Sensitive Axis Research Articles

A sensitive micromachined resonant accelerometer for moving-base gravimetry

A sensitive micromachined resonant accelerometer that exhibits extremely low noise floor and excellent bias stability is presented for future application of moving-base gravimetry. An overall structure optimization is presented for large scale factor and low noise, which is significant for measuring variations in the gravitational field of the Earth. The experimental results show that the MEMS accelerometer has a scale factor up to 876 Hz/g and a noise floor down to 75ng/Hz by setting a relatively low full-scale range of ±5 g. The experimental results of the resonant accelerometer with ±0.01°C temperature control show that the averaged bias stability for one day duration is 0.197 μg and the bias repeatability within about 3 months is 1.56 μg. Furthermore, a six-day measurement duration of the accelerometer with its sensitive axis perpendicular to the ground shows a sensitive measurement synchronously with the Earth's tidal gravity, which demonstrates that the resonant accelerometer has the capability for high-performance applications such as moving-base gravimeters and shipborne inertial navigation systems.

Modelling and calculating the stiffness of a cross-shaped element of a microelectromechanical gyroscope-accelerometer

This article investigates the design of a linear acceleration and angular velocity sensor with three axis of sensitivity. The modelling of the parametrized geometry of the gyroscope-accelerometer and its cruciform stiffener is carried out based on the ANSYS software package. The dependence of the movement of proof mass on the change in the thickness of the elastic beams of the cruciform element of the gyroscope-accelerometer is obtained.

Pendulum Accelerometer with Digital Control and New Functionality

In this paper, we consider a compensation-type quartz pendulum accelerometer, a feature of which is the use of a digital feedback amplifier in the control loop (for the implementation of a discrete controller and algorithmic compensation for errors from the pendulum unbalance and temperature dependences of the zero offset and scale factor). The problem is related to the construction of a digital control system for the considered accelerometer, which provides a high-precision measurement of the projection onto the sensitivity axis of the actual apparent acceleration of the object on which the accelerometer is installed. A solution to this problem, which allows finding digital control algorithms using various methods of synthesis of discrete controllers of the control loop, is provided. The obtained solutions in the time and frequency domains are analyzed, confirming the high quality of regulation. The results of experimental studies are presented.

Mathematical Model of Satellite-Inertial Mobile Computational Gravimetry

The article proposes a mathematical model of a hybrid system installed on board of a moving object and represented by an inertial sensor of the vector of specific forces — a three-component newtonometer with orthogonal sensitivity axes and a network of receivers of a navigation satellite system (HSS). The purpose of this hybrid system is the temporal estimations of the nearEarth gravitational field on the trajectory of the object. Within the Newtonian mechanics the possibility of choosing an inertial reference system with a beginning at the center of mass of the Earth is assumed; сomplementary to the PZ-90 (Russia) and WGS-84 (USA) standards, the following are introduced: 1) an ellipsoidal (geodesic) coordinate system, rigidly connected with the solid Earth; 2) two movable accompanying right-angled trihedrals with a common origin as a point whose movement forms the trajectory of the object; the instrument one, is rigidly connected with the object as a solid body, and is thus freely oriented, other one are geographic, and permanently oriented to the cardinal points (East, North, Zenith). In the presentation of kinematics, attention is drawn to the fact that the variability of the absolute linear velocity in inertial space explained by the motion of an object relative to solid Earth and its own rotation is characterized by rotational vectors of relative and portable velocities which identify the vectors of relative and portable angular rotational velocities of the undeformable geographic trihedron and are represented projections on its axis. The causality of the trajectory is determined by Newton’s second law; in projections on the axis of the moving geographic trihedron, component-wise recording of the equations of dynamics is performed, which are resolved with respect to the components of the strength of the gravitational field. It is noted that the previous article by the authors is devoted to the problem of a high-precision estimate of the kinematic parameters of motion equations. In such a context it is indicated that direct calculation of the gravitational field strength requires the convertting of Newtonometer measurements from the instrument trihedron to the geographic one. The required linear transformation for this is constructed considering the possibilities of multiposition of the NSS object. A computational experiment is described and some of its results are presented.

Tmc Reliance Is Biased by the Hair Cell Subtype and Position Within the Ear.

Hair cells are heterogenous, enabling varied roles in sensory systems. An emerging hypothesis is that the transmembrane channel-like (Tmc) proteins of the hair cell’s mechanotransduction apparatus vary within and between organs to permit encoding of different mechanical stimuli. Five anatomical variables that may coincide with different Tmc use by a hair cell within the ear are the containing organ, cell morphology, cell position within an organ, axis of best sensitivity for the cell, and the hair bundle’s orientation within this axis. Here, we test this hypothesis in the organs of the zebrafish ear using a suite of genetic mutations. Transgenesis and quantitative measurements demonstrate two morphologically distinct hair cell types in the central thickness of a vestibular organ, the lateral crista: short and tall. In contrast to what has been observed, we find that tall hair cells that lack Tmc1 generally have substantial reductions in mechanosensitivity. In short hair cells that lack Tmc2 isoforms, mechanotransduction is largely abated. However, hair cell Tmc dependencies are not absolute, and an exceptional class of short hair cell that depends on Tmc1 is present, termed a short hair cell erratic. To further test anatomical variables that may influence Tmc use, we map Tmc1 function in the saccule of mutant larvae that depend just on this Tmc protein to hear. We demonstrate that hair cells that use Tmc1 are found in the posterior region of the saccule, within a single axis of best sensitivity, and hair bundles with opposite orientations retain function. Overall, we determine that Tmc reliance in the ear is dependent on the organ, subtype of hair cell, position within the ear, and axis of best sensitivity.

Об оценивании параметров модели погрешностей вращающегося измерительного модуля на ВОГ бесплатформенной ИНС в условиях объекта

The paper studies the possibility of updating the parameters of error model of a rotating inertial measurement unit (IMU)with fiber-optic gyroscopes (FOG) in a strapdown inertial navigation system (SINS)under operating conditions. The IMU is placed in a two-axis gimbal for modulation rotation.The main focus is made on the estimation of scale factor errors of the FOG and accelerometers, non-orthogonality of their sensitive axes, and relative time delays (group delays) of inertial sensors during the IMU normal rotation according to the navigation solution of the INS in the observation mode of its operation. Also, the paper presents the description and results of estimation of so-called rhumb drifts of the IMU, which may occur due to the perturbingforces associated with the geographical axes or the axes of the system central device body.The research is based on the results of FOG-based INS simulation.

Passing zenith stabilization method of two-dimensional gyro platform based on disturbance sources classification control

Aiming at the instability problem caused by the nonlinear constraint between the driving axis and the sensitive axis of the azimuth line-of-sight (LOS) control with the two-dimensional gyro platform, the variation rules of influence of azimuth line-of-sight (LOS) by different types of disturbance sources were analyzed, and a passing zenith stabilization method based on the disturbance sources classification control was proposed. This method used the feedback and feedforward dual channel compound control structure, eliminated the endogenous torque disturbance caused by gyro measurement noise amplification in the zenith position based on the control structure itself, and the torque disturbance caused by the high frequency component of the roll disturbance was suppressed by adding the filtering link of the feedforward channel, then the vibration problem of the azimuth drive axis in zenith position was solved. At the same time, the azimuth and the low frequency component of the roll disturbance were effectively isolated by the feedback channel and the feedforward channel. The simulation results show that this method can effectively suppress the amplitude of azimuth motor torque disturbance caused by the gyro measurement noise and high frequency component of the roll disturbance, and enhance the system stability. Finally, an experiment was carried out on a two-dimensional gyro platform. The stabilization precision of the line-of-sight bearing subjected to vibration in zenith position was reduced from 82.4 μrad to 44.6 μrad, and the isolation ratio was increased from −14.54 dB to −27.85 dB under the swing condition. The experimental results show that this method can effectively improve the disturbance isolation performance of azimuth line-of-sight in zenith position.

Accurate Analytical Accelerometer–Magnetometer Axes Alignment Guaranteeing Exact Orthogonality

A complete analytical solution to the problem of aligning the sensitivity axes (coordinate frames) of a three-axis accelerometer and a three-axis magnetometer, fixed on the same rigid platform, is introduced. It exploits the magnetic inclination phenomenon to analytically derive the axes alignment rotation matrix and the inclination angle. Starting from a popular formulation of the problem as a constrained optimization one, it introduces a transformation and a parameterization, converting it to an unconstrained one within the special orthogonal group. In contrast to existing methods using the same principle, it guarantees the orthogonality of the axes-alignment rotation matrix and achieves best-of-class accuracy at the same time. It is two orders of magnitude faster than the gradient descent and Newton–Raphson-based methods and about three times faster than state-of-the-art semianalytical approaches achieving the same accuracy. Multiple sets of the sensor data are used to demonstrate the method’s accuracy and computational efficiency.

ECONDARY INFORMATION PROCESSING METHODS WHILE ESTIMATING THE SPATIAL ORIENTATION OF OBJECTS

The study is devoted to solving the scientific problem of ensuring unbiasedness and increasing the efficiency of assessing the spatial orientation of objects by applying new methods of secondary information processing in software and hardware components of computer systems. The paper describes a developed method for compensating for magnetic anomalies that affect magnetically sensi-tive sensors of the inclinometer rotation angles. It is based on recording the inclinometer readings and the angle of rotation of the drill pipe as it rotates in the mouth of well in a range of 360 degrees. This makes it possible to determine and further take into account the value of the magnetic deviation from the drill string in the readings of the inclinometer. A method is described for determining the parameters of a magnetic anomaly from an external stationary source of a constant magnetic field by using redundant information from the readings of inclinometery transducers in the mouth of well and at the point of assessment. This allows to expand the bound-aries and scope of magnetometric transducers in difficult conditions. Methods for calculating the desired azimuth, as well as the pa-rameters of the intensity vector of the magnetic anomaly are proposed. The errors of inclinometers based on sensor devices of various physical nature (fluxgates, gyroscopes, accelerometers), both rigidly fixed and with the use of gimbals pendulum suspensions, are considered. The factors influencing the bias of the estimation of the angles of the spatial orientation of the drilling tool, expressed through the Euler angles, are analyzed. The analysis took into account the effect of various reasons: deviations of the transducers' sensitivity axes from mutual orthogonality and the reference trihedron of the axes associated with the body; changes in the zero sig-nal and transfer ratios under the influence of temperature; non-identical electrical parameters; inaccurate installation of the pendulum gimbal sensor frames in the tilt plane and along the vertical of the place. The permissible boundary values of each of the given errors have been determined. Consideration of these errors can significantly increase the unbiasedness of the assessment of the position of the object in difficult conditions. The practical significance of the results presented in the paper is the development of software and hardware components for assessing the spatial orientation of objects on the basis of the designed inclinometers capable of operating in difficult operating conditions and having a small diameter of the protective casing. Similar software and hardware components for assessing the spatial orientation of objects can be used: for the construction of underground communications; for the assembly of large-sized and remote objects; for static sounding of soils; for monitoring the state of building structure elements during operation.

Two basic systems of maxwell’s equations in a rotating frame: application in theory of ring laser gyro

In the paper, using a linear in angular velocity approximation, two basic well-known systems of Maxwell’s equations in a uniformly rotating frame of reference are considered. The first system of equations was first obtained in the work [L. I. Schiff, Proc. Natl. Acad. Sci. USA 25, 391 (1939)] on the base of use of the formalism of the theory of general relativity, and the second one – in the work [W. M. Irvine, Physica 30, 1160 (1964)] on the base of use of the method of orthonormal tetrad in this theory. In the paper, in the approximation of plane waves, these two vectorial systems of Maxwell’s equations are simplified and rewritten in cylindrical coordinates in scalar component form in order to find the lows of propagation of transversal components of electromagnetic waves in a circular resonator of ring laser gyro in the case of its rotation about sensitivity axis. On the base of these two simplified systems of Maxwell’s equations, the well-known wave equation and its analytical solutions for the named transversal components are obtained. As a result of substitution of these solutions into the first and second simplified systems of Maxwell’s equations, it is revealed that they satisfy only the second one. On this basis, the conclusion is made that the second system of Maxwell’s equations is more suitable for application in the theory of ring laser gyro than the first one.

Research of a micromechanical accelerometer with three sensitivity axes

Micromechanical linear acceleration sensors are widely used in modern inertial orientation and navigation systems of technical equipment used in industry. The paper presents the developed design of MEMS linear acceleration sensor with three sensitivity axes, modal and static analysis is performed, design parameters are found that ensure equality of natural frequencies along the sensitivity axes, and experimental samples are created and studied.

Investigation of the Effects of Random Vibration on the Characteristics of Micromechanical Accelerometers

For modern information, measuring, and optoelectronic systems based on micro- and nanomechanical sensors of angular velocity and linear acceleration, it is important to ensure their stable functioning in the presence of external factors. The paper presents the results of a study of the effect of a random vibration on the characteristics of micromechanical accelerometers (MMAs) obtained using the LDS V455 vibration bench. The dependence of the spectral density of vibration acceleration on the frequency of one of the samples, intended for acceleration measurements in the range up to ±1.2 g, has a noticeable shift from its predetermined profile. To establish the reasons for this discrepancy, the design of the MMAs’ sensitive element (SE) under the effect of a random vibration is studied. Calculations and simulations are performed in the ANSYS program. The deformations of the MMAs’ SE along the sensitivity axis Z and the capacitance changes due to the acceleration and random vibration along the X, Y, and Z axes, taking into account the crystallographic orientation of the SE’s material (silicon) are determined. The effect of the crystallographic orientation of silicon used to manufacture the MMAs’ SE on the deformation (deflection) of the rotor is considered. The presented results of the theoretical and experimental studies, as well as computer modeling, coincide, which allows us to improve the design of the MMAs’ SE.

Constrained single-axis path planning of underactuated spacecraft

The single-axis maneuver planning problem is investigated for underactuated spacecraft with one unactuated axis fixed in a certain direction of the spacecraft in the presence of a single conical forbidden pointing zone. Specifically, a nonnominal Euler rotation scenario is formulated by imposing admissible constraints on rotation axes, and it is proven that the singular sensitive axis can be pointed along an arbitrary inertial direction outside the forbidden zone by at most two principal rotations. Given this fact, an exact solution is obtained by numerically solving a quartic trigonometric function equation about the first rotation angle, while enforcing the rotation axes tangent to the forbidden cone for the shorter path. Furthermore, an approximate but computationally efficient solution is analytically developed by Ferrari's formulas for the linearized quartic trigonometric function equation around the first tangent direction, where the smallest real one is selected from the four candidate roots. The solvability of the two-step planning schemes is also assured by the corresponding accessible regions. Finally, comprehensive numerical simulations are conducted to corroborate the effectiveness of both the exact and approximate planning schemes.

Magnetoresistive Sensor in Two-Dimension on a 25 μm Thick Silicon Substrate for In Vivo Neuronal Measurements.

Neuronal electrical activity is widely studied in vivo, and the ability to measure its magnetic equivalent to obtain an undisturbed signal with both amplitude and direction information leading to neuronal signal mapping would be a promising tool for neuroscience. To provide such a tool, a probe with spin-electronics-based magnetic sensors with orthogonal axes of sensitivity for two directions of measurement is realized, thanks to a local magnetization re-orientation technique induced by Joule heating. This probe is tested under in vivo measurement conditions in the brain of an anesthetized rat. To be as close as possible to neurons and to create minimal damage during the probe's insertion, the tip thickness has been drastically decreased using a silicon-on-insulator substrate. Our probes provide the ability to perform in vivo magnetic measurements on two orthogonal axes on a 25 μm thick silicon tip with a sensitivity of 1.7%/mT along one axis and 0.9%/mT along the perpendicular axis in the sensor plane, for a limit of detection at 1 kHz of 1.0 and 1.3 nT, respectively. These probes have been tested through a phantom study and during an in vivo experiment. The robustness and stability over one year are demonstrated.

A Cosine-Fitting Self-Alignment Method of MEMS-Based Inertial Navigation System Consisting of a Skew FOG

MEMS inertial measurement unit (MIMU) has widely used in low-cost inertial navigation fields, such as pedestrian navigation system. However, the realization of self-alignment function and high-grade navigation performance are still uprising challenges. In present study, a novel MIMU/FOG compound system consisting of the MEMS inertial sensors and a skew fiber optic gyro (FOG) is proposed. The configuration which is based on the rotation modulation technology, realizes self-alignment function, and the skew FOG used as the redundant angular velocity measurement unit improves the navigation accuracy. During the rotation process, the projection of the fiber optic gyro sensitive axis is a direct current component, the earth rotation rate projected on the sensitive axis of the fiber optic gyro is a cosine component, and the initial phase is the yaw. Further, a cosine-fitting self-alignment method which requires no latitude information is introduced to calculate initial yaw alignment accuracy. The alignment time is adjustable by setting various rotation rate of rotary mechanism. When the rotary mechanism rate is fixed at 1°/s, the proposed method achieves better yaw alignment accuracy of 0.37° ( $1\boldsymbol {\sigma }$ ) by using the 0.1°/h (100s, $1\boldsymbol {\sigma }$ ) fiber optic gyro. Our work opens up a new perspective to implement self-alignment of the MIMU/FOG compound system.

100\u2009pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer

Magnetic sensing is present in our everyday interactions with consumer electronics and demonstrates the potential for the measurement of extremely weak biomagnetic fields, such as those of the heart and brain. In this work, we leverage the many benefits of microelectromechanical system (MEMS) devices to fabricate a small, low-power, and inexpensive sensor whose resolution is in the range of biomagnetic fields. At present, biomagnetic fields are measured only by expensive mechanisms such as optical pumping and superconducting quantum interference devices (SQUIDs), suggesting a large opportunity for MEMS technology in this work. The prototype fabrication is achieved by assembling micro-objects, including a permanent micromagnet, onto a postrelease commercial MEMS accelerometer using a pick-and-place technique. With this system, we demonstrate a room-temperature MEMS magnetic gradiometer. In air, the sensor’s response is linear, with a resolution of 1.1 nT cm−1, spans over 3 decades of dynamic range to 4.6 µT cm−1, and is capable of off-resonance measurements at low frequencies. In a 1 mTorr vacuum with 20 dB magnetic shielding, the sensor achieves a 100 pT cm−1 resolution at resonance. This resolution represents a 30-fold improvement compared with that of MEMS magnetometer technology and a 1000-fold improvement compared with that of MEMS gradiometer technology. The sensor is capable of a small spatial resolution with a magnetic sensing element of 0.25 mm along its sensitive axis, a >4-fold improvement compared with that of MEMS gradiometer technology. The calculated noise floor of this platform is 110 fT cm−1 Hz−1/2, and thus, these devices hold promise for both magnetocardiography (MCG) and magnetoencephalography (MEG) applications.

Estimate of the Ratio of the Data and Background Signals in Detecting the Magnetic Fields of Surface Defects by Magnetic Measurement Transducers

The problems of identifying defective segments of the surface of monitored objects and estimating the parameters of the defects are examined. The use of magnetic measurement transducers is described as a means of detecting and measuring the parameters of the locally distributed magnetic fields which appear above defective segments of the surface of a monitored object in an applied constant magnetic field. Algorithms are proposed for quantitative evaluation of the ratio of the data and background components of the output signal from magnetic measurement transducers. A method is derived for separating the data and background components. It is based on the summation property and the determined character of the distributions of the magnetic field intensity of a defect and the background magnetic field along the coordinate axis parallel to the monitored surface and on an analysis of the topography of the distribution of the magnetic field intensity. The approach to the choice and experimental definition of the estimated parameters characterizing the level of the data and background signals is validated. Formulas are given for calculating the signal-to-background ratio from the measured estimates for ordinary magnetostatic, differential magnetostatic and differentiating magnetic measurement measurement transducers taking into account the direction of orientation (normal, tangential) of their sensitivity axis. The signal-to-background ratio of a transducer is calculated for the example of the output signal from a magnetic measurement transducer during detection of the distribution of the magnetic field intensity over the surface of a monitored sample with artificial defects of specified sizes. A comparative analysis is made of these kinds of magnetic measurement transducers in terms of their signal-to-background ratio and general recommendations are made for increasing that ratio.

An Effective In-Field Calibration Method for Triaxial Magnetometers Based on Local Magnetic Inclination

This article presents an innovative in-field calibration method for portable triaxial magnetometers (TMs). For in-field calibration of portable sensors, it is difficult to provide accurately measured inputs to each sensitivity axis due to the unavailability of high-precision turntables. Because of this limitation, most existing in-field calibration methods often require nonlinear optimization to identify model parameters. According to the fact that the angle between the local gravity and magnetic field is invariant, a new in-field calibration approach called inclination-based calibration (I-Calibration) was proposed. The I-Calibration could reliably estimate model parameters of the magnetometers by simply using a linear least square estimator. A 12-observation icosahedron experimental scheme was performed for a microinertial measurement unit, which contains both triaxial accelerometers (TAs) and TMs. The effectiveness, as well as the robustness with the misalignments of the TAs and TMs, of the proposed calibration method, was first verified by using numerical simulations. Thereafter, in real data experiments, the proposed method was compared with an existing calibration approach, namely, magnitude-based calibration (M-Calibration), which is based on the fact that the magnitude of the local magnetic field is invariant. The calibrated results together with the comparison between the two methods demonstrated the effectiveness of the proposed method.

Performance enhancements of the spherical detector for pipeline spanning inspection through posture stabilization

Spherical detector (SD) is promising in the field of subsea pipeline defect detection because of low risk of blockage and quasi-real-time capacity. However, rolling stability has great influence on the detection performance of the SD. This paper proposes posture stabilization measures for enhancing performances of the SD in pipeline spanning inspections via analyzing the mathematical model of detection and experimental validations. Mass of the SD should be concentrated on a plane as much as possible, so that the SD can steadily roll around the unique normal axis with strong immunity to sudden disturbance and uncertainty of launch postures. Especially, when the rotation axis of the SD is one sensitive axis of the triaxial accelerometer equipped, the other two acceleration components can both achieve highest signal to noise ratio and are thus capable of sensitively and reliably detecting low-frequency vibration and downward bend of a spanning steel pipeline.

Parametric synthesis of the digital system of the course stability of a car

The problem of choosing the variable parameters of a control algorithm, implemented by a digital electronic unit of the system of the course stability of a car and providing the maximum stability margin and the maximum speed of the stabilized process during car braking is considered. It is believed that the angular velocity sensors of the car body are used as the sensitive elements of the system, whose sensitivity axes coincide in direction with the main central axes of the body inertia, and the angular deviation of the longitudinal axis of the body from a given direction is calculated by a digital electronic unit using algorithms of platformless inertial systems (PINS) in the form of a lattice function. Information about the angular velocity of a body rotation is a lattice function at the output of the Lanczos digital low-pass filter, whose input is supplied with the lattice function of the angular deviation of the body from a given direction of the car movement. The lattice control function is a weighted sum of these functions, the weight coefficients of which are variable digital parameters of the Vehicle Stability Controls that are to be selected. The perturbed motion of the continuous part of the closed system is described by ordinary differential equations, the work of the discrete part is described by relations in finite differences. By means of special transformations, the mathematical model of the perturbed motion of the closed-loop control system is represented in the form of a system of difference equations, using which the characteristic equation of the closed discrete system of the course stability of the car is constructed. Using the bilinear W-transformation, the characteristic equation is reduced to a form convenient for constructing the lines of equal degree of stability in the plane of the variable parameters of the digital electronic control unit, followed by determining the optimal values of its variable parameters, as well as assessing the effect of the selected value of the quantization period of the digital electronic unit on the area of stability of the closed digital system of the course stability of a car. Key words: system of the course stability of a car, Rodrigue Hamilton parameters, lattice function, low-frequency digital filters, variable system parameters.