CN111750831A - Method for measuring inclination rate of cylinder - Google Patents
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
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Abstract
The invention provides a method for measuring the inclination rate of a cylinder. The method comprises the following steps: setting a total station, and taking a space coordinate at the top of the total station as a coordinate origin of a space coordinate system; measuring a first horizontal plane of the cylinder to be measured at a preset first height by using a total station to obtain the spatial coordinates of n points of the surface of the cylinder to be measured on the first horizontal plane; calculating the space coordinate of the center of the first horizontal plane according to the space coordinates of n points on the first horizontal plane; measuring a horizontal plane of the cylinder to be measured at a preset second height by using a total station to obtain the spatial coordinates of n points of the surface of the cylinder to be measured on the second horizontal plane; calculating the space coordinate of the center of the second horizontal plane according to the space coordinates of n points on the second horizontal plane; and calculating to obtain the inclination rate of the cylinder to be measured according to the space coordinate of the center of the first horizontal plane and the space coordinate of the center of the second horizontal plane. The invention can improve the reliability and accuracy of the measurement result.
Description
Technical Field
The application relates to the technical field of civil engineering measurement, in particular to a method for measuring inclination rate of a cylinder.
Background
The building structure column is often inclined due to uneven settlement of a foundation, self defects, horizontal thrust caused by design, load accumulation and the like. For a circular section column, the currently popular tilt rate measuring method is to measure the coordinates of three points of the column on the same horizontal plane by a total station, then fit the equation of a circle according to the measured coordinates of the three points, calculate the coordinates of the center of the circle, and determine the tilt rate of the column by the coordinates of the centers of the circle of different horizontal planes.
However, in the method for measuring the inclination rate of the cylinder in the prior art, the three selected points generally have great randomness, and when the cylinder is inclined, the horizontal section of the cylinder is elliptical rather than circular, so that the inclination rate of the cylinder finally measured according to the method generally has a large error from the inclination rate of the real situation.
Disclosure of Invention
In view of the above, the present invention provides a method for measuring the inclination rate of a cylinder, so as to improve the reliability and accuracy of the measurement result.
The technical scheme of the invention is realized as follows:
a method of measuring the slope of a cylinder, the method comprising:
setting a total station, and taking a space coordinate at the top of the total station as a coordinate origin of a space coordinate system;
measuring a first horizontal plane of the cylinder to be measured at a preset first height by using a total station to obtain the spatial coordinates of n points of the surface of the cylinder to be measured on the first horizontal plane; n is an integer greater than or equal to 5;
calculating the space coordinate of the center of the first horizontal plane according to the space coordinates of n points on the first horizontal plane;
measuring a horizontal plane of the cylinder to be measured at a preset second height by using a total station to obtain the spatial coordinates of n points of the surface of the cylinder to be measured on the second horizontal plane;
calculating the space coordinate of the center of the second horizontal plane according to the space coordinates of n points on the second horizontal plane;
and calculating to obtain the inclination rate of the cylinder to be measured according to the space coordinate of the center of the first horizontal plane and the space coordinate of the center of the second horizontal plane.
Preferably, the calculating the spatial coordinates of the center of the horizontal plane according to the spatial coordinates of the n points may include:
obtaining an ellipse formula which takes the center of a horizontal plane as the center of an ellipse according to the ellipse formula which takes the origin of coordinates as the center of the ellipse;
and respectively substituting the space coordinates of n points on the horizontal plane into an ellipse formula which takes the center of the horizontal plane as the center of the ellipse, and calculating according to the least square principle to obtain the space coordinates of the center of the ellipse.
Preferably, the coordinate of the center of the first horizontal plane is (x)0，y0，z0) The ellipse formula with the center of the first horizontal plane as the center of the ellipse is:
x2+gxy+cy2+dx+ey+f＝0；
wherein,
let the coordinate of the center of the second horizontal plane be (x)1，y1，z1) The ellipse formula with the center of the second horizontal plane as the center of the ellipse is:
x2+gxy+cy2+dx+ey+f＝0
wherein,
preferably, the inclination rate of the cylinder to be measured is calculated according to the following formula:
wherein alpha is the inclination of the cylinder to be measured.
As can be seen from the above, in the method for measuring the inclination rate of the cylinder in the present invention, the total station is used to measure the first horizontal plane at the preset first height and the horizontal plane at the preset second height of the cylinder to be measured, so as to obtain the spatial coordinates of n points on the first horizontal plane and the second horizontal plane of the surface of the cylinder to be measured, respectively, then the spatial coordinates of the center of the first horizontal plane and the center of the second horizontal plane are obtained through calculation, and finally the calculation is performed according to the spatial coordinates of the center of the first horizontal plane and the center of the second horizontal plane, so that the inclination rate of the cylinder to be measured can be accurately obtained through calculation. By using the method for measuring the inclination rate of the cylinder, the reliability and the accuracy of the measurement result can be effectively improved.
Drawings
FIG. 1 is a flow chart of a method for measuring a tilt rate of a cylinder in an embodiment of the present invention.
FIG. 2 is a first schematic diagram illustrating a method for measuring a cylinder tilt rate according to an embodiment of the present invention.
FIG. 3 is a schematic diagram of a method for measuring a cylinder tilt rate according to an embodiment of the present invention.
FIG. 4 is a third schematic diagram illustrating a method for measuring a cylinder tilt rate according to an embodiment of the present invention.
FIG. 5 is a diagram illustrating a fourth principle of a method for measuring a cylinder tilt rate according to an embodiment of the present invention.
Fig. 6 is a partial schematic view of fig. 2.
Detailed Description
In order to make the technical scheme and advantages of the invention more apparent, the invention is further described in detail with reference to the accompanying drawings and specific embodiments.
FIG. 1 is a flow chart of a method for measuring a tilt rate of a cylinder in an embodiment of the present invention.
As shown in fig. 1 to 6, the method for measuring the inclination rate of the cylinder in the embodiment of the present invention includes the following steps:
and 11, setting the total station, and taking the space coordinates at the top of the total station as the origin (0, 0, 0) of the space coordinate system.
And step 12, measuring the first horizontal plane of the cylinder to be measured at the preset first height by using a total station to obtain the spatial coordinates of n points of the surface of the cylinder to be measured on the first horizontal plane.
In this step, a total station is used to measure a first horizontal plane of the cylinder to be measured, the first horizontal plane being located at a preset first height z above the cylinder to be measured0。
The cylinder to be measured is not vertical to the ground but inclined, and the included angle alpha between the cylinder to be measured and the ground is less than 90 degrees, so that the first horizontal plane can be regarded as an ellipse in practice, and n points of the surface of the cylinder to be measured on the first horizontal plane obtained by measurement are n points on the ellipse in practice. And measuring the surface of the cylinder to be measured by a total station to obtain the space coordinates of n points on the ellipse.
Since the first horizontal plane is an ellipse, it is generally necessary to measure the spatial coordinates of several points more. Therefore, in the technical solution of the present invention, n is an integer greater than or equal to 5. For example, n may be 5 or 6, or may be another suitable value.
And step 13, calculating the space coordinate of the center of the first horizontal plane according to the space coordinates of the n points on the first horizontal plane.
After obtaining the spatial coordinates of n points on the first horizontal plane, the spatial coordinates (x) of the center of the first horizontal plane can be calculated according to the spatial coordinates of the n points0，y0，z0) I.e. the spatial coordinates of the center of the ellipse on the first horizontal plane.
And step 14, measuring the horizontal plane of the cylinder to be measured at the preset second height by using a total station to obtain the spatial coordinates of n points of the surface of the cylinder to be measured on the second horizontal plane.
In this step, a total station is further used to measure a second horizontal plane of the cylinder to be measured, so as to obtain spatial coordinates of n points on the second horizontal plane of the surface of the cylinder to be measured, where the second horizontal plane is located at a preset second height z on the cylinder to be measured1In practice, it may be regarded as an ellipse, i.e. the second horizontal plane is also an ellipse.
The specific measurement method is the same as that in step 12, and therefore, the detailed description thereof is omitted.
And step 15, calculating the space coordinate of the center of the second horizontal plane according to the space coordinates of the n points on the second horizontal plane.
After obtaining the spatial coordinates of n points on the second horizontal plane, the spatial coordinates (x) of the center of the second horizontal plane can be calculated according to the spatial coordinates of the n points1，y1，z1) I.e. the spatial coordinates of the center of the ellipse on the second horizontal plane.
The specific measurement method is the same as step 13, and therefore, the detailed description thereof is omitted.
And step 16, calculating to obtain the inclination rate of the cylinder to be measured according to the space coordinate of the center of the first horizontal plane and the space coordinate of the center of the second horizontal plane.
Through the steps 11-16, the inclination rate of the cylinder to be measured can be obtained.
In addition, in the technical solution of the present invention, the above steps 13 and 15 may be implemented by using various implementation methods. The technical solution of the present invention will be described in detail below by taking one specific implementation manner as an example.
For example, in an embodiment of the present invention, the calculating the spatial coordinates of the center of the horizontal plane according to the spatial coordinates of the n points may include the following steps:
and step 21, obtaining an ellipse formula which takes the center of the horizontal plane as the center of the ellipse according to the ellipse formula which takes the origin of coordinates as the center of the ellipse.
In this step, an ellipse formula with the center of the horizontal plane as the center of the ellipse can be obtained by a coordinate transformation manner according to the ellipse formula with the origin of coordinates as the center of the ellipse.
For example, in one embodiment of the present invention, the spatial coordinates of the center of the first horizontal plane may be assumed to be (x) in advance0，y0，z0) Spatial coordinates (x) of the center of the second horizontal plane1，y1，z1) (ii) a Then, an ellipse formula with the center of the first horizontal plane as the center of the ellipse and an ellipse formula with the center of the second horizontal plane as the center of the ellipse can be obtained respectively according to the ellipse formulas with the origin of coordinates (0, 0, 0), i.e., the spatial coordinates of the top of the total station, as the center of the ellipse.
Specifically, for example, in a preferred embodiment of the present invention, it can be assumed that n points on the first horizontal plane are respectively a1、A2、...，Ai、AnWherein the spatial coordinate of the ith point is (x)i，yi，z0) (ii) a N points on the second horizontal plane are respectively B1、B2、...，Bi、BnWherein the spatial coordinate of the jth point is (x)j，yj，z1)。
On the x-y plane, the ellipse formula with origin of coordinates (0, 0, 0) as the center of the ellipse can be generally expressed as:
in the technical scheme of the invention, in an actual application environment, compared with an ellipse formula taking the origin of coordinates as the center of the ellipse, the ellipse taking the center of the horizontal plane as the center of the ellipse not only displaces the center of the ellipse, but also can rotate by a corresponding angle theta on an x-y plane.
Therefore, after rotating an ellipse counterclockwise by θ on the x-y plane with the origin of coordinates (0, 0, 0) as the center of rotation, the ellipse equation of the ellipse can be generally expressed as:
by developing the above formula, we can obtain:
order:
then it can be obtained:
Ax2+By2+Cxy＝1。
the ellipse center of the ellipse can then be moved from the origin of coordinates to the horizontal plane center again.
For example, in one embodiment of the present invention, when the ellipse center of the ellipse is moved from the origin of coordinates (0, 0, 0) to the first horizontal plane center (x)0，y0，z0) Then, the following can be obtained:
A(x-x0)2+B(y-y0)2+C(x-x0)(y-y0)＝1。
after unfolding, obtaining:
order:
then a first horizontal plane center (x) may be obtained0，y0，z0) Ellipse formula for ellipse center:
x2+gxy+cy2+dx+ey+f＝0。
similarly, a second horizontal plane center (x) may also be obtained1，y1，z1) Ellipse formula for ellipse center:
x2+gxy+cy2+dx+ey+f＝0，
wherein:
and step 22, respectively substituting the space coordinates of n points on the horizontal plane into an ellipse formula which takes the center of the horizontal plane as the center of the ellipse, and calculating according to the least square principle to obtain the space coordinates of the center of the ellipse.
For example, in a preferred embodiment of the present invention, the spatial coordinates of n points on the horizontal plane can be respectively substituted into an elliptical formula with the center of the horizontal plane as the center of the ellipse, and according to the principle of least squares, let:
according to the extreme value principle, setting:
order:
by solving the above equations, the parameters (e.g., parameters g, c, d, e, and f) in the least-squares sense of the elliptic formula can be obtained by calculation; then, the spatial coordinates of the center of the ellipse (i.e., the center of the horizontal plane) can be calculated by the relational expression between each parameter and the center of the ellipse.
For example, in one embodiment of the present invention, after the parameters g, c, d, e and f in the ellipse equation are calculated, the following relationship can be used:
calculating to obtain the space coordinate (x) of the center of the first horizontal plane0，y0，z0) The rotation angle θ and the major and minor axes a and b of the ellipse are also obtained.
Similarly, after the parameters g, c, d, e and f in the elliptic formula are obtained by calculation, the following relations can be obtained:
calculating to obtain the space coordinate (x) of the center of the second horizontal plane1，y1，z1) The rotation angle θ and the major and minor axes a and b of the ellipse are also obtained.
Therefore, it can be seen that, through the above steps 21 and 22, the coordinates of the center of the horizontal plane can be calculated from the spatial coordinates of the n points.
In addition, preferably, in an embodiment of the present invention, the inclination rate of the cylinder to be measured can be calculated according to the following formula:
wherein alpha is the inclination of the cylinder to be measured.
In summary, in the technical solution of the present invention, a total station is used to measure a first horizontal plane and a horizontal plane of a cylinder to be measured at a preset first height and a preset second height respectively, so as to obtain spatial coordinates of a plurality of points of the surface of the cylinder to be measured on the first horizontal plane and the second horizontal plane respectively, then spatial coordinates of a center of the first horizontal plane and a center of the second horizontal plane are obtained through respective calculation according to the spatial coordinates, and finally, calculation is performed according to the spatial coordinates of the center of the first horizontal plane and the center of the second horizontal plane, so that the inclination rate of the cylinder to be measured can be accurately calculated. By using the method for measuring the inclination rate of the cylinder, the reliability and the accuracy of the measurement result can be effectively improved, and the method has great significance for improving the authenticity of the measurement result of the inclination of the cylinder in engineering.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (4)
1. A method of measuring the slope of a cylinder, the method comprising:
setting a total station, and taking a space coordinate at the top of the total station as a coordinate origin of a space coordinate system;
measuring a first horizontal plane of the cylinder to be measured at a preset first height by using a total station to obtain the spatial coordinates of n points of the surface of the cylinder to be measured on the first horizontal plane; n is an integer greater than or equal to 5;
calculating the space coordinate of the center of the first horizontal plane according to the space coordinates of n points on the first horizontal plane;
measuring a horizontal plane of the cylinder to be measured at a preset second height by using a total station to obtain the spatial coordinates of n points of the surface of the cylinder to be measured on the second horizontal plane;
calculating the space coordinate of the center of the second horizontal plane according to the space coordinates of n points on the second horizontal plane;
and calculating to obtain the inclination rate of the cylinder to be measured according to the space coordinate of the center of the first horizontal plane and the space coordinate of the center of the second horizontal plane.
2. The method of claim 1, wherein calculating the spatial coordinates of the center of the horizontal plane from the spatial coordinates of the n points comprises:
obtaining an ellipse formula which takes the center of a horizontal plane as the center of an ellipse according to the ellipse formula which takes the origin of coordinates as the center of the ellipse;
and respectively substituting the space coordinates of n points on the horizontal plane into an ellipse formula which takes the center of the horizontal plane as the center of the ellipse, and calculating according to the least square principle to obtain the space coordinates of the center of the ellipse.
3. The method of claim 2, wherein the first horizontal center is assigned a coordinate of (x)0,y0,z0) The ellipse formula with the center of the first horizontal plane as the center of the ellipse is:
x2+gxy+cy2+dx+ey+f＝0；
wherein,
let the coordinate of the center of the second horizontal plane be (x)1,y1,z1) The ellipse formula with the center of the second horizontal plane as the center of the ellipse is:
x2+gxy+cy2+dx+ey+f＝0
wherein,
4. the method according to claim 3, wherein the tilt rate of the cylinder to be measured is calculated according to the following formula:
wherein alpha is the inclination of the cylinder to be measured.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113670259A (en) * | 2021-07-07 | 2021-11-19 | 福建省建研工程检测有限公司 | Method for measuring inclination of large and small-head cylinder of historic building timber structure |
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| CN113670259A (en) * | 2021-07-07 | 2021-11-19 | 福建省建研工程检测有限公司 | Method for measuring inclination of large and small-head cylinder of historic building timber structure |
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