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1、<p> 靜電懸浮式三軸加速度傳感器設(shè)計(jì)及其空間</p><p><b> 應(yīng)用前景論述</b></p><p><b> 摘要</b></p><p> 靜電懸浮幾三軸加速度計(jì)的針對(duì)太空的微重力水平設(shè)計(jì)的,理論分析表明加速度計(jì)最大的量程為35 g0,分辨率為1ng0,她可以滿足多方面的太空應(yīng)用。同時(shí)分析
2、了可能存在的誤差源。研究了一些相關(guān)技術(shù)和加工工藝?;谠O(shè)計(jì)一種高精度的加速度計(jì),本文提出了一種用于低軌道衛(wèi)星的測(cè)量重力加速度的加速度計(jì)的理論設(shè)計(jì)方案。一般來(lái)講,獲得來(lái)自人造衛(wèi)星的地球重力的方法如下所示:使用GPS數(shù)據(jù)獲得作用于衛(wèi)星的合力,非重力性質(zhì)的力使用衛(wèi)星上的微型加速度計(jì)檢測(cè),二者之差就是我們要求的重力,它與地球重力場(chǎng)有直接的聯(lián)系。最后我們得出如下結(jié)論:用于重力加速度檢測(cè)的最適頻寬為0.0008 Hz to 0.15 Hz。理論結(jié)果
3、將對(duì)將來(lái)衛(wèi)星上重力場(chǎng)的檢測(cè)具有一定的價(jià)值。</p><p> 關(guān)鍵詞:靜電懸浮 加速度計(jì) 重力場(chǎng)檢測(cè) 分辨率 GPS 頻帶 </p><p><b> 引言</b></p><p> 微重力是太空環(huán)境的主要特性,為了精確的監(jiān)控空間的微重力場(chǎng),,必須設(shè)計(jì)一種低偏差,高分辨率的特殊加速度傳感器,靜電懸浮加速度計(jì)在低于1HZ的低頻帶
4、具有很高的分辨率和精度。因此,它在地球場(chǎng)檢測(cè)和微重力科學(xué)中具有得天獨(dú)厚的優(yōu)勢(shì)。已經(jīng)有好多種靜電懸浮加速度計(jì)面世。CHAMP公司的STAR加速度計(jì),由法國(guó)的ONERA發(fā)展而來(lái),用于檢測(cè)衛(wèi)星上的非重力加速度計(jì)其頻帶從足夠的頻帶的交流電到0.05HZ。這些力包括空氣阻力,太陽(yáng)射線壓力。地面返照率以及姿態(tài)調(diào)整力。STAR 生產(chǎn)了一批量程為10 g0 ,在10-4 Hz 到 10-1 HZ內(nèi)Z軸和Y軸分辨率小于0.3ng 的加速度計(jì)。ASTRE加
5、速度計(jì),和 ESA合作。在STS-78任務(wù)期間,檢測(cè)了剩余的微重力干擾其頻帶從交流電到不到1 Hz。ASTRE加速度計(jì)量程精確到1 mg 。 精度小于1ng 是一種高性能的加速度計(jì)。用于精確檢測(cè)空間站或太空實(shí)驗(yàn)室的環(huán)境因素。MACEK的加速度計(jì),得到GRANT的大力支持,被用于STS-79 的儀表盤上用于檢測(cè)微重力作用。項(xiàng)目團(tuán)的數(shù)據(jù)顯示:MACEK的量程為40 g0 , 精度達(dá)到了150 ng0.靜電懸浮微</p>
6、<p> 靜電懸浮加速度計(jì)設(shè)計(jì)的理論分析</p><p> 如圖所示靜電懸浮加速度傳感器主要由一個(gè)中心檢測(cè)質(zhì)量和六個(gè)電容極板組成,外加固定極板用的外殼(圖中未示出) 。檢測(cè)質(zhì)量采用立方體結(jié)構(gòu)設(shè)計(jì),由金屬材料制成;電容極板由絕緣材料并在其內(nèi)表面濺射金屬薄膜加工而成 </p><p> 1. 2 靜電懸浮原理</p><p> 靜電懸
7、浮式三軸測(cè)量加速度傳感器在進(jìn)行地面檢測(cè)時(shí),由于在垂直于地面方向(設(shè)為x 方向) 中心質(zhì)量塊受到地球吸引力的作用, 因此必須給質(zhì)量塊施加一反方向的靜電力,以使其達(dá)到力平衡,并通過(guò)反饋電壓的施力作用使中心質(zhì)量塊在x 、y 、z 三方向均處于零位(平衡位置) 附近, 實(shí)現(xiàn)懸浮。而當(dāng)傳感器工作于空間飛行器上時(shí), 慣性力平衡了地球引力,因此僅需施力反饋回路的作用便可實(shí)現(xiàn)中心質(zhì)量塊的懸浮。</p><p> 1. 3 電
8、容位移檢測(cè)原理</p><p> 不失一般性,此處僅討論一個(gè)方向( x 軸) 位移的電容檢測(cè)原理,其它兩軸的檢測(cè)原理相同。當(dāng)無(wú)加速度輸入時(shí),控制回路使檢測(cè)質(zhì)量處于初始平衡位置(零位) ,檢測(cè)質(zhì)量表面距相對(duì)兩極板的距離相等,如圖2 所示。此時(shí)電容C1 與C2 相等。當(dāng)存在加速度輸入時(shí),檢測(cè)質(zhì)量沿與加速度相反的方向發(fā)生微小位移, C1 和C2 分別改變,兩者電容之差ΔC 可化簡(jiǎn) </p>
9、<p><b> ?。?)</b></p><p> 式中 ε為真空介電常數(shù); S 為電容極板面積; d 為電容極板與檢測(cè)質(zhì)量之間的距離;Δd 為檢測(cè)質(zhì)量微小位移。</p><p> 1. 4 加速度測(cè)量原理</p><p> 當(dāng)檢測(cè)質(zhì)量因加速度的輸入而發(fā)生位移時(shí), 引起電容變化, 進(jìn)而由控制電路產(chǎn)生反饋施力電壓Uf ,兩電極
10、板電壓由原來(lái)的定值偏置電壓Us 分別變?yōu)閁s + Uf 和Us - Uf ,從而對(duì)檢測(cè)質(zhì)量產(chǎn)生靜電力為:</p><p><b> (2)</b></p><p> 式中 Us 為偏置電壓; Uf = AΔC 為反饋施力電壓; A 為檢測(cè)電路增益。由力平衡條件ma = F( m 為檢測(cè)質(zhì)量塊的質(zhì)量; a 為外界輸入的加速度) , 可得到加速度與檢測(cè)到的反饋電壓的關(guān)
11、系</p><p> 當(dāng)檢測(cè)質(zhì)量(立方體) 體積為l3 , 材料密度為ρ時(shí),則上式變?yōu)?lt;/p><p><b> (3)</b></p><p> 通過(guò)測(cè)量反饋電壓便可以知道外界輸入的加速度值。</p><p> 重力場(chǎng)檢測(cè)在太空中的應(yīng)用 </p><p> 由德國(guó)航天局組建的 CHAM
12、P項(xiàng)目組,致力于地球監(jiān)測(cè)的多方位研究。它的目的之一就是精確重現(xiàn)地球的重力場(chǎng)。高靈敏度加速度計(jì)STAR被用來(lái)檢測(cè)非重力性質(zhì)的作用力。GPS接受器被用來(lái)精確確定衛(wèi)星的軌道。GPS的數(shù)據(jù)顯示,作用于CHAMP 的合力是可測(cè)的。兩者的差值便是地球重力,這種力與地球重力常有直接的聯(lián)系。地球重力加速度,非重力加速度和合力的加速度存在以下關(guān)系:</p><p><b> ?。?) </b></p
13、><p> 是地球引力的加速度;是合力的總體加速度由GPS數(shù)據(jù)得到;是非重力加速度由儀表上的加速度計(jì)得到;從上面的公式可以看出,如果測(cè)得合力的總體加速度和非重力加速度,則可以確定地球引力加速度。但是,這里必須聲明,在矢量標(biāo)定之前,必須讓時(shí)間匹配同時(shí)完成坐標(biāo)轉(zhuǎn)換.大氣層阻力和太陽(yáng)射線壓力是加速度計(jì)在200-500 km高空可檢測(cè)的主要的非重力性質(zhì)力。它們可以由以下兩個(gè)公式大致得到:</p><p&
14、gt; ?。?) </p><p><b> ?。?) </b></p><p> 如果衛(wèi)星的結(jié)構(gòu)是專門為檢測(cè)地球引力場(chǎng)定做的,非重力加速度</p><p> 應(yīng)該小于10 g0.航天飛行器的正交化比,是空氣的密度,是飛行器相對(duì)于空氣的速率, 是太陽(yáng)射
15、線能量的密度, 和 分別是大氣層阻力和太陽(yáng)射線壓力的系數(shù)。</p><p> ?。?) </p><p> 為了滿足地球重力場(chǎng)的的檢測(cè),合理的檢測(cè)頻帶是非常重要的。飛行器在300-500 km的低軌道運(yùn)行時(shí)速率大約為8 km/s. 設(shè)在地球重力場(chǎng)中太空分辨力為 km,更高的檢測(cè)頻率可以定義為:&l
16、t;/p><p><b> ?。?) </b></p><p> 從上面的公式可以得到頻率為0.146 Hz。在二級(jí)模型中, 大約是10,000 km,,因此頻率應(yīng)該減少到0.0008 Hz. 地球重力場(chǎng)的空間檢測(cè)目的是為了把中等模型定義到更低的級(jí)別,因此加速度計(jì)的頻帶范圍應(yīng)該是0.0008 Hz (or lower) to 0.15Hz.</p>&
17、lt;p> Electrostatically Suspended Triaxial Accelerometer</p><p> and Its Future Space Application</p><p><b> Abstract</b></p><p> An electrostatically suspended t
18、riaxial accelerometer is tentatively designed for space applications. Theoretical analysis shows that the maximum measurable acceleration of the accelerometer is expected to be 35 g0, and that the resolution is ,expected
19、 to be 1ng0, which would meet many space applications. Some error sources of the accelerometer are analyzed. The related techniques and machining processes is being studied.Based on the high performance of the accelerome
20、ter, a theoretical method fo</p><p> Keywords: Electrostatically suspended accelerometer; Earth gravitational field measurement; Resolution; GPS; Frequency bandwidth</p><p> Introduction</p
21、><p> The microgravity is one of the major characteristics of the space environment. To finely monitor the space microgravity level, specific accelerometer must be developed with a much lower bias and a high r
22、esolution. The electrostatically suspended accelerometer has high resolution and high sensitivity in the very low frequency range below 1Hz. Thus, it gains an advantage in the fields of the Earth’s observation and microg
23、ravity science.</p><p> Many electrostatically suspended accelerometers have been developed around the world. On board CHAMP, STAR accelerometer [1][2], developed under ONERA, France, is used to measure all
24、 non-gravitational accelerations of the satellite in a sufficient frequency bandwidth from DC to a few tenth of one Hertz. These forces include air drag, solar radiation pressure, Earth albedo and attitude manoeuvres. ST
25、AR presents a measurement range of 10 g0 with a resolution of better than 0.3ng0 for y- and z-axes</p><p> Theoretical design of electrostatic accelerometer</p><p> As shown in Figure 1, the e
26、lectrostatically suspended triaxial accelerometer mechanics is mainly constituted by a proofmass, six electrode-plates and a housing (the housing is not shown in Fig 1). The proofmass, coated with gold, can be made of Pl
27、atinum-Rhodium alloy. The electrode-plates can be made of dielectric materials, like porcelain or quartz, also coated with gold. The same electrodes are used for the capacitive position sensing and for exerting the elect
28、rostatic forces.</p><p> The principle of operation [6][7] of this accelerometer depends on the measurement of force that is necessary to maintain the proofmass at the center of the cage. Figure 2 shows the
29、 principle of the capacitive sensor along one axis, for example, x-axis. When no acceleration is applied to the center proofmass, the proofmass remains at the original balance position by a control circuit. The gap betwe
30、en the proofmass and the upper electrode equals the distance between the proofmass and the lower el</p><p> ?。?) </p><p> where, is the vacuum dielectric co
31、nstant; is the area of the golden electrode; is the gap between the proofmass and the electrode; is the small displacement of the proofmass.</p><p> When the proofmass leaves off the balance position, th
32、e feedback circuit brings a feedback voltage to the electrodes, which can apply an electrostatic force on the proofmass to move it back. The electrostatic force can be described as</p><p><b> (2)
33、 </b></p><p> where, is originally voltage applied on the electrodes; is the feedback voltage .</p><p> According to the force balance condition, (where m is the mass of the proofmass
34、; a is the applied acceleration), we can find the relationship between and a:</p><p> (3) </p><p> Space application on gr
35、avitational field measurement</p><p> The German CHAMP mission, funded by the German Space Agency, is dedicated to multi-purpose Earth’s observation [1][2]. One of its main purposes is the accurate recovery
36、 of the Earth gravitational field. A very sensitive accelerometer, STAR, is used to measure the non-gravitational forces. A GPS receiver is used to determine the precise orbit of the satellite. From the GPS data, the tot
37、al forces acting on the CHAMP are obtained. The difference between the two is the gravitational force, which is </p><p> ?。?) </p><p> where, is the Earth gr
38、avitational acceleration; is the total acceleration obtained from GPS data; is the non-gravitational acceleration measured by on-board accelerometer. From the above formula (6), we can see that, if the non-gravitationa
39、l acceleration and the total acceleration are measured, the Earth gravitational acceleration can be confirmed. However, it is necessary to point that, before the above vector operation, time matching and coordinate conve
40、rsion must be made. </p><p> The atmospheric drag and the solar radiation pressure are the main sources of the non-gravitational forces that the accelerometer may measure in the 200-500 km space [8]. They c
41、an be approximately calculated by the following two equations (7) and (8). If the structure of the small satellite is carefully designed for the Earth gravitational field measurement, the non-gravitational acceleration i
42、ntroduced by all non-gravitational forces should be smaller than 10 g0.</p><p> (5) </p><p> ?。?) </p&
43、gt;<p> where, is the spacecraft cross sectional area (perpendicular to the velocity); is the density of the air; is the velocity of the spacecraft relative to the air; is the density of the solar radiant ene
44、rgy; and are the coefficients of the atmospheric drag and the solar radiation pressure respectively. </p><p> To meet the measurement of the Earth gravitational field, suitable measurement frequency bandw
45、idth of accelerometer is very important. The velocity (v) of the spacecraft in low orbit of 300-500 km is about 8 km/s. Given the space resolution of the Earth gravitational field model is km, the higher frequency () of
46、 measurement is defined by :</p><p> (7) </p><p> for degree 360 of the Earth gravitational field model, is about 55 km. From the above equation
47、(9), a frequency of 0.146 Hz is obtained. For degree 2 of the model, is about 10,000 km, so the frequency should be decreased to 0.0008 Hz. The purpose of space measurement of the Earth gravitational field is to define
48、the model of middle to lower degree, so the accelerometer should have a frequency bandwidth of 0.0008 Hz (or lower) to 0.15Hz.</p><p><b> eferences</b></p><p> Touboul P. Foulon B.
49、 and Le Clerc. Star, the accelerometer of geodesic mission CHAMP. Melbourne, Australia: 49th International Astronautical Congress, 1998. IAF-98-B.3.07.</p><p> Perret A. Star, the accelerometric system to m
50、easure non-gravitational forces on the CHAMP S/C. Melbourne, Australia: 49th International Astronautical Congress, 1998. IAF-98-U.1.06.</p><p> Touboul P., Foulon B. and Willemenot E. Electrostatic space ac
51、celerometers for present and future missions. Beijing, China: 47th International Astronautical Congress, 1996. IAF-96-J.1.02.</p><p> Peresty R., Sehnal L., Lundquist C. A., and Bijvoet J. Measurements of M
52、icrogravity Environment by Three-axial Electrostatically Compensated Microaccelerometer. Turin, Italy. 48th International Astronautical Congress, 1997. IAF-97-J.2.05.</p><p> Robert W. D., James C. F. and W
53、illiam G. L. An electrostatically suspended cube proofmass triaxial accelerometer for electric propulsion thrust measurement. Lake Buena Vista, FL, USA: 32nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 1996. AIAA 96-
54、2734. </p><p> Bemard A. and Touboul P. The GRADIO accelerometer: design and development status. Anacapri, Italy: Proceedings of the workshop on solid-earth mission ARISTOTELES, 1991. 61-67.</p><
55、p> Josselin V., Touboul P. and Kielbasa R. Capacitive detection scheme for space accelerometers applications. Sensors and Actuators A, 1999, 78: 92-98.</p><p> Andrea M., Anna M. N., and Paolo F. Non-gr
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