CN112648916B - Three-dimensional micro-displacement measuring method and system - Google Patents

Three-dimensional micro-displacement measuring method and system Download PDF

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CN112648916B
CN112648916B CN202110061164.5A CN202110061164A CN112648916B CN 112648916 B CN112648916 B CN 112648916B CN 202110061164 A CN202110061164 A CN 202110061164A CN 112648916 B CN112648916 B CN 112648916B
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capacitive
displacement
voltage value
sensor
ratio
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CN112648916A (en
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李新娥
年夫顺
金怀智
张智超
赵夏青
王川东
汪洋
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North University of China
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    • G01—MEASURING; TESTING
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Abstract

The invention discloses a three-dimensional micro-displacement measuring method and a system, which relate to the technical field of micro-displacement measurement, and the method comprises the following steps: obtaining a model of a displacement object to be measured; three capacitive grating sensor groups are arranged on the model of the displacement object to be measured; the model comprises a first sub-model and a second sub-model, and the first sub-model is arranged in the second sub-model; the movable grid of the capacitive grid sensor group is arranged on the outer side wall of the first sub-model and the static grid is arranged on the inner side wall of the second sub-model or the movable grid of the capacitive grid sensor group is arranged on the inner side wall of the second sub-model and the static grid is arranged on the outer side wall of the first sub-model; the movable grid and the static grid of each capacitive grid sensor group form a channel, and each channel is used for detecting the polar distance change and the area change of the movable grid; the area change is the relative area change of the movable grid and the static grid; respectively acquiring voltage values of the three capacitive gate sensor groups; and determining the displacement according to the voltage value of the capacitive gate sensor group. The invention can realize the measurement of the three-dimensional space micro displacement.

Description

Three-dimensional micro-displacement measuring method and system
Technical Field
The invention relates to the technical field of micro displacement measurement, in particular to a three-dimensional micro displacement measurement method and system.
Background
With the rapid development of aerospace, ship heavy industry and the like in China, higher requirements are made on precision measurement. The micro-displacement measurement is a key basic technology of precision measurement, and the development of the advanced manufacturing industry is restricted. The micro-displacement measurement technology is greatly developed through years of research, and mainly comprises a laser displacement measurement technology, a grating displacement measurement technology, an LVDT displacement sensor, a PSD displacement sensor and the like, the sensors have a remarkable defect, the sensor has a large volume, and cannot be thinned, so that the capability of measuring the micro-displacement in a narrow space is restricted; and the optical sensor has higher power consumption and higher requirement on the capacity of a battery, and is not beneficial to the installation and the arrangement of the sensor.
Disclosure of Invention
The invention aims to provide a three-dimensional micro-displacement measuring method and a three-dimensional micro-displacement measuring system, which are used for measuring three-dimensional space micro-displacement.
In order to achieve the purpose, the invention provides the following scheme:
a three-dimensional displacement measurement method, comprising:
obtaining a model of a displacement object to be measured; three capacitive grating sensor groups are arranged on the model of the displacement object to be measured; the model comprises a first submodel and a second submodel, and the first submodel is arranged in the second submodel; the movable grid of the capacitive grid sensor group is arranged on the outer side wall of the first sub-model and the static grid is arranged on the inner side wall of the second sub-model or the movable grid of the capacitive grid sensor group is arranged on the inner side wall of the second sub-model and the static grid is arranged on the outer side wall of the first sub-model; the movable grid and the static grid of each capacitive grid sensor group form a channel, and each channel is used for detecting the polar distance change and the area change of the movable grid; the area change is the relative area change of the movable grid and the static grid;
respectively acquiring voltage values of the three capacitive gate sensor groups;
and determining the displacement according to the voltage value of the capacitive gate sensor group.
Optionally, the determining the displacement according to the voltage value of the capacitive gate sensor group specifically includes:
when the first sub-model and the second sub-model are both hemispheres, determining a voltage component of a capacitive gate sensor channel according to a voltage value of a capacitive gate sensor group, and determining displacement according to the voltage component of the capacitive gate sensor channel; each capacitive gate sensor group comprises a capacitive gate sensor; the three capacitive grid sensors are arranged in a delta shape;
when the first sub-model and the second sub-model are both cuboids, determining displacement according to the voltage value of the capacitive gate sensor group; a bottom surface and two adjacent side surfaces of the cuboid are provided with a capacitive gate sensor group; the capacitive grating sensor group on the same surface of the cuboid comprises two capacitive grating sensors which are arranged at intervals.
Optionally, the determining a displacement according to the voltage component of the capacitive sensor channel specifically includes:
determining the displacement from the voltage component of the capacitive sensor channel using the following equation:
Figure BDA0002902621630000021
wherein u is 1 Voltage value of the first capacitive sensor being hemispherical u 2 Voltage value, u, of the second capacitive-gate sensor being hemispherical 3 Voltage value of the third capacitive-gate sensor being hemispherical, G is amplification factor, u 0 Is an initial voltage, I is a current value, t is time, x is a displacement value in the x-direction, y is a displacement value in the y-direction, z is a displacement value in the z-direction, d 0 The initial polar distance is l, the positive length of the initial position of the capacitive gate, b, the width of the capacitive gate and epsilon, the dielectric constant.
Optionally, after determining the displacement according to the voltage value of the capacitive gate sensor group, the method further includes:
determining the displacement direction of the displacement object to be measured in the y direction according to the ratio of the voltage value of the second capacitive grating sensor to the voltage value of the third capacitive grating sensor;
determining the displacement direction of the displacement object to be measured in the x direction according to the ratio of the voltage value of the capacitive gate sensor to the initial voltage; the capacitive grating sensor is a first capacitive grating sensor or a second capacitive grating sensor or a third capacitive grating sensor;
and determining the displacement direction of the displacement object to be measured in the z direction according to the ratio of the voltage value of the first capacitive grating sensor to the voltage value of the second capacitive grating sensor.
Optionally, when the first sub-model and the second sub-model are both cuboids, determining a displacement according to a voltage value of the capacitive gate sensor group specifically includes:
when the first sub-model and the second sub-model are both cuboids, determining displacement according to the voltage value of the capacitive gate sensor group by using the following formula:
Figure BDA0002902621630000031
Figure BDA0002902621630000032
wherein,
Figure BDA0002902621630000033
is the voltage value of the first capacitive sensor corresponding to the first side surface of the cuboid,
Figure BDA0002902621630000034
the voltage value of the second capacitive sensor corresponding to the first side surface of the cuboid,
Figure BDA0002902621630000035
the voltage value of the third capacitive sensor corresponding to the second side surface of the cuboid,
Figure BDA0002902621630000036
the voltage value of the fourth capacitive sensor corresponding to the second side surface of the cuboid,
Figure BDA0002902621630000037
is the voltage value of the fifth capacitive sensor corresponding to the bottom surface of the cuboid,
Figure BDA0002902621630000038
the voltage value l of the fifth capacitive sensor corresponding to the bottom surface of the cuboid x Is a length of a rectangular parallelepiped z Is the height of a cuboid l y Is the width of a cuboid, alpha 1 、α 2 、α 3 、α 4 、α 5 、α 6 Respectively after the moving grid rotates x Angle l with y-axis x Angle with z axis, < l > y Angle l with x-axis y Angle l with z-axis z Angle l with x-axis x Included angle with the y-axis, Δ d x 、Δd y 、Δd z Every two pairs of capacitive grating sensors respectively having three channelsThe mounting interval, I is a current value, t is time, x is a displacement value along the x direction, y is a displacement value along the y direction, z is a displacement value along the z direction, epsilon is a dielectric constant, and s is a facing area between the moving grid and the static grid of the capacitive grid sensor.
Optionally, after determining the displacement according to the voltage value of the capacitive gate sensor group, the method further includes:
determining the displacement direction of the displacement object to be detected in the x direction according to the first ratio or the second ratio; the first ratio is the ratio of the voltage value of the first capacitive sensor to the initial voltage; the second ratio is the ratio of the voltage value of the second capacitive sensor to the initial voltage;
determining the displacement direction of the displacement object to be detected in the y direction according to the third ratio or the fourth ratio; the third ratio is the ratio of the voltage value of the third capacitive-gate sensor to the initial voltage; the fourth ratio is the ratio of the voltage value of the fourth capacitive sensor to the initial voltage;
determining the displacement direction of the to-be-detected displacement object in the z direction according to the fifth ratio or the sixth ratio; the fifth ratio is the ratio of the voltage value of the fifth capacitive sensor to the initial voltage; the sixth ratio is a ratio of a voltage value of the sixth capacitive sensor to an initial voltage.
A three-dimensional displacement measurement system comprising:
the model acquisition module is used for acquiring a model of the displacement object to be measured; three capacitive gate sensor groups are arranged on the model of the displacement object to be detected; the model comprises a first submodel and a second submodel, and the first submodel is arranged in the second submodel; the movable grid of the capacitive grid sensor group is arranged on the outer side wall of the first sub-model and the static grid is arranged on the inner side wall of the second sub-model or the movable grid of the capacitive grid sensor group is arranged on the inner side wall of the second sub-model and the static grid is arranged on the outer side wall of the first sub-model; the movable grid and the static grid of each capacitive grid sensor group form a channel, and each channel is used for detecting the polar distance change and the area change of the movable grid; the area change is the relative area change of the movable grid and the static grid;
the voltage value acquisition module is used for respectively acquiring the voltage values of the three capacitive gate sensor groups;
and the displacement determining module is used for determining displacement according to the voltage value of the capacitive gate sensor group.
Optionally, the displacement determining module specifically includes:
the first displacement determining submodule is used for determining the voltage component of a capacitive grating sensor channel according to the voltage value of the capacitive grating sensor group and determining the displacement according to the voltage component of the capacitive grating sensor channel when the first submodel and the second submodel are both hemispheres; each capacitive gate sensor group comprises a capacitive gate sensor; the three capacitive grid sensors are arranged in a delta shape;
the second displacement determining submodule is used for determining displacement according to the voltage value of the capacitive gate sensor group when the first sub-model and the second sub-model are both cuboids; a bottom surface and two adjacent side surfaces of the cuboid are provided with a capacitive gate sensor group; the capacitive gate sensor group on the same surface of the cuboid comprises two capacitive gate sensors which are arranged at intervals.
Optionally, the first displacement determining sub-module specifically includes:
a first displacement determination unit for determining a displacement from the voltage component of the capacitive sensor channel using the following formula:
Figure BDA0002902621630000051
wherein u is 1 Voltage value, u, of a first capacitive-gate sensor being hemispherical 2 Voltage value, u, of the second capacitive-gate sensor being hemispherical 3 Voltage value of the third capacitive-gate sensor being hemispherical, G is amplification factor, u 0 Is an initial voltage, I is a current value, t is time, x is a displacement value in the x-direction, y is a displacement value in the y-direction, z is a displacement value in the z-direction, d 0 Is the initial polar distance, l is the volumeThe initial position of the gate is just opposite to the length, b is the width of the capacitor gate, and epsilon is the dielectric constant.
Optionally, the second displacement determining sub-module specifically includes:
a second displacement determining unit, configured to determine, when the first sub-model and the second sub-model are both cuboids, a displacement according to a voltage value of the capacitive gate sensor group by using the following formula:
Figure BDA0002902621630000061
Figure BDA0002902621630000062
wherein,
Figure BDA0002902621630000063
the voltage value of the first capacitive sensor corresponding to the first side surface of the cuboid,
Figure BDA0002902621630000064
the voltage value of the second capacitive sensor corresponding to the first side surface of the cuboid,
Figure BDA0002902621630000065
the voltage value of the third capacitive sensor corresponding to the second side surface of the cuboid,
Figure BDA0002902621630000066
the voltage value of the fourth capacitive sensor corresponding to the second side surface of the cuboid,
Figure BDA0002902621630000067
the voltage value of the fifth capacitive sensor corresponding to the bottom surface of the cuboid,
Figure BDA0002902621630000068
the voltage value l of the fifth capacitive sensor corresponding to the bottom surface of the cuboid x Is a length of a rectangular parallelepiped z Is a cuboidHigh, | y Is the width of a cuboid, alpha 1 、α 2 、α 3 、α 4 、α 5 、α 6 Respectively after the moving grid rotates x Angle l with y-axis x Angle l with z-axis y Angle l with x-axis y Angle with z axis, < l > z Angle l with x-axis x Angle of included angle with y-axis, Δ d x 、Δd y 、Δd z The method is characterized in that the method comprises the following steps that the installation intervals between every two pairs of capacitive grating sensors of three channels are respectively adopted, I is a current value, t is time, x is a displacement value along the x direction, y is a displacement value along the y direction, z is a displacement value along the z direction, epsilon is a dielectric constant, and s is the opposite area between a movable grating and a static grating of each capacitive grating sensor.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides a three-dimensional displacement measurement method and a three-dimensional displacement measurement system.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flow chart of a three-dimensional displacement measurement method of the present invention;
FIG. 2 is a diagram showing the basic components of a capacitance-grid sensor according to the three-dimensional displacement measurement method of the present invention;
FIG. 3 is a schematic diagram of a sphere model coordinate system of the three-dimensional displacement measurement method of the present invention;
FIG. 4 is a schematic diagram of the arrangement of capacitive grating sensors of a sphere model according to the three-dimensional displacement measurement method of the present invention;
FIG. 5 is a schematic diagram of the arrangement of a cuboid model capacitive grating sensor according to the three-dimensional displacement measurement method of the present invention;
FIG. 6 is a schematic diagram of an included angle of a rectangular parallelepiped model channel in the three-dimensional displacement measurement method of the present invention;
FIG. 7 is a schematic view of a calibration test platform for the three-dimensional displacement measurement method according to the present invention;
FIG. 8 is a schematic diagram of a three-dimensional displacement measurement system according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
The invention aims to provide a three-dimensional micro-displacement measuring method and a three-dimensional micro-displacement measuring system, which are used for measuring three-dimensional space micro-displacement.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
As shown in fig. 1, the three-dimensional displacement measurement method provided by the present invention includes:
step 101: obtaining a model of a displacement object to be measured; three capacitive gate sensor groups are arranged on the model of the displacement object to be detected; the model comprises a first submodel and a second submodel, and the first submodel is arranged in the second submodel; the movable grid of the capacitive grid sensor group is arranged on the outer side wall of the first sub-model and the static grid is arranged on the inner side wall of the second sub-model or the movable grid of the capacitive grid sensor group is arranged on the inner side wall of the second sub-model and the static grid is arranged on the outer side wall of the first sub-model; the movable grid and the static grid of each capacitive grid sensor group form a channel, and each channel is used for detecting the polar distance change and the area change of the movable grid; the area change is a relative area change of the movable grid and the static grid.
Step 102: and respectively acquiring voltage values of the three capacitive gate sensor groups.
Step 103: and determining the displacement according to the voltage value of the capacitive gate sensor group.
Wherein, step 102: the method specifically comprises the following steps:
when the first sub-model and the second sub-model are both hemispheres, determining a voltage component of a capacitive gate sensor channel according to a voltage value of a capacitive gate sensor group, and determining displacement according to the voltage component of the capacitive gate sensor channel; each capacitive gate sensor group comprises a capacitive gate sensor; the three capacitive grid sensors are arranged in a delta shape.
In addition, the determining the displacement according to the voltage component of the capacitive sensor channel specifically includes:
determining the displacement from the voltage component of the capacitive-gate sensor channel using the formula:
Figure BDA0002902621630000081
wherein u is 1 Voltage value, u, of a first capacitive-gate sensor being hemispherical 2 Voltage value, u, of the second capacitive-gate sensor being hemispherical 3 Voltage value of the third capacitive-gate sensor being hemispherical, G is amplification factor, u 0 Is an initial voltage, I is a current value, t is time, x is a displacement value in the x-direction, y is a displacement value in the y-direction, z is a displacement value in the z-direction, d 0 The initial polar distance is l, the positive length of the initial position of the capacitive gate, b, the width of the capacitive gate and epsilon, the dielectric constant.
As shown in fig. 3, in practical applications, when the displacement object to be measured is a hemisphere, in order to determine the displacement direction of the displacement object to be measured along the coordinate axis, after determining the displacement according to the voltage value of the capacitive gate sensor group, the method further includes:
and determining the displacement direction of the displacement object to be measured in the y direction according to the ratio of the voltage value of the second capacitive grating sensor to the voltage value of the third capacitive grating sensor. When the ratio of the voltage value of the second capacitive-gate sensor to the voltage value of the third capacitive-gate sensor is continuously increased, that is, the ratio of the voltage value of the second capacitive-gate sensor to the voltage value of the third capacitive-gate sensor is greater than the ratio of the voltage value of the second capacitive-gate sensor to the voltage value of the third capacitive-gate sensor at the initial position, it is indicated that the object moves in the positive y-axis direction.
Determining the displacement direction of the displacement object to be measured in the x direction according to the ratio of the voltage value of the capacitive gate sensor to the initial voltage; the capacitive grating sensor is a first capacitive grating sensor or a second capacitive grating sensor or a third capacitive grating sensor; when the ratio of the voltage value of the capacitive gate sensor to the initial voltage is continuously increased, namely, the voltage value of the capacitive gate sensor is continuously increased, the object moves towards the positive direction of the x axis.
And determining the displacement direction of the displacement object to be measured in the z direction according to the ratio of the voltage value of the first capacitive grating sensor to the voltage value of the second capacitive grating sensor. When the ratio of the voltage value of the first capacitive grating sensor to the voltage value of the second capacitive grating sensor is continuously reduced, namely, the ratio of the voltage value of the first capacitive grating sensor to the voltage value of the second capacitive grating sensor is smaller than the ratio of the voltage value of the first capacitive grating sensor to the voltage value of the second capacitive grating sensor at the initial position, the object moves towards the positive direction of the z axis.
Wherein, the first capacitive grating sensor is a sensor composed of a channel 1 moving grating and a channel 1 static grating in the figure, the second capacitive grating sensor is a sensor composed of a channel 2 moving grating and a channel 2 static grating in the figure, the third capacitive grating sensor is a sensor composed of a channel 3 moving grating and a channel 3 static grating in the figure,
when the first sub-model and the second sub-model are cuboids, determining displacement according to the voltage value of the capacitive gate sensor group; a bottom surface and two adjacent side surfaces of the cuboid are provided with a capacitive gate sensor group; the capacitive gate sensor group on the same surface of the cuboid comprises two capacitive gate sensors which are arranged at intervals.
In addition, when the first sub-model and the second sub-model are cuboids, determining displacement according to the voltage value of the capacitive gate sensor group, specifically comprising:
when the first sub-model and the second sub-model are both cuboids, determining displacement according to the voltage value of the capacitive gate sensor group by using the following formula:
Figure BDA0002902621630000101
Figure BDA0002902621630000102
wherein,
Figure BDA0002902621630000103
is the voltage value of the first capacitive sensor corresponding to the first side surface of the cuboid,
Figure BDA0002902621630000104
the voltage value of the second capacitive sensor corresponding to the first side surface of the cuboid,
Figure BDA0002902621630000105
the voltage value of the third capacitive sensor corresponding to the second side surface of the cuboid,
Figure BDA0002902621630000106
the voltage value of the fourth capacitive sensor corresponding to the second side surface of the cuboid,
Figure BDA0002902621630000107
the voltage value of the fifth capacitive sensor corresponding to the bottom surface of the cuboid,
Figure BDA0002902621630000108
the voltage value l of the fifth capacitive sensor corresponding to the bottom surface of the cuboid x Is the length of a rectangular parallelepiped z Is the height of a cuboid y Is the width of a cuboid, alpha 1 、α 2 、α 3 、α 4 、α 5 、α 6 Respectively after the moving grid rotates x Angle l with y-axis x Angle l with z-axis y Angle l with x-axis y Angle l with z-axis z Angle with x-axis, < l > x Included angle with the y-axis, Δ d x 、Δd y 、Δd z The method is characterized in that the method is respectively used for installing intervals between every two pairs of capacitive grating sensors of three channels, I is a current value, t is time, x is a displacement value along the x direction, y is a displacement value along the y direction, z is a displacement value along the z direction, epsilon is a dielectric constant, and s is the dead-against area between a movable grating and a static grating of each capacitive grating sensor. Wherein, as shown in FIG. 5,. DELTA.d x For the mounting spacing of two grid sensors of the X channel, Δ d y For mounting spacing of two grid sensors of Y channel, Δ d z The installation interval of two capacitive grid sensors of the Z channel is shown.
As shown in fig. 5, in practical application, when the displacement object to be measured is a rectangular parallelepiped, in order to determine the displacement direction of the displacement object to be measured along the coordinate axis, after determining the displacement according to the voltage value of the capacitive gate sensor group, the method further includes:
determining the displacement direction of the displacement object to be detected in the x direction according to the first ratio or the second ratio; the first ratio is the ratio of the voltage value of the first capacitive sensor to the initial voltage; the second ratio is the ratio of the voltage value of the second capacitive-gate sensor to the initial voltage; and when the first ratio or the second ratio is smaller, namely the voltage value of the first capacitive grating sensor or the second capacitive grating sensor is smaller than the initial voltage, the object to be detected moves along the positive direction of the x axis.
Determining the displacement direction of the displacement object to be detected in the y direction according to the third ratio or the fourth ratio; the third ratio is the ratio of the voltage value of the third capacitive sensor to the initial voltage; the fourth ratio is the ratio of the voltage value of the fourth capacitive sensor to the initial voltage; and when the third ratio or the fourth ratio becomes smaller, namely the voltage value of the third capacitive grating sensor or the fourth capacitive grating sensor is smaller than the initial voltage, the object to be detected moves along the positive direction of the y axis.
Determining the displacement direction of the object to be measured in the z direction according to the fifth ratio or the sixth ratio; the fifth ratio is the ratio of the voltage value of the fifth capacitive sensor to the initial voltage; the sixth ratio is a ratio of a voltage value of the sixth capacitive sensor to an initial voltage. And when the fifth ratio or the sixth ratio becomes smaller, namely the voltage value of the fifth capacitive grating sensor or the sixth capacitive grating sensor is smaller than the initial voltage, the object to be detected moves along the positive direction of the z axis.
Fig. 2 is a basic constituent unit of a capacitive sensor, and as shown in fig. 2, the capacitive sensor used in the three-dimensional displacement measurement method of the present invention is manufactured based on a flat capacitive grid, the capacitive sensor is composed of a movable grid and a static grid (equivalent to an upper electrode plate and a lower electrode plate in a capacitor), the movable grid and the static grid are connected to a test system through wires, and when the movable grid displaces, the area and the polar distance of the movable grid change, so as to change the output voltage.
The dynamic and static grid sensors are all N grids which are connected in parallel to form a comb shape, and an ideal insulating medium is arranged between the grids. The thickness of the grid is 0.07mm, the width of the grid is 0.08mm, the distance between the grids is 0.005mm, and a protection ring is arranged around the movable grid and the static grid to reduce the edge effect of the capacitive sensor. The capacitive sensor adopts a flexible processing technology and can be attached to a non-planar object.
When the influence of the edge effect is not considered, each basic unit of the capacitive grating sensor has the following calculation formula:
Figure BDA0002902621630000121
Figure BDA0002902621630000122
Figure BDA0002902621630000123
wherein C is the capacitance of the sensor, N is the number of the grid bars of the capacitive grid sensor, s is the area opposite to the two grid bars of the capacitive grid, d is the distance between the two grid bars, and epsilon 0 Denotes the vacuum dielectric constant,. Epsilon r Is the dielectric constant in air, wherein ε r Equal to 1, Q is the capacitance, I is the current, and t is the time.
When d, s, N and ε 0 When one or more of the capacitance values are changed, the capacitance value is changed, when the movable grid and the static grid generate relative displacement in different directions, the polar distance d or the dead-facing area s is changed, the capacitance value of the capacitance grid is correspondingly changed, the plane micro displacement can be measured according to the variation of the capacitance value of the sensor, and the direction of displacement can be judged according to the variation trend of the capacitance value of the sensor.
In order to complete the measurement of the space displacement, the invention provides two models of the displacement object to be measured, namely a spherical model and a rectangular model.
When the model of the object to be displaced is a sphere model, as shown in fig. 4, the model is two nested concentric spheres with different radii. Three identical capacitive grating sensors are combined in a 'pin' shape and are arranged on the inner surface of a sphere with a larger radius to serve as a static grating, three separated capacitive gratings are adhered on the outer surface of a sphere with a smaller radius to serve as a movable grating, the whole model and the sphere are concentric, the static grating and the movable grating are opposite to form two concentric spherical surfaces, the sphere center is used as an original point, the polar distance direction is changed to serve as an x axis, and the area direction is changed to serve as a y axis and a z axis to establish a coordinate system, as shown in figure 3. In addition, in practical application, the three static grids can be separately arranged. A sensor consisting of a z-axis positive static grid and a moving grid is C 1 The sensor composed of a negative y-axis static grid and a dynamic grid is C 2 The sensor composed of the y-axis positive static grid and the dynamic grid is C 3 Where C1, C2 and C3 are channel 1, channel 2 and channel 3 as shown in fig. 3. The grid direction of the channel 1 is parallel to the y axis, the grid directions of the channels 2 and 3 are parallel to the z axis, and a parameter equation is established according to the model as follows:
Figure BDA0002902621630000131
in the formula, I is a current value, t is time, and x, y and z are three-directional displacement values. U is the output voltage of the system when the displacement occurs in any direction of space, U 0 Is the voltage at two ends of the standard capacitor, namely the voltage when one channel is not displaced, U r When the centre of the sphere is displaced in any direction in spaceValue of change of voltage, U x Represents U r Voltage variation, U, resulting from variation of resolution, i.e. of the capacitance-gate spacing, on the x-axis y Represents U r Voltage variation, U, resulting from variation of resolution in the y-axis, i.e. the area directly opposite the grid z Represents U r Voltage variation generated by z-axis resolution, i.e. change in area directly opposite to the capacitive grid, d 0 And l is the initial pole distance, i is the positive facing length of the initial position of the capacitive grid, i.e. the overlapping length, b is the width of the capacitive grid, i.e. the overlapping width, and the positive facing area is s = l × b. In addition, U is the system (single channel) output voltage, U r The channel-varying voltage generated for the displacement variation having a difference between an initial voltage and an amplification factor, the initial voltage U 0 And the amplification factor G is a known quantity. When the moving grid generates micro displacement along with an object in any direction of a three-dimensional space, according to a displacement decomposition theory in physics and by combining the last two formulas in the formula 1, a formula 2 is obtained, the displacement can be decomposed into displacement components of an x axis, a y axis and a z axis, and the displacement components are converted into voltage components of three channels as shown in the formula:
Figure BDA0002902621630000132
wherein u is 0 The initial voltages of the three channels are consistent; xyz are displacement amounts in three directions respectively, formula 1 actually calculates the moving gate channels 1, 2 and 3 as a whole, and the relationship between the obtained voltage and the displacement is also an integral relationship; the formula 2 decomposes the whole moving grid of the formula 1, because three channels are measured in actual field measurement, the three channels are decomposed into displacement components in the xyz three directions, and the formula 2 is also used in coupling calculation. The relationship of equation (1) to equation (2): u in formula (1) X 、U Y 、U Z Refers to the voltage component of the voltage of one channel on the xyz axis, such as the moving gate C1: at a voltage of U 1 Will U is 1 Substituting into equation (1), i.e. substituting U1 for U in equation (1), and Ur is the output voltage generated by displacement, U 0 ＝U 0 To U, to U r The evolution process is carried out (note: formula (1) for easy understanding U Y U Z Separate calculation, which is converted in equation (2)Change to a common change to area).
In formula 1, U X 、U Y 、U Z The voltage values expressed by the voltage variation amounts due to the displacement are divided into the total voltage values in the XYZ axes, and the total voltage values are the result of theoretical calculation, and u is actually measured 1 、u 2 、u 3 The voltages of the three channels. The voltages of the three channels are related to the displacement of the xyz axes.
In practical applications, the amplification factor G is unknown and needs to be solved by using algorithmic coupling. And (3) driving the sphere model to move by using a three-dimensional moving platform, respectively obtaining the displacements in the XYZ directions by using a micrometer, respectively obtaining the voltages of the three channels, repeating the process to obtain a plurality of groups of data, and fitting by using the obtained displacements and voltages by adopting a BP Neural Network algorithm to obtain an amplification parameter G.
When the model of the displacement object to be measured is a cuboid model, as shown in fig. 5, the outer surface of the small cuboid inside is a movable grid with the side length of 40mm, the inner surface of the large cuboid outside is a static grid with the side length of 80mm, and each channel has two pairs. Different from a spherical model, the model of the displacement object to be measured takes one vertex of a cuboid as an original point and three edges as coordinate axes to establish a three-dimensional coordinate system. The three channels are respectively arranged on three surfaces, specifically a bottom surface and two adjacent side surfaces. Each channel is provided with two pairs of capacitive grating sensors, namely six movable gratings, and all the movable gratings and the static gratings of the six static gratings are separated. The area of the static gate is 4 times that of the movable gate, the side length is 2 times, the influence of a non-local channel on the capacitance value of the capacitive gate of the channel can be reduced, parameters are reduced, and the method has certain significance on model optimization. With the sphere model, the displacement of the measured object in any spatial direction can be decomposed into displacement components in three directions of x, y and z axes, and the x, y and z axes are polar distance changes. When the model is built, the included angle between the moving grid and the static grid is also taken into consideration, for example, fig. 6 is a schematic diagram of the included angle of one of the channels, and accordingly, a parameter equation of the model is built as follows:
Figure BDA0002902621630000151
Figure BDA0002902621630000152
in the formula,
Figure BDA0002902621630000153
U y2 、
Figure BDA0002902621630000154
is the output voltage value l of the capacitance grid sensor corresponding to the surface of the cuboid model x 、l z 、l y Length of three edges, alpha, respectively, at the vertex of the origin of coordinates 1 、α 2 、α 3 、α 4 、α 5 、α 6 Respectively after the moving grid rotates x Angle l with y-axis x Angle with z axis, < l > y Angle l with x-axis y Angle l with z-axis z Angle l with x-axis x Angle of included angle with y-axis, Δ d x 、Δd y 、Δd z The installation intervals of each two pairs of capacitive grating sensors of the three channels are respectively. Alpha is alpha 1 、α 2 、α 3 、α 4 、α 5 、α 6 The angle between the static grid and the dynamic grid can be understood, and the angle between the edge of the cuboid and the static grid can be understood.
When the coupling cuboid model is used, the displacement and the angle can be obtained by adopting a BP Neural Network algorithm to calculate according to the obtained voltage value.
In actual use, the experimental calibration was performed using the calibration test platform shown in fig. 8.
1. The calibration platform adopts a micrometer calibration method, the design precision is 0.01mm, and the minimum precision requirement required by the experiment is met.
2. And installing the configured sensor.
3. A micrometer is used for giving a displacement, then the corresponding voltage value is recorded, the process is repeated, and sufficient data are obtained, so that the unknown number of the parameter equation can be fitted by using a BP Network algorithm. Only the sphere model has unknown parameters and needs to be fitted under the experimental condition, and whether the installation is correct or not is checked when the fitting maximum effect is achieved under the experimental state of the cuboid model.
When the parameter fitting is completed, all parameters are known, and the using method of the model is as follows:
1. again using the BP Networks algorithm.
2. Except that the known displacement, voltage fitting unknown parameters were preceded; now the voltage fitting displacement is known.
3. Because the used test circuit is a dynamic measurement method, the numerical value is changed in real time, the adopted AD chip has 12 bits, the precision is very high, the displacement and the voltage measured by the same group are constantly changed, and the average value of each group is also taken although the precision is very high.
4. For equation (3), the displacement is 3 unknowns, and the angle is also 3 unknowns (three pairs of opposite angles are included), and there are six equations, and the displacement and the angle are directly obtained by the BP Network algorithm.
As shown in fig. 7, the present invention provides a three-dimensional displacement measurement system, which includes:
a model obtaining module 701, configured to obtain a model of a displacement object to be measured; three capacitive grating sensor groups are arranged on the model of the displacement object to be measured; the model comprises a first submodel and a second submodel, and the first submodel is arranged in the second submodel; the movable grid of the capacitive grid sensor group is arranged on the outer side wall of the first sub-model; the static gate is arranged on the inner side wall of the second submodel; the movable grid and the static grid of each capacitive grid sensor group form a channel, and each channel is used for detecting the polar distance change and the area change of the movable grid; the area change is a relative area change of the movable grid and the static grid.
A voltage value obtaining module 702, configured to obtain voltage values of the three capacitive gate sensor groups respectively.
And a displacement determining module 703, configured to determine a displacement according to the voltage value of the capacitive gate sensor group.
The displacement determining module 703 specifically includes:
the first displacement determining submodule is used for determining the voltage component of a capacitive grating sensor channel according to the voltage value of the capacitive grating sensor group and determining the displacement according to the voltage component of the capacitive grating sensor channel when the first submodel and the second submodel are both hemispheres; each capacitive gate sensor group comprises a capacitive gate sensor; the three capacitive grid sensors are arranged in a delta shape.
The second displacement determining submodule is used for determining displacement according to the voltage value of the capacitive gate sensor group when the first sub-model and the second sub-model are both cuboids; a bottom surface and two adjacent side surfaces of the cuboid are provided with a capacitive gate sensor group; the capacitive grating sensor group on the same surface of the cuboid comprises two capacitive grating sensors which are arranged at intervals.
The first displacement determining submodule specifically includes:
a first displacement determining unit for determining a displacement from the voltage component of the capacitive-gate sensor channel using the following formula:
Figure BDA0002902621630000171
wherein u is 1 Is the voltage value of the seventh capacitive-gate sensor u 2 Is the voltage value of the eighth capacitive sensor, u 3 Is the voltage value of the ninth capacitive sensor, G is the amplification factor, u 0 Is an initial voltage, I is a current value, t is time, x is a displacement value in the x-direction, y is a displacement value in the y-direction, z is a displacement value in the z-direction, d 0 The initial polar distance is l, the positive length of the initial position of the capacitive gate, b, the width of the capacitive gate and epsilon, the dielectric constant.
Wherein, the second displacement determining submodule specifically includes:
a second displacement determining unit, configured to determine, when the first sub-model and the second sub-model are both cuboids, a displacement according to a voltage value of the capacitive gate sensor group by using the following formula:
Figure BDA0002902621630000181
Figure BDA0002902621630000182
wherein,
Figure BDA0002902621630000183
the voltage value of the first capacitive sensor corresponding to the first side surface of the cuboid,
Figure BDA0002902621630000184
the voltage value of the second capacitive sensor corresponding to the first side surface of the cuboid,
Figure BDA0002902621630000185
the voltage value of the third capacitive sensor corresponding to the second side surface of the cuboid,
Figure BDA0002902621630000186
the voltage value of the fourth capacitive sensor corresponding to the second side surface of the cuboid,
Figure BDA0002902621630000187
is the voltage value of the fifth capacitive sensor corresponding to the bottom surface of the cuboid,
Figure BDA0002902621630000188
the voltage value l of the fifth capacitive sensor corresponding to the bottom surface of the cuboid x Is the length of a rectangular parallelepiped z Is the height of a cuboid y Is the width of a cuboid, alpha 1 、α 2 、α 3 、α 4 、α 5 、α 6 Respectively after the moving grate rotates x Angle l with y-axis x Angle l with z-axis y Angle l with x-axis y Angle l with z-axis z Angle l with x-axis x Angle of included angle with y-axis, Δ d x 、Δd y 、Δd z Three channels are respectively arranged in each two pairsThe mounting interval between the capacitive grating sensors, I is the current value, t is the time, x is the displacement value along the x direction, y is the displacement value along the y direction, and z is the displacement value along the z direction.
The three-dimensional micro-displacement measuring method and system provided by the invention use the three-dimensional capacitive grating micro-displacement sensor which is developed on the basis of the capacitance sensor, and are characterized by high operation speed, small volume, simple result and low test power consumption, thereby being an accurate and feasible method for measuring the micro-displacement in a narrow space. The advantages are as follows:
1. the capacitance-grid sensor occupies small space and has thin thickness, so that the measurement of micro displacement can be completed in a narrow space.
2. The capacitive grating sensor has a simple structure, and the main sensitive elements are the movable grating and the static grating, so that great convenience is brought to actual installation and debugging.
3. The test circuits all adopt low-power consumption chips, wherein the MCU has a low-power consumption mode. The direct physical quantity measured by the capacitive gate sensor is voltage, data refreshing is kept through continuous charging and discharging of a constant-benefit source, other large-current devices are not arranged, the standby current is in the mu A level, the working current does not exceed 10mA, and one sensor can work for more than one year at 180 mAh.
4. Different test models are designed aiming at different test environments, so that the data volume required by decoupling parameters is greatly reduced; different coupling algorithms are provided for different models, and the decoupling speed is improved.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (7)

1. A method of measuring three-dimensional displacement, comprising:
obtaining a model of a displacement object to be measured; three capacitive gate sensor groups are arranged on the model of the displacement object to be detected; the model comprises a first submodel and a second submodel, and the first submodel is arranged in the second submodel; the movable grid of the capacitive grid sensor group is arranged on the outer side wall of the first sub-model and the static grid is arranged on the inner side wall of the second sub-model or the movable grid of the capacitive grid sensor group is arranged on the inner side wall of the second sub-model and the static grid is arranged on the outer side wall of the first sub-model; the movable grid and the static grid of each capacitive grid sensor group form a channel, and each channel is used for detecting the polar distance change and the area change of the movable grid; the area change is the relative area change of the movable grid and the static grid;
respectively acquiring voltage values of the three capacitive gate sensor groups;
determining displacement according to the voltage value of the capacitive gate sensor group;
when the displacement object that awaits measuring is the cuboid, in order to confirm that the displacement object that awaits measuring is concrete along the displacement direction of coordinate axis still include after confirming the displacement according to the voltage value of capacitive gate sensor group:
determining the displacement direction of the displacement object to be detected in the x direction according to the first ratio or the second ratio; the first ratio is the ratio of the voltage value of the first capacitive gate sensor to the initial voltage; the second ratio is the ratio of the voltage value of the second capacitive gate sensor to the initial voltage;
determining the displacement direction of the displacement object to be detected in the y direction according to the third ratio or the fourth ratio; the third ratio is the ratio of the voltage value of the third capacitive gate sensor to the initial voltage; the fourth ratio is the ratio of the voltage value of the fourth capacitive sensor to the initial voltage;
determining the displacement direction of the to-be-detected displacement object in the z direction according to the fifth ratio or the sixth ratio; the fifth ratio is the ratio of the voltage value of the fifth capacitive sensor to the initial voltage; the sixth ratio is the ratio of the voltage value of the sixth capacitive sensor to the initial voltage;
when the first sub-model and the second sub-model are cuboids, determining displacement according to the voltage value of the capacitive gate sensor group, and specifically comprising:
when the first sub-model and the second sub-model are cuboids, determining displacement according to the voltage value of the capacitive gate sensor group by using the following formula:
Figure FDA0003870558650000021
Figure FDA0003870558650000022
wherein,
Figure FDA0003870558650000023
the voltage value of the first capacitive sensor corresponding to the first side surface of the cuboid,
Figure FDA0003870558650000024
the voltage value of the second capacitive sensor corresponding to the first side surface of the cuboid,
Figure FDA0003870558650000025
the voltage value of the third capacitive sensor corresponding to the second side surface of the cuboid,
Figure FDA0003870558650000026
the voltage value of the fourth capacitive sensor corresponding to the second side surface of the cuboid,
Figure FDA0003870558650000027
is rectangularThe voltage value of the fifth capacitive-gate sensor corresponding to the bottom surface of the body,
Figure FDA0003870558650000028
the voltage value l of the sixth capacitive sensor corresponding to the bottom surface of the cuboid x Is a length of a rectangular parallelepiped z Is the height of a cuboid y Is the width of a cuboid, alpha 1 、α 2 、α 3 、α 4 、α 5 、α 6 Respectively after the moving grid rotates x Angle with y-axis, l x Angle l with z-axis y Angle l with x-axis y Angle l with z-axis z Angle l with x-axis x Angle of included angle with y-axis, Δ d x 、Δd y 、Δd z The method is characterized in that the method is respectively used for installing intervals between every two pairs of capacitive grating sensors of three channels, I is a current value, t is time, x is a displacement value along the x direction, y is a displacement value along the y direction, z is a displacement value along the z direction, epsilon is a dielectric constant, and s is the dead-against area between a movable grating and a static grating of each capacitive grating sensor.
2. The three-dimensional displacement measurement method according to claim 1, wherein the determining of the displacement according to the voltage value of the capacitive gate sensor group specifically comprises:
when the first sub-model and the second sub-model are both hemispheres, determining a voltage component of a capacitive gate sensor channel according to a voltage value of a capacitive gate sensor group, and determining displacement according to the voltage component of the capacitive gate sensor channel; each capacitive gate sensor group comprises a capacitive gate sensor; the three capacitive grid sensors are arranged in a delta shape;
when the first sub-model and the second sub-model are both cuboids, determining displacement according to the voltage value of the capacitive gate sensor group; a bottom surface and two adjacent side surfaces of the cuboid are provided with a capacitive gate sensor group; the capacitive gate sensor group on the same surface of the cuboid comprises two capacitive gate sensors which are arranged at intervals.
3. The three-dimensional displacement measurement method according to claim 2, wherein the determining the displacement according to the voltage component of the capacitive sensor channel specifically comprises:
determining the displacement from the voltage component of the capacitive sensor channel using the following equation:
Figure FDA0003870558650000031
wherein u is 1 Voltage value, u, of a first capacitive-gate sensor being hemispherical 2 Voltage value, u, of the second capacitive-gate sensor being hemispherical 3 Voltage value of the third capacitive-gate sensor being hemispherical, G is amplification factor, u 0 Is an initial voltage, I is a current value, t is time, x is a displacement value in the x-direction, y is a displacement value in the y-direction, z is a displacement value in the z-direction, d 0 The initial polar distance is l, the positive length of the initial position of the capacitive gate, b, the width of the capacitive gate and epsilon, the dielectric constant.
4. The three-dimensional displacement measurement method according to claim 3, wherein after determining the displacement according to the voltage value of the capacitive gate sensor group, the method further comprises:
determining the displacement direction of the displacement object to be measured in the y direction according to the ratio of the voltage value of the second capacitive grating sensor to the voltage value of the third capacitive grating sensor;
determining the displacement direction of the displacement object to be measured in the x direction according to the ratio of the voltage value of the capacitive gate sensor to the initial voltage; the capacitive grating sensor is a first capacitive grating sensor or a second capacitive grating sensor or a third capacitive grating sensor;
and determining the displacement direction of the displacement object to be measured in the z direction according to the ratio of the voltage value of the first capacitive grating sensor to the voltage value of the second capacitive grating sensor.
5. A three-dimensional displacement measurement system, comprising:
the model acquisition module is used for acquiring a model of the displacement object to be measured; three capacitive gate sensor groups are arranged on the model of the displacement object to be detected; the model comprises a first submodel and a second submodel, and the first submodel is arranged in the second submodel; the movable grid of the capacitive grid sensor group is arranged on the outer side wall of the first sub-model and the static grid is arranged on the inner side wall of the second sub-model or the movable grid of the capacitive grid sensor group is arranged on the inner side wall of the second sub-model and the static grid is arranged on the outer side wall of the first sub-model; the movable grid and the static grid of each capacitive grid sensor group form a channel, and each channel is used for detecting the polar distance change and the area change of the movable grid; the area change is the relative area change of the movable grid and the static grid;
the voltage value acquisition module is used for respectively acquiring the voltage values of the three capacitive gate sensor groups;
the displacement determining module is used for determining displacement according to the voltage value of the capacitive gate sensor group;
when the displacement object that awaits measuring is the cuboid, in order to confirm that awaits measuring the displacement object specifically along the displacement direction of coordinate axis still include after the voltage value according to the capacitive gate sensor group confirms the displacement:
determining the displacement direction of the displacement object to be detected in the x direction according to the first ratio or the second ratio; the first ratio is the ratio of the voltage value of the first capacitive gate sensor to the initial voltage; the second ratio is the ratio of the voltage value of the second capacitive gate sensor to the initial voltage;
determining the displacement direction of the displacement object to be detected in the y direction according to the third ratio or the fourth ratio; the third ratio is the ratio of the voltage value of the third capacitive-gate sensor to the initial voltage; the fourth ratio is the ratio of the voltage value of the fourth capacitive sensor to the initial voltage;
determining the displacement direction of the to-be-detected displacement object in the z direction according to the fifth ratio or the sixth ratio; the fifth ratio is the ratio of the voltage value of the fifth capacitive sensor to the initial voltage; the sixth ratio is the ratio of the voltage value of the sixth capacitive sensor to the initial voltage;
the second displacement determination submodule specifically includes:
a second displacement determining unit, configured to determine, when the first sub-model and the second sub-model are both cuboids, a displacement according to a voltage value of the capacitive gate sensor group by using the following formula:
Figure FDA0003870558650000051
Figure FDA0003870558650000052
wherein,
Figure FDA0003870558650000053
the voltage value of the first capacitive sensor corresponding to the first side surface of the cuboid,
Figure FDA0003870558650000054
the voltage value of the second capacitive sensor corresponding to the first side surface of the cuboid,
Figure FDA0003870558650000055
the voltage value of the third capacitive sensor corresponding to the second side surface of the cuboid,
Figure FDA0003870558650000056
the voltage value of the fourth capacitive sensor corresponding to the second side surface of the cuboid,
Figure FDA0003870558650000057
the voltage value of the fifth capacitive sensor corresponding to the bottom surface of the cuboid,
Figure FDA0003870558650000058
the voltage value l of the sixth capacitive sensor corresponding to the bottom surface of the cuboid x Is the length of a rectangular parallelepiped z Is the height of a cuboid y Is the width of a rectangular parallelepiped, α 1 、α 2 、α 3 、α 4 、α 5 、α 6 Respectively after the moving grate rotates x Angle l with y-axis x Angle l with z-axis y Angle l with x-axis y Angle l with z-axis z Angle with x-axis, < l > x Angle of included angle with y-axis, Δ d x 、Δd y 、Δd z The method is characterized in that the method is respectively used for installing intervals between every two pairs of capacitive grating sensors of three channels, I is a current value, t is time, x is a displacement value along the x direction, y is a displacement value along the y direction, z is a displacement value along the z direction, epsilon is a dielectric constant, and s is the dead-against area between a movable grating and a static grating of each capacitive grating sensor.
6. The three-dimensional displacement measurement system according to claim 5, wherein the displacement determination module specifically comprises:
the first displacement determining submodule is used for determining the voltage component of a capacitive grating sensor channel according to the voltage value of the capacitive grating sensor group and determining the displacement according to the voltage component of the capacitive grating sensor channel when the first submodel and the second submodel are both hemispheres; each capacitive gate sensor group comprises a capacitive gate sensor; the three capacitive grid sensors are arranged in a delta shape;
the second displacement determining submodule is used for determining displacement according to the voltage value of the capacitive gate sensor group when the first sub-model and the second sub-model are both cuboids; a bottom surface and two adjacent side surfaces of the cuboid are provided with a capacitive gate sensor group; the capacitive grating sensor group on the same surface of the cuboid comprises two capacitive grating sensors which are arranged at intervals.
7. The three-dimensional displacement measurement system according to claim 6, wherein the first displacement determination submodule specifically comprises:
a first displacement determination unit for determining a displacement from the voltage component of the capacitive sensor channel using the following formula:
Figure FDA0003870558650000061
wherein u is 1 Voltage value, u, of a first capacitive-gate sensor being hemispherical 2 Voltage value of the second capacitive-gate sensor being hemispherical u 3 Voltage value of the third capacitive-gate sensor being hemispherical, G is amplification factor, u 0 Is an initial voltage, I is a current value, t is time, x is a displacement value in the x-direction, y is a displacement value in the y-direction, z is a displacement value in the z-direction, d 0 The initial polar distance is l, the positive length of the initial position of the capacitive gate, b, the width of the capacitive gate and epsilon, the dielectric constant.
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