A voice coil based electromagnetic system for calibration of a sub-micronewton torsional thrust stand

(1)

A voice coil based electromagnetic system for calibration of a sub-micronewton torsional thrust stand

Jiang Kai Lam

^a

, Seong Chun Koay

^a

, Chie Haw Lim

^b

, Kean How Cheah

^c,^⇑

aSchool of Engineering, Taylor’s University, Malaysia

bFaculty of Engineering, University of Nottingham Malaysia Campus, Malaysia

cSchool of Engineering and Physical Sciences, Heriot-Watt University Malaysia, Malaysia

a r t i c l e i n f o

Article history:

Received 26 June 2018

Received in revised form 2 August 2018 Accepted 10 September 2018 Available online 11 September 2018

Keywords:

Electromagnetic calibration Sub-micronewton Torsional thrust stand Micropropulsion

a b s t r a c t

This paper presents the development of an alternative electromagnetic calibration system. Utilising commercially available voice coils and permanent magnets, the proposed system is able to generate linear, repeatable, and consistent steady-state calibration forces at over four orders of magnitude (30–23,000mN). It is also capable of producing calibration impulse bits in the range of 12–668mNs.

The maximum uncertainty errors of the calibrator are evaluated as 18.48% and 11.38% for steady-state and impulsive forces calibration, respectively. Its performance is compared to other existing electromagnetic calibration techniques. Capability of the system is then demonstrated in calibrating a sub- micronewton torsional thrust stand.

1. Introduction

Nanosatellites (<10 kg) are finding new applications in various areas[1]. They are simpler and require shorter development time.

Thus, they are inherently cost effective and ideal for demonstrating new and innovative ideas in outer space. In a nanosatellite, one of the desired sub-systems is micropropulsion system. The inclusion of microthrusters into nanosatellites is beneficial for improved operations in attitude control, station keeping, drag compensation, and orbital transfer [2]. Over the years, various microthrusters have been developed with the help of microelectromechanical systems (MEMS)[2–5].

Throughout the development campaign, the performance of a microthruster needs to be evaluated accurately. Since the forces produced by microthrusters are extremely low (in the order of micronewton), resolving them requires measuring instruments of high sensitivity. Pendulum thrust stand is widely regarded as the efficient and suitable method for measuring the micronewton forces[6]. Essentially, it is a mass-spring-damper system in which a structure holding the microthruster is supported by a torsional spring. The structure oscillates as forces are applied. By analysing the oscillation, the forces produced by microthrusters can be determined. There are three main configurations for pendulum thrust

stand, i.e. hanging[7–9], inverted[10,11], and torsional[12–14], each with their own advantages and limitations.

Calibration is a necessary process for any measuring instrument. It establishes the relationship between the thrust stand response in terms of displacement and the forces applied. There are two categories of calibration techniques, namely contact and non-contact. Contact calibration techniques include string-pulley- weight system [7], impact hammer [15], and impact pendulum [16]. Although they are the earliest methods used in calibration and easy to set up, the calibration force is comparatively larger than the non-contact techniques [17], in the order of sub- micronewton and above. In addition, the contact nature of the techniques tends to induce zero drift on the thrust stand.

Non-contact calibration systems include gas dynamic[17,18], electrostatic (ES) [15,19–21], and electromagnetic (EM) [13,22,23]. Gas dynamic calibrators are reliable in producing calibration forces between nanonewton and sub-micronewton [18].

In contrast, ES calibrators are able to provide a wider range of calibration forces, typically between hundreds of nanonewton and thousands of micronewton [21]. Nevertheless, this versatile calibration technique requires high voltage for generation of sufficiently large calibration force. This results in the need of more costly equipment, e.g. high voltage amplifier. For EM calibrators, the reported calibration forces are sub-micronewton and above.

They exhibit good consistency and repeatability. Besides, EM calibrators are easier to be implemented compared to gas dynamic and ES. They mostly consist of an electromagnet (solenoid) coupled

⇑ Corresponding author.

E-mail address:[email protected](K.H. Cheah).

Contents lists available atScienceDirect

Measurement

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / m e a s u r e m e n t

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with permanent magnet, current-carrying copper wire, or metal conductor. Unlike ES calibration system which is well established, EM calibration for torsional thrust stand is a relatively new idea. It can be further improved in terms of performance, as well as simpli- fied for its implementation.

While the fundamental working principles remain straightfor- ward and simple, effective yet commercially available components can be implemented in order to innovate EM as an alternative technique for thrust stand calibration. In this study, we explore the fea- sibility of using commercially available voice coils as an alternative EM calibration system for a sub-micronewton torsional thrust stand. Due to the nature of its construction, voice coil acts as a small and light weight electromagnet that can be utilised as part of the calibration system. Combining with a coin-sized permanent magnet, this newly developed calibration system is very compact.

Compact calibration system is beneficial for integration with small testing facilities, in particular the vacuum chamber, in which the setup cost is proportional to the overall size.

The selected voice coil is first tested with different permanent magnets to investigate the characteristics of the EM calibration force generated. The calibration system is then implemented onto the thrust stand to showcase its performance as a calibrator for both steady-state and impulse forces. Lastly, the uncertainty error of the calibrator is evaluated and its performance is compared with other EM calibrators.

2. Torsional thrust stand setup

A thrust stand based on the working principle of torsional pendulum is designed and built in existing study. Generally, torsional pendulum thrust stand has good balance of high measuring and low vibrational noise sensitivities[6]. The dynamic motion of a torsional pendulum is described as:

J€hþkh_þkh¼Ftrt ð1Þ

where J is the moment of inertia about the rotational axis, PleaseCheckis the angular displacement of the pendulum,kis the damping coefficient, k is the torsional elastic constant and Ft is the externally applied force at a distance ofrtfrom the rotational axis.

Our thrust stand consists of a 60 cm torsional arm made of U- shaped aluminium beam. It is light weight (210 g) yet sufficiently stiff to support external loadings mounted onto it. The torsional arm was supported by a single-ended flexural pivot (F-20, C- Flex) that acts as torsional spring. The pivot was clamped and connected to a heavy rectangular aluminium base (3 kg). Four anti- vibration mounts (126–3904, RS Pro) were installed to enhance its stability against external vibration. A strong permanent magnet was placed in close proximity under the torsional arm to induce an eddy current brake in order to dampen the oscillation of the arm. A high resolution (0.5mm) laser displacement sensor (HL-G103-S-J, Panasonic) was positioned at one end of the torsional arm to measure its deflection. The EM calibrator was installed at the other end of the arm. The fluctuation of surrounding temperature and ambi- ent air could affect the thrust stand response. The thrust stand was set up in an air-conditioned laboratory and enclosed with a trans- parent acrylic casing, where the temperature remains stable. The voice coil releases heat when excessively high current is applied.

The electrical current was capped at 0.4 A and the voice coil was mounted externally. These precautionary steps minimise if not eliminate any significant heat transfer through the torsional arm that may cause undesired motion. The CAD drawing and actual setup of the thrust stand are shown in Fig. 1(a) and (b), respectively.

3. Electromagnetic calibration system

3.1. Voice coil and permanent magnet as electromagnetic calibrator

The EM calibration system used in this study consists of a voice coil and a permanent magnet, as shown inFig. 2. Voice coil is commercially available in different sizes and commonly used in loud- speakers. It is essentially a solenoid, whereby an electromagnetic field can be generated when electrical current passes through the coil. Electromagnetic field strength of the voice coil,B, is governed by Ampere’s Law:

B¼

l

0nI ð2Þ

where

l

0is the permeability of vacuum,nis the number of turns of wire per unit length, andIis the amount of electrical current flow through the coils.

In this study, electrical current of various levels were supplied to the voice coil in order to generate electromagnetic field of different strengths. The voice coil was then engaged to a permanent magnet to induce interactions between their magnetic fields. They were arranged in a way such that they repel each other. As a result,

(a)

(b)

Displacement sensor Current sensor

Torsional arm Casing

EM calibrator assembly

Base

Pivot EM calibrator

Anti-vibration mounts Base

Torsional arm

Displacement sensor

Pivot and clamp

Magnetic damper

Fig. 1.(a): Thrust stand drawing and (b): Actual setup for existing study.

Voice coil

Magnet

Fig. 2.Voice coils of various diameters and two different permanent magnets.

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it produces the electromagnetic force needed for the calibration of the thrust stand.

3.2. Electromagnetic force measurement using weighing balance

The amount of electromagnetic force generated by the EM calibration system was first measured experimentally. After a few tri- als, a 25.5 mm diameter voice coil was selected as it provides a wide range of calibration force. In addition, a voice coil of this size is compact thus easy to be set up. Two different types of permanent magnet, i.e. a ferrite disk magnet (weaker magnetic field strength, 100 Gauss) and a neodymium disk magnet (stronger magnetic field strength, 2000 Gauss) were used (see Fig. 3). By using magnets of different levels of magnetic field strength, the range of calibration forces becomes wider. As such, existing torsional thrust stand can be calibrated to characterize different types of micropropulsion systems.

The setup for electromagnetic force measurement is schemati- cally shown inFig. 4. A weighing balance (HR250AZ, A&D Weigh- ing) with a resolution of 0.1 mg (0.981mN) was used to measure the electromagnetic force. The permanent magnet was fixed onto the weighing balance while the voice coil was fixed externally to a mechanical stage (PT3/M, Thorlabs) for position and engagement adjustment. The permanent magnet was placed on top of a long plastic rod instead of directly on the weighing pan. This is to avoid any magnetic interaction that could affect the measurement. A power supply (MP303-3, Meguro) was used to supply electrical current to the voice coil. A current sensor (CTSR1-P, LEM) with a resolution of 10 mA and a digital oscilloscope (DS1102E, Rigol) were used to measure the amount of electrical current that flows through the coil. Electrical current ranges from 0.01 A to 0.4 A were supplied and the corresponding readings from the weighing balance were recorded.

The effect of engagement distance between the voice coil and the magnet on the stability of electromagnetic force has also been studied. This is to identify the acceptable range of engagement distance for generation of consistent and repeatable electromagnetic force. For this purpose, the current was fixed at three distinct levels (0.1 A, 0.25 A and 0.4 A) which represents low, mid and high range of forces, respectively. The engagement distance was varied from 3 mm to 3 mm using the mechanical stage. The actual setup is shown inFig. 5.

3.3. Implementation onto torsional thrust stand

After the force measurement, the EM calibrator was installed onto the thrust stand as shown inFig. 6. The permanent magnet was fixed to the other end of the torsional arm as opposed to the

end with the laser displacement sensor. The voice coil was placed externally and its positioning and engagement to the magnet were adjusted using the mechanical stage. The electromagnetic forces were then applied to the torsional arm.

Steady-state force and impulsive force were applied for the calibration. For steady-state force calibration, the operational proce- dure is similar to the description inSection 3.2, where the same power supply was used to provide electrical current of various levels through the voice coil. As for impulsive force calibration, the power supply was replaced with a function generator (FG- 8202, Dagatron) for generating impulse bits of various amplitudes and pulse widths. As the calibration forces were applied, the

Coil height : 13 mm Overall height :

35 mm

Diameter:

25.5 mm

Side View Top View

Neodymium Ferrite Diameter:

13 mm

Diameter:

9 mm

Thickness: 3 mm (both)

Fig. 3.Specifications of voice coil (left) and magnets (right) used.

Top View

Magnet Voice coil

Power Supply

Oscilloscope Current sensor

Weighing balance

Fig. 4. Schematics of EM force measurement setup and arrangement of voice coil and magnet.

Mechanical stage

Voice coil

Magnet

Fig. 5.Actual experimental setup for EM force measurement. Inset picture shows a close-up view of the EM calibrator on the weighing balance.

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corresponding deflections of the arm were recorded using the linear displacement sensor.

4. Results and discussion

4.1. Electromagnetic force measurement

Using the setup shown inFig. 5, the force generated can be measured.Fig. 7shows the electromagnetic forces generated by the EM calibration system at varying electrical current levels. Overall, the neodymium magnet-based system generates much higher force than the counterpart of ferrite magnet. This is predominantly due to the difference in their magnetic field strengths. Neodymium magnet is well known for its strong magnetism. Thus, given the same amount of electrical current through the voice coil, the magnet with stronger field strength repels harder, thus the force generated is higher, and vice versa.

It is noted that the relationship between the electromagnetic force generated and the electrical current supplied is linear and directly proportional. This is in agreement with previous finding [22]which proposed the electromagnetic force produced, FEM, is governed by:

FEM¼BmN

p

^r^c^I ^ð3Þ

whereBmis magnetic flux density at the coil location,Nis the number of coil turns,rcis the radius of coil andIis the electrical current passes through the coil. The equation indicates thatFEMis directly proportional to the amount ofIsupplied.Nandrcare fixed as only the 25.5 mm voice coil was used.Bmis related to the engagement distance between voice coil and magnet as its magnitude is affected by the location of the two components, which in turns affectFEM.

Such relationship indicates that the electromagnetic force generated using the proposed EM calibrator is predictable and reliable as long as theBmstays relatively constant. This is crucial for its

applications onto the torsional thrust stand later on. The combina- tion of the two magnets has an extended range of electromagnetic forces that covers four orders of magnitude, i.e. 30–2200mN and 920–23,000mN, for ferrite magnet based and neodymium magnet based calibrator, respectively.

With the same setup as above, the change in electromagnetic force with the engagement distance for both ferrite and neodymium based calibrators were determined as shown inFig. 8. Note that 0 mm distance (initial position) represents that the coiled edge of voice coil and the upper surface of magnet are in the same plane (seeFig. 4). For example, 1 mm adjustment means that the magnet is 1 mm apart from the voice coil edge while 1 mm adjustment means that the magnet is 1 mm into the voice coil edge.

An apparent trend observed is that the electromagnetic force decreases regardless of the current level and the polarity of the engagement distance (magnet separated from or into the voice coil). This indicates that if the magnet is too far away (both positive and negative distances) from the coiled edge of voice coil, theBm

becomes less uniform, which causes a reduction in magnetic field interaction between the voice coil and the magnet. As a result, the force generated also decreases, as outlined in Eq.(3).

Further investigation reveals that for all current levels tested, the percentage difference in deviation of forces generated exceeds 10% at engagement distances beyond ±2 mm, which can cause negative impacts on the repeatability and consistency of the system.

This serves as a guideline for installing the EM calibrator onto the thrust stand, where the engagement distance has been kept within ±2 mm for reproducible and consistent calibration force generation.

4.2. Steady-state force calibration

The motion of torsional thrust stand can be characterized using linear displacement sensor. When an external constant force,Fc, is applied to the thrust stand atrt, its motion is described as:

Fcrt¼kDh ð4Þ

whereDhis the steady state angular displacement of the thrust stand caused by the force.

Considering the very small magnitude of rotation, angular displacement of the thrust stand can be approximated using linear displacement as:

D^x¼rLDSh ð5Þ

whererLDSis the distance between the linear displacement sensor (LDS) and the rotational axis.

After the EM calibrator was installed as shown inFig. 6, different levels of steady-state (constant) electromagnetic forces were generated and applied to the torsional arm.Fig. 9shows the typical torsional arm response to the force applied.

Voice coil

Magnet Torsional arm

EM calibrator LDS

Thrust Stand (Top View)

Mechanical stage

Fig. 6.Schematic (left) and actual (right) installation of EM calibrator onto the thrust stand.

R² = 0.9982 R² = 0.9994

0 5000 10000 15000 20000 25000

0.00 0.10 0.20 0.30 0.40

Force, μN

Current, A Ferrite

Neodymium Linear (Ferrite) Linear (Neodymium)

Fig. 7.Electromagnetic force generated by ferrite and neodymium magnets at varying electrical currents.

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As observed, the torsional arm reaches a steady deflection of 1819mm when 0.1 A of current is supplied to the EM calibrator.

Damped oscillation induced by the passive magnetic damping mechanism can be observed at2 s,7 s,11 s, and16 s. This shows that the damper installed is effective. As the force is removed, the displaced arm returned to its initial position. It is noteworthy that the difference in origin before and after the calibration force applied is a mere 0.4

l

m. This indicates that the system is stable with negligible zero drift.

Combining Eqs.(4) and (5), the relationship between constant calibration force,F_cal, and linear displacement measured by LDS, D^xLDS, can be expressed as:

Fcal¼ k

rtrLDSDxLDS ð6Þ

Based on Eq. (6), a calibration curve of linear displacement against the calibration force was plotted, as shown inFig. 10. By using the combined ferrite and neodymium magnet-based EM calibrator, the thrust stand is calibrated to resolve steady-state forces for four orders of magnitude i.e. 30–16,000mN. The range of calibration force is sufficient for most micropropulsion systems with the exception for some high-thrust solid propellant micropropulsion systems which could produce thrust force as high as mN and above. The overlapping region between EM calibrator using ferrite and neodymium magnets is magnified and presented as inset graph inFig. 10. The deviation between them is well within 5% of tolerance which implies a good transition of calibration force.

4.3. Impulsive force calibration

Maintaining the same setup as inFig. 6, calibration for impulsive force measurement was done by applying various impulse bits to the thrust stand. To produce impulse bits, the EM calibrator was connected to the function generator with squared input signals. By

adjusting the signal amplitude (amount of electrical current) and the pulse time, different levels of calibration impulse bit can be produced.

In order to obtain a linear relationship between thrust stand response and calibration impulse bit applied, the pulse time should be much shorter than the natural period of the thrust stand, 1/fnat

[19]. Ideally, the pulse time should be within one-tenth of the natural period[24]. Hence, the natural period of existing thrust stand was determined by using the Fourier transform of the displacement readings acquired under free motion for 1 min. Thefnatwas evaluated as 1.8 Hz (peak of the curve) from power spectral density curve as shown inFig. 11. This implies that the pulse time should not exceed 55 ms to ensure linearity between thrust stand response and calibration impulse bit.

When an impulsive force,Ibit, is applied to the torsional thrust stand, the maximum angular displacement,hmax, is given by:

hmax¼rtIbit

J

x

^o ^ð7Þ

wherex^ois the natural frequency of the torsional thrust stand.

Re-arranging Eq. (7) with the consideration of small angle approximation, the impulsive force can be related to linear displacement as:

Ibit¼ J

x

^o

rtrLDSD^xmax ð8Þ

An example of the squared signal produced using the function generator for the EM calibrator is shown inFig. 12, where the pulse width is adjusted to 48 ms and the voice coil output signal amplitude is 0.18 V. The current sensor used has a sensitivity of 1.2 V/A, so the corresponding current reading is 0.15 A. FromFig. 7, 0.15 A produces 833mN and 12,200mN of force for ferrite based and neodymium based calibrator, respectively. The resultant calibration impulse bit can be determined by multiplying the pulse width with the forces, which gives 40mNs for ferrite based and 585mNs for neodymium based calibrator.

By adjusting the function generator, the range of calibration impulse bits produced is 12–668mNs. Subsequently, they were applied to the thrust stand and the corresponding response (maximum deflection range,D^xmax) was recorded using the laser displacement sensor. Fig. 13 shows the typical thrust stand response to a calibration impulse bit of 585mNs. The same impulse bit was repeated three times within a duration of 25 s. It can be observed that the maximum deflection range obtained (663mm in this case) is very consistent with a standard deviation of 1.57

l

m (0.24% of the measured value). This shows that the control 0

500 1000 1500 2000 2500

-3 -2 -1 0 1 2 3

Force, μN

Distance, mm

0 5000 10000 15000 20000 25000 30000 35000

-3 -2 -1 0 1 2 3

Force, μN

Distance, mm

0.1A 0.25A 0.4A

Fig. 8.Electromagnetic force generated by ferrite (left) and neodymium (right) magnets corresponding to varying engagement distances at three current levels.

-3000 -2000 -1000 0 1000 2000

0 5 10 15 20 25

Displacement, μm

Time, s

Fig. 9.Displacement of the torsional arm due to the force generated by the neodymium magnet-based EM calibrator at 0.1 A. Pointing arrow indicates the steady-state deflection.

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of the pulses is precise and the signal itself is of good quality, resulting in consistent impulse bit generation.

Each maximum deflection range corresponding to the applied impulse bit is plotted to produce the calibration curve for impulsive force measurement, as shown inFig. 14. The curve has shown good linearity. Furthermore, the calibration impulse bits from ferrite based and neodymium-based EM calibrator overlap and the difference is within 5%, as shown in the inset graph. The good agreement in the overlapping region allows the thrust stand to be calibrated using ferrite-based EM calibrator at the lower range of impulse bits and switch to neodymium-based EM calibrator from medium range of impulse bits onwards until maximum

allowable calibration impulse bits. After this calibration, the thrust stand can be used to measure impulsive forces from pulsed mode micropropulsion systems, e.g. pulsed plasma thruster[25].

4.4. Uncertainty error analysis

Uncertainty in the EM calibrator system stems from the resolution of the instrumentations used. Aggregating the component errors contributed by each instrument, the uncertainty error in EM calibration can be calculated as:

dF

F ¼ð1þbÞ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dI

I

2

þ dFc

Fc

2

þ dx x

2

þ dtc

tc 2

þ dD^x D^x

2

þðDFchÞ² s

ð9Þ bis included as additional consideration for other unpredictable sources of error. It also accounts for the inaccuracy in estimating the known sources of error as summarized inTable 1.

Electrical current,I, produced by the power supply used in this study has a resolution of 1 mA. The EM calibration forces,Fc, were measured using a weighing balance of 0.1 mg resolution which is equivalent to 0.981mN. The engagement distance,x, between the permanent magnet and voice coil was adjusted using a mechanical stage with 10mm resolution. The squared wave signal or pulse width,tc, was controlled on the function generator with an identi- cal rise and fall time of 0.1 ms. The linear displacement sensor that R² = 0.9993

0 500 1000 1500 2000 2500 3000 3500 4000

0 5000 10000 15000 20000 25000 30000 35000

Force, μN Ferrite

Neodymium Linear (Combined)

0 200 400 600 800 1000

0 2000 4000

Linear (Ferrite) Linear (Neodymium)

Fig. 10.Calibration curve for steady-state force measurement.

-80 -60 -40 -20 0

0 5 10 15 20 25

Power, dB

Frequency, Hz f_nat= 1.8 Hz

Fig. 11.Power spectral density of the free motion displacement signal determined using Fourier transform. The peak is 1.8 Hz.

-0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25

0.0 0.1 0.2 0.3 0.4 0.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Output voltage, V

Time, s

Input voltage, V

Funcon generator input Voice coil output

Fig. 12.Squared input signal from the function generator (48 ms pulse width) and the corresponding voice coil output signal.

-400 -300 -200 -100 0 100 200 300 400

0 5 10 15 20 25

Time, s

Fig. 13.Thrust stand response to impulse bit produced at 0.15 A and 48 ms pulse width using neodymium-based EM calibrator. Pointing arrow indicates the maximum deflection range.

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was used to measure the deflection,Dx, of the torsional arm has a resolution of 0.5mm.

The characteristics of existing EM calibrator also contribute to the uncertainty error. They are the non-equivalence between two permanent magnets (up to 5%) and non-linearity of EM forces (up to 2%), as shown inFig. 10. These factors are accounted for and consolidated into the variable ofDFch.

Considering the known sources of error and a conservative value of 20% forb, uncertainty errors were computed. For steady- state calibration, the error is 18.48% for the minimum calibration force of 30mN. A closer examination reveals that the power supply contributes the most for this considerably high error. In this case, 1 mA of resolution is rather low as the electrical power drew by the voice coil to generate the smallest calibration force is 10 mA.

Nevertheless, the error has been reduced to 7.80% as the magnitude of calibration force increases. For impulsive calibration, the error is in the range of 7.86–11.38%. The order of error in current study is comparable with those from previous studies [26,27]

which ranges from 8.8% to 15%.

4.5. Performance comparison with other EM calibrators

Performance of existing EM calibrator has been compared with other EM calibration systems reported previously, as summarized inTable 2. Our voice coil-based calibration system exhibits a comparable capability in generating both steady state and impulsive calibration forces. The calibration system has extended the steady state calibration force to four(4)orders (from 10 s to 10000 s of micronewton) of magnitude. This is attributed to the use of two magnets of different magnetic strengths in the system. The

extended range of calibration force is advantageous for the torsional thrust stand to characterize the performance of a wider range of micropropulsion systems.

Apart from extended range of forces, existing system is more compact than previous EM calibration systems[22,23]. The coin- sized magnets used in this study weigh less than 10 g, which can be considered as insignificant to affect the dynamics of torsional arm. Too much additional weight mounted to the arm can cause balance and sensitivity issues. The use of voice coils has reduced the overall footprint of the system. In addition, the double-layer coiling architecture of voice coil has facilitated the production of a more uniform and stronger magnetic field.

5. Conclusion

In conclusion, the proposed EM calibrator has been demonstrated as a feasible alternative thrust stand calibration technique.

It offers the advantages of easy to set up, requires no sophisticated equipment, cost effective and compact in size. With the combina- tion of commercially available voice coils and various small magnets, steady-state calibration force over four orders of magnitude

R² = 0.9957

0 100 200 300 400 500 600 700 800

0 200 400 600 800 1000 1200 1400

Maximum range, μm

Impulse bit, μNs

Ferrite

Neodymium Linear (Combined)

0 50 100 150

0 50 100

Linear (Ferrite) Linear (Neodymium)

Fig. 14.Calibration curve for impulsive force measurement.

Table 1

Known source of error for uncertainty analysis.

Equipment Resolution Steady state Impulsive

Min Max Min Max

Current,I(mA) Power supply 1 10 400 40 170

Calibration force,Fc(mN) Weighing balance 0.981 30.41 23669.57 244.27 13931.18

Engagement distance,x(mm) Mechanical stage 10 2000 2000 2000 2000

Pulse width,tc(ms) Function generator 0.2 N/A N/A 15 48

Deflection,Dx(mm) LDS 0.5 10.0 4166.0 11.5 797.0

Non-equivalence between two magnets (5%) 0.05 0.05

Non-linearity of EM forces (2%) 0.02 0.02

Uncertainty Error withoutb(%) 15.40 6.50 9.48 6.55

Uncertainty Error withb= 0.2 (%) 18.47 7.80 11.38 7.86

Table 2

Performance comparison of different EM calibration systems.

Type Force (mN) Impulse (mNs) References

Coil and magnet 300–2000 10–1000 [22]

Electromagnet and copper wire 15.73–291.5 14.15–566.1 [23]

Coil and metal conductor 1–100 – [13]

This study 30–23,000 12–668 –

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ranging from 30 to 23,000mN was produced. Using a pulsed signal, impulsive calibration force in the range of 12–668mNs was achieved. The system exhibits good repeatability and linearity with a maximum uncertainty of 18.47% and 11.38% for steady-state and impulsive calibrations, respectively. Installing this EM calibrator system to a torsional thrust stand provides a diagnostic tool that is capable to evaluate the performance of a variety of micropropulsion systems.

Acknowledgement

Funding: This work was supported by the Taylor’s Research Grant Scheme by Taylor’s University, Malaysia [grant number TRGS/MFS/1/2016/SOE/001].

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