CN109211152B - Method for simultaneously detecting precision ball hinge ball head eccentricity and ball rod space attitude - Google Patents

Method for simultaneously detecting precision ball hinge ball head eccentricity and ball rod space attitude Download PDF

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CN109211152B
CN109211152B CN201810869841.4A CN201810869841A CN109211152B CN 109211152 B CN109211152 B CN 109211152B CN 201810869841 A CN201810869841 A CN 201810869841A CN 109211152 B CN109211152 B CN 109211152B
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CN109211152A (en
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王文
仇文军
杨贺
时光
卢科青
唐超锋
吴海梅
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Hangzhou Dianzi University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B17/00—Measuring arrangements characterised by the use of infrasonic, sonic or ultrasonic vibrations
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
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Abstract

The invention discloses a method for simultaneously detecting the eccentricity of a ball head of a precision ball hinge and the spatial attitude of a ball rod. At present, methods for effectively measuring the ball head eccentricity and the ball rod space attitude of the ball hinge are available. According to the invention, the distance between the emergent point of the ultrasonic transmitter and the receiving points of the four ultrasonic receivers is obtained, and the included angle between the central axis of the ball rod and the Z axis and the included angle between the projection line of the central axis of the ball rod on the XOY plane and the X axis are decoupled by the geometrical principle; by detecting spherical crown type electrodes G1Capacitor C ofG1And a spherical crown type electrode G3Capacitor C ofG3Obtaining the differential capacitance of the two capacitors; by detecting spherical crown type electrodes G2Capacitor C ofG2And a spherical crown type electrode G4Capacitor C ofG4Obtaining the differential capacitance of the two capacitors; by detecting a ball-ribbon type electrode D1Capacitor C ofD1And a ball-and-ribbon type electrode D2Capacitor C ofD2Obtaining the differential capacitance of the two capacitors; and then obtaining X, Y, Z value of the eccentricity of the ball head. The invention obtains the space attitude of the ball hinge ball rod in real time based on the ultrasonic distance measurement principle, and accurately obtains the eccentricity of the ball hinge ball head based on the spherical capacitance principle.

Description

Method for simultaneously detecting precision ball hinge ball head eccentricity and ball rod space attitude
Technical Field
The invention belongs to the technical field of measurement, and particularly relates to a method capable of simultaneously detecting the eccentricity of a ball head of a precision ball hinge and the spatial attitude of a ball rod.
Background
The ball hinge is a commonly used three-degree-of-freedom mechanical joint, has the advantages of compact structure, flexible movement, strong bearing capacity and the like, and has become a key component in mechanical equipment such as parallel mechanisms, industrial robots (mechanical arms), automobile parts and the like.
Due to manufacturing, installation errors and other reasons, in practical application, a gap is inevitably formed between a ball head and a ball socket of the ball hinge, and the ball head is inevitably eccentric relative to an ideal position in the process of transmitting motion and force by the ball hinge, so that the transmission precision of the system is influenced. For example, in a parallel mechanism, the manufacturing error of a rod and the clearance error of a ball hinge have the largest influence on the precision, the manufacturing error of the rod and the installation position error of a component can be well compensated and corrected through kinematic modeling and error calibration, but the eccentric error of a ball head generated by the fit clearance of a precise ball hinge is not well solved so far, and a method for effectively and directly measuring the ball head eccentricity of the ball hinge is provided at present.
The traditional angle measurement is mainly based on a single-degree-of-freedom moving object, and methods such as mechanical angle measurement, electromagnetic angle measurement and optical angle measurement are usually adopted, but the traditional single-degree-of-freedom angular displacement detection method is difficult to be directly applied to the detection of the space posture of the ball rod of the ball hinge, so that a plurality of researchers provide some new mechanisms and methods aiming at relevant problems. Currently, the measurement of the motion pose of a spherical rotor can be classified into a contact type and a non-contact type according to the measurement mode. The contact measurement mainly represents the problem that decoupling on a measurement structure is realized by adopting a slide support mechanism and three rotary encoders, and the decoupling is converted into single-degree-of-freedom measurement; the non-contact measurement structure is mainly designed based on the principles of an optical sensor, a visual sensor, a Hall sensor and the like, and decoupling of multi-degree-of-freedom angular displacement is realized from data processing. However, the detection method has the disadvantages of complex system construction, high processing difficulty of measured data, high requirements on installation space, working environment and the like in practical application, high cost investment and obvious limitation on research schemes.
If the posture of the ball hinge ball rod in any direction of the space and the ball head eccentricity of the ball hinge can be known in real time, the robot and the parallel mechanism can be controlled in real time in the space, the gap error of the ball and the chain can be corrected and compensated, and meanwhile, the robot and the parallel mechanism have important significance for controlling and reducing the motion error generated by the joint gap of the ball hinge and optimizing the motion control.
Disclosure of Invention
The invention aims to provide a method for simultaneously detecting the eccentricity of a ball head of a precision ball hinge and the spatial attitude of a ball rod, aiming at the defects of the prior art.
The technical scheme adopted by the invention is as follows:
the method comprises the following specific steps:
step one, arranging an origin of a Cartesian coordinate system XYZ at the center of a lower ball socket; a spherical crown type electrode plate G1And G3Symmetrically arranged about the origin of the Cartesian coordinate system XYZ, and a spherical crown type electrode plate G1And G3The spherical center of the lower ball socket is superposed with the spherical center of the lower ball socket, and the spherical crown type electrode plate G1And G3The central axes of the electrode plates are coincident with the X axis, and the spherical crown type electrode plate G1Is arranged in the positive direction of the X axis; a spherical crown type electrode plate G2And G4Symmetrically arranged about the origin of the Cartesian coordinate system XYZ, and a spherical crown type electrode plate G2And G4The spherical center of the lower ball socket is superposed with the spherical center of the lower ball socket, and the spherical crown type electrode plate G2And G4The central axes of the electrode plates are coincident with the Y axis, and the spherical crown type electrode plate G2Arranged in the Y-axis forward direction; electrode plate D of spherical belt type1And D2Symmetrically arranged about the origin of the Cartesian coordinate system XYZ, and a spherical strip electrode plate D1And D2The center of the ball coincides with the center of the lower ball socket, and the spherical strip type electrode plate D1And D2All of the central axes ofCoincident with Z axis, spherical strip type electrode plate D1Is arranged in the positive direction of the Z axis; ball belt type electrode plate D1Fixed on the inner wall of the upper ball socket; ball belt type electrode plate D2Fixed on the inner wall of the lower ball socket; spherical crown type electrode plate G1、G2、G3And G4The lower parts of the ball sockets are all fixed on the inner wall of the lower ball socket;
fixing an ultrasonic transmitter on a ball rod, wherein the distance between the emergent point of the ultrasonic transmitter and the center of the ball head is r, and the optical axis of the ultrasonic transmitter is coaxial with the ball rod; four ultrasonic receivers are uniformly distributed along the circumferential direction of the lower ball socket, receiving points of the four ultrasonic receivers are all located on a plane which passes through the spherical center of the lower ball socket and is parallel to the contact surface of the upper ball socket and the lower ball socket, and the receiving points of the ultrasonic receivers are all separated from the spherical center of the lower ball socket by a distance L.
Step three, obtaining the time difference between the sound wave sent by the ultrasonic transmitter and the sound wave received by the four ultrasonic receivers to obtain the distances between the emergent point of the ultrasonic transmitter and the receiving points of the four ultrasonic receivers, wherein the distances are respectively represented as r1,r2,r3,r4(ii) a Decoupling an included angle theta between the central axis of the ball rod and the Z axis and an included angle between a projection line of the central axis of the ball rod on an XOY plane and the X axis according to a geometric principle
Figure BDA0001751869000000021
Figure BDA0001751869000000022
Figure BDA0001751869000000023
Step four, detecting the spherical crown type electrode G1Capacitor C ofG1And a spherical crown type electrode G3Capacitor C ofG3To obtain the differential capacitance Δ C of the twoX＝CG1-CG3Thereby obtaining the X value of the eccentricity of the ball head; by detecting spherical crown type electrodes G2Capacitor C ofG2And a spherical crown type electrode G4Capacitor C ofG4To obtain the differential capacitance Δ C of the twoy＝CG2-CG4Thus obtaining the Y value of the eccentricity of the ball head; by detecting the ball belt type electrode plate D1Capacitor C ofD1And ball belt type electrode plate D2Capacitor C ofD2To obtain the differential capacitance Δ C of the twoZ＝CD1-CD2Thereby obtaining the Z value of the eccentric amount of the ball head.
Further, in the step one, a spherical belt type electrode plate D1Is aligned with the inner wall of the upper ball socket, and a spherical strip-shaped electrode plate D2Is aligned with the inner wall of the lower ball socket, and a spherical crown type electrode plate G1、G2、G3And G4Is aligned with the inner wall of the lower socket.
Furthermore, in the third step, the included angle theta between the central axis of the ball rod and the Z axis and the included angle between the projection line of the central axis of the ball rod on the XOY plane and the X axis are decoupled by the geometric principle
Figure BDA0001751869000000031
The specific process is as follows:
assuming that the coordinates of the exit point of the ultrasonic transmitter are (x, y, z), the following relationship can be obtained by geometric principles:
Figure BDA0001751869000000032
Figure BDA0001751869000000033
substituting the formula (2) into the formula (1) to obtain:
Figure BDA0001751869000000034
subtracting formula ① from formula ② in formula (3), and subtracting formula ③ from formula ④ yields:
Figure BDA0001751869000000035
finally, according to formula (4)The included angle theta between the central axis of the decoupled ball rod and the Z axis and the included angle between the projection line of the central axis of the ball rod on the XOY plane and the X axis
Figure BDA0001751869000000036
Further, the calculation of the X value, the Y value and the Z value of the eccentric amount of the ball head in the fourth step is as follows:
the mathematical model of the clearance between the ball head and the ball socket is as follows:
Figure BDA0001751869000000041
e is the radial clearance between a certain point of the ball head and the corresponding point of the ball socket, R is the radius of the inner spherical surface of the ball socket0Is the radius of the ball head, deltaxIs the X value, delta, of the eccentricity of the ball headyIs the Y value, delta, of the eccentricity of the ball headzIs the Z value of the eccentric amount of the ball head, theta' is the included angle between the connecting line of a certain point on the ball head and the ball center of the ball socket and the Z axis,
Figure BDA0001751869000000047
the included angle between the projection line of a connecting line of a certain point on the ball head and the center of the ball socket on the XOY plane and the X axis;
obtaining the capacitance between the ball head and a certain spherical crown type electrode or spherical belt type electrode plate according to the capacitance principle as follows:
Figure BDA0001751869000000042
epsilon is the air dielectric constant, and A is the area of the spherical cap type electrode or the spherical belt type electrode plate, wherein the spherical surface is opposite to the ball head.
Order to
Figure BDA0001751869000000043
Thereby obtaining:
Figure BDA0001751869000000044
and (3) expanding according to a Meglan formula to obtain:
Figure BDA0001751869000000045
wherein n is 0,1,2, …; when calculating the capacitance CG1And CG2Where a is 0 and b is θ in formula (8)0(ii) a When calculating the capacitance CG3And CG4Where a in formula (8) is ═ pi-theta0B is pi; when calculating the capacitance CD1Where in formula (8), a is θ1，b＝θ2(ii) a When calculating the capacitance CD2Where a in formula (8) is ═ pi-theta2，b＝π-θ1(ii) a Omitting higher order terms above third order is obtained:
Figure BDA0001751869000000046
Figure BDA0001751869000000051
Figure BDA0001751869000000052
finally, get deltaXAnd Δ Cx、δyAnd Δ CyAnd deltazAnd Δ CzThe relationship of (A) is as follows:
Figure BDA0001751869000000053
Figure BDA0001751869000000054
Figure BDA0001751869000000055
wherein, theta0Is the included angle theta between the spherical diameter of the bottom surface sideline of the spherical crown type electrode and the geometric central line of the spherical crown type electrode1The diameter of the ball and the electrode in the shape of a spherical strip are smaller than the cross-sectional area of the electrode plate in the shape of a bottom sidelineAngle of geometric centre line of plate, theta2The included angle theta between the spherical diameter of the bottom side line with larger cross-sectional area of the spherical strip-shaped electrode plate and the geometric center line of the spherical strip-shaped electrode plate1＜θ2，
Figure BDA0001751869000000056
Furthermore, the spherical crown type electrode and the spherical belt type electrode plate are made of brass; the bulb is made of aluminum alloy.
Furthermore, the surfaces of the spherical crown type electrode, the spherical belt type electrode plate and the ball socket, which are opposite to the ball head, are coated with epoxy resin or polytetrafluoroethylene.
The invention has the following beneficial effects:
1. according to the ultrasonic distance measurement principle, the real-time detection of the spatial attitude of the ball hinge ball rod is realized.
2. According to the invention, the spherical capacitance electrodes are arranged according to the principle that the change of the output capacitance is caused by the change of the distance between the capacitance electrode plates, so that the non-contact detection of the three-free eccentric displacement of the ball joint space of the ball hinge is realized.
3. The invention has the advantages of simple algorithm, high efficiency, low cost and simple space installation.
Drawings
FIG. 1 is an assembled perspective view of the present invention during testing;
FIG. 2 is a geometric schematic of the present invention for pose detection;
FIG. 3 is a relative position diagram of the ball head and each electrode plate in the present invention;
FIG. 4 is a schematic diagram of the distribution of electrode plates in a coordinate system according to the present invention;
FIG. 5 is an assembled cross-sectional view of each electrode plate and ball socket of the present invention;
FIG. 6 is a mathematical model diagram of the ball head and ball socket clearance in the present invention;
FIG. 7-1 is a schematic front view of a spherical crown type electrode plate;
FIG. 7-2 is a schematic cross-sectional view taken along line D-D of FIG. 7-1;
FIG. 7-3 is a schematic side view of a spherical cap type electrode plate;
FIG. 8-1 is a schematic front view of a spherical belt-type electrode plate;
FIG. 8-2 is a perspective view of a ball-and-socket electrode plate;
in the figure: 1-1 parts of a positioning ring, 1-2 parts of an ultrasonic receiver, 1-3 parts of an upper ball socket, 1-4 parts of an ultrasonic transmitter, 1-5 parts of an installation cylinder, 1-6 parts of a ball head, 1-7 parts of a lower ball socket, 2-1 parts of a spherical crown type electrode group, 2-2 parts of a spherical strip type electrode plate group.
Detailed Description
The invention will be further explained with reference to the drawings.
The method for simultaneously detecting the eccentricity of the ball head of the precision ball hinge and the spatial posture of the ball rod comprises the following specific steps:
step one, as shown in fig. 3, 4 and 5, arranging an origin of a cartesian coordinate system XYZ at the center of a lower ball socket; a spherical crown type electrode plate G1And G3Symmetrically arranged about the origin of the Cartesian coordinate system XYZ, and a spherical crown type electrode plate G1And G3The spherical center of the lower ball socket is superposed with the spherical center of the lower ball socket, and the spherical crown type electrode plate G1And G3The central axes of the electrode plates are coincident with the X axis, and the spherical crown type electrode plate G1Is arranged in the positive direction of the X axis; a spherical crown type electrode plate G2And G4Symmetrically arranged about the origin of the Cartesian coordinate system XYZ, and a spherical crown type electrode plate G2And G4The spherical center of the lower ball socket is superposed with the spherical center of the lower ball socket, and the spherical crown type electrode plate G2And G4The central axes of the electrode plates are coincident with the Y axis, and the spherical crown type electrode plate G2Arranged in the Y-axis forward direction; electrode plate D of spherical belt type1And D2Symmetrically arranged about the origin of the Cartesian coordinate system XYZ, and a spherical strip electrode plate D1And D2The center of the ball coincides with the center of the lower ball socket, and the spherical strip type electrode plate D1And D2The central axes of the electrode plates are coincident with the Z axis, and the electrode plates D are spherical strip-shaped1Is arranged in the positive direction of the Z axis; ball belt type electrode plate D1Fixed on the inner wall of the upper ball socket 1-3 and a spherical belt type electrode plate D1Is aligned with the inner wall of the upper socket 1-3; ball belt type electrode plate D2Fixed on the inner wall of the lower ball socket 1-7 and a spherical belt type electrode plate D2Aligned with the inner walls of the lower sockets 1-7;spherical crown type electrode plate G1、G2、G3And G4Are all fixed on the inner walls of the lower ball sockets 1-7, and a spherical crown type electrode plate G1、G2、G3And G4Aligned with the inner walls of the lower sockets 1-7; spherical crown type electrode plate G1、G2、G3And G4Constituting a spherical crown type electrode group 2-1, a spherical belt type electrode plate D1And D2To form the spherical strip type electrode plate group 2-2.
As shown in fig. 7-1, 7-2, and 7-3, the spherical crown electrode has a thickness d, an inner spherical surface radius R, and a height h ═ R-R cos θ0，θ0The included angle between the spherical diameter passing through the bottom surface sideline of the spherical crown type electrode and the geometric center line of the spherical crown type electrode is formed; as shown in fig. 8-1 and 8-2, the thickness of the electrode is d, the radius of the inner sphere is R, and the height h is R cos θ1-R cosθ2(ii) a Wherein
Figure BDA0001751869000000071
θ1＜θ2，θ1The included angle theta between the spherical diameter of the bottom side line with smaller cross-sectional area of the spherical strip-shaped electrode plate and the geometric center line of the spherical strip-shaped electrode plate2The included angle between the spherical diameter of the bottom side line with larger cross section area of the spherical strip-shaped electrode plate and the geometric center line of the spherical strip-shaped electrode plate is formed.
Step two, as shown in figures 1, 3 and 5, placing the ball heads 1-6 in the lower ball sockets 1-7, sleeving the upper ball sockets 1-3 by a ball rod and fixing the upper ball sockets 1-3 with the lower ball sockets 1-7, and arranging a spherical crown type electrode plate G1、G2、G3And G4The upper parts of the ball sockets are embedded into the spherical belt-shaped ring track of the upper ball sockets 1-3; fixing the ultrasonic transmitter 1-4 in the mounting cylinder 1-5, and then fixing the mounting cylinder on the ball rod, wherein the distance between the emergent point of the ultrasonic transmitter and the center of the ball head 1-6 can be ensured to be r, and the optical axis of the ultrasonic transmitter is coaxial with the ball rod; fixedly sleeving the positioning ring 1-1 outside the lower ball socket 1-7 and coaxially arranging the positioning ring and the lower ball socket 1-7; four ultrasonic receivers 1-2 are uniformly distributed and fixed on a positioning ring 1-1 along the circumferential direction, the positioning ring can ensure that receiving points of the four ultrasonic receivers are all positioned on a plane which passes through the spherical center of a lower ball socket 1-7 and is parallel to the contact surface of an upper ball socket 1-3 and the lower ball socket 1-7,the receiving point of each ultrasonic receiver is separated from the center of the lower ball socket by L.
Step three, obtaining the time difference between the sound wave sent by the ultrasonic transmitter and the sound wave received by the four ultrasonic receivers to obtain the distances between the emergent point of the ultrasonic transmitter and the receiving points of the four ultrasonic receivers, wherein the distances are respectively represented as r1,r2,r3,r4As shown in FIG. 2, M represents the exit point of the ultrasonic transmitter, M' represents the projection point of the exit point M of the ultrasonic transmitter on the X0Y plane, M1,M2,M3,M4Respectively showing the reception points of four ultrasonic receivers. Assuming that the coordinates of M are (x, y, z), the following relationship can be obtained by geometric principles:
Figure BDA0001751869000000072
Figure BDA0001751869000000073
substituting equation (2) into equation (1) can yield:
Figure BDA0001751869000000081
subtracting formula ① from formula ② in formula (3), and subtracting formula ③ from formula ④ can result in:
Figure BDA0001751869000000082
finally, according to the formula (4), the included angle between the central axis of the ball rod and the Z axis, namely the deviation angle theta of the ball rod relative to the Z axis, and the included angle between the projection line of the central axis of the ball rod on the XOY plane and the X axis, namely the azimuth angle of the ball rod relative to the X axis can be decoupled
Figure BDA0001751869000000083
Thereby decoupling the spatial attitude of the cue:
Figure BDA0001751869000000084
Figure BDA0001751869000000085
step four, detecting the spherical crown type electrode G1Capacitor C ofG1And a spherical crown type electrode G3Capacitor C ofG3Then, the differential capacitance Δ C of the two is obtainedX＝CG1-CG3Thereby obtaining the X value of the eccentricity of the ball head; by detecting spherical crown type electrodes G2Capacitor C ofG2And a spherical crown type electrode G4Capacitor C ofG4Then, the differential capacitance Δ C of the two is obtainedy＝CG2-CG4Thus obtaining the Y value of the eccentricity of the ball head; by detecting the ball belt type electrode plate D1Capacitor C ofD1And ball belt type electrode plate D2Capacitor C ofD2Then, the differential capacitance Δ C of the two is obtainedZ＝CD1-CD2So as to obtain the Z value of the eccentricity of the ball head; the X value, the Y value and the Z value of the eccentricity are calculated as follows:
as shown in fig. 6, the mathematical model of the ball-and-socket clearance is:
Figure BDA0001751869000000086
e is the radial clearance (PQ length in FIG. 6) between a certain point of the ball head and the corresponding point of the socket, R is the radius of the socket0Is the radius of the ball head e0Is an intermediate variable, δxIs the X value, delta, of the eccentricity of the ball headyIs the Y value, delta, of the eccentricity of the ball headzIs the Z value of the eccentric amount of the ball head, theta' is the included angle between the connecting line (PO in figure 6) of a certain point on the ball head and the ball center O of the ball socket and the Z axis, namely the deflection angle relative to the Z axis,
Figure BDA0001751869000000087
the included angle between the projection line of a certain point on the ball head and the ball socket center O (PO in fig. 6) in the XOY plane and the X axis, i.e. the azimuth angle relative to the X axis. Delta is the eccentricity of the ball head relative to the socketAmount of the compound (A).
The capacitance between the spherical surfaces between the ball head and a certain spherical crown type electrode or spherical belt type electrode plate can be obtained according to the capacitance principle as follows:
Figure BDA0001751869000000091
epsilon is the air dielectric constant, and A is the area of the spherical cap type electrode or the spherical belt type electrode plate, wherein the spherical surface is opposite to the ball head.
Order to
Figure BDA0001751869000000092
Thereby obtaining:
Figure BDA0001751869000000093
since the joint clearance of the ball joint is very small, λ is much smaller than 1, so the expansion according to the maculing formula can be obtained:
Figure BDA0001751869000000094
where n is 0,1,2, …, i.e., n is taken to infinity; when calculating the capacitance CG1And CG2Where a is 0 and b is θ in formula (8)0(ii) a When calculating the capacitance CG3And CG4Where a in formula (8) is ═ pi-theta0B is pi; when calculating the capacitance CD1Where in formula (8), a is θ1，b＝θ2(ii) a When calculating the capacitance CD2Where a in formula (8) is ═ pi-theta2，b＝π-θ1(ii) a Since the influence of the higher order terms is very small, it can be obtained by omitting the higher order terms above the third order:
Figure BDA0001751869000000095
Figure BDA0001751869000000096
Figure BDA0001751869000000097
finally, delta can be obtainedXAnd Δ Cx、δyAnd Δ CyAnd deltazAnd Δ CzThe relationship of (A) is as follows:
Figure BDA0001751869000000101
Figure BDA0001751869000000102
Figure BDA0001751869000000103

Claims (6)

1. the method for simultaneously detecting the eccentricity of the ball head of the precision ball hinge and the spatial posture of the ball rod is characterized in that: the method comprises the following specific steps:
step one, arranging an origin of a Cartesian coordinate system XYZ at the center of a lower ball socket; a spherical crown type electrode plate G1And G3Symmetrically arranged about the origin of the Cartesian coordinate system XYZ, and a spherical crown type electrode plate G1And G3The spherical center of the lower ball socket is superposed with the spherical center of the lower ball socket, and the spherical crown type electrode plate G1And G3The central axes of the electrode plates are coincident with the X axis, and the spherical crown type electrode plate G1Is arranged in the positive direction of the X axis; a spherical crown type electrode plate G2And G4Symmetrically arranged about the origin of the Cartesian coordinate system XYZ, and a spherical crown type electrode plate G2And G4The spherical center of the lower ball socket is superposed with the spherical center of the lower ball socket, and the spherical crown type electrode plate G2And G4The central axes of the electrode plates are coincident with the Y axis, and the spherical crown type electrode plate G2Arranged in the Y-axis forward direction; electrode plate D of spherical belt type1And D2Symmetrically arranged about the origin of the Cartesian coordinate system XYZ, and a spherical strip electrode plate D1And D2The center of the ball coincides with the center of the lower ball socket, and the spherical strip type electrode plate D1And D2The central axes of the two electrodes are coincident with the Z axis, and the spherical strip type power supplyPolar plate D1Is arranged in the positive direction of the Z axis; ball belt type electrode plate D1Fixed on the inner wall of the upper ball socket; ball belt type electrode plate D2Fixed on the inner wall of the lower ball socket; spherical crown type electrode plate G1、G2、G3And G4The lower parts of the ball sockets are all fixed on the inner wall of the lower ball socket;
fixing an ultrasonic transmitter on a ball rod, wherein the distance between the emergent point of the ultrasonic transmitter and the center of the ball head is r, and the optical axis of the ultrasonic transmitter is coaxial with the ball rod; the four ultrasonic receivers are uniformly distributed along the circumferential direction of the lower ball socket, receiving points of the four ultrasonic receivers are all positioned on a plane which passes through the spherical center of the lower ball socket and is parallel to the contact surface of the upper ball socket and the lower ball socket, and the receiving points of the ultrasonic receivers are spaced from the spherical center of the lower ball socket by L;
step three, obtaining the time difference between the sound wave sent by the ultrasonic transmitter and the sound wave received by the four ultrasonic receivers to obtain the distances between the emergent point of the ultrasonic transmitter and the receiving points of the four ultrasonic receivers, wherein the distances are respectively represented as r1,r2,r3,r4(ii) a Decoupling an included angle theta between the central axis of the ball rod and the Z axis and an included angle between a projection line of the central axis of the ball rod on an XOY plane and the X axis according to a geometric principle
Figure FDA0002367890030000011
Figure FDA0002367890030000012
Figure FDA0002367890030000013
Step four, detecting the spherical crown type electrode plate G1Capacitor C ofG1And spherical crown type electrode plate G3Capacitor C ofG3To obtain the differential capacitance Δ C of the twoX＝CG1-CG3Thereby obtaining the X value of the eccentricity of the ball head; by detecting spherical crown type electrode plate G2Capacitor C ofG2And spherical crown type electrode plate G4Capacitor C ofG4To obtain the differential capacitance Δ C of the twoy＝CG2-CG4Thus obtaining the Y value of the eccentricity of the ball head; by detecting the ball belt type electrode plate D1Capacitor C ofD1And ball belt type electrode plate D2Capacitor C ofD2To obtain the differential capacitance Δ C of the twoZ＝CD1-CD2Thereby obtaining the Z value of the eccentric amount of the ball head.
2. The method for simultaneously detecting the eccentricity of the ball head of the precision ball hinge and the spatial posture of the ball rod as claimed in claim 1, wherein: in the step one, a spherical belt type electrode plate D1Is aligned with the inner wall of the upper ball socket, and a spherical strip-shaped electrode plate D2Is aligned with the inner wall of the lower ball socket, and a spherical crown type electrode plate G1、G2、G3And G4Is aligned with the inner wall of the lower socket.
3. The method for simultaneously detecting the eccentricity of the ball head of the precision ball hinge and the spatial posture of the ball rod as claimed in claim 1, wherein: in the third step, the included angle theta between the central axis of the ball rod and the Z axis and the included angle between the projection line of the central axis of the ball rod on the XOY plane and the X axis are decoupled by the geometric principle
Figure FDA0002367890030000021
The specific process is as follows:
assuming that the coordinates of the exit point of the ultrasonic transmitter are (x, y, z), the following relationship can be obtained by geometric principles:
Figure FDA0002367890030000022
Figure FDA0002367890030000023
substituting the formula (2) into the formula (1) to obtain:
Figure FDA0002367890030000024
subtracting formula ① from formula ② in formula (3), and subtracting formula ③ from formula ④ yields:
Figure FDA0002367890030000025
finally, an included angle theta between the central axis of the ball rod and the Z axis and an included angle between a projection line of the central axis of the ball rod on the XOY plane and the X axis are decoupled according to the formula (4)
Figure FDA0002367890030000026
4. The method for simultaneously detecting the eccentricity of the ball head of the precision ball hinge and the spatial posture of the ball rod as claimed in claim 1, wherein: the X value, the Y value and the Z value of the ball head eccentricity in the fourth step are calculated as follows:
the mathematical model of the clearance between the ball head and the ball socket is as follows:
Figure FDA0002367890030000031
e is the radial clearance between a certain point of the ball head and the corresponding point of the ball socket, R is the radius of the inner spherical surface of the ball socket0Is the radius of the ball head, deltaxIs the X value, delta, of the eccentricity of the ball headyIs the Y value, delta, of the eccentricity of the ball headzIs the Z value of the eccentric amount of the ball head, theta' is the included angle between the connecting line of a certain point on the ball head and the ball center of the ball socket and the Z axis,
Figure FDA0002367890030000032
the included angle between the projection line of a connecting line of a certain point on the ball head and the center of the ball socket on the XOY plane and the X axis;
obtaining the inter-spherical capacitance between the ball head and a certain spherical crown type electrode plate or spherical belt type electrode plate according to the capacitance principle as follows:
Figure FDA0002367890030000033
epsilon is the air dielectric constant, A is the area of the spherical cap type electrode plate or the spherical belt type electrode plate, wherein the inner spherical surface of the spherical cap type electrode plate is opposite to the ball head;
order to
Figure FDA0002367890030000034
Thereby obtaining:
Figure FDA0002367890030000035
and (3) expanding according to a Meglan formula to obtain:
Figure FDA0002367890030000036
wherein n is 0,1,2, …; when calculating the capacitance CG1And CG3Where a is 0 and b is θ in formula (8)0(ii) a When calculating the capacitance CG2And CG4Where a in formula (8) is ═ pi-theta0B is pi; when calculating the capacitance CD1Where in formula (8), a is θ1，b＝θ2(ii) a When calculating the capacitance CD2Where a in formula (8) is ═ pi-theta2，b＝π-θ1(ii) a Omitting higher order terms above third order is obtained:
Figure FDA0002367890030000041
Figure FDA0002367890030000042
Figure FDA0002367890030000043
finally, get deltaXAnd Δ Cx、δyAnd Δ CyAnd deltazAnd Δ CzThe relationship of (A) is as follows:
Figure FDA0002367890030000044
Figure FDA0002367890030000045
Figure FDA0002367890030000046
wherein, theta0Is the included angle theta between the spherical diameter of the bottom side line of the spherical crown type electrode plate and the geometric center line of the spherical crown type electrode plate1The included angle theta between the spherical diameter of the bottom side line with smaller cross-sectional area of the spherical strip-shaped electrode plate and the geometric center line of the spherical strip-shaped electrode plate2The included angle theta between the spherical diameter of the bottom side line with larger cross-sectional area of the spherical strip-shaped electrode plate and the geometric center line of the spherical strip-shaped electrode plate1＜θ2，
Figure FDA0002367890030000047
5. The method for simultaneously detecting the eccentricity of the ball head of the precision ball hinge and the spatial posture of the ball rod as claimed in claim 1, wherein: the spherical cap type electrode plate and the spherical belt type electrode plate are both made of brass; the bulb is made of aluminum alloy.
6. The method for simultaneously detecting the eccentricity of the ball head of the precision ball hinge and the spatial posture of the ball rod as claimed in claim 1, wherein: the surfaces of the spherical crown type electrode plate, the spherical belt type electrode plate and the ball socket, which are opposite to the ball head, are coated with epoxy resin or polytetrafluoroethylene.
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* Cited by examiner, † Cited by third party
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CN112212822B (en) * 2020-09-22 2022-03-22 杭州电子科技大学 Method for detecting ball center space offset error of ball joint by using three-ball bar instrument

Citations (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS5872522U (en) * 1981-11-09 1983-05-17 リズム自動車部品製造株式会社 Ball joint wear indicator
JPS63292001A (en) * 1987-05-25 1988-11-29 Musashi Seimitsu Ind Co Ltd Abrasion-sensitive ball joint
JPH11271014A (en) * 1998-03-19 1999-10-05 Kawasaki Heavy Ind Ltd Rotation detecting apparatus for ball joint
DE10134259A1 (en) * 2001-07-18 2003-02-06 Zf Lemfoerder Metallwaren Ag Ball joint with integrated angle sensor
CN101213100A (en) * 2005-06-30 2008-07-02 Zf腓特烈港股份公司 Ball-and-socket joint comprising a sensor device, method for measuring loads, and method for measuring wear
CN104132675A (en) * 2014-07-14 2014-11-05 杭州电子科技大学 Spherical hinge movement direction measuring method based on spherical capacitor
CN104457554A (en) * 2014-12-17 2015-03-25 重庆花金王科技开发有限公司璧山分公司 Cup-and-ball joint type three-dimensional angular sensor
CN104677257A (en) * 2015-02-05 2015-06-03 杭州电子科技大学 Precision spherical hinge joint gap detection method based on spherical capacitance principle
CN107000521A (en) * 2014-11-20 2017-08-01 Zf腓特烈斯哈芬股份公司 Mechanical part with force snesor
CN107462145A (en) * 2017-07-31 2017-12-12 南京宽运检测技术有限公司 Digital display centimeter based on wireless telecommunications
CN108138836A (en) * 2015-10-23 2018-06-08 Zf腓特烈斯哈芬股份公司 The ball-and-socket joint for vehicle with tilt angle measuring apparatus

Patent Citations (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS5872522U (en) * 1981-11-09 1983-05-17 リズム自動車部品製造株式会社 Ball joint wear indicator
JPS63292001A (en) * 1987-05-25 1988-11-29 Musashi Seimitsu Ind Co Ltd Abrasion-sensitive ball joint
JPH11271014A (en) * 1998-03-19 1999-10-05 Kawasaki Heavy Ind Ltd Rotation detecting apparatus for ball joint
DE10134259A1 (en) * 2001-07-18 2003-02-06 Zf Lemfoerder Metallwaren Ag Ball joint with integrated angle sensor
CN101213100A (en) * 2005-06-30 2008-07-02 Zf腓特烈港股份公司 Ball-and-socket joint comprising a sensor device, method for measuring loads, and method for measuring wear
CN104132675A (en) * 2014-07-14 2014-11-05 杭州电子科技大学 Spherical hinge movement direction measuring method based on spherical capacitor
CN107000521A (en) * 2014-11-20 2017-08-01 Zf腓特烈斯哈芬股份公司 Mechanical part with force snesor
CN104457554A (en) * 2014-12-17 2015-03-25 重庆花金王科技开发有限公司璧山分公司 Cup-and-ball joint type three-dimensional angular sensor
CN104677257A (en) * 2015-02-05 2015-06-03 杭州电子科技大学 Precision spherical hinge joint gap detection method based on spherical capacitance principle
CN108138836A (en) * 2015-10-23 2018-06-08 Zf腓特烈斯哈芬股份公司 The ball-and-socket joint for vehicle with tilt angle measuring apparatus
CN107462145A (en) * 2017-07-31 2017-12-12 南京宽运检测技术有限公司 Digital display centimeter based on wireless telecommunications

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
Simulation on measurement of five-DOF motion;Zhang M等;《International Symposium on Precision Engineering Measurement and Instrumentation》;20151231;第1-9页 *
智能球铰链优化设计与精度提升;胡鹏浩等;《仪器仪表学报》;20180330;第 39 卷(第 3 期);第132-140页 *
球铰链的多维回转角度测量方法研究综述;王文等;《电子测量与仪器学报》;20170131;第31卷(第1期);第1-8页 *

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