RU2239785C2 - Method of differential measurement of deviation from roundness - Google Patents

Abstract

FIELD: measuring engineering.

SUBSTANCE: method includes measuring eccentricity and initial phase of the first order harmonic of the Fourier series, making the coordinate system corresponding to the minimum methodical error, and determining the deviation from roundness in this coordinate system.

EFFECT: enhanced accuracy of measurements.

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Description

The method relates to the field of technical measurements and can be used to measure deviations from the roundness of the surfaces of rotation of the products.

The following methods and tools have become widespread for measuring deviations from roundness (see Avdulov AN, Monitoring and evaluation of roundness of machine parts. - M .: Publishing house of standards, 1974. - P.11): exemplary spindle rotation on round gauges; differential measurement on prisms using measuring heads of small linear displacements; coordinate measurement on coordinate measuring machines (see RTM 2 N20-13-85. Methods of measuring deviations from roundness on coordinate measuring machines and devices equipped with computer technology. - M .: VNIITEMR, 1986. - 12 pp.).

The methods of measurement on circular meters with exemplary spindle rotation and coordinate measuring machines are the most accurate. However, the cost of such devices is up to $ 2 million. In addition, special measurement conditions and highly qualified staff are required. Therefore, these methods and means of measuring deviations from roundness are mainly used in laboratory conditions.

In the difference method, not the absolute values of the sought value are measured, but the difference between its successive values. However, for this method of measurement there is no analytical relationship between the measured and the desired values (see Avdulov AN Control and evaluation of roundness of machine parts. - M .: Publishing house of standards, 1974. - P.19).

In mass production in workshop conditions, the most widely used method of differential measurement on three-pin devices in the form of various combinations of prisms and measuring heads of small linear displacements that are simple to operate and quite productive (see Gebel I.D., Avrutin Yu.D., Khrolenko VF Devices for centerless measurement of non-circularity // Machine tools and instruments, 1977, No. 3. - S.24-25). However, the measurement errors on them can reach 100% deviation from roundness. This error value is due to the displacement of the center of rotation of the product (the point of intersection of the axis of rotation with the section plane) relative to its geometric center. The reproduction coefficient of the deviation value depends on the parameters of the device and the nature of the errors of the measured product.

The closest technical solution (prototype) for the totality of features to the claimed method is a differential measurement method using a patch gage interacting with the surface of a rotating product in such a way that the sensor readings correspond to deviations of the product profile (see Ya. I. Binder, I. Goeb. ., Nefedov A.I., V.N.Bakunin, V.A. Shapiro. Precision round gage // Measuring equipment, 1999, No. 8. - S.25-29).

The disadvantages of the known method of measuring overhead gage are methodological error, equal to an average of 18% (see Binder Ya.I., Gebel I.D., Nefedov A.I., V.N.Bakulin, V.A. Shapiro. Precision round gage // Measuring equipment, 1999, No. 8. - S.25-29), associated with the impossibility of taking into account the entire spectral composition of the errors in the shape of the product and the limited ability to control the parameters of multi-stage supports, as well as the complexity of the design of the device, which largely leads to a decrease in the accuracy and reliability of measurements .

The objective of the present invention is to improve the accuracy of measurements and simplify the design of measuring instruments.

The problem is achieved in that in the method of differential measurement of deviations from roundness, according to the invention, instead of stabilizing the geometric center of the rotating product, the resulting eccentricity e and the initial phase ψ of the first-order harmonic of the Fourier series are fixed, a coordinate system corresponding to the minimum methodological error is created, the value of the product error is determined r (φ) in this coordinate system by the formulas:

Where

New in the proposed method is that the measurement can be carried out directly on the processing equipment.

New in the proposed method is also that the measured product can be installed in cam, collet chucks and centers.

The technical result of the claimed invention consists in increasing the accuracy of measurements and simplifying the design of measuring instruments by introducing a coordinate system with a minimum methodological error.

Figure 1 shows the calculated measurement scheme, figure 2 is a schematic diagram of the measurement.

When measuring deviations from roundness by the difference method, it is necessary to strive to ensure that the readings of the measuring sensor are equal to the actual deviations of the product profile. In this case, the deviation from roundness δ represents the maximum value of the difference of the sensor readings:

δ = max {Δ r _i }.

If during the measurement process the geometric center of the product O ’does not coincide with the center of rotation O (eccentricity appears), then it becomes impossible to determine the deviation from roundness in this way.

The way to solve this problem was proposed in the work: Lyandon Yu.N. Fundamentals of interchangeability in mechanical engineering. - M .: Mashgiz, 1951. - P.26. It was shown that when describing the product profile by the Fourier series, the first term of the expansion depends only on the choice of the pole of the polar coordinate system and is an eccentricity. However, this conclusion was obtained approximately without estimating the error.

We calculate the error of replacing the circle eccentrically located relative to the origin of the polar coordinate system with the first-order harmonic of the Fourier series. The estimate is carried out in the form of the integral Ф of the square of the difference of the first-order harmonic equations r ₁ (φ) and the eccentrically located circle r ₂ (φ).

First-order harmonic equation:

where r ₀ is the radius of the middle circle;

e is the harmonic amplitude (in this case, corresponds to the eccentricity value);

ψ is the initial phase of the harmonic.

Eccentric Circle Equation:

The difference in the origin of the polar angle for the circle φ ’and the harmonic φ does not matter, since integration over a period of 2π leads to the same results.

Then we have

Thus, the error in replacing the eccentric circle with a first-order harmonic of the Fourier series is commensurate with the magnitude of the eccentricity itself, which is unsatisfactory.

Obviously, the first-order harmonic not only does not coincide with the eccentrically located circle, but also does not correspond to the best approximation by the principle of least squares. Although the direction of the eccentricity is uniquely determined by the initial phase ψ of the harmonic.

We calculate the eccentricity e corresponding to the principle of best approximation of the curves by the least squares method.

The first two harmonics of the full Fourier series are as follows:

r ₁ (φ) = r ₀ + a sin sin + b cos cos.

The coefficients of the Fourier series r ₀ , a, b for harmonics of zero and first order are determined by the Bessel formulas (see Serebrennikov MG Harmonic analysis. - M .: Gostekhizdat, 1948. - 504 p.):

where r _i is the radius of the i-th measured point of the part profile;

φ _i is the polar angle of the i-th measured point of the part profile.

From the conditions {r ₁ (φ) -r ₂ (φ)} ² → min after the transformations, we obtain the following expression for the eccentricity value:

Thus, when measuring the product profile with the eccentric location of its geometric center relative to the origin of the polar coordinate system, the desired error value will be equal to

Where

Claims (4)

1. The method of differential measurement of deviation from roundness, namely, that the product is installed, it is rotated relative to the measuring sensor and the product shape error is measured, characterized in that the resulting eccentricity e and the initial phase ψ of the first-order harmonic of the Fourier series are fixed, a coordinate system is created corresponding to the minimum methodological error, determine the value of the error in the shape of the product in this coordinate system. 2. The method according to claim 1, characterized in that the eccentricity e, the initial phase ψ of the first-order harmonic of the Fourier series and the value of the error in the shape of the product r (φ) are calculated by the formulas

Where

r ₀ , a, b are the coefficients of the Fourier series for harmonics of zero and first order, respectively. 3. The method according to claim 1 or 2, characterized in that the measurement can be carried out directly on the processing equipment. 4. The method according to claim 1 or 2, characterized in that the measured product can be installed in cam chucks, as well as in centers.

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