CN105865712A - Three-axis flexible air bearing table balance adjusting state judgment method - Google Patents

Abstract

The invention provides a three-axis flexible air bearing table balance adjusting state judgment method and relates to an air bearing table balance adjusting state judgment method, aiming at solving the problem that a balance state cannot be adjusted under an extreme condition in balance adjustment of a flexible air bearing table in the prior art. Firstly, a table body is upward lifted in a horizontal plane direction for the maximum working angle; then the table body is put down to freely fall off; if the table body does reciprocating swinging, the table body falls off until the table body is nearly overturned; if the table body is overturned for a large angle, a critical state is an extreme balance adjustment state of the air bearing table; at the moment, a movement period is the longest, and a deflection angle of the table body when the air bearing table reaches an extreme value imbalance torque is calculated; if the table body is overturned for a small angle, the table body is put on a horizontal plane to keep static and then freely falls off; if the table body cannot rotate at the maximum working angle, the table ball falls off until the table body can rotate at the maximum working angle; the critical state is the extreme balance adjustment state of the air bearing table; at the moment, the movement period is the longest, and the deflection angle of the table body when the air bearing table reaches the extreme value imbalance torque is calculated.

Description

Three axle flexibility air floating table balancing condition judgement methods

Technical field

The present invention relates to a kind of air floating table balancing condition judgement method, belong to field of measuring technique.

Background technology

Three-axis air-bearing table is one of most important equipment of space mechanics environmental simulation system, and its principle is dependent on gases at high pressure Air film between air-floating ball bearing and bearing block supports stage body, forms the Three Degree Of Freedom rotation of micro-damping, micro tribology so that platform Body motion can the mechanical environment of virtual space subtle disruption moment, therefore air floating table balancing is one of air floating table core technology. Only considering gravity unbalance moment and think that stage body is rigid body when, three-axis air-bearing table presents 3D pendular motion, and single shaft presents Compound motion.Calculating theoretically, air floating table can infinitely (will regulate to infinite approach rotation by balancing in center of gravity regulation The heart, unbalanced moments is infinitely close to zero, and now the stage body period of motion is close to endless).Can according to current data-searching To find, it is theoretical that the decision method of air floating table balancing is based on this.As Lin Laixing proposes consideration gravity unbalance moment Under the conditions of, the period of motion being made air floating table by regulation barycenter is the longest, and final poised state is come with period of motion length Judge poised state (Lin Laixing, current Small Satellite Technology level and the countermeasure of development China moonlet application, the science and technology of air floating table Leader, vol.2, pp:7-10,1998)；Mention in " three-axis air-bearing table automatic adjusting balance method " literary composition eastwards, can basis The period of motion and static balance angle judge air floating table poised state, and (eastwards, Yang Qingjun, Baogang, Wang Zuwen, three-axis air-bearing table is certainly Dynamic balancing method.Maritime Affairs University Of Dalian's journal, 32 (3): 25-29,2008).

Necessarily have certain flexibility due to air floating table, its position of centre of gravity there will be skew in rotation process, especially at weight During heart infinite approach center of rotation, air floating table is not in balancing state, it is possible that the phenomenon of upset in rotation process, The compound pendulum model characteristics of motion is not followed in now its motion.

Li Yanbin proposes the center of gravity of flexible air floating table and can offset in rotation, its side-play amount and the two of stage body angle Become sine relation again, and this side-play amount may produce compensation with original weight heart deviation, and (three freedom degree air floating platform that gravity causes is each Class unbalanced moments relation and impact, Li Yanbin, eastwards, mechanical engineering journal, Vol.51No.21,2015), but it is not transported Dynamic feature is studied, and does not the most study the decision criteria of its poised state.

To sum up, in the balancing of flexible air floating table, air-float turntable can not infinitely balancing, each air-float turntable There are its balancing limit state, i.e. extreme value unbalanced moments minimum state.But how air floating table is regulated so far state, and such as What judges adjusted so far state, not yet mentions in current achievement in research.

Summary of the invention

The present invention is for solving in the balancing of existing flexible air floating table, it is impossible to realizes the limit and lowers asking of poised state Topic, and then a kind of three axle flexibility air floating table balancing condition judgement methods are provided.

The present invention solves that the problems referred to above adopt the technical scheme that: three axle flexibility air floating table balancing state judgement sides Method, first, is lifted up stage body 1 to maximum functional angle, θ in horizontal plane side_max, then, put down allowing its free-falling, if platform Body 1 does reciprocally swinging, then raise the barycenter of air floating table along Z axis, until stage body 1 is close to upset；

If stage body 1 is when wide-angle overturns, this critical state is the limit balancing state of air floating table, now, motion Cycle is the longest, and can be according to formulaIt is calculated air floating table and reaches extreme value not The deflection angle θ of stage body 1 during trimming moment₀₁；

If stage body 1 is when low-angle overturns, then stage body 1 being placed in horizontal plane more static, then free-falling, if can not be Maximum functional angle rotary, then lower the barycenter of solar term floating platform along Z-axis direction, until stage body can be at maximum functional angle rotary, this Critical state is the limit balancing state of air floating table, and now the period of motion is the longest, and can according to formula,It is calculated air floating table and reaches extreme value The deflection angle θ of stage body 1 during unbalanced moments₀₂。

The invention has the beneficial effects as follows: stage body is raised up to maximum functional angle, then free-falling by the present invention, by platform The direction of motion of body, judges whether stage body has reached limit balancing state respectively, it is possible to calculate the limit of stage body not There is position in trimming moment.This method is easily achieved, it is not necessary to measures and calculates unbalanced moments and i.e. can determine whether air floating table the most Through reaching balancing state, and this method is the shortest, and expense is low.Have only to the perusal stage body direction of motion and i.e. can determine that gas The balancing state of floating platform, it is possible to calculating limit unbalanced moments location point, provides for measurement extreme value unbalanced moments and depends on According to (directly can measure unbalanced moments by torgue measurement instrument in this operating point)；Technical staff also can directly pass through the method Regulation air floating table, and without calculating stage body unbalanced moments.The method is also applied for single shaft flexibility air floating table balancing state Judge.For judging that air floating table has reached balancing limit state (extreme value unbalanced moments is minimum), and can calculate To stage body reach extreme value unbalanced moments time operating point, can be used for calculate stage body extreme value unbalanced moments.

Accompanying drawing explanation

Fig. 1 is the air floating table kinestate schematic diagram of the present invention.

Detailed description of the invention

Detailed description of the invention one: combine Fig. 1 explanation, three axle flexibility air floating table balancing state judgement sides of present embodiment Method is such that

First, stage body 1 is lifted up to maximum functional angle, θ in horizontal plane side_max, then, put down under allowing it freely Fall, if stage body 1 does reciprocally swinging, then raise the barycenter of air floating table along Z axis, until stage body 1 is close to upset；

If stage body 1 is when wide-angle overturns, this critical state is the limit balancing state of air floating table, now, motion Cycle is the longest, and can be according to formulaIt is calculated air floating table and reaches extreme value not The deflection angle θ of stage body 1 during trimming moment₀₁；

If stage body 1 is when low-angle overturns, then stage body 1 being placed in horizontal plane more static, then free-falling, if can not be Maximum functional angle rotary, then lower the barycenter of solar term floating platform along Z-axis direction, until stage body can be at maximum functional angle rotary, this Critical state is the limit balancing state of air floating table, and now the period of motion is the longest, and can according to formula,It is calculated air floating table and reaches extreme value The deflection angle θ of stage body 1 during unbalanced moments₀₂。

In Fig. 1,1 is the stage body of air floating table, and 2 is air-floating ball bearing.X and Z represents coordinate system.

Embodiment

First, stage body 1 is lifted up to maximum functional angle, θ in horizontal plane side_max, then put down allowing its free-falling, As air-float turntable stage body 1 does reciprocally swinging, then raise the barycenter of air-float turntable along Z axis, until stage body 1 is close to upset；

By the moment formula of air floating table: M=kmg sin2 θ+mgr sin θ (1)

Wherein, k is the deformation coefficient of the stage body of air floating table, and m is air floating table quality, and the unit of m is kg；θ is air floating table Stage body corner, the unit of θ is °；R is absolute offset values, and the unit of r is m, is also rice；

The unbalanced moments that in formula (1), Section 1 is brought because of the deforming displacement amount rotating generation by air floatation ball center of gravity； Section 2 is the unbalanced moments that the center of gravity absolute offset values when horizontal level is brought；

In above-mentioned formula (1), as k, < when 0, Section 1 and Section 2 are in the same direction；Section 1 swings for the stage body of air-float turntable Being restoring moment, if allowing the stage body of air floating table not overturn, then needing to make M is negative value, i.e. r ＜-k2cos θ； (2)

The now absolute centroid motion of stage body 1 of air-float turntable side in the horizontal plane, owing to the maximum functional angle of stage body is θ_max, therefore, barycenter ultimate value is, r₀=-2k cos θ_max； (3)

Wherein, r₀For the ultimate value of absolute barycenter, r₀Unit be m；

The stage body of air floating table now is in upset critical state, if beyond critical state, then the stage body of air floating table is to greatly Angular movement overturns, according to formula (1) direct solution equation；

The deflection angle θ of stage body 1 when air floating table reaches extreme value unbalanced moments can be calculated₀₁,θ₀₁Unit For °；

${\mathrm{\&theta;}}_{01}=\&PlusMinus;arccos\frac{{\mathrm{cos\&theta;}}_{max}+\sqrt{{\cos }^2{\mathrm{\&theta;}}_{max}+8}}{4};---\left(4\right)$

In above-mentioned formula (1), if during k > 0, two reversely.It is to obstruct the power that stage body is replied that Section 1 swings for stage body 1 Square, if allowing stage body 1 not overturn, need to make M is negative value, now, due to k > 0, for the most minimum for M regulation, needing first be adjusted to by r Negative, i.e. it is adjusted to below horizontal plane, then absolute for the stage body of air floating table centre-of gravity shift need to be adjusted up below horizontal plane.This Time motion artifacts be: as r ＜-k2cos θ, the stage body of air floating table does not overturns, then when up regulating, near 0 ° Operation interval [-θ₁,θ₁Stage body 1 in] can overturn；

Wherein ,-θ₁,θ₁Refer to the angular interval of a uncertain value；

After stage body 1 movement angle jumps out this interval, stage body 1 starts backswing.Therefore, the limit shape of air floating table centroid adjustment The motion artifacts of state is when the stage body 1 of air floating table starts to swing from close to horizontal plane, before the maximum functional angle of arrival side Start revolution.According to this principle, to formula (1) derivation, can be calculated centroid motion ultimate value isr₀ Referring to barycenter ultimate value, unit is m, if beyond critical state, then air floating table moves at zero point, goes out nothing to maximum functional angle Method returns.In this case, according to formula (1), the stage body unbalanced moments when operating point that can be calculated air floating table reaches pole Limit value deflection angle:

${\mathrm{\&theta;}}_{02}=\&PlusMinus;arccos\frac{(1-cos2{\mathrm{\&theta;}}_{\max })+\sqrt{{(1-cos2{\mathrm{\&theta;}}_{\max })}^2+32{(1-{\mathrm{cos\&theta;}}_{max})}^2}}{8(1-{\mathrm{cos\&theta;}}_{max})}.$

Claims (1)

1. three axle flexibility air floating table balancing condition judgement method, it is characterised in that: the method is such that

First, stage body (1) is lifted up to maximum functional angle, θ in horizontal plane side_max, then, put down allowing its free-falling, If stage body (1) does reciprocally swinging, then raise the barycenter of air floating table along Z axis, until stage body (1) is close to upset；

If stage body (1) is when wide-angle overturns, this critical state is the limit balancing state of air floating table, now, motion week Phase is the longest, and can be according to formulaIt is calculated air floating table and reaches extreme value injustice The deflection angle θ of stage body (1) during weighing apparatus moment₀₁；

If stage body (1) is when low-angle overturns, then stage body (1) being placed in horizontal plane more static, then free-falling, if can not be Maximum functional angle rotary, then lower the barycenter of solar term floating platform along Z-axis direction, until stage body can be at maximum functional angle rotary, this Critical state is the limit balancing state of air floating table, and now the period of motion is the longest, and can according to formula,It is calculated air floating table and reaches extreme value The deflection angle θ of stage body (1) during unbalanced moments₀₂。