JPH06317431A - Method for calibrating encoder - Google Patents

Abstract

PURPOSE:To calibrate a linear scale or rotary encoder to be evaluated without using any reference linear scale nor rotary encoder which is one-rank higher in accuracy than the linear scale or rotary encoder to be evaluated. CONSTITUTION:Three linear scale signal reproducing heads 3A, 3B, and 3C which measure the relative moving amount of a mounting table 5 against a linear scale 1 by reproducing the signal of the scale 1 are arranged on the mounting table 5 at intervals La and Lb in the relative moving direction of the table 5 against the scale 1. The cumulative pitch error of the scale 1 is found from measured values within a prescribed moving extent by successively moving the table 5 against the scale 1 and obtaining the measured values of the heads 3A, 3B, and 3C at each moving distance.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for calibrating an encoder, and more particularly, it is relatively easy to determine the cumulative pitch error of a linear scale which is a type of movement detector or a rotary encoder which is a type of rotation angle detector. The present invention relates to an improvement for measuring by measurement work and simple arithmetic processing. However, the encoder is a general term for the linear scale and the rotary encoder.

[0002]

2. Description of the Related Art In recent years, the demand for linear scales and rotary encoders has increased, and encoders with higher precision and higher resolution have been developed. In order to develop a high-precision encoder, (1) technology for producing a basic scale with high accuracy, and at the same time, (2) technology for evaluating the accuracy of the completed encoder with high accuracy are essential. is there. A conventional encoder accuracy evaluation method will be described with reference to FIG. 3 by taking accuracy measurement of a linear scale as an example.

In FIG. 3, 1 is a linear scale to be evaluated (hereinafter referred to as an evaluation linear scale), 2
Is a high-precision linear scale serving as a reference (hereinafter referred to as a reference linear scale), and both are arranged substantially in parallel. 3 and 4 are heads for reproducing the linear scale signal, one head 3 is arranged to reproduce the signal of the linear scale 1 to be evaluated, and the other head 4 reproduces the signal of the reference linear scale 2. It is arranged.
Reference numeral 5 denotes a mount for the heads 3 and 4, which is installed along a guide surface (not shown) so as to be reciprocally movable substantially parallel to the graduation direction of the linear scales 1 and 2. For simplicity, the signal processing for processing and displaying the detection signals of the heads 3 and 4 and the display unit are omitted.

With the configuration shown in FIG. 3, the accuracy of the linear scale 1 to be evaluated, that is, the accumulated pitch error is grasped by the following procedure. (1) First, the mount 5 is moved to the measurement start position (origin), and the measurement values of the heads 3 and 4 are set to zero. (2) Next, the mount 5 is sequentially moved to move each moving distance X _i.
The measured value S of the head 3 at (i = 1, 2, ..., N)
(X _i , 3) and the measured value S (X _i , 4) of the head 4 are obtained. Here, as the movement distance X _i , for example, the measurement value S (X _i , 4) of the reference linear scale 2 by the head 4 is adopted. (3) From these measured values, the accuracy δ (X _i ) of the evaluation target linear scale 1 at each moving distance X _i is obtained by the equation 1 with the reference linear scale 2 being positive. However, i =
1, 2, 3, ..., N.

[0005]

## EQU1 ## δ (X _i ) = S (X _i , 3) -S (X _i , 4)

[0006]

As can be seen from the description with reference to FIG. 3, as a conventional encoder accuracy evaluation method, an encoder to be evaluated and a reference encoder which is one step more accurate than this are compared and measured. Although the method has been implemented, the recent required accuracy of the encoder is 0.1μ in length.
Since m or the angle is increased to about 0.1 seconds, it is not easy to secure a reference encoder that is one step more accurate than this and to realize highly accurate comparative measurement.

In view of the above-mentioned problems of the prior art, the present invention uses a relatively easy measuring operation and a simple arithmetic process.
It is an object of the present invention to provide a calibration method capable of highly accurately evaluating the accuracy of an encoder without the aid of another highly accurate encoder serving as a reference.

[0008]

A method for calibrating an encoder according to a first aspect of the present invention, which achieves the above object, is a linear scale for detecting a linear movement amount. The linear scale and the linear scale signal reproduction are provided. And a mounting base of a head for movement are provided so as to be relatively movable substantially parallel to the scale direction of the linear scale, and a signal of the linear scale is reproduced to measure a relative movement amount between the mounting base and the linear scale. The linear scale signal reproducing heads are arranged on the mounting table with a space therebetween in the relative movement direction of the mounting table and the linear scale, and the mounting table and the linear scale are sequentially moved relative to each other, and at each moving distance. It is characterized in that the measured values of three heads are obtained and the cumulative pitch error of the linear scale is obtained by calculation from the measured values over a predetermined moving range.

The encoder calibration method according to a second aspect of the present invention relates to a rotary encoder for detecting a rotation angle, wherein a rotary encoder and a mount for the rotary encoder signal reproducing head are provided on the rotary encoder scale. On the mount, three rotary encoder signal reproducing heads, which are provided so as to be relatively rotatable substantially coaxially with each other in a direction, reproduce the signal of the rotary encoder to measure the relative rotation angle between the mount and the rotary encoder. The mount and the rotary encoder are arranged at an angle relative to each other in a relative rotation direction, and the mount and the rotary encoder are sequentially rotated relative to each other to obtain measured values of the three heads at each rotation angle, and a predetermined value is obtained. It is characterized in that the cumulative pitch error of the rotary encoder is obtained from the measurement value over the rotation range.

[0010]

According to the first aspect of the present invention, the measurement values of the three heads obtained over the entire measurement range of the linear scale, for example, are arithmetically processed to perform comparative measurement with another high-precision linear scale serving as a reference. Without this, the cumulative pitch error of the linear scale to be evaluated can be obtained.

According to the second aspect of the present invention, the measurement values of the three heads of the rotary encoder obtained over one rotation, for example, are arithmetically processed to perform comparative measurement with another highly accurate rotary encoder serving as a reference. Instead, the cumulative pitch error of the rotary encoder to be evaluated can be obtained.

[0012]

Embodiments of the present invention will be described below with reference to the drawings.

<Example of Linear Scale> FIG. 1
Shows an example in the case where the present invention is applied to the accuracy measurement of a linear scale, and 1 is a linear scale to be evaluated, 3A,
3B and 3C are linear scale signal reproducing heads, and 5 is a head mount. In the present embodiment, for simplicity, the linear scale 1 is fixed, and the head mount 5 is reciprocally moved along a guide surface (not shown) substantially parallel to the scale direction of the linear scale 1 (left-right direction indicated by an arrow in FIG. 1). It is installed freely. The three heads 3A, 3B, 3C are head mounts 5 so that the signals of the linear scale 1 can be reproduced.
3A, 3C, 3B from the left, and at intervals L _b and L _a , respectively. For simplicity,
Illustration of the processing and display unit of the detection signal in each of the heads 3A, 3B, and 3C and the calculation processing unit of the measurement value is omitted.

<Measurement of amount of movement by each head 3A, 3B, 3C> Measurement value S (X _i , A) at head 3A, head 3B
Measured value S (X _i , B) at the head 3C and measured value S at the head 3C
(X _i , C) is given by Expression 2.

[0015]

## EQU2 ## S (X _i , A) = X _i + δ (X _i −L _b ) + K _A S (X _i , B) = X _i + δ (X _i + L _a ) + K _B S (X _i , C) = X _i + δ (X _i ) + K _C

In the equation 2, L _a is the distance between the heads 3C and 3B, L _b is the distance between the heads 3A and 3C, and X _i is the amount of movement of the head mount 5 from the measurement start position, which is the linear scale 1. A value indicating the upper position, δ (X _i ) is the cumulative pitch error of the linear scale 1 at the position X _i , K _A , K _B , K
_C is the offset amount of the measured values at the heads 3A, 3B and 3C, respectively. (For example, when all the measured values at the measurement start position X _i = 0 are set to zero, K _A = δ (−L _a ),
This is equivalent to setting K _B = δ (L _b ) and K _C = δ (0). )

Therefore, the head mount 5 is set at the measurement start position.
(X₀= 0) to X₁, X₂, ..., X _nSequentially moved to
The measured value S (X_i，
A), S (X_i, B), S (X_i, C) (however,
i = 1, 2, ..., N).

<Acquisition of Cumulative Pitch Error by Calculation Processing> [I] Calculation of combined measurement value by addition of weight of measurement values First, X is calculated by using constants a and b given by equation (3)._iIn
Combined measurement value Y (X_i) = A · S (X_i, B) + b ・ S
(X_i, A) + S (X_i, C) is obtained, from Equation 3
Since there is a relationship of a + b + 1 = 0, by substituting equation 2,
Combined measurement value Y (X _i) Is obtained as in Equation 4.

[0019]

[Number 3] _{a = -L b / (L a} + L b) b = -L a / (L a + L b)

[0020]

## EQU00004 ## Y ( _X.sub.i ) = a.S ( _X.sub.i , B) + b.S ( _X.sub.i , A) + S ( _X.sub.i , C) = (a + b + 1) _X.sub.i + (a.K _B + b.K) _{A + K C) + a ·} δ (X i + L a) + b · δ (X i -L b) + δ (X i) = (a · K B + b · K A + K C) + a · δ (X i + L a) _{+ b · δ (X i -L} b) + δ (X i) = K 0 + a · δ (X i + L a) + b · δ (X i -L b) + δ (X i)

Here, in the equation 4, K ₀ = a · K _B + b · K _A
+ K _C , and K ₀ is an unknown constant value determined by the setting conditions of the measurement system.

As can be seen from the equation (4), the synthetic measured value Y (X
_i), The movement amount X of the head mount 5_iTerm containing
Constant value K determined by the setting conditions of the measurement system
₀And the cumulative pitch error δ (X_i+ L
_a), Δ (X_i-L_b), Δ (X _i) Only
Remain. Of these, K₀Is the movement amount X_iMay not change
Is a constant value (DC component), and there are multiple measurement positions X_i(I
= 1, 2, ..., N) synthetic measurement values obtained from the measurement values
Data string Y (X_i) (I = 1, 2, ..., N)
The cumulative pitch of linear scale 1 is incorrect during
The difference will be included.

[II] Derivation of Cumulative Pitch Error δ (X _i ) In general, the linear scale cumulative Bitch error δ (X _i )
Can be considered in the form of the sum of Fourier series as shown in Equation 5.

[0024]

[Equation 5]

In Equation 5, L is the linear scale measurement length, C _j is the amplitude value of each order component, and ψ _j is the phase shift amount of each order component.

Therefore, by substituting the equation 4 into the equation 5, the equation 6 is obtained.

[0027]

[Equation 6]

In Equation 6, f _j = {(1 + a · cos jα + b · cos jβ) ² + (a · sin jα−b
・ Sin jβ) ² } ^1/2 , φ _j = tan ^-1 {-(a ・ sin jα-b ・ sin jβ) / (1 + a ・ cos
jα + b · cos jβ)}, α = 2πL _a / L, β = 2πL _b / L, and these are all values obtained by calculation if the measurement system is fixed.

That is, as can be seen from the above, the measured values S (X _i , A), S of the three heads 3A, 3B, 3C are measured.
(X _i , B), S (X _i , C) data sequence Y (X _i ) (i = 1, 2,
, N) is such that the amplitude of the cumulative pitch error of the linear scale 1 is enlarged by f _j and the phase is changed by φ _j .

Therefore, using the Fourier transform method,
The cumulative pitch error δ (X _i ) can be obtained from the AC component Y (X _i ) _{AC of the} synthetic measurement data string Y (X _i ) (i = 1, 2, ..., N), and the method will be described below. To do.

First, consider the AC component Y (X _i ) _AC in Eq. 6 in the form of the sum of Fourier series as in Eq. Then, the relationship between the coefficients F _j , G _{j of} the Fourier series and the above-mentioned f _j , G _j , ψ _j , φ _j is as shown in Formula 8. Therefore, the cumulative pitch error δ is calculated using the coefficients F _j and G _j.
(X _i ) can be expressed as in Expression 9.

[0032]

[Equation 7]

[0033]

Equation 8] _{F j = f j · C j} · (cosψ j · cosφ j -sinψ j · sin φ j) G j = -f j · C j · (sinψ j · cosφ j + cosψ j · sin φ j)

[0034]

[Equation 9]

The above procedure is summarized as follows. (I) The three heads 3A, 3B, 3C are arranged at intervals as shown in FIG. 1, and the measured values at the moving distance X _i given by the equation 2 while sequentially moving the head mount 5. To get (Ii) The measured values obtained in (i) above are weighted using the constants a and b given by the equation 3 to obtain a combined measured value Y (X _i ) represented by the equation 4. (iii) Next, a plurality of measurement positions X _i (i = 1, 2, ...,
Data sequence Y of synthetic measured values obtained from the measured values in n)
(X _i ) (i = 1, 2, ..., N) is obtained, and the AC component Y (X _i ) _AC is Fourier-transformed to obtain the Fourier transform coefficient F.
_{Find j} and G _j . (Iv) Finally, from the coefficients F _j and G _j obtained in (iii), the cumulative pitch error δ (X
_i ) is asked.

Since the cumulative pitch error δ (X _i ) is generally sufficiently smaller than the moving distance X _i , the head mount 5
As the moving distance X _i , for example, the measurement value S (X _i , C) at the central head 3C can be directly used. At this time, the cumulative pitch error of the linear scale 1 can be grasped with reference to the position of the head 3C.

Contrary to the above embodiment, the head mount 5 is
May be fixed, the linear scale 1 may be reciprocally installed, and the linear scale 1 may be sequentially moved for measurement.

As described above, the linear scale 1 is calibrated by measuring the cumulative pitch error δ (X _i ) of the linear scale 1.

<Example of Rotary Encoder>
FIG. 2 shows an embodiment in which the present invention is applied to accuracy measurement of a rotary encoder, 1 is a rotary encoder to be evaluated, 13A, 13B and 13C are rotary encoder signal reproducing heads respectively, and 15 is a head mount. . In this embodiment, for the sake of simplicity, the head mount 15 is fixed, and the rotary encoder 11 is mounted by a bearing (not shown) so as to be rotatable about the scale of the rotary encoder 11 (direction shown by an arrow in FIG. 2) substantially coaxially. is there. Three
The individual heads 13A, 13B, 13C are mounted on the head mount 15 so that the signals from the rotary encoder 11 can be reproduced.
It is attached in the order of 13A, 13C, 13B in the clockwise direction and at intervals β and α. For simplification, the processing and display unit of the detection signal in each of the heads 13A, 13B, and 13C, and the calculation processing unit of the measurement value are not shown.

The measurement of the head 13A <respective heads 13A, 13B, an angle measurement at _{13C> R (θ i, A} ), the measured value R of the head 13B (θ _i, B), measured at the head 13C R (θ _i , C) is given by Expression 10.

[0041]

## EQU10 ## R (θ _i , A) = θ _i + δ (θ _i −β) + K _A R (θ _i , B) = θ _i + δ (θ _i + α) + K _B R (θ _i , C) = θ _i + δ (θ _i ) + K _C

In the equation (10), α is the heads 13C and 13
B angle, β is the angle between the heads 13A and 13C, θ _i is the rotation angle of the rotary encoder 11 from the measurement start position, and δ is
(Θ _i ) is the rotary encoder 1 at the angular position θ _i
The cumulative pitch error of 1, K _A , K _B , and K _C are the offset amounts of the measured values at the heads 13A, 13B, and 13C, respectively. (For example, when all the measured values at the measurement start position θ _i = 0 are zero, K _A = δ (−α), K _B = δ
(Β) and K _C = δ (0) are equivalent. )

Therefore, the rotary encoder 11 is sequentially rotated from the measurement start position (θ ₀ = 0) to θ ₁ , θ ₂ , ..., θ _n , and the measurement value R (of each head is measured over the entire rotation range (1 rotation). θ _i , A), R (θ _i , B), R (θ _i ,
C) is obtained (however, i = 1, 2, ..., N).

<Acquisition of Cumulative Pitch Error by Computation> [I] Calculation of Combined Measured Value by Adding Weights of Measured Values First, using constants a ′ and b ′ given by the equation 11, θ
_Combined measurement value at _i Y (θ _i ) = a ′ · R (θ _i , B) +
When b ′ · R (θ _i , A) + R (θ _i , C) is obtained, the relation of a ′ + b ′ + 1 = 0 is obtained from the formula 11, and therefore the formula 2
By substituting, the composite measured value Y (θ _i ) can be obtained as in Expression 12.

[0045]

A ′ = − β / (α + β) b ′ = − α / (α + β)

[0046]

## EQU12 ## Y (θ _i ) = a'R (θ _i , B) + b'R (θ _i , A) + R (θ _i , C) = (a '+ b' + 1) X _i + (a ′ · K _B + b ′ · K _A + K _C ) + a ′ · δ (θ _i + α) + b ′ · δ (θ _i −β) + δ (θ _i ) = (a ′ · K _B + b ′ · K _A + K _C ) + A ′ · δ (θ _i + α) + b ′ · δ (θ _i −β) + δ (θ _i ) = K ₀ + a ′ · δ (θ _i + α) + b ′ · δ (θ _i −β) + δ (θ _i )

Here, in the _equation 12, K ₀ = a ′ · K _B + b ′
• K _A + K _C , and K ₀ is an unknown constant value determined by the setting conditions of the measurement system.

As can be seen from the equation (12), the synthetic measured value Y
From (θ _i ), the rotation angle θ of the rotary encoder 11
There is no term including _i, and a constant value K ₀ determined by the setting conditions of the measurement system and cumulative pitch errors δ (θ _i + α), δ (θ _i −β), δ (θ _i ) of the rotary encoder 11 are included. Only terms remain. Of these, K ₀ is a constant value (DC component) that does not change depending on the rotation angle θ _i , and is a combined measurement value obtained from measurement values at a plurality of measurement positions θ _i (i = 1, 2, ..., N). Data string Y (θ _i ) (i = 1, 2, ...,
The accumulated pitch error of the rotary encoder 11 is included in the fluctuation component (AC component) of n).

[II] Derivation of cumulative pitch error δ (θ _i ) In general, the cumulative bite error δ of the rotary encoder
(Θ _i ) can be considered by expressing it in the form of the sum of Fourier series as shown in Expression 13.

[0050]

[Equation 13]

In Equation 13, L is the rotary encoder measurement angle, C _j is the amplitude value of each order component, and ψ _j is the phase shift amount of each order component.

Then, by substituting Equation 12 into Equation 13 and rearranging, Equation 14 is obtained.

[0053]

[Equation 14]

Here, in Expression 14, f _j = {(1 + a ′ · cos jα ′ + b ′ · cos jβ ′) ² + (a ′ ·
sin jα'-b '・ sin jβ') ² } ^1/2 , φ _j = tan ^-1 {-(a '・ sin jα'-b' ・ sin jβ ') / (1
+ A ′ · cos jα ′ + b ′ · cos jβ ′)}, α ′ = 2πα / L, β ′ = 2πβ / L, which are all values obtained by calculation if the measurement system is fixed.

That is, as can be seen from the above, the measured values R (θ _i , 3) of the three heads 13A, 13B, 13C are
A), R (θ _i , B), and R (θ _i , C), the data string Y (θ _i ) (i =
1, 2, ..., N) are such that the amplitude of the cumulative pitch error of the rotary encoder 11 is enlarged by f _j and the phase is changed by φ _j .

Therefore, using the Fourier transform method,
The cumulative pitch error δ (θ _i ) can be obtained from the AC component Y (θ _i ) _{AC of the} combined measurement data string Y (θ _i ) (i = 1, 2, ..., N), and the method will be described below. To do.

First, the AC component Y (θ _i ) _AC in equation 14 is
It is considered in the form expanded to the form of the sum of Fourier series as in the equation (15). Then, the relationship between the Fourier series coefficients F _j and G _j and the above-mentioned f _j , G _j , ψ _j , and φ _j is as shown in Expression 16. Therefore, the cumulative pitch error δ (θ _i ) can be expressed by the equation 17 using the coefficients F _j and G _j .

[0058]

[Equation 15]

[0059]

Equation 16] _{F j = f j · C j} · (cosψ j · cosφ j -sinψ j · sin φ j) G j = -f j · C j · (sinψ j · cosφ j + cosψ j · sin φ j)

[0060]

[Equation 17]

The above procedure is summarized as follows. (I) The three heads 13A, 13B, 13C are arranged at an angle to each other as shown in FIG.
While rotating 1 sequentially, the measured value at the rotation angle θ _i given by the equation 10 is obtained. (Ii) mentioned above measurements obtained in (i), equation (11) at given constant a ', b' and weighted addition using, obtain the number 12 composite measurement represented by formula Y (θ _i) . (iii) Next, a plurality of measurement positions θ _i (i = 1, 2, ...,
Data sequence Y of synthetic measured values obtained from the measured values in n)
(Θ _i ) (i = 1, 2, ..., N) is obtained, the AC component Y (θ _i ) _AC is Fourier transformed, and the coefficient F of the Fourier transform is calculated.
_{Find j} and G _j . (Iv) Finally, from the coefficients F _j and G _j obtained in (iii), Equation 1
The accumulated pitch error δ of the rotary encoder 1
Find (θ _i ).

[0062] Since generally accumulated pitch error δ (θ _i) is sufficiently smaller than the rotation angle theta _i, as the rotation angle theta _i of the rotary encoder 11, for example, the measurement value R of the central head @ 13 C (theta _i , C) can be directly adopted. At this time, the cumulative pitch error of the rotary encoder 11 can be grasped with reference to the position of the head 13C.

Contrary to the above embodiment, the rotary encoder 11 may be fixed, the head mount 15 may be rotatably mounted by a bearing or the like, and the head mount 15 may be sequentially rotated for measurement. .

The rotary encoder 11 is calibrated by measuring the cumulative pitch error δ (θ _i ) of the rotary encoder 11 as described above.

[0065]

According to the present invention, when measuring and calibrating the cumulative pitch error (accuracy) of a linear scale which is a kind of movement amount detector or a rotary encoder which is a kind of rotation angle detector, It is possible to calibrate by a relatively easy measurement work and a simple arithmetic process without requiring a reference linear scale or rotary encoder that is one step more accurate than the linear scale or rotary encoder to be evaluated.

[Brief description of drawings]

FIG. 1 is a diagram showing a measuring system of a linear scale as an embodiment of the present invention.

FIG. 2 is a diagram showing a measuring system of a rotary encoder as another embodiment of the present invention.

FIG. 3 is a diagram showing a conventional example.

[Explanation of symbols]

1 Linear scale 3A, 3B, 3C Linear scale signal reproduction head 5 Head mounting base 11 Rotary encoder 13A, 13B, 13C Rotary encoder signal reproduction head 15 Head mounting base

Claims (2)

[Claims] 1. A linear scale and a mount for a head for reproducing the linear scale signal are provided so as to be relatively movable substantially parallel to a scale direction of the linear scale, and a signal from the linear scale is reproduced to be mounted on the mount. Three linear scale signal reproducing heads for measuring the relative movement amount with respect to the linear scale are arranged on the mounting base at intervals in the relative movement direction of the mounting base and the linear scale, and the mounting base and the linear scale. Are sequentially moved relative to each other to obtain the measured values of the three heads at each moving distance, and the accumulated pitch error of the linear scale is obtained by calculation from the measured values over a predetermined moving range. Method. 2. A rotary encoder and a mounting base for the rotary encoder signal reproducing head are provided so as to be relatively rotatable substantially coaxially with each other in a scale direction of the rotary encoder, and the rotary encoder is reproduced to reproduce the signal from the rotary encoder. Three rotary encoder signal reproducing heads for measuring the relative rotation angle with respect to the rotary encoder are arranged on the mounting base at an angle in the relative rotation direction of the mounting base and the rotary encoder, and the mounting base and the rotary encoder. Are sequentially rotated relative to each other to obtain the measured values of the three heads at each rotation angle, and the cumulative pitch error of the rotary encoder is obtained by calculation from the measured values over a predetermined rotation range. Method.