RU2592734C1 - Method of calibrating angular sensor - Google Patents

Abstract

FIELD: measuring equipment.

SUBSTANCE: invention relates to instrumentation for measurement of turning angle and angular velocity and can be used in metrology, measuring systems and control systems of various objects. Method of calibrating angular sensor involves using calibrated angular sensor and sensor selected as reference comparison, mounted on common axis of rotation. At that, change in relative position of calibrated angular sensor scale and sensor scale, selected as reference comparison is made by identical pitches Δφ = 2 π/m, where m is integer number, for each selected location scales mutual position of calibrated scale marks is measured angular sensor relative to scale marks of sensor selected as reference comparison. Measurement results are recorded since beginning of angular sensor calibrated scale mark, after making of m comparisons results relating to same stroke of calibrated angular sensor, are added and averaged on number of comparisons, m. In each of m selected comparisons, locations of spatial position of mark spatial position of beginning scale sensor selected as reference comparison is recorded, function of scale error sensor selected as reference comparison is determined, at which registered data are displaced on obtained value of scale beginning position mark of sensor selected as reference comparison, determining contribution of scale of sensor selected as reference comparison, into result of calibrated scale of calibration angular sensor developed for m comparisons, and calibration result is subtracted from calibrated angular sensor.

EFFECT: technical result is reduced uncertainty of angular sensor calibrating to 1% and duration of calibration procedure.

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Description

The proposed technical solution relates to the field of measuring equipment for measuring the angle of rotation and angular velocity and can find application in metrology, measuring systems and control systems for various objects.

A widely known method of calibrating angle sensors using reference sensors, in which the error in the conversion of the angle is many times smaller than the expected error of the calibrated sensor. In this case, any discrepancies in the obtained values of the angles, set using the reference sensor and recorded at the output of the calibration system, are unambiguously interpreted as the error of the calibrated sensor. The use of this method of calibrating angle sensors did not cause any difficulties in cases where the expected error of the calibrated sensor lay in the range from (15 ... 20) arc seconds and above. To do this, it was enough to take a sensor with a measurement error of the order of (1.5 ... 2.0) angular seconds, which is quite simple to purchase from domestic or foreign manufacturers of angle measuring devices.

It is noticeably more difficult to calibrate the angular sensors, the expected error of which should be within (1.5 ... 2.0) angular seconds. According to the requirements of the above calibration method, the error of the sensor selected as a reference should be of the order of (0.15 ... 0.2) arc second. Converters of this accuracy class are expensive, unique devices. For example, the angle sensor model RON-905 of the famous company Dr. Heidenhain (Germany) with a conversion error of ± 0.4 arc second stands on the market about 12,000 € or 780,000 rubles (in 2015 prices).

Reducing the measurement error to ± 0.2 arc second due to the use of an additional electronic unit leads to an increase in the cost of the measuring kit (in 2015 prices) up to 1,000,000 rubles.

A technical solution of the calibration procedure of angle sensors is known (see Portman V., Peschansky B. Phase-statistical method and device for high precise and high efficiency angular measurements. Precision Engineering, v. 25, 2001, p. 309), which can be used in as a reference instrument sensor, the accuracy class of which is comparable with the expected accuracy class of the calibrated device. Thanks to the phase-statistical method, the required accuracy of the calibration of angle sensors is ensured with a marked reduction in economic costs.

The essence of the phase-statistical method of calibration is that they take two scales with n strokes, one of which is calibrable, and the other is “reference”, set them on a common axis of rotation so that, on the one hand, it is possible to rotate them synchronously relative to the reading heads, and on the other hand, to be able to change their relative position. With synchronous rotation of the scales register the relative position of each stroke of one scale relative to the strokes of another scale. Here, the reference scale is indicated in quotation marks because it does not require the mandatory smallness of its own error. Both sensors can be of the same class. But the calibrated scale must have some reference point, for example, the mark of the beginning of a revolution.

The result of measuring the mutual displacement of the strokes is stored as a data file F ₁ :

in which the order of placement of the measured displacements of the strokes in phase ΔФ _{i is} tied to the mark of the beginning of the revolution of the calibrated scale. In turn, the phase shift ΔФ _i between two strokes can be represented in the form of three terms (Fig. 1):

Here the term Δφ ₀ is a constant shift of the strokes of one scale relative to the strokes of another, due to the random position of the scales when they are installed on the axis of rotation. In the future, this component, as a rule, is not taken into account, because its contribution is the same for all strokes, and for this reason it contributes only a total phase shift. The terms δφ _1i and δφ _2i are random scatter of the positions ix of the strokes of the reference and calibrated scales relative to their ideal position, respectively. δφ ₁ and δφ ₂ characterize the manufacturing quality of each of the scales used.

After the data file F _{1 is} registered, one scale is disconnected from the axis and rotate it relative to the other scale by one stroke, i.e. angle Δφ equal to:

Then repeat the cycle of measuring the displacements of the strokes of one scale relative to another. The measurement result is stored as a new data file F ₂ .

After that, the scale is shifted again by an angle Δφ and the measurement cycle is repeated. The measurement result is stored in the form of a new data file F ₃ . And so on, until one scale rotates relative to another by a whole turn. By this time, a data matrix of dimension [n × n] is formed in the memory of the processor registering the measurement results.

After the matrix is formed, the obtained data is added line by line and averaged over the number of rows of the matrix. As a result of these manipulations, a new data file F is generated.

Moreover, each element of the generated file will characterize the deviation of each stroke of the scale of the calibrated sensor relative to its ideal position. And, most importantly, the contribution of the scale error of the reference sensor in the measurement results will be minimized.

To show this, imagine each element of a new file as follows:

where i = (1 ... n) is the current number of the bar of the scale, to the beginning of the turn of which the data is “tied”, j = (1 ... m) is the current number of the phase shift of the relative position of the scales, Δφ _ref is the angular deviation of the position of the i-th bar reference raster, Δφ _mes is the angular deviation of the position of the i-th stroke of the calibrated raster. The first term of expression (4) is the average value of the contribution to the result of determining Δφ _i introduced by all n strokes of the reference raster. The second term of this expression is the average value of the contribution made by the ith stroke of the calibrated raster for n measurements. It is known from the course of mathematics that the integral over a closed loop is equal to zero if there is no singular point in the integrand. The first term in expression (4) can be replaced by an integral over a closed loop if the passage to the limit is carried out n → ∞. Therefore, the more precisely the condition n → ∞ is satisfied, the more precisely the first term of expression (4) can be replaced by an integral over a closed circuit and, accordingly, the more precisely the first term of expression (4) will be zero. Thus, the phase-statistical method, in principle, allows you to accurately measure deviations in the positions of the strokes from their ideal value.

However, this technical solution has a significant drawback: the calibration procedure is too long. For example, if a sensor is subjected to calibration with the number of strokes n = 36000, then even if 1 second is spent on a set of one data file, the measurement procedure is delayed by 10 hours, which is already a lot. In fact, it takes significantly more time to set up a single data file. Therefore, in its initial form, the phase-statistical method has not found wide application.

Another technical solution is known (see Klistorin I.F., Kiryanov V.P., Kiryanov A.V. Evaluation of the potential accuracy of angular displacement sensors with limbs made by the circular scanning method // Sensors and Systems, 2006. No. 1. C . 25-29), taken as a prototype, according to which the phase-statistical method of calibration is used in the case where the number of mutual displacements of two scales m is set significantly less than the number of strokes n in the scales used. In this case, the calibration result of the ith stroke of the calibrated raster can be represented as follows:

- текущий номер штриха второй шкалы, который сравнивается с i - штрихом первой шкалы, n - число штрихов калибруемой шкалы, m - число сдвигов эталонной шкалы относительно калибруемой.where i = (1 ... n) is the current number of the bar of the scale, to the beginning of the turn of which the data is “tied”, j = (1 ... m) is the current number of the shift in the phase of the relative position of the scales, $$j\frac{n}{m}$$

- the current number of the stroke of the second scale, which is compared with i - the stroke of the first scale, n - the number of strokes of the calibrated scale, m - the number of shifts of the reference scale relative to the calibrated.

- дестабилизирующий суммарный вклад δ от m штрихов шкалы эталонного датчика. Для реальных измерений выбирается m<<n. В этом случае равенство нулю первого слагаемого в (5) выполняется неточно. Конкретные значения δ-вклада эталонной шкалы и выбранного m зависят от метрологических характеристик шкалы датчика, используемого в качестве эталонного.Here, on the right side of expression (5), the second term - (Δ _{mes i} ) is the average value of the angular displacement of the i-th stroke of the calibrated scale relative to its true position, and the first term: $$\frac{\mathrm{one}}{m}{\displaystyle \sum _{j=\mathrm{one}}^m\Delta {\varphi }_{re{f}_{i+j\frac{n}{m}}}}$$

- the destabilizing total contribution δ from m strokes of the scale of the reference sensor. For real measurements, m << n is selected. In this case, the first term in (5) vanishes inaccurately. The specific values of the δ-contribution of the reference scale and the selected m depend on the metrological characteristics of the sensor scale used as the reference.

In this technical solution, to evaluate the accuracy of the calibration procedure, it is proposed to use a parameter called the accuracy class of the device. This refers to the device taken in the measuring circuit as a reference. The accuracy class is usually certified by the manufacturer. In addition, it was suggested that a quantitative indicator of the accuracy class be brought into correspondence with a confidence interval of 3σ, in which, with a probability of 98%, all measurement results performed with this instrument are located. Here, σ is the standard deviation of the measurement results. Considering that the final result (5) is formed by adding m random values of the error of the position of the strokes of the scale of the reference sensor, it was also suggested that the contribution from the addition of m values of the error of the selected strokes of the scale of the sensor taken as a reference be evaluated in the calibration result according to the law of adding random values to according to the following expression:

For example, for the widespread angle converter model ROD-800 in the directories of the German company Dr. Heidenhain is given an accuracy class corresponding to ± 1.0 arc second. If these values are interpreted as the boundaries of the confidence interval, then σ will lie within ± 0.33 arc second. For m = 10, the value of δ will be estimated at the level of ± 0.103 arc second, which is in good agreement with the requirements for the metrological indicators of the sensor selected as a reference in accordance with the classical methodology.

However, this set of operations characterizing the known calibration method, taken as a prototype in this application, has a noticeable disadvantage. First of all, the statement that the used m error values of the selected strokes of the sensor scale, taken as a reference, are random variables, is not entirely correct. Indeed, the absolute values of each of the m error values of the selected strokes of the sensor scale, taken as a reference, can be considered random. But during the calibration procedure from one comparison of scales to another, these values remain unchanged. Therefore, they must be considered as systematic components of the error of the spatial position of the strokes of the scale.

In general, the systematic components of the error are characterized by the spectral composition of spatial harmonics. The spectral composition of spatial harmonics uniquely characterize the shape of the error curve of each specific scale, which remains constant from experiment to experiment. With the known spectral composition of the instrumental error of the scale, selected as a reference standard, the calibration result of another scale can be estimated with higher accuracy.

A disadvantage of the known technical solution is the increased level of uncertainty in the calibration of the angle sensor.

The authors were tasked with developing a method for calibrating an angular sensor, which allows an order of magnitude reduction in the uncertainty of calibrating an angular sensor.

It is proposed to solve this problem by the fact that in the known method of calibrating an angular sensor, including the use of a calibrated angular sensor and a sensor selected as a reference standard, mounted on a common axis of rotation with the possibility of sequentially changing their relative position within a full revolution, while changing the relative position the scales of the calibrated angular sensor and the scales of the sensor selected as the reference standard are carried out in the same steps equal to Δφ = 2π / m, where m is an integer , at each selected location of the scales, the relative position of the scales of the calibrated angle sensor scale relative to the strokes of the sensor scale selected as a reference standard is measured, the measurement results are recorded from the moment the beginning mark of the scale of the calibrated angle sensor appears, after m comparisons are made, results related to the same stroke of the calibrated angle sensor, add and average over the number of comparisons m, elements of the obtained data file are used as a characteristic of spatial the deviations of the strokes of the calibrated angular sensor from their ideal positions specified in the design documentation, in addition to each of the m selected comparisons of the scale arrangements, the spatial position of the beginning mark of the sensor scale selected as a reference standard is recorded, the error function of the sensor scale selected as a reference standard is determined, by recounting the recorded data, in which the registered data is shifted by the obtained value of the position of the start mark of the sensor scale selected as a reference standard, determine the contribution of the sensor scale selected as the reference standard to the calibration result of the calibrated angle sensor scale generated in m comparisons, and subtract it from the calibration result of the calibrated angle sensor.

The technical effect of the proposed method for calibrating an angular sensor is to reduce the uncertainty of calibrating an angular sensor to 1% of the calibrated value and the duration of the calibration procedure due to the use of a small number of comparisons.

In FIG. 1 shows the phase shift ΔΦ _i between two strokes of the same scale.

In FIG. 2 shows a system for calibrating an angle sensor, where 1 is a precision spindle, 2 is a calibrated angle sensor, 3 is a reference sensor, 4 is a coupling, 5 is an electronic processing unit, 6 is a control computer.

In FIG. 3 (a) shows the error curve of a calibrated angle sensor with four read heads; (b) the spectral composition of the error curve of the calibrated angle sensor is presented.

In FIG. Figure 4 shows (a) the error curve of the ROD-800 sensor (together with the coupling), (b) the harmonic spectrum of the error curve of the ROD-800 sensor along with the coupling.

In FIG. Figure 5 shows (a) the curve of corrections to the calibration result of the angle sensor introduced by the ROD-800 sensor, (b) the harmonic spectrum of the correction curve.

In FIG. 6 shows the result of computer simulation of the contribution of the calibrated angle sensor to the result of in-house calibration: FIG. 6 (a) is a function of distortions introduced by the calibrated angle sensor into the correction curve, FIG. 6 (b) is the spectrum of harmonics of the distortion function introduced from the side of the calibrated angle sensor into the correction curve.

The inventive method of calibrating an angular sensor is implemented as follows. It is technically proposed that simultaneously with the registration of the spatial position of the strokes of the sensor scale taken as a reference standard, also register the spatial position of the mark of the beginning of the sensor scale used as a reference standard. After processing the data matrix according to a previously known algorithm and obtaining a data file characterizing the deviation of each stroke of the scale of the calibrated angle sensor relative to their ideal position, the data is reformatted, which consists in “re-linking” the measured data to the reference mark for the start of revolution of the reference scale. If in the k-th experiment the mark of the start of revolution of the reference scale coincided with the q-stroke of the scale of the calibrated angle sensor, then subtracting the coordinate of the qth stroke from each coordinate of the recorded strokes, a new row of data is obtained whose address values are “attached” to the start mark reference scale turnover. Applying this operation to each row of the original matrix, a new data matrix is obtained. In turn, applying the well-known processing algorithm to the obtained new matrix, we obtain a new file, each element of which characterizes the deviation of each stroke of the scale of the reference sensor relative to their ideal position, i.e. represents the error curve of the reference scale. By analogy with the prototype, each element of the new file can be represented as follows:

It is easy to verify that here the estimate of the deviation of each stroke of the sensor scale, taken as a reference standard, is distorted, in turn, by the contribution from m strokes of the calibrated scale.

The contribution of the scale of the reference sensor to the calibration result of the scale of the calibrated angle sensor is estimated using an additional procedure that simulates the phase-statistical calibration procedure. For this, the data array Δφ _i obtained after the first additional operation and characterizing the deviation of each stroke of the scale of the reference sensor relative to their ideal position is shifted by N / m numbers and added to the original array. Then the original array is shifted by 2N / m numbers and added to the previous addition result. Then the original array is shifted by 3N / m numbers and added up with the last addition result. And so on. Finally, the original array is shifted by (m-1) N / m numbers and added to the previous one. The resulting array is averaged over m and a new array is obtained characterizing the contribution of the scale of the reference sensor to the result of calibrating the spatial position of the strokes of the calibrated angle sensor.

In general, the result of evaluating the contribution of the scale of the reference sensor is a periodic function whose spectral composition contains only selected harmonics whose numbers are multiples of the number of shifts m. Moreover, each value of the contribution of the reference scale is distorted by the contribution from the calibrated scale participating in the experiment. This contribution is formed as a result of m real scale shifts and, in accordance with the physics of the process, is a periodic function whose spectral composition contains only selected harmonics whose numbers are also a multiple of the number of shifts m. As a result of computer simulation of the contribution of the reference scale, the contribution of the calibrated scale to the result of its own calibration does not change due to the phase coherence of the periodic function with its multiple shifts.

If now the result of computer modeling of the contribution of the reference scale is subtracted from the results of estimating the error of the spatial position of the strokes of the calibrated angle sensor, then the calibration result will be free from inaccuracy in the spatial position of the strokes of the reference sensor. But the accuracy of the calibration scale of the controlled calibrated angular sensor will still be limited by the contribution of the own high-frequency components of the harmonic spectrum, which “screen” the process of their compensation.

The technical effect of the proposed method for calibrating an angular sensor, consisting in reducing (by an order of magnitude) the uncertainty of calibration of an angular sensor, we evaluate the following example. Let the task be set to calibrate the angular sensor of the built-in type used in the angle measuring machine created on the basis of the aerostatic spindle. In a simplified form, the angle sensor calibration system is shown in FIG. 2. It includes: a precision spindle 1 on an aerostatic suspension, a calibrated angle sensor 2 having several read heads, a reference sensor 3, a coupling 4, an electronic processing unit 5 and a control computer 6.

For unambiguous estimates, we assume that the calibrated angle sensor 2 is made according to the built-in type photoelectric transducer based on a regular raster with 36,000 strokes and has four read heads, and the commercially available ROD-800 angular converter connected to the spindle rotor is used as a reference sensor 3 1 through the connecting sleeve 4 of the LIR-805 model. In this case, when the clutch 4 is opened, slippage is carried out from the connection side of the clutch 4 and the rotor, i.e. the coupling 4 and the angular transducer of the ROD-800 model act as a whole (i.e., they are practically an analog of the more expensive RON-905 transducer having an integrated coupling).

Let as a result of applying the phase-statistical method performed with a shear step equal to twenty-four degrees (15 shifts), we obtain a calibration curve for the calibrated angle sensor 2 with four read heads, presented in FIG. 3a. The spectral composition of the spatial harmonics of the calibration curve is shown in FIG. 3b. The cumulative error of the calibrated angle sensor 2 is ± 0.3 arc seconds. The spectrum is represented by harmonics with numbers divisible by four: 4th, 8th, 12th, etc., which is fully consistent with the theory of track averaging in angle sensors (see, for example, Ionak V.F. Kinematic control devices . - M.: Mechanical Engineering, 1981. 128 p.).

). По отношению к калибруемой шкале (накопленная погрешность шкалы равна ±0,3 угловой секунды) неопределенность калибровки составляет 28%, что представляется достаточно грубым результатом.The calibration uncertainty introduced by the ROD-800 sensor, according to (6) at 15 shifts in absolute value, will be: ± 0.085 arc second (σ = ± 0.33 arc second, $$\sqrt{\mathrm{fifteen}}=3.87$$

) Relative to the calibrated scale (accumulated scale error is ± 0.3 arc seconds), the calibration uncertainty is 28%, which seems to be a rather crude result.

The uncertainty of the calibration results can be reduced by using the proposed method for calibrating an angle sensor. To do this, we will provide for registration of the coordinates of the zero mark of the scale taken as a reference standard in each shift of the scales, and we will apply the additional operations described in this application above.

After the data is re-referenced, the row-by-row addition of the latter makes it possible to obtain the error curve of the ROD-800 sensor (together with the coupling) (Fig. 4a).

As follows from the estimation of the peak values of the obtained curve, the accumulated error of the reference sensor lies within ± 1.0 arc second (which is in good agreement with the accuracy class of this device guaranteed by the manufacturer). The spectrum of the error curve contains, in addition to the predicted harmonics that are multiples of the 4th, also “forbidden” by the theory: 1st, 2nd, 3rd, 5th, etc. harmonics. It is most likely that the “forbidden” harmonics are introduced by the coupler 4. Moreover, the 4th, 8th, etc., are “allowed” by the theory. harmonics that are directly related to the calibrated angle sensor are most significant (Fig. 4b).

The next operation of the proposed method is the determination by computer simulation of the contribution of the reference sensor to the calibration result. For this, as described above, the data array characterizing the deviation of each stroke of the scale of the reference sensor relative to their ideal position is shifted by 2400 numbers and added to the original array. Then the original array is shifted by 4800 numbers and added to the result of the previous addition. Then the original array is shifted to 7200 numbers and added to the previous result. And so on. Finally, the original array is shifted to 33600 numbers and added to the previous one. The resulting array is averaged over 15 and a new array is obtained that characterizes the contribution of the scale of the reference sensor to the result of calibrating the spatial position of the strokes of the calibrated angle sensor. The correction curve for the calibration result of the angle sensor is shown in FIG. 5 (a), the harmonic spectrum of the correction curve is shown in FIG. 5 B).

As follows from the results of the model experiment, the contribution of the reference sensor to the calibration error in absolute value reaches ± 0.047 arc seconds, which is created mainly by the 60th harmonic, but the presence of the 15th, 30th and 45th harmonics is also noticeable. In relative units, the calibration uncertainty introduced by the reference sensor, calculated from the analysis of the spectrum of the error curve of the reference sensor, is 15.6%. The resulting estimate shows that the phase-statistical method itself with a limited number of shifts provides a higher calibration quality than previously thought.

Moreover, knowledge of the specific contribution of the reference sensor to the uncertainty of the calibration of the angle sensor improves the accuracy of the method.

To do this, perform the third additional operation of the proposed method: subtracting the contribution of the reference sensor from the calibration curve. This eliminates the destabilizing contribution of the reference sensor.

But in assessing the contribution of the reference sensor, there is a contribution from the high-frequency part of the spectrum of harmonics of the error curve of the calibrated angle sensor, which limits the effectiveness of compensation of the error of calibration of the angle sensor. The residual uncertainty of the calibration of the angular sensor is created due to the fact that when subtracting these high-frequency components mask the corresponding spatial harmonics of their own measuring raster.

To assess the maximum achievable uncertainty of the calibration of the angle sensor of the angle measuring machine, we will carry out a computer simulation of the contribution from the measuring raster of the calibrated angle sensor to our own calibration. To do this, repeat the above procedure of a 15-fold shift of the error curve for the calibrated angle sensor. The result of computer simulation is shown in FIG. 6. Here in FIG. 6a shows the function of distortions introduced by the calibrated angle sensor into the correction curve; in FIG. 6b is the spectrum of harmonics of the distortion function curve. For the 15 shifts used, all harmonics are suppressed, up to the 60th. It determines the contribution from the measuring raster of the calibrated angle sensor to the error of its own calibration. This contribution from this measurement raster will not exceed ± 0.003 ". Therefore, the relative value of the calibration uncertainty of the angle sensor after subtracting the contribution of the reference sensor will be 1% of the calibrated value, which can be considered as a metrologically reliable result of the calibration of the angle sensor.

Claims (1)

A method of calibrating an angular sensor, including the use of a calibrated angular sensor and a sensor selected as a reference standard, installed on a common axis of rotation with the possibility of sequentially changing their relative position within a full revolution, while changing the relative position of the calibrated angle sensor scale and the sensor scale selected as a reference standard, carry out the same steps equal to Δφ = 2 π / m, where m is an integer, at each selected location of the scales measure mutual the position of the strokes of the scale of the calibrated angle sensor relative to the strokes of the scale of the sensor selected as the reference standard, the measurement results are recorded from the moment the start mark of the scale of the calibrated angle sensor appears, after m comparisons are performed, the results related to the same stroke of the calibrated angle sensor are added and averaged by the number of comparisons m, the elements of the obtained data file are used as a characteristic of the spatial deviation of the strokes of the calibrated angle sensor from their idea of positions specified in the design documentation, characterized in that in each of the m selected comparisons of the locations of the scales, the spatial position of the start mark of the sensor scale selected as a reference standard is additionally recorded, the error function of the sensor scale selected as a reference standard is determined by recalculating the registered data, in which the recorded data is shifted to the obtained value of the position of the mark of the beginning of the scale of the sensor selected as the reference standard, determined they take the contribution of the sensor scale selected as the reference standard to the calibration result of the calibrated angle sensor scale, formed in m comparisons, and subtract it from the calibration result of the calibrated angle sensor.

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