JPH02236410A - Method for measuring shape of curved surface symmetrical with respect to axis of revolution - Google Patents

Abstract

PURPOSE:To calculate plural fixed error elements of an arbitrary curved surface with a high precision in a short time by analyzing output data of a displacement meter moved to the measuring position on the curved surface symmetrical with respect to the axis of revolution by the multiple regression analysis method. CONSTITUTION:An X-axis table 2 and a main arm 3 are arbitrarily moved in the X-axis direction and the Y-axis direction respectively on a measuring base 1. An object 4 to be measured is fixed on the table 2 so that the curbed surface symmetrical with respect to the axis of revolution as the surface to be measured is directed to the Z axis. A displacement meter contact 5 is fixed to an electric displacement meter 6, and the displacement meter 6 is attached to a Z-axis column 7 which can be arbitrarily moved in the Z-axis direction. X-axis, Y-axis, and Z-axis driving motors 8, 9, and 10 are controlled by a numerical controller 12 to drive the table 2, the main arm 3, and the Z-axis column 7 respectively. The contact 5 is moved to the measuring position on the curved surface symmetrical with respect to the axis of revolution, and output data of the displacement meter 6 is inputted to a calculation processing device 11, and output data values are corrected with plural error factor values obtained by the multiple regression analysis method to calculate the shape error of the curved surface.

Description

[Detailed Description of the Invention] [Industrial Application Field] The present invention relates to a method for measuring the shape of a rotationally symmetrical surface such as a plastic lens mold, and in particular, a method for measuring shape errors of the surface to be measured with high precision and high efficiency. Concerning measurement methods that are suitable for measurement.

[Conventional technology]

The shape accuracy of a surface that is rotationally symmetrical is generally evaluated by measuring the cross-sectional shape of the surface to be measured that includes the axis of symmetry.

For this reason, shape measurements are carried out by aligning the measurement coordinates with the axis of symmetry of the surface to be measured and the origin, but these are not always possible due to installation errors of the object to be measured and other errors. They do not match, and therefore the measurement results include measurement errors. In the prior art, for example, Japanese Patent Application Laid-open No. 1986
-114445, the measurement data was approximated to a quadratic curve, the error of each measurement value was calculated individually, and each measurement value was corrected.

[Problem to be solved by the invention]

In the conventional technology described above, measurement error factors are calculated after the shape of the surface to be measured is approximated to a quadratic curve, so there are limitations to the shape of the surface to be measured, and it is not possible to separate the error factors individually. , there were problems such as long calculation time.

The purpose of the present invention is to calculate multiple measurement error factors for any curved surface in a short time and obtain them all at once with high accuracy, and further to obtain a lubrication error from the calculated measurement error factors. An object of the present invention is to provide a method for measuring the shape of a curved surface.

[Means to solve the problem]

In order to achieve the above object, the shape measuring means is moved to a fixed position on the rotation axis symmetrical curved surface, and the output data of the shape measuring means is analyzed by multiple regression analysis. The shape error of the curved surface is calculated by correcting each of the output data values using a plurality of error factor values. [Operation] Shape measurement of the rotation axis symmetric curved surface configured as described above. The law is
For example, the three types of error factor values that occur when attaching the object to be measured are calculated using a multiple regression method using a large amount of measurement data, so they can be calculated with high accuracy and calculated using these error factor values. The accuracy of correction of the measurement data can be significantly improved.

〔Example〕 An embodiment of the present invention will be described below with reference to FIG.

In FIG. 1, reference numeral 1 denotes a measurement stand on which an X-axis table 2 is freely movable in the X-axis direction and a main arm 3 is movable in the Y-axis direction. The object to be measured 4 is fixed on the X-axis table 2 with its rotation axis-symmetric curved surface, which is the surface to be measured, facing in the positive direction of the Z-axis. The displacement meter contact 5 is fixed to an electric displacement meter 6, and the electric displacement meter 6 is attached to a Z-axis column 7 that can be moved arbitrarily in the Z-axis direction. The X-axis percussion motor 8 is controlled by a numerical control device 12 to move the X-axis table 2. The Y-axis heel motor 9 is controlled by a numerical control device 12 to move the main arm 3 in the Y-axis direction. Z
The shaft beating motor 10 is controlled by a numerical control device 12,
Controls the Z-axis column.

The calculation processing device 11 is electrically connected to the numerical control device 12 and the electric displacement meter 6.

In this configuration, first, the outer diameter, reference plane position, etc. of the object to be measured 4 are measured to find the position of the axis of symmetry of the object to be measured. The numerical control device 12 moves the displacement meter contactor 5 within a plane including the axis of symmetry, successively measures the coordinate values of the surface to be measured, and compares the measurement results with the shape of a preset reference cross section. , this is defined as the shape error.

In the above-mentioned measurement method, the position of the axis of symmetry is determined based on the outer diameter of the object to be measured 4 and the distance from the reference plane, but in reality, the position of the axis of symmetry is determined by processing errors, errors in mounting the object to be measured 4 on the measuring machine, etc. Measurement errors occur.

FIG. 2 illustrates the occurrence of errors in the above measurements. Reference section 1 inputted in advance to the numerical control device 11
30 and the cross section 13 of the object 4 actually left to be measured, there are errors γ in the radial direction, errors d in the depth direction, angular errors φ in the axis of symmetry, etc., and in reality, the surface 13 to be measured is will be measured.

First, the shape data of the reference cross section 130 and the calculation formula for the above-mentioned error factors are input to the calculation processing device 11.

Now, the measurement procedure of the present invention, which will be explained below, will be briefly explained using the flowchart of FIG.

In FIG. 3, step I is the process of inputting the shape data of the reference cross section and the error factor calculation formula described above.

■ is the process of fixing the object to be measured 4 to the X-axis table 2, ■ is the process of measuring the outer diameter of the object to be measured 4 or the reference surface with an electric displacement meter, and ■ is the process of measuring the measurement result of ■ to the numerical control device. 12 into X, Y, Z coordinate values, from which the position of the axis of symmetry 14 is determined by the calculation processing device 11, and the process of setting the intersection 15 of the surface to be measured l3 and the axis of symmetry 14 as the measurement origin,
(2) is a process of measuring the surface to be measured 13 on a cross section including the axis of symmetry 14 by the numerical control device 12 using the electric displacement meter 6;
(2) is a process in which the calculation processing device 11 compares the measurement results in (2) with pre-input reference cross-sectional data to calculate a shape error; (2) is a process in which asymmetry and other errors of the actual measurement surface are corrected; (2) is the process of producing results.

Next, a method for calculating the above-mentioned error constraints γ, d, φ, etc. will be explained using Fig. 4. In Fig. 4, reference section 13
0, the surface to be measured when the deviation in the χ axis direction is γ is 1
31. What is the surface to be measured when the above γ, angular error φ, and depth error d exist? When expressed as χ), the surface to be measured 13
The measurement error ΔZ at the distance χ of 2 is expressed as Δ2,=Δ2■+ΔZ2+d (1) from FIG. Therefore, ΔZ1 is the error when the reference section 130 is translated by γ in the χ axis direction, and if γ is sufficiently small with respect to χ, ΔZ1 = f (χ, +γ) - f (χ,) = γf' ( χ■)...(2) It can be approximated as follows. Tazoshi? γU, +φ■■+d...(5) Tazoshi Ui=f'(χ,) ■i=f(χ1)・f'(χ,)+χ1.

In Figure 4, by setting n measurement points along the X-axis and applying the multiple regression analysis method shown in equation (6) to the measurement results, error components such as γ, φ, and d can be obtained with high accuracy. be able to.

The values of γ, φ, d, etc. calculated in this step are respectively γ. ,φ.

t ct, the above equation (6) becomes. Also, Δ
Similarly, when γ is sufficiently small with respect to χ, Z2 is approximately ΔZ, = {f(z z)・f' (z +) + z
t) sinφ --- It can be approximated as (4). If there is an error d in the depth direction, the sum of Δz1 and ΔZ2 will move in the Z-axis direction by d as a whole, so assuming that φ is sufficiently small, the sum of each error can be expressed by equations (1) to (3). It can be expressed as follows.

ΔZ r = yf' (z ,)"(f(z +)4
' (z +) + z z)φ+d. child\
γ determined by ,φ. By substituting values such as l dn into equation (5), ΔZl' shown in equation (7) can be obtained as the estimated value of the measurement error at each measurement point. ΔZ1'=Y. tL+$. Vi+d,---(7)
By subtracting this ΔZ t' from the actual measured value, the measurement error can be corrected. To describe an example of error correction according to the present invention described above, the shape of the reference cross section is expressed by equation (8) and the rotation axis symmetry plane with a radius of 14 nm is 0.
When measured at 2 rm intervals, the measurement error ΔZ1 is: , m. 1:1'C = 3.2504X10-"K
=-5.0503X10-' A4=-6.8 7 6 5 X 1 0°4A, =3
,3117399xlO゜9 A,=-3.8 9 8 4 7 2 8 X 1 0
-11A1. =-1.314145xlO-" If the present invention is not applied, the result will be as shown in FIG. 5, and if the present invention is applied, the result will be as shown in FIG. 6.

In Figure 5, there is no symmetry with respect to the axis of symmetry, and it is not possible to obtain the correct information necessary for corrective machining. On the other hand, the results of applying the present invention shown in Figure 6 have excellent symmetry and are easy to evaluate the shape accuracy. Further, the required computation time in the present invention was about 30 seconds, whereas in the case of the conventional method shown in FIG. 5, about 3 minutes were required.

〔Effect of the invention〕

According to the present invention, it is possible to accurately determine the three error components when setting the measurement origin in the shape measurement of a surface symmetric about the rotational axis, so that it is possible to significantly improve the correction accuracy of the measurement results. Since the measurement error correction calculation time that used to take 3 minutes can be shortened to 30 seconds, the effect of shortening the measurement time can also be obtained.

[Brief explanation of drawings]

Fig. 1 is a diagram showing an embodiment of the present invention, Fig. 2 is a sectional view explaining the installation error of the object to be measured, Fig. 3 is a procedure diagram of the error correction method according to the invention, and Fig. 4 is the object to be measured. FIG. 5 is a diagram illustrating the measurement error that occurs depending on the installation error of an object, FIG. 5 is a diagram showing the measurement result of shape error by the conventional method, and FIG. 6 is a diagram showing the measurement result of shape error by the present invention. . DESCRIPTION OF SYMBOLS 1... Measuring stand, 2... X-axis table, 3... Main arm, 4... Measured object, 5... Displacement 1f contact, 6... Electric displacement meter 7...・Z-axis column,
8...X-axis rotation motor, 9-y IllI shame motor, 1 0-Z IdliH movement motor, 11...
・Calculation processing device, 12... Numerical control device, 130・
...Reference cross section, 13...Measurement surface, 131...
Surface to be measured when radial deviation γ exists, 132...
131 plus the angular error φ and depth error d, 14...Axis of symmetry of the measured surface 13, 15...13 and 14
intersection. 4th heat / bad weather

Claims (1)

[Claims] 1. In a method for measuring the shape of a curved surface that is symmetrical about the rotational axis, the shape measuring means is moved to a measurement position on the curved surface, and the output data of the shape measuring means is analyzed by multiple regression analysis. A method for measuring the shape of a rotationally symmetric curved surface, characterized in that a shape error of the curved surface is calculated by correcting each of the output data values using a plurality of error factor values.