N of pitch intervals. They form the basis of the angle measurement technique by returning to the full angle 2π rad = 360 ° and are predominantly used as radial grating washers in angle encoders and in measuring devices such. B. Theodolites, in use. Also by area circle divisions such as mirror polygons or gears partial circles are formed.

The manufacturing and assembly-related pitch deviations due to irregularities of the pitch intervals, eccentricity of the disc and roundness deviations of the axis of rotation lead to a substantially uniform division of the pitch circle in pitch intervals. The pitch deviations can be more or less compensated for by mounting several, generally at least 2 diametrically arranged scanning heads on the circumference of the pitch circle. For this purpose, the sum is formed via the discrete measured values of the scanning heads and thus certain components of the pitch deviation are eliminated. It applies the mathematical law that a number of R scanning heads arranged evenly over the scale of division cancel in their measured value sum all Fourier coefficients or harmonics of the pitch deviations, except for those of the order R, 2R, 3R, discrete Fourier spectrum be filtered out. This technique is used on accurate commercial angle encoders up to a maximum of R = A scanheads. When using conventional amplitude gratings, an accuracy of the angle measurement of about 0.5 "is achieved. The accuracy requirements of angle measurements are steadily increasing in many fields, such as astronomy, optics and laser technology, as well as micro and nanotechnology. With phase grating technology or holographically produced gratings today angle measuring devices can be produced with significantly higher pitch, improved signal quality and higher electronic interpolation, which in principle a reduction of the measurement uncertainty can be achieved to less than 0.1 "However, this is only possible with elaborate calibration and the Maintaining very tight mounting tolerances Self-calibrating these subcircuits uses so-called self-calibration techniques, which are calibration procedures in which the subcircuits calibrate themselves through a particular array of scanning heads by determining and evaluating the differences and sums of the readhead readings. However, these methods are expensive and uneconomical, so they are not suitable for industrial application.

A method for self-calibration of subcircuits based on the aforementioned principle is described in the article "Six Nanoradians in 2π Radian - A Primary Standard for Angle Measurement" by R. Probst and M. Krause, in the Proc. Of 2 ^nd euspen International Conference - Turin, Italy - May 27 ^th - ^st 31, 2001. In the process presented therein 16 scanning heads are arranged around the pitch circle, from which 8 scanheads for angle measurement and another 8 scanheads used alone for the self-calibration, together with the first. 8 16 readheads are not suitable for industrial use.

The object of the present invention is therefore to provide a self-calibration method for pitch circles in angle measurement technology and for related applications, which manages with a relatively small number of scanning heads and with which the pitch deviations can be determined quickly and efficiently. A further object of the present invention is to provide a device for the self-calibration of sub-circuits in angle measurement technology and for related applications, which manages with a relatively small number of scanning heads and with which the division deviations can be determined quickly and efficiently. The object is achieved by a method mentioned above according to the invention by the following steps:

a) The pitch circle is factored into a first and a second subcircuit to the integer, non-divisive factors R and S, respectively, where N = R -S; b) For each division interval a division deviation difference d _{k is} determined; c) The pitch deviation differences d _k are relative to the first

Subcircuit transformed from the spatial domain into the frequency domain; d) From the transformation result, transformation coefficients F _nk of pitch deviations f _k with respect to the first

Subcircuit calculated; e) The transform coefficients F _nk the pitch deviations f _k with respect to one base circle are transformed into the frequency domain with respect to the second sub-part circuit from the spatial domain, thereby transform coefficients F of the pitch circle are obtained _nn the pitch deviations f _k with respect to; f) The transform coefficients F _{nn of} the pitch deviations f _k with respect to the pitch circle are transformed from the frequency space to the space space, whereby the pitch deviations f _k are obtained.

The inventive method for self-calibration of pitch circles for the angle measurement makes it possible to quickly and efficiently determine the pitch deviations in a relatively high pitch with a relatively small number of scanheads (a scanhead is also a sensor) in only a partial cycle. The calibration and recalibration of partial circuits can also be done in the installed state. There is thus no expansion of the pitch circle required, which then in a laboratory by conventional calibration, such. B. rosette method, is calibrated. The self-calibration method according to the invention avoids uncertainties which in conventional comparison measuring devices are avoided by the mechanical coupling to the common axis of rotation are inevitable. Thus, the inventive method for industrial use is particularly suitable.

Preferably, R should be as small a number as possible (eg R = 2 or 3), while S can be significantly larger, but must not have a common divisor> 1 with R.

In one embodiment, the pitch deviation differences are determined from a plurality of successive pitch cycles with only one scanhead located on the pitch circle, where R pitch circles with one another

Angular distance of the scanning head of ³⁶⁰ % and a pitch circle circulation with a Win¬

Scanning distance of the scanning head of ³⁶⁰ % with respect to one of the other circular recirculation.

In this embodiment, the pitch intervals are read out and latched by the scanhead for each pitch recirculation. In addition to the readout of a lattice slice with the scanning, for example, tooth flanks of a gear with a probe as a sensor or the surfaces of a mirror polygon can be measured with an autocollimator as a sensor. The mutual angular distance of the partial circulation circuits is achieved by a corresponding change in angle between the pitch circle and the scanning head by means of an adjusting mechanism. The individual pitch cycles must be reproducible only at an angle for reading out the pitch intervals, but may contain unknown systematic angle errors, since these are eliminated in the calculation of the pitch deviation differences. This embodiment has the advantage that it manages with only one scanning head. Thus, the process can be carried out space-saving and with low equipment costs.

In another embodiment, the pitch deviation differences are determined with R equally spaced around the pitch scanhead and at least one reference scanhead with the reference scanhead located on the pitch circle at a ³⁶⁰ % angular separation from one of the other scanheads. In this embodiment, all divisional intervals in a single pitch cycle are read out simultaneously from all the scanheads, and the divisional deviation differences are determined therefrom. Thus, the method according to the invention can be carried out in a very short time.

The readings of the division intervals provide discrete measured values. Therefore, the transformations from the spatial domain into the frequency domain are advantageously performed by means of discrete Fourier transformation and the transformations from the frequency domain to the spatial domain by means of inverse discrete Fourier transformation.

Preferably, for the Fourier transformation, an FFT variant (FFT: Fast Fourier Transform) by LH Thomas "Using a computer to solve problems in physics" in Application of Digital Computers, Boston, Mass .: Ginn, 1963, and IJ Good " The interaction algorithm and practical Fourier analysis "in J. Roy. Statist. Soα, ser. B, vol. 20. pp.361-372, 1958; Addendum, vol.22, 1960, pp.372-375. This variant is based on the following one-to-one decomposition of an index k into an index pair (k _o , k,):

k = (RR _s k ₀ + SS _R k _ι ) moάN, 0≤k≤Nl with k ₀ = kmoάS, O≤k _o ≤Sl k ^ kmoάR, O≤ ^ ≤Rl and the equations of determination

SS _R = lmodR, S _R <R

RR _s = lmoάS, R _s <S.

If the division intervals are first indexed by the index k, the above decomposition of the index k into the index pair (Jt ₀ , £) leads to a factorization of the pitch circle N, which is particularly advantageous for the method according to the invention, into the index k ₀ and the second sub-pitch circle R to the index A ₁ . The pitch deviation differences d _k can be determined against an average of pitch deviations and defined as follows:

where f _{k is} the pitch deviations and f _{k is} an arithmetic mean over R equally distributed pitch deviations.

The factor decomposition according to Thomas and Good leads to the following indexing advantageous for the calculations for the pitch deviation differences d _k :

i r ö ^ kQ + R, Kγ - 'ftQ

R-I

_ 1

Jk _{0 R} 2-, Jk ₀ ^ ₁ ^■

Ar ₁ = O

The pitch _deviation differences d _{kι> kχ} are preferably according to the following

Regulation with respect to the first subcircuit S transformed into the frequency domain:

SI D ' _k = Y d _kk - W " ^llCo 0 <U ₁ ≤ S - 1

Ar ₀ = O

with W _s = e ^{/ s} .

The factor decomposition of Thomas and Good was exploited and the discrete Fourier transform was used for periodic functions.

The index n in the frequency domain is decomposed according to the index k in the space according to the following rule into an index pair (n _o , n _λ ): n = ₍₀ + Sn Rn _ι) moάN, O≤n≤Nl n _o = n mod R, _o O≤n ≤Rl

1

This assignment is likewise unambiguous, as a result of which the inverse discrete Fourier transformation from the frequency domain to the spatial unit is also clearly defined.

With this decomposition, the transformation coefficients of the division deviations with respect to the first sub-division S can be written as follows:

R-I

Ar ₁ = O

Further transformation of the thus obtained transformation coefficients of the division deviations with respect to the first sub-division S into the frequency space with respect to the second sub-division R leads in a simple manner directly to the following transformation coefficients of the pitch deviations with respect to the pitch circle:

■ w / "^> , o ≤« ₀ <R - 1

Taking into account the circle symme- try condition

k% ^R [R, furn _o = O and the definition of the discrete Fourier transforms of the pitch deviation differences

RI a - VD '. _W "oK

"0>" l

Ar ₁ = O

the following case distinction results for the transformation coefficients of the pitch deviations with respect to the pitch circle, which allows a simple evaluation:

F _n ^ _n ^ D _n ^ - W ^ for ^ n ₁ ≠ O

F _{0 0} = O for W ₀₉ W ₁ = O.

The last line applies because of the so-called closed circuit condition, which states that all pitch deviations of a pitch circle together give the value zero.

With the above equations, all the transform coefficients F _nn

of the absolute pitch _deviations f _kk from the transform coefficients

D _nn the measured differences d _kk uniquely determined: the coefficient

M) _9W1 ^{in the first} equation is for all

Values 0 <nγ ≤ S - 1, since the denominator (l - W £ ^x J can not become zero, since

R and S are non-prime. The known pole problem in the discrete Fourier transformation of measurement differences can therefore not occur here. From this one finally obtains the sought division deviations f _k by the

inverse discrete Fourier transform f _k =

and the known assignments of the F _n "to the F _n .

The object is further achieved by a device for calibrating a pitch circle for the angular measurement of an object rotatably mounted about an axis, which is configured to carry out the method according to one of claims 1 to 9, comprising at least one scanning head, a data memory and an evaluation unit.

With the device according to the invention, a pitch circle in the installed state can be easily self-calibrated. Good results, which are sufficient for most industrial applications, can already be achieved with a very small number of scanning heads. The calculations for the method are simple and not very compute-intensive, so that the device can be realized with a simple and cost-effective data memory and a simple and cost-effective evaluation unit, for example a microcontroller or a processor.

The invention will be described in more detail with reference to the following figures. Show it:

FIG. 1 shows a first pitch circle;

FIG. 2 shows a further partial circle;

3 shows the pitch circle of Figure 2 in the spatial space and

FIG. 4 shows the pitch circle from FIG. 2 in the frequency domain.

FIG. 1 shows a partial circle 1.

The pitch circle 1 has an angular pitch 2 with six pitch intervals 3. The division intervals 3 would ideally each form a circular arc 4 to a center angle of ² ^ / = 60 °. Due to manufacturing and assembly-related tolerances of this ideal case is not achievable. Therefore, the actual divide dividing intervals 3 from the ideal circle segments 4. This results in division deviations φ _k (0 <k <5), which lead to divisional intervals 3 of different sizes. The pitch deviations φ _k (0 <k <5) occur in both clockwise and counterclockwise directions, which is indicated by the differently oriented arrows along the circumference of the circle. The differently sized graduation intervals 3 result in an angle measurement to deviations from the actual angle. To be able to take these deviations into account either during the measurement or to be able to subsequently correct the measurement results, it is necessary to calibrate the pitch circle 1, that is to say to determine the φ _k (0 <k <5). The pitch deviations lead to measurement deviations in the form of discrete numerical values f _k , which are proportional to the values φ _k (0 <k <5).

FIG. 2 schematically shows a device 5 according to the invention for calibrating a pitch circle 6. The factorization N = R -S is realized here with R = 3 and S = 4.

The pitch circle 6 has twelve pitch intervals 7. On the circumference of the pitch circle 6, three scanning AK ₀ , AKi and AK ₂ are arranged at the same angular distance from each other. The angles between adjacent scanning heads AKo, AKi and AK ₂ are 120 °.

On the circumference of the pitch circle 6 is also a Referenzabtastkopf AKs in one

Angular distance of ³⁶⁰ % 4 ^' - = 90 ° in the counterclockwise direction of the scanning AK ₀ arranged.

The measured values of the scanning heads AK ₀ , AKi and AK ₂ and the reference scanning head AKs are transmitted via a suitable wired or wireless data connection to a computer unit, not shown. The computer unit comprises a data memory for storing the measured values and further data, such as intermediate results, as well as an evaluation unit which processes the measured values according to the method according to the invention. In addition, the computer unit 16 for controlling the rotation of the pitch circle 6 set. This can be done for example via an electric motor, not shown.

The self-calibration of the pitch circle 6 will be explained in more detail below.

In a complete circular recirculation, the three scanning heads AK ₀ , AKi and AK _{2 are} respectively read in difference from the reference scanning head AKs, whereby measured value differences are obtained. The Referenzabtastkopfes AKs serves as a clock. At each clock, the arithmetic mean of the measured value differences is formed. The mean value describes a triangular pitch circle with its position relative to the reference scanning head AKs.

It can be seen in FIG. 3 that, according to the subdivision with N = 12, R = 3 and S = 4, a number of exactly 4 triangles 8a, 8b, 8c, 8d are read out with their positional deviations, which together form the complete pitch circle 6 form.

The evaluation of these twelve averaged pitch deviations now takes place according to the method of the invention, which represents a two-stage Fourier algorithm.

First, the index k is decomposed in the space according to Thomas and Good into an index pair (k _o , k _λ ). The values of the index k are in FIG. 3 inside the circle circumference 9 in FIG

Counterclockwise shown and the values of the associated index pairs (k _o , k _λ ) outside the circumference 9. Accordingly, the values of the index n in the frequency domain and the values of the associated index pairs (" ₀ ,",) in Figure 4 are shown on a circumference 10th shown. The decompositions lead to the following assignment tables:

Table 1 Table 2

By way of example, it can be seen from Table 1 that, for the index £ = 11, the index pair (£ _< ,, £,) = (3,2) and the index n-4 are the index pair (W ₀₁ W ₁ ) = (1,0) assigned. It can also be seen that the assignments are one-to-one.

In the first stage, the Fourier transform results in the pitch deviation differences

over the first subcircle (to the factor S = 4) to the transformation coefficients

D _{nι A} = Σd _koA - WW, P n, k ^K _n °

Ic ₀ = O

This function represents a function in the frequency domain with respect to the index i \ and a function in the position space with respect to the index k _x .

By evaluating and reshaping you get the function

In the second stage, the Fourier transformation of this function over the second subcircuit (to the factor R = 3) leads to transformation coefficients of the pitch deviations, which are represented by the following rule:

The evaluation of this function leads to the following case distinction:

F _{0 0} = O for W ₀₅ H ₁ = O.

From this one finally obtains the sought division deviations f _k by the

inverse discrete Fourier transform

and the known assignments of F _nn to F _n .

Claims

claims

A method of self-calibrating a pitch circle (1,6) for angular measurement of an object rotatably mounted about an axis, wherein the pitch circle (1,6) is divided into a number N of substantially uniform pitch intervals (7) characterized by the following steps : g) The pitch circle (1, 6) is factor-divided into a first and a second sub-pitch circle to the integer, non-divisive factors R and S, respectively, where N = R-S; h) For each division interval (7) a division deviation difference d _{k is} determined; i) The pitch deviation differences d _k are relative to the first

Subcircuit transformed from the spatial domain into the frequency domain; j) From the transformation result, transformation coefficients F _nk of pitch deviations f _k are calculated with respect to the first sub-pitch circle; k) The transform coefficients F _n ^ of the pitch deviations f _k with respect to the second sub-part circuit from the spatial domain are transformed to the frequency domain with respect to the first base circle, thereby transform coefficients F _nn the pitch deviations f _k with respect to the partial circuit (1, 6) can be obtained; I) The transformation coefficients F _{nn of} the pitch deviations f _k with respect to the pitch circle are transformed from the frequency space into the space space, whereby the pitch deviations f _k are obtained.

2. Method according to claim 1, characterized in that the pitch deviation differences are determined with a scanning head arranged on the pitch circle (1, 6), where R comprises pitch circles with a mutual scanning head pitch of ^{36 (} % and 1 pitch round

with an angular distance of the scanning head of ³⁶⁰ % with respect to one of the other pitch cycles.

3. The method according to claim 1, characterized in that the pitch deviation differences with R evenly around the pitch circle (6) arranged scanning heads (AK ₀ , AKi, AK ₂ ) and at least one reference scanning (AKs) are determined, wherein the reference scanning head (AKs) is arranged on the pitch circle (6) at an angular distance of ³⁶⁰ % from one of the scanning heads (AK ₀ , AKi, AK ₂ ).

4. The method according to any one of the preceding claims, characterized in that the division intervals (7) before the factorization by an index k and after the factorization by an index pair {k ₀ , k _x ) are indexed, for which applies:

k = (RR _s k ₀ + SS _R k _ι ) moάN _t O≤k≤Nl where k ₀ = kmoάS, O≤k _o ≤S- \ k _λ = kmoάR, 0 <k _λ <R- \ and the equations of determination

SS _R = \ moάR, S _R <R

RR _s = lmoάS, R _s <S.

5. The method according to any one of the preceding claims, characterized in that the pitch deviation differences d _k from the pitch deviations f _{k are} defined by:

6. Method according to claim 5, characterized in that the division deviation differences d _k after factoring are represented as follows: d - f - f

•

7. The method according to claim 6, characterized in that the division deviation differences are transformed according to the following rule with respect to the first sub-division into the frequency domain:

8. The method according to claim 7, characterized in that the transformation coefficients of the pitch deviations f _{k are defined} with respect to the first sub-pitch circle as follows:

9. The method according to claim 8, characterized in that the transformation _{coefficients of} the pitch deviations f _{k are transformed} with respect to the first sub-division according to the following rule with respect to the second sub-division into the frequency domain:

10. A device for self-calibration of a pitch circle (6) for the angle measurement of an object rotatably mounted about an axis, which is adapted to carry out the method according to one of claims 1 to 9, comprising at least one scanning head (AK ₀ , AKi, AK ₂ X a Data memory and an evaluation unit.