Natural convection gas pendulum and its application in accelerometer and tilt sensor

PROGRESS IN NATURAL SCIENCEVol. 15, No 9, September 2005SHORT COMMUNICATIONSNatural convection gas pendulum and its application inaccelerometer and tilt sensorZHANG FuxUeResearch Center of Sensor Technology, Beijing Information Technology Institute, Beijing 100101, China)Received December 6, 2004: revised February 22, 200Abstract It is discovered that the natural convection gas has the peharacteristic, which leads to the introduction of theew concept of gas pendulum. In this paper, the buoyancy lift of naturalon gas is analyzed in a hermetic chamber, and the relaonship between the buoyancy lift and the change of temperature is formulated. The experimental results show that the gas pendulummilar to the solid pendulum and liquid pendulum, can be utilized to sense the acceleration and the tilt angleKeywords: natural convection, accelerometer, tilt sensor.In the inertial technology fieldknown that keeps the vertical upward direction Fig. 1 (b))the pendulum characteristics of solid or liquid have This phenomenon of natural convection gas in a her-been utilized to sense the acceleration and the tilt an- metic chamber resembles the pendulum characteristicsgle. In 1989, it was discovered that similar to the of solid and liquid shown in Figs. 2 and 3, respectivelysolid pendulum and liquid pendulum, the natural con-vection gas has the pendulum characteristic, and thuscan be utilized to sense the acceleration and tilt angleBecause the proof mass of a gas pendulum accelerome-ter and tilt sensor is gas with very small mass, the aclerometer and tilt sensor can resist powerful vibration and strong shocks. The gas pendulum has maradvantages that solid and liquid penduluhave, such as short responding time, low fabricationcost and so on. This paper summarizes the investiga-tion in acceleration and tilt angle sensors of the gasndulum for the past few vears[2,33Pendulous phenomena of natural convection gas in a hermetic chamberAs shown in Fig. 1(a), ri and r2 represent hotwires,if a heat source is placed in a hermetic chamber, the gas nearby the heat source will move up forits higher temperature and smaller density p, and thegas far from the heat source will sink for its lower中国煤化工temperature and larger density poo, which forms theCNMHGerect up natural convection gas in the hermetic chaber. When the chamber is inclined with an angle e(bit is discovered that the natural convection gas alwaysFig. 1. Schematic diagram of gas pendulum. a)Horizontal(b) tiltEP=据Natural Science Foon of China( grant No. 60272001)(a263. netwww.tandf.co.uk/journalsProgressinNaturalScienceVol.15No.92005re-expressed asFbMt=(p∞-p)(a-G),(2)where a is the absolute acceleration of the chamberand G is the constant of universal gravitation. Because of the no-gravitational acceleration (the specificforce)f=a-G, we can obtainF1(3)Fig. 2. Schematic diagram of solid pendulum. (a)Horizontstate:(b) tilt stateFrom Eg.(3), we can know that the directionof the buoyancy lift is the same as the direction of thespecific force f and the magnitude of the buoyancy liftis proportional to that of f2.3 Relationship between buoyancy lift and changeof temperature(b)In the natural convection gas, the density difference of fluid is caused by the temperature differenceF1hematic diagram of liquid pendulum. ( a)Horizontalstate:(b) tilt stateand therefore the buoyancy lift is a function of thetemperature difference. When the fluid pressure is aconstant, the change ratio of volume caused by a unit2 Buoyancy lift of natural convection gas in of temperature variation is called the B-coefficienta hermetic chamberof volume expansion. Let j equal the specific volumeof the fluid (j=1/p), and B can be expressed as2. 1 Buoyancy lift on the surface of the EarthAccording to the theory of heat transfer 4,thenatural convection gas is affected by the local bodyforce of gravity pg and the force- poog, which iswhere the subscript p representing the pressure is acaused by the gas static pressure gradient. The sumonstant. For gas, from j=1/p, we can deduceof these two forces is the buoyancy lift which can beexpre(p∞-p)gHere,p is the density of the gas heated by the heat Therefore, the coefficient of the gas thermal expan-source,Poo is the density of the surrounding unheatedgas, g is the gravitational acceleration, and Fbuoliftthe driving force of the natural convection gas. Be-1(9cause the density of the heated gas is less than that ofthe unheated gas, the direction of the buoyancy liftin the opposite direction of the gravity. Driven by the When the change of temperature is small, the densitybuoyancy lift, the heated gas rises vertically upward. difference of gas can be approximately equal to 4J△p=p3△T2.2 Buoyancy lift in absolute coordinateTherefore, the buoyancy lift of a unit volume isg. (1) is the expression of the buoyancy lift in中国煤化工N△1(4)a relative coordinate regardless of the gravitational acationIn the absolute coordinate, when theCNMHGometer and tilt sen-gravitational acceleration of the hermetic chamber isconsidered, the local body force of gravity pg and the Sorforce produced by the gas static pressure gradientSolid and liquid pendulum accelerometer and tiltPoog should be replaced by-P(a-g) and sensor utilize the pendulum characteristics of solid andPoo(a-C), elEctively. The buoyancy lift can be liquid respectively in the gravitation operation, andProgressinNaturalScienceVol.15No.92005www.tandf.co.uk/journalsthey can measure the acceleration and tilt angle al- of gas pendulum accelerometer can reach t g andcan use mature tech- the non-linearity is less than 1% FS. Fig. 6 showsnologies such as capacitance, resistance or other the output voltage of a gas pendulum accelerometermethods. Gas pendulum accelerometer and tilt sensor utilize the pendulum characteristic of the buoyancylift generated by natural convection gas( Fig. 1)Two thermal sensing resistors rI and r2, namelyAcceleration SensingOperationalcomponenthotwires, in the hermetic chamber were employed tomeasure the acceleration and tilt angle. 6.Fig.4shows the sensing component structure of a gas pendulum accelerometer. In this structure, two hotwiresZero compensaterI and r2 form the variable arms of the WhetstoneBridge. The invariable arms have equal resistancescompensationIncuri.e. RI equals R2. The input axis is along the symmetry axis of the chamber. When the power is onNon-linearitythe hotwire heats theas around it, and a naturalconvection is produced as shown in Fig. 1(a). In theFig. 5. Block diagram of signal processing circuitconvection field, two hot wires of ri and r2 are symetric. Because they sense the same temperaturetheir resistances are equal. The output of the bridgecircuit is zero. When the chamber is affected by acceleration, the symmetry of the natural convection fieldis distorted. The intension of heat gas flow heats r2more than it heats rI. Therefore, the tempand the corresponding resistances of ri and r2 are notequal to each other. The bridge outputs a voltage sigAcceleration (g)nal corresponding to the acceleration. The signal processing circuit is shown in Fig. 5. When the voltagesignal is applied the signal processing circuit gives anoutput signal corresponding to the input accelerationig. 6. Output voltage of the gas pendulum accelerometer.In gravitational field, experiments are conductedThe shell ofwith the structure shown in Fig. 7. The chamber isensing componentcylindrical. The two hot wires are placed in parallelwith the axis of the chamber acting as the heat sourceElectrodeas well as the sensing elements. The natural convec-tion chamber of this structure can be used to measureIRUR2Output axis中国煤化nput axisSensor component sketch map of gas pendulum ac-ergometerCNMHGIn the structure of sensitive element with chamber shown in Fig 4, the two hotwires not only actthe heat source but also as the sensing element. Experiershow that the measurement rangelement structure of the gas pendulum tilt sensorwww.tandf.co.uk/journalsProgressinNaturalScienceVol.15No.92005tilt angles as well. Experiments have shown that the(2)Under the action of buoyancy lift, naturalmeasurement range can be as large as 45, and the convection gas has the pendulum characteristicnon-linearity is less than 1% FS with the resolutionless than 0. 01. The output voltage of the gas pendu(3) The pendulum characteristic of natural conlum tilt sensor is shown in Fig 8vection gas can be utilized to make accelerometer andtilt6000Ref4000I Yu B, Chen Y.X. and Guo X.Z. Inertial Technology(in Chiese), 1st ed. Beijing: Publishing House of Beijing, University ofAeronautics and Astronautics, 19942 Zhang F.X. The omnidirection gas pendulum horizontal attitude-50-30-10103050sensor. The Defensive patent of China 99 1 16757.0,1999-08.20Tilt angle3 Zhang F.X. The gas pendulum horizontal attitude sensor. The Defensive Patent of China 99 1 18007.0, 2000-01-314 Warren M.R., Games P H. and Ejup N G. Handbook of HeatTransfer Fundamentals, 2nd ed. New York: McGraw-Hill, 19855 Zhang F.X. Pendulons characteristics of the gas flow in a hermeticFig,8. The output voltage( Va )of the gas pendulum tilt anglehamber. Acta Electronica Sinica (in Chinese ), 1999, 27(11)6 Zhang F.X. Gas pendulum acceleration sensor, Chinese Journal of4 ConclusionElectronics, 2000, 9(1):16(1) The buoyancy lift is the driving force of natural convection gas中国煤化工CNMHG