Misalignment Errors Research Articles

Analytical calculation of the tooth surface contact stress of spur gear pairs with misalignment errors in multiple degrees of freedom

Misalignment errors (MEs) in multiple degrees of freedom (multi-DOFs) along gear pair axis are unavoidable under actual working conditions. These MEs lead to changes in tooth surface contact stress (TSCS) and make its accurate calculation complicated and difficult. Unlike the traditional methods of obtaining TSCS with MEs in multi-DOFs via experimental tests, finite element methods (FEMs) or coefficient methods following international standards, a new analytical calculation model is proposed in this paper. The profile equation of a gear pair with MEs in multi-DOFs is first established. Then, a new profile equation for meshing pairs of gear and pinion slices with non-standard shapes that are coplanar with the line of action of the meshing force is obtained. On this basis, the correctness of meshing force transmission, as well as the accuracy and speed of calculation, can be guaranteed with the contact analysis of gear pairs. Finally, the magnitude and distribution of the TSCS of a gear pair with MEs in multi-DOFs are obtained. Compared with the results of a FEM model, the new model can accurately and rapidly calculate the TSCS of a gear pair with MEs in multi-DOFs.

In situ absolute surface metrology for a 600 mm aperture interferometer

In this paper, a novel absolute measurement method based on multisurface interference is proposed for a 600 mm aperture interferometer. Compared to existing 3-flat testing methods, which generally require two transmission flats and one reflection flat, our method does not require the replacement of the transmission flat with another flat and rotation of the reflection flat about the z-axis of the 600 mm aperture interferometer. Only by rotating an auxiliary parallel flat about the z-axis can we realize the in situ absolute measurement of the reference flat surface error of the interferometer without losing the medium-frequency error. The principle of absolute measurement based on the proposed novel method is discussed. The various sources of measurement error are analyzed, including the number of rotations, the rotation angle error and the pixel misalignment error of the coordinate axis. Based on these analysis results, an auxiliary rotating device for a large aperture flat is designed. Repeatability experiments were carried out on the 600 mm aperture interferometer produced by Zygo. The experimental results show that the RMS value of the repeatability precision is less than 2 nm.

Twin-field quantum key distribution based on twisted photon

Quantum key distribution (QKD) is a promising application to establish unconditional secure communications by quantum mechanics. However, its widespread application still faces a great challenge, that is, the fundamental linear key-rate constraint called Pirandola-Laurenza-Ottaviani-Banchi (PLOB) bound. Recently, twin-field QKD (TF-QKD) was proposed (Lucamarini et al., 2018 [4]), it overcomes the constraint mentioned above. However, the original TF-QKD is based on the phase-encoding strategy, which requires active alignment. In this paper, we improve the original TF-QKD with the photon orbital angular momentum (OAM), and propose a novel reference frame independent protocol to overcome the reference frame dependence. No more alignment procedure is needed, and the intrinsic misalignment errors are eliminated by utilizing the rotation-invariance of OAM photons. Besides, the security performance is also improved.

Bayesian uncertainty evaluation of stitching interferometry for cylindrical surface

Uncertainty evaluation is one of the most important concepts in metrological characterizations. This paper proposes a method for uncertainty evaluation of measurements of cylindrical surfaces by means of stitching interferometry. The proposed method is based on the Bayesian statistical analysis. The prior deviation for a tested surface is determined by both calculation of standard deviation through multiple measurements of a single sub-aperture and calibration of the optical system error. The probability distribution functions (PDF) of the prior and real misalignment error and measured data of the aperture are derived according to the stitching model. Simulated observations are approximated with the Gibbs Sampler using the Markov Chain Monte Carlo (MCMC) method. Our proposed method is a promising alternative to the ordinary least square technique (LST) with the maximum likelihood estimation (MLE) for obtaining the uncertainty of the misalignment and measurement error in the stitching results. Moreover, it can take the inevitable environment errors into account. The prediction of the uncertainty interval makes our method more attractive in industrial applications.

Compensation Method for Diurnal Variation in Three-Component Magnetic Survey

Considering that diurnal variation interferes with three-component magnetic surveys, which inevitably affects survey accuracy, exploring an interference compensation method of high-precision is particularly desirable. In this paper, a compensation method for diurnal variation is proposed, the procedure of which involves calibrating the magnetometer error and the misalignment error between magnetometer and non-magnetic theodolite. Meanwhile, the theodolite is used to adjust the attitude of the magnetometer to unify the observed diurnal variation into the geographic coordinate system. Thereafter, the feasibility and validity of the proposed method were verified by field experiments. The experimental results show that the average error of each component between the observed value of the proposed method and that of Changchun Geomagnetic station is less than 1.2 nT, which indicates that the proposed method achieves high observation accuracy. The proposed method can make up for the deficiency that traditional methods cannot meet the requirements of high accuracy diurnal variation compensation. With this method, it is possible for us to set up temporary diurnal variation observation station in areas with complex topography and harsh environment to assist aeromagnetic three-component survey.

Wellbore Positional Uncertainty and Correction of Directional Drilling

Wellbore surveying is the interactive process used to obtain wellbore positions according to well trajectory which connects surface coordinates to subsurface coordinates. The measured values such as the measured depth, inclination, and azimuth are used to calculate well paths with a specified reference system. However, errors exist between the true wellbore position and surveyed wellbore position, including depth measurement errors of the drillstring and wireline, misalignment errors, geomagnetic model, and magnetic interference errors. Therefore understanding and evaluating wellbore positional errors is critical for hitting reservoir targets, collision avoidance, and drilling relief wells. In this paper, wellbore positional uncertainty has been reviewed and the application of survey corrections in single and multiple wells has been investigated.

Impact of Intra-Cluster Angular Spread on the Performance of NLoS Millimeter Wave Links With Imperfect Beam Alignment

Beam misalignment is an unavoidable occurrence in millimeter wave (mmWave) wireless communication systems which causes a drop in achievable spectral efficiency (SE) and adversely affects the link-level performance. Spatial parameters of the mmWave propagation channel, especially angle distributions of multi-path components are vital in assessing the loss in achievable capacity due to imperfect beam alignment in such systems. In this paper, we present a tractable approach to quantify the achievable SE of beamformed Non-Line-of-Sight (NLoS) links in mmWave fading channels with intra-cluster angular spread. We derive the expression for achievable SE of a point-to-point mmWave NLoS link after accounting for random beam misalignment errors at the transmitter as well as receiver end. Using analytic approximations, we consider the impact of antenna beam pattern parameters, and use a comprehensive mmWave channel model for performance evaluation. The analysis provides realistic bounds on achievable SE since the intra-cluster angular spread of rays at both ends is taken into account. We provide insights into the interplay between antenna half power beam width, the degree of misalignment, channel fading coefficient, channel coherence parameter and the angular spread of rays to demonstrate the decisive impact of intra-cluster spread on the performance of mmWave point-to-point NLoS links.

Performance of Generalized QAM/FSO Systems With Pointing Misalignment and Phase Error Over Atmospheric Turbulence Channels

This article investigates the performance of free-space optical (FSO) systems using sub-carrier quadrature amplitude modulation (SC-QAM) signaling for broadband terrestrial applications. While previous studies ignored the influence of phase noise, we theoretically analyze and derive closed-form expressions of the system's average bit error rate (ABER) considering the combined effect of pointing misalignment, turbulence-induced fading, and phase error. The log-normal distribution is used to model the atmospheric turbulence in the weak regime while the gamma-gamma distribution is applied for modeling the turbulent atmosphere in the moderate and strong regimes. The phase error, which becomes complicated under the effect of atmospheric turbulence, is modeled by Tikhonov distribution. The numerical results reveal that the influence of the phase error on the system performance is dominant in the weak turbulence and high order modulation while the fading becomes more severe in the moderate-to-strong turbulence regime. The accuracy of analytical results is also validated by Monte-Carlo simulations and a good match can be confirmed.

Error Analysis and Correction of a Downhole Rotating Magnetic Full-Tensor Gradiometer

Compared with ground magnetic measurement and aeromagnetic survey, downhole magnetic measurements can provide more abundant and accurate distribution information of ore deposits. Measurement of the full magnetic tensor gradient affords more information than either traditional magnetic total field or three, orthogonal axes, vector field measurements. Gradient field measurements are less influenced by any time and/or spatial changes of the Earth's magnetic field during the measurement period. CSIRO has developed the world first downhole magnetic full tensor gradiometer and carried out field tests. This gradiometer is based on a rotation of two fluxgate vector field sensors to enable frequency separation of the common mode from the gradient signals. Reposition of the gradiometer about three, nominally orthogonal axes, enables measurement of the full gradient tensor with one pair of fluxgate sensors. This paper describes a method to improve the accuracy of this type of gradiometer. System errors have been analyzed and classified according to the effect of the errors on the measurement accuracy. Major errors include scale factor error of the two fluxgates, misalignment and motion errors of these two sensors relative to the model system, and transformation errors when moving from the sensor to the instrument coordinate frame of reference. Minor errors include errors of finite length measurement parameters, errors associated with ignoring high-order tensors, the deviation of the rotation axis from ideal, and the temperature co-efficient of the fluxgates' signals. We have developed the error models for the major errors and calibrated the full-tensor gradiometer by using the two independent tensor rotation invariants. 1000 simulations with random errors show the root mean squares of relative error are less than 8% after calibration. The calibration technique was applied to field trail measurements made using a gradiometer that was re-oriented multiple times around a fixed point while measuring a known gradient. Applying the calibration method resulted in an improvement of the tensor magnitude accuracy by a factor of 3.74. This result validated the calibration method.

Theoretical investigation on the effect of misalignment error in a chromatic differential confocal probe

Theoretical investigation on the effect of misalignment error in a chromatic differential confocal probe

Sending-or-not-sending twin-field protocol for quantum key distribution with asymmetric source parameters

The sending-or-not-sending (SNS) protocol of the twin-field quantum key distribution (TFQKD) can tolerant large misalignment error and its key rate can exceed the bound of repeaterless QKD. But the original SNS protocol requires the two users to use the same source parameters. Here we propose a general protocol with asymmetric source parameters and give the security proof of this protocol. Our general protocol has a much better performance than that of the original SNS protocol when the channel of the system is asymmetric.

A Calibration Method for the Misalignment Error Between Inertial Navigation System and Tri-Axial Magnetometer in Three-Component Magnetic Measurement System

In order to calibrate the misalignment error between inertial navigation system and tri-axial magnetometer in the three-component magnetic measurement system, a novel calibration method is proposed in the paper. Considering that the magnetometer error is inevitable, the calibration of which is the prerequisite to misalignment error calibration. Therefore, the calibration models of magnetometer error and misalignment error are established firstly, based on which, the objective function is constructed to calibrate the misalignment error. The magnetometer error calibration is based on the principle that the norm of the magnetic survey data keeps constant during the process of solving the objective function. Hence, the objective function solving problem is considered as the equality constrained nonlinear optimization problem, that is, the MATLAB's FMINCOM function is used to solve the objective function. The feasibility and validity of the proposed method were verified by simulation and field experiment, the results of which indicate high accuracy in misalignment error calibration. In the field experiment, the range of x, y, z components are decreased to 1.34%, 1.75% and 1.77% while the absolute errors are reduced to 2.13%, 2.11% and 3.47% respectively after calibration. Method comparisons indicate that the proposed method is superior to traditional methods, which can guarantee the accuracy for three-component magnetic measurement.

A Novel Method for Plane Extraction from Low-Resolution Inhomogeneous Point Clouds and its Application to a Customized Low-Cost Mobile Mapping System

Over the last decade, increasing demands for building interior mapping have brought the challenge of effectively and efficiently acquiring geometric information. Most mobile mapping methods rely on the integration of Simultaneous Localization And Mapping (SLAM) and costly Inertial Measurement Units (IMUs). Meanwhile, the methods also suffer misalignment errors caused by the low-resolution inhomogeneous point clouds captured using multi-line Mobile Laser Scanners (MLSs). While point-based alignments between such point clouds are affected by the highly dynamic moving patterns of the platform, plane-based methods are limited by the poor quality of the planes extracted, which reduce the methods’ robustness, reliability, and applicability. To alleviate these issues, we proposed and developed a method for plane extraction from low-resolution inhomogeneous point clouds. Based on the definition of virtual scanlines and the Enhanced Line Simplification (ELS) algorithm, the method extracts feature points, generates line segments, forms patches, and merges multi-direction fractions to form planes. The proposed method reduces the over-segmentation fractions caused by measurement noise and scanline curvature. A dedicated plane-to-plane point cloud alignment workflow based on the proposed plane extraction method was created to demonstrate the method’s application. The implementation of the coarse-to-fine procedure and the shortest-path initialization strategy eliminates the necessity of IMUs in mobile mapping. A mobile mapping prototype was designed to test the performance of the proposed methods. The results show that the proposed workflow and hardware system achieves centimeter-level accuracy, which suggests that it can be applied to mobile mapping and sensor fusion.

Practical Long-Distance Side-Channel-Free Quantum Key Distribution

We present a simple protocol where Alice and Bob only needs sending out a coherent state or not-sending out a coherent state to Charlie. There is no bases switching. We show that this protocol is both encoding-state-side-channel free to the source part and measurement-device-independent. We don't have to control exactly the whole space state of the light pulse, which is an impossible task in practice. The protocol is immune to all adverse due to encoding-state imperfections in side-channel space such as the photon frequency spectrum, emission time, propagation direction, spatial angular moment, and so on. Numerical simulation shows that our scheme can reach a side-channel-free result for quantum key distribution over a distance longer than 200 km given the single-photon-interference misalignment error rate of $20\%$.

Secure communication for FSO links in the presence of eavesdropper with generic location and orientation.

When the beam waist at the receiver is significantly larger than the receiver size, free-space optical (FSO) links may be vulnerable to some optical tapping risks at the physical layer. In this paper, we conduct a new framework for the analysis of the secrecy performance in terms of the secrecy outage probability (SOP) of FSO systems affected by gamma-gamma (GG) turbulence-induced fading channels with pointing errors. As a key feature, we evaluate the SOP in the presence of an external eavesdropper with generic location and orientation. For that reason, a new misalignment error model is proposed to consider a non-orthogonal optical beam with respect to the photodetector plane at the eavesdropper's receiver, where the effective area is determined by a rotated ellipse. New approximate and asymptotic solutions at high signal-to-noise-ratio (SNR) for the secrecy performance are obtained in closed-form, which are verified by exact Monte Carlo simulations. By using the developed expressions, we analyze in greater detail some effects such as the SNR of the eavesdropper's channel, the normalized beamwidth at the receiver-side, and the location and orientation of the eavesdropper on the secrecy performance for different turbulence conditions.

Low Emittance Tuning of FCC-ee

The FCC-ee project studies the design of a future 100 km e+/e circular collider for precision studies and rare decay observations in the range of 90 to 350 GeV center of mass energy with luminosities in the order of 1035 cm–2 s–1. In order to reach these luminosity requirements, strong focusing is needed in the interaction regions. Large maximum beta values (of 7736 m for the Z energy) and the small beta star values, make the FCC-ee lattices particularly susceptible to misalignments and field errors. FCC-ee therefore presents an appreciable challenge for emittance tuning. In this paper, we describe a comprehensive correction strategy used for the low emittance tuning. The strategy includes programs that have been developed to optimise the lattice based on Dispersion Free Steering, linear coupling compensation based on Resonant Driving Terms and beta beat correction utilising response matrices. One hundred misalignment and field error random seeds were introduced in MAD-X simulations and the final corrected lattices are presented.

Weighted Double Sampling to Obtain the Average Value of Triangular Current for Accurate Droop Control in DC Power Distribution Systems

Droop control is broadly used in dc power distribution systems, e.g., dc microgrids. Implementing droop control for switch mode power supplies requires the measurement of average current. Synchronous sampling is used in digital control systems to obtain the average of a triangular inductor waveform. However, the dead time, semiconductor turn- on and turn- off delays, and signal conditioning delays shift the sensed waveform and change the effective duty cycle, resulting in a misalignment and measurement error from the average value. This paper proposes a duty cycle weighted averaging method based on double sampling. By sampling twice per switching period and averaging the results using duty cycle as the weighting factor, the error due to waveform misalignment is theoretically eliminated. The result always equals the average value of the triangle. This method does not rely on the knowledge of circuit delays, making it easy to implement and robust to parameter variations. Simulations and experimental measurements validate the superior performance compared with conventional single and double sampling methods. The experiment on a droop-controlled dc–dc converter demonstrates a more accurate droop characteristic.

Steerable reflector-assisted communication in obstructed line-of-sight FSO link with optimal mitigation of dust-induced signal fading

This paper introduces an effective technique for bridging free-space optical (FSO) communication between end-to-end nodes with obstructed direct line-of sight (LOS) by incorporating a steerable mirror-and-lens-assisted (MLA) reflector assembly. The consistency of the proposed MLA-assisted FSO system is then experimentally evaluated and contrasted against a plane mirror (PM) reflector over a test-bed link set in a laboratory-fostered dusty environment for analyzing the system performance in terms of the received beam irradiance, received signal quality and noise-inflicted signal distortions. Furthermore, an intensity-dependent steerable MLA system is implemented to cater for the beam misalignment errors during the FSO link operation. It is observed that the proposed MLA assembly, in contrast to the PM reflector, can effectively harvest and focus the dust-induced scattered information-laden laser beam to a narrow-beam spot with intense irradiance level at the receiver aperture. Finally, the signal eye diagram is obtained for analyzing the signal quality in the presence and absence of background light. Based on the experimental study, it is apparent that the MLA reflectors not only aids in establishing a reliable direct LOS-obstructed FSO link but also effectively mitigates the dusty channel-induced beam fading effect and enhances the system immunity to noise and jitter effects.

Beam Misalignment Aware Hybrid Transceiver Design in mmWave MIMO Systems

In this letter, we design a beam misalignment aware hybrid analog-digital transceiver to minimize the performance loss owing to imperfect beam alignment in millimeter-wave (mmWave) communication systems. Specifically, we consider the inclusion of the ‘error statistics’ into the precoder and combiner design, where the array response that incorporates the distribution of the misalignment error is first derived. The derived array response spreads the directivity of the beam pattern around the desired direction, thereby minimizing the loss in the array gain under beam misalignment. Accordingly, based on the derived array response, we design the hybrid precoder and combiner approach by approximating their fully-digital design using the gradient projection method. Numerical results show that the proposed hybrid precoder and combiner design can effectively alleviate the performance degradation incurred by beam misalignment.

Error Mechanism and Self-Calibration of Single-Axis Rotational Inertial Navigation System

With the rapid development of inertial technology, the rotational inertial system has been widely used for high-accuracy navigation. In addition, the single-axis rotational inertial navigation system is one of the most popular navigation systems due to its low cost. However, the fact which cannot be ignored is that although single axis rotational inertial navigation system can restrain divergence of attitude error, it cannot eliminate velocity error, which is mainly caused by the gyro misalignment and scale factor error related to rotational axis. A novel calibration method established on filter has been proposed. Position, velocity, and attitude are chosen to be the state variables. In order to estimate the gyro errors related to rotational axis, these errors must be included in the state equation. Correspondingly, zero velocity and rate of turntable are chosen to be measured. Simulation has been carried out to verify the correctness of the theory, and the real test has been performed to further demonstrate the validity of the method. By compensating the main error estimated by filter, it can be found that the accumulated errors in velocity and attitude are decreased. So, the precision of navigation is greatly improved with the proposed method.