CN109871658A - The multi-pose optimal estimation method measured for guided missile warhead rotary inertia and the product of inertia - Google Patents
The multi-pose optimal estimation method measured for guided missile warhead rotary inertia and the product of inertia Download PDFInfo
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Abstract
For the multi-pose optimal estimation method that guided missile warhead rotary inertia and the product of inertia measure, the present invention relates to guided missile warhead multi-pose optimal estimation methods.The purpose of the present invention is to solve the low problems of the measurement accuracy of existing guided missile warhead rotary inertia and the product of inertia.Detailed process are as follows: Step 1: establishing product rotary inertia, product of inertia Parameter matrix J；Step 2: establishing coefficient matrices A based on 18 measurement postures of product to be measured；Step 3: rotary inertia value and tooling based on i-th of pose product to be measured and tooling combination calculate the rotary inertia value of i-th of pose product to be measured relative to the rotary inertia value for rocking axis；Specifically: Step 4: being based on product rotary inertia, product of inertia Parameter matrix J, coefficient matrices A and rotary inertia value, calculate the optimal measured value of product rotary inertia, product of inertia parameter.The present invention estimates field for guided missile warhead multi-pose.
Description
Technical field
The present invention relates to guided missile warhead multi-pose optimal estimation methods.
Background technique
Inertia Based on Torsion Pendulum Method is a kind of high-precision method for measuring rotary inertia, by test product high-precision when Inertia Based on Torsion Pendulum Method measures
Realize that friction free rocks, and rocks the period by measurement and rotary inertia is calculated on air-float turntable.Test desk is rocked in air bearing
Torsion bar coefficient needs to carry out preparatory calibration using standard component.The rotary inertia and inertia of product can be calculated using Inertia Based on Torsion Pendulum Method
Product.
Guided missile warhead is more demanding to the measurement accuracy of rotary inertia and the product of inertia, existing usual 6 sides of simultaneous of method
Journey group is difficult to meet measurement demand, and measurement accuracy is low.
Summary of the invention
The purpose of the present invention is to solve the low problem of the measurement accuracy of existing guided missile warhead rotary inertia and the product of inertia,
And propose the multi-pose optimal estimation method measured for guided missile warhead rotary inertia and the product of inertia.
The multi-pose optimal estimation method detailed process measured for guided missile warhead rotary inertia and the product of inertia are as follows:
Step 1: establishing product rotary inertia, product of inertia Parameter matrix J；
Step 2: establishing coefficient matrices A based on 18 measurement postures of product to be measured；
Step 3: rotary inertia value and tooling based on i-th of pose product to be measured and tooling combination are relative to rocking axis
Rotary inertia value, calculate i-th of pose product to be measured rotary inertia value；
Step 4: it is based on product rotary inertia, product of inertia Parameter matrix J, coefficient matrices A and rotary inertia value, meter
Calculate the optimal measured value of product rotary inertia, product of inertia parameter.
The invention has the benefit that
The present invention by the measurements of 18 postures, i.e. the X, Y, Z axis of product coordinate system relative to the angle for rocking axis, and
The rotary inertia value of i-th of pose product to be measured, is readily available A using Gaussian elimination methodTThe inverse matrix of A realizes the overdetermination
The least square solution of equation obtains the optimal measured value of product rotary inertia, product of inertia parameter, realizes and improves measurement accuracy.Turn
Inertia uncertainty of measurement is moved by 1kgm2It improves to 0.1kgm2, the product of inertia is increased to 0.05kgm2。
Detailed description of the invention
Fig. 1 is the unloaded 18 measurement posture schematic diagrames of present device；
Fig. 2 a is product of the present invention rotary inertia JxMonte Carlo simulation measurement result figure；
Fig. 2 b is product of the present invention rotary inertia JyMonte Carlo simulation measurement result figure；
Fig. 2 c is product of the present invention rotary inertia JzMonte Carlo simulation measurement result figure；
Fig. 2 d is product of the present invention product of inertia JyzMonte Carlo simulation measurement result figure；
Fig. 2 e is product of the present invention product of inertia JxzMonte Carlo simulation measurement result figure；
Fig. 2 f is product of the present invention product of inertia JxyMonte Carlo simulation measurement result figure.
Specific embodiment
Specific embodiment 1: multi-pose of the present embodiment for guided missile warhead rotary inertia and the product of inertia to measure is optimal
Estimation method detailed process are as follows:
Testee is placed on rocking on platform by bearing support, rocks platform and is connect by twiot arm with casing.It is external when having
After excitation, testee freely swings with platform is rocked, and can calculate rotary inertia according to swing curve.
If torsion bar angle of oscillation is θ, product is J relative to the rotary inertia for rocking axis, and torsion bar stiffness coefficient is that (value of K can by K
To be obtained by measurement calibration counterweight, that platform is rocked when measuring no measured piece rocks the period, has and rocks platform when standard test weight
With counterweight it is total rock the period, obtain two formula and subtract each other that K can be obtained), damping moment coefficient C, in pivot angle very little
It is considered that torsion bar stiffness coefficient is constant；
Assuming that the damping torque that air damping generates is directly proportional to the angular speed for rocking platform, torsional movement equation is
In formula, t is the time；
For convenience of calculation, definition undamped natural frequency is ωn,Definition air damping ratio is ζ,
Then formula (1) is deformed into
It as ζ < 1, rocks platform and does under-damped motion, solve following formula (2) and obtain θ (t):
In formula, θ (t) is to rock the angle amount of changing with time, θ0For initial pendulum angle；
Thus calculation formula of the product relative to the rotary inertia for rocking axis is obtained:
In formula, TdIt (can actually be measured) for the damping vibrition period, TnFor the non-damping vibration period,
The value of K can be obtained by measurement calibration counterweight, TdIt can actually measure；In addition it is also necessary to know the value of dampingratioζ.It is surveying
The not high occasion of precise requirements is measured, damping can be ignored, it is believed that ζ=0, it is only necessary to which the period is rocked in measurement, so that it may calculate
Rotary inertia.Measurand of the present invention is revolving body, and influence of the air damping to measurement process is minimum, ignores damping torque.When
When measuring a certain axis rotary inertia of product, need to adjust product pose keeps axis parallel with axis is rocked.
The product of inertia uses inertial ellipsoid method, and test product is as follows relative to the rotary inertia J for rocking axis under a certain posture
Shown in equation:
J-md2=Jxcos2α+Jycos2β+Jzcos2γ-2Jyzcosβcosγ-2Jxzcosαcosγ-2Jxycosαcosβ
In formula, J is product relative to the rotary inertia for rocking axis；M is product quality；D is product mass center to rocking axis
Distance, this project deisgn product mass center, which is always positioned at, to be rocked on axis, therefore this is 0 (when actual measurement, even if there are larger inclined
Difference, the order of magnitude differ larger with tested rotary inertia, can be neglected)；Jx、Jy、JzRespectively product turns around X, Y, Z axis
Dynamic inertia；α, β, γ are respectively product coordinate system X, Y, Z axis and the angle for rocking axis；JxyIt is product relative to axis X, the inertia of Y
Product；JyzThe product of inertia for product relative to axis Y, Z；JxzThe product of inertia for product relative to axis X, Z；
In order to measure 3 rotary inertias and 3 products of inertia, the measurement of 6 poses is at least carried out to product, passes through simultaneous 6
A above equation group resolves this 6 measured parameters.Due to needing to position product with auxiliary mould when measurement, because
The rotary inertia that this every wheel measurement obtains includes two parts of tooling rotary inertia and test product rotary inertia.To eliminate tooling
Influence to rotation inerttia, therefore tooling measurement need to be carried out, then carry out tooling and part measurement in a closed series to be measured, the difference of two wheel measurements
It can Simultaneous Equations:
In formula, Ji1For the rotary inertia value of i-th of pose product to be measured and tooling combination；Ji0For i-th of pose standard component
With the rotary inertia value of tooling combination.
Design scheme of the present invention uses 18 measurement postures, it is clear that will obtain an overdetermined equation, can solve it
Least square solution, the optimal estimation as rotary inertia and the product of inertia.
Step 1: establishing product rotary inertia, (under measured piece coordinate system, three rotations are used for product of inertia Parameter matrix J
Amount and three products of inertia)；
Step 2: establishing coefficient matrices A based on 18 measurement postures of product to be measured；
Step 3: rotary inertia value and tooling based on i-th of pose product to be measured and tooling combination are relative to rocking axis
Rotary inertia value, calculate i-th of pose product to be measured rotary inertia value；
Step 4: it is based on product rotary inertia, product of inertia Parameter matrix J, coefficient matrices A and rotary inertia value, meter
Calculate the optimal measured value of product rotary inertia, product of inertia parameter.
Specific embodiment 2: the present embodiment is different from the first embodiment in that, it establishes and produces in the step 1
Product rotary inertia, product of inertia Parameter matrix J (under measured piece coordinate system, three rotary inertias and three products of inertia)；
J expression formula are as follows:
J=[Jx,Jy,Jz,Jyz,Jxz,Jxy]T
In formula, Jx、Jy、JzThe rotary inertia of product X, Y, Z axis respectively to be measured；JxyIt is sat for product to be measured relative to product
Mark system X, the product of inertia of Y-axis；JyzIt is product to be measured relative to the Y of product coordinate system, the product of inertia of Z axis；JxzFor product phase to be measured
For the product of inertia of the X of product coordinate system, Z axis.
Other steps and parameter are same as the specific embodiment one.
Specific embodiment 3: the present embodiment is different from the first and the second embodiment in that, base in the step 2
Coefficient matrices A is established in 18 measurement postures of product to be measured；
Coefficient matrices A are as follows:
In formula, T representing matrix transposition；αiIt indicates under i-th of posture, the X-axis of product coordinate system to be measured is relative to rocking axis
Angle, i=1,2 ... 18；βiIt indicates under i-th of posture, the Y-axis of product coordinate system to be measured is relative to the angle i=for rocking axis
1,2…18；γiIt indicating under i-th of posture, the Z axis of product coordinate system to be measured is relative to the angle for rocking axis, i=1, and 2 ... 18.
Other steps and parameter are the same as one or two specific embodiments.
Specific embodiment 4: unlike one of present embodiment and specific embodiment one to three, the step 3
In rotary inertia value based on i-th of pose product to be measured and tooling combination and tooling relative to the rotary inertia value for rocking axis,
Calculate the rotary inertia value of i-th of pose product to be measured；Specifically:
Constant term matrix B are as follows:
B=[b1,b2,…,b18]T
Wherein, biFor the rotary inertia value of i-th of pose product to be measured, bi=Ji1-Ji0, i=1,2 ..., 18；Ji1It is
The rotary inertia value of i pose product to be measured and tooling combination；Ji0It is tooling relative to the rotary inertia value for rocking axis.
Other steps and parameter are identical as one of specific embodiment one to three.
Specific embodiment 5: unlike one of present embodiment and specific embodiment one to four, described i-th
The rotary inertia value b of appearance product to be measurediIt is specific to solve expression formula are as follows:
It also needs to obtain the opposite angle for rocking axis of each three reference axis of posture product coordinate system in original equation group.?
In the measurement process that the measurement of product overall length and centroidal axis and tooling are demarcated, the conversion square between each coordinate system has been obtained
Battle array, it may be convenient to come out 3 axial vector of product coordinate system with the angle calculation for rocking center line.According to the rotation in each joint
Angle.The transition matrix of product coordinate system and test desk coordinate system under different measurement postures can also be calculated, each is surveyed in this way
The opposite angle for rocking axis of three reference axis of product coordinate system can also be calculated under amount posture.
Other steps and parameter are identical as one of specific embodiment one to four.
Specific embodiment 6: unlike one of present embodiment and specific embodiment one to five, the step 4
In be based on product rotary inertia, product of inertia Parameter matrix J, coefficient matrices A and rotary inertia value, it is used to calculate product rotation
The optimal measured value of amount, product of inertia parameter；Detailed process are as follows:
AJ=B
Namely
ATAJ=ATB
Then least square solution are as follows:
J=(ATA)-1ATB
A is readily available using Gaussian elimination methodTThe inverse matrix of A, therefore the overdetermination is easily achieved in software algorithm
The least square solution of equation.Also can be obtained by the measurement of 18 postures product rotary inertia, product of inertia parameter it is optimal
Measured value.The J that step 4 least square solution obtains is that J carries out the average value that 18 measurements obtain in step 1.
Other steps and parameter are identical as one of specific embodiment one to five.
Beneficial effects of the present invention are verified using following embodiment:
Embodiment one:
The present embodiment is specifically to be prepared according to the following steps:
The unloaded 18 measurement posture schematic diagrames of equipment as shown in Figure 1；
The method that the measurement of product rotary inertia and the product of inertia uses multi-pose optimal estimation.Using minimum in mathematical model
The solution of square law realization overdetermined equation.Measurement model is complicated, therefore the analysis of uncertainty in measurement of rotary inertia and the product of inertia
The same method for using Monte Carlo simulation.In rotary inertia and the measurement model of the product of inertia, constant vector and coefficient matrix
There are random errors in the practice of each element, can generate random number with matlab come simulation error.
Coefficient matrices A in rotary inertia and product of inertia measurement model are as follows:
The random error of each element of coefficient matrices A is by test desk coordinate system and product Conversion Matrix of Coordinate calculating process
It causes, angle position error caused by the random error of angle encoder feedback signal when mainly including the rotation of big forearm.Each seat
The error that mark system transition matrix calibration process generates then causes systematic error to measurement.
Constant vector B are as follows:
B=[b1,b2,…,b18]T
Wherein,C is torsion bar coefficient, Ti1I-th when to load product
Torsional movement period under posture, Ti0The torsional movement period under i-th of posture when for zero load.Ignore torsion bar coefficient calibrated error, often
Each element random error of number vector B is mainly by period measurement error, product quality measurement error and product mass center to torsion
The measurement error of balance staff causes.Vector element biUncertainty of measurement can be expressed from the next:
The design that platform part is rocked according to air bearing, the diameter for choosing torsion bar is 16mm, length 600mm, then being easy meter
Calculate the coefficient C=21.4583 of torsion bar.In general it is analyzed using photoelectric counting or grating signal, the survey in torsional movement period
Accuracy of measurement is easy to reach 0.001s.For present design, no matter how product posture adjusts its mass center falls in torsion always
Center of oscillation, the rotary inertia that product bias generates are high-order small quantity, therefore negligible.It is uncertain in rotation inerttia
When degree analysis, measurement error caused by rocking period measurement and the positioning of big forearm rotation angle degree is only considered.
Under 18 measurement postures, the opposite rotary inertia for rocking axis of products C AD model is as shown in table 1.It can from table
There is the element of constant vector comparable uncertainty of measurement uniformly to take when doing Monte Carlo simulation analysis for convenience out
Uncertainty of measurement is 0.001kgm2。
The emulation of 1 products C AD model inertial parameter of table
The uncertainty of each element of coefficient matrices A is then caused by the rotation of size shoulder joint, when Monte Carlo simulation, is passed through
The random error for generating coefficient matrix element is simulated to rotation angle addition random error.
2 product rotary inertia of table and product of inertia theoretical value
| Serial number | ||
| 1 | Jx | 15.68 |
| 2 | Jy | 122.47 |
| 3 | Jz | 122.72 |
| 4 | Jyz | 0.30 |
| 5 | Jxz | 0.05 |
| 6 | Jxy | -0.03 |
Be the Monte Carlo simulation of product rotary inertia and the product of inertia as shown in Fig. 2 a, 2b, 2c, 2d, 2e, 2f as a result,
2 Theoretical Design value of contrast table is it is found that the scheme that the present invention designs can accurately realize three axis rotary inertia of product and the product of inertia
The repeatability of measurement, measurement is higher.Fig. 2 e shows that the error of each transition matrix calibration can make the measurement generation system of the product of inertia
Error should use standard component to carry out calibration to systematic error before measurement.200 Monte Carlo simulations the results show that the present invention
The canonical measure uncertainty of the system X-axis rotary inertia of design is 0.01kgm2, the canonical measure of Y-axis rotary inertia is true
Fixed degree is 0.08kgm2, the canonical measure uncertainty of Z axis rotary inertia is 0.06kgm2, Moments of inertia JyzCanonical measure
Uncertainty is 0.05kgm2, Moments of inertia JxzCanonical measure uncertainty be 0.02kgm2, Moments of inertia JxyStandard survey
Amount uncertainty is 0.02kgm2.Under the requirement for reducing precision index, the measurement posture of product can be suitably reduced.
The present invention can also have other various embodiments, without deviating from the spirit and substance of the present invention, this field
Technical staff makes various corresponding changes and modifications in accordance with the present invention, but these corresponding changes and modifications all should belong to
The protection scope of the appended claims of the present invention.
Claims (6)
1. the multi-pose optimal estimation method measured for guided missile warhead rotary inertia and the product of inertia, it is characterised in that: the side
Method detailed process are as follows:
Step 1: establishing product rotary inertia, product of inertia Parameter matrix J；
Step 2: establishing coefficient matrices A based on 18 measurement postures of product to be measured；
Step 3: rotary inertia value and tooling based on i-th of pose product to be measured and tooling combination are relative to turn for rocking axis
Dynamic inertia value, calculates the rotary inertia value of i-th of pose product to be measured；
Step 4: being based on product rotary inertia, product of inertia Parameter matrix J, coefficient matrices A and rotary inertia value, calculates and produce
The optimal measured value of product rotary inertia, product of inertia parameter.
2. the multi-pose optimal estimation method measured according to claim 1 for guided missile warhead rotary inertia and the product of inertia,
It is characterized by: establishing product rotary inertia, product of inertia Parameter matrix J in the step 1；
J expression formula are as follows:
J=[Jx,Jy,Jz,Jyz,Jxz,Jxy]T
In formula, Jx、Jy、JzThe rotary inertia of product X, Y, Z axis respectively to be measured；JxyIt is product to be measured relative to product coordinate system
X, the product of inertia of Y-axis；JyzIt is product to be measured relative to the Y of product coordinate system, the product of inertia of Z axis；JxzFor product to be measured relative to
The product of inertia of the X of product coordinate system, Z axis.
3. the multi-pose optimal estimation side according to claim 1 or claim 2 measured for guided missile warhead rotary inertia and the product of inertia
Method, it is characterised in that: establish coefficient matrices A based on 18 measurement postures of product to be measured in the step 2；
Coefficient matrices A are as follows:
In formula, T representing matrix transposition；αiIt indicates under i-th of posture, the X-axis of product coordinate system to be measured is relative to the folder for rocking axis
Angle, i=1,2 ... 18；βiIt indicating under i-th of posture, the Y-axis of product coordinate system to be measured is relative to the angle i=1 for rocking axis, and 2 ...
18；γiIt indicating under i-th of posture, the Z axis of product coordinate system to be measured is relative to the angle for rocking axis, i=1, and 2 ... 18.
4. the multi-pose optimal estimation method measured according to claim 3 for guided missile warhead rotary inertia and the product of inertia,
It is characterized by: opposite with the rotary inertia value and tooling of tooling combination based on i-th of pose product to be measured in the step 3
In the rotary inertia value for rocking axis, the rotary inertia value of i-th of pose product to be measured is calculated；Specifically:
Constant term matrix B are as follows:
B=[b1,b2,…,b18]T
Wherein, biFor the rotary inertia value of i-th of pose product to be measured, bi=Ji1-Ji0, i=1,2 ..., 18；Ji1It is i-th
The rotary inertia value of pose product to be measured and tooling combination；Ji0It is tooling relative to the rotary inertia value for rocking axis.
5. the multi-pose optimal estimation method measured according to claim 4 for guided missile warhead rotary inertia and the product of inertia,
It is characterized by: the rotary inertia value b of i-th of pose product to be measurediIt is specific to solve expression formula are as follows:
6. the multi-pose optimal estimation method measured according to claim 5 for guided missile warhead rotary inertia and the product of inertia,
It is characterized by: based on product rotary inertia, product of inertia Parameter matrix J, coefficient matrices A and turning in the step 4
Dynamic inertia value, calculates the optimal measured value of product rotary inertia, product of inertia parameter；Detailed process are as follows:
AJ=B
Namely
ATAJ=ATB
Then least square solution are as follows:
J=(ATA)-1ATB
The optimal measured value of product rotary inertia, product of inertia parameter is obtained by the measurement of 18 postures.
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| CN115452251A (en) * | 2022-09-13 | 2022-12-09 | 哈尔滨工业大学 | Method for measuring rotational inertia of large-scale high-speed rotating equipment based on unified reference of rotating shaft and inertial main shaft |
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