Indirect Counterbalanced Pendulum Optical Lever Thrust Balance Engineering Essay

Development of an indirect counterbalanced-pendulum optical lever push balance for micro-to-milli-Newton thrust measuring. This paper describes the design and testing of an indirect hanging-pendulum push balance utilizing a laser-optical-lever rule to supply micro-to-milli-Newton thrust measuring for the development of electric propulsion systems. The design doctrine allows the choice of the entire push scope in order to maximise declaration through a counterpoised pendulum rule, every bit good as inactive magnetic damping in order to let comparatively rapid transient push measuring. The balance was designed for the intent of hollow cathode microthruster word picture but could be applied to other electric propulsion devices in the thrust scope of micro to milli-Newtons. An initial push word picture of the T5 hollow cathode is presented.

Keywords: Indirect push balance, electric propulsion, plasma, hollow cathode microthruster

( Some figures in this article are in coloring material merely in the electronic version )

Introduction

In recent old ages miniaturisation of propulsion systems has been sought for high indicating truth missions and besides to enable higher energy missions with big speed alteration demands. Of peculiar involvement is the development of micro-electric propulsion systems, trusting on the acceleration of the working propellent through electrothermal, electrostatic or electromagnetic agencies. Electric propulsion systems offer important propellent mass nest eggs over conventional exothermal chemical-based systems. Several such system are presently under development at the University of Southampton including hollow cathode microthrusters based on the T5 and T6 hollow cathodes [ 1 ] , miniaturized bi-directional RF gridded ion pushers [ 2 ] and pulsed plasma pushers [ 3 ] operating in assorted thrust scopes and thrust manners ( pulsed/continuous ) necessitating micro-to-milli-Newton push declaration. This paper describes a flexible push measuring system to provide for theses demands and an initial push word picture for of hollow cathode microthrusters is presented. This includes the appraisal of thermic impetus, beginnings of noise and adjustment coefficient due to the nature of indirect measurings.

Sub-milli-Newton push measurings have antecedently been made by either mounting pushers straight to the measuring system [ 4 ] or indirectly by mounting a mark in the direct way of the ejected propellent [ 5 ] . This has typically been performed through either hanging [ 6 ] , inverted [ 7 ] , or torsional pendulums [ 8 ] . Hanging pendulums have the advantage of simpleness of building ( low cost ) and high stableness. However, due to their stableness and low addition, high sensitiveness can merely be attained with a long pendulum arm, which is impractical for little trial installations ( vacuum Chamberss ) . Inverted pendulum push bases are less stable with higher addition, and therefore more sensitive than the hanging pendulum constellation. A important issue with the upside-down pendulum constellation is that the stableness is a strong map of the stiffness of the supporting flections, and considerable attending must be made to guarantee that the belongingss of the flections do non alter during the class of a trial ( due to heating for illustration ) to avoid impetus of the initial baseline supplanting ( zero-drift ) . Additional thermic direction systems are frequently required to minimise impetus.

Unlike both the conventional and upside-down pendulum constellations, the reconstructing force in a torsional pendulum constellation ( which rotates about an axis that is parallel to the gravitation vector ) can be made independent of the pusher mass, which is a important advantage. The drawback is that the horizontal, asymmetric agreement of its members can be hard to set up in a vacuum chamber. Some torsional push bases have hence incorporated mechanical linkages which translate horizontal supplanting into perpendicular supplanting This provides important benefits ; the sensitiveness is independent of the length of the pendulum arm ; the sensitiveness can be continuously adjusted by a simple rotary motion of one of the linkage elements ; no independent mention construction is required [ 6 ] . Methods of geting measurement end product from the system include the usage of strain gages [ 9 ] , photo-detectors [ 5 ] , capacitive [ 10 ] and additive transducer [ 6 ] and interferometeric techniques [ 11 ] . Of these techniques non-contact methods offer the least possible of perturbation or intervention with measurings. The system supplanting due to the thrust force in these systems is inherently little, even through the addition in the pendulum lever arm, therefore the motion is frequently amplified for easiness of measuring through extra mechanical linkage levers [ 6, 12 ] , optical levers [ 5 ] or through interferometry [ 11 ] . Again non-contact techniques offer the least possible for presenting measurings mistakes.

Direct measuring techniques, where the pusher is mounted straight to the measuring system, are considered a more accurate signifier of measuring, particularly when covering with higher push devices, nevertheless as micro-Newton push degrees are attack propellent provender lines and electrical connexions to pushers bring forth counter-mechanical emphasis on the order of the thrust force as the pendulum arm is displaced. In peculiar, electrical wires experience Joule warming, doing them to deform during pusher, which can use time-varying forces and torsions to the push base arm. Some solutions have used liquid metals to present power to the pusher without utilizing solid wire connexions [ 12 ] . Alternatively, some milli-Newton scope measuring systems incorporate an extra electrostatic or electromagnetic force feedback mechanism to reconstruct the void place of the balance and bound zero-drift consequence [ 10, 13-15 ] . The free-torsional or swing gestures besides have to be restored via the actuator to enlarge the measuring bandwidth up to the mark values which can show actuator noise in the measuring informations. Passive Eddie-current systems have antecedently been employed in magnetic damping of thrust balances [ 6, 10 ] to disperse oscillating gestures.

By mounting the balance downstream of the pusher, in the fumes plume, indirect push measuring can be made by impulse transportation to the balance [ 16, 17 ] . This method has the advantage of mounting the measuring mark independently of pusher and external connexions therefore the development procedure is well simplified and costs reduced. Double indirect pendulums have besides been used in order to graduate out mechanical system noise [ 18 ] . The disadvantage of indirect methods nevertheless is that the influence of elastic or inelastic atom hits with the mark needs to be considered and so in general, direct push measurings are considered more accurate and are preferred to indirect techniques. The method has been shown to be within 10 per centum of the measured push value and those theoretically calculated on the footing of electrical measurings in ion pushers [ 17 ] . Indirect measurings besides include the usage of ion investigations, retarding possible and hemispherical energy analysers and emissive investigations to set up the downstream beam profile and ion energy distribution, nevertheless this method do non account for the flux of neutrals which could show important inaccuracy in pushers with a low ionisation fraction such as hollow cathode pushers.

In the present system, shown in, an indirect system was defined because of its built-in simpleness, low cost and because our involvement was more in comparative push measurings and non absolute 1s. The system consists of a laser-optical-lever method to supply a non-contact angular measuring of a fresh counterweight indirect suspended-pendulum with inactive magnetic damping. Through altering the counterweight weight and place, therefore the Centre of gravitation, the push scope can be set as required. Since the balance is non required to back up the weight of the pusher assembly the balance can be tuned to really high or really low push scopes, similar to mechanical elaboration, nevertheless in this instance optical warp feeling provides non-contact measuring. The benefit in choosing the push scope is that as it is reduced, declaration additions proportionately such that the sensitiveness remains changeless. This flexible design allows the measuring of push degrees from ion pushers ( manganese ) down to pulsed plasma pushers ( I?N ) .

Figure Solid theoretical account of the suspended in-direct pendulum mounted axially downstream of a microthruster

The Experimental Apparatus

The Vacuum Chamber

The vacuity installation used to retroflex the infinite environment in this experiment consists of a 500mm diameter by 500mmm long chamber with ISO and CF rims. A cylindrical H2O cooled Cu shroud fitted around the interior of the vacuity chamber wall dissipates the heat burden during pusher operation. Vacuum pumping is achieved with a water-cooled turbo molecular pump ( Pfeiffer Balzers TPH 520KTG, 500l/s ) controlled by a TCP 380 power supply ( with a TCS303 pump control unit ) backed by a rotary vane pump ( Pfeiffer Balzers DUO 016B ) , accomplishing an ultimate vacuity of 8.0×10-7 mbar. This degree of vacuity ensures the partial force per unit area of O in the system is low plenty to forestall toxic condition of the chemically sensitive hollow cathode thermionic emitter, indispensable for operation. A Spectra Gasses 7120 high truth double-stage regulator supplies propellant to the provender system. Propulsion class ( 99.997 % pure ) propellent flows to the cathodes through high and low capacity bespeaking O traps via an Edwards FCV10K excess mulct control needle valve. Vacuum force per unit area is monitored with a Balzers TPG300 force per unit area gage bundle representing a pirani ( 1000-5.4×10-4mbar ) and cold cathode gage caput ( 5×10-3 – 1×10-9mbar ) . A trying cylinder ( bypassed during experiment ) and Druck PDCR910 force per unit area transducer are used for flow standardization before each unit of ammunition of proving with a repeatability of better than 4 % . During operation chamber force per unit area varies between 5.7×10-5 mbar and 1.8×10-3 mbar at Ar flowrates between 0.05mgs-1 and 0.3mgs-1 severally.

The Thrust Balance

The Optical Setup

Optical apparatus consists of a Melles Grilot He-Ne ( 543.5nm ) optical maser passed through a Keplerian beam expander, directed through the chamber on to a mirror, stiffly connected to a suspended Mo pendulum mark shown in and schematically in. The optics system guides the reflected beam out of the chamber onto a exposure sensitive sensor ( PSD ) at a way length of 0.9m organizing a optical maser optical lever with an order of magnitude addition. The sensor is coupled with a C4674 signal processing circuit ( end product +/-2.5V at 1V/mm on each axis ) and designed to supply planar place informations on the incident light topographic point independent of the light strength and is powered by a 30V Instec dual-tracking power supply ( rippling less than 3mV ) . The end product from the signal processing circuit is displayed on a Tektronix TDS 410A 2-channel digital CRO ( resolution +/-0.01V ) . A pivoting mechanism allows the mark to be positioned both perpendicular to the push vector and through a full 90Es expanse of angles while besides leting the pendulum to be electrically floated, grounded or biased.

Figure A additive schematic of the experimental system and rule of operation

Figure Vacuum chamber and push balance

The Photodetector

The signal returned from the push balance falls onto a Hamamatsu 4.7×4.7mm planar tetra-lateral photo-sensitive-detector ( declaration of 600nm ) . A narrow-bandpass intervention filter with a transmittal curve centered at the optical maser frequence, placed in forepart of the PSD, eliminates ambient visible radiation, which may interfere with the measuring. When the optical maser visible radiation topographic point strikes the sensor, an electric charge relative to the light strength is generated at the incident place. The baseline upper limit thrust scope was defined as 0-1.8mN. The returning optical maser topographic point size was ~0.5mm hence the pendulum was designed such that over the thrust scope required the maximal crossbeam of the topographic point on the PSD was limited to 2mm, ~40 % of the swath. This ensured the full topographic point was incident on the photodetector over the maximal scope. At an optical way length of 0.9 m and PSD declaration of 600nm a push measuring declaration of ~3I?N is obtained, although this is an upper bound due to other undetermined beginnings of mistake.

The Pendulum

The pendulum consisted of a round mark suspended on the center line of the push vector by two steel point pivots resting on a level steel shelf with negligible clash. The balance was designed to hold a Centre of gravitation below the pivot point which could be controlled by the usage of an adjustable counterweight mounted at the top of the assembly as shown in. In this design, choice of an appropriate counterbalance place can either widen or shorten the mensurable push scope. By cognizing the complete mass belongingss of the balance by 3D patterning before industry, the pendulum could be built such that its Centre of gravitation and mass were close to optimum for the awaited push scope to use the full swath of the photodetector, maximising declaration and signal to resound ratio.

The pendulum was designed in a sandwich construction to give a high grade of rigidness and cut down the possibility of dynamic manners of oscillation whilst being designed symmetrically about the pivot point to minimise the influence of any geometrical alterations due to thermic effects in the Centre of gravitation. Molybdenum was selected as the preferable mark stuff given its little coefficient of thermic enlargement ( CTE ) and low spatter output since the mark is exposed to a comparatively strength plasma and high energy ions.

Figure Pendulum schematic ( left ) and thrust balance assembly ( right )

Thrust Calculation and Uncertainty

The mark can be considered as a compound inertial pendulum and underdamped harmonic oscillator and as such is good understood [ 19 ] . No direct standardization of the balance was conducted, nevertheless the pendulum C of G location was measured really accurately by mounting the pendulum at 90A° supported at the pivot points so mensurating the force constituent on the thrust line with a commercial SA131 weighing graduated table, accurate to 0.1g in comparing to the pendulum weight ( 398.7g without counterbalances ) ; a little rig was built for this intent. The force produced by the pusher can so be derived from conventional mechanics based on the mensural warp of the pendulum. The counterweight weight gives a agency to command the centre of gravitation place, therefore the addition in the lever arm. By traveling the Centre of gravitation closer to the pivot points the measureable push scope can be adjusted from milli-to-micro-Newton while increasing declaration by utilizing of the full swath of the PSD. The measureable push scope and declaration lessening proportionately with increasing counterweight mass, hence the system maintains its sensitiveness. The maximal angle of warp of the pendulum at a way length of 0.9m was 0.0433A° which consequences in ~2mm optical maser topographic point supplanting on the photodetector. Given the little angle of warp ( upper limit of 0.0433A° ) the force F, moving about the centre of gravitation is merely given by

, ( 1 )

where g0 is the gravitative invariable and m is the balance mass. In this instance nevertheless, the existent force produced at the thrust line for a given warp angle is hence dependent the entire balance mass and besides the ratio of the distances from the pivot to the Centre of gravitation Lcg, and the pivot to the centre of thrust Lcot ( fixed at 107.4mm ) . If MS, is the structural mass and mw is the mass of the counterweight, the measured jab force, Fm, is given by

. ( 2 )

As shown in, increasing the counterbalance mass reduces the push scope and declaration proportionately. Weights of 0g – 460g, represent push ranges between 1739AµN and 150 AµN. Fine tuning of counterweight mass allows micro-Newton thrust measuring ; a weight of 500.00g for illustration, would give a thrust scope of 12.66AµN with a declaration of 3.80nN. These values of class represent an upper bound of truth for the balance and back uping measuring system. In world the declaration is lower due to external beginnings of noise.

Figure Changing thrust scope and declaration by adding counterbalances

The chief deciding mistakes with fractional uncertainness in the system include mass flow standardization ( A±4 % ) , declaration of the optical detector over the scope used ( A±0.3 % ) , measuring of the optical way length ( A±0.1 % ) , location of the pusher axis on the mark center line ( A±0.1 % ) , and the deliberation of the balance ( A±0.025 % ) giving a entire fractional mistake of A±4.525 % with a quadrature uncertainness of 4.01 % . We besides have an extra constituent of uncertainness due to the consequence of elastic propellent atom hits with the mark ; an analysis of this uncertainness and undetermined beginnings of mistake is discussed subsequently.

Performance

System Response

One issue encountered was the long clip invariable for the system to make steady province, since the pendulum is about frictionless. Since typical base force per unit areas within the chamber are ~5×10-4 millibar during operation of the cathode, the ambient gas is rarified, nevertheless there remains a limited transportation of kinetic energy from the hovering pendulum to the gas and clash dissipated as heat at the pivot points. This resulted in some hours to disperse oscillations in the system. shows the transeunt behaviour from an initial forced oscillation of A±1.5V with no damping, stand foring a release from a 1.3mN steady-state push measuring. The logarithmic decrease is used to happen the muffling ratioA of an underdamped system in the clip sphere and can be found by the natural logA of the amplitudes of any two extremums by

. ( 3 )

The damping ratio, I› , of the system can be found from the logarithmic decrease I? [ 20 ] by

. ( 4 )

whereA x0A is the greater of the two amplitudes andA xnA is the amplitude of a peakA nA periods off. In this instance, muffling factors for the system are shown in. It can be seen that the damping factor for the free push balance is about 5.8 x10-5, an highly low value. Such a low damping coefficient generated many proficient jobs which limited thrust declaration ; oscillations in the system required a significant clip to shack, steady province was unachievable since and background excitements induced oscillation into the system and pendulum oscillations were by and large much greater than the supplanting due to the thrusting force. In this instance a signifier of damping was necessary to cut down the influence of external excitements and to return the thrust balance to steady province Oklahoman.

Figure Muffling factors calculated for the free push balance system as a consequence of an external A±1.5V input

Magnetic Damping

A inactive magnetic Eddy current damping system mounted at the rear of the mark was used to disperse oscillations and quivers in the system. As the mark is continuously traveling in the magnetic field it experiences a uninterrupted alteration in flux that induces an electromotive force ( voltage ) , leting the induced currents to renew. The currents dissipate energy from the system, therefore leting the magnet and music director to map like a syrupy damper. A ring magnet of 0.1Tessla was selected and mounted on an adjustable assembly at the rear of the Mo mark. The distance between the magnet and mark was consistently altered to 4 places of 1mm, 2.5mm, 5mm, and 10mm in order to look into the dynamic response. Transeunt pealing informations for the 2.5mm and 1mm instance is shown in and severally. The corresponding damping factors for several magnet-target spacing ‘s are shown in. As shown in and, the add-on of magnetic muffling non merely significantly shortens the clip for oscillations to disintegrate from hours to seconds, but moistnesss background induced quiver oscillations to cut down noise in the system.

Figure Passively damped oscillations of thrust balance from a measure input with a pendulum/magnet separation of 2.5mm

Figure Passively damped oscillations of thrust balance from a measure input with a pendulum/magnet separation of 1mm

Table System response due to magnetic damping

Separation [ millimeter ]

Muffling factor

Steady province reached after

1

6.28×10-2

12s

2.5

1.29×10-2

71s

5

2.17×10-3

~5.5minutes

10

5.34 x10-5

~2.5hours

No magnet

5.79 x10-5

~3hours

System Noise

An analysis of the FFT power spectra is of the sinusoid system response shown in. In this instance power spectra are displayed in dBm, the power ratio inA decibelsA ( dubnium ) of the mensural power, P, referenced to oneA milliHYPERLINK “ hypertext transfer protocol: //en.wikipedia.org/wiki/Milliwatt ” -watt. Zero dBm therefore peers one milli-watt with a 3 dB addition stand foring approximately a doubling of the power. Power addition in dBm is hence expressed as

and. ( 5 )

Figure Noise power spectra with roughing pump in operation and out of operation

The FFT reveals peaks chiefly of 49.21Hz at 13.12dBm and 24.21Hz at 22.98dBm severally. The higher frequence extremum is consistent with the stated roughing pump 3-phase chief motor at 50Hz ( 3000RPM ) with the lower frequence consistent with the 2nd mechanical phase of the roughing pump at a ratio of 2:1 ( 1410RPM ) . All other low frequence extremums are present both with and without the roughing pump. The extremum at 87.5Hz at 38dBm is consistent with the CRO difficult thrust rotary motion velocity of 90Hz ( 5400RPM ) , action was therefore taken to relocate the CRO farther from the proving setup. In making so the extremums of 60.9Hz at 34.7dBm besides disappeared bespeaking that the 60Hz signal was probably the CRO fan velocity. Noise above 400Hz was negligible. The really low frequence extremum of 10.93Hz at 16.9dBm is likely to be the natural structural frequence of the trial edifice. In order to well cut down noise the roughing pump was mounted on isolation dampers.

Figure Resonant frequences of the thrust balance assembly during turbopump start-up

The resonating frequences of the system can be analyzed by exciting the system with an externally goaded oscillation. In this instance the turbopump velocity can be monitored during spin-up to the steady province velocity of 839Hz. A hint of system response during startup can be seen in with the critical frequences indicated. As shown above the chief resonating manner of the balance occurs at about 56Hz with lesser manners at 32Hz, 167Hz, 207Hz and 332Hz. The primary resonating frequence was identified as 56Hz which was near to the roughing pump chief motor frequence ( 50Hz ) . Vibrations from the roughing pump are transmitted to the chamber via a linking vacuity line to the turbopump mounted on the chamber. Weights were added in the centre of the line to make a standing node and duplicate the transmittal frequence to the chamber to 100Hz.

Thermal Stability

Trials were conducted to look into the transient thermic behavior of the thrust measuring assembly. First heater currents of 2.2 Amps and 2.5Amps were applied to the warmer on the T6 cathode without a discharge. The warmer is used for cathode ignition and raises the organic structure temperatures to about 1200A°C as it would be during operation. As the cathode heats up, heat is radiatively transferred to the pendulum and back uping beam, and conductively to the pusher backplate. No propellent was fluxing through the cathode during these trials so the signal represented the nothing or baseline place of the thrust balance. This trial is shown in. In a 2nd set of trials the cathode warmer was switched off after runing at 2.2Amps for 2 hours in one instance and in another instance the detector response was monitored instantly after the pusher was operated in a discharge. The immediate bead in push followed by thermic impetus is shown in.

Figure Thrust balance zero-baseline impetus with 2.2 Amperes applied heater current and 2.5 Amps applied heater current. Sensor supplanting in this instance represents 0.8 mm/mN.

Figure Thrust balance zero-baseline impetus after the switch-off of a discharge and besides of merely the warmer at 2.2 Amps. Sensor supplanting in this instance represents 0.8 mm/mN.

As the detector outputs in show, during heating a slow but important displacement in the zero place is observed. Since no effort was made to keep a thermally inert environment to avoid extra complexness, a thermic impetus was expected. Typically hollow cathodes take 15-minutes to make a steady province discharge electromotive force where a thrust measuring would so be taken. The impetus is important plenty to lose the zero-line standardization over this period, hence push measurings were made by taking comparative detector measuring between thrusting, so instantly afterwards as the pusher is switched off. shows that the impetus at thruster switch-off is low plenty for zero-baseline readings to be made shortly after thrust measurings. Since both signals impetus in opposite waies at switch away, this may bespeak that assembly distortion during warmer application and in operation of a discharge is slightly different. This is sensible given that the anode radiates much more heat in the way of the thrust balance assembly further downstream of the cathode during operation than the warmer entirely.

Target Biasing

One concern was that bear downing of the mark could ensue in interaction between the plasma and the mark as a consequence of electrostatic forces moving upon the surface. To guarantee the mark was non being influenced by the plasma in which it is immersed, the pendulum mark was biased +/- 30V, electrically floated and straight grounded during high current and low current operation for the T5 ( 3.2A, 0.8A ) and T6 ( 30A, 5A ) cathodes. The thrust measuring system showed no mark of an addition or lessening in the comparative push measuring at the several current degrees. The mark was so left electrically drifting for all predating measurings to guarantee that the mark was non actively involved in pulling an negatron or ion current from the discharge.

Initial Testing

Accommodation Coefficient

As portion of initial testing, a preliminary probe was made into the consequence of elastic atom hits with the mark. We have to see that the push force, Fm, measured by the balance in relation to the alteration in atom speed, I”v, is given by

. ( 6 )

Since propellent atoms will bounce from the mark as they collide with some kinetic energy, the existent transferred impulse to the thrust balance, Fm, will be greater than the impulse imparted on the pusher assembly, FT. The grade of this thrust overestimate will depend on the nature of the physical particle/target interaction. If atoms undergo elastic mirrorlike kick from the mark with preservation of impulse, the thrust force with regard to the measured force bears the relation

. ( 7 )

If all propellent atoms are reflected diffusely a separate rectification must be used for the end point normal force constituent on the mark for a diffuse distribution of flinching propellent atoms. Assuming a cosine distribution of N figure of atoms where N0 cos I? equals the figure of atoms per unit solid angle at any angle of contemplation I? the attendant force moving on the mark is relative to cos I? . The attendant push can be calculated for a cosine distribution by incorporating over the entire scope of contemplation. This constituent may be expressed as a fraction of the measured push due to contemplation by spliting by the entire figure of atoms.

( 8 )

( 9 )

In our instance the grade of diffuse contemplation can merely be estimated by theoretical comparings or direct push measurings which define the adjustment coefficient and so the restriction of the measuring technique. In this subdivision we make a basic analytical appraisal of the theoretical push production to compare with the measured push in order to find a preliminary adjustment coefficient. A full description of the cathodes used in this experiment can be found in mention [ 1 ] . 3D Navier-Stokes continuum calculations have shown the upstream force per unit area in cathodes such as the T6 to be between 1000-2000Pa in a continuum government [ 21 ] . The cathode opening can be assumed to move as a conventional constrictor, which is just given the opening diameter of the T5 cathode ( 0.25mm ) used here is much smaller than the interior dispenser cross-section ( 1mm ) , therefore the cross subdivision is 16 times smaller. During operation with argon the upstream force per unit area varied between 100mbar to 445mbar at flowrates between 0.1mgs-1 and 1mgs-1. For Xe and argon the critical force per unit area ratio is ~0.49 and given that cathode internal force per unit area, even with low mass flowrate, is far above ambient, the premise of clogged flow in the opening of the cathode is sensible. Assuming inviscid flow the gas speed through the opening will be sonic, equal to the thermic speed and a map of the gas temperature [ 22 ] ,

, ( 10 )

where, vor is the opening flow speed, I? is the ratio of specific heats, R is the specific gas invariable and T is the gas temperature. As a simple estimation, presuming a unvarying speed profile across the opening, thrust generated as a consequence of force per unit area and impulse push at the opening issue is given by

, ( 11 )

where pex is the orifice issue force per unit area, pam is the ambient chamber force per unit area and Aor is the orifice country. In this instance pam is at least 5 orders of magnitude less than pex and can be neglected. Assuming that all atoms behave like an ideal gas, the gas force per unit area at the cathode issue can be evaluated from the equation of province,

, ( 12 )

where N is the atom denseness and K is Boltzmann ‘s invariable. The thrust part at the opening issue will therefore dwell of constituents of impulse and force per unit area push by neutrals at the opening issue given by

. ( 13 )

shows the mensural values of push made with the pendulum for Xe and Ar. The theoretical push is calculated based on ( 13 ) for the T5 cathode for assorted mass flowrates. The adjustment coefficient ( measured thrust/theoretically calculated push ) with regard to mass flowrate is shown diagrammatically in. It should be noted that boundary effects will besides act upon the flow government and no effort has been made to formalize the theoretical push anticipations at this clip. It must besides be stressed that this adjustment coefficient represents a comparing to the theoretically calculated value instead than a comparing to direct measurings as a means to give a preliminary estimation of mistake. Ideally this would be done by comparing to direct push measurings.

Table Measured values of push compared to the theoretically deliberate values of push

Gas

Flowrate

[ mg/s ]

Push measured

[ manganese ]

Theoretical sum push [ manganese ]

Accommodation coefficient [ Measured/ theoretical push ]

Cold

Xenon

( 298K )

0.717

0.216

0.2

1.079

1.263

0.35

0.353

0.99

1.585

0.427

0.443

0.963

Cold

Argon

( 298K )

0.2

0.141

0.12

1.17

0.6

0.391

0.361

1.082

1

0.577

0.602

0.958

Hot

Xenon

( 1500K )

0.936

0.146

0.515

0.284

0.533

0.092

0.293

0.313

0.261

0.048

0.144

0.332

Hot

Argon

( 1500K )

0.25

0.194

0.272

0.712

0.5

0.365

0.545

0.668

1

0.631

1.091

0.577

The mean standard divergence of repetition cold gas push measurings was 24.5AµN over the range 0-577AµN.Comparison of the theoretically predicted push to existent measured values gives some penetration into the effects of elastic hits with the mark and besides the divergency of the plume. If all atoms collide inelastically with the mark the adjustment factor would be 1, nevertheless in world the adjustment factor should be greater than 1 due to atoms which undergo elastic hits and kick from the mark, nevertheless this is merely true at lower flowrates. An adjustment factor & lt ; 1 at higher flowrates may propose that the plume expands at greater divergency angles with increasing flowrate ; this is sensible given the issue force per unit area will increase as in ( 13 ) .

The T5 cathode, when runing on Ar operates at higher internal force per unit areas and receives a greater proportion of its push from the force per unit area constituent ( ~35 % for Ar, ~22 % for xenon cold gas ) . The gas speed through the opening for Ar and Xe is likely to be similar for each gas ( given I? ) and changeless at increasing flowrate due to the flow choking through the opening. For the same mass flowrate Ar will hold a higher atom denseness and therefore issue force per unit area than Xe, given the lower atomic mass, which may increase divergency. This is a sensible account as to why the adjustment coefficient shows a steeper gradient for Ar than Xe and is by and large lower for Ar than Xe with increasing mass flowrate.

The heated gas adjustment coefficient for Xe and Ar is systematically less than 1. This may be due to the abode clip of the propellent within the cathode organic structure being deficient for flow to make thermic equilibrium with the cathode walls, therefore theoretical push computation based on the cathode wall temperature is much excessively high. The cold gas push measurings are more utile since we can state with good certainty that the gas temperature is ~ 298K, therefore we can do sensible estimates of the theoretical push. Although the measured push does worsen at higher flowrates most likely due to divergence, following the adjustment coefficient back to the intercept should give a value with little divergency losingss since as mass flow attacks zero, so does the issue force per unit area, yet the flow speed is changeless in the clogged flow status. At this point we can gauge that the impulse push is over estimated by 22.9 % for Ar and 17.4 % for Xe by the pendulum mark measuring system nevertheless we can non in this instance history for increasing divergency losingss at higher mass flowrates and issue force per unit areas. The other possibility is that the theoretical push computation merely outputs excessively higher push. Such comparings require either direct push measuring comparings or farther measurings which investigate mark geometry.

Figure Accommodation coefficients with regard to mass flowrate for hot and cold Xe and Ar

Hollow Cathode Discharge Thrust Measurements

Initial push measurings were performed for the T5 cathode runing on Ar in the presence of a discharge. Thrust measurings as an norm of repetition measurings are in. All information is shown in its natural signifier with no rectification due to the antecedently estimated adjustment factor ~ 20 % . The standard divergence of measurings in the scope of 0-2.46mN was 0.135mN as a consequence of both determinate and undetermined beginnings of mistake chiefly arising from quiver induced divergence from the roughing pump. In order to contradict the consequence of thermic impetus the measuring procedure was performed as discussed in subdivision 3.4, by taking the comparative detector reading during pusher firing instantly followed by measuring of the current nothing place.

Figure Thrust degrees for the T5FO cathode at assorted current conditions

Specific urge is a factor used to depict propulsive public presentation. Specific impulse, Isp, is given by

( 14 )

in the units of seconds, where vex is the effectual issue speed of the propellent to give the mensural push. Results show near monotone dependance discharge current with increasing Isp below 0.4mgs-1, peculiarly for the 3.2A and 1.6A current conditions with a less marked addition at 0.8A.

Figure Specific impulse vs. mass flow rate for assorted currents and mass flowrates in the T5 cathode

Transient Measurements

The push balance besides allowed transeunt measuring for Xe and Ar as shown in. In this instance mass flow rate was set and consecutive changed between 1mgs-1 and 5mgs-1 cold gas flow ( no discharge ) with Ar and xenon. Absolute oscillations are seen to fluctuate about the clip averaged measuring chiefly due to beginnings of external noise as antecedently described. The damped natural frequence of the thrust balance in this constellation is 1.25Hz therefore the clip to passage between push degrees is non related to the clip invariable of the system. This is because the propellent lines are of important volume in comparing to the cathode and act as a plenum, hence there is a lag-time ( 8-9seconds ) associated with stabilisation of the upstream force per unit area as mass flowrate is changed.

Figure Transient detector informations ( 0.41mN/mm ) made with measure alterations in mass flowrate for cold gas

Decision

The rule, design and initial testing of a comparatively simple yet flexible indirect pendulum push balance has been presented. The work is an indispensable tool in the on-going development of electric microthrusters, leting comparative push measurings and other public presentation parametric quantities to be measured under a broad scope of operating conditions. Preliminary estimations of the adjustment coefficient for cold gas conditions suggest an overestimation of push by 20 % at low flowrates due to the elastic hit of atoms with the mark, nevertheless this besides indicates that there may be extra divergency losingss at higher flowrates due to higher operating force per unit areas. Comparisons with direct push measurings are required calculate an accurate adjustment factor and quantify uncertainnesss in the absolute push measurings. Initial consequences from the T5 hollow cathode pusher have shown the measuring systems ability to qualify both the steady province and transeunt public presentation of a hollow cathode microthruster.