DE102006059491B3 - Pitch circle calibrating method for industrial application, involves determining pitch variation-differences for pitch interval, and transforming transformation-coefficients of pitch variations from frequency space into local space - Google Patents

Abstract

The method involves determining pitch variation-differences for a pitch interval (7), and transforming the pitch variation-differences relative to lower pitch circles from a local space into a frequency space. Transformation-coefficients of pitch variations relative to the lower pitch circles are calculated from a transformation result. Transformation-coefficients of the pitch variations relative to a pitch circle (6) are transformed from the frequency space into the local space.

Description

The The invention relates to a method for self-calibration of pitch circles for the Angle measurement of a rotatably mounted about an axis object at the pitch circle into a number N of substantially uniform pitch intervals shared.

Further The invention relates to a device for self-calibration of Subcircuits for the angle measurement of a rotatably mounted about an axis object.

partial circles are angular scale embodiments, where a circle is in a defined number N of pitch intervals evenly and is measurably shared. They form the basis of the angle measurement technology by returning to the full angle 2π rad = 360 ° and are predominantly as radial grating washers in angle encoders and in measuring devices, such as z. B. Theodolites, in use. Also by area circle divisions like mirror polygons or gears Subcircles are formed.

The production and assembly-related division deviations in consequence of irregularities the pitch intervals, eccentricity of the disc and roundness deviations lead the axis of rotation to a substantially uniform division of the pitch circle in division intervals. The division deviations can be achieved by Attaching several, generally at least 2 diametrically arranged scanning heads Compensate more or less on the circumference of the pitch circle. For this is the sum over formed the discrete readings of the scanheads and thus certain Components of the pitch deviation eliminated. It applies the mathematical lawfulness that a number of R evenly over the Scope arranged scanning heads in their Sum Sum all Fourier coefficients or harmonics of the pitch deviations extinguish, except for those of order R, 2R, 3R, ..., which are from the discrete Fourier spectrum be filtered out. This technique is accurate at commercial angle encoders up to at most R = 4 scanheads applied. When using conventional Amplitude grating hereby becomes an accuracy of angle measurement of about 0.5 "reached.

The Precision requirements for angle measurements are increasing many fields such as astronomy, optics and laser technology as well as the micro and nano technology constantly too. With phase grating technology or holographically produced grids can today with angle measurement higher Division number, improved signal quality and higher electronic interpolation which, in principle, reduce the measurement uncertainty can be reached to less than 0.1 ". However, this only succeeds with elaborate calibration procedures and adherence to very tight assembly tolerances. For self-calibration of this Subcircuits use so-called self-calibration methods. These are calibration procedures in which the pitch circles through a particular array of scanheads themselves calibrate. For this differences and sums of the measured values are calculated the scanning heads determined and evaluated. However, these methods are expensive and uneconomical, so they are not suitable for industrial application suitable.

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 Other methods of calibrating pitch circles are in the publications DE 197 20 968 A1 and US 2004/0107063 A1 shown.

task Therefore, the present invention is a self-calibration method for subcircles in angle measurement and for To provide related applications with a relatively low Number of scanheads and with which the pitch deviations quickly and efficiently can be determined. Furthermore, it is an object of the present invention a facility for Self-calibration of subcircuits in angle measurement technology and for To provide related applications with a relatively low Number of scanheads and with which the pitch deviations quickly and efficiently can be determined.

• a) Der Teilkreis wird in einen ersten und einen zweiten Unterteilkreis zu den ganzzahligen, teilerfremden Faktoren R bzw. S, mit N = R·S, faktorzerlegt;
• b) Für jedes Teilungsintervall wird eine Teilungsabweichungs-Differenz d_k ermittelt;
• c) Die Teilungsabweichungs-Differenzen d_k werden bezüglich des ersten Unterteilkreises vom Ortsraum in den Frequenzraum transformiert;
• d) Aus dem Transformationsergebnis werden Transformations-Koeffizienten
  
  von Teilungsabweichungen f_k bezüglich des ersten Unterteilkreises berechnet;
• e) Die Transformations-Koeffizienten
  
  der Teilungsabweichungen f_k bezüglich des einen Unterteilkreises werden bezüglich des zweiten Unterteilkreises vom Ortsraum in den Frequenzraum transformiert, wodurch Transformations-Koeffizienten
  
  der Teilungsabweichungen f_k bezüglich des Teilkreises erhalten werden;
• f) Die Transformations-Koeffizienten
  
  der Teilungsabweichungen f_k bezüglich des Teilkreises werden vom Frequenzraum in den Ortsraum transformiert, wodurch die Teilungsabweichungen f_k erhalten werden.

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 transformed from the spatial domain into the frequency domain with respect to the first subcircuit;
• d) The transformation result becomes transformation coefficients
  
  calculated from pitch deviations f _k with respect to the first sub-pitch circle;
• e) The transformation coefficients
  
  the pitch deviations f _k with respect to the one subcircuit are transformed with respect to the second subcircuit from the spatial domain into the frequency domain, whereby transformation coefficients
  
  the pitch deviations f _{k are obtained} with respect to the pitch circle;
• f) The transformation coefficients
  
  the pitch deviations f _k with respect to the pitch circle are transformed from the frequency space to the location space, whereby the pitch deviations f _k are obtained.

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

Prefers R should be as possible small number (eg R = 2 or 3), while S can be significantly larger, but no common divisor> 1 with R may have.

In an embodiment the pitch deviation differences become of several successive ones Teilkreisumläufen determined with only one scanning head, which is arranged on the pitch circle is, where R is circular circulations with a mutual angular distance of the scanning head of 360 ° / R and a Partial circulation with an angular distance of the scanning head of 360 ° / R in relation be performed on one of the other subcircuits.

at this embodiment The dividing intervals from the scanning head will be for each Circulating circuit read out and buffered. In addition to reading a lattice slice with the scanning head, for example, tooth flanks a gear with a probe as a sensor or the surfaces of a mirror polygon with an autocollimator as a sensor. The mutual Angular distance of the pitch circle circulations is caused by a corresponding change in angle between pitch circle and Scanning achieved by means of an adjustment mechanism. The individual subcircuits have to for reading the pitch intervals reproducible only at an angle could be however, contain unknown systematic angle errors, since these eliminated in the calculation of the pitch deviation differences become.

These embodiment has the advantage that it works with only one scanning head. In order to The process can save space and with low equipment costs carried out become.

In a further embodiment For example, the pitch deviation differences with R are equal to the Pitch circle arranged scanning heads and at least one reference scanhead, wherein the reference scanhead arranged at the pitch circle at an angular distance of 360 ° / S from one of the other scanning heads is.

at this embodiment all divisional intervals are in a single circular circulation from all readheads at the same time read out and therefrom the division deviation differences determined. This can be the inventive method in a very short time.

The Readings of the division intervals provide discrete measured values. Therefore the transformations of the spatial space in the frequency space are expedient means discrete Fourier transform and the transformations of frequency space into the spatial domain by means of inverse discrete Fourier transformation carried out.

Preferably, an FFT variant (FFT: Fast Fourier Transform) by LH Thomas "Using Computers 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., Soc.Sec., ser.B, vol., 20, pp. 361-372, 1958, Addendum, vol., 22, 1960, pp. 372-375 is based on the following one-to-one decomposition of an index k into an index pair (k ₀ , k ₁ ): k = (R · R S k 0 + S · S R k 1 ) modN, 0≤k≤N-1 With k 0 = kmodS, 0≤k 0 ≤ S - 1 k 1 = kmodR, 0≤k 1 ≤ R - 1 and the equations of determination S · S R = 1modR, S R <R R · R S = 1modS, R S <P.

If the division intervals are first indexed by the index k, then the above decomposition of the index k into the index pair (k ₀ , k ₁ ) leads to a factorization of the pitch circle N, which is particularly advantageous for the method according to the invention, into the index k and the second subcircuit R to the index k.

wobei f_k die Teilungsabweichungen und

ein arithmetischer Mittelwert über R gleichverteilte Teilungsabweichungen sind.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

an arithmetic mean over R are 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 :

werden vorzugsweise nach folgender Vorschrift bezüglich des ersten Unterteilkreises S in den Frequenzraum transformiert:

The pitch deviation differences

are preferably transformed according to the following rule with respect to the first subcircuit S in the frequency domain:

in this connection was the Factor decomposition of Thomas and Good exploited and the discrete Fourier transform for periodic functions applied.

The index n in the frequency domain is decomposed according to the index k in the space according to the following rule in an index pair (n ₀ , n ₁ ): n = (S · n 0 + Rn 1 ) modN, 0 ≦ n ≦ N - 1 n 0 = n mod R, 0 ≤ n 0 ≤ R - 1 n 1 = nmodS, 0 ≤ n 1 ≤ S - 1

These Mapping is also one-to-one, which also makes the inverse discrete Fourier transformation from frequency domain to spatial domain is defined.

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

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:

und der Definition der diskreten Fouriertransformierten der Teilungsabweichungs-Differenzen

ergibt sich die folgende Fallunterscheidung für die Transformations-Koeffizienten der Teilungsabweichungen bezüglich des Teilkreises, die eine einfache Auswertung ermöglicht:

Taking into account the circle symme- try condition

and the definition of the discrete Fourier transforms of the pitch deviation differences

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

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

der absoluten Teilungsabweichungen

aus den Transformations-Koeffizienten

der gemessenen Differenzen

eindeutig bestimmt: Der Koeffizient

in vorstehender Bestimmungsgleichung ist für alle Werte 0 ≤ n₁ ≤ S – 1 definiert, da der Nenner

nicht Null werden kann, da R und S teilerfremd sind. Das bekannte Polstellenproblem bei der diskreten Fouriertransformation von Messdifferenzen kann deshalb hier nicht auftreten.With the above equations, all are transform coefficients

the absolute pitch deviations

from the transformation coefficients

the measured differences

uniquely determined: the coefficient

in the above equation, 0 ≤ n ₁ ≤ S - 1 is defined for all values, since the denominator

can not become zero because R and S are non-prime. The known pole problem in the discrete Fourier transform of measurement differences can therefore not occur here.

und den bekannten Zuordnungen der

zu den F_n.From this, finally, the sought division deviations f _{k are} obtained by the inverse discrete Fourier transformation

and the known assignments of

to the F _n .

The Task is further solved by a device for calibrating a pitch circle for the angle measurement an object rotatably mounted about an axis, the set up is 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 let yourself Simply calibrate one pitch circle in the installed state. Good and for the Most industrial applications have sufficient results already achieve with a very small number of scanning heads. The calculations for the process is simple and not very computationally intensive, so that the device with a simple and inexpensive data storage and a simple and inexpensive Evaluation unit, for example a microcontroller or a processor, can be realized.

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

1 a first pitch circle;

2 another subcircle;

3 the partial circle 2 in the physical space and

4 the partial circle 2 in frequency space.

In 1 is a partial circle 1 shown.

The circle 1 has an angle division 2 with six dividing intervals 3 on. The division intervals 3 Ideally, each would be a circular arc 4 to form a center angle of 2π / 6 = 60 °. Due to manufacturing and assembly-related tolerances of this ideal case is not achievable. Therefore, the actual dividing intervals are different 3 from the ideal circle segments 4 from. This results in division deviations φ _k (0 ≦ k ≦ 5), which lead to division intervals of different sizes 3 to lead. 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 different size division intervals 3 lead to deviations from the actual angle in an angle measurement. 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 set the pitch circle 1 to calibrate, ie the φ _k (0 ≤ k ≤ 5) to determine. 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).

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

The circle 6 has twelve division intervals 7 on. On the circumference of the pitch circle 6 are three scanning AK ₀ , AK ₁ and AK _{2 arranged} at the same angular distance from each other. The angles between adjacent scanning heads AK ₀ , AK ₁ and AK ₂ are 120 °.

On the circumference of the pitch circle 6 Further, a reference scanning AK _S at an angular distance of 360 ° / 4 = 90 ° counterclockwise from the scanning AK _{0 is} arranged.

The measured values of the scanning heads AK ₀ , AK ₁ and AK ₂ and the reference scanning head AK _S 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 up. 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 , AK ₁ and AK _{2 are} respectively read in difference from the reference scanning head AK _S , whereby measured value differences are obtained. The Referenzabtastkopfes AK _S 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 with respect to the reference scanning head AK _S.

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

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

First, the index k is decomposed in place according to Thomas and Good into an index pair (k ₀ , k ₁ ). The values of the index k are in 3 inside the circumference 9 shown in the counterclockwise direction and the values of the associated index pairs (k ₀ , k ₁ ) outside the circumference 9 , Accordingly, the values of the index n in the frequency domain and the values of the associated index pairs (n ₀ , n ₁ ) are in 4 represented on a circumference 10 shown.

The decompositions lead to the following assignment tables:

For example, Table 1 shows that the index pair (k ₀ , k ₁ ) = (3,2) and the index n = 4 represent the index pair (n ₀ , n ₁ ) = (1,0) for index k = 11. assigned. It can also be seen that the assignments are one-to-one.

über den ersten Unterteilkreis (zu dem Faktor S = 4) zu den Transformations-Koeffizienten

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

over the first sub-division (to the factor S = 4) to the transformation coefficients

This function represents a function in frequency space with respect to index n ₁ and a function in space with respect to index k ₁ .

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:

und den bekannten Zuordnungen der

zu den F_n.From this, finally, the sought division deviations f _{k are} obtained by the inverse discrete Fourier transformation

and the known assignments of

to the F _n .

Claims (10)

Method for self-calibration of a pitch circle ( 1 . 6 ) for the angle measurement of an object rotatably mounted about an axis, in which the pitch circle ( 1 . 6 ) into a number N of substantially uniform pitch intervals ( 7 ), characterized by the following steps: a) the pitch circle ( 1 . 6 ) is factor-divided into first and second subcircuits into the integer, non-divisive factors R and S, respectively, where N = R · S; b) For each division interval ( 7 ), a pitch deviation d _{k is} determined; c) the pitch deviation differences d _k are transformed from the spatial domain into the frequency domain with respect to the first subcircuit; d) The transformation result becomes transformation coefficients

calculated from pitch deviations f _k with respect to the first sub-pitch circle; e) The transformation coefficients

the pitch deviations f _k with respect to the first subcircuit are transformed with respect to the second subcircuit from the spatial domain into the frequency domain, whereby transformation coefficients

the pitch deviations f _k with respect to the pitch circle ( 1 . 6 ) are obtained; f) The transformation coefficients

the pitch deviations f _k with respect to the pitch circle are transformed from the frequency space to the location space, whereby the pitch deviations f _k are obtained. A method according to claim 1, characterized in that the pitch deviation differences with ei A scanning head can be determined on the pitch circle ( 1 . 6 ), wherein R circular recirculations are performed with a mutual angular distance of the scanning head of 360 ° / R and a pitch circulation with an angular distance of the scanning head of 360 ° / S with respect to one of the other circular recirculations. Method according to Claim 1, characterized in that the pitch deviation differences with R are uniform around the pitch circle ( 6 ) arranged scanning heads (AK ₀ , AK ₁ , AK ₂ ) and at least one reference scanning head (AK _S ) are determined, wherein the reference scanning head (AK _S ) at the pitch circle ( 6 ) is arranged at an angular distance of 360 ° / S from one of the scanning heads (AK ₀ , AK ₁ , AK ₂ ). Method according to one of the preceding claims, characterized in that the division intervals ( 7 ) are indexed before the factorization by an index k and after the factorization by an index pair (k ₀ , k ₁ ), for which: k = (R · R S k 0 + S · S R k 1 ) modN, 0≤k≤N-1 With k 0 = kmodS, 0≤k 0 ≤ S - 1 k 1 = kmodR, 0≤k 1 ≤ R - 1 and the equations of determination S · S R = 1modR, S R <R R · R S = 1modS, R S <P. Method according to one of the preceding claims, characterized in that the pitch deviation differences d _k from the pitch deviations f _{k are} defined by:

A method according to claim 5, characterized in that the division deviation differences d _k after factoring are represented as follows:

A 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 space:

A method according to claim 7, characterized in that the transformation coefficients of the pitch deviations f _k with respect to the first sub-pitch circle are defined as follows:

A method according to claim 8, characterized in that the transformation _{coefficients of} the pitch deviations f _{k are transformed} with respect to the first subcircuit in accordance with the following rule with respect to the second subcircuit in the frequency domain:

Device for self-calibration of a pitch circle ( 6 ) for the angular 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 , AK ₁ , AK ₂ ), a data memory and an evaluation unit.