CN110058097B - A kind of Hall thruster accelerated life test method - Google Patents
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- 229910052582 BN Inorganic materials 0.000 description 5
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Abstract
本发明涉及一种霍尔推力器加速寿命试验方法，属于霍尔推力器的性能测试技术领域。该方法对霍尔推力器进行一段短时间的实际点火试验，在此过程中测量多个不同时刻的放电通道壁面轮廓，根据放电通道壁面侵蚀速率公式，反求出这一段时间的离子源参数，再根据壁面侵蚀速率公式和离子源参数外推出下一段长时间的放电通道壁面轮廓，用机械加工的方法去除壁面材料，使放电通道的壁面轮廓达到预测的轮廓。采用实际点火试验与模型外推指导下的机械加工去除壁面材料交替迭代直至霍尔推力器放电通道壁面被侵蚀完，将试验时间和预测时间累积得到推力器的寿命。
The invention relates to an accelerated life test method of a Hall thruster, belonging to the technical field of performance testing of a Hall thruster. In this method, a short-term actual ignition test is performed on the Hall thruster. During this process, the discharge channel wall profile at multiple different times is measured. According to the discharge channel wall erosion rate formula, the ion source parameters for this period of time are reversely obtained. Then, according to the wall erosion rate formula and ion source parameters, the next long-term discharge channel wall contour is extrapolated, and the wall material is removed by machining, so that the discharge channel wall contour reaches the predicted contour. The actual ignition test and the machining under the guidance of model extrapolation are used to remove the wall material alternately and iteratively until the wall of the Hall thruster discharge channel is eroded, and the test time and the predicted time are accumulated to obtain the life of the thruster.
Description
Technical Field
The invention relates to an accelerated life test method for a Hall thruster, in particular to a life test method for a discharge channel of the Hall thruster, and belongs to the technical field of performance test of the Hall thruster.
Background
The Hall thruster is a typical electric propulsion device in the world at present. Fig. 1 is an axial cross-sectional view of an example of a hall thruster. Propellant xenon gas enters the annular discharge channel (20) from an anode (30) upstream of the channel, the anode simultaneously providing a high potential; electrons are ejected from a cathode (40) at the downstream exit of the annular discharge channel, the cathode providing a low potential. Part of electrons sprayed out of the cathode enter the annular discharge channel, Hall drift motion is carried out under the action of a radial magnetic field generated by the external magnetic circuit (10) and an axial electric field generated by self-consistency inside, the electrons and propellant atoms collide and ionize to generate ions, the ions are sprayed out by acceleration of the axial electric field to generate thrust, and the electrons reach the anode through various conduction mechanisms. And the other part of electrons sprayed from the cathode enter the plume region and are neutralized by the ions sprayed at high speed, so that the electric neutrality of the plume is maintained. The main components of the Hall thruster comprise an annular discharge channel, a magnetic circuit, an anode, a cathode and the like. The discharge channel is typically made of a boron nitride-based ceramic material that is resistant to ion sputtering.
The reaction thrust F generated by the working medium injection of the Hall thruster is restricted by the electric power P consumed by the thruster, the injection speed v of the working medium, the conversion efficiency eta of the electric power to the kinetic energy power and the like: f is 2P eta/v;
because the working medium jet speed v of the Hall thruster is generally in the range of 15 km/s-25 km/s, the power P which can be provided for the Hall thruster by the spacecraft is generally in the range of 700W-5000W at present, and the thrust of the Hall thruster is about in the range of 40 mN-250 mN. Because the thrust of the Hall thruster is very small, in order to meet the task requirement of the spacecraft, the working life of the Hall thruster is very long, and the Hall thruster is required to be within thousands of hours to tens of thousands of hours. Taking the application of the current large geostationary orbit communication satellite as an example, a 5kW Hall thruster is adopted to carry out the tasks of orbit transfer and position maintenance, and the working life of the 5kW Hall thruster needs to reach at least 1 ten thousand hours.
At present, the most main technical factors limiting the service life of the Hall thruster are that the wall surface of a discharge channel of the Hall thruster is bombarded by high-energy ions in the channel, a wall surface material is gradually sputtered and eroded, the wall surface is gradually thinned until the wall surface is completely eroded and penetrated by the ions, an outer magnetic pole (11) or an inner magnetic pole (12) is directly exposed under the bombardment of the high-energy ions, and due to the fact that the sputtering resistance of a magnetic pole material is poor and the protection of the discharge channel is lacked, the shape of the magnetic pole is changed by sputtering very quickly or the magnetic pole is easily bombarded and overheated by the ions, the magnetic field in the discharge channel is damaged, and the thruster cannot work. Generally, either the outer wall (21) or the inner wall (22) of the discharge channel is penetrated by ion sputtering erosion as an end-of-life sign of the thruster.
At present, a method for verifying a full-life test is generally adopted in a life test of a Hall thruster, namely, a vacuum ignition test of 1:1 (ground test time: on-orbit working time) is required to be carried out in a vacuum environment simulation device built on the ground, the working condition and the accumulated working time of the thruster on a spacecraft are simulated, and even the ground test time of the thruster is required to reach 1.2-1.5 times of the on-orbit working time. The jet propulsion laboratory of the national aerospace agency (NASA JPL) performed 5730 hours of life testing on the 1.35kW hall thruster SPT-100, the french Snekma (SNECMA) performed 10530 hours of life testing on the 1.5kW hall thruster PPS-1350G, and the american aviation jet company (Aerojet) performed 10400 hours of life testing on the 4.5kW hall thruster BPT-4000.
The problems faced by the Hall thruster life test are mainly reflected in three aspects: the expenditure is high, the period is long and the technical risk is high. Taking a 5kW Hall thruster as an example, about 900 ten thousand of high-purity xenon (more than 99.9995%) for electric propulsion needs to be consumed in one life test, about 800 thousand of electric charge of a vacuum environment simulation device is consumed, equipment maintenance and depreciation cost, tester cost and the like in the life test process are included, and the whole test expenditure is about 2500 thousand; the accumulated ignition time of the thruster reaches more than 1 ten thousand hours, the time required in the test process, such as shutdown cooling of the thruster, regular performance of the thruster, contour detection of the wall surface of the discharge channel, maintenance of test equipment and the like, is also included, and the whole life test period is about 3 years; the service life test does not guarantee one-time passing, is likely to repeat, and has great uncertainty of test results.
The Harbin industry university provides a Hall thruster life estimation method (CN200810136846.2), and the invention adopts the life obtained by ion bombardment on an easy-sputtering ceramic tube to calculate the actual life of a boron nitride-based ceramic discharge channel. However, the method mainly has the following problems:
(1) different ceramic materials have different secondary electron emission coefficients, heat conductivity coefficients and ion sputtering resistance, the material of the discharge channel is replaced by the ceramic which is easy to sputter, although sputtering is accelerated, the actual secondary electron emission and heat conductivity of the wall surface of the discharge channel are changed, plasma parameter change and discharge channel temperature change in the channel can be caused, the energy of ions in the channel is changed, the sputtering mechanism is changed, and the accuracy of an acceleration test is not high;
(2) at present, a discharge channel material is generally hexagonal boron nitride-based ceramic, if a sputtering mechanism is ensured to be unchanged, the components of a wall material, the surface binding energy and a sputtering threshold value cannot be changed, and the sputtering is only implemented by reducing the density of the material in engineering, but the reduction of the density is limited by about 15%, the test time and cost saved by the easily sputtered ceramic are also limited, and the acceleration efficiency is low.
Disclosure of Invention
The technical problem solved by the invention is as follows: the problems of high expenditure, long period and high technical risk of a Hall thruster full-life test and the problems of low efficiency and poor precision of the existing acceleration test are solved, and the effective Hall thruster acceleration life test method is provided.
The technical solution of the invention is as follows:
a method for testing the accelerated life of a Hall thruster includes such steps as measuring the profiles of the wall surfaces of discharge channels at different moments, calculating the ion source parameters of the discharge channels at the moment, deducing the profile of the wall surface of the discharge channel for a long time according to the erosion rate formula of the wall surface and the ion source parameters, and mechanically machining the wall surface to obtain the predicted profile of the wall surface of the discharge channel. And removing wall material by adopting mechanical processing under the guidance of an actual ignition test and model extrapolation to perform alternating iteration until the wall of the discharge channel of the Hall thruster is corroded, and accumulating the test time and the predicted time to obtain the service life of the thruster. The method mainly comprises the following steps:
(1) the Hall thruster for igniting the vacuum tank for the first time is carried out for a period of time (0 to t)0Moment), the wall surface of the discharge channel is pretreated, and the influence of the Hall thruster material, especially the wall surface of the discharge channel, the exciting coil and other adsorbed gases on the service life test is eliminated; the period of time is 6-20 h; vacuum degree of not less than 5 x 10 in vacuum ignition test-3Pa; the pretreatment is to carry out high-temperature deflation treatment on the Hall thruster which is ignited in the vacuum tank for the first time by utilizing the high-temperature action and the ion bombardment action generated by vacuum ignition;
(2) after the vacuum ignition test is finished, i.e. at t0Measuring coordinates under rz coordinate system of wall surface contour (including outer wall surface contour and inner wall surface contour) of discharge channel of Hall thruster by using contact type contour gauge or non-contact type optical contour gauge at any moment to obtain t0Coordinate r of profile of outer wall surface of discharge channel at momentOuter cover(z,t0) And coordinates r of the contour of the inner wall surfaceInner part(z,t0)；
The method for determining the rz coordinate system comprises the following steps: taking the axis of the Hall thruster as the z-axis and the diameter of the Hall thrusterThe original point O is not limited to be selected as the r axis, and a certain point outside the Hall thruster can be selected to facilitate the wall surface contour measurement of the profiler. The contour of the wall surface of the discharge channel of the hall thruster corresponding to the time t is represented by a set of position coordinates (r, z) of a series of points on the wall surface in an rz coordinate system, and is recorded as r (z, t), and for the sake of convenience, the contour coordinates of the inner wall surface are recorded as rInner part(z, t), the outer wall contour coordinates are denoted as rOuter cover(z,t)。
(3) Carrying out vacuum ignition tests on the Hall thruster for 3 time periods (N is an integer, N is more than or equal to 2, and N is generally 3 to ensure the precision and reduce the measurement times) at the end time (t) of each time period1、t2、…、tN) Measuring the coordinates of the outline of the outer wall surface of the discharge channel and the coordinates of the outline of the inner wall surface according to the method in the step (2), wherein the coordinate of the outline of the outer wall surface is marked as rOuter cover(z,t1)、rOuter cover(z,t2)、…、rOuter cover(z,tN) (ii) a Coordinate of the inner wall surface profile is denoted as rInner part(z,t1)、rInner part(z,t2)、…、rInner part(z,tN)；
(4) Utilizing the wall contour coordinates of the discharge channel at least 3 different moments measured in the step (3), and reversely solving the position (z) of the equivalent ion source S according to the discharge channel wall erosion rate formulas，rs) And ion sputtering strength F (alpha), and calculating the operation time delta t of the Hall thruster by utilizing a wall surface erosion rate formulaN+1Outer wall surface contour coordinate r of rear discharge channelOuter cover(z,tN+1) And inner wall surface contour coordinate rInner part(z,tN+1) (ii) a Calculating the predicted duration Δ tN+1The actual working time (delta t) of the thruster in the step (3)1+△t2+……+△tN) 1-8 times of the total amount of the1＝t1-t0，△t2＝t2-t1，…，△tN＝tN-tN-1，△tN+1＝tN+1-tN. Defining the acceleration ratio as the predicted duration DeltatN+1With actual operating time Δ t1+△t2+……+△tNThe acceleration ratio of the Hall thruster is small in the initial stage of the life test (before 1000h (less than or equal to 1000h)), generally 1-3, due to the characteristic of deceleration corrosion of the Hall thruster; the acceleration ratio at the later stage of the life test (after 1000h (more than 1000h)) is selected to be larger, and is generally 5-8; (. DELTA.t)1,△t2,…,△tN) Is selected so that after the period of operation, the wall profile changes by at least 10-1mm, and simultaneously, the period of time is ensured to be as short as possible so as to improve the acceleration efficiency; initial stage of life test (1000hr before (1000 h) (Δ t ≦) of the test sample)1,△t2,…,△tN) Generally, the life test time is 50-100 hr, and the later period of the life test (after 1000hr (more than 1000h)) (. DELTA.t)1,△t2,…,△tN) Generally, the time is 200 to 400 hr.
(5) Machining the discharge channel of the Hall thruster, and predicting the outline coordinate r of the outer wall surface according to the step (4)Outer cover(z,tN+1) Processing the outer wall surface contour of the discharge channel, and predicting the inner wall surface contour coordinate r according to the step (4)Inner part(z,tN+1) Processing the contour of the inner wall surface of the discharge channel;
(6) repeating the steps (2) to (5) m times (m is a natural number) until the thickness of any wall surface of the outer wall surface or the inner wall surface of the discharge channel becomes zero, and recording the practical working time of the Hall thruster for the p (p is an integer, p is more than or equal to 1 and less than or equal to m) th time of repetition as
The corresponding calculated predicted duration is noted
(7) Accumulating the actual running time and the predicted time of the Hall thruster to obtain the service life t of the Hall thrusterlife；
In the step (3), the Hall push rodThe force device is an axisymmetric structure with an annular channel, and the contours of the inner and outer ceramic wall surfaces are respectively used as a function rInner part(z, t) and rOuter cover(z, t) indicates that the ion current moving to the channel wall surface is from the coordinate (z)s,rs) The included angle between the ion incidence direction and the radial direction (r direction) is alpha, the included angle between the tangential direction of the ion incidence to a certain point on the wall surface and the axial direction (z direction) is beta, gamma is the included angle between the ion incidence direction and the normal direction of the wall surface of the channel, and gamma is alpha + beta;
utilizing the wall contour coordinates of the discharge channel at 3 different moments measured in the step (3), and reversely calculating the position (z) of the equivalent ion source S according to the wall erosion rate formula of the discharge channels，rs) And ion sputtering strength F (alpha), and calculating the operation time delta t of the Hall thruster by utilizing a wall surface erosion rate formulaN+1Outer wall surface contour coordinate r of rear discharge channelOuter cover(z,tN+1) And inner wall surface contour coordinate rInner part(z,tN+1)。
For the outer wall of the discharge channel, r (z, t) ═ rOuter cover(z, t), r (z, t) are general wall coordinates that do not distinguish between the outer wall surface and the inner wall surface, and the detailed calculation procedure is as follows:
wall erosion rate formula:
gamma is the wall ion incidence angle at the axial coordinate z at time t, and is calculated according to the following formula:
Yγ(gamma) is the angle sputtering yield corresponding to the ion incidence angle gamma, the discharge channel is generally made of boron nitride-based ceramics, and the angle sputtering yield YγThe equation for (γ) is (3), where f is 2.23, γopt＝67.9°。YγThe (. gamma.) can also be measured by a material sputtering property test.
And uniformly dispersing the wall coordinates r (z, t) into M nodes by adopting a finite difference method. The axial coordinate of the ith node of the wall surface is recorded as zi(the coordinate is independent of time t), the radial coordinate of the ith node of the wall surface at the time t is recorded as ri(t) ion incident angle γ at ith node of wall surface at time ti(t) is discretized into the form of equation (4):
at the time t, the included angle alpha between the ion incidence direction at the ith node of the wall surface and the r axisi(t) is discretized into the form of equation (5):
for t1，t2The erosion rate of the ith node of the wall surface at two moments is expressed by the formula (1) in a discrete form as shown in the formula (6):
for i 2., M-1, the discrete equation is in the form:
for i ═ 1, the discrete equation form is:
for i ═ M, the discrete equation form is:
for t2，t3At two moments, the erosion rate of the ith node of the wall surface is in a discrete form according to formula (1): for i 2., M-1, the discrete equation is in the form:
for i ═ 1, the discrete equation form is:
for i ═ M, the discrete equation form is:
at time t, the ion sputtering intensity F (alpha) at the ith node of the wall surfacei(t)) is of the general form:
{mj,k,nj,k(ii) a j is 1,2, …, M is a composition function F (α)i) A set of coefficients.
Position of ion source S (z)s，rs) And ion sputtering intensity F (. alpha.)i) The solving steps are as follows:
b. assume ion source position coordinates (z)s，rs) Is positioned at a certain position in the discharge channel;
b. from t1、t2The coordinates of the node of the channel wall surface measured at the moment are calculated according to the discrete equation (6) to obtain F (alpha)i(t1) ); from t2、t3The coordinates of the node of the channel wall surface measured at the moment are calculated according to the discrete equation (7) to obtain F (alpha)i(t2)). Coefficient set { mj,k,nj,kInitial value of { m }j,0,nj,0Is calculated according to equation (9):
c. from the set of coefficients { mj,k,nj,kInitial value of { m }j,0,nj,0Using the formulas (6) and t1The coordinates of the node of the wall surface of the channel measured at the moment are calculated to obtain t2Radial coordinate calculation value of channel wall surface node at moment
Using equations (6) and t2The coordinates of the node of the wall surface of the channel measured at the moment are calculated to obtain t3Radial coordinate calculation value of wall surface node of time channel
Using equations (8), (5) and
calculate t1Ion sputtering intensity F (alpha) at timei(t1))0Using equations (8), (5) and
calculate t2Ion sputtering intensity F (alpha) at timei(t2))0；
d. Variance sigma between channel wall node radial coordinate calculation value and measurement value0Calculated according to equation (10):
k in the formula (10) is subscript and is an unnatural number, and the value of k is from 0 to the maximum iteration number;
e. a new set of coefficient sets m is selected according to equation (11)j,k,nj,k}
K in the formula (11) is subscript, k is a natural number, and the value of k is from 1 to the maximum iteration number;
f. according to the selected coefficient set mj,k,nj,kUsing the formulas (8), (5) and
recalculate t1Ion sputtering intensity F (alpha) at timei(t1))1Using equations (8), (5) and
recalculate t2Ion sputtering intensity F (alpha) at timei(t2))1And calculating the relative error res of the sputtering intensity of the last two ions:
g. according to equation (6), using t1The coordinates of the channel wall node measured at the moment are solved again2Radial coordinate calculation value of channel wall surface node
According to equation (6), using t2The coordinates of the node of the channel wall surface measured at the moment are solved again3Radial coordinate calculation value of channel wall surface node at moment
According to the formula (10)) Recalculating variance σ between channel wall node radial coordinate calculation and measurement1；
h. If the variance σ1＜σ0Then consider { mj,1,nj,1Is valid, will mj,1,nj,1Add to { m }j,k,nj,kIn the queue, the next set of coefficients m is selected according to equation (11)j,2,nj,2}; if the variance σ1≥σ0Reselecting { m) according to equation (12)j,1,nj,1}；
i. Repeating the steps e, f, g and h until the relative error res of the ion sputtering strength is less than 1e-3 or the iteration times reach the set maximum value (generally 1000-5000 times), and recording the corresponding final variance under the position coordinates of the ion source;
j. ion source coordinate (z) is scanned according to a certain rule (scanning can be performed according to row and column coordinates or scanning can be performed according to radius and angle coordinates)s，rs) Traversing all positions in the discharge channel, repeating the steps b-i to obtain corresponding variances under different ion source position coordinates, and taking the ion source position corresponding to the minimum variance as the finally determined ion source position coordinate (z)s，rs) The coefficient set corresponding to the minimum variance is finally determined F (alpha)i) Coefficient set of { m }j,k,nj,k}。
k. For the outer wall surface of the discharge channel, ri(tN)＝ri Outer cover(tN)，ri(tN+1)＝ri Outer cover(tN+1) Directly using the ion source position coordinates (z) obtained in step js，rs) And the ion sputtering intensity F (alpha), using the known tNWall node coordinate r of timei(tN) And the formula (13) calculates the running time delta t of the Hall thrusterN+1Wall node coordinate r of rear discharge channeli(tN+1)。
For i 2., M-1, the radial coordinate of the wall node i is calculated as:
for i equal to 1, the radial coordinate of the wall node i is calculated as:
for i-M, the radial coordinate of the wall node i is calculated as:
for the inner wall surface of the discharge channel, firstly, the node coordinate r of the inner wall surface isi Inner part(t1)、ri Inner part(t2)、ri Inner part(t3) Coordinate transformation into a general wall coordinate form r according to equation (14)i(t1)、ri(t2)、ri(t3) Then, according to the steps a to j, the ion source position coordinate (z) corresponding to the inner wall surface is solveds，rs) And an ion sputtering intensity F (α),
r in formula (14)meanThe initial average radius of the discharge channel is the distance between the center line of the annular discharge channel and the axis of the Hall thruster before the life test is started.
Using known tNWall node coordinate r of timei(tN)(ri(tN)＝2Rmean-ri Inner part(tN) And equation (13) to calculate the operating time Deltat of the Hall thrusterN+1Wall node coordinate r of rear discharge channeli(tN+1) Then, the coordinates are inversely transformed according to the formula (15) to obtain the coordinates r of the node of the inner wall surface at the next timei Inner part(tN+1)。
ri Inner part(tN+1)＝2Rmean-ri(tN+1) (15)。
Compared with the prior art, the invention has the advantages that:
(1) the profile of the wall surface of the discharge channel is used as an acceleration factor to accelerate, and the efficient acceleration is realized by removing the material of the wall surface of the discharge channel through mechanical processing, so that the efficiency of an acceleration test can be ensured;
(2) the acceleration method of the invention has high precision. On one hand, the material of the discharging channel of the thruster is not changed, the physical process of the actual operation of the thruster and the existing life failure rule are not changed, and the actual situation of the wall surface erosion of the discharging channel during the actual operation of the thruster is directly reflected by the erosion test data of the discharging channel of the thruster; on the other hand, the method is based on a discharge channel wall surface erosion formula, reversely deduces the position and the parameters of the ion source bombarding the wall surface by means of the wall surface profiles at a plurality of different moments obtained by test measurement, ensures that the position and the parameters of the ion source are fully verified by a historical test, and predicts the discharge channel wall surface profile after a period of time in the future on the basis of the position and the parameters, so that the prediction precision can be effectively ensured, and the precision of an acceleration test is ensured;
(3) the accelerated life test method is easy to implement and strong in operability, and a special ceramic material easy to sputter is not required to be developed for the accelerated test.
Drawings
FIG. 1 is a schematic diagram of a Hall thruster;
FIG. 2 is a schematic diagram of a Hall thruster acceleration test flow;
FIG. 3 is a schematic diagram of an ion source inverse-solved according to the erosion profile of the channel wall, the ion source bombarding the wall is from the coordinate (z)s,rs) Is emitted from a point source, the ion incidence direction and the radial direction (r direction) form an included angle alpha, and the ions are incident to the wallThe included angle between the tangential direction of a certain point on the surface and the axial direction (z direction) is beta;
fig. 4 is an example of the change of the wall profile of the discharge channel with time during the accelerated life test (N-3, m-2), oo' being the center line of the circular discharge channel;
FIG. 5 shows the ion source position (z) corresponding to the outer wall surface of the discharge channels,rs) And solving process of ion sputtering strength F (alpha);
FIG. 6 shows the profile of a wall surface of a Hall thruster accelerated from 0-200 hr to 400 hr;
FIG. 7 shows the profile of a wall surface of a Hall thruster accelerated from 400-600 hr to 1200 hr;
FIG. 8 shows the profile of the wall surface of a Hall thruster accelerated from 1200-1600 hr to 4000 hr;
FIG. 9 shows the change of wall profile of a Hall thruster of a certain type accelerated from 4000-4700 hr to 10485 hr.
Detailed Description
As shown in fig. 1-5, the implementation steps of the present invention are as follows:
(1) the Hall thruster is carried out for a period of time (t)0Approximately 6-20 hours), performing high-temperature exhaust treatment on the wall surface of the discharge channel by utilizing the high-temperature action and the ion bombardment action generated by vacuum ignition, and eliminating the influence of gas adsorbed on the wall surface of the discharge channel on the service life test;
(2) after the vacuum ignition test is finished, measuring the wall surface profile (including the inner wall surface profile and the outer wall surface profile) of the discharge channel of the Hall thruster by using a contact type profiler or a non-contact type optical profiler to obtain t0Wall contour coordinate r of discharge channel inner wall at timeInner part(z,t0) And wall contour coordinate r of the outer wallOuter cover(z,t0)；
(3) Vacuum ignition test is carried out on the Hall thruster for 3 (N is 3) time periods, and the end time (t) of each time period1、t2、t3) Measuring the wall surface profiles of the inner wall and the outer wall of the discharge channel according to the method in the step (2), and recording the profile of the inner wall surface as rInner part(z,t1)、rInner part(z,t2)、rInner part(z,t3) (ii) a Outer wall profile rOuter cover(z,t1)、rOuter cover(z,t2)、rOuter cover(z,t3)；
(4) Utilizing the profiles r of the outer wall surfaces of the discharge channels at 3 different moments measured in the step (3)Outer cover(z,t1)、rOuter cover(z,t2)、rOuter cover(z,t3) Firstly, according to the formula (1) of the erosion rate of the wall surface of the discharge channel, the position (zs, r) of the equivalent ion source S corresponding to the outer wall of the discharge channel is reversely solveds) And ion sputtering strength F (alpha), and calculating the operation time delta t of the Hall thruster by utilizing a wall surface erosion rate formula (1)4Outer wall surface contour coordinate r of rear discharge channelOuter cover(z,t4)；
Utilizing the contour r of the inner wall surface of the discharge channel at 3 different moments measured in the step (4)Inner part(z,t1)、rInner part(z,t2)、rInner part(z,t3) Firstly, the coordinates of the inner wall surface are converted into the general coordinates r (z, t)1)、r(z,t2)、r(z,t3) According to the formula (1) of the erosion rate of the wall surface of the discharge channel, the position (z) of the equivalent ion source S corresponding to the outer wall of the discharge channel is reversely calculateds,rs) And ion sputtering strength F (alpha), and calculating the operation time delta t of the Hall thruster by utilizing a wall surface erosion rate formula (1)4Wall profile coordinates r (z, t) of the rear discharge channel4) Finally, the general wall coordinates are inversely transformed according to the formula (14) to obtain the coordinates r of the inner wall surfaceInner part(z,t4)；
Calculating the predicted duration Δ t4For the actual working time (Δ t) of the thruster1+△t2+△t3) About 1 to 8 times of the total to ensure the prediction accuracy, wherein Δ t1＝t1-t0，△t2＝t2-t1，△t3＝t3-t2，△t4＝t4-t3(ii) a Defining the acceleration ratio as the predicted duration Deltat4With actual operating time Δ t1+△t2+△t3Due to the fact that the Hall thruster has the characteristic of decelerating corrosionThe acceleration ratio at the initial stage of the life test (before 1000h (less than or equal to 1000h)) is selected to be smaller, and is generally 1-3; the acceleration ratio at the later stage of the life test (after 1000h (more than 1000h)) is selected to be larger, and is generally 5-8; (. DELTA.t)1,△t2,△t3) Is selected so that after the period of operation, the wall profile changes by at least 10-1mm, and simultaneously, the period of time is ensured to be as short as possible so as to improve the acceleration efficiency; initial stage of life test (1000hr before (1000 h) (Δ t ≦) of the test sample)1,△t2,△t3) Generally, the life test time is 50-100 hr, and the later period of the life test (after 1000hr (more than 1000h)) (. DELTA.t)1,△t2,△t3) Generally, the time is 200 to 400 hr.
(5) Machining the discharge channel of the Hall thruster, and respectively machining the inner wall and the outer wall of the discharge channel to the inner wall surface profile r predicted in the step 4Inner part(z,t4) And an outer wall surface profile rOuter cover(z,t4)；
(6) Repeating the steps (2) to (5) for m times (m is a natural number) until the thickness of the inner wall or the outer wall of the discharge channel becomes zero, and recording the practical working time of the thruster of the p (p is an integer, p is more than or equal to 1 and less than or equal to m) of the repetition as
The corresponding calculated predicted duration is noted
(7) Accumulating the actual running time and the predicted time of the Hall thruster to obtain the service life t of the Hall thrusterlife:
In the step (3), the Hall thruster is of an axisymmetric structure with an annular channel, and the outlines of the inner and outer ceramic wall surfaces are respectively used as a function rInner part(z, t) and rOuter cover(z, t) as shown in FIG. 3. The ion current moving to the channel wall is from the coordinate of (zs,rs) As can be seen from fig. 3, γ is α + β, where α is an angle between the ion incidence direction and the radial direction (r direction), β is an angle between the tangential direction of the ion incidence to a certain point on the wall surface and the axial direction (z direction), and γ is an angle between the ion incidence direction and the normal direction of the wall surface of the channel.
Utilizing the wall contour coordinates of the discharge channel at 3 different moments measured in the step (3), and reversely calculating the position (z) of the equivalent ion source S according to the wall erosion rate formula of the discharge channels，rs) And ion sputtering strength F (alpha), and calculating the operation time delta t of the Hall thruster by utilizing a wall surface erosion rate formulaN+1Outer wall surface contour coordinate r of rear discharge channelOuter cover(z,tN+1) And inner wall surface contour coordinate rInner part(z,tN+1)。
For the outer wall of the discharge channel, r (z, t) ═ rOuter cover(z, t), r (z, t) are general wall coordinates that do not distinguish between the outer wall surface and the inner wall surface, and the detailed calculation procedure is as follows:
wall erosion rate formula:
gamma is the wall ion incidence angle at the axial coordinate z at time t, and is calculated according to the following formula:
Yγ(gamma) is the angle sputtering yield corresponding to the ion incidence angle gamma, the discharge channel is generally made of boron nitride ceramics, and the angle sputtering yield YγThe equation for (γ) is (3), where f is 2.23, γopt＝67.9°。YγThe (. gamma.) can also be measured by a material sputtering property test.
And uniformly dispersing the wall coordinates r (z, t) into M nodes by adopting a finite difference method. The axial coordinate of the ith node of the wall surface is recorded as zi(the coordinate is independent of time t), the radial coordinate of the ith node of the wall surface at the time t is recorded as ri(t) ion incident angle γ at ith node of wall surface at time ti(t) is discretized into the form of equation (4):
at the time t, the included angle alpha between the ion incidence direction at the ith node of the wall surface and the r axisi(t) is discretized into the form of equation (5):
for t1，t2The erosion rate of the ith node of the wall surface at two moments is expressed by the formula (1) in a discrete form as shown in the formula (6):
for i 2., M-1, the discrete equation is in the form:
for i ═ 1, the discrete equation form is:
for i ═ M, the discrete equation form is:
for t2，t3At two moments, the erosion rate of the ith node of the wall surface is in a discrete form according to formula (1): for i 2., M-1, the discrete equation is in the form:
for i ═ 1, the discrete equation form is:
for i ═ M, the discrete equation form is:
at time t, the ion sputtering intensity F (alpha) at the ith node of the wall surfacei(t)) is of the general form:
{mj,k,nj,k(ii) a j is 1,2, …, M is a composition function F (α)i) A set of coefficients.
Position of ion source S (z)s，rs) And ion sputtering intensity F (. alpha.)i) The solving steps are as follows:
c. assume ion source position coordinates (z)s，rs) Is positioned at a certain position in the discharge channel;
b. from t1、t2The coordinates of the node of the channel wall surface measured at the moment are calculated according to the discrete equation (6) to obtain F (alpha)i(t1) ); from t2、t3The coordinates of the node of the channel wall surface measured at the moment are calculated according to the discrete equation (7) to obtain F (alpha)i(t2)). Coefficient set { mj,k,nj,kInitial value of { m }j,0,nj,0Is calculated according to equation (9):
c. from the set of coefficients { mj,k,nj,kInitial value of { m }j,0,nj,0Using the formulas (6) and t1The coordinates of the node of the wall surface of the channel measured at the moment are calculated to obtain t2Radial coordinate calculation value of channel wall surface node at moment
Using equations (6) and t2The coordinates of the node of the wall surface of the channel measured at the moment are calculated to obtain t3Node coordinate calculation value of time channel wall surface
Using equations (8), (5) and
calculate t1Ion sputtering intensity F (alpha) at timei(t1))0Using equations (8), (5) and
calculate t2Ion sputtering intensity F (alpha) at timei(t2))0；
d. Variance sigma between channel wall node radial coordinate calculation value and measurement value0Calculated according to equation (10):
k in the formula (10) is subscript and is a natural number, and the value of k is from 0 to the maximum iteration number;
e. a new set of coefficient sets m is selected according to equation (11)j,k,nj,k}
K in the formula (11) is subscript, k is a natural number, and the value of k is from 1 to the maximum iteration number;
f. according to the selected coefficient set mj,k,nj,kUsing the formulas (8), (5) and
recalculate t1Ion sputtering intensity F (alpha) at timei(t1))1Using equations (8), (5) and
recalculate t2Ion sputtering intensity F (alpha) at timei(t2))1And calculating the relative error res of the sputtering intensity of the last two ions:
g. according to equation (6), using t1The coordinates of the channel wall node measured at the moment are solved again2Calculated value of coordinates of nodes on wall surface of channel
According to equation (6), using t2The coordinates of the node of the channel wall surface measured at the moment are solved again3Calculated value of coordinates of wall surface nodes of channel at moment
Recalculating the variance σ between the calculated and measured values of the radial coordinates of the nodes of the channel wall as in equation (10)1；
h. If the variance σ1＜σ0Then consider { mj,1,nj,1Is valid, will mj,1,nj,1Add to { m }j,k,nj,kIn the queue, the next set of coefficients m is selected according to equation (11)j,2,nj,2}; if the variance σ1≥σ0Reselecting { m) according to equation (12)j,1,nj,1}；
i. Repeating the steps e, f, g and h until the relative error res of the ion sputtering strength is less than 1e-3 or the iteration times reach the set maximum value (generally 1000-5000 times), and recording the corresponding final variance under the position coordinates of the ion source;
j. ion source coordinate (z) is scanned according to a certain rule (scanning can be performed according to row and column coordinates or scanning can be performed according to radius and angle coordinates)s，rs) Traversing all positions in the discharge channel, repeating the steps b-i to obtain corresponding variances under different ion source position coordinates, and taking the ion source position corresponding to the minimum variance as the finally determined ion source position coordinate (z)s，rs) The coefficient set corresponding to the minimum variance is finally determined F (alpha)i) Coefficient set of { m }j,k,nj,k}。
k. For the outer wall surface of the discharge channel, ri(tN)＝ri Outer cover(tN)，ri(tN+1)＝ri Outer cover(tN+1) Directly using the ion source position coordinates (z) obtained in step js，rs) And the ion sputtering intensity F (alpha), using the known tNWall node coordinate r of timei(tN) And the formula (13) calculates the running time delta t of the Hall thrusterN+1Wall node coordinate r of rear discharge channeli(tN+1)。
For i 2., M-1, the radial coordinate of the wall node i is calculated as:
for i equal to 1, the radial coordinate of the wall node i is calculated as:
for i-M, the radial coordinate of the wall node i is calculated as:
for the inner wall surface of the discharge channel, firstly, the node coordinate r of the inner wall surface isi Inner part(t1)、ri Inner part(t2)、ri Inner part(t3) The coordinate is changed into a universal wall coordinate form r according to the formula (14)i(t1)、ri(t2)、ri(t3) Then, according to the steps a to j, the ion source position coordinate (z) corresponding to the inner wall surface is solveds，rs) And an ion sputtering intensity F (α),
r in formula (14)meanThe initial average radius of the discharge channel is the distance between the center line of the annular discharge channel and the axis of the hall thruster before the life test is started (see fig. 1).
Using known tNWall node coordinate r of timei(tN)(ri(tN)＝2Rmean-ri Inner part(tN) And equation (13) to calculate the operating time Deltat of the Hall thrusterN+1Wall node coordinate r of rear discharge channeli(tN+1) Then, the coordinates are inversely transformed according to the formula (15) to obtain the coordinates r of the node of the inner wall surface at the next timei Inner part(tN+1)。
ri Inner part(tN+1)＝2Rmean-ri(tN+1) (15)。
Examples
In the accelerated life test process of the Hall thruster, a selected example of actual running time and predicted time is listed below, a certain type of 5kW Hall thruster is selected as an example to carry out the accelerated life test, the average diameter D of a discharge channel of the thruster at the initial stage of the life is phi 120mm, the width W of the discharge channel is 20mm, the thickness of the inner wall of the discharge channel is 10mm, and the thickness of the outer wall of the discharge channel is 10 mm.
(1) Carrying out pretreatment exhaust time of 10hr before the thruster is formally operated, and marking the time as 0;
(2) performing a 0-200 hr running test on the thruster, wherein the contour measurement time is selected to be 0hr, 100hr and 200hr, and a 400hr wall contour is obtained by extrapolation prediction according to the wall contours at the three times, as shown in fig. 6;
(3) processing the channel shape within 400hr, performing 400-600 hr operation test, selecting the profile measurement time as 400hr, 500hr and 600hr, and extrapolating and predicting the wall profile according to the three time to obtain 1200hr wall profile, as shown in FIG. 7;
(4) machining the channel shape at 1200hr, performing a 1200-1600 hr operation test, selecting the contour measurement time as 1200hr, 1400hr and 1600hr, and extrapolating and predicting the wall contour at 4000hr according to the wall contour at the three times, as shown in FIG. 8;
(5) machining the channel shape at 4000hr, performing 4000-4700 hr operation test, selecting 4000hr, 4350hr and 4700hr for contour measurement, and extrapolating and predicting to obtain 10485hr wall contour according to the wall contour at the three moments, as shown in FIG. 9, since the wall thickness of the discharge channel of the thruster is corroded to zero, the service life of the thruster is 10485 hr.
Claims (7)
1. A Hall thruster accelerated life test method is characterized by comprising the following steps:
(1) for the first timeThe Hall thruster ignited in the vacuum tank carries out a vacuum ignition test, the starting time of the vacuum ignition test is 0 moment, and the ending time of the vacuum ignition test is t0；
(2) After the vacuum ignition test is finished, t is measured0Coordinate r of outer wall surface contour of discharge channel of Hall thruster in rz coordinate systemOuter cover(z,t0) And the coordinates r of the contour of the inner wall surface in the rz coordinate systemInner part(z,t0)；
(3) Vacuum ignition test is carried out on the Hall thruster for N time periods, and the ending time (t) of each time period is measured1、t2、…、tN) Coordinates of the contour of the outer wall surface of the discharge channel and coordinates of the contour of the inner wall surface, the coordinates of the contour of the outer wall surface being denoted by rOuter cover(z,t1)、rOuter cover(z,t2)、…、rOuter cover(z,tN) (ii) a Coordinate of the inner wall surface profile is denoted as rInner part(z,t1)、rInner part(z,t2)、…、rInner part(z,tN)；
(4) Utilizing the wall contour coordinates of the discharge channel at different moments measured in the step (3), and reversely calculating the position (z) of the equivalent ion source S according to the wall erosion rate formula of the discharge channels，rs) And ion sputtering strength F (alpha), and calculating the operation predicted time length delta t of the Hall thruster by utilizing a wall surface erosion rate formulaN+1Outer wall surface contour coordinate r of rear discharge channelOuter cover(z,tN+1) And inner wall surface contour coordinate rInner part(z,tN+1)；
(5) According to the external wall surface contour coordinate r predicted in the step (4)Outer cover(z,tN+1) Processing the outer wall surface contour of the discharge channel, and predicting the inner wall surface contour coordinate r according to the step (4)Inner part(z,tN+1) Processing the contour of the inner wall surface of the discharge channel;
(6) repeating the steps (2) to (5) for m times until the thickness of any wall surface of the outer wall surface and the inner wall surface of the discharge channel becomes zero, and obtaining the service life t of the Hall thrusterlife：
The practical working time of the repeated p-th Hall thruster is recorded as
The corresponding calculated predicted duration is noted
In the step (2), the determination method of the rz coordinate system comprises the following steps: the axial line of the Hall thruster is used as a z-axis, the radial direction of the Hall thruster is used as an r-axis, the wall surface contour of the discharge channel of the Hall thruster corresponding to the time t is represented by a set of position coordinates (r, z) of a series of points on the wall surface in an rz coordinate system, and the contour coordinate of the inner wall surface is recorded as rInner part(z, t), the outer wall contour coordinates are denoted as rOuter cover(z,t)；
In the step (4), the erosion rate formula of the wall surface of the discharge channel is shown as the formula (1):
gamma is the wall ion incidence angle at the axial coordinate z at time t, and is calculated according to the following formula:
Yγ(γ) is the angular sputtering yield corresponding to the ion incidence angle γ:
uniformly dispersing the wall surface coordinates r (z, t) into M nodes and the ith node of the wall surface by adopting a finite difference methodAxial coordinate ziAnd the radial coordinate of the ith node of the wall surface at the time t is recorded as ri(t) ion incident angle γ at ith node of wall surface at time ti(t) is discretized into the form of equation (4):
at the time t, the included angle alpha between the ion incidence direction at the ith node of the wall surface and the r axisi(t) is discretized into the form of equation (5):
for t1，t2The erosion rate of the ith node of the wall surface at two moments is expressed by the formula (1) in a discrete form as shown in the formulas 6a, 6b and 6 c:
for i 2., M-1, the discrete equation is in the form:
for i ═ 1, the discrete equation form is:
for i ═ M, the discrete equation form is:
for t2，t3The erosion rate of the ith node of the wall surface at two moments is shown in the formula (1) in a discrete form in the formulas 7a, 7b and 7 c:
for i 2., M-1, the discrete equation is in the form:
for i ═ 1, the discrete equation form is:
for i ═ M, the discrete equation form is:
at time t, the ion sputtering intensity F (alpha) at the ith node of the wall surfacei(t)) is:
{mj,k,nj,k(ii) a j is 1,2, …, M is a composition function F (α)i) A set of coefficients of (a);
calculating the predicted time duration DeltatN+1Is (Δ t)1+△t2+……+△tN) 1 to 8 times of, wherein Δ t1＝t1-t0，△t2＝t2-t1，…，△tN＝tN-tN-1，△tN+1＝tN+1-tN。
2. The accelerated life test method of the Hall thruster according to claim 1, characterized in that: in the step (1), the time of performing the vacuum ignition test on the Hall thruster which firstly enters the vacuum tank for ignition is 6-20h, and the vacuum degree in the vacuum ignition test is not lower than 5 x 10-3Pa。
3. The accelerated life test method of the Hall thruster according to claim 1, characterized in that: in the step (3), N is 3.
4. The accelerated life test method of the Hall thruster according to claim 1, characterized in that: in the early stage of the test, the duration Deltat is predictedN+1Is (Δ t)1+△t2+……+△tN) 1-3 times of the total amount of the active carbon;
at the end of the test, the duration Deltat is predictedN+1Is (Δ t)1+△t2+……+△tN) 5-8 times of the total weight of the powder.
5. The accelerated life test method of the Hall thruster according to claim 4, characterized in that: the early stage of the test refers to the test of the thruster for 0-1000 h, and the later stage of the test refers to the test of the thruster for more than 1000 h.
6. The accelerated life test method of the Hall thruster according to claim 4, characterized in that: at the early stage of the test, Δ t1,△t2,…,△tNIs 50-100 hr, and at the later stage of the test, the value of delta t1,△t2,…,△tNThe value of (1) is 200-400 hr.
7. The accelerated life test method of the Hall thruster according to claim 1, characterized in that: position of ion source S (z)s，rs) And ion sputtering intensity F (. alpha.)i) The solving steps are as follows:
a. assume ion source position coordinates (z)s，rs) Is positioned at a certain position in the discharge channel;
b. from t1、t2The coordinates of the node of the channel wall surface measured at the moment are calculated according to the discrete equations (6a), (6b) and (6c) to obtain F (alpha)i(t1) ); from t2、t3The coordinates of the node of the channel wall surface measured at the moment are calculated according to the discrete equations (7a), (7b) and (7c) to obtain F (alpha)i(t2) Set of coefficients { m) }j,k,nj,kInitial value of { m }j,0,nj,0Is calculated according to equation (9):
c. from the set of coefficients { mj,k,nj,kInitial value of { m }j,0,nj,0Using the formulas (6) and t1The coordinates of the node of the wall surface of the channel measured at the moment are calculated to obtain t2Radial coordinate calculation value of channel wall surface node at moment
Using equations (6) and t2The coordinates of the node of the wall surface of the channel measured at the moment are calculated to obtain t3Calculation value of node radial coordinate of wall surface of time channel
Using equations (8), (5) and
calculate t1Ion sputtering intensity F (alpha) at timei(t1))0Using equations (8), (5) and
calculate t2Ion sputtering intensity F (alpha) at timei(t2))0；
d. Variance sigma between channel wall node radial coordinate calculation value and measurement value0Calculated according to equation (10):
k in the formula (10) is subscript and is a natural number, and the value of k is from 1 to the maximum iteration number;
e. a new set of coefficient sets m is selected according to equation (11)j,k,nj,k}
K in the formula (11) is subscript, k is a natural number, and the value of k is from 1 to the maximum iteration number;
f. according to the selected coefficient set mjk,njkUsing the formulas (8), (5) and
recalculate t1Ion sputtering intensity F (alpha) at timei(t1))1Using equations (8), (5) and
recalculate t2Ion sputtering intensity F (alpha) at timei(t2))1And calculating the relative error res of the sputtering intensity of the last two ions:
g. according to equation (6), using t1The coordinates of the channel wall node measured at the moment are solved again2Radial coordinate calculation value of channel wall surface node
According to equation (6), using t2The coordinates of the channel wall node measured at the time,re-finding t3Radial coordinate calculation value of channel wall surface node at moment
Recalculating the variance σ between the calculated and measured values of the radial coordinates of the nodes of the channel wall as in equation (10)1；
h. If the variance σ1＜σ0Then consider { mj,1,nj,1Is valid, will mj,1,nj,1Add to { m }j,k,nj,kIn the queue, the next set of coefficients m is selected according to equation (11)j,2,nj,2}; if the variance σ1≥σ0Reselecting { m) according to equation (12)j,1,nj,1}；
i. Repeating the steps e, f, g and h until the relative error res of the ion sputtering strength is less than 1e-3 or the iteration times reach the set maximum value, wherein the maximum value is 5000 times, and recording the corresponding final variance under the position coordinate of the ion source;
j. according to set rules to the ion source coordinate (z)s，rs) Traversing all positions in the discharge channel, repeating the steps b-i to obtain corresponding variances under different ion source position coordinates, and taking the ion source position corresponding to the minimum variance as the finally determined ion source position coordinate (z)s，rs) The coefficient set corresponding to the minimum variance is finally determined F (alpha)i) Coefficient set of { m }j,k,nj,kScanning according to the coordinates of rows and columns or scanning according to the coordinates of radius and angle;
k. for the outer wall surface of the discharge channel, ri(tN)＝ri Outer cover(tN)，ri(tN+1)＝ri Outer cover(tN+1) Directly using the ion source position coordinates (z) obtained in step js，rs) And strong ion sputteringDegree F (α), using known tNWall node coordinate r of timei(tN) And the formula (13) calculates the running time delta t of the Hall thrusterN+1Wall node coordinate r of rear discharge channeli(tN+1)；
For i 2., M-1, the radial coordinate of the wall node i is calculated as:
for i equal to 1, the radial coordinate of the wall node i is calculated as:
for i-M, the radial coordinate of the wall node i is calculated as:
for the inner wall surface of the discharge channel, firstly, the node coordinate r of the inner wall surface isi Inner part(t1)、ri Inner part(t2)、ri Inner part(t3) Coordinate transformation into a general wall coordinate form r according to equation (14)i(t1)、ri(t2)、ri(t3) Then, according to the steps a to j, the ion source position coordinate (z) corresponding to the inner wall surface is solveds，rs) And an ion sputtering intensity F (α),
r in formula (14)meanIs the initial average radius of the discharge channel, i.e. the center line of the annular discharge channel before the life test is startedThe distance between the Hall thruster and the axis of the Hall thruster;
using known tNWall node coordinate r of timei(tN) Wherein r isi(tN)＝2Rmean-ri Inner part(tN) And the formulas (13a), (13b) and (13c) are used for calculating the running time Deltat of the Hall thrusterN+1Wall node coordinate r of rear discharge channeli(tN+1) Then, the coordinates are inversely transformed according to the formula (15) to obtain the coordinates r of the node of the inner wall surface at the next timei Inner part(tN+1)；
ri Inner part(tN+1)＝2Rmean-ri(tN+1) (15)。
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| CN111042999B (en) * | 2019-12-11 | 2020-11-24 | 北京理工大学 | A Pulsed Plasma Thruster System Including Ignition Automatic Counting Device |
| CN111561431B (en) * | 2020-04-20 | 2021-03-12 | 哈尔滨工业大学 | Heat radiation anode structure for removing condensation product of iodine working medium electric thruster |
| CN112347610B (en) * | 2020-09-30 | 2022-09-23 | 兰州空间技术物理研究所 | Hall thruster service life evaluation method based on hollow cathode |
| CN117148020B (en) * | 2023-10-30 | 2024-04-12 | 宁德时代新能源科技股份有限公司 | Service life detection method of electronic product and terminal equipment |
| CN117647682B (en) * | 2023-10-30 | 2024-08-23 | 遨天科技(北京)有限公司 | Electric thruster life prediction method and device |
| CN118090517B (en) * | 2024-04-19 | 2024-07-30 | 哈尔滨工业大学 | Optical monitoring method for erosion products on the wall of Hall thruster channel |
| CN118641211B (en) * | 2024-08-16 | 2024-11-08 | 兰州空间技术物理研究所 | Method and device for testing working life of key part component of ion thruster |
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