Scholarly article on topic 'Virtual metrology frame technique for improving dynamic performance of a small size machine tool'

Virtual metrology frame technique for improving dynamic performance of a small size machine tool Academic research paper on "Mechanical engineering"

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Abstract of research paper on Mechanical engineering, author of scientific article — Jonathan Abir, Stefano Longo, Paul Morantz, Paul Shore

Abstract This paper presents a novel concept, a virtual metrology frame, for enhancing the dynamic performance of a machine tool with a flexible structural frame. The dynamic properties of a machine are directly affected by the stiffness of its frame, and its reference system; thus, by having an unstressed metrology frame, superior dynamic capabilities can be achieved. The developed concept does not require physical components associated with metrology frame; hence it is ideal for machine tools with requirements for small footprint and ultra-precision performance. The concept relies on an accelerometer based dynamic displacement feedback technique, where the accelerometer is used as a precision frame displacement sensor. The concept does not require a complex controller, and was realized in an off-the-shelf CNC controller. The concept was demonstrated on a linear motion system, a simplified version of a compact size CNC machine, and its servo bandwidth and dynamic stiffness were improved by 36% and 70% respectively, which are the key parameters for improving the machining accuracy.

Academic research paper on topic "Virtual metrology frame technique for improving dynamic performance of a small size machine tool"

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Precision Engineering xxx (2016) xxx-xxx

§ 1 18S1 Contents lists available at ScienceDirect

V I I Precision Engineering

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ELSEVIER journal homepagewww.elsevier.com/locate/precision

Virtual metrology frame technique for improving dynamic performance of a small size machine tool

Jonathan Abira*, Stefano Longob, Paul Morantza, Paul Shoreac

a The Precision Engineering Institute, School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield, MK43 0AL, UK b The Centre for Automotive Engineering and Technology, Cranfield University, Cranfield, MK43 0AL, UK c The National Physical Laboratory, Teddington, TW11 0LW, UK

ARTICLE INFO

ABSTRACT

Article history:

Received 9 August 2016

Received in revised form 17 October 2016

Accepted 7 November 2016

Available online xxx

Keywords:

Acceleration based displacement Flexible frame PID controller Sensitivity function Virtual metrology frame

This paper presents a novel concept, a virtual metrology frame, for enhancing the dynamic performance of a machine tool with a flexible structural frame. The dynamic properties of a machine are directly affected by the stiffness of its frame, and its reference system; thus, by having an unstressed metrology frame, superior dynamic capabilities can be achieved. The developed concept does not require physical components associated with metrology frame; hence it is ideal for machine tools with requirements for small footprint and ultra-precision performance. The concept relies on an accelerometer based dynamic displacement feedback technique, where the accelerometer is used as a precision frame displacement sensor. The concept does not require a complex controller, and was realized in an off-the-shelf CNC controller. The concept was demonstrated on a linear motion system, a simplified version of a compact size CNC machine, and its servo bandwidth and dynamic stiffness were improved by 36% and 70% respectively, which are the key parameters for improving the machining accuracy.

© 2016 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license

(http://creativecommons.org/licenses/by/4.0/).

1. Introduction

Reduction of machining error enables higher dimension accuracy in Computerized Numerical Control (CNC) machines. The significant fraction (90%) of machining error is cause by dynamic positioning error in a machine tool servo [1]; this positioning error results in a contour error on the machined part. In ProportionalIntegral-Derivative (PID) type servo controllers, the most common controller used in industrial CNCs [2], tracking error contributes to error in position; tracking error occurs in a closed-loop control system due to an inability to follow rapidly varying position commands [3]. This error can be reduced by increasing feedback gains and servo bandwidth [4-7]; however, the amounts by which these parameters can be increased are limited by sensitivity to measurement noise and mechanical resonance excitation, respectively [4,7,8].

There are three important types of mechanical resonances that can limit machine dynamics [9]: actuator flexibility, guiding system flexibility, and frame flexibility. Actuator flexibility occurs when

* Corresponding author. E-mail addresses: j.h.abir@cranfleld.ac.uk (J. Abir), s.longo@cranfleld.ac.uk (S. Longo), P.Morantz@cranfleld.ac.uk (P. Morantz), paul.shore@npl.co.uk (p. Shore).

there is compliance between the motor and the load, typically where there is a gear in the system. Guiding system flexibility occurs when the driving force is not coincident with the center of gravity and stiffness is limited. Frame flexibility occurs due to servo-reaction forces causing dynamic deformation, resulting in frame resonance excitation i.e. a stressed frame. The problem of servo control limited by mechanical resonance in machine tools is well studied in literature, most references focus on actuator flexibility; few papers describe the problem of flexible frames [10-13].

Notch filtering is commonly used in industry to attenuate mechanical resonances in the control signal [14]; however this reduces the drives' bandwidths, limiting its application in improving machine tool performance [15].

Pre-filtering trajectory techniques can be used to reduce machine structure excitation [16], however their implementation is challenging [8]. Impulse/jerk decoupling technology [17,18] utilizes a mechanical low-pass filter, which adds another degree of freedom to the system. An expansion to this technology, which is often used in the lithographic industry, is a dual stage motion system [19,20]. In this concept a fine short stroke motor with ultra-precision positioning is mounted to a coarse driving mechanism; however, this concept is complex and requires additional sensors, actuators, volume, and cost.

Acceleration feedback was used for damping structural resonances [16,21,22]; by adding acceleration feedback to the position

http://dx.doi.org/10.1016/j.precisioneng.2016.11.002

0141-6359/© 2016 The Authors. Published by Elsevier Inc. This is an open access article underthe CC BY license (http://creativecommons.org/licenses/by/4XI/).

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control loop, as an inner feedback loop, the disturbance force experiences a virtually larger mass, improving the process sensitivity [23]. Process dynamics, controller calculation delay, and accelerometer roll-off result in instability. Reducing the acceleration loop gain for higher frequencies counteract this instability; however to maintain position loop stability margins the acceleration loop requires a high bandwidth [21,24]. Controllers in industrial feed drives commonly use position feedback only, since other movement variables are not available [16,21], this limits acceleration feedback realization in commercial CNC. Acceleration can be measured directly by an accelerometer, calculated from the second derivative of position measurements, or by observer techniques. Using accelerometer provides absolute acceleration measurement; however, both rigid body and structural vibrations are mixed in the signal. Differentiation of position signal produces quantization noise [25], passing this signal through filters limits the closed loop control performance [26]. Acceleration observers offers lower noise content than differentiation, however these are limited by parameter dependence [26,27].

The position signal in a linear motion system is typically provided by a linear encoder which is generally located at the machine frame; hence, deformation in flexible elements anywhere between the encoder scale and the point to be controlled is not compensated [28]. In [29] an accelerometer located close to the Tool Center Point (TCP) is used. The TCP position is estimated by a state space observer, and used as position feedback, improving dynamic behavior; however, this implementation is non-trivial due to the non-collocated control [22]. In [8] a model-based control is used to estimate the machine frame deformation with respect to the TCP, where no additional drive is required; however, frequency and damping of structural modes may vary over time, and also as a function of machine configuration [16].

This paper addresses the problem of frame flexibility, which is often neglected in the design stage, thus leading to unexpected problems during the prototype test phase [10]. A virtual metrology frame technique was developed to achieve high dynamic performance as though the machine has a separate stiff metrology frame, by measuring machine frame displacement using an acceleration sensor. The developed technique was implemented on a commercial PID controller, while other structural resonance compensation techniques cannot be applied in commercial CNC systems [30].

2. Virtual metrology frame concept

The Virtual Metrology Frame (VMF) concept was designed to improve the performance of a machine with flexible frame phenomena that limit performance. The dynamic properties of the machine are directly affected by the stiffness of the frame and its reference system. By utilizing an unstressed metrology frame, superior dynamic capabilities can be achieved [10,19,31,32].

The VMF concept is realized (Fig. 1a) by distinguishing between the carriage position, with respect to the stressed frame Xc, and the frame displacement due to flexible modes Xf; hence, an unperturbed position signal Xvmf can be obtained in the presence of these frame flexible modes. A typical PID controller structure C can be applied using the VMF (Fig. 1b). A reference position signal Xset is fed into the controller C, with output u, the control signal. The plant P is the system to be controlled, it has input u, and output Xc measured by a position sensor, typically a linear encoder; however, in the VMF concept a second output to the plant Xf, the frame displacement, is added to Xc within the controller; thus, the controlled position signal Xvmf is the sum of the position measurement signals, enabling attenuation of the machine frame resonance.

In a system with a flexible frame, there are two possible plant Transfer Functions (TFs): Pc (1) and Pvmf (2) depending on the car-

Fig. 1. The Virtual Metrology Frame (VMF) concept.

Fig. 2. Plant Transfer Functions (TFs). Pc and Pvmf are the plant TFs where the position signal is Xc and Xvmf respectively.

riage position signalXc andXvmf respectively, where mc and mf are the carriage and the frame mass respectively and kf is the frame stiffness. The Pc consists of two modes: a carriage rigid body mode and a flexible frame mode. In the Pvmf, there is only carriage rigid body mode. In a system with an infinite frame stiffness, the flexible frame mode is negligible and Pc ^ Pvmf. The Bode diagram of the plant TFs is shown in Fig. 2; the Pvmf is a double integrator type while Pc is Antiresonance-Resonance type [9]. In practice, Pc may con-

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Fig. 3. Bode plot of displacement estimator Hest and ideal double integrator Hdbl. JM and JP are the magnitude and phase errors of the estimator.

tain multiple flexible frame modes while Pvmf may not completely attenuate these modes.

Pc (S) =

Pvmf (S) =

Xc (S) = _^_

F (s) mcs2 mjs2 + kf

Xvmf(s) 1

The VMF concept does not require physical components associated with a metrology frame, hence it is ideal for a compact size machine tool with the requirement for small footprint [33,34] and ultra-precision performance [35,36]. Furthermore, this concept is very suitable for industrial deployment as it allows implementation within an off-the-shelf controller without modification. The concept was simply implemented in a PID controller, which is the most common controller found in industrial machine tools [2,5,37].

The VMF concept relies on real-time measurement of the frame displacement - "frame displacement sensor" (Fig. 1b). Common techniques for precision displacement sensors require a fixed reference system [38,39], i.e. a secondary physical frame. A unique frame displacement measurement technique using accelerometers was developed [40], which offers a superior solution without a secondary physical frame. The accelerometer measures the acceleration of a point without a fixed reference system; thus, by double integration the frame displacement Xf can be estimated relative to its "unstressed state" (Fig. 1a).

The VMF concept uses an accelerometer to measure frame displacement, thus it differs from acceleration feedback techniques as no special inner loop, i.e. acceleration feedback, is required; hence no special technique is required to tune the controller gains. Furthermore, the technique offers wideband frame resonances attenuation, and there is no "targeted" resonance to attenuate as in other common techniques [14].

The frame displacement signal Xf and the carriage position signal Xc are complementary (Fig. 1a)

Xc = Xvmf +Xf.

The controller update rate is significantly lower than the encoder and frame displacement sensor update rates, thus the position feedback register (in the controller) is simply their sum according to (3); and no special sensors fusion technique is required.

2.1. Frame displacement sensor

Double integration of a signal is a straightforward task; however, integrating noise leads to an output that has a Root Mean Square (RMS) value that increases over integration time [41], which occurs even in the absence of accelerometer motion. A heave filter Hest (4) was used as a displacement estimator [42,43], which is a combination of a High Pass Filter (HPF) and double integrator. A pole-zero placement filter was added to correct phase delay as ifthe estimator is an ideal double integrator Hjbl (5).

Hest =

(s2 + 2Ç-Mc-s + ®c2)2 S-p

Hdbl = "2 >

where s is the Laplace variable, £ the damping coefficient, the cut-off frequency of the filter, p and z are the pole-zero pair where z<p<0 [40], and K is an additional gain parameter. Fig. 3 shows a comparison of Bode plots of the estimator and double integrator. Below the cut-off frequency (<rnc) the estimator acts as an HPF, while above the cut-off frequency (>rnc) it acts as a double integrator.

Real-time implementation of acceleration based displacement measurement in a control system has two main conflicting requirements: small phase error JP and low displacement noise Ja; thus, it is rarely reported [44], especially for long term (>10 s) and accurate (<0.1 |im) measurements [45].

The estimator was constrained to measure only dynamic displacement of the machine frame that occurs at flexible resonances frequencies (>®c); hence it optimize: the displacement noise Ja, phase error JP, and magnitude error JM resulting from double integration of, and HPF application to, the acceleration signal [40].

3. Experimental setup

The | 4 is a small size CNC machine with 6 axes which was conceived in 2008 by Cranfield University [36]. In order to reduce the

Fig. 4. The |x4 machine.

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Fig. 5. A simplified linear motion module.

Fig. 6. Flexible frame mode shape. Unstressed frame (a), and a flexible frame mode shape (b).

machine footprint and ease manufacturing, the design was based on modules with common design and simple interfaces; thus, the machine motion axes were split into two near identical modules. Each module consists of at least one rotary, and one linear motions made by direct drive motors (Fig. 4).

A simplified linear motion module [46], which represents one of the machine motion modules, consisting of: frame, air-bearings, linear motor, linear encoder, and carriage, was used for this study (Fig. 5). The driving force and the position sensor were not applied at the center of gravity but on the "master side", thus, the carriage movement is dependent on the high stiffness of the air-bearings, which suppresses motion in an undesired direction. The carriage and the frame mass are mc = 17 kg and mf = 24 kg respectively.

A software-based machine controller (Aerotech A3200) was used to control the motion system with a linear digital amplifier (Aerotech Ndrive ML). The digital servo amplifier has a current loop update rate of 50 |is, servo loop update rate of 125 |is, and a tunable PID digital control loop. The frame displacement sensor was connected to the auxiliary analogue input of the drive amplifier. Its update rate was equivalent to the servo update rate. Summation of the encoder and frame displacement signals was implemented in the controller (Fig. 1b).

A linear encoder (Renishaw RELM 20U) with 20 |im pitch was used as the position feedback sensor. Using a controller multiplication factor of 65536, the position resolution was 0.30 nm, and sub divisional error was nominally <±30 nm [47].

System identification techniques [48,49] showed flexible frame characteristics, where a relative movement between the frame and the carriage is measured by the encoder (Fig. 6). These appear as resonances in the plant Frequency Response Function (FRF) as the encoder scale is mounted to the machine frame, while its read-head is mounted to the carriage (Fig. 5).

To maintain co-located control, the accelerometer was fixed to the frame as close as possible to the encoder scale (Fig. 7), and

Fig. 7. Accelerometer fixed as closed as possible to the encoder scale.

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Fig. 8. Frame displacement sensor block diagram.

aligned with respect to the encoder. The accelerometer location was chosen based on the machine modal analysis [48,49].

3.1. Frame displacement sensor

The frame displacement sensor was realized using a combination of: an accelerometer, signal conditioner, and an xPC target machine (Fig. 8).

A triaxial ceramic shear Integrated Electronic Piezoelectric (IEPE) general purpose accelerometer (PCB 356A025) was used to determine the frame displacement. The accelerometer sensitivity was 25 mV/g. IEPE accelerometers are the appropriate sensor for low amplitude vibration measurements due to their: low noise; wide dynamic, frequency, and temperature range; high sensitivity; and availability in small sizes [50]. A low noise signal conditioner was used to power the IEPE accelerometer, and to decouple the acceleration signal (PCB 482C15). The signal conditioner has a typical phase distortion of ±1°.

The xPC target machine (Speedgoat performance) was used for Digital Signal Processing (DSP) with an update rate of 18 |is. It contains 16 bit Analogue Digital Converter (ADC) and Digital to Analogue Converter (DAC). The conversion time for the ADC and DAC is 5 | s and 3 | s, respectively. The xPC target machine is optimized for MathWorks® SIMULINK® and xPC Target™.

The frame displacement sensor has time delay xfjs. It is composed of accelerometer delay xacc, DSP delay xDSP, and estimator delay xest. The accelerometer delay is frequency dependent, and specified by the accelerometer manufacturer. The DSP delay is due to the time it takes to read and process the accelerometer signal, and therefore dependent on the computing power available. The frame displacement sensor delay Xfds, which is the sum of its components delays, must be smaller than the controller update rate xservo, to allow resonance attenuation:

Fig. 9. Frame displacement sensor time delay. Accelerometer delay tacc, DSP delay tdsp, estimator delay test, frame displacement sensor delay tfds, and the controller update rate tservo.

Bi-quad filter were designed to terminate the PID differentiating action and reduce multiple high-frequency resonances.

Hpid(s) = f [(TdS +1)•(s + 1)],

Hp (s) =

s2 + 2Çlp •(2nf, ) .s + (2f )

Hbq(s) =

s2 + 2^n -(2f •s + (2nfn)2 s2 +2?d .(2f ) •s + (2^fd)2 .

where K is the proportional gain and T and TD are the integral and derivative time respectively; fip and fp are the LPF damping ratio and frequency respectively; fn and f are the Bi-quad filter zero and pole frequencies respectively, and £n and are their damping ratios.

The Phase Margin (PM) and Gain Margin (GM) Gm relate servo drive stability to control design parameters. In order to maintain machine tool stability the PM and GM values should be [51,52]:

0m >45°, Gm > 6dB.

(10) (11)

A Matlab control system tuning toolbox was used to tune and optimise the controller by using nonsmooth optimisation algorithms [53], and computes the norm using the algorithm detailed in [54]. The PM and GM tuning goals were set according to (10) and (11) respectively. The first gain crossover of the open loop FRF fs, and overshoot Mp constraints were set according to (12) and (13), respectively.

10Hz < fs < 100Hz,

(12) (13)

°-5 • tservo > tfds = I^acc + test + %SPI-

The frame displacement sensor delay, based on an optimized displacement estimator, is shown in Fig. 9.

The frame displacement sensor was validated against a laser interferometer (Renishaw ML10 gold standard) [40] and capacitance sensors (Lion precision PX405HC) [42,43]. Displacement noise was ct < 30 nm over 10 min of measurement [40].

4. Proportional-Integral-Derivative controller tuning

The controller was composed of a PID filter, second order Low Pass Filter (LPF), and a Bi-quad filter, as in (7)-(9). The LPF and

5. Results

This section shows the experimental results validating the VMF concept, and comparison ofthe optimized controller with and without the VMF concept.

5.1. Validation ofthe virtual metrology frame concept

The VMF concept was realized by connecting the xPC target machine output Xf to the machine controller. Summation of the two signals in the controller was set to the maximum update rate - the servo update rate of 125 |is.

Using sinusoidal excitation the machine plant Transfer Function (TF) was measured. Comparison of the plant TFs with and without

Mp < 25%.

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Fig. 10. Plant Transfer Functions (TFs) with and without the Virtual Metrology Frame (VMF) concept.

Table 1

Optimized PID controllers parameters. K, TI, and TD are the PID proportional gain, integral time and derivative time respectively. flp and £lp are the LPF cut-off frequency and damping parameters, respectively. Mp is the closed loop overshoot and fs is the open loop crossover frequency. 0m, Gm, and Ms are the phase, gain, and vector margin respectively.

K Ti [s] Td[s] flp [Hz] tip fs [Hz] Mp [%] 0m [deg] Gm[dB] Ms [dB]

System without VMF 3.28.104 0.08 0.04 189.67 0.67 22.20 18.14 59.75 15.95 2.75

System with VMF 5.61.104 0.10 0.03 166.63 0.85 30.19 16.71 62.33 18.81 2.59

the VMF is shown in Fig. 10. A significant magnitude reduction of 12 dB in the frame's first resonance can be observed. Furthermore, the VMF has been shown to be a wide bandwidth resonance attenuation technique. The second resonance shows no attenuation by this setup as its mode shape produced a non-collinear displacement to the measured axis; this second resonance causes a relative movement between the encoder read-head and scale which is measured as displacement and appears as a resonance, while the frame displacement sensor measures only collinear displacement to the measured axis.

5.2. Optimized controller

A PID controller (Section 4) was designed and optimized based on curve fitted plant TFs with and without the VMF (Fig. 9); a 'peak picking' curve fitting method [55] was used to curve fit the measured plant TFs. A Bi-quad filter (9) was used to attenuate the machine second resonance, with the following parameters: = 0.0175, £d = 0.2156, and fn = fd = 198 Hz. The optimization results of the PID filter gains are shown in Table 1. To aid in the comparison between the two optimized controllers, a vector margin stability criteria Ms was used [56]. Because the vector margin is a single margin parameter, it removes all the ambiguities in assessing stability using gain and phase margins.

Implementing the VMF in the control system improved the proportional and derivative gains by 70% and 38% respectively, while the overshoot was reduced, and the stability margin remains almost the same (Fig. 11), thus, the open loop crossover frequency, i.e. servo bandwidth, was improved by 36%. The open loop Nyquist and Bode plots with and without the VMF concept are shown in Figs. 11 and 12.

Three sensitivity functions determine the feedback error of the system: sensitivity function S(s), complementary sensitivity function T(s), and process sensitivity function PS(s) [57]: these functions represent the ability of the feedback system to reject disturbances acting on the output of the system; the system response to the reference in case Xset = 1; and the machine dynamic compliance

Fig. 11. Open loop Nyquist plot with and without the Virtual Metrology Frame (VMF) concept.

Fig. 12. Open loop Bode plot with and without the Virtual Metrology Frame (VMF) concept.

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Frequency (Hz) Frequency (Hz)

Fig. 13. Sensitivity functions. S(s), T(s), and PS-1 (s) are the machine sensitivity, complementary sensitivity and inverse process sensitivity functions respectively. Svmf (s), Tvmf (s), and PS-1 vmf (s) are the machine with the virtual metrology frame sensitivity, complementary sensitivity and inverse process sensitivity functions respectively.

respectively. The sensitivity functions with and without the VMF are shown in Fig. 13. When the VMF was applied, the machine dynamic stiffness (inverse process sensitivity) and sensitivity function were shown to be equivalent to the improved proportional gain.

6. Conclusions

The Virtual Metrology Frame is a servo plant compensation technique to address frame flexibility. It offers a solution of enhancing machine performance utilizing a virtual metrology system, without a physical metrology frame. The developed concept is insensitive to plant frequency changes in contrast with common techniques.

The VMF concept is based on a technique to measure frame displacement without having a fixed reference system. Using bespoke signal processing, an accelerometer was used as a precision positioning (displacement) sensor.

Implementing the VMF concept on the linear motion system, the metrology loop showed superior rigidity; this was due to the virtual separation of the metrology system and the force system. The VMF was designed to measure encoder scale displacement that occurs due to frame flexible modes only; whilst floor vibrations and rigid body modes, which appear in the acceleration signal, are attenuated significantly by the HPF. The VMF concept could be implemented in a multi-axes system, such as CNC machine, for each motion axis independently; hence measuring the position of the carriage (or the tool) relative to the "unstressed state" of the reference frame. The effectiveness of the VMF concept in a multi-axes machine should be addressed in a future study. Furthermore, this technique could also be implemented in rotary axes by using angular accelerometers.

The concept can be implemented in any feedback controller, requiring only a summing of two position signals: encoder and frame displacement; thus it very suitable for industrial deployment. It can be used to improve the performance of an existing machine with minimal retro-fit to the machine. In the future, the Speedgoat controller could be replaced seamlessly by dedicated lower cost electronics, such as a field-programmable gate array

(FPGA), and would be connected to the auxiliary analogue input in the controller.

The concept was demonstrated on a simplified motion module of a commercial CNC machine equipped with a PID controller. The flexible frame resonances present in the position signal were attenuated significantly, but not completely. This can be explained by the fact that frame vibrations cause forced vibrations of the carriage; however, a significant improvement to the servo bandwidth and dynamic stiffness were shown, which are key parameters for improving the machining accuracy. These improvements were implemented with no affect upon the system stability.

Acknowledgment

This work was supported by the UK EPSRC under grant EP/I033491/1 and the Centre for Innovative Manufacturing in Ultra-Precision.J. Abir acknowledges the McKeown Precision Engineering and Nanotechnology foundation at Cranfield University, and B'nai B'rith Leo Baeck (London) for their financial support. The authors would like to thank James Norman for comments that improved the manuscript.

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