CN110631564A - Method for measuring inclination of cylinder with circular cross section - Google Patents
Method for measuring inclination of cylinder with circular cross section Download PDFInfo
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- CN110631564A CN110631564A CN201910878075.2A CN201910878075A CN110631564A CN 110631564 A CN110631564 A CN 110631564A CN 201910878075 A CN201910878075 A CN 201910878075A CN 110631564 A CN110631564 A CN 110631564A
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Abstract
The invention discloses a method for measuring the inclination of a cylinder with a circular section, which comprises the following steps: 1) selecting a test station A and a test station B; 2) selecting points to be measured on the top section and the bottom section of the cylinder to be measured; 3) erecting a prism-free total station at a measuring station A, taking the measuring station B as a rear viewpoint, and inputting hypothetical coordinates A (0,0,0) and B (x, 0,0) of the measuring station A and the measuring station B into the prism-free total station; 4) measuring observable points to be measured on the top cross section and the bottom cross section of the cylinder to be measured by using a prism-free total station; 5) erecting the prism-free total station to a measurement station B, and inputting the assumed coordinates A (0,0,0) and B (x, 0,0) of the measurement station A and the measurement station B into the prism-free total station; 6) measuring three-dimensional coordinates of a point to be measured which can be observed on the top cross section and the bottom cross section of the cylinder to be measured; 7) and calculating the inclination delta of the cylinder to be measured, wherein the method can measure the inclination of the cylinder.
Description
Technical Field
The invention relates to an inclination measuring method, in particular to an inclination measuring method for a cylinder with a circular section.
Background
In life, various cylindrical structures with circular cross sections can be seen everywhere, the cylindrical structures are as small as telegraph poles, street lamp supports and circular steel pipe supports with different functions, and the cylindrical structures are as large as tower barrels of wind power towers, high-rise chimneys, cylindrical monuments and the like, and whether the structures are important or not, the cylindrical structures are not expected to be inclined too much, so that visual sense defects and even potential safety hazards are caused. Therefore, the inclination of the cylinder is measured and the inclination is controlled, but the prior art has no similar method.
Disclosure of Invention
The present invention aims to overcome the disadvantages of the prior art described above and to provide a method for measuring the inclination of a cylinder with a circular cross section, which is capable of measuring the inclination of the cylinder.
In order to achieve the purpose, the method for measuring the inclination of the cylinder with the circular section comprises the following steps:
1) selecting a measuring station A and a measuring station B, wherein the distance between the measuring station A and the measuring station B and the bottom center point 01 of the cylinder to be measured is 1.5-2 times of the height of the cylinder to be measured, and the angle value of the angle A01B is more than or equal to 90 degrees, so that the measuring station A and the measuring station B can be mutually a measuring station and a rear viewpoint, and the measuring station A and the measuring station B can observe measuring points on the circumference of the cylinder to be measured 3/4;
2) selecting points to be measured on the top section and the bottom section of the cylinder to be measured, wherein each point to be measured can be observed through a measuring station A or a measuring station B, and the number of the points to be measured on the top section and the number of the points to be measured on the bottom section of the cylinder to be measured are both more than or equal to 6;
3) measuring the distance x between the measurement station A and the measurement station B, erecting a prism-free total station at the measurement station A, and inputting the assumed coordinates A (0,0,0) and B (x, 0,0) of the measurement station A and the measurement station B into the prism-free total station by using the station setting function of the prism-free total station after leveling and taking the measurement station B as a rear view point;
4) measuring observable points to be measured on the top cross section and the bottom cross section of the cylinder to be measured by using a prism-free total station, and recording three-dimensional coordinates of the observable points to be measured;
5) erecting the prism-free total station to a measurement station B, leveling, and inputting hypothetical coordinates A (0,0,0) and B (x, 0,0) of the measurement station A and the measurement station B into the prism-free total station by using a station setting function of the prism-free total station and taking the measurement station A as a rear viewpoint;
6) measuring three-dimensional coordinates of the point to be measured on the top cross section and the bottom cross section of the cylinder to be measured by using a prism-free total station at the measuring station B;
7) calculating the coordinate (X) of the circle center 01 of the cross section of the bottom of the cylinder to be measured according to the three-dimensional coordinate of the point to be measured obtained in the step 4) and the three-dimensional coordinate of the observation point obtained in the step 6)Bottom,YBottomZ) and the coordinate (X) of the center 02 of the cross section of the top of the cylinder to be measuredTop roof,YTop roof，Z)；
8) The coordinate (X) of the circle center 01 of the cross section of the bottom of the cylinder to be measured obtained in the step 7)Bottom,YBottomZ) and the coordinate (X) of the center 02 of the cross section of the top of the cylinder to be measuredTop roof,YTop roofAnd Z) calculating the inclination delta of the cylinder to be measured.
The inclination delta of the cylinder to be measured in the step 8) is as follows:
the specific operation of the step 7) is as follows:
setting a circular curve equation: f (x, y) ═ x2+ax+y2+by+c；
The points to be measured 1-n all satisfy: x is the number ofi 2+axi+yi 2+byi+c＝0，i＝1,2,3……n；
According to a transposition: axi+byi+c＝-(xi 2+yi 2)，i＝1,2,3……n；
Writing these n equations in matrix form:
let M × C ═ N, based on the least squares principle: c ═ MTM)-1MTN, the circular curve parameter [ a; b; c. C]；
The coordinates of the circle center are:
calculating the coordinate (X) of the circle center 01 of the cross section of the bottom of the cylinder body to be measured by utilizing a matlab algorithm based on a curve fitting circle center according to the three-dimensional coordinate of the point to be measured obtained in the step 4) and the three-dimensional coordinate of the observation point obtained in the step 6) in the step 7) and according to the three-dimensional coordinate of the point to be measured obtained in the step 6)Bottom,YBottomZ) and the coordinate (X) of the center 02 of the cross section of the top of the cylinder to be measuredTop roof,YTop roof，Z)。
The invention has the following beneficial effects:
during the concrete operation of the method for measuring the inclination of the cylinder with the circular section, the prism-free total station is utilized to measure the observed points to be measured on the top cross section and the bottom cross section of the cylinder to be measured at the measuring station A and the measuring station B, and the coordinate (X) of the circle center 01 of the bottom cross section of the cylinder to be measured is calculated according to the points to be measuredBottom,YBottomZ) and the coordinate (X) of the center 02 of the cross section of the top of the cylinder to be measuredTop roof,YTop roofZ) and then according to the coordinate (X) of the circle center 01 of the cross section of the bottom of the cylinder to be measuredBottom,YBottomZ) and the coordinate (X) of the center 02 of the cross section of the top of the cylinder to be measuredTop roof,YTop roofAnd Z) calculating the inclination delta of the cylinder to be measured, and the operation is convenient and simple.
Drawings
FIG. 1 is a diagram showing the relative positions of a measuring station and a cylinder to be measured according to the present invention;
FIG. 2 is a distribution diagram of points to be measured in the present invention.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings:
referring to fig. 1, the method for measuring the inclination of the cylinder with the circular section comprises the following steps:
1) selecting a measuring station A and a measuring station B, wherein the distance between the measuring station A and the measuring station B and the bottom center point 01 of the cylinder to be measured is 1.5-2 times of the height of the cylinder to be measured, and the angle value of the angle A01B is more than or equal to 90 degrees, so that the measuring station A and the measuring station B can be mutually a measuring station and a rear viewpoint, and the measuring station A and the measuring station B can observe measuring points on the circumference of the cylinder to be measured 3/4;
2) selecting points to be measured on the top section and the bottom section of the cylinder to be measured, wherein each point to be measured can be observed through a measuring station A or a measuring station B, and the number of the points to be measured on the top section and the number of the points to be measured on the bottom section of the cylinder to be measured are both more than or equal to 6;
3) measuring the distance x between the measurement station A and the measurement station B, erecting a prism-free total station at the measurement station A, and inputting the assumed coordinates A (0,0,0) and B (x, 0,0) of the measurement station A and the measurement station B into the prism-free total station by using the station setting function of the prism-free total station after leveling and taking the measurement station B as a rear view point;
4) measuring observable points to be measured on the top cross section and the bottom cross section of the cylinder to be measured by using a prism-free total station, and recording three-dimensional coordinates of the observable points to be measured;
5) erecting the prism-free total station to a measurement station B, leveling, and inputting hypothetical coordinates A (0,0,0) and B (x, 0,0) of the measurement station A and the measurement station B into the prism-free total station by using a station setting function of the prism-free total station and taking the measurement station A as a rear viewpoint;
6) measuring three-dimensional coordinates of the point to be measured on the top cross section and the bottom cross section of the cylinder to be measured by using a prism-free total station at the measuring station B;
7) calculating the coordinate (X) of the circle center 01 of the cross section of the bottom of the cylinder to be measured according to the three-dimensional coordinate of the point to be measured obtained in the step 4) and the three-dimensional coordinate of the observation point obtained in the step 6)Bottom,YBottomZ) and the coordinate (X) of the center 02 of the cross section of the top of the cylinder to be measuredTop roof,YTop roof，Z)；
8) The coordinate (X) of the circle center 01 of the cross section of the bottom of the cylinder to be measured obtained in the step 7)Bottom,YBottomZ) and the coordinate (X) of the center 02 of the cross section of the top of the cylinder to be measuredTop roof,YTop roofZ) calculating the inclination delta of the cylinder to be measured, wherein the inclination delta of the cylinder to be measured in the step 8) is as follows:
the point to be measured obtained in the step 7) according to the step 4)The three-dimensional coordinates of the observation points obtained in the step 6) and coordinates (X) of the circle center 01 of the cross section of the bottom of the cylinder to be measured are calculated by utilizing a matlab algorithm based on curve fitting circle centersBottom,YBottomZ) and the coordinate (X) of the center 02 of the cross section of the top of the cylinder to be measuredTop roof,YTop roofZ), the specific algorithm is:
setting a circular curve equation: f (x, y) ═ x2+ax+y2+by+c；
The points to be measured 1-n all satisfy: x is the number ofi 2+axi+yi 2+byi+c＝0，i＝1,2,3……n；
According to a transposition: axi+byi+c＝-(xi2+yi2)，i＝1,2,3……n；
Writing these n equations in matrix form:
let M × C ═ N, based on the least squares principle: c ═ MTM)-1MTN, the circular curve parameter [ a; b; c. C]；
The coordinates of the circle center are:
it should be noted that, during the specific operation, the coordinates of the measurement station and the rear viewpoint can be freely set, the actual coordinates are not required to be determined, the error source is reduced, and in addition, the prism-free total station is adopted to directly obtain the relative three-dimensional coordinates of the point to be measured, so that the method has good operability.
In addition, the invention adopts double-test stations for measurement, compared with a single-test station, the invention has the characteristics of wide coverage range and high precision, and simultaneously the double-test station is convenient for ensuring that all measured coordinate data are in the same coordinate system.
The invention adopts the matlab algorithm for fitting the circle center based on the least square principle to fit the circle center, fully considers the distribution state of a plurality of measured discrete coordinates, improves the reliability of the fitted circle center coordinate, and has no high requirement on the measurement precision of the measuring instrument. Through tests, the circle center coordinate obtained by fitting the matlab algorithm by using the coordinate data of the measuring point obtained by the prism-free total station with the precision within 5mm can meet the higher precision requirement.
Claims (4)
1. The method for measuring the inclination of the cylinder with the circular section is characterized by comprising the following steps of:
1) selecting a measuring station A and a measuring station B, wherein the distance between the measuring station A and the measuring station B and the bottom center point 01 of the cylinder to be measured is 1.5-2 times of the height of the cylinder to be measured, and the angle value of the angle A01B is more than or equal to 90 degrees, so that the measuring station A and the measuring station B can be mutually a measuring station and a rear viewpoint, and the measuring station A and the measuring station B can observe measuring points on the circumference of the cylinder to be measured 3/4;
2) selecting points to be measured on the top section and the bottom section of the cylinder to be measured, wherein each point to be measured can be observed through a measuring station A or a measuring station B, and the number of the points to be measured on the top section and the number of the points to be measured on the bottom section of the cylinder to be measured are both more than or equal to 6;
3) measuring the distance x between the measurement station A and the measurement station B, erecting a prism-free total station at the measurement station A, and inputting the assumed coordinates A (0,0,0) and B (x, 0,0) of the measurement station A and the measurement station B into the prism-free total station by using the station setting function of the prism-free total station after leveling and taking the measurement station B as a rear view point;
4) measuring observable points to be measured on the top cross section and the bottom cross section of the cylinder to be measured by using a prism-free total station, and recording three-dimensional coordinates of the observable points to be measured;
5) erecting the prism-free total station to a measurement station B, leveling, and inputting hypothetical coordinates A (0,0,0) and B (x, 0,0) of the measurement station A and the measurement station B into the prism-free total station by using a station setting function of the prism-free total station and taking the measurement station A as a rear viewpoint;
6) measuring three-dimensional coordinates of the point to be measured on the top cross section and the bottom cross section of the cylinder to be measured by using a prism-free total station at the measuring station B;
7) calculating the coordinate (X) of the circle center 01 of the cross section of the bottom of the cylinder to be measured according to the three-dimensional coordinate of the point to be measured obtained in the step 4) and the three-dimensional coordinate of the observation point obtained in the step 6)Bottom,YBottomZ) and the coordinate (X) of the center 02 of the cross section of the top of the cylinder to be measuredTop roof,YTop roof，Z)；
8) The coordinate (X) of the circle center 01 of the cross section of the bottom of the cylinder to be measured obtained in the step 7)Bottom,YBottomZ) and the coordinate (X) of the center 02 of the cross section of the top of the cylinder to be measuredTop roof,YTop roofAnd Z) calculating the inclination delta of the cylinder to be measured.
2. The method for measuring the inclination of the cylinder with the circular cross section according to claim 1, wherein the inclination δ of the cylinder to be measured in step 8) is as follows:
3. the inclination measurement method of a cylinder with a circular section according to claim 1, characterized in that the specific operation of step 7) is:
setting a circular curve equation: f (x, y) ═ x2+ax+y2+by+c；
The points to be measured 1-n all satisfy: x is the number ofi 2+axi+yi 2+byi+c＝0，i＝1,2,3……n；
According to a transposition: axi+byi+c＝-(xi 2+yi 2)，i＝1,2,3……n；
Writing these n equations in matrix form:
let M × C ═ N, based on the least squares principle: c ═ MTM)-1MTN, the circular curve parameter [ a; b; c. C]；
The coordinates of the circle center are:
4. the method for measuring the inclination of the cylinder with the circular section according to claim 1, wherein the coordinate (X) of the center 01 of the cross section of the bottom of the cylinder to be measured is calculated by a matlab algorithm based on a curve fitting center according to the three-dimensional coordinate of the point to be measured obtained in the step 4) and the three-dimensional coordinate of the observation point obtained in the step 6) in the step 7) according to the three-dimensional coordinate of the point to be measured and the three-dimensional coordinate of theBottom,YBottomZ) and the coordinate (X) of the center 02 of the cross section of the top of the cylinder to be measuredTop roof,YTop roof，Z)。
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| CN111578915A (en) * | 2020-04-22 | 2020-08-25 | 中国华冶科工集团有限公司 | Roadway measuring method for erecting total station at will |
| CN111982069A (en) * | 2020-09-08 | 2020-11-24 | 中冶建筑研究总院（深圳）有限公司 | Gradient measuring method |
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Application publication date: 20191231 |