CN101949954B - Redundant parallel six-dimensional acceleration transducer and measuring method thereof - Google Patents
Redundant parallel six-dimensional acceleration transducer and measuring method thereof Download PDFInfo
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Abstract
The invention discloses a redundant parallel six-dimensional acceleration transducer. The acceleration transducer comprises a rigid shell, a mass block and nine branch chains, wherein the mass block is arranged in an accommodating cavity of the shell; the nine branch chains consist of three composite elastic spherical hinges, nine ordinary elastic spherical hinges and nine groups of piezoelectric ceramics; every three branch chains form a group; one end of each branch chain is connected with one composite elastic spherical hinge, while the other end thereof is connected with one ordinary elastic spherical hinge respectively; the piezoelectric ceramics is connected between the composite elastic spherical hinge and each ordinary elastic spherical hinge; the three composite elastic spherical hinges are fixed to the centers of different side faces of the mass block and the side faces on which the three composite elastic spherical hinges are fixed are adjacent and vertical to one another; and the ordinary elastic spherical hinges are fixed to the shell. A transducer structure can realize measurement of six-dimensional acceleration of a vibrating body to be tested and has high instantaneity and measurement accuracy. The invention also discloses a method for measuring the six-dimensional acceleration by the redundant parallel six-dimensional acceleration transducer.
Description
Technical field
The invention belongs to field of measuring technique, relate to a kind of six-dimension acceleration sensor device of redundant parallel and the method for acceleration measurement thereof, more specifically to utilizing a kind of novel redundancy parallel mechanism measurement to comprise the method for the six-dimension acceleration data of the linear acceleration of three orthogonal directionss in space and angular acceleration.
Background technology
Theory and the technology of tradition acceleration transducer become better and approaching perfection day by day, and the various acceleration transducer products on the market are also of common occurrence, but basically to realize the master that is measured as of single shaft.Along with people improve constantly and scientific and technical development the requirement of understanding objective world, the multidimensional characteristic in the physical environment is surveyed seem more and more important.The acceleration of object of which movement is a space vector, and for example the motion in robot finger, limbs, joint all is spatial movement.On the one hand, the motion state of object be accurately understood, its component on three coordinate axis must be recorded; On the other hand, under the occasion of not knowing in advance the object of which movement situation, can only use multi-axis accelerometer and detect corresponding acceleration signal.
Describing position and the attitude that an object moves in the space needs six Independent Parameters, comprises three attitude inclination angles of three coordinates and the object of mass center position of object.By adopt acceleration transducer obtain along three orthogonal axes of space inertial coordinate system to linear acceleration and angular acceleration, and then its integration obtained the information such as position, attitude and speed that measurand is moved in space coordinates, for the analysis and control motion provides foundation.
At present inertial measuring unit generally comprises 3 accelerometers and 3 gyroscopes in the inertial navigation system, measures respectively the acceleration of 3 translations of vehicle and the angular displacement of 3 rotations.Accelerometer is the element that separates with gyroscope, and volume is large, has lacked the angular acceleration information of rotating, and moves very difficult for control great-attitude angle, large maneuvering condition.Utilize six-dimension acceleration sensor then can directly obtain above-mentioned information, and can improve precision, reduce cost, for vehicle control, identification provide foundation.Based on the robot of power control, its service load additional load that measurement brings on power can affect to be measured and control accuracy.If in the ergometry process, can introduce three linear accelerations, then can overcome the flexible impact of working arm; If introduce simultaneously the impact of angular acceleration, can realize full decoupled to six-dimensional force, and irrelevant with the load of robot, can consist of real Force control system like this, greatly improve robot manipulation's dirigibility and precision.In addition, six-dimension acceleration sensor also has widely application in fields such as industry automatic control, communications and transportation monitoring, earthquake prediction, weapon technologies, photography and vedio recording, medical diagnosiss.
The development of six-dimension acceleration sensor mainly contains both direction, and a direction is to adopt the MEMS technology that sensor is carried out microminiaturization, and this class sensor bulk is little, lightweight, dependable performance, but its sensitivity and range have much room for improvement; Another direction is to explore the detection that various Novel measuring methods are realized six-dimension acceleration.Yet, up to the present can also not have as the six-dimension acceleration sensor of product issue, its reason is the full decoupled difficulty between the six-dimension acceleration, circuit is complicated, be subjected to the impact of external environment larger, the complex structure of sensor, price is high, in addition, conflicting often between the performances such as the sensitivity of sensor, precision, range, working band.At present, the research of six-dimension acceleration sensor still is in the starting stage both at home and abroad, its research is the Focal point and difficult point of sensor field.Therefore, seek the important topic that is designed to the multi-axis accelerometer research field that a kind of new approach carries out six-dimension acceleration sensor, the development six-dimension acceleration sensor has huge theory significance and more practical value.
Along with the progress to the parallel robot area research, it is ripe that the parallel institution theory is tending towards, add parallel institution and have the good characteristics such as rigidity is large, error accumulation is little, simple in structure, bearing accuracy is high, so that the research of parallel institution is become gradually the focus of academia, and great successes have been obtained in theoretical and application facet.At present, lot of domestic and international scientific research institution or unit are designed to six-dimension force sensor with parallel institution, have realized sextuple broad sense force measurement.Yet the situation that parallel institution is designed to six-dimension acceleration sensor is also very rarely seen, mainly is because there is very large difference between acceleration and the power, is not just can equivalence by simple conversion.At first, the application point of power sensor is on moving platform, and the application point of acceleration transducer also is that the sound platform all moves on the silent flatform of parallel institution, and therefore, the cross-couplings degree between the six-dimension acceleration is high than the degree of coupling between the six-dimensional force; Secondly, the frequency range of acceleration signal is wider, needs sensor to have fast response characteristic, yet kinematics, the dynamics normal solution of general parallel institution found the solution very time-consuming, retrained the response frequency of acceleration transducer.Therefore, be necessary to design the elastomer structure that a kind of novel six-degree-of-freedom parallel connection mechanism serves as six-dimension acceleration sensor.
Based on aforementioned analysis, the inventor furthers investigate six-dimension acceleration surveying instrument and measuring method, and this case produces thus.
Summary of the invention
Fundamental purpose of the present invention is to provide a kind of redundant parallel six-dimensional acceleration transducer and measuring method thereof, and it can realize treating the measurement of vibration measuring kinetoplast six-dimension acceleration, and real-time is good, and measuring accuracy is high.
In order to reach above-mentioned purpose, technical scheme of the present invention is:
A kind of redundant parallel six-dimensional acceleration transducer comprises shell, a mass and 3 groups of elastic hinge devices of a rigidity, and mass and 3 groups of elastic hinge devices all are located in the accommodating cavity of shell; Wherein, described mass is cube, one end of 3 groups of elastic hinge devices is individually fixed in the center, 3 adjacent and orthogonal sides of mass, and the other end is individually fixed on the inwall relative with 3 adjacent and orthogonal sides of described mass of shell;
Wherein, described elastic hinge device comprises a composite elastic spherical hinge, 3 general elastic ball hinges, 3 groups of piezoelectric ceramics; One end quality of connection piece of wherein said composite elastic spherical hinge, the other end is connected with an end of 3 groups of piezoelectric ceramics respectively, the other end of 3 groups of piezoelectric ceramics is connected with an end of 3 general elastic ball hinges respectively, the other end of 3 general elastic ball hinges is individually fixed on the inwall of shell, and described point of fixity is not same point.
To state piezoelectric ceramics to be connected in parallel by some piezoelectric ceramic pieces and to form, and by non-conductive adhesive respectively with composite elastic spherical hinge, general elastic ball hinge bonding.
A kind of method that adopts above-mentioned redundant parallel six-dimensional acceleration transducer to measure comprises the steps:
(1) sensor is rigidly secured on the vibrating mass to be measured;
(2) the output charge amount of nine piezoelectric ceramics on the pick-up transducers, and obtain the real time acceleration of vibrating mass to be measured according to it.
In the above-mentioned steps (2), respectively at fixed coordinate system { M}, { W}, { O} on mass, the shell and on the fixed bottom boundary, and so that during initial time three coordinate systems overlap, initial point is taken as the barycenter of mass, three coordinate axis are any three orthogonal directionss of pointing space respectively, and the step of then utilizing the output charge amount of nine groups of piezoelectric ceramics on the sensor to calculate the real time acceleration of vibrating mass to be measured is:
(1) the output charge amount with nine groups of piezoelectric ceramics is converted to voltage digital amount V
Oi
(2) by formula Q
i=C
FiV
Oi, wherein i is natural number 1～9, with aforesaid voltage digital quantity V
OiBe converted to the quantity of electric charge of input; In the formula, Q
iBe the actual quantity of electric charge of i passage, also be the quantity of electric charge that i group piezoelectric ceramics the two poles of the earth produce; C
FiFor the feedback capacity of charge amplifier i passage, adjustable; V
OiBe the output voltage of i passage, contain sign;
(3) respectively by formula Δ L
i=Q
i/ (K
iD
I33) and F
i=Q
i/ d
I33, the quantity of electric charge that nine groups of piezoelectric ceramics the two poles of the earth are produced is converted to the suffered pressure of piezoelectric ceramics on the actual elongation of each bar side chain and each side chain; In the formula, Δ L
iBe the actual elongation of i bar side chain, K
iBe the equivalent stiffness of i group piezoelectric ceramics, d
I33Be the equivalent piezoelectric modulus of i group piezoelectric ceramics, F
iBe the suffered pressure of each side chain piezoelectric ceramics;
(4) the row geometric coordinate that writes out the composite elastic spherical hinge barycenter that every group of side chain share { about three analytical expressions that prop up chain lengths, is designated as respectively b with the barycenter that is cemented in three composite elastic spherical hinges on the mass among the W} at coordinate system
1, b
2, b
3
(5) with b
1, b
2, b
3Geometric coordinate substitution formula b respectively
JW=P
MW+ R
MWb
JM, wherein j is natural number 1～3, the solving equation group obtains P
MWAnd R
MWAnalytical expression; In the formula, b
JW, b
JMBe respectively b
jGeometric coordinate at coordinate system { W} and { expression among the M}, P
MW{ { coordinate among the W} represents the initial point of M}, R at coordinate system for coordinate system
MWBe coordinate system { W} and { the rotational transform matrix between the M};
(6) with b
1, b
2, b
3{ geometric coordinate among the W} carries out a differentiate about the analytical expression of nine chain lengths to time t at coordinate system, obtain three composite elastic spherical hinge barycenter with respect to the speed of the shell analytical expression about nine side chain extension speeds, the speed with j composite elastic spherical hinge barycenter is designated as V herein
BjW, and the actual elongation of side chain carried out the extension speed that difference obtains each side chain; With V
BjWDifference substitution formula V
MW=V
BjW+ ω
W* r
JW, obtain V by the solving equation group
MWAnd ω
WAnalytical expression; In the formula, V
MWAnd ω
WBe respectively the angular velocity that the mass barycenter rotates with respect to shell with respect to the linear velocity of shell and mass; r
JWFor connecting b
jThe vector that obtains with the mass barycenter;
(7) with the V that tries to achieve in the step (6)
BjWTime t is carried out a differentiate, obtain three composite elastic spherical hinge barycenter with respect to the analytical expression of the acceleration of shell, the acceleration with j composite elastic spherical hinge barycenter is designated as a herein
BjW, with a
BjWDifference substitution formula a
MW=a
BjW+ ε
W* r
JW+ ω
W* (ω
W* r
JW), obtain a by the solving equation group
MWAnd ε
WAnalytical expression; In the formula, a
MWAnd ε
WBe respectively the angular acceleration that the mass barycenter rotates with respect to shell with respect to the linear acceleration of shell and mass;
(8) suppose P
WO{ { coordinate among the O} represents the initial point of W}, R at coordinate system for coordinate system
WOBe coordinate system { W} and { the rotational transform matrix between the O}, then { angular velocity omega that O} rotates can be by matrix R with respect to coordinate system for shell
WOIn each element and derivative thereof represent; According to the angular velocity addition formula, by formula ω
O=ω+ω
WCalculate mass with respect to the coordinate system { angular velocity omega that O} rotates
OIn addition, with ω
OAnalytical expression time t is asked first order derivative, obtain mass with respect to coordinate system { the angular acceleration ε that O} rotates
OCarry out vector addition, { { coordinate among the O} represents P to the initial point of M} at coordinate system to obtain coordinate system again
MO=P
MW+ P
WOWith aforementioned P
MOAnalytical expression time t is asked first order derivative, namely obtain the mass barycenter with respect to coordinate system { the linear velocity V that O} moves
MOWith V
MOAnalytical expression time t is asked first order derivative, namely obtain the mass barycenter with respect to coordinate system { the linear acceleration a that O} moves
MO
(9) select vector V
MOThree components and vector ω
OThree components as the general velocity of system, and inclined to one side speed and the drift angle speed of system is designated as V
(k)And ω
(k), wherein k is natural number 1～6, then passes through formula F
(k)=FV
(k)+ T ω
(k)Calculate the broad sense active force of system; In the formula, F
(k)Be k the broad sense active force that general velocity is corresponding; F, T represent respectively the resultant master of the main force square that mass is subject to;
(10) pass through respectively formula F
*=-Ma
MOAnd T
*=-I ε
O-ω
O* I ω
OThe inertial force of calculated mass piece is vowed F
*With moment of inertia T
*In the formula, M is the weight of mass, and I is the inertial matrix of mass; And pass through formula F
* (k)=F
*V
(k)+ T
*ω
(k)The broad sense inertial force F of computing system
* (k)
(11) according to the Kane method, obtain 6 scalar equation: F
(k)+ F
* (k)=0, it is found the solution obtain P
WOWith R
WOThe sealing solution; Again the pose sealing solution of shell being carried out difference processing twice, namely obtain the sealing solution of shell acceleration, also is the acceleration of vibrating mass motion to be measured.
After adopting such scheme, the present invention has following characteristics:
(1) the invention provides a kind of parallel institution of novelty, every group of side chain wherein (one has three groups) connects same composite elastic spherical hinge, consist of a tetrahedron, therefore, there are the normal solution of analytical form in parallel institution kinematics, dynamics, for the oscillatory differential equation of setting up and finding the solution the parallel institution system provides advantage, also the real-time measurement for the six-dimensional space acceleration information provides effective assurance;
(2) degree of coupling of this each basic kinematic chains of parallel institution is equal to 0, and kinematics, dynamics can be calculated respectively successively by each fundamental circuit, for the decoupling zero between the six-dimension acceleration provides assurance;
(3) three orthogonal directionss are symmetrical to the topological structure of this parallel institution in the space, have guaranteed the sensitivity isotropy of three orthogonal directionss in space;
(4) owing to having increased by three redundancy branched chains than traditional structure, on the one hand, this sensor has higher rigidity and larger load-bearing capacity, can measure the acceleration signal of broadband, amplitude; On the other hand, the electric weight measured of in this redundancy branched chain three groups redundant piezoelectric ceramics can other six groups of piezoelectric ceramics of effective compensation because the measuring error that various factors causes is conducive to improve measuring accuracy;
(5) this parallel institution is redundant unit, reduce or thoroughly eliminated Singularity, so that the work space of moving platform becomes more smooth, this just greatly reduces in the course of the work the unusual possibility that affects its measurement result owing to mechanism, improves the accuracy of measurement result.
Description of drawings
Fig. 1 is perspective view of the present invention.
Embodiment
Below with reference to drawings and the specific embodiments structure of the present invention and the course of work are elaborated.
At first with reference to shown in Figure 1, the invention provides a kind of redundant parallel six-dimensional acceleration transducer, comprise a shell 3, a mass 5 and 3 groups of elastic hinge devices, the below introduces respectively.
Mass 5 is cube, is located in the accommodating cavity 31 of shell 3.
3 groups of elastic hinge devices all are arranged in the accommodating cavity 31 of shell 3, wherein, one end of 3 groups of elastic hinge devices is individually fixed in the center, 3 adjacent and orthogonal sides of mass 5, can cooperate shown in Figure 1, the other end is individually fixed on the inwall relative with 3 adjacent and orthogonal sides of described mass 5 of shell 3, as in the present embodiment, be located at respectively upper surface, side surface and the front surface of shell 3.
Described each elastic hinge device includes a composite elastic spherical hinge 4,3 general elastic ball hinges 1,3 groups of piezoelectric ceramics 2; Wherein, an end quality of connection piece 5 of described composite elastic spherical hinge 4, the other end connects respectively an end of 3 groups of piezoelectric ceramics 2 by non-conductive adhesive; Described piezoelectric ceramics 2 is used for strain and the stress of responsive each side chain, this piezoelectric ceramics 2 is connected in parallel by some piezoelectric ceramic pieces and forms, and the other end of piezoelectric ceramics 2 is connected with an end of 3 general elastic ball hinges 1 respectively, the other end of these 3 general elastic ball hinges 1 is individually fixed on the inwall of shell 3, and described point of fixity is not same point.
During actual measurement, shell 3 of the present invention is rigidly fixed on the vibrating mass to be measured, makes sensor follow vibrating mass to be measured and do identical motion, the six-dimension acceleration of shell 3 is the six-dimension acceleration of vibrating mass to be measured at this moment.Under the effect of inertial force and moment of inertia, mass 5 compresses or the nine groups of piezoelectric ceramics 2 that stretch, and produces electric charge at its plane of polarization.By detecting the electric weight of nine groups of piezoelectric ceramics 2 the two poles of the earth generations, just can calculate the six-dimension acceleration of vibrating mass to be measured.After the six-dimension acceleration that shell 3 sensitivities arrive is determined, just can determine inertial force and moment of inertia that mass 5 is subject to, the electric weight that such nine groups of piezoelectric ceramics 2 the two poles of the earth produce is also namely determined, so an acceleration is corresponding to a definite electric weight matrix.Otherwise, after the electric weight that on having determined nine groups of piezoelectric ceramics 2, has produced, because every group of side chain of the present invention consists of tetrahedron, inertial force and moment of inertia that can be unique definite mass 5 is suffered, and then the acceleration of unique definite shell 3.Therefore, satisfy one to one relation between the electric weight matrix that the six-dimension acceleration vector that arrives of shell 3 sensitivities and nine groups of piezoelectric ceramics 2 the two poles of the earth produce.
The present invention also provides a kind of measuring method of redundant parallel six-dimension acceleration, during concrete operations, the input end (not shown) that the two poles of the earth of nine groups of piezoelectric ceramics 2 is connected respectively nine passages of charge amplifier by wire, the output terminal output of charge amplifier is amplified through signal and impedance transformation is processed voltage analog afterwards, converts thereof into digital quantity by data collecting card again and process for Computer Analysis.Real-time voltage value by nine passage outputs of data collecting card can be calculated the six-dimension acceleration of shell 3 motions.Before calculating, at first respectively at fixed coordinate system { M}, { W}, { O} on the mass 5, on the shell 3 and on the fixed bottom boundary, initial time (sensor remains static lower), three coordinate systems overlap, initial point is taken as the barycenter of mass 5, three any three orthogonal directionss of coordinate axis difference pointing space.
Its detailed calculation procedure is as follows:
(1) by formula Q
i=C
FiV
Oi(i=1～9) are converted to the magnitude of voltage of nine passages of charge amplifier output the quantity of electric charge of input.In the formula, Q
iBe the actual quantity of electric charge of i passage, also be the quantity of electric charge that i group piezoelectric ceramics the two poles of the earth produce; C
FiFor the feedback capacity of charge amplifier i passage, adjustable; V
OiBe the output voltage of i passage, contain sign.
(2) respectively by formula Δ L
i=Q
i/ (K
iD
I33) and F
i=Q
i/ d
I33, the quantity of electric charge that nine groups of piezoelectric ceramics the two poles of the earth are produced is converted to the suffered pressure of piezoelectric ceramics on the actual elongation of each bar side chain and each side chain.In the formula, Δ L
iBe the actual elongation of i bar side chain, its sign is by Q
iDetermine; K
iBe the equivalent stiffness of i group piezoelectric ceramics, relevant with factors such as the size of piezoelectric ceramics, elastic compliant coefficients; d
I33Be the equivalent piezoelectric modulus of i group piezoelectric ceramics, relevant with factors such as the model of piezoelectric ceramics, force directions; F
iBe the suffered pressure of each side chain piezoelectric ceramics, its sign is by Q
iDetermine.
(3) for three side chains in every group of side chain, obtained the actual elongation Δ L of three side chains by step (2)
i, use tetrahedral relevant knowledge, can be listed as the geometric coordinate that writes out the composite elastic spherical hinge barycenter that this group side chain shared at coordinate system { among the W} about the analytical expressions of three chain lengths.The barycenter that might as well will be cemented in three composite elastic spherical hinges on the mass here is designated as b
1, b
2, b
3
(4) step (3) has solved b
1, b
2, b
3Geometric coordinate at the coordinate system { analytical expression among the W}.Obviously, b
1, b
2, b
3Geometric coordinate { analytical expression among the M} is known at coordinate system.With b
1, b
2, b
3Geometric coordinate substitution formula b respectively
JW=P
MW+ R
MWb
JM(j=1～3) can obtain R by the solving equation group
MWAnd R
MWAnalytical expression.In the formula, b
JW, b
JMBe respectively b
jGeometric coordinate in coordinate system { W} and the { expression among the M}; P
MW{ { coordinate among the W} represents the initial point of M} at coordinate system for coordinate system; R
MWBe coordinate system { W} and { the rotational transform matrix between the M}.
(5) step (3) has solved b
1, b
2, b
3{ geometric coordinate among the W} carries out a differentiate with them to time t about the analytical expressions of nine chain lengths, obtains three composite elastic spherical hinge barycenter with respect to the speed of the shell analytical expression about nine side chain extension speeds at coordinate system.Here, the speed of the individual composite elastic spherical hinge barycenter of j (j=1～3, lower same) might as well be designated as V
BjWIn addition, each side chain extension speed can be carried out difference and obtained by the actual elongation to side chain.With V
BjWDifference substitution formula V
MW=V
BjW+ ω
W* r
JW, can obtain V by the solving equation group
MWAnd ω
WAnalytical expression.In the formula, V
MWAnd ω
WBe respectively the angular velocity that the mass barycenter rotates with respect to shell with respect to the linear velocity of shell and mass; r
JWFor connecting b
jThe vector that obtains with the mass barycenter obviously can directly be obtained by the result of step (3), (4).
(6) with the V that tries to achieve in the step (5)
BjWTime t is carried out a differentiate, obtain three composite elastic spherical hinge barycenter with respect to the analytical expression of the acceleration of shell.Here, the acceleration of j composite elastic spherical hinge barycenter might as well be designated as a
BjWWith a
BjWDifference substitution formula a
MW=a
BjW+ ε
W* r
JW+ ω
W* (ω
W* r
JW), can obtain a by the solving equation group
MWAnd ε
WAnalytical expression.In the formula, a
MWAnd ε
WBe respectively the angular acceleration that the mass barycenter rotates with respect to shell with respect to the linear acceleration of shell and mass.
(7) suppose P
WO{ { coordinate among the O} represents the initial point of W} at coordinate system for coordinate system; R
WOBe coordinate system { W} and { the rotational transform matrix between the O}.Obviously, { angular velocity omega that O} rotates can be by matrix R with respect to coordinate system for shell
WOIn each element and derivative thereof represent; According to the angular velocity addition formula, mass is with respect to the coordinate system { angular velocity omega that O} rotates
OCan pass through formula ω
O=ω+ω
WCalculate.In addition, with ω
OAnalytical expression time t is asked first order derivative, namely obtain mass with respect to coordinate system { the angular acceleration ε that O} rotates
OBy vector addition, { { coordinate among the O} represents P to the initial point of M} at coordinate system can to obtain coordinate system
MO=P
MW+ P
WOWith P
MOAnalytical expression time t is asked first order derivative, namely obtain the mass barycenter with respect to coordinate system { the linear velocity V that O} moves
MOWith V
MOAnalytical expression time t is asked first order derivative, namely obtain the mass barycenter with respect to coordinate system { the linear acceleration a that O} moves
MO
(8) select vector V
MOThree components and vector ω
OThree components as the general velocity of system.According to definition, can be easy to obtain inclined to one side speed and the drift angle speed of native system, they are designated as V here
(k)And ω
(k)(k=1～6).The broad sense active force of system can be passed through formula F
(k)=FV
(k)+ T ω
(k)Calculate.In the formula, F
(k)Be k the broad sense active force that general velocity is corresponding; F, T represent respectively the resultant master of the main force square that mass is subject to, and they are that nine groups of piezoelectric ceramics are to synthesizing under its applied pressure and the effect of mass self gravitation.
(9) pass through respectively formula F
*=-Ma
MOAnd T
*=-I ε
O-ω
O* I ω
OThe inertial force of calculated mass piece is vowed F
*With moment of inertia T
*, in the formula, M is the weight of mass; I is the inertial matrix of mass.Pass through formula F
* (k)=F
*V
(k)+ T
*ω
(k)The broad sense inertial force F of computing system
* (k)
(10) according to the Kane method, the corresponding broad sense active force of each general velocity and broad sense inertial force sum are zero, obtain 6 scalar equation: F
(k)+ F
* (k)=0 (k=1～6).When finding the solution 6 scalar equations, for avoiding differentiating, can carry out difference processing, and then the differential equation is changed into algebraic equation, can find the solution at an easy rate the P that obtains hypothesis in step (7)
WOWith R
WOThe sealing solution.Pose sealing solution to shell is carried out difference processing twice, namely obtains the sealing solution of shell acceleration.Because shell and the vibrating mass rigidity to be measured of described sensor are fixed together, so the acceleration of shell also is the acceleration of vibrating mass motion to be measured.
Can find out: do not need to carry out numerical evaluation in aforesaid computation process, what obtain all is that sealing is separated; As long as in computing machine, write in advance calculation procedure according to above step, utilize redundant parallel six-dimensional acceleration transducer provided by the present invention just can realize the real-time measurement of six-dimension acceleration.In essence, utilize just the more special novel redundancy parallel mechanism of this configuration, just realized the decoupling zero of vibrating mass six-dimension acceleration to be measured and the real-time measurement of six-dimension acceleration.
To sum up, a kind of redundant parallel six-dimensional acceleration transducer of the present invention and measuring method thereof, focus on nine side chains of common employing, adopt novel configuration, so that parallel institution kinematics, there is the normal solution of analytical form in dynamics, for the decoupling zero between the six-dimension acceleration provides assurance, it is by being rigidly fixed in sensor on the vibrating mass to be measured, so that the two realizes interlock, when vibrating mass motion to be measured produces acceleration, sensor its mass under inertia effect can opposite shell produce the pose variation, thereby the pressure that causes piezoelectric ceramics on each bar side chain changes, by detecting the variation of piezoelectric ceramics output charge amount, can calculate the real time acceleration size of vibrating mass to be measured; Particularly utilize sensor construction provided by the present invention, can greatly simplify computation process, so that find the solution more simple, convenient.
Aforementioned is illustration of the present invention only, can not limit protection scope of the present invention with this.Any change or modification that the one of ordinary skilled in the art does under technological thought of the present invention all should fall within protection scope of the present invention.
Claims (3)
1. redundant parallel six-dimensional acceleration transducer, it is characterized in that: comprise shell (3), a mass (5) and 3 groups of elastic hinge devices of a rigidity, mass (5) and 3 groups of elastic hinge devices all are located in the accommodating cavity (31) of shell (3); Wherein, described mass (5) is cube, one end of 3 groups of elastic hinge devices is individually fixed in the center, 3 adjacent and orthogonal sides of mass (5), and the other end is individually fixed on the inwall relative with 3 adjacent and orthogonal sides of described mass (5) of shell (3);
Wherein, described elastic hinge device comprises a composite elastic spherical hinge (4), 3 general elastic ball hinges (1), 3 groups of piezoelectric ceramics (2); One end (4) the quality of connection piece (5) of wherein said composite elastic spherical hinge, the other end is connected with an end of 3 groups of piezoelectric ceramics (2) respectively, the other end of 3 groups of piezoelectric ceramics (2) is connected with an end of 3 general elastic ball hinges (1) respectively, the other end of 3 general elastic ball hinges (1) is individually fixed on the inwall of shell (3), and described point of fixity is not same point.
2. redundant parallel six-dimensional acceleration transducer as claimed in claim 1, it is characterized in that: described piezoelectric ceramics (2) is connected in parallel by some piezoelectric ceramic pieces and forms, and bonds with composite elastic spherical hinge (4), general elastic ball hinge (1) respectively by non-conductive adhesive.
3. a method that adopts redundant parallel six-dimensional acceleration transducer as claimed in claim 1 to measure is characterized in that comprising the steps:
(a) sensor is rigidly secured on the vibrating mass to be measured;
(b) the output charge amount of nine groups of piezoelectric ceramics on the pick-up transducers, and obtain the real time acceleration of vibrating mass to be measured according to following manner: respectively at fixed coordinate system { M}, { W}, { O} on mass, the shell and on the fixed bottom boundary, and so that during initial time three coordinate systems overlap, initial point is taken as the barycenter of mass, three coordinate axis are any three orthogonal directionss of pointing space respectively, and the step of then utilizing the output charge amount of nine groups of piezoelectric ceramics on the sensor to calculate the real time acceleration of vibrating mass to be measured is:
(1) the output charge amount with nine groups of piezoelectric ceramics is converted to voltage digital amount V
Oi
(2) by formula Q
i=C
FiV
Oi, wherein i is natural number 1～9, with aforesaid voltage digital quantity V
OiBe converted to the quantity of electric charge of input; In the formula, Q
iBe the actual quantity of electric charge of i passage, also be the quantity of electric charge that i group piezoelectric ceramics the two poles of the earth produce; C
FiFor the feedback capacity of charge amplifier i passage, adjustable; V
OiBe the output voltage of i passage, contain sign;
(3) respectively by formula Δ L
i=Q
i/ (K
iD
I33) and F
i=Q
i/ d
I33, the quantity of electric charge that nine groups of piezoelectric ceramics the two poles of the earth are produced is converted to the suffered pressure of piezoelectric ceramics on the actual elongation of each bar side chain and each side chain; In the formula, Δ L
iBe the actual elongation of i bar side chain, K
iBe the equivalent stiffness of i group piezoelectric ceramics, d
I33Be the equivalent piezoelectric modulus of i group piezoelectric ceramics, F
iBe the suffered pressure of each side chain piezoelectric ceramics;
(4) the row geometric coordinate that writes out the composite elastic spherical hinge barycenter that every group of side chain share { about three analytical expressions that prop up chain lengths, is designated as respectively b with the barycenter that is cemented in three composite elastic spherical hinges on the mass among the W} at coordinate system
1, b
2, b
3
(5) with b
1, b
2, b
3Geometric coordinate substitution formula b respectively
JW=P
MW+ R
MWb
JM, wherein j is natural number 1～3, the solving equation group obtains P
MWAnd R
MWAnalytical expression; In the formula, b
JW, b
JMBe respectively b
jGeometric coordinate at coordinate system { W} and { expression among the M}, P
MW{ { coordinate among the W} represents the initial point of M}, R at coordinate system for coordinate system
MWBe coordinate system { W} and { the rotational transform matrix between the M};
(6) with b
1, b
2, b
3{ geometric coordinate among the W} carries out a differentiate about the analytical expression of nine chain lengths to time t at coordinate system, obtain three composite elastic spherical hinge barycenter with respect to the speed of the shell analytical expression about nine side chain extension speeds, the speed with j composite elastic spherical hinge barycenter is designated as V herein
BjW, and the actual elongation of side chain carried out the extension speed that difference obtains each side chain; With V
BjWDifference substitution formula V
MW=V
BjW+ ω
W* r
JW, obtain V by the solving equation group
MWAnd ω
WAnalytical expression; In the formula, V
MWAnd ω
WBe respectively the angular velocity that the mass barycenter rotates with respect to shell with respect to the linear velocity of shell and mass; r
JWFor connecting b
jThe vector that obtains with the mass barycenter;
(7) with the V that tries to achieve in the step (6)
BjWTime t is carried out a differentiate, obtain three composite elastic spherical hinge barycenter with respect to the analytical expression of the acceleration of shell, the acceleration with j composite elastic spherical hinge barycenter is designated as a herein
BjW, with a
BjWDifference substitution formula a
MW=a
BjW+ ε
W* r
JW+ ω
W* (ω
W* r
JW), obtain a by the solving equation group
MWAnd ε
WAnalytical expression; In the formula, a
MWAnd ε
WBe respectively the angular acceleration that the mass barycenter rotates with respect to shell with respect to the linear acceleration of shell and mass;
(8) suppose P
WO{ { coordinate among the O} represents the initial point of W}, R at coordinate system for coordinate system
WOBe coordinate system { W} and { the rotational transform matrix between the O}, then { angular velocity omega that O} rotates can be by matrix R with respect to coordinate system for shell
WOIn each element and derivative thereof represent; According to the angular velocity addition formula, by formula ω
O=ω+ω
WCalculate mass with respect to the coordinate system { angular velocity omega that O} rotates
OIn addition, with ω
OAnalytical expression time t is asked first order derivative, obtain mass with respect to coordinate system { the angular acceleration ε that O} rotates
OCarry out vector addition, { { coordinate among the O} represents P to the initial point of M} at coordinate system to obtain coordinate system again
MO=P
MW+ P
WOWith aforementioned P
MOAnalytical expression time t is asked first order derivative, namely obtain the mass barycenter with respect to coordinate system { the linear velocity V that O} moves
MOWith V
MOAnalytical expression time t is asked first order derivative, namely obtain the mass barycenter with respect to coordinate system { the linear acceleration a that O} moves
MO
(9) select vector V
MOThree components and vector ω
OThree components as the general velocity of system, and inclined to one side speed and the drift angle speed of system is designated as V
(k)And ω
(k), wherein k is natural number 1～6, then passes through formula F
(k)=FV
(k)+ T ω
(k)Calculate the broad sense active force of system; In the formula, F
(k)Be k the broad sense active force that general velocity is corresponding; F, T represent respectively the resultant master of the main force square that mass is subject to;
(10) pass through respectively formula F
*=-Ma
MOAnd T
*=-I ε
O-ω
O* I ω
OThe inertial force of calculated mass piece is vowed F
*With moment of inertia T
*In the formula, M is the weight of mass, and I is the inertial matrix of mass; And pass through formula F
* (k)=F
*V
(k)+ T
*ω
(k)The broad sense inertial force F of computing system
* (k)
(11) according to the Kane method, obtain 6 scalar equation: F
(k)+ F
* (k)=0, it is found the solution obtain P
WOWith R
WOThe sealing solution; Again the pose sealing solution of shell being carried out difference processing twice, namely obtain the sealing solution of shell acceleration, also is the acceleration of vibrating mass motion to be measured.
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