CN110058097A - A kind of hall thruster acceleration service life test method - Google Patents

A kind of hall thruster acceleration service life test method Download PDF

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CN110058097A
CN110058097A CN201910223978.7A CN201910223978A CN110058097A CN 110058097 A CN110058097 A CN 110058097A CN 201910223978 A CN201910223978 A CN 201910223978A CN 110058097 A CN110058097 A CN 110058097A
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coordinate
wall
formula
wall surface
moment
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CN110058097B (en
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毛威
扈延林
沈岩
吴朋安
吴楠
李胜军
臧娟伟
胡大为
吴耀武
山世华
解舫
杨健
陈君
李栋
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Beijing Institute of Control Engineering
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    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F03MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
    • F03HPRODUCING A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
    • F03H1/00Using plasma to produce a reactive propulsive thrust
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F03MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
    • F03HPRODUCING A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
    • F03H1/00Using plasma to produce a reactive propulsive thrust
    • F03H1/0081Electromagnetic plasma thrusters

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Abstract

The present invention relates to a kind of hall thruster acceleration service life test methods, belong to the technical field of performance test of hall thruster.The actual ignition that this method carries out one section of short time to hall thruster is tested, the discharge channel wall profile at multiple and different moment is measured in the process, according to discharge channel wall surface erosion rate formula, reverse goes out the source parameters of this period of time, further according to the discharge channel wall profile of the extrapolated next rapid lapse of time of wall surface erosion rate formula and source parameters, the method removal wall surface material being machined into, makes the wall profile of discharge channel reach the profile of prediction.Wall surface material alternating iteration is removed up to hall thruster discharge channel wall surface has been etched using the actual ignition test machining lower with model extrapolation guidance, test period and predicted time are accumulated to obtain the service life of thruster.

Description

A kind of hall thruster acceleration service life test method
Technical field
The present invention relates to a kind of hall thruster acceleration service life test method more particularly to hall thruster discharge channels Life test method belongs to the technical field of performance test of hall thruster.
Background technique
Hall thruster is a kind of current electric propulsion device typical in the world.Fig. 1 is the exemplary axis of hall thruster To cross-sectional view.Propellant xenon enters in channel from the anode (30) of ring discharge channel (20) upstream, and anode provides height simultaneously Current potential;Electronics is sprayed from the cathode (40) in ring discharge passages downstream exit, and cathode provides low potential.One of cathode ejection Point electronics enters ring discharge channel interior, the radial magnetic field that generates in external magnetic circuit (10) and internal from being in harmony the axial direction of generation Hall drift motion is carried out under electric field action, electronics and propellant atom, which collide to ionize, generates ion, and ion is by axial electricity Field, which accelerates to spray, generates thrust, and electronics reaches anode by various transmission mechanisms.Another part electronics that cathode sprays enters plumage The ion for flowing area and high speed ejection neutralizes, and keeps the electroneutral of plume.The chief component of hall thruster is put including annular Electric channel, magnetic circuit, anode, cathode etc..Discharge channel generally makes of the boron nitride-base ceramic material of resistance to ion sputtering.
Electrical power P, the working medium that the reaction thrust F that the working medium injection of hall thruster generates is consumed by thruster are sprayed The restriction of speed v, electrical power to the transformation efficiency η of kinetic energy power etc.: F=2P η/v;
Since the working medium jet velocity v of hall thruster is generally in 15km/s~25km/s range, spacecraft can be at present The power P of hall thruster is supplied to generally in 700W~5000W range, this results in the thrust of hall thruster about to exist 40mN~250mN range.Due to hall thruster thrust very little, in order to meet the mission requirements of spacecraft, this results in Hall The working life of thruster is very long, it is desirable that in thousands of hours~hour up to ten thousand.It is defended with current large-scale geostationary orbit communication For the application of star, Orbit Transformation is carried out using 5kW hall thruster and position keeps task, the work of 5kW hall thruster At least up to 10,000 hours are needed as the service life.
The most important technical factor in limitation hall thruster service life is that hall thruster discharge channel wall surface is led at present High-energy ion bombardment in road, for wall surface material by gradually sputter erosion, wall surface is gradually thinning, until wall surface is completely by ion erosion It penetrates, outer magnetic pole (11) or internal magnetic pole (12) are directly exposed under the bombardment of energetic ion, due to the anti-sputtering of pole material Energy difference and the protection for lacking discharge channel, pole form is sputtered change quickly or magnetic pole is easy to by ion bombardment mistake Heat, the magnetic field in guiding discharge channel are destroyed, thruster cisco unity malfunction.Generally with discharge channel outer wall (21) or inner wall (22) any wall surface is corroded the mark penetrated as thruster end-of-life by ion sputtering.
Currently, the method that the life test of hall thruster has generallyd use life cycle test verifying, i.e., it must be on ground The vacuum firing test of 1:1 (Ground Test Time: operation on orbit time), simulation are carried out in the vacuum environment simulator of construction Thruster is in spaceborne operating condition and cumulative operation time, or even the Ground Test Time of thruster is required to reach operation on orbit 1.2~1.5 times of time.The jet propulsion laboratory (NASA JPL) of US National Aeronautics and Space Administration is to 1.35kW Hall thrust Device SPT-100 has carried out 5730 hours life tests, and French Snecma (SNECMA) company is to 1.5kW hall thruster PPS-1350G has carried out 10530 hours life tests, and US Airways jet company (Aerojet) is to 4.5kW hall thruster BPT-4000 has carried out 10400hr life test.
Hall thruster life test problems faced is mainly manifested in three aspects: funds are very big, the period is very long, technology Risk is very high.By taking 5kW hall thruster as an example, a life test need to consume electric propulsion high-purity xenon (99.9995% with On) about 9,000,000, the electricity charge about 8,000,000 of vacuum environment simulator, it further include the plant maintenance and depreciation during life test Expense, testing crew expense etc., it is entire to test funds about 25,000,000;The thruster accumulative duration of ignition reaches 10,000 hours or more, Further include the thruster required during test shut down cooling, thruster regularly performance and the detection of discharge channel wall profile with And the times such as testing equipment maintenance maintenance, about 3 years entire life test periods;Life test does not guarantee once to pass through, and very may be used Can occur repeatedly, the uncertainty of test result is very big.
Harbin Institute of Technology proposes a kind of evaluation method (CN200810136846.2) of Hall thruster life-span, should Invention calculates practical boron nitride-base ceramic discharge channel using the service life that ion bombardment obtains is carried out to easy sputtering ceramic tube Service life.But this method is primarily present following problems:
(1) different ceramic materials have different secondary electron yields, thermal coefficient, anti-ion sputtering performance, will The material of discharge channel is changed to easily sputtering ceramics, although accelerating sputtering, also changes discharge channel wall surface reality simultaneously The secondary and heating conduction on border can cause plasma parameter variation and discharge channel temperature change in channel, change The energy of ion in variable conduit, changes sputtering mechanism, and the accuracy that will lead to accelerated test is not high;
(2) discharge channel material is usually hexagonal boron nitride-base ceramic at present, if to guarantee that sputtering mechanism is constant, wall surface Component, dissimulated electricity energy and the sputtering threshold value of material can not all change, and can only be implemented by reducing density of material in engineering, But the reduction amount of density is than relatively limited, and about 15%, the easily test period saved of sputtering ceramics and cost accelerates also than relatively limited Efficiency is relatively low.
Summary of the invention
Technical problem solved by the present invention is overcoming, hall thruster life cycle test funds are high, the period is long, technical risk The problem of big problem and existing accelerated test low efficiency, low precision, provide a kind of effective hall thruster accelerated aging Test method.
The technical solution of the invention is as follows:
A kind of hall thruster acceleration service life test method, this method carry out the reality of one section of short time to hall thruster Fire trial measures the discharge channel wall profile at multiple and different moment in the process, corrodes speed according to discharge channel wall surface Rate formula, reverse go out the source parameters of this period of time, extrapolated further according to wall surface erosion rate formula and source parameters The discharge channel wall profile of next rapid lapse of time, the method removal wall surface material being machined into, makes the wall surface of discharge channel Profile reaches the profile of prediction.Replaced using actual ignition test with the machining removal wall surface material under model extrapolation guidance Iteration has been etched up to hall thruster discharge channel wall surface, and test period and predicted time are accumulated to obtain the longevity of thruster Life.Key step is as follows:
(1) a period of time (0~t is carried out to the hall thruster lighted a fire for the first time into vacuum tank0Moment) vacuum firing examination It tests, discharge channel wall surface is pre-processed, eliminate hall thruster material especially discharge channel wall surface and magnet exciting coil etc. Influence of the gas of absorption to life test;Described a period of time refers to 6-20h;Vacuum degree when vacuum firing is tested is not low In 5*10-3Pa;Pretreatment refers to the high temperature action generated using vacuum firing and ion bombardment effects to for the first time into vacuum tank point The hall thruster of fire carries out high-temperature outgassing processing;
(2) vacuum firing after the test, i.e., in t0Moment uses contact contourgraph or non-contact optical profile Instrument measures under the rz coordinate system of the wall profile (including outer wall facial contour and inner wall facial contour) of hall thruster discharge channel Coordinate obtains t0The coordinate r of the discharge channel outer wall facial contour at momentOutside(z,t0) and inner wall facial contour coordinate rIt is interior(z,t0);
The determination method of rz coordinate system are as follows: using the axis of hall thruster as z-axis, using hall thruster it is radial as R axis, origin O selection is unrestricted, can be chosen at the certain point outside hall thruster, to facilitate contourgraph to carry out wall profile survey Amount is principle.By the series of points on the wall profile wall surface of the hall thruster discharge channel of corresponding moment t in rz coordinate The set of the lower position coordinates (r, z) of system is indicated, and is denoted as r (z, t), for convenient for distinguishing, by inner wall facial contour coordinate note For rIt is interior(z, t), outer wall facial contour coordinate are denoted as rOutside(z,t)。
(3) to hall thruster progress 3, (N round numbers, N >=2, to guarantee that precision reduces pendulous frequency simultaneously, N is general The vacuum firing of 3) period is taken to test, in the finish time (t of each period1、t2、…、tN) surveyed by the method for step (2) The coordinate of discharge channel outer wall facial contour and the coordinate of inner wall facial contour are measured, the coordinate of outer wall facial contour is labeled as rOutside(z,t1)、rOutside(z,t2)、…、rOutside(z,tN);The coordinate of inner wall facial contour is labeled as rIt is interior(z,t1)、rIt is interior(z,t2)、…、rIt is interior(z,tN);
(4) the wall profile coordinate of the discharge channel at least three different moments measured using step (3), first basis is put Electric channel wall surface erosion rate formula reverse goes out the position (z of equivalent ion source Ss, rs) and ion sputtering intensity F (α), it recycles Wall surface erosion rate formula calculates hall thruster and runs a period of time △ tN+1The outer wall facial contour coordinate r of discharge channel afterwardsOutside (z,tN+1) and inner wall facial contour coordinate rIt is interior(z,tN+1);Calculate the duration △ t of predictionN+1For thruster real work in step (3) Duration (△ t1+△t2+……+△tN) 1~8 times, to guarantee precision of prediction, wherein △ t1=t1-t0, △ t2=t2-t1..., △tN=tN-tN-1, △ tN+1=tN+1-tN.Defining speed-up ratio is prediction duration △ tN+1With real work duration △ t1+△t2 +……+△tNRatio, due to hall thruster have slow down corrosion characteristic, life test initial stage (1000h in the past (≤ 1000h)) speed-up ratio is chosen smaller, and generally 1~3;The speed-up ratio in life test later period ((> 1000h) after 1000h) is chosen It is larger, generally 5-8;(△t1,△t2,…,△tN) selection should ensure that after this section of time service, wall profile Variation at least up to 10-1The magnitude of mm, while guaranteeing that this period of time is short as far as possible, to improve the efficiency accelerated;At the beginning of life test Phase (1000hr was in the past (≤1000h)) (△ t1,△t2,…,△tN) generally it is chosen for 50~100hr, life test later period ((> 1000h) after 1000hr) (△ t1,△t2,…,△tN) generally it is chosen for 200~400hr.
(5) hall thruster discharge channel is machined, the outer wall facial contour coordinate predicted according to step (4) rOutside(z,tN+1) processing discharge channel outer wall facial contour, the inner wall facial contour coordinate r predicted according to step (4)It is interior(z,tN+1) Process the inner wall facial contour of discharge channel;
(6) it repeats step (2)~(5) to have altogether m times (m is natural number), until in the outside wall surface of discharge channel or inner wall The thickness of any wall surface becomes zero, and the hall thruster real work duration of duplicate pth time (p round numbers, 1≤p≤m) is remembered ForCorresponding calculating prediction duration is denoted as
(7) hall thruster actual run time, predicted time are added up, obtains the service life t of hall thrusterlife
In the step (3), hall thruster is the axially symmetric structure with circular passage, the wheel of inside and outside ceramics wall surface It is wide to use function r respectivelyIt is interior(z, t) and rOutside(z, t) is indicated, it is (z that the ion stream for moving to channel wall, which is from coordinate,s,rs) point source It generates, the angle of ion incidence direction and radial (r to) are α, the tangential direction of ion incidence to wall surface point and axially (z To) angle be angle that beta, gamma is ion incidence direction Yu channel wall normal direction, γ=alpha+beta;
The wall profile coordinate of the discharge channel for 3 different moments measured using step (3), first according to discharge channel wall Face erosion rate formula reverse goes out the position (z of equivalent ion source Ss, rs) and ion sputtering intensity F (α), recycle wall surface to corrode Rate equation calculates hall thruster and runs a period of time △ tN+1The outer wall facial contour coordinate r of discharge channel afterwardsOutside(z,tN+1) and Inner wall facial contour coordinate rIt is interior(z,tN+1)。
For discharge channel outside wall surface, r (z, t)=rOutside(z, t), r (z, t) are do not distinguish outside wall surface and inner wall general Wall surface coordinate, detailed calculating process are as follows:
Wall surface erosion rate formula:
γ is the wall surface ion incident angles at t moment axial coordinate z, is calculated as follows:
Yγ(γ) is the corresponding angle sputtering yield of ion incident angles γ, and discharge channel generally selects boron nitride-base to make pottery Porcelain, angle sputtering yield YγThe equation of (γ) is (3), wherein f=2.23, γopt=67.9 °.Yγ(γ) can also carry out material Material sputtering attribute testing measurement.
Wall surface coordinate r (z, t) is uniformly separated by M node using finite difference calculus.The axial of i-th of node of wall surface is sat Labeled as zi(coordinate is unrelated with time t), i-th of node of wall surface are denoted as r in the radial coordinate of t momenti(t), in t moment wall Ionic incident angles γ at the node of i-th of facei(t) it is separated into the form of formula (4):
The angle α in ion incidence direction and r axis at i-th of node of t moment wall surfacei(t) it is separated into the shape of formula (5) Formula:
For t1, t2The discrete form at two moment, the erosion rate formula (1) of i-th of node of wall surface is shown in formula (6):
For i=2 ..., M-1, discrete equation form are as follows:
For i=1, discrete equation form are as follows:
For i=M, discrete equation form are as follows:
For t2, t3Erosion rate formula (1) discrete form at two moment, i-th of node of wall surface is as follows: for i= 2 ..., M-1, discrete equation form are as follows:
For i=1, discrete equation form are as follows:
For i=M, discrete equation form are as follows:
Ion sputtering intensity F (α at t moment, i-th of node of wall surfacei(t)) general type are as follows:
{mj,k,nj,k;J=1,2 ..., M } it is constituting-functions F (αi) coefficient set.
Position (the z of ion source Ss, rs) and ion sputtering intensity F (αi) solution procedure it is as follows:
B. assume ion source position coordinates (zs, rs) be located on some position in discharge channel;
B. by t1、t2The moment channel wall node coordinate of measurement calculates F (α according to discrete equation (6)i(t1));By t2、t3The moment channel wall node coordinate of measurement calculates F (α according to discrete equation (7)i(t2)).Coefficient set { mj,k, nj,kInitial value { mj,0,nj,0Calculated by formula (9):
C. according to coefficient set { mj,k,nj,kInitial value { mj,0,nj,0, utilize formula (6) and t1The conduit wall of moment measurement Face node coordinate, finds out t2The channel wall node radial coordinate calculated value at moment It utilizes Formula (6) and t2The channel wall node coordinate of moment measurement, finds out t3Moment channel wall node radial coordinate calculated valueUsing formula (8), formula (5) andCalculate t1When The ion sputtering intensity F (α at quarteri(t1))0, using formula (8), formula (5) andIt calculates t2The ion sputtering intensity F (α at momenti(t2))0
D. the variances sigma between channel wall node radial coordinate calculated value and measured value0It is calculated by formula (10):
The k of formula (10) is subscript, is non-natural number, and the value of k is from 0 to maximum number of iterations;
E. one group of new coefficient set { m is chosen by formula (11)j,k,nj,k}
The k of formula (11) is subscript, and k is natural number, and the value of k is from 1 to maximum number of iterations;
F. according to the coefficient set { m of selectionj,k,nj,k, using formula (8), formula (5) and Recalculate t1The ion sputtering intensity F (α at momenti(t1))1, using formula (8), formula (5) andRecalculate t2The ion sputtering intensity F (α at momenti(t2))1, and calculate recently twice The relative error res of ion sputtering intensity:
G. according to formula (6), t is utilized1The channel wall node coordinate of moment measurement, finds out moment t again2Conduit wall Face node radial coordinate calculated valueAccording to formula (6), t is utilized2The channel of moment measurement Wall surface node coordinate, finds out t again3The channel wall node radial coordinate calculated value at momentChannel wall node radial coordinate calculated value and measured value are recalculated by formula (10) Between variances sigma1
H. if variances sigma1< σ0, it is considered that { mj,1,nj,1It is effectively, by { mj,1,nj,1It is added to { mj,k,nj,k} In queue, next group of coefficient { m is chosen according to formula (11)j,2,nj,2};If variances sigma1≥σ0, chosen again according to formula (12) {mj,1,nj,1};
I. step e, f, g, h are repeated, until ion sputtering strength relative error res is less than 1e-3 or the number of iterations reaches Until the maximum value (generally taking 1000~5000 times) of setting, corresponding final variance under the ion source position coordinates is recorded;
J. ion source is sat according to certain rule (can scan by row, column coordinate or be scanned by radius, angle coordinate) Mark (zs, rs) traversal discharge channel in all positions, repeat step b~i, obtain corresponding under the coordinate of different ions source position Variance, the corresponding ion source position of minimum variance are as finally determining ion source position coordinates (zs, rs), minimum variance pair F (the α that the coefficient set answered as finally determinesi) coefficient set { mj,k,nj,k}。
K. for discharge channel outside wall surface, ri(tN)=ri Outside(tN), ri(tN+1)=ri Outside(tN+1), directly obtained using step j Ion source position coordinates (the z arriveds, rs) and ion sputtering intensity F (α), utilize known tNThe wall surface node coordinate r at momenti (tN) and formula (13) calculating hall thruster operation a period of time △ tN+1The wall surface node coordinate r of discharge channel afterwardsi(tN+1)。
For i=2 ..., M-1, the radial coordinate calculation formula of wall surface node i are as follows:
For i=1, the radial coordinate calculation formula of wall surface node i are as follows:
For i=M, the radial coordinate calculation formula of wall surface node i are as follows:
For discharge channel inner wall, first by the node coordinate r of inner walli It is interior(t1)、ri It is interior(t2)、ri It is interior(t3) according to formula (14) it is coordinately transformed into general wall surface coordinate form ri(t1)、ri(t2)、ri(t3), then asked according to above-mentioned steps a~j Solve the corresponding ion source position coordinates (z of inner walls, rs) and ion sputtering intensity F (α),
R in formula (14)meanFor the initial mean radius of discharge channel, ring discharge is logical before as life test starts The distance between the center line and hall thruster axis in road.
Utilize known tNThe wall surface node coordinate r at momenti(tN)(ri(tN)=2Rmean-ri It is interior(tN)) and formula (13) meter It calculates hall thruster and runs a period of time △ tN+1The wall surface node coordinate r of discharge channel afterwardsi(tN+1), further according to formula (15) into Row coordinate inversion obtains the inner wall node coordinate r of subsequent timei It is interior(tN+1)。
ri It is interior(tN+1)=2Rmean-ri(tN+1) (15)。
Advantage is the present invention compared with prior art:
(1) accelerate using discharge channel wall profile as accelerated factor, discharge channel wall is removed by machining The mode of plane materiel material realizes efficient acceleration, it is ensured that the efficiency of accelerated test;
(2) precision of accelerated method of the invention is high.On the one hand, thruster discharge channel is changed without material, does not change and pushes away The physical process of power device actual motion and existing life failure rule, thruster discharge channel erosion test data directly reflect The actual conditions that discharge channel wall surface corrodes when thruster actual motion;On the other hand, this method is invaded with discharge channel wall surface Based on losing formula, by the wall profile at multiple and different moment that test measurement obtains, the anti-ion source for releasing bombardment wall surface Position and parameter, ensure that the position of ion source and parameter have passed through the abundant verifying of history test, then go based on this Discharge channel wall profile after predicting following a period of time, can effectively guarantee the precision of prediction, to ensure that acceleration The precision of test;
(3) acceleration service life test method of the invention is easy to implement, strong operability, without in order to carry out accelerated test Develop the special ceramic material easily sputtered.
Detailed description of the invention
Fig. 1 is hall thruster schematic diagram;
Fig. 2 is hall thruster accelerated test flow diagram;
Fig. 3 is the ion source schematic diagram that profile reverse is corroded according to channel wall, and the ion source for bombarding wall surface is from coordinate For (zs,rs) point source issue, the angle of ion incidence direction and radial (r to) are α, certain point on ion incidence to wall surface The angle of tangential direction and axial (z to) are β;
Fig. 4 is the example (N=3, m=2) that discharge channel wall profile changes with time during accelerated life test, Oo ' is the center line in ring discharge channel;
Fig. 5 is the corresponding ion source position (z of discharge channel outside wall surfaces,rs) and ion sputtering intensity F (α) solution stream Journey;
Fig. 6 is the wall profile situation of change that certain type hall thruster accelerates to 400hr from 0~200hr;
Fig. 7 is the wall profile situation of change that certain type hall thruster accelerates to 1200hr from 400~600hr;
Fig. 8 is the wall profile situation of change that certain type hall thruster accelerates to 4000hr from 1200~1600hr;
Fig. 9 is the wall profile situation of change that certain type hall thruster accelerates to 10485hr from 4000~4700hr.
Specific embodiment
As shown in Figs. 1-5, implementation steps of the invention are as follows:
(1) a period of time (t is carried out to hall thruster0≈ 6~20 hours) vacuum firing test, utilize vacuum firing The high temperature action and ion bombardment effects of generation carry out high-temperature exhaust air processing to discharge channel wall surface, eliminate discharge channel wall surface and inhale Influence of the attached gas to life test;
(2) vacuum firing after the test, to the wall profile of hall thruster discharge channel (including inner wall facial contour and Outer wall facial contour) it is measured using contact contourgraph or non-contact optical profiler, obtain t0The electric discharge at moment is logical The wall profile coordinate r of road inner wallIt is interior(z,t0) and outer wall wall profile coordinate rOutside(z,t0);
(3) vacuum firing for carrying out 3 (N=3) periods to hall thruster is tested, each period at the end of Carve (t1、t2、t3) by step (2) method measurement discharge channel inner and outer wall wall profile, inner wall facial contour is denoted as rIt is interior (z,t1)、rIt is interior(z,t2)、rIt is interior(z,t3);Outer wall facial contour is rOutside(z,t1)、rOutside(z,t2)、rOutside(z,t3);
(4) the profile r of the discharge channel outside wall surface for 3 different moments measured using step (3)Outside(z,t1)、rOutside(z, t2)、rOutside(z,t3), first according to discharge channel wall surface erosion rate formula (1), reverse go out discharge channel outer wall it is corresponding it is equivalent from Position (zs, the r of component Ss) and ion sputtering intensity F (α), recycle wall surface erosion rate formula (1) to calculate hall thruster Run a period of time △ t4The outer wall facial contour coordinate r of discharge channel afterwardsOutside(z,t4);
The profile r of the discharge channel inner wall for 3 different moments measured using step (4)It is interior(z,t1)、rIt is interior(z,t2)、rIt is interior (z,t3), first by inner wall coordinate transformation at general wall surface coordinate r (z, t1)、r(z,t2)、r(z,t3), according to discharge channel wall Face erosion rate formula (1), reverse go out the position (z of the corresponding equivalent ion source S of discharge channel outer walls,rs) and ion sputtering it is strong It spends F (α), recycles wall surface erosion rate formula (1) to calculate hall thruster and run a period of time △ t4The wall of discharge channel afterwards Facial contour coordinate r (z, t4), general wall surface coordinate is finally obtained into inner wall areal coordinate r by formula (14) inverse transformationIt is interior(z,t4);
Calculate the duration △ t of prediction4For thruster real work duration (△ t1+△t2+△t3) 1~8 times or so, with Guarantee precision of prediction, wherein △ t1=t1-t0, △ t2=t2-t1, △ t3=t3-t2, △ t4=t4-t3;Defining speed-up ratio is prediction Duration △ t4With real work duration △ t1+△t2+△t3Ratio, due to hall thruster have slow down corrosion characteristic, the longevity It is smaller to order the selection of test initial stage (1000h was in the past (≤1000h)) speed-up ratio, generally 1~3;The life test later period (1000h with (> 1000h) afterwards) speed-up ratio choose larger, generally 5-8;(△t1,△t2,△t3) selection should ensure that by this section After time service, the variation of wall profile is at least up to 10-1The magnitude of mm, while guaranteeing that this period of time is short as far as possible, to improve The efficiency of acceleration;Life test initial stage (1000hr was in the past (≤1000h)) (△ t1,△t2,△t3) generally it is chosen for 50~ 100hr, life test later period ((> 1000h) after 1000hr) (△ t1,△t2,△t3) generally it is chosen for 200~400hr.
(5) hall thruster discharge channel is machined, the inner and outer wall of discharge channel is respectively machined to The inner wall facial contour r that step 4 predictsIt is interior(z,t4) and outer wall facial contour rOutside(z,t4);
(6) it repeats step (2)~(5) to have altogether m times (m is natural number), until the inner wall of discharge channel or the thickness of outer wall It becomes zero, the thruster real work duration of duplicate pth time (p round numbers, 1≤p≤m) is denoted as Corresponding calculating prediction duration is denoted as
(7) hall thruster actual run time, predicted time are added up, obtains the service life t of hall thrusterlife:
In the step (3), hall thruster is the axially symmetric structure with circular passage, the wheel of inside and outside ceramics wall surface It is wide to use function r respectivelyIt is interior(z, t) and rOutside(z, t) is indicated, as shown in Figure 3.The ion stream for moving to channel wall is to be from coordinate (zs,rs) point source generate, the angle of ion incidence direction and radial (r to) are α, the tangent line of ion incidence to wall surface point The angle of direction and axial (z to) are the angle that beta, gamma is ion incidence direction Yu channel wall normal direction, from the figure 3, it may be seen that γ=alpha+beta.
The wall profile coordinate of the discharge channel for 3 different moments measured using step (3), first according to discharge channel wall Face erosion rate formula reverse goes out the position (z of equivalent ion source Ss, rs) and ion sputtering intensity F (α), recycle wall surface to corrode Rate equation calculates hall thruster and runs a period of time △ tN+1The outer wall facial contour coordinate r of discharge channel afterwardsOutside(z,tN+1) and Inner wall facial contour coordinate rIt is interior(z,tN+1)。
For discharge channel outside wall surface, r (z, t)=rOutside(z, t), r (z, t) are do not distinguish outside wall surface and inner wall general Wall surface coordinate, detailed calculating process are as follows:
Wall surface erosion rate formula:
γ is the wall surface ion incident angles at t moment axial coordinate z, is calculated as follows:
Yγ(γ) is the corresponding angle sputtering yield of ion incident angles γ, and discharge channel generally selects boron nitride ceramics, Angle sputtering yield YγThe equation of (γ) is (3), wherein f=2.23, γopt=67.9 °.Yγ(γ) can also carry out material and splash Penetrate attribute testing measurement.
Wall surface coordinate r (z, t) is uniformly separated by M node using finite difference calculus.The axial of i-th of node of wall surface is sat Labeled as zi(coordinate is unrelated with time t), i-th of node of wall surface are denoted as r in the radial coordinate of t momenti(t), in t moment wall Ionic incident angles γ at the node of i-th of facei(t) it is separated into the form of formula (4):
The angle α in ion incidence direction and r axis at i-th of node of t moment wall surfacei(t) it is separated into the shape of formula (5) Formula:
For t1, t2The discrete form at two moment, the erosion rate formula (1) of i-th of node of wall surface is shown in formula (6):
For i=2 ..., M-1, discrete equation form are as follows:
For i=1, discrete equation form are as follows:
For i=M, discrete equation form are as follows:
For t2, t3Erosion rate formula (1) discrete form at two moment, i-th of node of wall surface is as follows: for i= 2 ..., M-1, discrete equation form are as follows:
For i=1, discrete equation form are as follows:
For i=M, discrete equation form are as follows:
Ion sputtering intensity F (α at t moment, i-th of node of wall surfacei(t)) general type are as follows:
{mj,k,nj,k;J=1,2 ..., M } it is constituting-functions F (αi) coefficient set.
Position (the z of ion source Ss, rs) and ion sputtering intensity F (αi) solution procedure it is as follows:
C. assume ion source position coordinates (zs, rs) be located on some position in discharge channel;
B. by t1、t2The moment channel wall node coordinate of measurement calculates F (α according to discrete equation (6)i(t1));By t2、t3The moment channel wall node coordinate of measurement calculates F (α according to discrete equation (7)i(t2)).Coefficient set { mj,k, nj,kInitial value { mj,0,nj,0Calculated by formula (9):
C. according to coefficient set { mj,k,nj,kInitial value { mj,0,nj,0, utilize formula (6) and t1The conduit wall of moment measurement Face node coordinate, finds out t2The channel wall node radial coordinate calculated value at moment Benefit With formula (6) and t2The channel wall node coordinate of moment measurement, finds out t3The node coordinate calculated value of moment channel wallUsing formula (8), formula (5) andCalculate t1 The ion sputtering intensity F (α at momenti(t1))0, using formula (8), formula (5) andIt calculates T out2The ion sputtering intensity F (α at momenti(t2))0
D. the variances sigma between channel wall node radial coordinate calculated value and measured value0It is calculated by formula (10):
The k of formula (10) is subscript, is natural number, and the value of k is from 0 to maximum number of iterations;
E. one group of new coefficient set { m is chosen by formula (11)j,k,nj,k}
The k of formula (11) is subscript, and k is natural number, and the value of k is from 1 to maximum number of iterations;
F. according to the coefficient set { m of selectionj,k,nj,k, using formula (8), formula (5) and Recalculate t1The ion sputtering intensity F (α at momenti(t1))1, using formula (8), formula (5) andRecalculate t2The ion sputtering intensity F (α at momenti(t2))1, and calculate recently twice The relative error res of ion sputtering intensity:
G. according to formula (6), t is utilized1The channel wall node coordinate of moment measurement, finds out moment t again2Conduit wall Face node coordinate calculated valueAccording to formula (6), t is utilized2The channel wall of moment measurement Node coordinate finds out t again3The channel wall node coordinate calculated value at momentBy formula (10) variances sigma between channel wall node radial coordinate calculated value and measured value is recalculated1
H. if variances sigma1< σ0, it is considered that { mj,1,nj,1It is effectively, by { mj,1,nj,1It is added to { mj,k,nj,k} In queue, next group of coefficient { m is chosen according to formula (11)j,2,nj,2};If variances sigma1≥σ0, chosen again according to formula (12) {mj,1,nj,1};
I. step e, f, g, h are repeated, until ion sputtering strength relative error res is less than 1e-3 or the number of iterations reaches Until the maximum value (generally taking 1000~5000 times) of setting, corresponding final variance under the ion source position coordinates is recorded;
J. ion source is sat according to certain rule (can scan by row, column coordinate or be scanned by radius, angle coordinate) Mark (zs, rs) traversal discharge channel in all positions, repeat step b~i, obtain corresponding under the coordinate of different ions source position Variance, the corresponding ion source position of minimum variance are as finally determining ion source position coordinates (zs, rs), minimum variance pair F (the α that the coefficient set answered as finally determinesi) coefficient set { mj,k,nj,k}。
K. for discharge channel outside wall surface, ri(tN)=ri Outside(tN), ri(tN+1)=ri Outside(tN+1), directly obtained using step j Ion source position coordinates (the z arriveds, rs) and ion sputtering intensity F (α), utilize known tNThe wall surface node coordinate r at momenti (tN) and formula (13) calculating hall thruster operation a period of time △ tN+1The wall surface node coordinate r of discharge channel afterwardsi(tN+1)。
For i=2 ..., M-1, the radial coordinate calculation formula of wall surface node i are as follows:
For i=1, the radial coordinate calculation formula of wall surface node i are as follows:
For i=M, the radial coordinate calculation formula of wall surface node i are as follows:
For discharge channel inner wall, first by the node coordinate r of inner walli It is interior(t1)、ri It is interior(t2)、ri It is interior(t3) according to formula (14) changes in coordinates is carried out into general wall surface coordinate form ri(t1)、ri(t2)、ri(t3), then asked according to above-mentioned steps a~j Solve the corresponding ion source position coordinates (z of inner walls, rs) and ion sputtering intensity F (α),
R in formula (14)meanFor the initial mean radius of discharge channel, ring discharge is logical before as life test starts The distance between the center line and hall thruster axis in road (see figure 1).
Utilize known tNThe wall surface node coordinate r at momenti(tN)(ri(tN)=2Rmean-ri It is interior(tN)) and formula (13) meter It calculates hall thruster and runs a period of time △ tN+1The wall surface node coordinate r of discharge channel afterwardsi(tN+1), further according to formula (15) into Row coordinate inversion obtains the inner wall node coordinate r of subsequent timei It is interior(tN+1)。
ri It is interior(tN+1)=2Rmean-ri(tN+1) (15)。
Embodiment
During hall thruster accelerated life test, a kind of choosing of actual run time and predicted time is listed below Example is taken, chooses and carries out accelerated life test for certain type 5kW hall thruster, discharge channel of the thruster in beginning of lifetime Average diameter D is φ 120mm, and discharge channel width W is 20mm, and discharge channel inner wall thickness is 10mm, the outer wall thickness of discharge channel Degree is 10mm.
(1) the pretreatment evacuation time that 10hr is first carried out before thruster commencement of commercial operation, will engrave at this time as 0 moment;
(2) 0~200hr operation test being carried out to thruster, the profile measurement moment is chosen for 0,100hr, 200hr, according to The wall profile outside forecast at these three moment obtains the wall profile of 400hr, as shown in Figure 6;
(3) channel pattern when 400hr is processed, 400~600hr operation test is carried out, the profile measurement moment is chosen for 400hr, 500hr, 600hr obtain the wall profile of 1200hr according to the wall profile outside forecast at these three moment, see Fig. 7 It is shown;
(4) channel pattern when 1200hr is processed, 1200~1600hr operation test is carried out, the profile measurement moment is chosen For 1200hr, 1400hr, 1600hr, the wall profile of 4000hr is obtained according to the wall profile outside forecast at these three moment, As shown in Figure 8;
(5) channel pattern when 4000hr is processed, 4000~4700hr operation test is carried out, the profile measurement moment is chosen For 4000hr, 4350hr, 4700hr, the wall profile of 10485hr is obtained according to the wall profile outside forecast at these three moment, As shown in Figure 9, since thruster discharge channel wall thickness has eroded to zero, the service life for obtaining thruster is 10485hr.

Claims (10)

1. a kind of hall thruster acceleration service life test method, it is characterised in that the step of this method includes:
(1) vacuum firing test, the initial time of vacuum firing test are carried out to the hall thruster lighted a fire for the first time into vacuum tank For 0 moment, the finish time of vacuum firing test is t0,
(2) vacuum firing after the test, measures t0The outer wall facial contour of moment hall thruster discharge channel is under rz coordinate system Coordinate rOutside(z,t0) and coordinate r of the inner wall facial contour under rz coordinate systemIt is interior(z,t0);
(3) vacuum firing for carrying out N number of period to hall thruster is tested, and measures the finish time (t of each period1、 t2、…、tN) coordinate of discharge channel outer wall facial contour and the coordinate of inner wall facial contour, the coordinate of outer wall facial contour is labeled as rOutside (z,t1)、rOutside(z,t2)、…、rOutside(z,tN);The coordinate of inner wall facial contour is labeled as rIt is interior(z,t1)、rIt is interior(z,t2)、…、rIt is interior(z, tN);
(4) the wall profile coordinate of the discharge channel for the different moments measured using step (3) is first invaded according to discharge channel wall surface Erosion rate equation reverse goes out the position (z of equivalent ion source Ss, rs) and ion sputtering intensity F (α), recycle wall surface erosion rate Formula calculates hall thruster operation prediction duration △ tN+1The outer wall facial contour coordinate r of discharge channel afterwardsOutside(z,tN+1) and inner wall Facial contour coordinate rIt is interior(z,tN+1);
(5) the outer wall facial contour coordinate r predicted according to step (4)Outside(z,tN+1) processing discharge channel outer wall facial contour, press The inner wall facial contour coordinate r predicted according to step (4)It is interior(z,tN+1) processing discharge channel inner wall facial contour;
(6) it repeats step (2)~(5) to have altogether m times, until the thickness of wall surface any in the outside wall surface of discharge channel and inner wall becomes It is zero, obtains the service life t of hall thrusterlife:
The hall thruster real work duration of duplicate pth time is denoted asDuration is predicted in corresponding calculating It is denoted as1≤p≤m。
2. a kind of hall thruster acceleration service life test method according to claim 1, it is characterised in that: the step It (1) is 6-20h, vacuum firing examination to the time that the hall thruster lighted a fire for the first time into vacuum tank carries out vacuum firing test in Vacuum degree when testing is not less than 5*10-3Pa。
3. a kind of hall thruster acceleration service life test method according to claim 1, it is characterised in that: the step (2) in, the determination method of rz coordinate system are as follows: using the axis of hall thruster as z-axis, using the radial direction of hall thruster as r Axis, by the series of points on the wall profile wall surface of the hall thruster discharge channel of corresponding moment t under rz coordinate system The set of position coordinates (r, z) is indicated, and inner wall facial contour coordinate is denoted as rIt is interior(z, t), outer wall facial contour coordinate are denoted as rOutside(z,t)。
4. a kind of hall thruster acceleration service life test method according to claim 1, it is characterised in that: the step (3) in, N=3.
5. a kind of hall thruster acceleration service life test method according to claim 1, it is characterised in that: the step (4) in, prediction duration △ t is calculatedN+1For (△ t1+△t2+……+△tN) 1~8 times, wherein △ t1=t1-t0, △ t2=t2- t1..., △ tN=tN-tN-1, △ tN+1=tN+1-tN
6. a kind of hall thruster acceleration service life test method according to claim 5, it is characterised in that: before the test Phase predicts duration △ tN+1For (△ t1+△t2+……+△tN) 1~3 times;
Phase after experiment predicts duration △ tN+1For (△ t1+△t2+……+△tN) 5~8 times.
7. a kind of hall thruster acceleration service life test method according to claim 6, it is characterised in that: test early period be Refer to the test of 0~1000h of thruster (containing 1000h), later stage refers to the later test of thruster 1000h.
8. a kind of hall thruster acceleration service life test method according to claim 6, it is characterised in that: before the test Phase, △ t1,△t2,…,△tNValue be 50~100hr, after experiment phase, △ t1,△t2,…,△tNValue be 200~ 400hr。
9. a kind of hall thruster acceleration service life test method according to claim 1, it is characterised in that: the step (4) in, shown in discharge channel wall surface erosion rate formula such as formula (1):
γ is the wall surface ion incident angles at t moment axial coordinate z, is calculated as follows:
Yγ(γ) is the corresponding angle sputtering yield of ion incident angles γ:
Wall surface coordinate r (z, t) is uniformly separated by M node, the axial coordinate note of i-th of node of wall surface using finite difference calculus For zi, i-th of node of wall surface be denoted as r in the radial coordinate of t momenti(t), the ion incidence at i-th of node of t moment wall surface Angle γi(t) it is separated into the form of formula (4):
The angle α in ion incidence direction and r axis at i-th of node of t moment wall surfacei(t) it is separated into the form of formula (5):
For t1, t2The discrete form at two moment, the erosion rate formula (1) of i-th of node of wall surface is shown in formula 6a, 6b, 6c:
For i=2 ..., M-1, discrete equation form are as follows:
For i=1, discrete equation form are as follows:
For i=M, discrete equation form are as follows:
For t2, t3Erosion rate formula (1) discrete form at two moment, i-th of node of wall surface is shown in formula 7a, 7b, 7c:
For i=2 ..., M-1, discrete equation form are as follows:
For i=1, discrete equation form are as follows:
For i=M, discrete equation form are as follows:
Ion sputtering intensity F (α at t moment, i-th of node of wall surfacei(t)) are as follows:
{mj,k,nj,k;J=1,2 ..., M } it is constituting-functions F (αi) coefficient set.
10. a kind of hall thruster acceleration service life test method according to claim 9, it is characterised in that: ion source S's Position (zs, rs) and ion sputtering intensity F (αi) solution procedure it is as follows:
A. assume ion source position coordinates (zs, rs) be located on some position in discharge channel;
B. by t1、t2The moment channel wall node coordinate of measurement calculates F (α according to discrete equation (6)i(t1));By t2、t3 The moment channel wall node coordinate of measurement calculates F (α according to discrete equation (7)i(t2)), coefficient set { mj,k,nj,kJust It is worth { mj,0,nj,0Calculated by formula (9):
C. according to coefficient set { mj,k,nj,kInitial value { mj,0,nj,0, utilize formula (6) and t1The channel wall node of moment measurement Coordinate finds out t2The channel wall node radial coordinate calculated value at moment Utilize formula (6) and t2The channel wall node coordinate of moment measurement, finds out t3The node radial coordinate calculated value of moment channel wallUsing formula (8), formula (5) andCalculate t1When The ion sputtering intensity F (α at quarteri(t1))0, using formula (8), formula (5) andIt calculates t2The ion sputtering intensity F (α at momenti(t2))0
D. the variances sigma between channel wall node radial coordinate calculated value and measured value0It is calculated by formula (10):
The k of formula (10) is subscript, is natural number, and the value of k is from 1 to maximum number of iterations;
E. one group of new coefficient set { m is chosen by formula (11)j,k,nj,k}
The k of formula (11) is subscript, and k is natural number, and the value of k is from 1 to maximum number of iterations;
F. according to the coefficient set { m of selectionj,k,nj,k, using formula (8), formula (5) and Weight Newly calculate t1The ion sputtering intensity F (α at momenti(t1))1, using formula (8), formula (5) andRecalculate t2The ion sputtering intensity F (α at momenti(t2))1, and calculate recently twice The relative error res of ion sputtering intensity:
G. according to formula (6), t is utilized1The channel wall node coordinate of moment measurement, finds out moment t again2Channel wall section Point radial coordinate calculated valueAccording to formula (6), t is utilized2The channel wall of moment measurement Node coordinate finds out t again3The channel wall node radial coordinate calculated value at momentIt presses Formula (10) recalculates the variances sigma between channel wall node radial coordinate calculated value and measured value1
H. if variances sigma1< σ0, it is considered that { mj,1,nj,1It is effectively, by { mj,1,nj,1It is added to { mj,k,nj,kQueue In, next group of coefficient { m is chosen according to formula (11)j,2,nj,2};If variances sigma1≥σ0, chosen again according to formula (12) {mj,1,nj,1};
I. step e, f, g, h are repeated, until ion sputtering strength relative error res is less than 1e-3 or the number of iterations reaches setting Maximum value, maximum value be 1000~5000 times until, record corresponding final variance under the ion source position coordinates;
J. according to setting rule to ion source coordinate (zs, rs) traversal discharge channel in all positions, repeat step b~i, obtain Corresponding variance under to different ions source position coordinate, the corresponding ion source position of minimum variance are as finally determining ion Source position coordinate (zs, rs), the F (α that the corresponding coefficient set of minimum variance as finally determinesi) coefficient set { mj,k,nj,k, if Fixed rule is to scan by row, column coordinate or scan by radius, angle coordinate;
K. for discharge channel outside wall surface, ri(tN)=ri Outside(tN), ri(tN+1)=ri Outside(tN+1), directly obtained using step j Ion source position coordinates (zs, rs) and ion sputtering intensity F (α), utilize known tNThe wall surface node coordinate r at momenti(tN) and Formula (13) calculates hall thruster and runs a period of time △ tN+1The wall surface node coordinate r of discharge channel afterwardsi(tN+1);
For i=2 ..., M-1, the radial coordinate calculation formula of wall surface node i are as follows:
For i=1, the radial coordinate calculation formula of wall surface node i are as follows:
For i=M, the radial coordinate calculation formula of wall surface node i are as follows:
For discharge channel inner wall, first by the node coordinate r of inner walli It is interior(t1)、ri It is interior(t2)、ri It is interior(t3) according to formula (14) It is coordinately transformed into general wall surface coordinate form ri(t1)、ri(t2)、ri(t3), then solved according to above-mentioned steps a~j The corresponding ion source position coordinates (z of inner walls, rs) and ion sputtering intensity F (α),
R in formula (14)meanFor the initial mean radius of discharge channel, as life test starts preceding annular discharge channel The distance between center line and hall thruster axis;
Utilize known tNThe wall surface node coordinate r at momenti(tN)(ri(tN)=2Rmean-ri It is interior(tN)) and formula (13) calculating is suddenly You run a period of time △ t by thrusterN+1The wall surface node coordinate r of discharge channel afterwardsi(tN+1), it is sat further according to formula (15) Inverse transformation is marked, the inner wall node coordinate r of subsequent time is obtainedi It is interior(tN+1);
ri It is interior(tN+1)=2Rmean-ri(tN+1) (15)。
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