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(a) Undamped oscillations, (b) magnetic damper, and (c) damped oscillations with increasing damping.
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The paper describes the design, calibration, and characterization of a thrust stand capable of nano-Newton resolution. A low uncertainty calibration method is proposed and demonstrated. A passive eddy current based damper, which is non-contact and vacuum compatible, is employed. Signal analysis techniques are used to perform noise characterization,...
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... a dynamical system is of critical importance to minimize noise and reduce the time required to reach a sta- ble deflection of the balance arm. In the absence of damping, the balance arm vibrates for a significant duration ( Fig. 2(a)), with ambient air providing only minimal damping, apart from structural/thermal dissipation at the torsion springs. To make the system damp more rapidly, a magnetic damper was in- troduced based on eddy current damping. A similar concept for damping of torsion balance oscillations was demonstrated by Polzin et al. 10 Their thrust ...
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... an ulti- mate resolution of 50 μN, 3 orders of magnitude lower than that aimed by the μNTS. For the μNTS damper, a cylindri- cal copper block (2 1 2 dia. × 1 height) of high conductivity was mounted on the balance arm, with a neodymium perma- nent magnet (1/2 dia. × 1 height, B surface = 6619 Gauss 11 ) placed under it in close proximity (O(mm), Fig. 2(b)). As the beam oscillates, the relative motion of the copper block and the magnet induces eddy currents in the block, which gener- ate their own magnetic field counter to the applied magnetic field. The applied and induced magnetic fields interact to pro- duce a retarding force proportional to the relative motion, es- sentially ...
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... the applied magnetic field. The applied and induced magnetic fields interact to pro- duce a retarding force proportional to the relative motion, es- sentially providing damping. The amount of damping can be controlled by controlling the gap between the copper block and the permanent magnet (0.5-3 mm), and close-to-critical damping can be achieved (Fig. 2(c)). Magnetic damping has inherent advantages of being a non-contact and vacuum com- patible (as opposed to a viscous damper). It also does not re- quire a power source and an active closed loop control (as op- posed to an electrostatic/electromagnetic damper). This setup provides similar damping characteristics as a viscous damper using ...
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... gives an estimate of I θ = 0.0385 kg-m 2 . The natural frequency for the undamped system is observed to be 2.240 rad/s from the time-series of Figure 2(a). These values, in conjunction with Eq. (8), give an estimate for k θ of around 0.0034 N-m/deg, close to the stip- ulated value of 0.0032 (two springs in parallel, each with k θ = 0.0016 N-m/deg) and within the 10% error margin quoted by the manufacturer. ...
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... this method to the data extracted from Fig. 2(a), we get an average value of k θ = 0.003379 N-m/deg based on several values of n, demonstrating that neglecting air damping results in a nominal error of approximately 0.7%. The damp- ing ratio in this case is found to be around 0.0028, justifying the undamped ...
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... The optical rotation readout of the thrust stand is a new type of interferometer, 2.5 cm in diameter, which responds only to rotation, not translation, and has a rotational resolution of 20 µrad [11]. The lowest thrust measured by Soni and Roy used the Applied Physics Research Group micro-Newton thrust stand is 1.3 µN with an uncertainty of ±20% [12]. Zhao et al built a torsion pendulum system using high-precision and large-range laser displacement sensors. ...
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... The torsional oscillation of the hybrid HTS bearing is studied when it works at different FCHs and air gaps L2. The torsional oscillation is analyzed by using a log decrement method [29], and the sequence shown in figure 11 is used to calculate dynamic parameters of the torsional oscillation such as period T, damping ratio ζ, natural frequency ωn, spring constant k and damping coefficient c. Finally, these calculated values related to the torsional oscillation in the conditions of FCH 8mm and 12mm are listed in table 2. Figure 11. ...
Characterized by very low rotational drag, applications of high temperature superconductor (HTS) bearings have been expanded in some high precision instruments. We developed a sensitive magnetic suspension stand based on an Evershed-type hybrid HTS bearing to measure the micro newton level thrust. The hybrid HTS bearing is to use the strong attractive force of a permanent magnet (PM) biased bearing to support main loading in the bearing, while the instability in the PM biased bearing was compensated by the magnetic stability from an HTS bearing. Compared to the single PM/HTS bearing, the hybrid HTS bearing is intended not only to support larger load and but also to suppress the rotation loss and levitation drift. Loading capacity, loss and damping torque were explored at different design parameters such as bearing gaps L1, L2, field cooling height (FCH) of bulk HTSs. Spin down testing suggested that the loss of the hybrid HTS bearing can be reduced by raising the HTS bearing gap L2 or reducing the field cooling height. The hybrid HTS bearing showed a typical oscillation behavior in the extreme low frequency, and torsional pendulum testing suggested that the spring constant k of the hybrid HTS bearing can be as low as 36.39 μN·m/°. A micro-thrust stand based on the hybrid HTS bearing was established to test an electrospray thruster in the vacuum chamber, and the measurement result of 26.61 μN presents the ability of micro-thrust stand to achieve μN level testing.
... These balances can be made exceptionally sensitive with a noise range between sub-mN down to mid-nN. [8][9][10][11][12] A less commonly used type is a freely rotating system with no restoring force due to gravity or a spring. 13,14 Except for the freely rotating system, all these balances are harmonic, damped oscillators,φ ...
... These improvements lead to a noise level in the lower single-digit nN range, which is one or more magnitudes lower than other torsion balances while still supporting experiments up to 2 kg of mass. [8][9][10][11][12]16,17 Sections II-IV will describe the design of the balance in more detail, followed by the performance. ...
... The damping of an oscillation can be calculated using the logarithmic decrement. 12 This method needs accurate values at two peaks of the oscillation. If the damping ratio increases, it becomes more and more difficult to determine the position of the second peak, distorting the calculated damping ratio. ...
Here, we present a novel torsion balance with a torsional spring that can reach a resolution in the nano-Newton range while allowing for a total experimental weight of 2 kg. The balance uses an off-the-shelf electromagnetic actuator, which was calibrated. The oscillation of the balance is damped using an adaptable eddy-current brake to fine-tune the damping factor. Experiments and electronics are controlled and powered through four coaxial liquid contacts. The balance is shown to be highly linear between 0.01 and 300 μN. After an automated post-processing, the noise of a measurement was 1.0 nN, and an applied force of 10 nN had a calculated error of 11.9%.
... One of the most typical techniques used for thrust measurement is the concept of the pendulum balance. In its simplest form, a pendulum thrust balance can be based on a hanging pendulum [40,56], an inverted pendulum [57][58][59] or be a torsional balance [60][61][62][63][64][65]. There are also more complicated implementations of this, such as the stand for vertically oriented thrust measurements system described in [67]. ...
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... Figure 25 compares the performance of the two configurations with respect to force and voltage. Another suitable approach not usually mentioned is the logarithmic decrement method, by which the natural frequency and moment of inertia of the balance are used to assess spring rate in accordance with equation 55 [83], [106]. As no additional force producing system is required for reference, the spring rate can be directly determined with fewer sources of uncertainty. ...
Light-matter interactions are fundamental to many technologies used today. They are complex, non-linear processes sensitive to the properties of the source, material, mechanisms, and environment in which they interact. In order to control a process, its key features must be measurable and characterised. To date, most efforts in doing so follow either empirical or theoretical approaches, requiring existing or potential users of laser technology to invest significant time and money in their attempted use. In this work a novel diagnostics platform is theorised for the study of light-matter interactions by assessing energy transfer within a process relative to certain performance attributes e.g. ablation efficiency (kg/W), coupling momentum efficiency (N.s/W) and kinetic energy ratio (plume energy over pulse energy) with the aim of producing widely relatable results which significantly lessen the need for heavily empirical or theoretical work. The missing element of the diagnostic platform, a torsion balance, capable of measuring impulsive forces and mass loss, was designed, constructed, and calibrated to the ultra precision standards required to measure nano-scale forces including a force and mass-loss resolution of nN and µg respectively. The tool was then used to characterise the behaviour of some ‘generic’ pulsed nano-second light matter inactions with varying source parameters such as total energy input (58.6 mJ to 468.8 mJ), repetition rate (5 kHz to 40 kHz), temporal pulse shape (up to 500 ns duration and 50 kW peak power), and materials (aluminium, silicon, and PVC), as well different environments (air and vacuum) and processing strategies (scanning and single point drilling). Three dimensional processing maps were then produced using the torsion balance, laser, environment, and material data to represent the quantitative and qualitative nature of results. When convoluted or stitched together, the maps uniquely enable the optimisation of process specific performance with respect to laser, material, and environmental parameters, to which the torsion balance data was very sensitive (ablation efficiencies from 10-7 to 10 13 kg/W, coupling momentum efficiency from 10-4 to 10-9 N/W and kinetic energy ratios from 10-5 to 437 %). Regions of high or low performance, could be easily identified using the qualitative map elements, whilst being relatable to quantitative data such as total energy, repetition rate and pulse shape, which are in turn relatable to theory using conventional methods. A single data set, for example, ablation efficiency plotted against total number of pulses and repetition rate for a given pulse shape, material, and environment, could be captured and processed in 16 minutes. In this work the ability to generically optimise a laser based process or technology very easily, quickly, and efficiently was demonstrated. For the first time, this has enabled high parameter resolution, light-matter-environmental parameter sweeps to be produced within hours, instead of months or years. This is important because it could revolutionize the way light-matter interactions are approached and completely change where time, energy and financial resources are spent in academia and industry. The end result could be the production of a well-defined process map for any given laser, material, and environment.
... One of the most typical techniques used for thrust measurement involves the concept of the pendulum. In its simplest form, a pendulum thrust balance can be based on a hanging pendulum (Charles et al., 2016;Wong et al., 2012), an inverted pendulum (Haag, 1991;Kokal and Celik, 2017;Asakawa et al., 2020), or be a torsional balance (Ziemer, 2001;Zhou et al., 2013;Soni and Roy, 2013;Little and Jugroot, 2019;Tang et al., 2011;Zhang et al., 2017). There are also more complicated implementations of this, such as the stand for vertically oriented thrust measurement system described in Moeller and Polzin (2010). ...
Reliable measurements of thrust from systems to be flown on satellites are essential to ensure repeatable maneuvering capability of small nanosatellites. Thrusters can be used to vary spacecraft orientation, detumbling, and orbit change. Tests have been conducted in a low-pressure vacuum system using a cold gas prototype thruster and two independently calibrated methods: a four-point pendulum with a laser interferometer displacement sensor and a load cell, both of which have measurement capabilities from tens of micronewtons to tens of millinewtons. The agreement is very good, lending confidence in both methods. The advantages and disadvantages of both methods will be discussed. They include absolute accuracy, low thrust accuracy, temporal resolution, simplicity of operation, cost, and sensitivity to vibrations generated by laboratory equipment such as pumps, fans, bumps, and human movement.
... Torsional-pendulum thrust stands have often been used to measure the steady-state thrust or impulse bit. [21][22][23][24] In a recent study, a magnetically levitated thrust stand has been proposed, and its proof of concept was demonstrated. 25 ...
This paper presents the development of a thrust stand to enable direct measurement of thrust and specific impulse for a CubeSat propulsion system during firing. The thrust stand is an inverted pendulum and incorporates a mass balance for direct in situ mass measurement. The proposed calibration procedure allows precise performance characterization and achieves a resolution of 80 μN thrust and 0.01 g mass loss, by taking into account the drift of the thrust-stand zero caused by propellant consumption. The performance of a water micro-resistojet propulsion system for CubeSats was directly characterized as a proof of concept of the thrust stand. Continuous profiles of thrust, specific impulse, and mass consumption were acquired under various conditions in a single firing test. A thrust from 1 mN to 10 mN and a specific impulse from 45 s to 100 s with a maximum measurement uncertainty of ±15.3% were measured for the throat Reynolds number in the range 100–400.
... The damping of a torsion balance is normally calculated using the logarithmic decrement 9 . In this case this is not feasible, because there is no clear second oscillation visible. ...
An innovative concept for propellantless space propulsion, originally proposed by Woodward using the so-called 'Mach Effect' and supported by peer-reviewed, experimental evidence, was investigated at TU Dresden in the framework of the SpaceDrive Project. The Mach-Effect-Thruster is a pre-stressed, multilayer piezoelectric stack driven by a sinusoidal voltage at an optimal frequency producing propellantless thrust, orders of magnitude more efficient than a photon rocket. As a follow-up to the previous test campaign, in which no significant thrust could be systematically detected above the noise range of the torsion balance in vacuum, the tests are repeated on a torsion balance with increased sensitivity. Equipped with two A-20 C-Flex pivot bearings, the background noise measured as a standard deviation of the beam displacement was reduced from 200 nN to around 5 nN. In this recent experimental campaign, Woodward's original equipment, which includes a Carvin audio amplifier and a 1:4 transformer in the driving electronics, was used. A force signal qualitatively similar to the effect described by Woodward could be observed. The switching on-off transients of 30 nN were, however, were significantly smaller than the force previously claimed at a similar voltage. Furthermore, the force signal was also observed when orienting the MET's theoretical 'thrust' vector parallel to the balance beam which should show zero thrust. In addition to these experiments, the mutual influence of the driving electronics and its piezoelectric load is carefully analyzed in a range of 24 to 48 kHz, the balance is fully characterized with a purely resistive dummy load, and is calibrated along its three principal axes using a voice coil. Finally, this paper presents an investigation of the thermal, vibration and electromagnetic artefacts that can occur in such torsion balance measurements.
