CN113310477B - Method for measuring angle of two independent planes and aligning two independent planes in parallel - Google Patents

Method for measuring angle of two independent planes and aligning two independent planes in parallel Download PDF

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CN113310477B
CN113310477B CN202110592116.9A CN202110592116A CN113310477B CN 113310477 B CN113310477 B CN 113310477B CN 202110592116 A CN202110592116 A CN 202110592116A CN 113310477 B CN113310477 B CN 113310477B
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李文龙
杨静萍
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Dalian Minzu University
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C17/00Compasses; Devices for ascertaining true or magnetic north for navigation or surveying purposes
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G01B21/22Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring angles or tapers; for testing the alignment of axes
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G01B21/22Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring angles or tapers; for testing the alignment of axes
    • G01B21/24Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring angles or tapers; for testing the alignment of axes for testing alignment of axes

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Abstract

The invention discloses a method for measuring angles of two independent planes and parallelly aligning the two independent planes, which relates to the technical field of relative position adjustment and base plane parallel alignment of processing equipment, measuring devices and the like.

Description

Method for measuring angle of two independent planes and aligning two independent planes in parallel
Technical Field
The invention relates to the technical field of relative position adjustment and base plane parallel alignment of processing equipment, measuring devices and the like, in particular to a method for measuring angles of two independent planes and aligning the angles of the two independent planes of a plurality of processing or measuring coordinate systems which are independent and separately arranged.
Background
In machining and measurement, it is often necessary to ensure a strict parallelism relationship between the machining or measured plane and the tool or gauge plane, otherwise the machining or measurement accuracy is greatly affected. The existing measuring method is generally based on a collimator or a micrometer, a measuring block and the like for measurement.
The invention patent application with publication number CN107677219A realizes the rapid and accurate measurement of the parallelism through the position relationship between two autocollimation collimator and the element to be measured, and is suitable for the element needing to test the plane parallelism;
the patent application with publication number CN109974566A is a measuring tool for detecting flatness and parallelism of a flat plate, which comprises: the pressing piece plate, the dial indicator and the supporting table can be used for detecting the planeness and the parallelism of a large-thickness plane;
the above-mentioned publications solve the problems of flatness and parallelism measurement of the component and the plane of large thickness, respectively, but the parallelism measurement between a large processing/measuring device arranged separately and the plane to be processed/measured is difficult to achieve, and especially when the two planes are located at a relatively long distance, the direct alignment is more difficult and inconvenient to operate.
Disclosure of Invention
In order to solve the defects in the prior art, the invention provides the angle measurement and parallel alignment method for the two independent planes, which can measure the included angle between the two planes or align the two independent planes in parallel and solve the problem of uniform reference and alignment of a plurality of processing or measurement coordinate systems which are independent and separately arranged.
The technical scheme adopted by the invention for solving the technical problem is as follows: a method for measuring angles of two independent planes and aligning the two independent planes in parallel comprises the following steps:
s1, respectively placing a cross-shaped base with a compass on two measured planes, and establishing a natural frame { O, T, S, E } and a measured frame { O, h, m, n };
s2, establishing a spatial relationship between the measured frame and the natural frame;
s3, respectively measuring the frame angles of the two measured planes through the compasses on the two measured planes, judging whether the frame angles are equal, and if not, adjusting the cross-shaped base to enable the frame angles to be equal;
the frame angle is an included angle between an h axis of the measured frame and an SOT plane of the natural frame;
s4, horizontally placing an electronic level meter on the cross-shaped base of the two measured planes respectively, measuring an included angle between the normal lines of the two measured planes and the EOT plane of the natural frame through the electronic level meter, and judging whether the normal lines are equal to the EOT plane of the natural frame; the electronic level meter is used for measuring the included angle between the normal lines of the two measured planes and the SOT plane of the natural frame and judging whether the two are equal,
if the measured planes are not equal, the two measured planes have included angles, the two measured planes are adjusted to enable the included angle between the normal line and the EOT plane of the natural frame and the included angle between the normal line and the SOT plane of the natural frame to be equal under the condition that the angles of the two measured planes are kept equal, and the two measured planes are parallel.
Furthermore, "ten" font base, including the square base body that has thickness, be equipped with square bellying of equal area, equal height respectively in base body four corners department, the compass is located on one of them bellying, forms "ten" character form recess between four bellyings.
Further, the natural frame { O, T, S, E }, wherein O is a coordinate origin, T is a plumb line direction of the electronic level, S is a south-pointing direction of the compass, and E is an east-pointing direction of the compass;
the measured mark frame { o, h, m, n }, o is the central point of the cross-shaped groove, n is the normal direction of the measured plane, and h and m are the positive south and positive east directions of the cross-shaped groove respectively;
the two measured planes are a plane 1 and a plane 2, and the measured mark frames are respectively { o1,h1,m1,n1And { o }2,h2,m2,n2Step S2 is: by reacting O with O1Overlapping, and establishing a spatial relation between the measured mark frame and the natural mark frame of the plane 1; by reacting O with O2And (4) overlapping, and establishing the spatial relationship between the measured mark frame and the natural mark frame of the plane 2.
Further, defining:
h1the angle between the SOT plane and the surface is theta13,n1The included angle between the EOT plane and the EOT plane is theta11,n1The angle between the SOT plane and the surface is theta12;h2The angle between the SOT plane and the surface is theta23,n2The included angle between the EOT plane and the EOT plane is theta21,n2The angle between the SOT plane and the surface is theta 22
The step S3 is: by means of a compass, measure theta13And theta23And determining theta13Whether or not equal to theta23If the two measured standards are not equal, the included angle between the two measured standards and the SOT plane is different, and the cross-shaped base is adjusted to enable the angle theta of the standards to be different13=θ23
The step S4 is: an electronic level meter is arranged at the central point of the cross-shaped groove and is in the same straight line with the m axis, and theta is measured11And theta21Judging whether the two are equal, placing the electronic level meter at the central point of the cross-shaped groove and on the same straight line with the h axis, and measuring theta12And theta22And judging whether the two are equal, if so, adjusting the measured plane to keep theta13=θ23Under the condition of (a), make theta11=θ21,θ12=θ22That is to say that,let theta11=θ21、θ12=θ22And theta13=θ23And simultaneously, the two measured planes are parallel.
Further, the included angle Δ between the two measured planes is calculated by the following formula:
Figure BDA0003089644170000021
wherein: theta1Is n1Angle of angle theta with T2Is n2Angle with T, i.e. angle of two measured planes relative to the horizontal, theta1And theta2Calculated by the following formula:
Figure BDA0003089644170000031
has the advantages that: the electronic level meter and the compass installed on the cross-shaped base are utilized to establish a natural frame, on the basis, the included angle between any two planes is measured or any two planes are aligned in parallel, the problem that the parallelism measurement between a large processing/measuring device which is separately arranged and a processed/measured plane is difficult to realize is solved, the parallel alignment of two planes far away from each other can be realized, and the operation is convenient.
Drawings
FIG. 1 shows the normal n of two measured planes under the natural frame of the present invention1、n2And its corresponding angle schematic;
FIG. 2 is a schematic view of a cross-shaped base and a tested stand for mounting the compass according to the present invention;
FIG. 3 is a schematic diagram of the spatial relationship between two measured frames and a natural frame according to the present invention;
FIG. 4 is a schematic view of the electronic level of the present invention in a deployed position;
FIG. 5 is a schematic view of the mounting structure of the cross-shaped base and the precise hexahedron in embodiment 2 of the present invention;
fig. 6 is a schematic diagram of a precise hexahedral bonding surface and its baseline labels according to embodiment 2 of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in detail with reference to the accompanying drawings and specific embodiments.
Example 1
Aiming at two planes on which a compass and an electronic level are easy to place, the two planes comprise two horizontal planes, two inclined planes with any small angle relative to the horizontal plane, two inclined planes with any large angle relative to the horizontal plane, two vertical planes, two inclined planes with any small angle relative to the vertical plane and the like:
a method for measuring angles of two independent planes and aligning the angles in parallel comprises the following steps of:
(1) if the two planes are parallel, the normal lines of the two planes are parallel, and vice versa;
(2) If the two orthogonal straight lines in the two planes are correspondingly parallel, the two planes are parallel;
(3) as shown in fig. 1, whether the two normal lines are parallel or not can be determined by measuring the corresponding angles of the two measured planes under the natural frame { O, T, S, E }:
if two angles of two measured planes are equal, that is theta11=θ21And theta12=θ22Then, the two planes can be judged to be parallel;
if the two angles of the two measured planes are not equal, the two angles can be equal by adjusting the normal directions of the two measured planes, and then the two planes are parallel.
Wherein: o is the origin of coordinates, T is the plumb line direction of the electronic level, S is the true south direction of the compass, E is the true east direction of the compass, n is the normal of the plane being measured, θ1Is n1Angle of angle theta with T2Is n2Angle of angle theta with T11Is n1Angle with respect to the EOT plane, θ12Is n1Angle with respect to the SOT plane, θ21Is n2Angle with respect to the EOT plane, θ22Is n2Angle with respect to the SOT plane, Δ n1And n2Is an angle with n1、n2The included angle of the two corresponding measured planes.
The method comprises the following specific steps:
s1, respectively placing cross bases with compasses on two measured planes, and establishing natural standard frames (O, T, S, E) and measured standard frames (O, h, m, n);
as shown in FIG. 2, the cross-shaped base comprises a square base body with thickness, square protrusions with equal area and equal height are respectively arranged at four corners of the base body, a compass is arranged on one of the protrusions, and a cross-shaped groove is formed among the four protrusions.
The measured mark frame { o, h, m, n }, o is the central point of the cross-shaped groove, n is the normal direction of the measured plane, and h and m are the positive south and positive east directions of the cross-shaped groove respectively;
the two measured planes are a plane 1 and a plane 2, and the measured mark frames are respectively { o1,h1,m1,n1And { o }2,h2,m2,n2};
S2, establishing a spatial relation between the measured frame and the natural frame;
make O and O1Overlapping, and establishing a spatial relation between the measured mark frame and the natural mark frame of the plane 1; by reacting O with O2And (4) overlapping, and establishing the spatial relationship between the measured mark frame and the natural mark frame of the plane 2.
S3, measuring the angle theta of the frame through the compass13And theta23And determines theta13Whether or not equal to theta23If the two measured standards are not equal, the included angle between the two measured standards and the SOT plane is different, and the cross-shaped base is adjusted to enable the angle theta of the standards to be different13=θ23
Wherein: h is1The angle between the SOT plane and the surface is theta13,h2The angle between the SOT plane and the surface is theta23
S4, placing the electronic level meter at the central point of the cross-shaped groove and on the same straight line with the m axis, and measuring theta11And theta21Judging whether the two are equal, placing the electronic level meter at the central point of the cross-shaped groove and on the same straight line with the h axis, and measuring theta12And theta22And judging whether the two are equal, if so, determining that the two are not equalThe two measured planes have included angles, and the measured planes are adjusted to keep theta 13=θ23Under the condition of (b), make theta11=θ21,θ12=θ22I.e. let θ11=θ21、θ12=θ22And theta13=θ23And simultaneously, the two measured planes are parallel.
The included angle delta of the two measured planes is calculated by the following formula:
Figure BDA0003089644170000041
as shown in fig. 3, wherein: theta.theta.1Is n1Angle of angle theta with T2Is n2Angle with T, i.e. angle of two measured planes relative to the horizontal, theta1And theta2Calculated by the following formula:
Figure BDA0003089644170000051
when theta is11=θ12=θ21=θ22When the angle is equal to 0, the two measured planes are horizontal planes, and the included angle is 0, namely the two measured planes are parallel.
Example 2
For two planes on which a compass and an electronic level are not easy to place, taking the parallelism measurement and adjustment of two measured planes close to a vertical plane as an example:
angular measurement and parallel alignment of the near-vertical planes can be achieved by angular measurement and parallel alignment of two near-horizontal planes perpendicular thereto. This embodiment uses precision hexahedron auxiliary measurement, and the specific operations are as follows:
firstly, a certain side surface Q of the precise hexahedron is attached to a plane close to a vertical surface to be measured, and the plane to be measured is synchronously adjusted by adjusting the Q surface;
secondly, placing a cross-shaped base on the top surface P of the precise hexahedron, and enabling h-h and the base line B to form a fixed angle (generally adjusted to be parallel) as shown in figure 5;
③ through the steps in the embodiment 1, the angles of the two precise hexahedron top surfaces P1 and P2 can be measured, and the two top surfaces P1 and P2 can also be aligned in parallel;
If two top planes P1// P2 of the two precision hexahedrons are parallel, as shown in fig. 6, their corresponding base lines are parallel, i.e. B1// B2, and their corresponding normal lines are also parallel, i.e. n1// n 2; in addition, two pairs of straight lines L11 and L12, and L21 and L22 are easily found in the attached planes Q1 and Q2, and L11// n1, L21// n2, L12// B1 and L22// B2 are provided with: l11// L21, L12// L22. If two orthogonal straight lines in two planes are correspondingly parallel, the two planes are parallel, and two bonding planes Q1 and Q2 can be parallel.
Thus: the angles of the two attaching planes Q1 and Q2 can be obtained by measuring the angles of the two precise hexahedron top surfaces P1 and P2, which is equivalent to the angles of the two measured planes, and the two attaching planes Q1 and Q2 can also be aligned in parallel by aligning the two top surfaces P1 and P2, namely the two measured planes are aligned in parallel.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be able to cover the technical solutions and the inventive concepts of the present invention within the technical scope of the present invention.

Claims (3)

1. A method for measuring angles of two independent planes and aligning the two independent planes in parallel is characterized by comprising the following steps:
S1, respectively placing cross bases with compass on two measured planes, and establishing a natural frameOTSEFront and back face of a subject mark frameo, h, m, n};
The cross-shaped base comprises a square base body with thickness, square convex parts with equal area and equal height are respectively arranged at four corners of the base body, the compass is arranged on one of the convex parts, and a cross-shaped groove is formed among the four convex parts;
said natural frameOTSE},OIs a coordinate origin,TIs in the direction of the plumb line of the electronic level meter,SIs the south of the compass,EThe east-ward direction of the compass;
said measured mark holdero, h, m, n},oIs the central point of the cross-shaped groove,nis the normal direction of the measured plane,hmthe cross-shaped groove is used for righting the south and the east directions respectively;
the two measured planes are plane 1 and plane 2, and the measured mark frame is ao 1, h 1, m 1, n 1Ano 2, h 2, m 2, n 2};
S2, establishing a spatial relation between the measured frame and the natural frame;
make itOAndo 1overlapping, and establishing a spatial relation between the measured mark frame and the natural mark frame of the plane 1; make itOAndo 2overlapping, and establishing a spatial relation between the measured standard frame and the natural standard frame of the plane 2;
s3, respectively measuring the frame angles of the two measured planes through the compasses on the two measured planes, judging whether the frame angles are equal, and if not, adjusting the cross-shaped base to enable the frame angles to be equal;
The angle of the mark frame is a measured mark framehAxle and nature frameSOTThe included angle between the planes;
s4, horizontally placing an electronic level gauge on the cross-shaped base of the two measured planes respectively, and measuring the normal lines of the two measured planes and the natural frame through the electronic level gaugeEOTThe included angle between the planes is judged whether the two are equal; measuring the normal of two measured planes and natural frame by electronic level meterSOTThe included angle between the planes is judged whether the two are equal or not,
if the angles of the two measured planes are not equal, the two measured planes have included angles, and the normal line and the natural frame are adjusted under the condition that the angles of the two frames are kept equalEOTAngle between plane, normal and natural frameSOTThe included angles between the planes are equal to obtain twoThe measured planes are parallel.
2. The method for two independent plane angle measurement and parallel alignment according to claim 1, wherein:
h 1andSOTincluded angle between planes ofθ 13n 1AndEOTincluded angle between planes ofθ 11n 1AndSOTincluded angle between planes ofθ 12h 2AndSOTincluded angle between planes ofθ 23n 2AndEOTincluded angle between planes ofθ 21n 2AndSOTincluded angle between planes ofθ 22
The step S3 is: by means of a compass, measureθ 13Andθ 23and judgeθ 13Whether or not equal toθ 23If they are not equal, then two measured standards and SOTThe included angles of the planes are different, and the angle of the frame is adjusted by adjusting the cross-shaped baseθ 13=θ 23
The step S4 is: an electronic level meter is arranged at the central point of the cross-shaped groove and connected with the cross-shaped groovemThe axes are in the same straight line, measureθ 11Andθ 21and judging whether the two are equal, placing the electronic level meter at the central point of the cross-shaped groove and making it be equal tohThe axes are in the same straight line, measureθ 12Andθ 22and judging whether the two are equal, if so, adjusting the measured plane to keep the sameθ 13=θ 23Under the conditions of (1) toθ 11=θ 21θ 12=θ 22I.e. makeθ 11=θ 21θ 12=θ 22Andθ 13=θ 23and simultaneously, the two measured planes are parallel.
3. Two independent planar angle measurement and parallelism pair according to claim 2Squaring method, characterized in that the angle between two measured planesΔCalculated by the following formula:
Figure DEST_PATH_IMAGE001
wherein:θ 1is composed ofn 1AndTthe angle of,θ 2is composed ofn 2AndTthe included angle of the two measured planes is the included angle of the two measured planes relative to the horizontal plane,θ 1andθ 2calculated by the following formula:
Figure 749672DEST_PATH_IMAGE002
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Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0651230A1 (en) * 1993-11-02 1995-05-03 Thyssen De Reus B.V. Method and apparatus for measuring stairs
CN103673966A (en) * 2012-09-04 2014-03-26 东北林业大学 Method for measuring depth of parallelism of two planes
CN104697489A (en) * 2015-04-02 2015-06-10 北京天源科创风电技术有限责任公司 Plane normal azimuth angle measuring device and method and application thereof
CN108917604A (en) * 2018-07-12 2018-11-30 上海航天设备制造总厂有限公司 A kind of normal direction measuring device and its scaling method
CN111046584A (en) * 2019-12-27 2020-04-21 哈尔滨工业大学 Precise adjustment method of satellite-borne instrument and equipment

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0651230A1 (en) * 1993-11-02 1995-05-03 Thyssen De Reus B.V. Method and apparatus for measuring stairs
CN103673966A (en) * 2012-09-04 2014-03-26 东北林业大学 Method for measuring depth of parallelism of two planes
CN104697489A (en) * 2015-04-02 2015-06-10 北京天源科创风电技术有限责任公司 Plane normal azimuth angle measuring device and method and application thereof
CN108917604A (en) * 2018-07-12 2018-11-30 上海航天设备制造总厂有限公司 A kind of normal direction measuring device and its scaling method
CN111046584A (en) * 2019-12-27 2020-04-21 哈尔滨工业大学 Precise adjustment method of satellite-borne instrument and equipment

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Title
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