CN109871658B - Multi-attitude optimal estimation method for measuring rotational inertia and inertia product of missile warhead - Google Patents
Multi-attitude optimal estimation method for measuring rotational inertia and inertia product of missile warhead Download PDFInfo
- Publication number
- CN109871658B CN109871658B CN201910232820.6A CN201910232820A CN109871658B CN 109871658 B CN109871658 B CN 109871658B CN 201910232820 A CN201910232820 A CN 201910232820A CN 109871658 B CN109871658 B CN 109871658B
- Authority
- CN
- China
- Prior art keywords
- product
- inertia
- rotational inertia
- rotational
- value
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Landscapes
- Testing Of Balance (AREA)
- Length Measuring Devices By Optical Means (AREA)
Abstract
The invention discloses a multi-attitude optimal estimation method for measuring the rotational inertia and the inertia product of a missile warhead, and relates to a multi-attitude optimal estimation method for a missile warhead. The invention aims to solve the problem that the measurement accuracy of the rotational inertia and the inertia product of the existing missile warhead is low. The specific process is as follows: step one, establishing a product rotational inertia and inertia product parameter matrix J; secondly, establishing a coefficient matrix A based on 18 measurement postures of the product to be measured; step three, calculating a rotational inertia value of the ith position to-be-detected product based on a rotational inertia value of the combination of the ith position to-be-detected product and the tool and a rotational inertia value of the tool relative to the torsional pendulum shaft; the method comprises the following specific steps: and fourthly, calculating the optimal measurement values of the rotational inertia and the inertia product parameters of the product based on the rotational inertia and inertia product parameter matrix J, the coefficient matrix A and the rotational inertia values. The method is used for the field of missile warhead multi-attitude estimation.
Description
Technical Field
The invention relates to a missile warhead multi-attitude optimal estimation method.
Background
The torsional pendulum method is a high-precision rotational inertia measuring method, during measurement by the torsional pendulum method, a measured product is subjected to frictionless torsional pendulum on a high-precision air floatation rotary table, and rotational inertia is obtained through measuring torsional pendulum period calculation. The torsion bar coefficient of the air floatation torsional pendulum measuring table needs to be calibrated in advance by using a standard component. The moment of inertia and the product of inertia of the product can be calculated by using a torsional pendulum method.
The missile warhead has higher requirement on the measurement accuracy of the rotational inertia and the inertia product, and the existing method usually combines 6 equation sets to hardly meet the measurement requirement and has low measurement accuracy.
Disclosure of Invention
The invention aims to solve the problem that the measurement accuracy of the rotational inertia and the inertia product of the existing missile warhead is low, and provides a multi-attitude optimal estimation method for measuring the rotational inertia and the inertia product of the missile warhead.
The multi-attitude optimal estimation method for measuring the rotational inertia and the inertia product of the missile warhead comprises the following specific processes:
step one, establishing a product rotational inertia and inertia product parameter matrix J;
step two, establishing a coefficient matrix A based on 18 measurement attitudes of the product to be measured;
thirdly, calculating the rotational inertia value of the ith position to-be-detected product based on the rotational inertia value of the combination of the ith position to-be-detected product and the tool and the rotational inertia value of the tool relative to the torsional pendulum shaft;
and fourthly, calculating the optimal measurement values of the rotational inertia and the inertia product parameters of the product based on the rotational inertia and inertia product parameter matrix J, the coefficient matrix A and the rotational inertia values.
The invention has the beneficial effects that:
the invention can easily obtain A by Gauss elimination method through the measurement of 18 postures, namely the included angle of X, Y, Z axes of a product coordinate system relative to a torsional pendulum shaft and the rotational inertia value of a product to be measured at the ith position T The inverse matrix of A realizes the least square solution of the over-determined equation to obtain the product rotational inertia and the inertia product parameterThe optimal measurement value of the number realizes the improvement of the measurement precision. The uncertainty of the moment of inertia measurement is 1 kg.m 2 Increased to 0.1kg · m 2 The inertia product is increased to 0.05kg · m 2 。
Drawings
FIG. 1 is a schematic view of the present invention showing 18 unloaded measurement positions;
FIG. 2a shows the moment of inertia J of the product of the invention x The Monte Carlo simulation measurement result graph;
FIG. 2b shows the moment of inertia J of the product of the invention y The Monte Carlo simulation measurement result graph;
FIG. 2c shows the moment of inertia J of the product of the invention z The Monte Carlo simulation measurement result graph;
FIG. 2d is product inertia product J of the present invention yz The Monte Carlo simulation measurement result graph;
FIG. 2e is the product of inertia product J of the present invention xz The Monte Carlo simulation measurement result chart;
FIG. 2f is product inertia product J of the present invention xy The Monte Carlo simulation measurement result chart.
Detailed Description
The first embodiment is as follows: the multi-attitude optimal estimation method for measuring the rotational inertia and the inertia product of the missile warhead in the embodiment comprises the following specific processes:
the object to be measured is placed on a torsional pendulum table supported by a bearing, and the torsional pendulum table is connected with the machine shell through an elastic torsion bar. When external excitation is available, the measured object freely swings along with the torsional pendulum table, and the moment of inertia can be calculated according to the swing curve.
Setting the swing angle of a torsion bar as theta, setting the rotational inertia of a product relative to a torsion and swing shaft as J, setting the rigidity coefficient of the torsion bar as K (the value of K can be obtained by measuring a calibration weight, measuring the torsion and swing period of a torsion and swing table when no measured part exists, subtracting two formulas to obtain the total torsion and swing period of the torsion and swing table and the weight when a standard weight exists, and obtaining K), setting the damping moment coefficient as C, and considering the rigidity coefficient of the torsion bar as a constant when the swing angle is very small;
assuming that the damping torque generated by air damping is in direct proportion to the angular velocity of the torsional pendulum platform, the torsional pendulum motion equation is
Wherein t is time;
for the convenience of calculation, the undamped natural vibration frequency is defined as omega n ，
The air damping ratio is defined as ζ,
the formula (1) is transformed into
When zeta is less than 1, the torsion pendulum platform does underdamping motion, and theta (t) is obtained by solving the following formula (2):
in the formula, theta (t) is the variation of the torsional pendulum angle with time, theta 0 Is an initial swing angle;
thereby obtaining a calculation formula of the rotational inertia of the product relative to the torsional pendulum shaft:
in the formula, T d For damped vibration periods (which can be measured practically), T n In order to have a vibration period without damping,
the value of K can be obtained by measuring a calibration weight, T d Can be actually measured; further, the value of the damping ratio ζ also needs to be known. In fields where the requirements on measurement accuracy are not highIn conclusion, damping can be ignored, and it is considered that ζ =0, and only the torsional period needs to be measured, so that the moment of inertia can be calculated. The measured object of the invention is a revolving body, the influence of air damping on the measuring process is very small, and the damping moment is ignored. When the rotational inertia of a certain axis of a product is measured, the position and the posture of the product are required to be adjusted to enable the axis to be parallel to the torsional pendulum shaft.
The inertia product adopts an inertia ellipsoid method, and the rotational inertia J of the measured product relative to the torsional pendulum shaft under a certain attitude is shown as the following equation:
J-md 2 ＝J x cos 2 α+J y cos 2 β+J z cos 2 γ-2J yz cosβcosγ-2J xz cosαcosγ-2J xy cosαcosβ
in the formula, J is the rotational inertia of the product relative to the torsional pendulum shaft; m is the product quality; d is the distance from the product mass center to the torsional pendulum shaft, and the product mass center is always positioned on the torsional pendulum shaft by the design of the project, so that the item is 0 (in actual measurement, even if large deviation exists, the order of magnitude of the product is larger than the measured moment of inertia and can be ignored); j is a unit of x 、J y 、J z The inertia moment of the product around the X, Y, Z axis; alpha, beta and gamma are respectively the included angles between the axis X, Y, Z of the product coordinate system and the torsional pendulum shaft; j. the design is a square xy Is the product of inertia of the product with respect to the axes X, Y; j. the design is a square yz Is the product of inertia of the product relative to axis Y, Z; j. the design is a square xz Is the product of inertia of the product relative to axis X, Z;
in order to measure 3 rotational inertias and 3 products of inertia, at least 6 poses of the product are measured, and the 6 measured parameters are solved by simultaneously establishing more than 6 equation sets. Because the auxiliary tool is needed to position the product during measurement, the rotational inertia obtained by each round of measurement comprises two parts, namely tool rotational inertia and measured product rotational inertia. In order to eliminate the influence of the tool on the measurement of the rotational inertia, the tool needs to be measured, then the tool and the to-be-measured piece are measured in a combined manner, and the difference between two measurement rounds can form a simultaneous equation set:
in the formula, J i1 The rotation inertia value of the combination of the product to be tested at the ith position and the tool is obtained; j. the design is a square i0 Is the rotation inertia value of the combination of the ith position standard component and the tool.
The design scheme of the invention adopts 18 measurement postures, obviously, an over-determined equation can be obtained, and the least square solution of the over-determined equation can be solved to be used as the optimal estimation of the rotational inertia and the inertia product.
Step one, establishing a product rotational inertia and inertia product parameter matrix J (three rotational inertias and three inertia products under a coordinate system of a measured piece);
secondly, establishing a coefficient matrix A based on 18 measurement postures of the product to be measured;
step three, calculating a rotational inertia value of the ith position to-be-detected product based on a rotational inertia value of the combination of the ith position to-be-detected product and the tool and a rotational inertia value of the tool relative to the torsional pendulum shaft;
and fourthly, calculating the optimal measurement values of the rotational inertia and the inertia product parameters of the product based on the rotational inertia and inertia product parameter matrix J, the coefficient matrix A and the rotational inertia values.
The second embodiment is as follows: the difference between the first embodiment and the first embodiment is that a parameter matrix J (three rotational inertias and three products of inertia in a coordinate system of a measured object) of the rotational inertia and the product of inertia of the product is established in the first step;
the expression J is as follows:
J＝[J x ,J y ,J z ,J yz ,J xz ,J xy ] T
in the formula, J x 、J y 、J z Respectively the rotational inertia of the X, Y, Z axis of the product to be measured; j. the design is a square xy The product is the inertia product of the product to be measured relative to the X and Y axes of the product coordinate system; j is a unit of yz The product is the inertia product of the product to be measured relative to the Y, Z axis of the product coordinate system; j is a unit of xz Is the product of inertia of the product to be measured relative to the X, Z axis of the product coordinate system.
Other steps and parameters are the same as those in the first embodiment.
The third concrete implementation mode: the difference between the second embodiment and the first or second embodiment is that in the second step, a coefficient matrix a is established based on 18 measurement postures of the product to be measured;
the coefficient matrix a is:
in the formula, T represents a matrix transpose; alpha is alpha i The included angle of the X axis of the coordinate system of the product to be detected relative to the torsion pendulum shaft under the ith posture is represented, i =1,2 …; beta is a i An included angle i =1,2 … of a Y axis of a coordinate system of a product to be detected relative to a torsional pendulum shaft under the ith posture is shown; gamma ray i And (3) an included angle of the Z axis of the coordinate system of the product to be measured relative to the torsional pendulum shaft in the ith posture is represented, i =1,2 ….
Other steps and parameters are the same as those in the first or second embodiment.
The fourth concrete implementation mode is as follows: the third step is to calculate a rotational inertia value of the ith position product to be measured based on a rotational inertia value of the combination of the ith position product to be measured and the tool and a rotational inertia value of the tool relative to the torsional pendulum shaft; the method specifically comprises the following steps:
the constant term matrix B is:
B＝[b 1 ,b 2 ,…,b 18 ] T
wherein, b i The rotational inertia value of the product to be measured in the ith position, b i ＝J i1 -J i0 ，i＝1,2,...,18；J i1 The rotation inertia value of the combination of the product to be tested at the ith position and the tool is obtained; j. the design is a square i0 The rotation inertia value of the tool relative to the torsional pendulum shaft.
Other steps and parameters are the same as those in one of the first to third embodiments.
The fifth concrete implementation mode: the difference between this embodiment and the first to the fourth embodiment is that the rotational inertia value b of the product to be measured at the ith position i The specific solving expression is as follows:
the angles of the three coordinate axes of the coordinate system of each attitude product relative to the torsional pendulum axis are also required to be obtained in the original equation set. In the measuring process of measuring the total length of the product and calibrating the centroid axis and the tooling, a conversion matrix among all coordinate systems is obtained, and the angle between the 3-axis vector of the product coordinate system and the torsional pendulum center line can be conveniently calculated. According to the rotation angle of each joint. And a transformation matrix of a product coordinate system and a measuring table coordinate system under different measuring postures can be calculated, so that the angles of three coordinate axes of the product coordinate system relative to the torsional pendulum axis under each measuring posture can be calculated.
Other steps and parameters are the same as in one of the first to fourth embodiments.
The sixth specific implementation mode: the difference between the present embodiment and one of the first to fifth embodiments is that, in the fourth step, based on the rotational inertia of the product, the inertia product parameter matrix J, the coefficient matrix a and the rotational inertia value, the optimal measurement values of the rotational inertia and the inertia product parameter of the product are calculated; the specific process is as follows:
A·J＝B
that is to say
A T AJ＝A T B
The least squares solution is then:
J＝(A T A) -1 A T B
a is easily obtained by Gaussian elimination method T The inverse matrix of a, so the least squares solution of the over-determined equation is easily implemented on a software algorithm. That is, the optimal measurement value of the product rotational inertia and the product of inertia parameters can be obtained through the measurement of 18 postures. J obtained by the least square solution of the step four is the average value obtained by measuring J18 times in the step one.
Other steps and parameters are the same as in one of the first to fifth embodiments.
The following examples were used to demonstrate the beneficial effects of the present invention:
the first embodiment is as follows:
the preparation method comprises the following steps:
the device is empty with 18 measurement postures as shown in the schematic diagram of FIG. 1;
and measuring the rotational inertia and the inertia product of the product by adopting a multi-attitude optimal estimation method. And solving an over-determined equation by adopting a least square method on the mathematical model. The measurement model is complex, so the measurement uncertainty analysis of the rotational inertia and the inertia product also adopts a Monte Carlo simulation method. In the measurement model of the rotational inertia and the inertia product, random errors exist in practice in each element of a constant vector and a coefficient matrix, and the errors can be simulated by using matlab to generate random numbers.
The coefficient matrix A in the measurement model of the moment of inertia and the product of inertia is as follows:
the random error of each element of the coefficient matrix A is caused by the calculation process of the transformation matrix of the coordinate system of the measuring table and the coordinate system of the product, and mainly comprises an angle positioning error caused by the random error of an angle coding feedback signal when the large arm and the small arm rotate. The errors generated in the calibration process of each coordinate system transformation matrix cause system errors to the measurement.
The constant vector B is:
B＝[b 1 ,b 2 ,…,b 18 ] T
wherein the content of the first and second substances,
c is the torsion bar coefficient, T i1 Period of torsional pendulum motion at ith attitude in loading product, T i0 The torsional pendulum motion period under the ith posture is in no-load. Neglecting the calibration error of the torsion bar coefficient, the random error of each element of the constant vector B is mainly caused by the periodic measurement error, the product quality measurement error and the measurement error from the product mass center to the torsional pendulum shaft. Vector element b i The measurement uncertainty of (a) can be represented by:
according to the design of the air-float torsion pendulum platform part, the diameter of the torsion bar is selected to be 16mm, and the length of the torsion bar is selected to be 600mm, so that the coefficient C =21.4583 of the torsion bar is easy to calculate. Generally, photoelectric counting or grating signal analysis is adopted, and the measurement precision of the torsional pendulum motion period can easily reach 0.001s. For the design scheme, no matter how the product posture is adjusted, the mass center of the product always falls in the center of the torsional pendulum, and the rotational inertia generated by the product eccentricity is high-order micro-quantity, so that the rotational inertia can be ignored. When the uncertainty of the moment of inertia measurement is analyzed, only the measurement errors caused by the torsional pendulum period measurement and the rotation angle positioning of the large arm and the small arm are considered.
The moment of inertia of the product CAD model relative to the torsional pendulum axis at 18 measurement poses is shown in table 1. It can be seen from the table that the elements of the constant vector have equivalent measurement uncertainty, and when Monte Carlo simulation analysis is performed for convenience, the measurement uncertainty is uniformly taken as 0.001kg m 2 。
TABLE 1 simulation of product CAD model inertial parameters
The uncertainty of each element of the coefficient matrix A is caused by the rotation of the joints of the large arm and the small arm, and random errors of the elements of the coefficient matrix are simulated and generated by adding random errors to a rotation angle during Monte Carlo simulation.
TABLE 2 theoretical values of product moment of inertia and product of inertia
| Serial number | ||
| 1 | J x | 15.68 |
| 2 | J y | 122.47 |
| 3 | J z | 122.72 |
| 4 | J yz | 0.30 |
| 5 | J xz | 0.05 |
| 6 | J xy | -0.03 |
As shown in fig. 2a, 2b, 2c, 2d, 2e, and 2f, which are monte carlo simulation results of the rotational inertia and the product of inertia of the product, it can be known from a comparison of theoretical design values in table 2 that the scheme designed by the present invention can accurately realize the measurement of the three-axis rotational inertia and the product of inertia of the product, and the measurement repeatability is high. Fig. 2e shows that the errors of calibration of each transformation matrix can cause systematic errors in the measurement of the products of inertia, and the systematic errors should be calibrated by using a standard component before measurement. The results of 200 Monte Carlo simulations show that the system designed by the present invention rotates about the X-axisThe uncertainty of standard measurement of inertia is 0.01 kg.m 2 The uncertainty of standard measurement of the rotational inertia of the Y axis is 0.08kg · m 2 And the uncertainty of standard measurement of the rotary inertia of the Z axis is 0.06 kg.m 2 Moment of inertia J yz Has a standard measurement uncertainty of 0.05 kg.m 2 Moment of inertia J xz Has a standard measurement uncertainty of 0.02kg · m 2 Moment of inertia J xy Has a standard measurement uncertainty of 0.02kg m 2 . Under the requirement of reducing the precision index, the measurement attitude of the product can be properly reduced.
The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope of the present invention.
Claims (5)
1. The multi-attitude optimal estimation method for measuring the rotational inertia and the inertia product of the missile warhead is characterized by comprising the following steps of: the method comprises the following specific processes:
step one, establishing a product rotational inertia and inertia product parameter matrix J;
secondly, establishing a coefficient matrix A based on 18 measurement postures of the product to be measured;
thirdly, calculating the rotational inertia value of the ith position to-be-detected product based on the rotational inertia value of the combination of the ith position to-be-detected product and the tool and the rotational inertia value of the tool relative to the torsional pendulum shaft;
calculating the optimal measurement values of the rotational inertia and the inertia product parameters of the product based on the rotational inertia and the inertia product parameter matrix J, the coefficient matrix A and the rotational inertia value of the product;
establishing a product rotational inertia and inertia product parameter matrix J in the first step;
the expression J is as follows:
J＝[J x ,J y ,J z ,J yz ,J xz ,J xy ] T
in the formula, J x 、J y 、J z Respectively a product X to be detected,The moment of inertia of the Y, Z shaft; j. the design is a square xy The product is the inertia product of the product to be measured relative to the X and Y axes of the product coordinate system; j. the design is a square yz The product is the inertia product of the product to be measured relative to the Y, Z axis of the product coordinate system; j. the design is a square xz The product is the inertia product of the product to be measured relative to the X, Z axis of the product coordinate system; t denotes a matrix transpose.
2. The multi-pose optimal estimation method for missile warhead inertia and product of inertia measurements as claimed in claim 1 wherein: in the second step, a coefficient matrix A is established based on 18 measurement postures of the product to be measured;
the coefficient matrix a is:
in the formula, alpha i Representing the included angle of the X axis of the coordinate system of the product to be measured relative to the torsion pendulum shaft under the ith posture, i =1,2 …; beta is a i Representing an included angle i =1,2 … of a Y axis of a coordinate system of a product to be detected relative to a torsional pendulum shaft under the ith posture; gamma ray i And (3) an included angle of the Z axis of the coordinate system of the product to be measured relative to the torsional pendulum shaft in the ith posture is represented, i =1,2 ….
3. The multi-pose optimal estimation method for missile warhead inertia and product of inertia measurements as claimed in claim 2 wherein: in the third step, the rotational inertia value of the ith position to-be-detected product is calculated based on the rotational inertia value of the combination of the ith position to-be-detected product and the tool and the rotational inertia value of the tool relative to the torsional pendulum shaft; the method specifically comprises the following steps:
the constant term matrix B is:
B＝[b 1 ,b 2 ,…,b 18 ] T
wherein, b i The rotational inertia value of the product to be measured in the ith position, b i ＝J i1 -J i0 ，i＝1,2,...,18；J i1 The rotation inertia value of the combination of the product to be tested at the ith position and the tool is obtained; j. the design is a square i0 For tooling to twistAnd the rotational inertia value of the pendulum shaft.
4. The multi-pose optimal estimation method for missile warhead inertia and product of inertia measurements as claimed in claim 3 wherein: the rotational inertia value b of the ith position to-be-detected product i The specific solving expression is as follows:
5. the multi-pose optimal estimation method for missile warhead inertia and product of inertia measurements as claimed in claim 4 wherein: calculating the optimal measurement values of the rotational inertia and the inertia product parameters of the product based on the rotational inertia and inertia product parameter matrix J, the coefficient matrix A and the rotational inertia value in the fourth step; the specific process is as follows:
A·J＝B
that is to say
A T AJ＝A T B
Obtaining the optimal measurement values of the product rotational inertia and the product of inertia parameters through least square solution:
J＝(A T A) -1 A T B
and measuring the 18 postures to obtain the optimal measurement value of the product rotational inertia and the product inertia parameter.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910232820.6A CN109871658B (en) | 2019-03-26 | 2019-03-26 | Multi-attitude optimal estimation method for measuring rotational inertia and inertia product of missile warhead |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910232820.6A CN109871658B (en) | 2019-03-26 | 2019-03-26 | Multi-attitude optimal estimation method for measuring rotational inertia and inertia product of missile warhead |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN109871658A CN109871658A (en) | 2019-06-11 |
| CN109871658B true CN109871658B (en) | 2022-11-15 |
Family
ID=66921304
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910232820.6A Active CN109871658B (en) | 2019-03-26 | 2019-03-26 | Multi-attitude optimal estimation method for measuring rotational inertia and inertia product of missile warhead |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN109871658B (en) |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113311852A (en) * | 2021-04-30 | 2021-08-27 | 北京控制工程研究所 | On-orbit estimation method for inertia product of spacecraft |
| CN115452251B (en) * | 2022-09-13 | 2024-05-07 | 哈尔滨工业大学 | Large-scale high-speed rotation equipment rotational inertia measurement method based on unified reference of rotation shaft and inertia main shaft |
Citations (23)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2000292096A (en) * | 1999-04-07 | 2000-10-20 | Masaya Nagasawa | Countermeasure for violation of territorial waters |
| CN1721269A (en) * | 2004-07-14 | 2006-01-18 | 郑悦 | Permanently floating vessel and its protection and power |
| CN101436073A (en) * | 2008-12-03 | 2009-05-20 | 江南大学 | Wheeled mobile robot trace tracking method based on quantum behavior particle cluster algorithm |
| CN101733749A (en) * | 2009-12-22 | 2010-06-16 | 哈尔滨工业大学 | Multidomain uniform modeling and emulation system of space robot |
| CN101745820A (en) * | 2009-12-14 | 2010-06-23 | 北京航空航天大学 | Three-degree-of-freedom parallel mechanism type dual head for five-axis machine tools and control method |
| CN201548380U (en) * | 2009-12-04 | 2010-08-11 | 北京卫星环境工程研究所 | Linear type three-coordinate coversion machine for testing satellite quality characteristics |
| CN102087104A (en) * | 2009-12-08 | 2011-06-08 | 北京卫星环境工程研究所 | Three-coordinate conversion machine for measuring aircraft quality characteristics, test system and method |
| CN102163059A (en) * | 2011-04-27 | 2011-08-24 | 南京航空航天大学 | Attitude control system and attitude control method of variable thrust unmanned aerial vehicle |
| CN102298390A (en) * | 2011-06-24 | 2011-12-28 | 北京航空航天大学 | Anti-disturbance flexible spacecraft attitude and vibration composite control method |
| CN102354123A (en) * | 2011-07-18 | 2012-02-15 | 北京航空航天大学 | Cross-platform extendible satellite dynamic simulation test system |
| CN102360216A (en) * | 2011-05-20 | 2012-02-22 | 南京航空航天大学 | Two-engine carrier-based aircraft with one engine off safety carrier landing control method |
| CN102620887A (en) * | 2012-01-18 | 2012-08-01 | 哈尔滨工业大学 | Device for testing quality characteristic of component |
| CN102692201A (en) * | 2012-06-19 | 2012-09-26 | 重庆大学 | Device for measuring spatial motion with six degrees of freedom and dynamic measuring method |
| CN106507925B (en) * | 2009-12-15 | 2013-12-11 | 上海航天测控通信研究所 | A kind of multi-faceted barycenter inertia test apparatus |
| CN103542981A (en) * | 2013-09-28 | 2014-01-29 | 大连理工大学 | Method for measuring rotary inertia through binocular vision |
| CN104155054A (en) * | 2014-08-20 | 2014-11-19 | 哈尔滨工业大学 | Rotational inertia frequency domain detection method based on floating torsion pendulum table |
| CN104180940A (en) * | 2014-09-03 | 2014-12-03 | 郑州机械研究所 | Measurement device for measuring object centroid, rotational inertia and product of inertia |
| CN104503241A (en) * | 2014-12-23 | 2015-04-08 | 哈尔滨工业大学 | Rotational inertia determination method for satellite attitude control system |
| CN104881553A (en) * | 2015-06-15 | 2015-09-02 | 哈尔滨工业大学 | Single sliding block rolling spray mode variable centroid aircraft model and designing method for structural layout parameters thereof |
| CN105259786A (en) * | 2015-10-29 | 2016-01-20 | 中国科学院力学研究所 | Method and apparatus for identifying inertial parameters of object to be identified |
| CN106482896A (en) * | 2016-09-28 | 2017-03-08 | 西北工业大学 | A kind of contactless factor of inertia discrimination method of arbitrary shape rolling satellite |
| CN108332909A (en) * | 2018-02-07 | 2018-07-27 | 哈尔滨工业大学 | A kind of multiple spot for centroid measurement is weighed the modification method of support construction model |
| CN108942942A (en) * | 2018-08-16 | 2018-12-07 | 居鹤华 | A kind of multi-axis robot Inverse Kinematics and calculation method based on axis invariant |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US9658044B2 (en) * | 2015-03-03 | 2017-05-23 | Raytheon Company | Method and apparatus for executing a weapon safety system utilizing explosive flux compression |
-
2019
- 2019-03-26 CN CN201910232820.6A patent/CN109871658B/en active Active
Patent Citations (23)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2000292096A (en) * | 1999-04-07 | 2000-10-20 | Masaya Nagasawa | Countermeasure for violation of territorial waters |
| CN1721269A (en) * | 2004-07-14 | 2006-01-18 | 郑悦 | Permanently floating vessel and its protection and power |
| CN101436073A (en) * | 2008-12-03 | 2009-05-20 | 江南大学 | Wheeled mobile robot trace tracking method based on quantum behavior particle cluster algorithm |
| CN201548380U (en) * | 2009-12-04 | 2010-08-11 | 北京卫星环境工程研究所 | Linear type three-coordinate coversion machine for testing satellite quality characteristics |
| CN102087104A (en) * | 2009-12-08 | 2011-06-08 | 北京卫星环境工程研究所 | Three-coordinate conversion machine for measuring aircraft quality characteristics, test system and method |
| CN101745820A (en) * | 2009-12-14 | 2010-06-23 | 北京航空航天大学 | Three-degree-of-freedom parallel mechanism type dual head for five-axis machine tools and control method |
| CN106507925B (en) * | 2009-12-15 | 2013-12-11 | 上海航天测控通信研究所 | A kind of multi-faceted barycenter inertia test apparatus |
| CN101733749A (en) * | 2009-12-22 | 2010-06-16 | 哈尔滨工业大学 | Multidomain uniform modeling and emulation system of space robot |
| CN102163059A (en) * | 2011-04-27 | 2011-08-24 | 南京航空航天大学 | Attitude control system and attitude control method of variable thrust unmanned aerial vehicle |
| CN102360216A (en) * | 2011-05-20 | 2012-02-22 | 南京航空航天大学 | Two-engine carrier-based aircraft with one engine off safety carrier landing control method |
| CN102298390A (en) * | 2011-06-24 | 2011-12-28 | 北京航空航天大学 | Anti-disturbance flexible spacecraft attitude and vibration composite control method |
| CN102354123A (en) * | 2011-07-18 | 2012-02-15 | 北京航空航天大学 | Cross-platform extendible satellite dynamic simulation test system |
| CN102620887A (en) * | 2012-01-18 | 2012-08-01 | 哈尔滨工业大学 | Device for testing quality characteristic of component |
| CN102692201A (en) * | 2012-06-19 | 2012-09-26 | 重庆大学 | Device for measuring spatial motion with six degrees of freedom and dynamic measuring method |
| CN103542981A (en) * | 2013-09-28 | 2014-01-29 | 大连理工大学 | Method for measuring rotary inertia through binocular vision |
| CN104155054A (en) * | 2014-08-20 | 2014-11-19 | 哈尔滨工业大学 | Rotational inertia frequency domain detection method based on floating torsion pendulum table |
| CN104180940A (en) * | 2014-09-03 | 2014-12-03 | 郑州机械研究所 | Measurement device for measuring object centroid, rotational inertia and product of inertia |
| CN104503241A (en) * | 2014-12-23 | 2015-04-08 | 哈尔滨工业大学 | Rotational inertia determination method for satellite attitude control system |
| CN104881553A (en) * | 2015-06-15 | 2015-09-02 | 哈尔滨工业大学 | Single sliding block rolling spray mode variable centroid aircraft model and designing method for structural layout parameters thereof |
| CN105259786A (en) * | 2015-10-29 | 2016-01-20 | 中国科学院力学研究所 | Method and apparatus for identifying inertial parameters of object to be identified |
| CN106482896A (en) * | 2016-09-28 | 2017-03-08 | 西北工业大学 | A kind of contactless factor of inertia discrimination method of arbitrary shape rolling satellite |
| CN108332909A (en) * | 2018-02-07 | 2018-07-27 | 哈尔滨工业大学 | A kind of multiple spot for centroid measurement is weighed the modification method of support construction model |
| CN108942942A (en) * | 2018-08-16 | 2018-12-07 | 居鹤华 | A kind of multi-axis robot Inverse Kinematics and calculation method based on axis invariant |
Non-Patent Citations (5)
| Title |
|---|
| Optimum design of mounting components of a mass property measurement system;MONDAL N;《Measurement》;20161231;第309-321页 * |
| 大尺寸非回转体质量特性一体化测量系统的设计;王超等;《仪器仪表学报》;20120715(第07期);第196-202页 * |
| 旋转导弹广义马格努斯动力学建模;王辉等;《上海航天》;20171225;第19-26页 * |
| 柔性质心测量方法及不确定度评定;王梅宝 等;《柔性质心测量方法及不确定度评定》;20190731;第1500-1507页 * |
| 航天器转动惯量和惯性积的集成一体化测试方法;边志强等;《航天制造技术》;20171225(第06期);第19-23+28页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN109871658A (en) | 2019-06-11 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN109871658B (en) | Multi-attitude optimal estimation method for measuring rotational inertia and inertia product of missile warhead | |
| CN109459061B (en) | Micro-inertia measurement unit calibration method, device and computer readable storage medium | |
| CN109483596B (en) | Method for testing load of tool end of robot | |
| CN112815900B (en) | Coordinate system establishing method and rigid body centroid and inertia parameter testing method | |
| CN109238199B (en) | Robot rotating shaft kinematic parameter calibration method | |
| CN109974749B (en) | Evaluation method for comprehensive pointing error of three-axis turntable | |
| CN111044220A (en) | Unmanned aerial vehicle mass center inertia integrated test method | |
| CN106994686A (en) | The computational methods and device, robot of joint external force torque | |
| CN109709628B (en) | Calibration method for gravity gradiometer of rotating accelerometer | |
| Renk et al. | Calibrating a triaxial accelerometer-magnetometer-using robotic actuation for sensor reorientation during data collection | |
| CN104981274A (en) | Apparatus for correcting golf address | |
| CN110501107B (en) | Spacecraft rotation load dynamic balance measurement method based on six-dimensional force tester | |
| CN110715769A (en) | Method for calibrating stress point position of weighing sensor of multi-point method centroid measuring equipment | |
| CN105043414B (en) | A kind of stage body control parameter computational methods of three axles inertially stabilized platform system | |
| Li et al. | A dynamic pre-travel error prediction model for the kinematic touch trigger probe | |
| CN112327942A (en) | Automatic leveling method for triaxial air-floatation satellite simulation platform | |
| CN112069612B (en) | Gear measurement center measurement uncertainty assessment method | |
| CN108917520B (en) | Method for detecting precision of rotating shaft of five-axis linkage machine tool | |
| CN110672268B (en) | High-precision mass center inertia measuring system and measuring method for small aircraft | |
| Gheorghe | Advanced calibration method for 3-axis MEMS accelerometers | |
| CN112444644A (en) | Calibration method of triaxial accelerometer | |
| Kim | The development of a six-component force/moment sensor testing machine and evaluation of its uncertainty | |
| CN106199758A (en) | Measurement data calibration steps and electronic equipment | |
| CN111006626A (en) | Method and device for calibrating rotating shaft of dispensing equipment | |
| CN113156167B (en) | Calibration method and device of triaxial accelerometer |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |