JPH06147879A - Measuring method of cylindrical profile - Google Patents

Abstract

PURPOSE:To provide a method for measuring cylindrical profile highly accurately with improved operability which is applicable even to a large heavy weight object. CONSTITUTION:Three displacement detectors 31, 32, 33 for measuring surface irregularities are arranged, while opposing to the outer periphery of an object 11 to be measured, on a fixing table 23 installed reciprocally in the direction substantially parallel with the axial direction of the substantially cylindrical object 11. The fixing table 23 is then moved in the axial direction of the object 11 and the variation is measured every time when the table 23 is moved by a predetermined distance over the entire peripheral direction of the object 11. Circularity the average diameter R, and the shift of axis of the object 11 at each measuring position are then operated based on the measurements and circularities (g), average diameters, and shifts of axis at a plurality of measuring positions are evaluated three-dimensionally thus determining cylindrical profile of the object 11.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a cylindrical shape measurement for measuring the cylindrical shape of a long round workpiece such as a spindle shaft for machine tools, work rolls for rolling plate materials, rolls for printing machines, etc. Regarding the method.

[0002]

2. Description of the Related Art Long-sized workpieces such as spindle shafts for machine tools, work rolls for rolling plate materials, and rolls for printing machines are generally used in parts that greatly affect the operating accuracy of machine structures. Therefore, high precision of shape and dimension is required for the processing.

The cylindricity is an important item for the shape and accuracy of a long round processed product. This cylindricity is a three-dimensional shape accuracy that integrates the change of the average radius along the axial direction of the round workpiece, the roundness shape, and the axial misalignment of the center point. At present, a measuring device and a measuring method having operability have not been realized yet.

As a conventional cylindrical measuring device and method, for example, a three-dimensional measurement having a driving device in the three-dimensional directions of X, Y and Z and a scale for measuring the amount of movement in the three-dimensional direction. There is a method in which a measurement target is placed on a machine and a three-dimensional contour shape of the target is grasped by a scale while moving a probe. In addition, the object to be measured is placed on a substantially flat reference surface, and the amount of sag between the reference surface and the contour of the object to be measured is measured by a dial gauge, a height gauge, or the like. There is one that grasps the three-dimensional contour shape.

[0005]

However, the above-mentioned conventional cylindrical measuring devices and methods cannot be applied to a large and heavy object to be measured, and the measuring procedure is not applicable. However, there is a problem that it is complicated, the operability is not good, and high-precision measurement is difficult.

The present invention solves such a problem, and can be applied to a large and heavy object to be measured, and provides a cylindrical measuring method with improved operability and measuring accuracy. The purpose is to provide.

[0007]

A method of measuring a cylindrical shape according to the present invention for achieving the above object is provided so as to be capable of reciprocating substantially parallel to the axial direction of a measuring object having a substantially cylindrical shape. The three displacement detectors, which face the outer circumference of the object to be measured and measure the surface irregularities of the object, are mounted on a mounting base on a cross section perpendicular to the axis of the object to be measured, and their detection sensitivity directions form a predetermined angle with each other. Arranged to intersect in the vicinity of the central axis of the measurement target, move the mounting base in the axial direction of the measurement target and change the measurement target over the entire circumference in the circumferential direction for each position moved by a predetermined distance. Measure, calculate the circularity shape and average radius of the measurement object at the measurement position, the amount of axial misalignment at this measurement position from the measured value, the perfect circle at a plurality of measurement positions in the axial direction of the measurement object Degree shape, average radius, axis It is characterized in that is obtaining the cylindrical shape of the measurement object from the amount.

[0008]

[Function] In order to measure the unevenness of the surface of the object to be measured, which has a substantially cylindrical shape, the three displacement detectors arranged on the mounting base so as to face the outer circumference of the object to be measured are provided along the guide rail with the axis line of the object. Direction is moved substantially parallel to each other, and the amount of sag between the object surface and the displacement detector arrangement point is measured over the entire circumference of the object at each position moved by a predetermined distance, and the measured value is arithmetically processed. By doing so, it becomes possible to obtain the roundness shape, average radius, and axial misalignment of the target object without being affected by the deformation of the guide rail during measurement, waviness, and whirling error during rotation of the target object. It is possible to determine the cylindrical shape of the object from the circularity shape of the object, the average radius, and the amount of axial misalignment at the predetermined movement position of the table.

[0009]

Embodiments of the present invention will now be described in detail with reference to the drawings.

FIG. 1 is a sectional view of a main part of a measuring apparatus for carrying out a cylindrical measuring method according to an embodiment of the present invention, FIG. 2 is a schematic front view of the measuring apparatus, and FIG. 3 is a cylindrical object to be measured. Of the circularity measurement and average radius measurement, FIG. 4 shows the principle of measuring the axial misalignment of the cylindrical measurement object, and FIG. 5 shows the principle of measuring the cylindrical shape.

As shown in FIGS. 1 and 2, reference numeral 11 denotes a cylindrical object to be measured, which is rotatably supported in the circumferential direction by a pair of supporting jigs 12 and 13 in the axial direction and has one axial end. A rotary drive device 14 is connected to the portion so that it can be driven and rotated.

A measuring device 21 for carrying out the cylindrical shape measuring method of the present invention is arranged adjacent to the measuring object 11, and is parallel to the guide rail 22 along the axial direction of the measuring object 11. Is arranged and this guide rail 2
A displacement detector mounting base 23 is attached to the unit 2 so as to be reciprocally movable. A screw shaft 25 having a motor 24 attached to one end is engaged with the displacement detector mount 23, and the displacement detector mount 23 is driven by the motor 24 to drive the screw shaft 25.
Can be moved by rotating. Also,
An arc-shaped mounting portion 26 is integrally formed on the displacement detector mounting base 23 along the circumferential direction of the measuring object 11.
Three displacement detectors 31, 32, 33 are attached to the.

Thus, the screw shaft 2 is driven by driving the motor 24.
5 is rotated to move the three displacement detectors 31, 32, and 33 together with the displacement detector mount 23 along the axial direction of the measuring object 11. At this time, the measuring object 11 is rotated by the rotation driving device 14 at a predetermined position, and the measuring object 1 is rotated.
Surface irregularities are measured over one revolution of 1. Then, the measured values detected by the displacement detectors 31, 32, 33 are subjected to arithmetic processing to form a circular shape from the roundness shape and average radius of the measurement object 11 at each measurement position, and the amount of axial misalignment. The cylindrical shape of the measuring object 11 can be obtained.

The principle of measuring the object 11 to be measured by the above-described measuring device 21 and the procedure for calculating the measured values by the displacement detectors 31, 32 and 33 will be described below.

(1) Formulation of the cross-sectional shape of the measuring object As shown in FIG. 3, the cross-sectional shape having the axis O of the measuring object 11 as the origin, that is, the points O on the circumference If the amount of sagging is h (θ, X), then h (θ, X) can be expressed as in Equation 1 below.

## EQU1 ## h (θ, X) = R (X) + g (θ, X)

Here, R (X) is the average radius of the measuring object 11 and is expressed as such because it is a value that changes depending on the axial position X of the measuring object 11. Also, g (θ,
X) is the roundness shape of the measuring object 11 expressed as a deviation from the average radius R (X), and in general, the measuring object 1
The position θ on the circumference of 1 and the position X in the axial direction of the measuring object 11
It is expressed like this because it is a value that changes depending on and.

(2) Measured value by displacement detector The displacement of the axis O of the measuring object 11 due to deformation or waviness of the guide rail 22 of the measuring device 21 or whirling error when the measuring object 11 rotates. Detector 31,3
Consider a case where a relative displacement Er occurs between the intersection point O ′ of the sensitivity directions 2 and 33. Let τ be the angle formed by the point OO′P, and ignore the deviation of the measured point (the point on the circumference of the measuring object 11 measured by the displacement detectors 31, 32, 33) caused by the relative displacement Er. And the displacement detector 3
The measured values da, db, dc of 1, 32, and 33 are the following mathematical formula 2
Given in.

[0018]

## EQU00002 ## da = h (.theta .-. Alpha., X) + Ka + Ercos (.tau .-. Alpha.)

(3) db = h (θ, X) + Kb + Ercosτ

(4) dc = h (θ + β, X) + Kc + Ercos (τ + β)

Here, Ka, Kb, and Kc are constants determined by the disposition points (displacement amount from the point O ') of the displacement detectors 31, 32, and 33 and the electrical offset at the time of measurement, respectively. The value is invariable unless the mounting state of the displacement detectors 31, 32, 33 is changed. Also, Er
cos (τ−α), Ercosτ, Ercos (τ + β) are error components caused by the relative displacement Er, and the amount of relative displacement Er
And the direction τ.

(3) Cancellation constants of error components due to relative displacement due to load addition of measured values a = -sin β / sin (α + β), b = -sin α / sin
(Α + β) is set and a constant a, which satisfies the following equations 5 and 6,
When the combined measurement value Y (θ, X) is calculated using b, this combined measurement value Y (θ, X) is given by the following mathematical expression 7.

[Equation 5] 1 + acosα + bcosβ = 0

[Equation 6] asinα-bsinβ = 0

[0021]

Y (θ, X) = ada + db + bdc = ah (θ−α, X) + h (θ, X) + bh (θ + β, X) + aKa + Kb + bKc + aErcos (τ−α) + Ercos (τ) + bcos (τ + β) = (1 + a + b) ) R (X) + {ag (θ−α, X) + g (θ, X) + bg (θ + β, X)} + (aKa + Kb + bKc)

As can be seen from the equation (7), the combined measured value Y (θ, X) does not include a term relating to the relative displacement Er, and the error due to the relative displacement Er is canceled each time by the load calculation of the measured value. I understand that

(4) Measurement of the circularity shape of the object to be measured Composite measurement value Y obtained over one revolution of the object to be measured 11
In the method and procedure for obtaining the roundness shape of the measurement object 11 from (θ, X), the roundness shape g (θ, X) expressed by the above-mentioned mathematical expression 1 is the sum of Fourier series as shown in the following mathematical expression 8. It is expressed in the form of. Each term in the Fourier series is actually the axial position X.
However, since it is a simple function here, X is omitted.

[0024]

[Equation 8]

Here, C _j and ψ _j are the amplitude and phase shift of the j-th order component of the roundness shape, respectively. Fourier series 1
The next component (j = 1) is a component resulting from axial misalignment of the cross-sectional shape, and if the point O is the least square center of the cross-sectional shape, then C _j
Since = 0, it is represented by the sum of series from j = 2 in Expression 8. Then, by using this formula 8, the combined measurement value Y (θ, X), that is, formula 7, can be expressed as the following formula 9. Note that f _j and δ _j are constants that are determined only by the angles α and β, and are given by the following mathematical formulas 10 and 11.

[0026]

[Equation 9]

[0027]

[Equation 10]

[0028]

[Equation 11]

Then, the AC component of the data string of the combined measurement value Y (θ, X) obtained over one revolution of the measurement object 11,
That is, when the third term of the equation 9 is represented by the sum of Fourier series as the following equation 12, the equation 1
The coefficients F _j and G _{j in} 2 are represented by the mathematical expressions 13 and 14. Then, using the coefficients F _j and G _j , the roundness shape g
(Θ, X) is calculated by each equation 15.

[0030]

[Equation 12]

[0031]

Equation 13] _{F j = f j C j (} cosψ j cosδ j -sinψ j sinδ j)

[0032]

Equation 14] _{G j = -f j C j (} sinψ j cosδ j -cosψ j sinδ j)

[0033]

[Equation 15]

That is, it is possible to obtain the roundness shape g (θ, X) at the axial position X of the object to be measured 11 by the following procedure, and moreover, this is the deformation of the guide rail 22, waviness, and measurement. It is a true roundness shape that is not affected by measurement errors caused by mechanical system defects such as axial misalignment and whirling of the object 11.

The displacement detectors 31, 32, and 33 measure the amount of sag between the surface of the object and the disposition points of the displacement detectors 31, 32, and 33 over one rotation of the measurement target 11 (described above ( See 1) and (2)). In this measurement, the displacement detector is rotated at a uniform rotation interval of, for example, 256 points per rotation of the measurement object 11 based on a pulse signal from a rotary encoder (not shown) that rotates at a constant rotation ratio with the measurement object 11. This can be done by sampling 31, 32, 33 measurements.

Displacement detectors 31, 3 for each rotational position
The measured values at 2 and 33 are weighted and the combined measured value Y (θ,
X) is obtained (see (3) described above).

The AC component of the signal sequence of the synthetic measurement value Y (θ, X) (for example, the data sequence consisting of 256 synthetic measurement values Y (θ, X)) obtained over one rotation of the measurement object 11 is Fourier-transformed. After conversion, the coefficient F of its cos and sin components
_j, circularity from equation 15 described above seeking G _j of shape g
Find (θ, X).

(5) Measurement of Change in Average Radius of Object to be Measured As can be seen from the equation (7), the combined measured value Y (θ,
In (X), a term (1 + a + b) R (X) relating to the average radius R (X) at the axial position X of the measuring object 11 and a constant term (aKa + Kb + bKc) determined by the setting conditions of the displacement detectors 31, 32, 33. And the term for roundness shape {a
g (θ-α, X) + g (θ, X) + bg (θ + β,
X)} and are included.

Here, as shown in FIG. 3, the roundness shape g
From the definition of (θ, X), the average value of this circularity shape g (θ, X) is 0 over the entire circumference of the measurement object 11,
The average value of the data sequence of the combined measurement values Y (θ, X) obtained by sampling the measurement object 11 sufficiently finely (actually, about 64 to 128 electric currents) is given by
Given in.

[0040]

[Equation 16]

[0041] Thus, X = X average value of the composite measurements at positions _i and X = X average at the position of X _j using the difference between the average value of the composite measurement at the position of _j radius R ( difference ΔR between the mean radius R (X _i) at the position of X _j) and X _i is given by the following equation 17.

[0042]

[Equation 17]

That is, it is possible to obtain the difference between the average radii at the axial positions X _i and X _j of the measuring object 11 by the following procedure, and this is due to the deformation of the guide rail 22 and the waviness, the measuring object 11 It is the amount of change in the true average radius that is not affected by measurement errors caused by mechanical system defects such as axial misalignment and whirling.

The synthetic measurement value Y (θ, X) is obtained by the same procedure as in the above-mentioned item 4 and. The average value of the combined measurement values Y (θ, X) obtained over one revolution of the measurement object 11 is obtained. Various axial positions X _i , X _j , X of the measuring object 11
_If the average value at _k ... Is found, the axial positions X _i and X _j
The average radius difference ΔR _ij in X _i and X _k is the average radius difference ΔR _ik in X _i and X _k .

(6) Measurement of the amount of axial misalignment of the object to be measured When the object to be measured is rotated once, the amount of misalignment between the center of the object to be measured 11 and the center of rotation, that is, the amount of axial misalignment, is well known. A known method (radius method) will be described.

As shown in FIG. 4, when the displacement is from the center O ″ of the cross-sectional shape of the object 11 to be measured at the axial position X by the distance e and the direction φ, (e, φ) is the amount of axial misalignment. be called. When the deviation of the measured point due to the axis deviation is ignored, Δl shown in FIG. 4 and g (θ, X) shown in FIG. 3 are equal, and therefore Σ | from the definition of g (θ, X). g (θ, X)
| Circle, such as ² to the minimum, that is, circle, such as the ΣΔl ² to a minimum is the most probable average circle (least-squares center circle)
Becomes Therefore, (e, φ) that minimizes ΣΔl ² is the amount of axial misalignment.

(E, φ) can be obtained by the following procedure. Generally, R (X) >> e, and the following formula 18 is established.

[0048]

[Equation 18]

Therefore, ΣΔl ² is given by the following mathematical formula 19, and as a relation of e and φ that minimizes ΣΔl ² , the following is obtained from the condition of ∂ΣΔl ² / ∂e = 0 and ∂ΣΔl ² / ∂φ = 0. Equations 20 and 21 are obtained.

[0050]

[Formula 19]

[0051]

[Equation 20]

[0052]

[Equation 21]

Therefore, in FIG. 4, the axial deviations x, y
Is given by x = ecosφ, y = esinφ, and when expressed in a discrete system, the measurement value r at the displacement detector 32 is multiplied by cos θ, sin θ obtained from the rotation angle θ of the object, and the following formula 22,
Given in 23.

[0054]

[Equation 22]

[0055]

[Equation 23]

Here, n is the number of accumulated data. That is, the axial misalignment amount (e, φ) or (x, y) at the axial measurement position X of the measuring object 11 measured by the following procedure is obtained. Here, in the evaluation of the amount of axial misalignment, a measurement error due to whirling of the rotation center O ″ is mixed, but the process of adding the measurement values of the measurement object 11 over one rotation, that is, the above-mentioned mathematical expression 22 and 23, the influence is suppressed in the process of obtaining the integrated value of the measured value × cos θ and the measured value × sin θ.

The measurement target 11 rotates once over one rotation.
The values measured by the displacement detectors 32 and rcosθ and rsinθ determined from the rotation angle θ of the measurement object 11 are integrated. Formula 2 described above from the integrated value and the integrated data number n
2, 23 is used to obtain the amount of axial deviation.

As described above, the circularity shape and the axial misalignment amount at the axial position X of the measuring object 11 can be obtained by the methods and procedures as shown in (1) to (6), and the axial position X can be obtained. The difference ΔR _ij between the average radius R (X) at _i and X _j can be obtained.

Next, a procedure for obtaining the cylindrical shape of the measuring object 11 from these various measurement results at a plurality of axial positions X _i , X _j , X _k, ... Of the measuring object 11 will be described. As shown in FIG. 5, 41 is a straight line indicating an average rotation center axis when the measurement object 11 makes one rotation, and 51, 5
2, 53, 54 are axial positions X _i , X _j ,
The circularity shape, the average radius, and the amount of axial misalignment of the measurement object 11 at X _k and X _l are shown. In addition, the average radius is the average radius at the position of X = X _i , which is R (unknown value).
_Is shown as a reference, and the differences ΔR _ij , ΔR _ik , and ΔR _il from the reference are shown. The cylindrical shape of the measuring object 11 can be obtained by three-dimensionally evaluating these values and shapes.

Generally, when evaluating a cylindrical shape,
Not the average radius R of the cylinder, but the change amounts ΔR _ij and ΔR
_{Since ik} and ΔR _il are problematic, the cylindrical shape can be evaluated by the method of the present embodiment. However, when it is absolutely necessary to set an actual value for R, for example, the position of X = X ₀ The average radius as a reference is set in _advance , and ΔR _0i , ΔR _0j , ΔR _0k ...

[0061]

As described above in detail with reference to the embodiments, according to the cylindrical measuring method of the present invention, it is possible to reciprocate substantially parallel to the axial direction of the measuring object having a substantially cylindrical shape. Three displacement detectors, which face the outer circumference of the object to be measured and measure the surface irregularities, are mounted on the mounting base on the cross section perpendicular to the axis of the object, and their detection sensitivity directions form a predetermined angle with each other. Are arranged so as to intersect with each other in the vicinity of the central axis of the measuring object, and the mounting table is moved in the axial direction of the measuring object for each position moved by a predetermined distance to the surface of the measuring object over the entire circumference in the circumferential direction. Deformation or waviness of the guide rail during measurement, or measurement is performed by measuring the change in the amount of sag with respect to the displacement detector arrangement point and adding the load using the coefficient determined by the displacement detector arrangement angle. The axis of the object And the roundness shape of the measurement object at the measurement position by obtaining the measurement value including the average radius and roundness shape of the measurement object that is not subject to errors such as whirling and The change in the radial dimension of the measuring object in the axial direction can be obtained, and further, one displacement detector among the three displacement detectors can be used to obtain a measurement value including the axial displacement of the measuring subject, By performing arithmetic processing on this measurement value, it is possible to obtain the amount of axial misalignment of the measurement target at the measurement position where the influence of whirling error of the measurement target at the time of measurement is suppressed. By obtaining the circularity shape, average radius, and amount of axial misalignment at multiple measurement positions in the axial direction, the cylindrical shape of the measurement object can be increased with a relatively simple device configuration that includes various mechanical system defects. The accuracy can be set.

[Brief description of drawings]

FIG. 1 is a cross-sectional view of a main part of a measuring device for carrying out a cylindrical shape measuring method according to an embodiment of the present invention.

FIG. 2 is a schematic front view of a measuring device.

FIG. 3 is an explanatory diagram showing the principle of circularity measurement and average radius measurement of a cylindrical measurement object.

FIG. 4 is an explanatory diagram showing the principle of measuring the axial misalignment of a cylindrical measurement object.

FIG. 5 is an explanatory diagram showing the principle of cylindrical shape measurement.

[Explanation of symbols]

 11 Measurement Target 21 Measuring Device 22 Guide Rail 23 Displacement Detector Mounting Base 31, 32, 33 Displacement Detector

Claims (1)

[Claims] 1. A mounting base provided to be capable of reciprocating substantially parallel to the axial direction of an object to be measured having a substantially cylindrical shape and facing the outer periphery of the object to be measured to measure surface irregularities thereof. Displacement detectors are arranged on a cross section perpendicular to the axis of the object to be measured, and the detection sensitivity directions are arranged so as to intersect each other in the vicinity of the central axis of the object to be measured at a predetermined angle, and the mounting base is the object to be measured. Of the circularity shape of the measurement object at the measurement position by calculating the change from the measured value at each position moved in the axial direction of the measurement object for each position moved by the predetermined distance. And the average radius, the amount of axial misalignment is obtained, and the roundness shape and the average radius at a plurality of measurement positions in the axial direction of the object to be measured and the cylindrical shape of the object to be measured are obtained from the amount of axial misalignment. Characteristic cylindrical shape measurement Method.