Method for determining reflective surface of steering gear and focusing steering gear of external level gauge

Description

CROSS REFERENCE TO RELATED APPLICATION

The present application is a national stage application of International Patent Application No. PCT/CN2021/092086, filed on May 7, 2021, which claims priority to the Chinese Patent Application No. 202011574832.6, filed with the China National Intellectual Property Administration on Dec. 28, 2020, and entitled “METHOD FOR DETERMINING REFLECTIVE SURFACE OF STEERING GEAR AND FOCUSING STEERING GEAR OF EXTERNAL LEVEL GAUGE”, which is incorporated herein by reference in its entirety.

TECHNICAL FIELD

The present disclosure relates to the field of liquid level measuring technologies, and in particular, to a method for determining a reflective surface of a steering gear and a focusing steering gear of an external level gauge.

BACKGROUND

It is very common for petrochemical and chemical enterprises to measure a liquid level at an outer side of a liquid storage tank by an external level gauge. However, a vertical tank accounts for the vast majority of the liquid storage tank. Because a body of the vertical tank is mounted on a cement foundation, under a bottom of the tank, there is no suspended space for mounting a measuring head. The measuring head can only be mounted outside a side wall of the liquid storage tank, and a steering gear is mounted in the tank. An ultrasonic wave emitted by the measuring head is reflected at 45° by the steering gear to a liquid surface, and an echo from the liquid surface is reflected at 45° by the steering gear to the measuring head again. An included angle between the reflective surface of the steering gear and a horizontal plane is 45°.

A flat reflective surface doubles an error θ of an incidence angle of the ultrasonic wave emitted by the measuring head to 2 θ, and then the ultrasonic wave is reflected to the liquid surface. The liquid surface doubles an error of an incidence angle of an ultrasonic wave reflected by the steering gear to 4 θ, and then the ultrasonic wave is reflected to the steering gear. The steering gear doubles an error of an incidence angle to 8 θ again, and then the ultrasonic wave is reflected to the measuring head. For example, if the error of the incidence angle of the ultrasonic wave emitted by the measuring head is θ=4°, after an echo is reflected for three times, namely, reflected by the steering gear, the liquid surface, and the steering gear, and transmitted to the measuring head, an error of an incidence angle of the echo is 23*4°=32°. As a result, the echo is seriously offset from the measuring head. Therefore, the measuring head does not receive the echo completely, resulting that the measurement fails. This is a main reason why the steering gear of the external level gauge cannot be used in the vertical tank.

SUMMARY

An objective of the present disclosure is to provide a method for determining a reflective surface of a steering gear and a focusing steering gear of an external level gauge, to measure a liquid level at an outer side of a side wall of a vertical liquid storage tank.

Technical solutions of the present disclosure are as follows:

A method for determining a reflective surface of a steering gear includes: obtaining a focal length and a specific reflection angle, where the focal length is a distance between a ray source and a center of the reflective surface of the steering gear, and the specific reflection angle is an exit angle of an ultrasonic wave reflected by the reflective surface of the steering gear; determining a 0^th step reflective surface of the reflective surface of the steering gear based on the focal length and the specific reflection angle; determining an adjacent step reflective surface by a geometric method based on the 0^th step reflective surface, where the adjacent step reflective surface includes a positive step reflective surface and a negative step reflective surface; and if a number of steps of the reflective surface of the steering gear reaches a preset value, determining the reflective surface of the steering gear based on the 0^th step reflective surface and the adjacent step reflective surface.

Optionally, the determining a 0^th step reflective surface of the reflective surface of the steering gear based on the focal length and the specific reflection angle specifically includes: determining a unit angle of the reflective surface of the steering gear based on the focal length, where the unit angle is an included angle between a first side and a second side, the first side is a connecting line between a first end point of a longitudinal section of each step reflective surface and the ray source, and the second side is a connecting line between a second end point of the longitudinal section of each step reflective surface and the ray source; determining an inclination angle of the 0^th step reflective surface of the reflective surface of the steering gear based on the specific reflection angle, where the inclination angle of the 0^th step reflective surface of the reflective surface of the steering gear is an included angle between the 0^th step reflective surface of the reflective surface of the steering gear and a horizontal plane; determining side coordinates of the 0^th step reflective surface of the reflective surface of the steering gear based on the focal length, the unit angle, and the inclination angle of the 0^th step reflective surface of the reflective surface of the steering gear; and determining the 0^th step reflective surface of the reflective surface of the steering gear based on the side coordinates of the 0^th step reflective surface.

Optionally, the determining an adjacent step reflective surface by a geometric method based on the 0^th step reflective surface specifically includes: determining side coordinates of the adjacent step reflective surface by a reflection law based on the unit angle and the side coordinates of the 0^th step reflective surface; and determining the adjacent step reflective surface based on the side coordinates of the adjacent step reflective surface.

Optionally, the determining side coordinates of the adjacent step reflective surface by a reflection law based on the unit angle and the side coordinates of the 0^th step reflective surface specifically includes: if a number N of steps of the reflective surface is a positive integer, determining the side coordinates of the adjacent step reflective surface based on the unit angle according to the following equations:

(X_N,Y_N)=F((X_N−1,Y_N−1),l,c),

(X₀,Y₀)=(X₊₀,Y₊₀), where

(X_N, Y_N) represents side coordinates of an N^th step reflective surface, (X_N−1, Y_N−1) represents side coordinates of an (N−1)^th step reflective surface, c represents the unit angle, l represents the focal length, (X₀, Y₀) represents side coordinates of the 0^th reflective surface, and (X₊₀, Y₊₀) represents side coordinate values of a 1^st step reflective surface in a first quadrant; or if a number N of steps of the reflective surface is a negative integer, determining the side coordinates of the adjacent step reflective surface based on the unit angle according to the following equations:

(X_N,Y_N)=F((X_N+1,Y_N+1),l,c),

(X₀,Y₀)=(X₋₀,Y₋₀), where

(X_N+1, Y_N+1) represents side coordinates of an (N+1)^th step reflective surface, and (X₀₋₀, Y₋₀) represents side coordinate values of the 0^th step reflective surface in a third quadrant.

Optionally, after the determining the reflective surface of the steering gear based on the 0^th step reflective surface and the adjacent step reflective surface, the method further includes: storing the side coordinates, the focal length, and the unit angle of the adjacent step reflective surface into a database, where the database is configured to inquire the reflective surface of the steering gear.

Optionally, the determining an adjacent step reflective surface by a geometric method based on the 0^th step reflective surface specifically includes: determining a unit length of the reflective surface of the steering gear based on the focal length, where the unit length is a longitudinal cross-sectional length of each step reflective surface; determining the side coordinates of the adjacent step reflective surface by the reflection law based on the unit length and the 0^th step reflective surface; and determining the adjacent step reflective surface based on the side coordinates of the adjacent step reflective surface.

The present disclosure further describes a focusing steering gear of an external level gauge. The focusing steering gear of an external level gauge includes a reflective surface of a steering gear determined by any above-mentioned method for determining a reflective surface of a steering gear.

An included angle between the included angle between the 0^th step reflective surface of the reflective surface of the steering gear and a horizontal plane is a specific angle, to enable a direction of the ultrasonic wave reflected by the reflective surface of the steering gear to be a specific reflection angle. A midpoint of the 0^th step reflective surface of the reflective surface of the steering gear and the ray source are located in a same horizontal plane. The ray source is disposed on a concave side of the reflective surface of the steering gear. A transverse cross section of the reflective surface of the steering gear is an arc surface.

Optionally, a first side edge and a second side edge of the reflective surface of the steering gear are respectively in contact with an inner surface of a side wall of a liquid tank. The first side edge is a connecting line between end points on arc-shaped sides of adjacent step reflective surfaces of the reflective surface of the steering gear. The second side edge is a connecting line of end points on other sides of the arc-shaped sides of the adjacent step reflective surfaces of the reflective surface of the steering gear.

Optionally, the reflective surface of the steering gear includes the 0^th step reflective surface and the negative step reflective surface.

Optionally, the reflective surface of the steering gear includes the 0^th step reflective surface and the positive step reflective surface.

Compared with the prior art, the present disclosure has the following advantages.

According to the method for determining a reflective surface of a steering gear and the focusing steering gear of an external level gauge provided in the present disclosure, the 0^th step reflective surface of the reflective surface of the steering gear is determined based on the focal length and the specific reflection angle, the adjacent step reflective surface is determined by the geometric method based on the 0^th step reflective surface, the reflective surface of the steering gear is determined based on the 0^th step reflective surface and the adjacent step reflective surface, and the reflective surface of the steering gear is designed as a multi-step reflective surface, so that the ultrasonic wave emitted by the ray source is reflected to the liquid surface by the multi-step reflective surface of the reflective surface of the steering gear, to measure the liquid level at the outer side of the side wall of the vertical liquid storage tank.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure will be further described below with reference to the accompanying drawings.

FIG. 1 is a flowchart of a method for determining a reflective surface of a steering gear according to the present disclosure;

FIG. 2 is a front view of a reflective surface of a steering gear according to the present disclosure; and

FIG. 3 is a top view of a reflective surface of a steering gear according to the present disclosure.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The technical solutions in embodiments of the present disclosure will be described in detail below with reference to the accompanying drawings in the embodiments of the present disclosure. Apparently, the described embodiments are merely a part rather than all of the embodiments of the present disclosure. All other embodiments derived from the embodiments in the present disclosure by a person of ordinary skill in the art without creative work shall fall within the protection scope of the present disclosure.

In view of a defect that a steering gear of an external level gauge cannot be used in a vertical tank, the present disclosure provides a method for determining a reflective surface of a steering gear and a focusing steering gear of an external level gauge, to measure a liquid level at an outer side of a side wall of a vertical liquid storage tank.

To make the above objectives, features, and advantages of the present disclosure clearer and more comprehensible, the present disclosure will be further described in detail below with reference to the accompanying drawings and the specific examples.

Embodiment 1

As shown in FIG. 1, a method for determining a reflective surface of a steering gear provided in the present disclosure includes the following steps.

Step 101: Obtain a focal length and a specific reflection angle, where the focal length is a distance between a ray source and a center of the reflective surface of the steering gear, and the specific reflection angle is an exit angle of an ultrasonic wave reflected by the reflective surface of the steering gear.

Step 102: Determine a 0^th step reflective surface of the reflective surface of the steering gear based on the focal length and the specific reflection angle.

Step 103: Determine an adjacent step reflective surface by a geometric method based on the 0^th step reflective surface, where the adjacent step reflective surface includes a positive step reflective surface and a negative step reflective surface.

Step 104: If a number of steps of the reflective surface of the steering gear reaches a preset value, determine the reflective surface of the steering gear based on the 0^th step reflective surface and the adjacent step reflective surface.

In an optional implementation, the determining a 0^th step reflective surface of the reflective surface of the steering gear based on the focal length and the specific reflection angle specifically includes: determining a unit angle of the reflective surface of the steering gear based on the focal length, where the unit angle is an included angle between a first side and a second side, the first side is a connecting line between a first end point of a longitudinal section of each step reflective surface and the ray source, and the second side is a connecting line between a second end point of the longitudinal section of each step reflective surface and the ray source; determining an inclination angle of the 0^th step reflective surface of the reflective surface of the steering gear based on the specific reflection angle, where the inclination angle of the 0^th step reflective surface of the reflective surface of the steering gear is an included angle between the 0^th step reflective surface of the reflective surface of the steering gear and a horizontal plane; determining side coordinates of the 0^th step reflective surface of the reflective surface of the steering gear based on the focal length, the unit angle, and the inclination angle of the 0^th step reflective surface of the reflective surface of the steering gear; and determining the 0^th step reflective surface of the reflective surface of the steering gear based on the side coordinates of the 0^th step reflective surface.

Optionally, the determining an adjacent step reflective surface by a geometric method based on the 0^th step reflective surface specifically includes: determining side coordinates of the adjacent step reflective surface by a reflection law based on the unit angle and the side coordinates of the 0^th step reflective surface; and determining the adjacent step reflective surface based on the side coordinates of the adjacent step reflective surface. The determining side coordinates of the adjacent step reflective surface by a reflection law based on the unit angle and the side coordinates of the 0^th step reflective surface specifically includes: if a number N of steps of the reflective surface is a positive integer, determining the side coordinates of the adjacent step reflective surface based on the unit angle according to the following equations:

(X_N,Y_N)=F((X_N−1,Y_N−1),l,c),

(X₀,Y₀)=(X₊₀,Y₊₀), where

(X_N, Y_N) represents side coordinates of an N^th step reflective surface, (X_N−1, Y_N−1) represents side coordinates of an (N−1)^th step reflective surface, c represents the unit angle, l represents the focal length, (X₀, Y₀) represents side coordinates of the 0^th reflective surface, and (X₊₀, Y₊₀) represents side coordinate values of a 1^st step reflective surface in a first quadrant; or if a number N of steps of the reflective surface is a negative integer, determining the side coordinates of the adjacent step reflective surface based on the unit angle according to the following equations:

(X_N,Y_N)=F((X_N+1,Y_N+1),l,c),

(X₀,Y₀)=(X₋₀,Y₋₀), where

(X_N+1, Y_N+1) represents side coordinates of an (N+1)^th step reflective surface, and (X₋₀, Y₋₀) represents side coordinate values of the 0^th step reflective surface in a third quadrant.

After the determining the reflective surface of the steering gear based on the 0^th step reflective surface and the adjacent step reflective surface, the method further includes: storing the side coordinates, the focal length, and the unit angle of the adjacent step reflective surface into a database, where the database is configured to inquire the reflective surface of the steering gear.

In an optional implementation, the determining an adjacent step reflective surface by a geometric method based on the 0^th step reflective surface specifically includes: determining a unit length of the reflective surface of the steering gear based on the focal length, where the unit length is a longitudinal cross-sectional length of each step reflective surface; determining the side coordinates of the adjacent step reflective surface by the reflection law based on the unit length and the 0^th step reflective surface; and determining the adjacent step reflective surface based on the side coordinates of the adjacent step reflective surface.

Embodiment 2

A focusing steering gear of an external level gauge provided by the present disclosure includes a reflective surface of a steering gear determined by the method for determining a reflective surface of a steering gear according to the method for determining a reflective surface of a steering gear in embodiment 1.

An included angle between the included angle between the 0^th step reflective surface of the reflective surface of the steering gear and a horizontal plane is a specific angle, to enable a direction of the ultrasonic wave reflected by the reflective surface of the steering gear to be a preset direction. A midpoint of the 0^th step reflective surface of the reflective surface of the steering gear and the ray source are located in a same horizontal plane. The ray source is disposed on a concave side of the reflective surface of the steering gear. A transverse cross section of the reflective surface of the steering gear is an arc surface.

In an optional implementation, a first side edge and a second side edge of the reflective surface of the steering gear are respectively in contact with an inner surface of a side wall of a liquid tank. The first side edge is a connecting line between end points on arc-shaped sides of adjacent step reflective surfaces of the reflective surface of the steering gear. The second side edge is a connecting line of end points on other sides of the arc-shaped sides of the adjacent step reflective surfaces of the reflective surface of the steering gear.

In an optional implementation, the reflective surface of the steering gear includes the 0^th step reflective surface and the negative step reflective surface.

In an optional implementation, the reflective surface of the steering gear includes the 0^th step reflective surface and the positive step reflective surface.

Embodiment 3

In an implementation of a focusing steering gear of an external level gauge provided in this embodiment, the reflective surface of the steering gear is a focus reflective surface. An error of angle θ of an ultrasonic wave emitted by a measuring head in a direction is eliminated to 0° after the ultrasonic wave is reflected by the steering gear. Based on a property of the reflective surface of the steering gear, after ultrasonic waves emitted from a measuring head and scattered in all directions are reflected by the reflective surface of the steering gear, the ultrasonic waves are vertically reflected to the liquid surface, and then reflected by the liquid surface back to the reflective surface of the steering gear. After the ultrasonic waves are reflected by the reflective surface of the steering gear again, the ultrasonic waves are focused on the measuring head, so that an echo signal is greatly enhanced. Therefore, the steering gear is referred to as the focusing steering gear. An objective of conveniently measuring a liquid level of a vertical tank at an outer side of a side wall of the vertical tank by the focusing steering gear of an external level gauge is achieved.

Specifically, as shown in FIG. 2, OXYZ is a right-hand three-dimensional rectangular coordinate system, where coordinate axes OX and OY are on a paper, OX is horizontal to the right, OY is vertical to upward, OZ is a paper exit direction, and O being an origin of coordinates. T is an ultrasonic wave source through which an ultrasonic wave emitted by the measuring head is transmitted from the outside into the tank and emitted from an inner surface of the side wall, that is, a ray source. A ray source T is located at a negative value on the OX axis, a distance between the ray source T and an origin O of coordinates is a focal length l, and the reflective surface of the focusing steering gear is processed into a shape of the reflective surface of the steering gear. A center point of the reflective surface of the steering gear is the origin O of coordinates. It is assumed that an ultrasonic wave emitted from T to O is emitted to any point D on the reflective surface of the steering gear due to a direction error. According to the reflective surface of the steering gear provided in this embodiment, a ray emitted from a focal point to any point on the reflective surface of the steering gear is transmitted to a preset direction after being reflected. In this embodiment, the preset direction is vertical upward. That is, TD is reflected as a vertical upward DP by the reflective surface of the steering gear, and P is a point on the liquid surface. Because DP is perpendicular to the liquid surface, a reflected line PD of DP coincides with DP and is transmitted downward to the point D. The ray PD is transmitted to the focal point after being reflected by the reflective surface of the steering gear. As long as the reflective surface of the focusing steering gear is large enough to receive major ultrasonic waves that are emitted in all directions due to an error and scattering and that are emitted by the measuring head into the tank, the ultrasonic waves are vertically reflected upward to the liquid surface, and echoes reflected by the liquid surface are reflected and focused on the measuring head. In this way, when the liquid level is measured at the outer side of the side wall of the vertical tank by the external level gauge and the steering gear, a problem that the echoes reflected by the liquid surface cannot be received is resolved. In addition, the echo signal is greatly enhanced due to focusing, so that measurement can be performed normally when viscosity is high and a working condition is poor. Applicable liquid types and working conditions of the external level gauge are expanded.

A broken line in FIG. 2 is an intersecting line between the reflective surface of the steering gear and an XOY coordinate plane, and the broken line is formed by connecting 2N+1 straight line segments. The reflective surface of the steering gear is not a smooth curved surface. However, when a unit angle c tends to 0 and a number N of steps of the reflective surface tend to infinity, the reflective surface of the steering gear approaches a smooth surface. Although the reflective surface of the steering gear may be a paraboloid, a more complex case of focusing or diverging to any area can be designed by the determination method provided in this embodiment but cannot be designed by a paraboloid method. In comparison with the paraboloid method, mold machining accuracy by the determination method provided in this embodiment is high. The reflective surface of the steering gear has two parameters, namely, the focal length l and the unit angle c, recorded as reflection (l, c) by the steering gear. A focal length of a reflective (150, 4) surface of the steering gear is l=150 mm, and the unit angle is c=4°. The ray source, namely, a focal point T of the reflective surface of the steering gear is located on a negative half axis of the horizontal X axis. O is the origin of coordinates, and a length of TO is l. A ray is transmitted from T to O. An intersecting line between a 0^th step reflective surface of the reflective surface of the steering gear and an OXY coordinate plane is a straight line segment, a midpoint of this segment is located at O, and an included angle between this segment and the X axis is 45°. The ray TO is vertically transmitted upward to a P₀ point on a horizontal liquid surface after being reflected by the 0^th reflective surface, and then is reflected by the liquid surface to form a reflected line P₀O. The reflected line P₀O is reflected again by the 0^th step reflective surface again to form a ray OT. The ray OT is transmitted back to the ray source T. An upper right side of an N step reflective surface defined in a first quadrant is n, and n=2N+1. A lower side of an N step reflective surface defined in a third quadrant is n=2N−1. The ray emitted from the focal point is reversely transmitted to a preset direction by the reflective surface of the steering gear, that is, the ray focuses at a specified point, or is parallel to a specific direction, or diverges at a specified angle along a specific direction. The preset direction in this embodiment is vertical upward to the horizontal liquid surface.

When a drawing is drawn, it is required that an error of a length is less than 0.2 mm and an error of an angle is less than 0.5°. Coordinates (X₀, Y₀) of an upper right side of the 0^th step reflective surface may be determined based on an intersection of a ray and a 45° reflective surface, where the ray is emitted from the T and a ray angle is equal to c/2. Coordinates (X₋₀, Y₋₀) of a lower left side of the 0^th reflective may be determined based on an intersection of a ray and a 45° reflective surface, where the ray is emitted from the T and a ray angle is equal to −c/2. Coordinate values of (X₀, Y₀) and (X₋₀, Y₋₀) on the drawing are calculated by a geometric method. The unit angle c is an included angle between a ray from T to (X_N−1, Y_N−1) and a ray from T to (X_N, Y_N). In this embodiment, a unit angle of each step is c. Table 1 is a datasheet of a reflective (150, 4) surface of a steering gear. As shown in Table 1, in a third column in a first quadrant, ray angles θ=(2N+1)*c/2 or θ=(2N+1)*c/2 of odd sides corresponding to step N equal 0, 1, 2, 3 . . . are 2, 6, 14 . . . respectively. In a third quadrant, ray angles (2N−1)*c/2 or θ=(2N−1)*c/2 of odd sides corresponding to step N equal 0, −1, −2, −3 . . . are −2, −6, −10, −14 . . . respectively, and there is a difference c=4° between the step each. According to the determination method provided in this embodiment, the step may be divided by other methods. For example, lengths of sides of reflective surfaces at all steps may be set to be equal. In addition, coordinates of an upper right side of a 1^st step reflective surface are (X₁, Y₁), coordinates of an upper right side of a 2^nd step reflective surface are (X₂, Y₂), coordinates of an upper right side of a 3^rd step reflective surface are (X₃, Y₃), coordinates of an upper right side of a 4^th step reflective surface are (X₄, Y₄), coordinates of an upper right side of an −0^th step reflective surface are (X₋₀, Y₋₀), coordinates of an upper right side of a −1^st step reflective surface are (X₋₁, Y₋₁), coordinates of an upper right side of a −2^nd step reflective surface are (X₋₂, Y₋₂), coordinates of an upper right side of a −3^rd step reflective surface are (X₋₃, Y₋₃), coordinates of an upper right side of a −4^th step reflective surface are (X₋₄, Y₋₄), and coordinates of an upper right side of a −5^th step reflective surface are (X₋₅, Y₋₅).

Right-hand coordinates (X_N−1, Y_N−1) of a reflective surface at any step are determined. (X_N, Y_N) is calculated by the geometric method by accurately drawing based on the unit angle c for dividing the step or a length of the step and a required direction angle of the reflected line (vertical upward in this embodiment). Specifically, a ray on which the coordinates (X_N, Y_N) are located can be obtained by adding up a unit angle to the ray on the coordinates (X_N−1, Y_N−1), to obtain the coordinates (X_N, Y_N). Although a formula (X_N, Y_N)=F((X_N−1, Y_N−1), l, c) for calculating (X_N, Y_N) based on (X_N−1, Y_N−1) is complex, the formula is universal after a division rule of the step and a direction of the reflected line are determined. After the formula is input into an EXCEL datasheet or other datasheets, as long as the parameters l and c are input, in a front view, coordinates of odd sides of the reflective surfaces at all steps may be easily calculated by a recursive method based on a property of the datasheet, to form a datasheet of a reflective (l, c) surface of the steering gear as shown in Table 1. As shown in FIG. 3, a projection of a side of each step reflective surface in the Y axis direction is arcs, for example, a lower side of the −5^th step reflective surface is an arc with a radius of R-5.

Any ray TD that is emitted from the focal point T and of which emission angle is θ>0°, any ray TO of which emission angle is θ=0°, any ray TD₁ of which emission angle is θ<0°, and rays DP, OP₀, and P₁D₁ that are reflected by the reflective surface of the steering gear are all vertically transmitted upward to the horizontal liquid surface, where P, P₀, and P₁ are points on the liquid surface. Reflected lines PD, P₀O, and P₁D₁ reflected by the liquid surface are all vertically transmitted downward to the reflective surface of the steering gear, and rays DT, OT, and D₁T reflected by the reflective surface of the steering gear are all transmitted to the focal point T.

An ordinal of an even side of an N step reflective surface is n=2N, and a ray angle of the even side of the N step reflective surface is Nc, where the ray angle of the even side of the N step reflective surface is an included angle between the even side of the N step reflective surface and the X axis, and the even side is an accurate reflection position of the reflective surface, that is, after a reflected line of a ray from the ray source to an even side of a reflective surface at any step is reflected by a designated horizontal plane, the reflected line may be accurately transmitted to the even side and then reflected to the ray source, and an error of the reflection angle is 0. After a mold is machined based on the coordinates of the odd sides of the reflective surfaces at all steps, edges of the odd sides of the reflective surfaces at all steps are ground off during polishing, and an accurate coordinate plane of the even side of which error of the reflection angle is 0 is retained, so that focusing of the reflective surface of the steering gear is more accurate.

For example, in Table 1 of reflective (150, 4) surface of steering gear, in the second column, for a row in which a side ordinal n is even, a fourth column corresponding to this raw is a coordinate value XNE of the even side, and a fifth column corresponding to this raw is a coordinate value YNE of the even side. In the first quadrant, for steps N equal to 0, 1, 2, 3 . . . , ordinals of even sides are 0, 2, 4, 6 . . . respectively, ray angles of the even sides are 0°, 4°, 8°, 12° . . . respectively, and coordinate values (X_0E, Y_0E), (X_1E, Y_1E), (X_2E, Y_2E), (X_3E, Y_3E) . . . of the even sides are (0.000, 0.000), (10.855, 11.248), (22.555, 24.251), (35.235, 39.373) . . . respectively. In a third quadrant, for steps N equal to 0, c1, −2, −3 . . . , ordinals of even sides are 0, −2, −4, −6 . . . respectively, ray angles of the even sides are 0 0, −4°, −8°, −12° . . . respectively, and coordinate values (X_0E, Y₀E), (X_−1E, Y_−1E), (X_−2E, Y_−2E), (X_−3E, Y_−3E) . . . are (0.000, 0.000), (−10.123, −9.781), (−20.221, −18.239), (−29.637, −25.584) . . . respectively. In a front view of the reflective (150, 4) surface of the steering gear in FIG. 2, coordinates (X_0E, Y_0E) represent coordinates of even sides of the 0^th step reflective surface, that is, the origin O of coordinates, and coordinates (X_1E, Y_1E), (X_2E, Y_2E), (X_3E, Y_3E), (X_4E, Y_4E), (X_5E, Y_5E), (X_−1E, Y_−1E), (X_−2E, Y_−2E), (X_−3E, Y_−3E), (X_−4E, Y_−4E), and (X_−5E, Y_−5E) respectively represent coordinates of even sides of the 1^st, 2^nd, 3^rd, 4^th, 5^th, −1^st, −2^nd, −3^rd, −4^th, and −5^th reflective surfaces. In a top view of the reflective (150, 4) surface of the steering gear in FIG. 3, dotted arcs represent even sides of the reflective surfaces at all steps.

It is easy to calculate any small unit angle, that is, angle accuracy, and a coordinate table of a reflective surface of the steering gear having any multi-step reflective surface by using the datasheet on a computer. Table 2 is a datasheet of a reflective (1000, 0.2) surface of a steering gear. As shown in Table 2, a unit angle is 0.2°, and there are 240 reflective surfaces. Coordinate data show that the reflective surface of the steering gear is approximatively a smooth curved surface. After a mold is ground and polished based on the coordinate datasheet, edges of odd sides of the reflective surfaces at all steps are ground off, and accurate reflection positions of even sides are not ground off, so that angular accuracy is further improved and focusing effect is more accurate. Therefore, theoretically, the reflective surface of the steering gear calculated by this method can meet a requirement for accuracy of any angle.

If a tank wall at which the measuring head is mounted is not vertical, a partial reflective surface of the steering gear may be made based on different directions of focus rays. For example, if the tank wall is inclined outward and a direction of a ray emitted by the measuring head is upward, a focusing steering gear including only a partial upper area of the reflective surface of the steering gear can be made. If the tank wall is inclined inward and the direction of the ray emitted by the measuring head is downward, a focusing steering gear including only a partial lower area of the reflective surface of the steering gear can be made. If the tank wall is inclined leftward or rightward, and the direction of the ray emitted by the measuring head is leftward or rightward, a focusing steering gear including only a partial left or right area of the reflective surface of the steering gear can be made.

The determined method provided by this embodiment further includes a verification process. The verification process includes the following steps.

• • 1. Accurately draw a drawing (accuracy is determined by a specific requirement, such as length accuracy is 0.2 mm and angle accuracy is 0.5°).
  • 2. Calculate side coordinates of the 0^th step reflective surface by the geometric method and derive side coordinates of an adjacent step reflective surface based on side coordinates of the reflective surface at any step.
  • 3. Derive a universal formula for calculating the side coordinates of the adjacent step reflective surface based on the side coordinates of the reflective surface at any step by the geometric method.
  • 4. Input the universal formula into a spreadsheet; and based on a property of the spreadsheet, copy the side coordinates of the reflective surfaces at all steps according to the universal formula for calculating the side coordinates of the 0^th step reflective surface and the side coordinates of the adjacent step reflective surface, to easily generate, on a large scale, a datasheet of side coordinates of a reflective surface with any high accuracy requirement.
  • 5. Measure side coordinate values of the reflective surface on the drawing, check the side coordinate values of the reflective surface calculated and generated by the datasheet, and confirm that the universal formula is correct.

For different requirements for a reflection direction, for example, parallelism, focusing, and divergence, different methods of dividing a step, for example, emission angles c corresponding to the steps are equal, or lengths of all steps are equal, and datasheets for generating odd side coordinates or even side coordinates, universal formulae for deriving side coordinates of the adjacent step reflective surface are different. Calculated coordinate values are also different. However, the five steps of the method for generating the reflective surface of the steering gear are the same.

The steering gear provided by this embodiment is mounted in a storage tank, and a focal point T of a focusing surface is disposed at an inner wall facing the measuring head, the focal point T is located on an OX coordinate axis, the XOY coordinate plane is perpendicular to the inner wall of the tank, an XOZ coordinate plane is horizontal, and an OY axis is vertical upward. The measuring head of the external level gauge is used to send, aligning at a T point, an ultrasonic wave from the outer side of the side wall of the vertical tank to an inner side of the tank, and echoes reflected by the liquid surface are focused on the measuring head near the T point. Therefore, the measuring head can receive a powerful echo signal from the liquid surface, and the liquid level of the vertical tank can be measured at the side wall by the focusing steering gear of an external level gauge.

At present, the steering gear of an external level gauge is a flat reflective surface, and an included angle between the flat reflective surface and the horizontal plane is 45°. Therefore, an error of the emission angle of the ultrasonic wave emitted from the measuring head is magnified by 8 times when the ultrasonic wave returns to the measuring head after being reflected for many times. As a result, when the liquid level is measured at the side wall of the vertical by the external level gauge and the steering gear, the liquid level cannot be measured because no echo is received. In this embodiment, the reflective surfaces at all steps are derived by a recursive method from the 0^th reflective surface to the adjacent step reflective surface, and a datasheet of a reflective surface of the steering gear with any high accuracy requirement is easily generated by using a spreadsheet. Through the steering gear determined by the datasheet, ultrasonic waves emitted from the measuring head of the external level gauge in all directions are reflected by the focusing steering gear and vertically transmitted upward to the liquid surface, and echoes reflected from the liquid surface are focused and reflected back to the liquid level measuring head. Therefore, the measuring head can accurately receive the powerful echo signal from the liquid surface. The liquid level of the vertical storage tank can be measured at the side wall by the external level gauge and the focusing steering gear. In a practical application, the focusing steering gear may be made with a paraboloid instead of the reflective surface of the steering gear. However, the paraboloid cannot reflect in a non-parallel direction. In comparison with the paraboloid, the reflective surface of the steering gear has a wider application range, higher flexibility, and higher machining accuracy.

Table 1 is a datasheet of a reflective (150, 4) surface of a steering gear. As shown in Table 1, X and Y coordinate values of the odd sides of the reflective surfaces at all steps in the front view in FIG. 2 that are measured with a ruler are completely consistent with X and Y coordinate values calculated based on the datasheet of the reflective surface of the steering gear. This proves that the method for determining a reflective surface of a steering gear is accurate. Inputs in Table 1 are the focal length l and the unit angle c, where the focal length is 150 mm and the unit angle is 4°. In Table 1, data in the first quadrant includes data in a range from a row with a side ordinal of 11 to a raw with a side ordinal of 1, and data in the third quadrant includes data in a range from a row with a side ordinal of −1 to a row with a side ordinal of −11.

TABLE 1
Datasheet of reflective (150, 4) surface of steering gear
First quadrant

Step of

Ray

reflective	Side	angle	Coordinates of	Coordinates of	Coordinates of
surface	ordinal	of side	even side (mm)	odd side (mm)	mold (mm)

N	n	θ = nc/2	XNE	YNE	XN	YN	X′N	Y′N
5	11	22			72.601	89.937	114.949	12.260
	10	20	64.222	77.971
4	9	18			56.639	67.141	87.539	7.427
	8	16	49.057	57.079
3	7	14			42.146	47.907	63.687	4.075
	6	12	35.235	39.373
2	5	10			28.895	31.544	42.743	1.873
	4	8	22.555	24.251
1	3	6			16.705	17.521	24.206	0.577
	2	4	10.855	11.248
0	1	2			5.428	5.428	7.677	0.000
	0	0	0.000	0.000
	−1	−2			−5.061	−5.061	−7.159	0.000
−1	−2	−4	−10.123	−9.781
	−3	−6			−15.501	−14.136	−20.960	0.965
−2	−4	−8	−20.221	−18.239
	−5	−10			−25.215	−22.003	−33.393	2.272
−3	−6	−12	−29.637	−25.584
	−7	−14			−34.299	−28.848	−44.658	3.855
−4	−8	−16	−38.460	−31.984
	−9	−18			−42.830	−34.822	−54.916	5.664
−5	−10	−20	−46.763	−37.575
	−11	−22			−50.878	−40.048	−64.304	7.659
Step of		Ray

reflective	Side	Angle	Coordinates of	Coordinates of	Coordinates of
surface	ordinal	(°)	even side (mm)	odd side (mm)	mold (mm)

N	n	θ = nc/2	XNE	YNE	XN	YN	X′N	Y′N

Third quadrant

Table 2 is a datasheet of a reflective (1000, 0.2) surface of a steering gear. As shown in Table 2, X and Y coordinate values of the odd sides of the reflective surfaces at all steps in the front view in FIG. 3 that are measured with a ruler are completely consistent with X and Y coordinate values calculated from the datasheet of the reflective surface of the steering gear. This proves that the method for the reflective surface of the steering gear is accurate. Inputs in Table 2 are the focal length/and the unit angle c, where the focal length is 1,000 mm and the unit angle is 0.2°. In Table 2, data in the first quadrant includes data in a range, from top to bottom, from a third raw to a raw of which an ordinal of an odd side of a reflective surface of is 1. Data in a third quadrant includes data in a range, from top to bottom, from a row of which an ordinal of an odd side of the reflective surface is −1 to a row of which an ordinal of an odd side of the reflective surface is −120.

TABLE 2
Datasheet of reflective (1000, 0.2) surface of steering gear
First quadrant

Step of	Ordinal of odd	Ray angle of	X	Y	Coordinates
reflective	side of reflective	odd side	coordinate	coordinate	of mold
surface	surface	(°)	(mm)	(mm)	(mm)

N	n = 2N + 1	θ = nc/2	XN	YN	X′N	Y′N
120	241	24.1	542.815	690.134	871.958	104.186
119	239	23.9	536.931	681.074	861.390	101.940
118	237	23.7	531.079	672.096	850.902	99.730
117	235	23.5	525.257	663.201	840.494	97.555
116	233	23.3	519.467	654.386	830.165	95.416
115	231	23.1	513.707	645.651	819.914	93.312
114	229	22.9	507.978	636.995	809.740	91.242
113	227	22.7	502.279	628.417	799.643	89.207
112	225	22.5	496.609	619.916	789.622	87.204
111	223	22.3	490.970	611.491	779.675	85.235
110	221	22.1	485.359	603.142	769.802	83.298
109	219	21.9	479.777	594.867	760.003	81.393
108	217	21.7	474.225	586.665	750.276	79.520
107	215	21.5	468.700	578.536	740.620	77.678
106	213	21.3	463.204	570.479	731.035	75.867
105	211	21.1	457.736	562.494	721.520	74.086
104	209	20.9	452.296	554.578	712.075	72.335
103	207	20.7	446.883	546.732	702.698	70.614
102	205	20.5	441.497	538.954	693.388	68.922
101	203	20.3	436.139	531.244	684.146	67.260
100	201	20.1	430.807	523.601	674.970	65.625
99	199	19.9	425.502	516.025	665.860	64.019
98	197	19.7	420.223	508.514	656.815	62.440
97	195	19.5	414.970	501.067	647.834	60.889
96	193	19.3	409.744	493.685	638.917	59.365
95	191	19.1	404.542	486.366	630.063	57.867
94	189	18.9	399.367	479.110	621.271	56.396
93	187	18.7	394.216	471.916	612.541	54.950
92	185	18.5	389.091	464.783	603.871	53.531
91	183	18.3	383.990	457.711	595.262	52.136
90	181	18.1	378.914	450.699	586.713	50.767
89	179	17.9	373.862	443.745	578.223	49.422
88	177	17.7	368.834	436.851	569.792	48.102
87	175	17.5	363.831	430.014	561.418	46.806
86	173	17.3	358.851	423.235	553.102	45.533
85	171	17.1	353.895	416.512	544.842	44.284
84	169	16.9	348.962	409.846	536.639	43.058
83	167	16.7	344.052	403.235	528.491	41.855
82	165	16.5	339.165	396.679	520.399	40.674
81	163	16.3	334.301	390.177	512.361	39.516
80	161	16.1	329.460	383.729	504.377	38.380
79	159	15.9	324.641	377.334	496.446	37.265
78	157	15.7	319.844	370.991	488.568	36.172
77	155	15.5	315.069	364.701	480.743	35.100
76	153	15.3	310.317	358.462	472.969	34.049
75	151	15.1	305.586	352.274	465.247	33.019
74	149	14.9	300.876	346.136	457.576	32.009
73	147	14.7	296.188	340.048	449.955	31.019
72	145	14.5	291.520	334.010	442.384	30.049
71	143	14.3	286.874	328.020	434.862	29.099
70	141	14.1	282.249	322.079	427.389	28.168
69	139	13.9	277.644	316.185	419.964	27.256
68	137	13.7	273.060	310.339	412.588	26.364
67	135	13.5	268.496	304.539	405.258	25.490
66	133	13.3	263.953	298.786	397.976	24.634
65	131	13.1	259.429	293.078	390.741	23.797
64	129	12.9	254.925	287.416	383.551	22.978
63	127	12.7	250.441	281.799	376.408	22.177
62	125	12.5	245.977	276.226	369.309	21.393
61	123	12.3	241.531	270.698	362.255	20.627
60	121	12.1	237.105	265.212	355.246	19.878
59	119	11.9	232.698	259.770	348.281	19.146
58	117	11.7	228.310	254.371	341.359	18.430
57	115	11.5	223.941	249.014	334.480	17.732
56	113	11.3	219.591	243.698	327.644	17.049
55	111	11.1	215.258	238.424	320.851	16.383
54	109	10.9	210.945	233.191	314.099	15.733
53	107	10.7	206.649	227.999	307.389	15.099
52	105	10.5	202.372	222.846	300.720	14.480
51	103	10.3	198.112	217.734	294.092	13.877
50	101	10.1	193.870	212.661	287.504	13.289
49	99	9.9	189.646	207.626	280.956	12.716
48	97	9.7	185.439	202.631	274.448	12.158
47	95	9.5	181.250	197.673	267.980	11.615
46	93	9.3	177.078	192.754	261.550	11.086
45	91	9.1	172.923	187.872	255.159	10.572
44	89	8.9	168.785	183.027	248.806	10.072
43	87	8.7	164.664	178.219	242.491	9.586
42	85	8.5	160.559	173.447	236.214	9.114
41	83	8.3	156.471	168.711	229.973	8.656
40	81	8.1	152.400	164.011	223.770	8.211
39	79	7.9	148.345	159.346	217.603	7.780
38	77	7.7	144.306	154.716	211.473	7.362
37	75	7.5	140.283	150.121	205.378	6.957
36	73	7.3	136.277	145.560	199.319	6.566
35	71	7.1	132.286	141.034	193.295	6.187
34	69	6.9	128.311	136.541	187.306	5.820
33	67	6.7	124.351	132.081	181.352	5.467
32	65	6.5	120.407	127.654	175.432	5.125
31	63	6.3	116.479	123.260	169.547	4.796
30	61	6.1	112.565	118.899	163.695	4.479
29	59	5.9	108.667	114.570	157.876	4.174
28	57	5.7	104.784	110.272	152.091	3.881
27	55	5.5	100.916	106.006	146.338	3.600
26	53	5.3	97.063	101.771	140.618	3.330
25	51	5.1	93.224	97.568	134.931	3.072
24	49	4.9	89.400	93.395	129.275	2.825
23	47	4.7	85.591	89.252	123.651	2.589
22	45	4.5	81.796	85.139	118.059	2.365
21	43	4.3	78.015	81.056	112.497	2.151
20	41	4.1	74.248	77.003	106.967	1.948
19	39	3.9	70.496	72.979	101.468	1.756
18	37	3.7	66.758	68.984	95.998	1.575
17	35	3.5	63.033	65.018	90.559	1.404
16	33	3.3	59.322	61.080	85.150	1.243
15	31	3.1	55.625	57.171	79.771	1.093
14	29	2.9	51.942	53.289	74.421	0.953
13	27	2.7	48.272	49.435	69.100	0.823
12	25	2.5	44.615	45.609	63.808	0.703
11	23	2.3	40.972	41.810	58.544	0.592
10	21	2.1	37.342	38.038	53.309	0.492
9	19	1.9	33.725	34.292	48.103	0.401
8	17	1.7	30.121	30.573	42.924	0.320
7	15	1.5	26.530	26.881	37.773	0.248
6	13	1.3	22.952	23.214	32.649	0.185
5	11	1.1	19.387	19.573	27.553	0.132
4	9	0.9	15.834	15.958	22.484	0.088
3	7	0.7	12.294	12.368	17.441	0.052
2	5	0.5	8.766	8.803	12.426	0.026
1	3	0.3	5.251	5.264	7.436	0.009
0	1	0.1	1.748	1.748	2.473	0.000
0	−1	−0.1	−1.742	−1.742	−2.464	0.000
−1	−3	−0.3	−5.233	−5.209	−7.384	0.017
−2	−5	−0.5	−8.699	−8.651	−12.270	0.034
−3	−7	−0.7	−12.154	−12.069	−17.131	0.060
−4	−9	−0.9	−15.596	−15.464	−21.966	0.093
−5	−11	−1.1	−19.027	−18.836	−26.777	0.135
−6	−13	−1.3	−22.446	−22.184	−31.563	0.186
−7	−15	−1.5	−25.854	−25.509	−36.324	0.244
−8	−17	−1.7	−29.249	−28.811	−41.061	0.310
−9	−19	−1.9	−32.634	−32.091	−45.774	0.384
−10	−21	−2.1	−36.007	−35.348	−50.463	0.466
−11	−23	−2.3	−39.368	−38.583	−55.128	0.555
−12	−25	−2.5	−42.719	−41.796	−59.770	0.653
−13	−27	−2.7	−46.058	−44.987	−64.388	0.757
−14	−29	−2.9	−49.386	−48.156	−68.983	0.870
−15	−31	−3.1	−52.703	−51.304	−73.555	0.989
−16	−33	−3.3	−56.009	−54.430	−78.104	1.116
−17	−35	−3.5	−59.304	−57.535	−82.630	1.251
−18	−37	−3.7	−62.588	−60.620	−87.134	1.392
−19	−39	−3.9	−65.862	−63.683	−91.616	1.541
−20	−41	−4.1	−69.125	−66.726	−96.076	1.697
−21	−43	−4.3	−72.378	−69.748	−100.513	1.859
−22	−45	−4.5	−75.619	−72.750	−104.929	2.029
−23	−47	−4.7	−78.851	−75.732	−109.323	2.206
−24	−49	−4.9	−82.072	−78.694	−113.696	2.389
−25	−51	−5.1	−85.283	−81.636	−118.047	2.579
−26	−53	−5.3	−88.483	−84.559	−122.378	2.775
−27	−55	−5.5	−91.674	−87.462	−126.687	2.979
−28	−57	−5.7	−94.854	−90.346	−130.976	3.188
−29	−59	−5.9	−98.024	−93.210	−135.244	3.405
−30	−61	−6.1	−101.185	−96.056	−139.491	3.627
−31	−63	−6.3	−104.335	−98.882	−143.718	3.856
−32	−65	−6.5	−107.476	−101.690	−147.925	4.091
−33	−67	−6.7	−110.606	−104.480	−152.112	4.333
−34	−69	−6.9	−113.727	−107.251	−156.279	4.580
−35	−71	−7.1	−116.839	−110.004	−160.426	4.834
−36	−73	−7.3	−119.941	−112.738	−164.554	5.094
−37	−75	−7.5	−123.033	−115.455	−168.662	5.359
−38	−77	−7.7	−126.116	−118.154	−172.751	5.631
−39	−79	−7.9	−129.189	−120.835	−176.821	5.908
−40	−81	−8.1	−132.254	−123.499	−180.871	6.192
−41	−83	−8.3	−135.309	−126.145	−184.903	6.481
−42	−85	−8.5	−138.354	−128.774	−188.917	6.775
−43	−87	−8.7	−141.391	−131.386	−192.911	7.076
−44	−89	−8.9	−144.418	−133.981	−196.887	7.382
−45	−91	−9.1	−147.437	−136.559	−200.845	7.693
−46	−93	−9.3	−150.446	−139.120	−204.785	8.010
−47	−95	−9.5	−153.447	−141.664	−208.707	8.333
−48	−97	−9.7	−156.438	−144.193	−212.610	8.660
−49	−99	−9.9	−159.421	−146.704	−216.496	8.994
−50	−101	−10.1	−162.395	−149.200	−220.365	9.332
−51	−103	−10.3	−165.361	−151.680	−224.215	9.676
−52	−105	−10.5	−168.318	−154.143	−228.049	10.025
−53	−107	−10.7	−171.266	−156.591	−231.865	10.379
−54	−109	−10.9	−174.206	−159.023	−235.664	10.738
−55	−111	−11.1	−177.137	−161.439	−239.446	11.102
−56	−113	−11.3	−180.060	−163.840	−243.211	11.471
−57	−115	−11.5	−182.975	−166.226	−246.959	11.845
−58	−117	−11.7	−185.881	−168.596	−250.691	12.224
−59	−119	−11.9	−188.779	−170.951	−254.406	12.608
−60	−121	−12.1	−191.669	−173.291	−258.105	12.997
−61	−123	−12.3	−194.550	−175.616	−261.787	13.390
−62	−125	−12.5	−197.424	−177.927	−265.453	13.789
−63	−127	−12.7	−200.289	−180.223	−269.103	14.192
−64	−129	−12.9	−203.147	−182.504	−272.737	14.599
−65	−131	−13.1	−205.997	−184.770	−276.356	15.011
−66	−133	−13.3	−208.838	−187.023	−279.958	15.428
−67	−135	−13.5	−211.672	−189.261	−283.545	15.850
−68	−137	−13.7	−214.498	−191.485	−287.117	16.276
−69	−139	−13.9	−217.317	−193.695	−290.673	16.706
−70	−141	−14.1	−220.127	−195.890	−294.213	17.141
−71	−143	−14.3	−222.930	−198.073	−297.739	17.580
−72	−145	−14.5	−225.726	−200.241	−301.249	18.023
−73	−147	−14.7	−228.514	−202.396	−304.745	18.471
−74	−149	−14.9	−231.294	−204.537	−308.226	18.923
−75	−151	−15.1	−234.067	−206.665	−311.691	19.379
−76	−153	−15.3	−236.832	−208.779	−315.143	19.840
−77	−155	−15.5	−239.591	−210.880	−318.579	20.304
−78	−157	−15.7	−242.342	−212.968	−322.001	20.773
−79	−159	−15.9	−245.085	−215.043	−325.409	21.246
−80	−161	−16.1	−247.822	−217.105	−328.802	21.723
−81	−163	−16.3	−250.551	−219.154	−332.182	22.204
−82	−165	−16.5	−253.273	−221.191	−335.547	22.689
−83	−167	−16.7	−255.988	−223.214	−338.898	23.178
−84	−169	−16.9	−258.696	−225.225	−342.236	23.671
−85	−171	−17.1	−261.397	−227.224	−345.559	24.167
−86	−173	−17.3	−264.091	−229.210	−348.869	24.668
−87	−175	−17.5	−266.778	−231.184	−352.165	25.172
−88	−177	−17.7	−269.458	−233.146	−355.448	25.680
−89	−179	−17.9	−272.131	−235.095	−358.717	26.192
−90	−181	−18.1	−274.798	−237.033	−361.973	26.708
−91	−183	−18.3	−277.458	−238.958	−365.216	27.228
−92	−185	−18.5	−280.111	−240.872	−368.446	27.751
−93	−187	−18.7	−282.757	−242.773	−371.662	28.277
−94	−189	−18.9	−285.397	−244.663	−374.866	28.808
−95	−191	−19.1	−288.031	−246.542	−378.057	29.342
−96	−193	−19.3	−290.657	−248.408	−381.235	29.879
−97	−195	−19.5	−293.278	−250.264	−384.400	30.420
−98	−197	−19.7	−295.891	−252.107	−387.552	30.965
−99	−199	−19.9	−298.499	−253.940	−390.692	31.513
−100	−201	−20.1	−301.100	−255.761	−393.820	32.064
−101	−203	−20.3	−303.695	−257.571	−396.935	32.619
−102	−205	−20.5	−306.283	−259.370	−400.038	33.177
−103	−207	−20.7	−308.865	−261.158	−403.128	33.739
−104	−209	−20.9	−311.441	−262.935	−406.207	34.304
−105	−211	−21.1	−314.011	−264.701	−409.273	34.872
−106	−213	−21.3	−316.574	−266.457	−412.327	35.444
−107	−215	−21.5	−319.132	−268.201	−415.370	36.019
−108	−217	−21.7	−321.683	−269.935	−418.400	36.597
−109	−219	−21.9	−324.229	−271.658	−421.419	37.178
−110	−221	−22.1	−326.768	−273.371	−424.427	37.763
−111	−223	−22.3	−329.301	−275.074	−427.422	38.351
−112	−225	−22.5	−331.829	−276.766	−430.406	38.941
−113	−227	−22.7	−334.350	−278.447	−433.379	39.535
−114	−229	−22.9	−336.866	−280.119	−436.340	40.132
−115	−231	−23.1	−339.376	−281.780	−439.290	40.733
−116	−233	−23.3	−341.880	−283.431	−442.229	41.336
−117	−235	−23.5	−344.379	−285.072	−445.156	41.942
−118	−237	−23.7	−346.871	−286.703	−448.073	42.551
−119	−239	−23.9	−349.358	−288.325	−450.978	43.164
−120	−241	−24.1	−351.840	−289.936	−453.873	43.779
N	n = 2N − 1	θ = nb	XN	YN	X′N	Y′N

Step of	Ordinal of odd	Ray angle of	X	Y	Coordinates of
reflective	side of reflective	odd side	coordinate	coordinate	mold
surface	surface	(°)	(mm)	(mm)	(mm)

Third quadrant

Embodiments of the present disclosure are described in detail above with reference to the accompanying drawings, but the present disclosure is not limited to the above embodiments. Within the knowledge of a person of ordinary skill in the art, various variations can also be made without departing from the spirit of the present disclosure.