CN105823600B - The dynamical balancing method of motion on a kind of three-axis air-bearing table - Google Patents
The dynamical balancing method of motion on a kind of three-axis air-bearing table Download PDFInfo
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- CN105823600B CN105823600B CN201610160447.4A CN201610160447A CN105823600B CN 105823600 B CN105823600 B CN 105823600B CN 201610160447 A CN201610160447 A CN 201610160447A CN 105823600 B CN105823600 B CN 105823600B
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- 238000000034 method Methods 0.000 title claims abstract description 14
- 230000007246 mechanism Effects 0.000 claims abstract description 28
- 239000011159 matrix material Substances 0.000 claims description 5
- 238000006467 substitution reaction Methods 0.000 abstract 1
- 230000003068 static effect Effects 0.000 description 5
- 230000008859 change Effects 0.000 description 3
- 238000005516 engineering process Methods 0.000 description 3
- 238000005259 measurement Methods 0.000 description 3
- 230000000386 athletic effect Effects 0.000 description 2
- 238000004364 calculation method Methods 0.000 description 2
- 230000005486 microgravity Effects 0.000 description 2
- 238000009966 trimming Methods 0.000 description 2
- 230000009471 action Effects 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000009434 installation Methods 0.000 description 1
- 238000003032 molecular docking Methods 0.000 description 1
- NJPPVKZQTLUDBO-UHFFFAOYSA-N novaluron Chemical compound C1=C(Cl)C(OC(F)(F)C(OC(F)(F)F)F)=CC=C1NC(=O)NC(=O)C1=C(F)C=CC=C1F NJPPVKZQTLUDBO-UHFFFAOYSA-N 0.000 description 1
- 230000008569 process Effects 0.000 description 1
- 239000011435 rock Substances 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
- 230000003245 working effect Effects 0.000 description 1
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M1/00—Testing static or dynamic balance of machines or structures
- G01M1/30—Compensating imbalance
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Abstract
The dynamical balancing method of motion on a kind of three-axis air-bearing table of the present invention, solved according to the dynamics of ready to balance motion is counter, the unbalanced moments acted at the air-floating ball bearing centre of sphere is calculated, and balancing mechanism is controlled to compensate the torque, air floating table is kept dynamic equilibrium, including establish air floating table coordinate system；Ready to balance motion currently total centroid position vector is calculated under the coordinate system；The anti-solution of dynamics of vector substitution ready to balance motion is obtained acting on to the unbalanced moments expression formula at the air-floating ball bearing centre of sphere；Desired balancing mechanism position vector is calculated in the dynamics normal solution for substituting this expression into air floating table balancing mechanism；According to the vector controlled balancing mechanism kinematic.This method makes the barycenter of the air floating table comprising motion in load reach the purpose for keeping dynamic equilibrium, have higher practicality all the time at the centre of sphere of air-floating ball bearing.
Description
Technical field
The present invention relates to a kind of dynamical balancing method of turntable, more particularly on a kind of three-axis air-bearing table motion it is dynamic
State balance method.
Background technology
Three-axis air-bearing table is the support platform in ground simulation space microgravity environment aircraft athletic posture.In order to true to nature
Simulate the athletic posture of spacecraft, it is necessary to first adjust the position of air floating table balancing mechanism, make air floating table and its load
The centre of sphere of barycenter and air-floating ball bearing is completely superposed.But (such as mechanical arm, docking facilities when including motion in load
Deng), because load centroid position caused by mechanism kinematic changes, the original balance of air floating table is destroyed, so action must be entered
State compensates.
Existing air bearing table balance method belongs to static balancing method, it is desirable to the static state of leveling and the static state of measurement.Leveling
Static state to refer to that the load of air floating table is completely fixed motionless, therefore can not eliminate in load caused by the change of motion barycenter not
Trimming moment；When the static state of measurement refers to measure using the attitude measurement such as level meter or gyro instrument air floating table can not rock or
Person tilts, therefore when can not ensure air floating table attitudes vibration, the barycenter of air floating table and its load is always positioned at air-floating ball bearing
At the centre of sphere.
The content of the invention
Present invention solves the technical problem that：Existing air floating table leveling technology is overcome to eliminate fitness machine in air floating table load
A kind of out-of-balance force moment problem caused by the change of structure barycenter, there is provided the dynamical balancing method of motion on three-axis air-bearing table.
The technical scheme is that：The dynamical balancing method of motion on a kind of three-axis air-bearing table, including following step
Suddenly：
1) air floating table coordinate system is established, the origin of the coordinate system is located at the air-floating ball bearing centre of sphere, the x-axis and y of coordinate system
Axle is parallel with the table top of air floating table respectively, and the z-axis of coordinate system is vertical with the table top of air floating table and upward；
2) the air floating table coordinate system defined according to step 1), ready to balance motion currently total centroid position arrow is calculated
Amount
P in formulai(i=1,2 ..., n) is each part centroid position vector of ready to balance motion, mi(i=1,2 ..., n)
For each part quality of ready to balance motion；
3) the current total centroid position vector of the ready to balance motion obtained according to step 2), passes through ready to balance motion
The anti-solution of dynamics obtain acting on unbalanced moments expression formula at the air-floating ball bearing centre of sphere
R is three-axis air-bearing table current pose matrix in formula；
4) the unbalanced moments expression formula obtained according to step 3), the dynamics normal solution meter of air floating table balancing mechanism is passed through
Calculation draws desired balancing mechanism position vector
M is balancing mechanism balancing weight quality in formula, and C is that balancing weight installs matrix；
5) the balancing mechanism position vector drawn according to step 4), control balancing mechanism kinematic, with negative function in
Unbalanced moments at the air-floating ball bearing centre of sphere.
The present invention has advantages below compared with prior art：
(1) present invention is a kind of dynamical balancing method, is according to the ready to balance motion motion state of itself, by dynamic
Mechanics Calculation simultaneously controls balancing mechanism kinematic, so as to eliminate unbalanced moments caused by motion motion on air floating table.
(2) the balancing mechanism position that the present invention is calculated is unrelated with the posture of three-axis air-bearing table, therefore does not need appearance
State measuring instrument, even if during air floating table attitudes vibration, also the barycenter of air floating table and its load can be made to be always positioned at air-floating ball bearing
The centre of sphere at.
Brief description of the drawings
Fig. 1 is air floating table of the embodiment of the present invention and ready to balance motion schematic diagram.
Embodiment
The present invention is described in further detail with specific embodiment below in conjunction with the accompanying drawings：
The three-axis air-bearing table of the present embodiment is made up of (as shown in Figure 1) air floating platform, air-floating ball bearing and balancing mechanism.
Air floating platform is used for bearing test equipment.Air-floating ball bearing is put down between air floating platform and ground pedestal for holding up air supporting
Platform, make it at work only by the frictional resistance of very little, including air floatation ball and ball bowl two parts.Three are mounted with air floating platform
Individual balancing mechanism, play a part of adjusting air floating table centroid position.Each balancing mechanism is dragged by motor by leading screw respectively
Dynamic balancing weight (quality M) is for linear motion, kinematic axis and air supporting table top angleProjected with adjacent axle in air floating platform
Angle theta=120 °.To ensure the rotation process of air floating platform along preferable air-floating ball bearing central rotation, air floating table barycenter position
Putting should overlap with the pivot (i.e. the centre of sphere) of air-floating ball bearing, reach the mesh for simulating attitude motion under true microgravity environment
's.
The present embodiment is provided with (the i.e. ready to balance motion of the present embodiment of a three-freedom mechanical arm on three-axis air-bearing table
Mechanism), due to manipulator motion cause air floating platform barycenter change, destroy the original balance of three-axis air-bearing table, thus need into
Mobile state compensates.The mass of armed lever 1 of mechanical arm is m1, centroid position p1=(x1,y1,z1), the mass of armed lever 2 is m2, barycenter position
It is set to p2=(x2,y2,z2), the mass of armed lever 3 is m3, centroid position p3=(x3,y3,z3), above-mentioned parameter can obtain from mechanical arm
.
(1) coordinate system is established at air-floating ball bearing barycenter, as shown in Figure 1.
(2) according to mechanical arm current motion state on air floating table, mechanical arm currently total centroid position p is calculatedo=(xo,
yo,zo)T, wherein
(3) solved according to the dynamics of mechanical arm is counter, draw the unbalanced moments expression acted at the air-floating ball bearing centre of sphere
Formula
fo=(m1+m2+m3)R(xo,yo,zo)T
(4) according to the dynamics normal solution of balancing mechanism, desired balancing mechanism position vector is calculated
pd=(r1,r2,r3)T=(m1+m2+m3)(CM)-1(xo,yo,zo)T
Wherein, the balancing mechanism installation matrix of the present embodiment
In formulaFor balancing mechanism and air supporting table top angle (the present embodiment is 60 °), θ is that the adjacent axle of balancing mechanism exists
The angle (the present embodiment is 120 °) of air floating platform projection, substitutes into above formula and obtains
(5) it is calculated according to above formula
Three balancing mechanisms of control move r respectively1,r2,r3, so as to negative function at the air-floating ball bearing centre of sphere not
Trimming moment.
The working effect of the present embodiment is：For mechanical arm in motion, the axle of air floating table three still keeps poised state on air floating table,
Unbalanced moments is less than 1Nm.
The creative motion using motion on air floating table of air floating table dynamical balancing method disclosed in this invention is believed
Breath realizes the dynamic equilibrium of three-axis air-bearing table, can be generalized in the dynamic equilibrium of multi-axis turntable.
The non-detailed description of the present invention is known to the skilled person technology.
Claims (1)
1. the dynamical balancing method of motion on a kind of three-axis air-bearing table, it is characterised in that comprise the following steps：
1) air floating table coordinate system is established, the origin of the coordinate system is located at the air-floating ball bearing centre of sphere, the x-axis and y-axis point of coordinate system
Not parallel with the table top of air floating table, the z-axis of coordinate system is vertical with the table top of air floating table and upward；
2) the air floating table coordinate system defined according to step 1), ready to balance motion currently total centroid position vector is calculated
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P in formulaiFor each part centroid position vector of ready to balance motion, miFor each part quality of ready to balance motion, wherein
I=1,2 ..., n；
3) the current total centroid position vector of the ready to balance motion obtained according to step 2), passes through the dynamic of ready to balance motion
The anti-solution of mechanics obtains acting on the unbalanced moments expression formula at the air-floating ball bearing centre of sphere
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R is three-axis air-bearing table current pose matrix in formula；
4) the unbalanced moments expression formula obtained according to step 3), calculated by the dynamics normal solution of air floating table balancing mechanism
Go out desired balancing mechanism position vector
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M is balancing mechanism balancing weight quality in formula, and C is that balancing weight installs matrix；
5) the balancing mechanism position vector drawn according to step 4), balancing mechanism kinematic is controlled, with negative function in air supporting
Unbalanced moments at the ball bearing centre of sphere.
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| Application Number | Priority Date | Filing Date | Title |
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| CN201610160447.4A CN105823600B (en) | 2016-03-21 | 2016-03-21 | The dynamical balancing method of motion on a kind of three-axis air-bearing table |
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| CN201610160447.4A CN105823600B (en) | 2016-03-21 | 2016-03-21 | The dynamical balancing method of motion on a kind of three-axis air-bearing table |
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Families Citing this family (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106089102A (en) * | 2016-08-09 | 2016-11-09 | 中国地质大学（武汉） | Offshore rig self-levelling systems |
| CN111707412B (en) * | 2020-07-10 | 2022-06-07 | 哈尔滨工业大学 | Large-scale triaxial air bearing table rotational inertia online identification system and inertia algorithm |
| CN112595457B (en) * | 2020-12-07 | 2023-07-21 | 上海卫星工程研究所 | Triaxial air bearing table centroid pre-adjustment balancing device and application method thereof |
| CN112985694B (en) * | 2021-02-04 | 2023-06-09 | 上海卫星工程研究所 | Method and system for balancing mass center of triaxial air bearing table |
| CN115793498A (en) * | 2023-02-06 | 2023-03-14 | 湖南揽月机电科技有限公司 | Leveling device of three-degree-of-freedom semi-physical simulation system and working method thereof |
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| CN101509820A (en) * | 2009-03-13 | 2009-08-19 | 哈尔滨工业大学 | Triaxial air bearing table balance method and apparatus thereof |
| CN101509819A (en) * | 2009-03-13 | 2009-08-19 | 哈尔滨工业大学 | Uniaxial air bearing table balance adjustment method |
| CN102620892A (en) * | 2011-12-15 | 2012-08-01 | 上海卫星工程研究所 | Dynamic balance testing method for rotatable part |
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| KR101420519B1 (en) * | 2012-10-31 | 2014-07-16 | 영남대학교 산학협력단 | Device and Method for Measuring dynamic characteristic of air bearing |
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| CN101509820A (en) * | 2009-03-13 | 2009-08-19 | 哈尔滨工业大学 | Triaxial air bearing table balance method and apparatus thereof |
| CN101509819A (en) * | 2009-03-13 | 2009-08-19 | 哈尔滨工业大学 | Uniaxial air bearing table balance adjustment method |
| CN102620892A (en) * | 2011-12-15 | 2012-08-01 | 上海卫星工程研究所 | Dynamic balance testing method for rotatable part |
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| Title |
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| 3自由度气浮台力学性能研究_自重作用对转动惯量矩阵及惯量主轴方向的影响;李延斌 等;《机械工程学报》;20060430;第42卷(第4期);第191-195页 * |
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