CN112284340A - Disc spring capacitance type inclination angle tester and testing method - Google Patents

Disc spring capacitance type inclination angle tester and testing method Download PDF

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Publication number
CN112284340A
CN112284340A CN202011020127.1A CN202011020127A CN112284340A CN 112284340 A CN112284340 A CN 112284340A CN 202011020127 A CN202011020127 A CN 202011020127A CN 112284340 A CN112284340 A CN 112284340A
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chassis
xoy
plane
oscillator
sliding block
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CN112284340B (en
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张照锋
吴明康
聂子健
蔡纪源
王顺华
李璟
殷家腾
高燕
孙冬
顾斌
吴珊珊
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
    • G01B7/00—Measuring arrangements characterised by the use of electric or magnetic techniques
    • G01B7/30—Measuring arrangements characterised by the use of electric or magnetic 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

Abstract

The invention relates to the technical field of angle detection, in particular to a disc spring capacitance type inclination angle tester and a test method thereof.A capacitor is formed by two polar plates, a metal slide block forms one polar plate, and M metal chassis boundary walls covered by the slide block form the other polar plate; calculating the oscillation frequency of the sine wave oscillator according to the capacitance value and the inductance value of the capacitor; measuring the included angle between the inclined plane and the horizontal plane by detecting different oscillation frequencies generated by capacitors formed by boundary walls at different positions; calculating component force module value G of the gravity G of the sliding block on the chassis according to the serial number of the chassis boundary wall opposite to the arc surface of the sliding blockxoyCounterclockwise rotation from the x-axis to calculate the sum G in the inclined planexoyAn orthogonal vector; finally according to the included angle between the inclined plane and the horizontal plane and the included angle G in the xoy planexoyOrthogonal vector gxoyAnd calculating the normal vector of the inclined plane to obtain a target result, and realizing the detection of the inclination of the inclined plane to be detected.

Description

Disc spring capacitance type inclination angle tester and testing method
Technical Field
The invention relates to the technical field of angle detection, in particular to a disc spring capacitance type inclination angle tester and a test method.
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 disc spring capacitance type inclination angle tester and a test method, which realize inclination detection and have high detection precision.
In order to solve the technical problems, the technical scheme of the invention is as follows: the disc spring capacitance type inclination tester comprises a signal acquisition module, a signal conversion module and a control processing module;
the signal acquisition module comprises a circular chassis, a chassis boundary wall, an arched sliding block, two springs and a high-frequency cable; the chassis boundary walls are a plurality of separated and closely arranged and uniformly distributed in the circumferential direction on the edge of the circular chassis, one arc side of the arched slide block is close to the chassis boundary walls, the chassis boundary walls and the arched slide block are both made of metal materials, and each chassis boundary wall is electrically connected with an analog switch; the two ends of the arc of the arched sliding block are respectively connected with one end of each spring, the other ends of the two springs are fixed at the circle center of the circular chassis, and the two ends of the arc of the arched sliding block are electrically connected with one end of the high-frequency cable;
the signal conversion module comprises a sine wave oscillator, a comparator and a counter which are connected in sequence; the sine wave oscillator is electrically connected with the other end of the high-frequency cable and the analog switch; one end of the counter is electrically connected with the comparator, and the other end of the counter is electrically connected with the control processing module; the sine wave oscillator generates a sine wave signal and then converts the sine wave signal into a square wave signal through the comparator, and the counter is used for recording the pulse number of the square wave signal;
the control processing module is electrically connected with the analog switch and used for selecting a part of adjacent chassis boundary walls to be electrically communicated with the oscillator, obtaining the oscillation frequency of the oscillator according to the division of the time slot width by the pulse number input in the specified time slot recorded by the counter and calculating the normal vector of the inclined plane according to the detected sequence number set of the chassis boundary walls opposite to the center of the arc surface of the sliding block.
According to the scheme, the control processing module comprises a microprocessor, a display, a voice player and a keyboard, wherein the microprocessor is electrically connected with the counter to calculate the normal vector of the inclined plane, and the display, the voice player and the keyboard are electrically connected with the microprocessor for human-computer interaction; the microprocessor is also electrically connected to the analog switch to select a portion of the adjacent chassis interface wall to be in electrical communication with the oscillator.
According to the scheme, the tester also comprises a case, a separation disc, a face disc, an electronic module box and a battery box; the case is of a square structure with a hollow interior, the partition disc is horizontally arranged in the case and 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 in the case, the bottom surface of the case is parallel to the bottom plate, the electronic module box is arranged in the upper cavity in the case and used for placing the signal conditioning module and the control module, the battery box is also arranged in the upper cavity in the case and used for supplying power to the system, and the face disc is horizontally arranged on the upper surface of the upper cavity in the case and used for fixing and opening.
The disc spring capacitance type inclination angle test method adopts the disc spring capacitance type inclination angle tester, and the test method comprises the following steps:
step 1: assigning the serial number k of the current chassis boundary wall as 0;
step 2: outputting a coding instruction for controlling the analog switch, and electrically communicating a chassis interface wall with the serial number ranging from max (0, k- (M-1)/2) to min (N-1, k + (M-1)/2) with a channel connected with the oscillator; wherein, N represents the number of the chassis boundary walls, and M represents the number of the chassis boundary walls in the capacitor formed by the sliding block and the chassis boundary walls;
and step 3: dividing the number of pulses input in the specified time slot recorded by the counter by the time slot width to obtain the oscillation frequency f of the oscillatork；
And 4, step 4: judging whether the serial number k of the current chassis boundary wall is equal to the total number N-1 of the chassis boundary walls on the chassis, if so, executing the step 5, otherwise, adding 1 to the serial number k of the current chassis boundary wall and returning to the step 2;
and 5: calculating the serial number n of the chassis boundary wall opposite to the center of the arc surface of the slide block, wherein the serial number n is the oscillation frequency fkWhen the minimum value except 0 is reached, the value of the serial number k of the chassis boundary wall is assigned as follows: n ← argkmin({fk|k＝0…N-1}\{fk|f k0, k-0 … N-1}), wherein the operator X \ Y represents the difference between sets X and Y, i.e., such that the result belongs to X but not to Y;
step 6: taking the plane of the chassis as an xoy plane, the straight line where the connecting line of the center O of the chassis and the center of the boundary wall of the chassis with the serial number of 0 is positioned as an x axis, and the straight line which passes through the center O of the chassis and is orthogonal to the x axis is a y axis, and calculating the component force G of the gravity G of the sliding block on the chassisxoyCounterclockwise rotation phi of direction from the x-axisnThe following assignments were made: phi is an←2πn/N；
And 7: computing sum G in xoy planexoyOrthogonal vector gxoy＝[gx,gy]The following assignments were made: gx←-sinφn，gy←cosφn；
And 8: calculating the included angle between the inclined plane, i.e. the plane of the chassis, and the horizontal plane
Figure BDA0002700356660000021
The following assignments were made:
Figure BDA0002700356660000022
wherein k represents the spring constant of the spring; psi represents the angle between the two springs; g represents the modulus value of the gravity G of the slide block; r represents the radius of the chassis; r is0Representing the length of the spring when the chassis is horizontal; epsilonrRepresenting the relative dielectric constant of the medium contained between the capacitor plates, wherein the relative dielectric constant of air is substituted; ξ represents the electrostatic force constant; s represents the surface area of the centripetal surface of each chassis boundary wall; l is the inductance value of the oscillator configuration; f. ofnThe oscillation frequency of the sine wave oscillator under the current slide block position is obtained;
and step 9: based on g obtained in step 7xoy＝[gx,gy]And obtained in step 8
Figure BDA0002700356660000024
Calculating a normal vector n of an inclined plane in an xyz coordinate system taking a horizontal plane as an xoy plane, and assigning as follows:
Figure BDA0002700356660000023
the invention has the following beneficial effects: the invention forms a capacitor by two polar plates, a metal slide block forms one polar plate, a part of adjacent metal chassis boundary wall covered by the slide block forms the other polar plate, and the air in the gap between the two polar plates forms a medium. Upon detection of the oscillation frequency f of the sine-wave oscillatornAnd a configured total inductance value L, wherein n represents the serial number of the chassis boundary wall opposite to the center of the arc surface of the slide block, and then based on fnAnd L and the present capacitance value C of the capacitornObtaining C from the relational formula ofn(ii) a WhilefnBy detecting the oscillation frequency f of the oscillator, scan by scan (by a counter)kK is 0 … N-1, where N represents the number of chassis bounding walls, fnI.e. { fkAnd | k | -0 … N-1 }. This has the advantage that the component force G of G on the inclined surface can be easily obtainedxoy(including its modulus and direction), and then through GxoyThe normal vector n of the inclined plane in the xyz coordinate system, in which the xoy coordinate system lies in the horizontal plane, can be conveniently obtained as explained below:
based on fnFrom the formula f of the oscillation frequencyn＝1/[(2π(LCn)1/2]The capacitance C can be obtainednAnd further by the capacitance value CnThe distance between the slide block and the circle center of the circle of the boundary wall can be obtained by a calculation formula of the area and the space of the polar plate, so that the component force G of the gravity G of the slide block on the inclined plane can be obtained through Hooke's lawxoyThereby obtaining the angle between the inclined plane and the horizontal plane
Figure BDA0002700356660000031
Two, based on { f k0 … N-1 and fnThe serial number n of the chassis boundary wall opposite to the center of the arc surface of the sliding block can be obtained, so that the component force G of the gravity G of the sliding block on the chassis can be obtainedxoyCan be expressed by its counterclockwise rotation phi from the x-axis, and thus in the inclined plane with GxoyOrthogonal vector gxoyIs also easy to obtain; the xyz coordinate system which locates the xoy coordinate system at the inclined plane is wound around gxoyRotation angle
Figure BDA0002700356660000032
The habitually used xyz coordinate system with the xoy coordinate system located in the horizontal plane is then obtained, and therefore, the xoy coordinate system will be
Figure BDA0002700356660000033
And gxoyThe transformation matrix T for the above coordinate system rotation transformation can be obtained by substituting into the relevant literature formula, and the normal vector of the inclined plane in the coordinate system before transformation just passes through the z-axis, so that the normal vector can be very simply expressed as nold＝[0,0,1]Therefore, the calculation of the normal vector n of the inclined plane in the transformed coordinate system is also simple: n is TnoldAnd n is the target result.
Therefore, the inclination measurement of the measured plane by adopting the method can take into account three conditions of low complexity, high precision and low cost, which obviously are mutually restricted and difficult for common designers to take into account.
Drawings
FIG. 1 is a schematic block diagram of the overall structure of an embodiment of the present invention;
FIG. 2 is a system diagram of the tester of the present embodiment;
FIG. 3 is an internal structural view of the tester of the present embodiment;
FIG. 4 is a schematic diagram of a signal acquisition module according to the present embodiment;
FIG. 5 is a diagram illustrating a force analysis of the slider on the chassis surface in the present embodiment;
FIG. 6 is a diagram illustrating force analysis of the slider on the inclined plane in the present embodiment;
FIG. 7 is a flowchart of an incline direction measuring algorithm.
Reference numerals: 1. a chassis; 2. a chassis boundary wall; 3. a slider; 4. a spring; 5. a high-frequency cable; 6. a display; 7. a voice player; 8. a keyboard; 9. a chassis; 10. a separation disc; 11. a dough disc; 12. an electronic module cartridge; 13. 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 7, the present invention provides a disc spring capacitive tilt angle tester, which includes a signal acquisition module, a signal conversion module and a control processing module;
the signal acquisition module comprises a circular chassis 1, a chassis boundary wall 2, an arched slider 3, two springs 4 and a high-frequency cable 5; the number of the chassis boundary walls 2 is a plurality of separated and closely arranged and evenly distributed in the circumferential direction on the edge of the circular chassis 1, one arc side of the arched sliding block 3 is close to the chassis boundary walls 2, the chassis boundary walls 2 and the arched sliding block 3 are both made of metal materials, and each chassis boundary wall 2 is electrically connected with an analog switch; the two ends of the arc of the arched sliding block 3 are respectively connected with one end of a spring 4, the other ends of the two springs 4 are fixed at the position of the circle center of the circular chassis 1, and the two ends of the arc of the arched sliding block 3 are electrically connected with one end of a high-frequency cable 5;
the signal conversion module comprises a sine wave oscillator, a comparator and a counter which are connected in sequence; the sine wave oscillator is electrically connected with the other end of the high-frequency cable 5 and the analog switch; one end of the counter is electrically connected with the comparator, and the other end of the counter is electrically connected with the control processing module; the sine wave oscillator generates a sine wave signal and then converts the sine wave signal into a square wave signal through the comparator, and the counter is used for recording the pulse number of the square wave signal;
the control processing module is electrically connected with the analog switch and used for selecting a part of adjacent chassis boundary walls 2 to be electrically communicated with the oscillator, obtaining the oscillation frequency of the oscillator according to the division of the time slot width by the pulse number input in the specified time slot recorded by the counter and calculating the normal vector of the inclined plane according to the detected sequence number set of the chassis boundary walls 2 opposite to the center of the arc surface of the sliding block 3.
The control processing module comprises a microprocessor, a display 6, a voice player 7 and a keyboard 8, the microprocessor is electrically connected with the counter to calculate the normal vector of the inclined plane, and the display 6, the voice player 7 and the keyboard 8 are electrically connected with the microprocessor for man-machine interaction; the microprocessor is also electrically connected to the analog switch to select a portion of the adjacent chassis interface wall 2 to be in electrical communication with the oscillator.
The tester also comprises a case 9, a separation disc 10, a panel 11, an electronic module box 12 and a battery box 13; the case 9 is a square structure with a hollow interior, the partition plate 10 is horizontally arranged in the case 9 and is used for dividing the interior of the case 9 into an upper cavity and a lower cavity, the bottom plate is arranged in the lower cavity in the case 9, the bottom surface of the case 9 is parallel to the bottom plate, the electronic module box 12 is arranged in the upper cavity in the case 9 and is used for placing the signal conditioning module and the control module, the battery box 13 is also arranged in the upper cavity in the case 9 and is used for supplying power to the system, and the face plate 11 is horizontally arranged on the upper surface of the upper cavity in the case 9 and is used for fixing and opening the.
The invention also provides a test method for performing inclination test by adopting the disc spring capacitive inclination tester, which comprises the following specific steps of:
step 1: assigning the serial number k of the current chassis boundary wall as 0;
step 2: outputting a coding instruction for controlling the analog switch, and electrically communicating a chassis interface wall with the serial number ranging from max (0, k- (M-1)/2) to min (N-1, k + (M-1)/2) with a channel connected with the oscillator; wherein, N represents the number of the chassis boundary walls, and M represents the number of the chassis boundary walls in the capacitor formed by the sliding block and the chassis boundary walls;
and step 3: dividing the number of pulses input in the specified time slot recorded by the counter by the time slot width to obtain the oscillation frequency f of the oscillatork；
And 4, step 4: judging whether the serial number k of the current chassis boundary wall is equal to the total number N-1 of the chassis boundary walls on the chassis, if so, executing the step 5, otherwise, adding 1 to the serial number k of the current chassis boundary wall and returning to the step 2;
and 5: calculating the serial number n of the chassis boundary wall opposite to the center of the arc surface of the slide block, wherein the serial number n is the oscillation frequency fkWhen the minimum value except 0 is reached, the value of the serial number k of the chassis boundary wall is assigned as follows: n ← argkmin({fk|k＝0…N-1}\{fk|f k0, k-0 … N-1}), wherein the operator X \ Y represents the difference between sets X and Y, i.e., such that the result belongs to X but not to Y;
step 6: taking the plane of the chassis as an xoy plane, the straight line where the connecting line of the center O of the chassis and the center of the boundary wall of the chassis with the serial number of 0 is positioned as an x axis, and the straight line which passes through the center O of the chassis and is orthogonal to the x axis is a y axis, and calculating the component force G of the gravity G of the sliding block on the chassisxoyCounterclockwise rotation phi of direction from the x-axisnThe following assignments were made: phi is an←2πn/N；
And 7: computing sum G in xoy planexoyOrthogonal vector gxoy＝[gx,gy]The following assignments were made: gx←-sinφn，gy←cosφn；
And 8: calculating the included angle between the inclined plane, i.e. the plane of the chassis, and the horizontal plane
Figure BDA0002700356660000054
The following assignments were made:
Figure BDA0002700356660000051
wherein k represents the spring constant of the spring; psi represents the angle between the two springs; g represents the modulus value of the gravity G of the slide block; r represents the radius of the chassis; r is0Representing the length of the spring when the chassis is horizontal; epsilonrRepresenting the relative dielectric constant of the medium contained between the capacitor plates, wherein the relative dielectric constant of air is substituted; ξ represents the electrostatic force constant; s represents the surface area of the centripetal surface of each chassis boundary wall; l is the inductance value of the oscillator configuration; f. ofnThe oscillation frequency of the sine wave oscillator under the current slide block position is obtained;
and step 9: based on g obtained in step 7xoy＝[gx,gy]And obtained in step 8
Figure BDA0002700356660000055
Calculating a normal vector n of an inclined plane in an xyz coordinate system taking a horizontal plane as an xoy plane, and assigning as follows:
Figure BDA0002700356660000052
the following gives the specific procedure of the above formula derivation:
in fig. 1, when the number of the base plate boundary wall facing the center of the arc surface is equal to k, the oscillation frequency of the sine wave oscillator at this time is represented as fkIt can be calculated by equation (1):
Figure BDA0002700356660000053
where k is 0 … N-1, L is the total inductance value, CkIs the total capacitance value of the oscillation currently generated.
Electricity in figure 1As shown in figure 4, the container is composed of two polar plates, a metal slide block forms one polar plate, M adjacent metal chassis boundary walls which are covered by the slide block and take a serial number k as a center form the other polar plate, the capacitance value between the metal slide block and one chassis boundary wall is represented by C, and obviously CkThe capacitor is formed by connecting M small capacitors c in parallel, so that a formula (2) exists:
Ck＝Mc (2)
based on the capacitance decision equation, c can be calculated by equation (3):
Figure BDA0002700356660000061
where ξ represents the electrostatic force constant, εrRepresents the relative dielectric constant of the medium contained between the capacitor plates, where the relative dielectric constant of air is substituted, s represents the surface area of the centripetal face of each chassis boundary wall, R represents the chassis radius, and R represents the current spring length.
In steps 1-4, part of adjacent channels of the analog switch in fig. 1 are communicated in a scanning manner one by one, and in the process of gradually increasing k to N-1 from 0, a plurality of adjacent chassis boundary walls ranging from max (0, k- (M-1)/2) to min (N-1, k + (M-1)/2) are electrically communicated with the oscillator at the kth time. After the position of the slide block is stabilized, assuming that the slide block currently covers M adjacent metal chassis boundary walls with the serial number N as the center, in the scanning process k being 0 … N-1, only when k being N, the M adjacent chassis boundary walls with the slide block cambered surface electrically communicated with the oscillator are completely opposite, the effective plate area forming the oscillator is the largest, and therefore the capacitance is the smallest, and the oscillation frequency f at this time is known by formula (1)nAt the lowest, however, it should be excluded that the oscillator stops vibrating f because the boundary wall communicated with the oscillator through the analog switch is far away from the arc surface of the sliding block, so that the formed capacitance is too smallk0, thus fnThe formula (4) is adopted:
Figure BDA0002700356660000062
where the operator symbol X \ Y represents the difference between sets X and Y, i.e., such that the result belongs to X but not Y.
Therefore, let k be n, then substitute equation (3) into equation (2), and substitute equation (2) into equation (1), resulting in r and fnIs shown in formula (5):
Figure BDA0002700356660000063
as shown in fig. 4 and 5, a modulus F of a tensile force F of a spring applied to a slider on a chassis inclined based on hooke's law can be calculated by equation (6):
F＝k(r-r0) (6)
wherein k represents the spring constant of the spring, r0Representing the length of the spring when the chassis is horizontal.
As shown in fig. 5, the slider is balanced when it comes to rest on the inclined surface, so equation (7) holds:
2Fcos(ψ/2)＝Gxoy (7)
wherein psi represents the angle between the two springs, GxoyComponent force G representing the weight G of the slide block on the inclined planexoyModulus value of (2), as shown in FIG. 6, GxoyCan be expressed as equation (8):
Figure BDA0002700356660000064
wherein G represents a modulus value of gravity G of the slider,
Figure BDA0002700356660000065
representing the angle between the inclined plane and the horizontal plane, i.e. the elevation angle.
Substituting the formula (8) into the formula (7), and substituting the formula (7) into the formula (6) to obtain rkAnd
Figure BDA0002700356660000076
is expressed by the following formula (9): ' Qiyi
Figure BDA0002700356660000071
Simultaneous equations (5) and (9), eliminating r, to obtain
Figure BDA0002700356660000077
And fnIs shown in formula (10):
Figure BDA0002700356660000072
the formula (10) means that the angle between the inclined plane and the horizontal plane
Figure BDA0002700356660000078
By detecting the oscillation frequency f of the oscillator at the current position of the slidenMeasurements were taken as shown in fig. 1.
In the xoy plane, as shown in FIG. 5, G isxoyThe unit vector in the direction is expressed as [ cos φ, sin φ]And G isxoyThe orthogonal vector is denoted as gxoy＝[gx,gy]Then, in the xyz coordinate system where the xoy coordinate system is parallel to the measured tilt, there exists the formula (11):
Figure BDA0002700356660000073
wherein phi isnRepresenting the slide at the current position GxoyThe counterclockwise rotation angle from the x-axis is calculated using equation (12):
Figure BDA0002700356660000074
wherein N is shown in formula (4), and N represents the total number of the boundary walls on the chassis. In this embodiment, the total number N of chassis boundary walls is 36, the number M of chassis boundary walls covered by the slider arc surface is 7, and the median N of the serial number sets of the adjacent serial chassis boundary walls covered by the slider arc surface is 27.
Since the tilt direction of the tilt plane is determined by its normal, it is reasonable to use its normal vector for the tilt measurement. The algorithm principle based on the normal vector of a certain inclined plane of the invention is as follows:
using a three-dimensional rectangular coordinate system which takes figure 5 as xoy plane and takes the reader pointed by the center of a circle of the chassis as a z axis, and winding a unit vector g according to the right hand rulexoyRotate
Figure BDA0002700356660000079
And a three-dimensional rectangular coordinate system which is more in line with the habit and takes the horizontal plane as the xoy plane can be obtained. G is prepared fromxoy＝[gx,gy]And
Figure BDA00027003566600000710
substituting into the transformation matrix formula for the above coordinate transformation provided by the related document, the formula of transformation matrix T as shown in formula (13) is obtained:
Figure BDA0002700356660000075
Figure BDA0002700356660000081
in the xyz coordinate system where the xoy plane shown in FIG. 5 is parallel to the measured plane and the z-axis passes through the center of the chassis and points to the reader, the unit normal vector of the measured plane passes through the z-axis and is represented as [0,0,1 ]]TWherein the superscript T represents transpose, and can be represented by a three-dimensional rectangular coordinate system which is more conventional in the art and takes a horizontal plane as xoy plane, and the symbol is n, by using formula (13), the calculation formula of n is shown as formula (14):
Figure BDA0002700356660000082
wherein, gxAnd gyIs shown in equation (11),
Figure BDA0002700356660000083
is solved as shown in equation (10);
equation (14) is the target result.
The parts not involved in 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 the practice of the invention is not to be considered limited to those descriptions. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (4)

1. Disc spring capacitance type inclination tester, its characterized in that: the device comprises a signal acquisition module, a signal conversion module and a control processing module;
the signal acquisition module comprises a circular chassis (1), a chassis boundary wall (2), an arched sliding block (3), two springs (4) and a high-frequency cable (5); the number of the chassis boundary walls (2) is a plurality of separated and closely arranged and uniformly distributed on the edge of the circular chassis (1) in the circumferential direction, one arc side of the arched sliding block (3) is close to the chassis boundary walls (2), the chassis boundary walls (2) and the arched sliding block (3) are both made of metal materials, and each chassis boundary wall (2) is electrically connected with an analog switch; the two ends of the arc of the arched sliding block (3) are respectively connected with one end of the spring (4), the other ends of the two springs (4) are fixed at the position of the circle center of the circular chassis (1), and the two ends of the arc of the arched sliding block (3) are electrically connected with one end of the high-frequency cable (5);
the signal conversion module comprises a sine wave oscillator, a comparator and a counter which are connected in sequence; the sine wave oscillator is electrically connected with the other end of the high-frequency cable (5) and the analog switch; one end of the counter is electrically connected with the comparator, and the other end of the counter is electrically connected with the control processing module; the sine wave oscillator generates a sine wave signal and then converts the sine wave signal into a square wave signal through the comparator, and the counter is used for recording the pulse number of the square wave signal;
the control processing module is electrically connected with the analog switch and used for selecting a part of adjacent chassis boundary walls (2) to be electrically communicated with the oscillator, obtaining the oscillation frequency of the oscillator according to the division of the time slot width by the pulse number input in the specified time slot recorded by the counter and calculating the normal vector of the inclined plane according to the detected sequence number set of the chassis boundary wall (2) opposite to the arc surface center of the sliding block (3).
2. The disc spring capacitive inclinometer according to claim 1, characterized in that: the control processing module comprises a microprocessor, a display (6), a voice player (7) and a keyboard (8), the microprocessor is electrically connected with the counter to calculate the normal vector of the inclined plane, and the display (6), the voice player (7) and the keyboard (8) are electrically connected with the microprocessor for man-machine interaction; the microprocessor is also electrically connected to the analog switch to select a portion of the adjacent chassis interface wall (2) to be in electrical communication with the oscillator.
3. The disc spring capacitive inclinometer according to claim 1, characterized in that: the tester also comprises a case (9), a separation disc (10), a face disc (11), an electronic module box (12) and a battery box (13); the case (9) is of a square structure with a hollow interior, the partition disc (10) is horizontally arranged in the case (9) and used for dividing the interior of the case (9) into an upper cavity and a lower cavity, the bottom plate is arranged in the lower cavity in the case (9), the bottom surface of the case (9) is parallel to the bottom plate, the electronic module box (12) is arranged in the upper cavity in the case (9) and used for placing the signal conditioning module and the control module, the battery box (13) is also arranged in the upper cavity in the case (9) and used for supplying power to a system, and the face disc (11) is horizontally arranged on the upper surface of the upper cavity in the case (9) and used for fixing and opening the display (6), the voice player.
4. A disc spring capacitance type inclination angle test method, which is characterized in that the disc spring capacitance type inclination angle tester of any one of the claims 1 to 3 is adopted, and the test method is as follows:
step 1: assigning the serial number k of the current chassis boundary wall as 0;
step 2: outputting a coding instruction for controlling the analog switch, and electrically communicating a chassis interface wall with the serial number ranging from max (0, k- (M-1)/2) to min (N-1, k + (M-1)/2) with a channel connected with the oscillator; wherein, N represents the number of the chassis boundary walls, and M represents the number of the chassis boundary walls in the capacitor formed by the sliding block and the chassis boundary walls;
and step 3: dividing the number of pulses input in the specified time slot recorded by the counter by the time slot width to obtain the oscillation frequency f of the oscillatork；
And 4, step 4: judging whether the serial number k of the current chassis boundary wall is equal to the total number N-1 of the chassis boundary walls on the chassis, if so, executing the step 5, otherwise, adding 1 to the serial number k of the current chassis boundary wall and returning to the step 2;
and 5: calculating the serial number n of the chassis boundary wall opposite to the center of the arc surface of the slide block, wherein the serial number n is the oscillation frequency fkWhen the minimum value except 0 is reached, the value of the serial number k of the chassis boundary wall is assigned as follows: n ← argkmin({fk|k＝0...N-1}\{fk|fkN-1}), where the operator X \ Y represents the difference between sets X and Y, i.e., such that the result belongs to X but not Y;
step 6: taking the plane of the chassis as an xoy plane, the straight line where the connecting line of the center O of the chassis and the center of the boundary wall of the chassis with the serial number of 0 is positioned as an x axis, and the straight line which passes through the center O of the chassis and is orthogonal to the x axis is a y axis, and calculating the component force G of the gravity G of the sliding block on the chassisxoyCounterclockwise rotation phi of direction from the x-axisnThe following assignments were made: phi is an←2πn/N；
And 7: computing sum G in xoy planexoyOrthogonal vector gxoy＝[gx，gy]The following assignments were made: gx←-sinφn，gy←cosφn；
And 8: calculating the included angle between the inclined plane, i.e. the plane of the chassis, and the horizontal plane
Figure FDA0002700356650000021
The following assignments were made:
Figure FDA0002700356650000022
wherein k represents the spring constant of the spring; psi represents the angle between the two springs; g represents the modulus value of the gravity G of the slide block; r represents the radius of the chassis; r is0Representing the length of the spring when the chassis is horizontal; epsilonrRepresenting the relative dielectric constant of the medium contained between the capacitor plates, wherein the relative dielectric constant of air is substituted; ξ represents the electrostatic force constant; s represents the surface area of the centripetal surface of each chassis boundary wall; l is the inductance value of the oscillator configuration; f. ofnThe oscillation frequency of the sine wave oscillator under the current slide block position is obtained;
and step 9: based on g obtained in step 7xoy＝[gx，gy]And obtained in step 8
Figure FDA0002700356650000023
Calculating a normal vector n of an inclined plane in an xyz coordinate system taking a horizontal plane as an xoy plane, and assigning as follows:
Figure FDA0002700356650000024
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JPH07159165A (en) * 1993-12-06 1995-06-23 Sony Corp Tilt sensor
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US4528760A (en) * 1980-02-28 1985-07-16 Pa Consulting Services Limited Clinometer
US4636792A (en) * 1984-07-02 1987-01-13 Itt Corporation Capacitive angular position transducer
US5029251A (en) * 1988-06-15 1991-07-02 Rune Sundberg Transducer for measuring angles of inclination, angular positions and other positions, and apparatus comprising such transducer
JPH07159165A (en) * 1993-12-06 1995-06-23 Sony Corp Tilt sensor
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