CN112284342B - Annular reed flattening type inclination angle tester and testing method - Google Patents

Annular reed flattening type inclination angle tester and testing method Download PDF

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Publication number
CN112284342B
CN112284342B CN202011021697.2A CN202011021697A CN112284342B CN 112284342 B CN112284342 B CN 112284342B CN 202011021697 A CN202011021697 A CN 202011021697A CN 112284342 B CN112284342 B CN 112284342B
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reed
phi
rotating rod
axis
ellipse
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CN112284342A (en
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吴珊珊
吴明康
聂子健
蔡纪源
王顺华
李璟
殷家腾
高燕
孙冬
顾斌
张照锋
汤滟
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Nanjing College of Information Technology
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Nanjing College of Information Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C9/00—Measuring inclination, e.g. by clinometers, by levels
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B5/00—Measuring arrangements characterised by the use of mechanical techniques
    • G01B5/24—Measuring arrangements characterised by the use of mechanical techniques for measuring angles or tapers; for testing the alignment of axes
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C1/00—Measuring angles

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Abstract

The invention relates to the technical field of angle detection, in particular to a flattening type inclination angle tester and a test method for an annular reed, wherein the length of a long semi-axis of an ellipse with a certain circumference is measured to measure the tensile force applied to the ellipse, and the direction of the tensile force applied to the ellipse is measured in the direction of the long axis of the ellipse; a rotating rod rotates around an end point A of the long axis of the ellipse, and the rotating rod and the ellipse have two contact points M 1 And M 2 The direction of the tensile force being determined by measuring AM 1 And AM 2 The direction of the angle bisector of (a) is obtained, and the magnitude of the tensile force is measured by measuring AM 1 And AM 2 The included angle is further substituted and solved with an equation F (a) of the length of the long half shaft, the equation F (a) is 0, the reed drawing force F comprises the magnitude and the direction of the component force of the gravity of the slide block on the inclined plane, a unit vector g orthogonal to the component force is obtained, and the included angle between the inclined plane and the horizontal plane can be obtained according to the magnitude and the gravity value of the slide block
Figure DDA0002700851390000011
According to g and
Figure DDA0002700851390000012
and obtaining the normal linear value of the inclined plane in the horizontal coordinate system to realize the inclination measurement. The invention has high measurement precision.

Description

Annular reed flattening type inclination angle tester and testing method
Technical Field
The invention relates to the technical field of angle detection, in particular to a flattening type inclination angle tester and a test method for an annular reed.
Background
Angle or inclination measurement is often required in industrial and agricultural production and service, scientific research and daily life, for example in the fields of equipment installation, machining, building construction and transportation. However, the current angle measuring instrument generally has the defects of low precision or low cost performance, and the invention aims to solve the problem.
Disclosure of Invention
The invention aims to provide a flattening type inclination angle tester and a testing method for an annular reed, which are used for realizing inclination detection and have the advantages of higher detection precision, low calculation complexity and high cost performance.
In order to solve the technical problems, the technical scheme of the invention is as follows: the annular reed flattening type inclination angle tester comprises a signal acquisition module and a control processing module;
the signal acquisition module comprises a bottom plate, a middle column, a direct current motor, a rotating rod, a reed and a sliding block; the cylindrical center post is axially fixed on the bottom plate and is grounded, the direct current motor is arranged on the center post, a motor shaft of the direct current motor is vertically arranged, the rotating rod is horizontally arranged, one end of the rotating rod is connected to the motor shaft of the direct current motor, and the motor shaft and the rotating rod are grounded; the reed is of an annular structure arranged on the bottom plate and is made of metal materials, and the sliding block is cylindrical; the central column and the sliding block are both arranged in the range of the annular reed; when the bottom plate inclines, the slide block slides towards the inclined direction to form tensile force on the reed; the annular reed is electrically connected with the control processing module, and is also connected with a pull-up resistor and then connected with a power supply;
the control processing module is used for driving a motor shaft of the direct current motor to rotate through the direct current motor driving circuit so as to drive the rotating rod to rotate, and when the rotating rod is not in contact with the reed, the control processing module detects a high level; when the rotating rod rotates to contact the reed, the control processing module detects a low level, and the tensile force F of the reed is obtained at the low level so as to calculate the normal vector quantity value of the inclined surface.
According to the scheme, the control module comprises a microprocessor, a display, a voice player and a keyboard, the microprocessor is electrically connected with the reed to acquire the input level Uin detected by the rotating rod contact reed to calculate the slope normal line to the magnitude, and the display, the voice player and the keyboard are electrically connected with the microprocessor for man-machine interaction; the microprocessor is also electrically connected with the direct current motor driving circuit to drive the direct current motor to rotate.
According to the scheme, the tester also comprises a case, a partition plate, a panel, an electronic module box and a battery box; the case is of a square structure with a hollow interior, the partition board is horizontally arranged in the case and is used for dividing the interior of the case into an upper cavity and a lower cavity, the bottom plate is arranged in the lower cavity of the case, the bottom surface of the case is parallel to the bottom plate, the electronic module box is arranged in the upper cavity of the case and is used for placing the signal conditioning module and the control module, the battery box is also arranged in the upper cavity of the case and is used for supplying power to a system, and the panel is horizontally arranged on the upper surface of the upper cavity of the case and is used for fixing and opening the display, the voice player and the keyboard.
According to the scheme, the sliding block and the middle column are of cylindrical structures and have the same radius.
A method for testing the flattening type inclination angle of the annular reed comprises the following steps:
step 1: the circular reed keeps circular under the condition of no external tensile force, and if the circular reed is subjected to the external tensile force, the circular reed is flattened, namely becomes an ellipse; if the center of the ellipse is at the point O, one end of the long axis is at the point A, namely the far intersection point with the circumference of the center post, the OA direction is defined as an x' axis, a straight line which is parallel to the side length of the bottom plate and passes through the point O is defined as an x axis, and the straight line intersects with the long axis of the ellipse at the point O; two contacts M are arranged on the position of the ellipse with the distance A being the length d of the rotating rod 1 And M 2 ，AM 1 And AM 2 With clips parallel to the x-axisAngle is respectively phi 1 And phi 2 ，AM 1 And AM 2 The angle between the direction of the bisector and the direction parallel to the x-axis is represented by phi, AM 1 And AM 2 The included angle is expressed as delta phi, the larger the stretching force borne by the reed is, the smaller delta phi is;
the initial test was as follows:
step 2: the control processing module sends a clockwise rotation instruction to the direct current motor driving circuit;
and step 3: in the rotating process of the rotating rod, the control processing module can detect that the input level Uin is a low level when the rotating rod is contacted with the reed, and can detect a high level when the rotating rod is not contacted with the reed, so that whether the current input level Uin is at the low level or not is judged; if yes, executing the step 4, otherwise, returning to the step 2;
and 4, step 4: sending a rotation stopping instruction to a direct current motor driving circuit;
and 5: recording the counterclockwise included angle phi between the current rotating rod and the x axis 1 ；
Step 6: sending a counterclockwise rotation instruction to a direct current motor driving circuit;
and 7: judging whether the current input level Uin is at a low level; if yes, executing the step 8, otherwise, returning to the step 6;
and 8: sending a rotation stopping instruction to a direct current motor driving circuit;
and step 9: recording the counterclockwise included angle phi between the current rotating rod and the x axis 2 ；
Step 10: according to phi 1 And phi 2 Calculation and G xoy The unit vector g of the xoy coordinate system in the direction of the orthogonal y' axis is [ g ] x ，g y ，g y ]And the included angle between the inclined plane and the horizontal plane
Figure BDA0002700851370000021
Sine value of
Figure BDA0002700851370000028
And cosine value
Figure BDA0002700851370000022
According to
Figure BDA0002700851370000023
And g ═ g x ，g y ，g y ]Calculating a coordinate system transformation matrix T, specifically:
according to phi 1 And phi 2 Calculating the included angle between the inclined plane and the horizontal plane
Figure BDA0002700851370000024
Sine value of
Figure BDA0002700851370000025
And cosine value
Figure BDA0002700851370000026
The step 10a specifically includes:
step 10 a.1: calculating the included angle delta phi between two contact points of the rotating rod and the elliptical ring reed, wherein the included angle delta phi is equal to | phi 2 -φ 1 |；
Step 10 a.2: estimating the length a of the major semiaxis of the ellipse:
Figure BDA0002700851370000027
wherein p represents the perimeter of the elliptical ring reed;
step 10 a.3: inquiring the a-F comparison table to obtain a stress value F corresponding to the current a value, thereby obtaining a component force value G of the slide block gravity value G on the bottom plate xoy ，G xoy ＝F；
Step 10 a.4: calculating the included angle between the inclined plane and the horizontal plane
Figure BDA0002700851370000031
Sine and cosine values of (c):
Figure BDA0002700851370000032
according to phi 1 And phi 2 Calculation and G xoy The unit vector g in the direction of the orthogonal y' axis is [ g ] x ，g y ，g y ]The step 10b specifically includes:
step 10 b.1: calculating the tensile force G to which the reed is subjected xoy The direction of the X-axis and the x-axis form an anticlockwise included angle phi;
Figure BDA0002700851370000033
wherein phi is 1 And phi 2 Respectively representing AM 1 And AM 2 The included angle with the direction parallel to the x axis;
step 10 b.2: calculation and G xoy The unit vector in the direction of the orthogonal y' axis is expressed as g ═ g in the xyz three-dimensional coordinate system x ，g y ，g y ]The following assignments were made:
Figure BDA0002700851370000034
calculating a variation matrix from the results of steps 10a and 10 b:
Figure BDA0002700851370000035
step 11: the normal vector of the measured plane is expressed by a three-dimensional coordinate system with the horizontal plane as the xoy plane as follows:
Figure BDA0002700851370000036
the invention has the following beneficial effects:
firstly, the length of a major semi-axis of an ellipse with a certain circumference (reflecting the flattening degree) is measured to measure the tensile force applied to the ellipse, and the direction of the tensile force applied to the ellipse is measured in the direction of the major axis of the ellipse to obtain a reed tensile force vector F. Since direct measurement of the long axle length and tensile force is difficult, and the motor rotational angle measurement is much easier, both are converted to a measure of the motor rotational angle, as follows: by one fixingThe rotating rod with fixed length rotates around one end point A of the long axis of the ellipse, and two contact points M exist between the rotating rod and the ellipse 1 And M 2 Whereby the direction of the tensile force is measured by measuring AM 1 And AM 2 The direction of the angle bisector of (a) is obtained, and the magnitude of the tensile force is measured by measuring AM 1 And AM 2 The angle of (c) is further substituted into and solved for the equation f (a) for the major-axis length to be 0. The component of the spring tension force F, i.e. the gravity G of the slide block, on the inclined plane is obtained from the direction of F, the unit vector G orthogonal to the inclined plane is obtained from the direction of F, and the included angle between the inclined plane and the horizontal plane can be obtained from the ratio of the magnitude of F to the magnitude of the gravity G of the slide block
Figure BDA0002700851370000037
G is mixed with
Figure BDA0002700851370000038
The slope normal vector value in a horizontal coordinate system can be obtained by substituting a relevant formula, so that the slope measurement is realized, and the method has the advantages that the low complexity of a hardware system is realized under the same precision;
and secondly, a fast algorithm for solving the equation f (a) ═ 0 is provided, and an error correction term is introduced to save the iteration process required by the iteration algorithms such as a currently common dichotomy method and a Newton method, so that the solution can be carried out without iteration, the complexity reduction is large, the precision reduction is small, and the low complexity of the algorithm is realized under the same precision.
Drawings
FIG. 1 is a schematic block diagram of the overall structure of a measuring instrument according to an embodiment of the present invention;
FIG. 2 is an external view of a system of a measuring instrument according to an embodiment of the present invention;
FIG. 3 is a view showing an internal structure of the measuring instrument according to the embodiment of the present invention;
FIG. 4 is a structural schematic diagram of measuring inclination based on ellipticity flattening, according to an embodiment of the present invention;
FIG. 5 is a top view coordinate diagram of a structure for measuring inclination based on ellipticity flattening in accordance with an embodiment of the present invention;
FIG. 6 is a force analysis diagram of the slider on the measured plane according to the embodiment of the present invention;
FIG. 7 is a flowchart of an inclined plane normal vector algorithm in an embodiment of the present invention;
fig. 8 is a diagram comparing the algorithm principle and the solution result for solving equation f (a) ═ 0;
FIG. 9 is a graph of the effect of error correction terms;
fig. 10 is a graph of the accuracy comparison of various algorithms for solving equation f (a) ═ 0;
fig. 11 is a comparison graph of the complexity of various algorithms for solving equation f (a) ═ 0.
Reference numerals: 1. a base plate; 2. a center pillar; 3.a direct current motor; 3a, a motor shaft; 4. a rotating rod; 5. a reed; 6. a slider; 7. a display; 8.a voice player; 9. a keyboard; 10. a chassis; 11. a partition plate; 12. a panel; 13. an electronic module case; 14. a battery case.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
Referring to fig. 1 to 11, the present invention is a flattened tilt angle tester for a ring-shaped reed 5, which includes a signal collecting module and a control processing module;
the signal acquisition module comprises a bottom plate 1, a center post 2, a direct current motor 3, a rotating rod 4, a reed 5 and a sliding block 6; 2 axial fixings of columniform center pillar are in bottom plate 1 and ground connection, and center pillar 2 is the metal material, and direct current motor 3 locates on center pillar 2 and the vertical setting of motor shaft 3a of direct current motor 3, and 4 levels of bull stick set up and 4 one ends of bull stick are connected in direct current motor 3 motor shaft 3a, and motor shaft 3a and bull stick 4 keep ground connection.
The reed 5 is an annular structure arranged on the bottom plate 1 and is made of metal, and the sliding block 6 is cylindrical; the middle column 2 and the sliding block 6 are both arranged in the range of the annular reed 5, and the sliding block 6 and the middle column 2 are both in cylindrical structures and have the same radius; when the bottom plate 1 tilts, the slide block 6 slides towards the tilting direction to form tensile force on the spring leaf 5; the annular reed 5 is electrically connected with the control processing module, and the annular reed 5 is also connected with a pull-up resistor and then connected with a power supply.
The control processing module is used for driving a motor shaft 3a of the direct current motor 3 to rotate through a direct current motor 3 driving circuit so as to drive the rotating rod 4 to rotate, and when the rotating rod 4 is not contacted with the reed 5, the control processing module detects a high level; when the rotating rod 4 rotates to contact the reed 5, the control processing module detects a low level and obtains the stretching force F of the reed 5 according to the detected input level so as to calculate the normal vector value of the inclined plane; the control module comprises a microprocessor, a display 7, a voice player 8 and a keyboard 9, the microprocessor is electrically connected with the reed 5 to acquire the input level Uin detected by the contact reed 5 of the rotating rod 4 to calculate the slope normal line quantity, and the display 7, the voice player 8 and the keyboard 9 are electrically connected with the microprocessor for man-machine interaction; the microprocessor is also electrically connected with a driving circuit of the direct current motor 3 to drive the direct current motor 3 to rotate.
The tester also comprises a case 10, a partition 11, a panel 12, an electronic module box 13 and a battery box 14; the case 10 is a square structure with a hollow interior, the partition plate 11 is horizontally arranged in the case 10 and is used for dividing the interior of the case 10 into an upper cavity and a lower cavity, the bottom plate 1 is arranged in the lower cavity of the case 10, the bottom surface of the case 10 is parallel to the bottom plate 1, the electronic module box 13 is arranged in the upper cavity of the case 10 and is used for placing the signal conditioning module and the control module, the battery box 14 is also arranged in the upper cavity of the case 10 and is used for supplying power to the system, and the panel 12 is horizontally arranged on the upper surface of the upper cavity of the case 10 and is used for fixing and opening the display 7, the voice player 8 and the keyboard 9.
Referring to fig. 4 to 11, the present invention further provides a flattened inclination angle measuring method for a ring reed, wherein the ring reed is kept circular without external tensile force, and is flattened, i.e. changed into an ellipse, if the ring reed is subjected to external tensile force F, the larger the F, the flatter the ellipse, the longer the major axis 2a, and thus the measurement of the F size can be converted into the measurement of the length of the semi-major axis a of the ellipse, which is one of the basic ideas of the present invention; if the center of the ellipse is at the point O, one end of the major axis is at the point A, and two points M exist at the position of the ellipse with the distance A and the length of d 1 And M 2 ，AM 1 And AM 2 Respectively having an angle phi with respect to a direction parallel to the x-axis 1 And phi 2 ，AM 1 And AM 2 Is expressed as the angle between the bisector direction and the direction parallel to the x axis as phi, AM 1 And AM 2 The angle is represented as Δ φ, the greater the tensile force F experienced by the spring, the smaller Δ φ. When the flat plate is inclined, the slide block slides towards the inclined direction, and the acting force on the reed, namely the tensile force F is generated, so that the magnitude of F can be measured, then the magnitude of delta phi is substituted into an equation F (a) which is 0 to solve a, and the value of the long half axis a of the ellipse is obtained, and the function F is obtained through geometric analysis. After obtaining the value a, the comparison table of a and F (the table is provided by the reed supplier, or the comparison table is detected and obtained by the equipment manufacturer in the previous process) is queried to obtain the value of the tensile force F, and the magnitude of F can be obtained by measuring the magnitude of delta phi instead of the magnitude of a, which is the second basic idea of the invention. Since delta phi is equal to phi 2-phi 1 ，φ＝(φ 1 + φ 2)/2, φ represents the direction of F, so that the magnitude and direction of F can be measured 1 And phi 2 Obtaining, the method comprises the following steps: a motor shaft is arranged at a point A, a rotating rod with the length of d is fixed on a rotating shaft of the motor and is vertical to the rotating shaft, and the motor shaft and the rotating rod are grounded; connecting the reed with the data port of the microprocessor by using a metal flexible wire, connecting the reed with a power supply by using a pull-up resistor, and detecting a high level by the data port of the microprocessor when the rotating rod is not in contact with the reed; when the rotating rod rotates to contact the reed, the microprocessor data port detects low level, so that phi can be detected 1 And phi 2 The magnitude of the force F of the spring, which includes the component force G of the gravity G of the slider on the inclined surface XOY In the size and direction of (1), from G XOY The direction obtains a unit vector G orthogonal thereto, from G and G XOY The included angle between the inclined plane and the horizontal plane can be obtained
Figure BDA0002700851370000061
G is mixed with
Figure BDA0002700851370000062
And substituting the correlation formula to obtain the slope normal vector value of the horizontal coordinate system. In addition, for solving the problem of equation f (a) ═ 0, the invention provides a fast algorithm, and the basic idea is to omit the commonly used dichotomy and Newton method by introducing an error correction termThe iterative process required by the iterative algorithm is equal, so that the complexity reduction is large and the precision reduction is small, which is the third basic idea of the invention. .
The test method comprises the following specific steps:
step 1: the circular reed keeps circular under the condition of no external tensile force, and if the circular reed is subjected to the external tensile force, the circular reed is flattened, namely becomes oval; if the center of the ellipse is at the point O, one end of the long axis is at the point A, namely the far intersection point of the point A and the circumference of the center post, the OA direction is defined as an x' axis, a straight line which is parallel to the side length of the bottom plate and passes through the point O is defined as an x axis, and the straight line intersects the long axis of the ellipse at the point O; two contacts M exist at the position of the ellipse with the distance A as the length d of the rotating rod 1 And M 2 ，AM 1 And AM 2 Respectively has an included angle phi with the direction parallel to the x axis 1 And phi 2 ，AM 1 And AM 2 The angle between the direction of the bisector and the direction parallel to the x-axis is represented by phi, AM 1 And AM 2 The included angle is expressed as delta phi, the larger the tensile force borne by the reed is, the smaller delta phi is;
the initial test was as follows:
and 2, step: the control processing module sends a clockwise rotation instruction to the direct current motor driving circuit;
and step 3: in the rotating process of the rotating rod, the control processing module can detect that the input level Uin is a low level when the rotating rod is contacted with the reed, and can detect a high level when the rotating rod is not contacted with the reed, so that whether the current input level Uin is at the low level or not is judged; if yes, executing the step 4, otherwise, returning to the step 2;
and 4, step 4: sending a rotation stopping instruction to a direct current motor driving circuit;
and 5: recording the counterclockwise included angle phi between the current rotating rod and the x axis 1 ；
And 6: sending a counterclockwise rotation instruction to a direct current motor driving circuit;
and 7: judging whether the current input level Uin is at a low level; if yes, executing step 8, otherwise, returning to step 6;
and 8: sending a rotation stopping instruction to a direct current motor driving circuit;
and step 9: recording the counterclockwise included angle phi between the current rotating rod and the x axis 2 ；
Step 10: according to phi 1 And phi 2 Calculation and G xoy The unit vector g of the xoy coordinate system in the direction of the orthogonal y' axis is [ g ] x ，g y ，g y ]And the included angle between the inclined plane and the horizontal plane
Figure BDA0002700851370000063
Sine value of
Figure BDA0002700851370000064
And cosine value
Figure BDA0002700851370000065
According to
Figure BDA0002700851370000066
And g ═ g x ，g y ，g y ]Calculating a coordinate system transformation matrix T, specifically:
according to phi 1 And phi 2 Calculating the included angle between the inclined plane and the horizontal plane
Figure BDA0002700851370000067
Sine value of
Figure BDA0002700851370000068
And cosine value
Figure BDA0002700851370000069
The step 10a specifically includes:
step 10 a.1: calculating the included angle delta phi between two contact points of the rotating rod and the elliptical ring reed, wherein the included angle delta phi is equal to | phi 2 -φ 1 |；
Step 10 a.2: estimating the length a of the semi-major axis of the ellipse:
Figure BDA0002700851370000071
wherein p represents the perimeter of the elliptical ring reed;
step 10 a.3: inquiring the a-F comparison table to obtain a stress value F corresponding to the current a value, thereby obtaining a component force value G of the slide block gravity value G on the bottom plate xoy ，G xoy ＝F；
Step 10 a.4: calculating the included angle between the inclined plane and the horizontal plane
Figure BDA0002700851370000072
Sine and cosine values of:
Figure BDA0002700851370000073
according to phi 1 And phi 2 Calculation and G xoy The unit vector g in the direction of the orthogonal y' axis is [ g ] x ，g y ，g y ]The step 10b specifically includes:
step 10 b.1: calculating the tensile force G to which the reed is subjected xoy The direction of the X-axis and the X-axis form an anticlockwise included angle phi;
Figure BDA0002700851370000074
wherein phi is 1 And phi 2 Respectively representing AM 1 And AM 2 The included angle with the direction parallel to the x axis;
step 10 b.2: calculation and G xoy The unit vector in the direction of the orthogonal y' axis is expressed as g ═ g in the xyz three-dimensional coordinate system x ，g y ，g y ]The following assignments were made:
Figure BDA0002700851370000075
calculating a variation matrix from the results of steps 10a and 10 b:
Figure BDA0002700851370000076
step 11: calculating a target result: the normal vector of the measured plane is expressed by a three-dimensional coordinate system with the horizontal plane as the xoy plane as follows:
Figure BDA0002700851370000077
the following gives the specific procedure of the above formula derivation:
as shown in FIG. 4, the rotating rod rotates for one circle and has two contacts with the elliptical ring reed, M 1 And M 2 . Parametric equation based on ellipses, M 1 And M 2 Can be expressed by equation (1):
Figure BDA0002700851370000078
as shown in FIG. 5, the length of the turn bar is equal to d, M 1 Or M 2 And a (a, 0) is equal to d, then equation (2) exists:
(acost-a) 2 +(bsint-0) 2 ＝d 2 (2)
suppose M in FIG. 5 1 A and M 2 The angle between a is equal to Δ Φ, then equation (3) exists:
Figure BDA0002700851370000079
Δφ＝|φ 2 -φ 1 | (3.b)
wherein phi 1 And phi 2 The angle between the rotation rod and the direction parallel to the x-axis when it rotates to the reed contact, where | represents the absolute value.
Will sintAnd costConsidered as variables, the solution is based on equations (2) and (3). Based on the formula (3.a)bsintAvailable acostExpressed, and then substituted into equation (2) to obtain equation (4):
Figure BDA0002700851370000081
substitution of equation (4) into sin 2 t+cos 2 t is 1, and an equation reflecting the relationship between a and b is obtained, as shown in equation (5):
Figure BDA0002700851370000082
the perimeter of the elliptic ring reed is a fixed constant after the design scheme of the product is shaped, is a known quantity, is represented by a symbol p, and is based on an approximate formula p ≈ 2 pi (ab) of the elliptic perimeter given by Kepler 1/2 There is formula (6):
Figure BDA0002700851370000083
substituting equation (6) into equation (5) eliminates b, yielding equation (7):
Figure BDA0002700851370000084
equation (7) is a quadratic equation about the ellipse major semi-axis a, and many algorithms exist for solving the equation: firstly, if a strict closed solution is obtained, a root-finding formula of Ferrari (1522-1565) can be adopted, the algorithm is quite complex, four roots exist in a complex field, and obviously, a real root is needed, so that the problems of root judgment and root selection are also involved; second, if an approximate numerical solution is obtained, an iterative algorithm, such as a dichotomy, a newton tangent, a chord intercept, etc., is generally used. The calculation complexity of each algorithm is high, in order to reduce the calculation complexity, the invention provides a low-complexity approximation algorithm without iteration, and the principle of the algorithm is described as follows:
the expression on the left of the equation shown in equation (7) is expressed as a function f (a), as shown in equation (8. a):
Figure BDA0002700851370000085
wherein u is as shown in equation (8. b):
Figure BDA0002700851370000086
let the derivative of f (a) over a, shown in equation (8.a), be equal to zero, resulting in the equation shown in equation (9):
Figure BDA0002700851370000087
solving the equation shown in equation (9) yields an expression of the solution shown in equation (10):
Figure BDA0002700851370000091
as shown in FIG. 8, f (a) 0 ) Is the minimum value of f (a), and has f (a) 0 ) Is less than 0. f (a) there are two intersections with the a-axis, i.e. there are two real solutions, each at a > a 0 And a < a 0 The position of (a). Let a ═ b ═ r, in which case the ellipse becomes a special case, i.e. a ═ p/(2 pi) in a circle with radius equal to r, so a reasonable real number solution should satisfy a > - ═ p/(2 pi), found by numerical experiments, a < a ═ p/(2 pi) 0 Time is not satisfied, therefore, a reasonable real number solution satisfies a > a 0 。
The last term of f (a) shown in equation (8.a) is deleted, denoted as g (a), and g (a) is made equal to 0, so that the equation shown in equation (11) is obtained:
Figure BDA0002700851370000092
solving the equation shown in equation (11) yields a solution a of g (a) 0 as shown in equation (12) 1 ：
Figure BDA0002700851370000093
Due to g (a) < f (a), and twoWhich differ by a constant, so that f (a) 1 ) > 0, so a reasonable real solution of f (a) 0 satisfies a 0 ＜a＜a 1 As shown in fig. 8.
Let a 01 ＝(a 0 +a 1 ) And/2 is an approximate solution with a large error of f (a) and 0, namely a dichotomy which is not subjected to an iterative process. A numerical solution of f (a) equal to 0, which is obtained by sufficiently repeating the bisection method a plurality of times, is represented as a itr The error value e of the two is a 01 -a itr The dependence on Δ φ is shown in FIG. 9, which shows that e (Δ φ) resembles a sinusoidal function, and therefore, the error correction term shown in equation (13) is used:
Figure BDA0002700851370000094
wherein
Figure BDA0002700851370000095
Therefore, the approximate solution of error-corrected f (a) ═ 0 is denoted by a c ＝a 01 -e c (Δ φ), as shown in equation (14):
Figure BDA0002700851370000096
and u is shown as a formula (8.b), and is substituted into the formula (8.b) for post-treatment to obtain an approximate solution formula with higher precision (f) (a) being 0 without iteration, namely an estimation formula of the change of the ellipse major semiaxis a along with the included angle delta phi of the rotating rod between two contact points of the elliptical ring reed, which is shown as a formula (15):
Figure BDA0002700851370000097
fig. 8 to 11 are comparative diagrams of various algorithms, where p is 2 pi and d is 2 in fig. 8 to 11 1/2 The accuracy threshold set by the bisection multiple iterations is 1/1000.
To determine if equation (15) is correct, we can use special cases to verify as follows. Assumed to be adopted during design
Figure BDA0002700851370000101
In this case, if the bottom plate shown in fig. 3 is horizontal, it is obvious that: Δ Φ ═ pi/2, and a ═ r ═ p/(2 pi). Substituting Δ Φ ═ pi/2 into equation (15) results in the following:
Figure BDA0002700851370000102
the error between the above result and the accurate solution a, r, p/(2 pi) is several thousandth, so that it is seen that the algorithm shown in formula (15) provided by the present invention can achieve higher operation accuracy under the condition of greatly reducing the calculation complexity.
Therefore, the included angle Δ φ between the two contact points of the rotating rod on the elliptical ring reed can be obtained by measurement, the value of the major-axis a of the elliptical ring reed in FIG. 4 can be estimated based on the formula (15), and then the component force value G of the slider gravity G on the bottom plate in FIG. 6 can be obtained by inquiring an a-F comparison table of the major-axis a and the tensile force F applied to the major-axis a (the table is provided by a reed supplier or detected and obtained by the equipment manufacturer in the previous process step) xoy I.e. G xoy F, and then obtaining the angle between the inclined plane and the horizontal plane
Figure BDA0002700851370000103
Sine and cosine values of (a), as shown in equation (16):
Figure BDA0002700851370000104
in addition, as shown in FIG. 4, the microprocessor controls the motor bearing to rotate, so as to drive the rotating rod to rotate, there are two contacts with the oval metal spring, since the central column is grounded, the rotating rod is grounded, when the rotating rod contacts the spring, the spring is grounded, so the contact between the rotating rod and the spring can be detected by the circuit shown in FIG. 1,the microprocessor detects a Uin low level when the two are in contact and detects a Uin high level when the two are not in contact. The rotating rod is driven by the motor, and the motor is controlled by the microprocessor, so that the microprocessor can know the current rotating angle of the rotating rod at any time, and can know the stretching force G applied to the reed xoy Is angled counterclockwise from a direction parallel to the x-axis, as shown in fig. 5. The calculation of φ is shown in equation (17):
Figure BDA0002700851370000105
wherein phi 1 And phi 2 Represents AM in FIG. 5 1 And AM 2 Counterclockwise from a direction parallel to the x-axis.
In the xoy two-dimensional coordinate system shown in FIG. 5, the slope is aligned with G xoy The unit vector in the direction of the orthogonal y' axis is expressed as g ═ g in the xyz three-dimensional coordinate system x ，g y ，g y ]Then, it can be expressed as formula (18):
Figure BDA0002700851370000111
in the three-dimensional coordinate system with the xoy plane of FIG. 5, the right-hand rotation around the unit vector g facing the z-axis
Figure BDA0002700851370000112
The required coordinate transformation matrix formula T is obtained by substituting formula (18) into the formula provided in the relevant literature, as shown in formula (19):
Figure BDA0002700851370000113
in the three-dimensional xyz rectangular coordinate system shown in fig. 5 with the plane to be measured as the xoy plane, the normal vector of the plane to be measured is [0, 0, 1 ]] T Using equation (19), a more general three-dimensional coordinate system with horizontal plane as xoy plane, denoted by the symbol n, can be used, as shown in equation (20)The following steps:
Figure BDA0002700851370000114
wherein the content of the first and second substances,
Figure RE-GDA0002819864190000115
and
Figure RE-GDA0002819864190000116
the calculation of (c) is shown in formula (16), and the calculation of phi is shown in formula (17).
The non-related parts of the present invention are the same as or implemented using the prior art.
The foregoing is a more detailed description of the present invention that is presented in conjunction with specific embodiments, and specific implementations of the present invention are not to be considered as limited by these descriptions. For those skilled in the art to which the invention pertains, numerous simple deductions or substitutions may be made without departing from the spirit of the invention, which shall be deemed to belong to the scope of the invention.

Claims (5)

1. Annular reed formula inclination tester that flattens, its characterized in that: comprises a signal acquisition module and a control processing module;
the signal acquisition module comprises a bottom plate (1), a middle column (2), a direct current motor (3), a rotating rod (4), a reed (5) and a sliding block (6); the cylindrical center post (2) is axially fixed on the bottom plate (1) and is grounded, the direct current motor (3) is arranged on the center post (2), a motor shaft (3a) of the direct current motor (3) is vertically arranged, the rotating rod (4) is horizontally arranged, one end of the rotating rod (4) is connected to the motor shaft (3a) of the direct current motor (3), and the motor shaft (3a) and the rotating rod (4) are grounded; the reed (5) is of an annular structure arranged on the bottom plate (1) and is made of metal, and the sliding block (6) is cylindrical; the middle column (2) and the sliding block (6) are both arranged in the range of the reed (5); when the bottom plate (1) tilts, the sliding block (6) slides towards the tilting direction to form tensile force on the spring leaf (5); the reed (5) is electrically connected with the control processing module, and the reed (5) is also connected with a pull-up resistor and then connected with a power supply;
the control processing module is used for driving a motor shaft (3a) of the direct current motor (3) to rotate through a direct current motor (3) driving circuit so as to drive the rotating rod (4) to rotate, and when the rotating rod (4) is not in contact with the reed (5), the control processing module detects a high level; when the rotating rod (4) rotates to contact the reed (5), the control processing module detects a low level, and the tensile force F of the reed (5) is obtained at the low level so as to calculate the normal linear quantity of the inclined surface.
2. The annular reed flattening tilt angle tester of claim 1, wherein: the control module comprises a microprocessor, a display (7), a voice player (8) and a keyboard (9), the microprocessor is electrically connected with the reed (5) to acquire the input level Uin detected by the contact reed (5) of the rotating rod (4) to calculate the slope normal line to the magnitude, and the display (7), the voice player (8) and the keyboard (9) are electrically connected with the microprocessor for human-computer interaction; the microprocessor is also electrically connected with a driving circuit of the direct current motor (3) to drive the direct current motor (3) to rotate.
3. The ring reed flattening tilt angle tester according to claim 1, wherein: the tester also comprises a case (10), a partition plate (11), a panel (12), an electronic module box (13) and a battery box (14); the case (10) is of a hollow square structure, a partition plate (11) is horizontally arranged in the case (10) and used for dividing the inside of the case (10) into an upper cavity and a lower cavity, the bottom plate (1) is arranged in the lower cavity in the case (10), the bottom surface of the case (10) is parallel to the bottom plate (1), the electronic module box (13) is arranged in the upper cavity in the case (10) and used for placing the signal conditioning module and the control module, the battery box (14) is also arranged in the upper cavity in the case (10) and used for supplying power to a system, and the panel (12) is horizontally arranged on the upper surface of the upper cavity in the case (10) and used for fixing and opening the display (7), the voice player (8) and the keyboard (9).
4. The annular reed flattening tilt angle tester of claim 1, wherein: the sliding block (6) and the middle column (2) are both of cylindrical structures and have the same radius.
5. The annular reed flattening type inclination angle testing method is characterized by comprising the following steps: the annular reed flattening tilt angle tester of any one of the preceding claims 1 to 4 is used, and the test method is as follows:
step 1: the circular reed keeps circular under the condition of no external tensile force, and if the circular reed is subjected to the external tensile force, the circular reed is flattened, namely becomes oval; if the center of the ellipse is at the point O, one end of the long axis is at the point A, namely the far intersection point of the point A and the circumference of the center post, the OA direction is defined as an x' axis, a straight line which is parallel to the side length of the bottom plate and passes through the point O is defined as an x axis, and the x axis intersects the long axis of the ellipse at the point O; two contacts M exist at the position of the ellipse with the distance A as the length d of the rotating rod 1 And M 2 ，AM 1 And AM 2 Respectively has an included angle phi with the direction parallel to the x axis 1 And phi 2 ，AM 1 And AM 2 The angle between the direction of the bisector and the direction parallel to the x-axis is represented by phi, AM 1 And AM 2 The included angle is expressed as delta phi, the larger the tensile force borne by the reed is, the smaller delta phi is;
the initial test was as follows:
step 2: the control processing module sends a clockwise rotation instruction to the direct current motor driving circuit;
and step 3: in the rotating process of the rotating rod, the control processing module can detect that the input level Uin is a low level when the rotating rod is contacted with the reed, and can detect a high level when the rotating rod is not contacted with the reed, so that whether the current input level Uin is at the low level or not is judged; if yes, executing the step 4, otherwise, returning to the step 2;
and 4, step 4: sending a rotation stopping instruction to a direct current motor driving circuit;
and 5: recording the counterclockwise included angle phi between the current rotating rod and the x axis 1 ；
Step 6: sending a counterclockwise rotation instruction to a direct current motor driving circuit;
and 7: judging whether the current input level Uin is at a low level or not; if yes, executing the step 8, otherwise, returning to the step 6;
and 8: sending a rotation stopping instruction to a direct current motor driving circuit;
and step 9: recording the counterclockwise included angle phi between the current rotating rod and the x axis 2 ；
Step 10: according to phi 1 And phi 2 Calculating the tensile force G applied to the reed xoy The unit vector g ═ g of the xoy coordinate system in the direction of the orthogonal y' axis x ,g y ,g y ]And the included angle between the inclined plane and the horizontal plane
Figure FDA0003598481070000021
Sine value of
Figure FDA0003598481070000022
And cosine value
Figure FDA0003598481070000023
According to
Figure FDA0003598481070000024
Figure FDA0003598481070000025
And g ═ g x ,g y ,g y ]Calculating a coordinate system transformation matrix T, specifically:
according to phi 1 And phi 2 Calculating the included angle between the inclined plane and the horizontal plane
Figure FDA0003598481070000026
Sine value of
Figure FDA0003598481070000027
And cosine value
Figure FDA0003598481070000028
The step 10a specifically includes:
step 10 a.1: calculating the included angle delta phi between two contacts of the rotating rod in the elliptical ring reed, wherein the delta phi is equal to | phi 2 -φ 1 |；
Step 10 a.2: estimating the length a of the major semiaxis of the ellipse:
Figure FDA0003598481070000029
wherein p represents the perimeter of the elliptical ring reed; the approximate solution of error corrected f (a) ═ 0 is denoted as a c Namely, the change of an included angle delta phi of the ellipse major semi-axis a along with the change of the rotating rod between two contacts of the elliptical ring reed;
step 10 a.3: inquiring the a-F comparison table to obtain a stress value F corresponding to the current a value, thereby obtaining a component force value G of the slide block gravity value G on the bottom plate xoy ：G xoy ←F；
Step 10 a.4: calculating the included angle between the inclined plane and the horizontal plane
Figure FDA00035984810700000210
Sine and cosine values of (c):
Figure FDA00035984810700000211
Figure FDA00035984810700000212
according to phi 1 And phi 2 Calculation and G xoy The unit vector g in the direction of the orthogonal y' axis is [ g ] x ,g y ,g y ]The step 10b specifically includes:
step 10 b.1: calculating the tensile force G to which the reed is subjected xoy The direction of the X-axis and the X-axis form an anticlockwise included angle phi;
Figure FDA0003598481070000031
wherein phi is 1 And phi 2 Respectively representing AM 1 And AM 2 The included angle with the direction parallel to the x axis;
step 10 b.2: calculation and G xoy The unit vector in the direction of the orthogonal y' axis is expressed as g ═ g in the xyz three-dimensional coordinate system x ,g y ,g y ]The following assignments were made:
Figure FDA0003598481070000032
calculating a variation matrix from the results of steps 10a and 10 b:
Figure FDA0003598481070000033
step 11: the normal vector of the measured plane is expressed by a three-dimensional coordinate system with the horizontal plane as the xoy plane as follows:
Figure FDA0003598481070000034
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DE19822834A1 (en) * 1997-05-24 1999-02-25 Behrens Erika Sensor, especially position or inclination sensor
CN106338272A (en) * 2016-11-25 2017-01-18 广州市建筑科学研究院有限公司 Testing device and testing method for measuring inclination angle of component
CN206160999U (en) * 2016-11-01 2017-05-10 武汉东湖学院 Engine cylinder block levelness testing arrangement

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JP2007139485A (en) * 2005-11-16 2007-06-07 Citizen Miyota Co Ltd Pendulum type sensor
CN104931020A (en) * 2015-04-23 2015-09-23 青岛科技大学 Object inclination angle measuring method and device thereof

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE19822834A1 (en) * 1997-05-24 1999-02-25 Behrens Erika Sensor, especially position or inclination sensor
CN206160999U (en) * 2016-11-01 2017-05-10 武汉东湖学院 Engine cylinder block levelness testing arrangement
CN106338272A (en) * 2016-11-25 2017-01-18 广州市建筑科学研究院有限公司 Testing device and testing method for measuring inclination angle of component

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