Low Cross-axis Sensitivity Research Articles

Resonant MEMS Accelerometer with Low Cross-Axis Sensitivity-Optimized Based on BP and NSGA-II Algorithms.

This article proposes a low cross-axis sensitivity resonant MEMS(Micro-Electro-Mechanical Systems) accelerometer that is optimized based on the BP and NSGA-II algorithms. When resonant accelerometers are used in seismic monitoring, automotive safety systems, and navigation applications, high immunity and low cross-axis sensitivity are required. To improve the high immunity of the accelerometer, a coupling structure is introduced. This structure effectively separates the symmetric and antisymmetric mode frequencies of the DETF resonator and prevents mode coupling. To obtain higher detection accuracy and low cross-axis sensitivity, a decoupling structure is introduced. To find the optimal dimensional parameters of the decoupled structure, the BP and NSGA-II algorithms are used to optimize the dimensional parameters of the decoupled structure. The optimized decoupled structure has an axial stiffness of 6032.21 N/m and a transverse stiffness of 6.29 N/m. The finite element analysis results show that the sensitivity of the accelerometer is 59.1 Hz/g (Y-axis) and 59 Hz/g (X-axis). Cross-axis sensitivity is 0.508% (Y-axis) and 0.339% (X-axis), which is significantly lower than most resonant accelerometers. The coupling structure and optimization method proposed in this paper provide a new solution for designing resonant accelerometers with high interference immunity and low cross-axis sensitivity.

Cantilever-based biaxial FBG inclinometer with low cross-axis sensitivity

This work proposes and demonstrates a biaxial sensing inclinometer based on two FBGs surface-mounted on two separate thin cantilevers with a diminishable cross-axis sensitivity. The measured sensitivities for the inclination angles in the x-z plane and y-z plane are 34.87 and 33.49 pm/deg, respectively. To enhance the protection of the delicate FBGs and minimize axis-to-axis cross-sensitivity, the carbon-steel cantilevers are strategically arranged in a perpendicular configuration, resulting in an impressively low cross-sensitivity value of just 0.9275%. This alignment not only offers mechanical shielding but also ensures optimal performance and accuracy for the FBGs.

Ultra-high-sensitivity micro-accelerometer achieved by pure axial deformation of piezoresistive beams

Microfabricated piezoresistive accelerometers with purely axially deformed piezoresistive beams have demonstrated high performance. However, the conventional design of such accelerometers requires complex theoretical calculations and specific dimensional conditions to achieve purely axial deformation, which inevitably increases the difficulty and cost of the design and manufacturing. We propose an innovative structure that can simply realize pure axial deformation of piezoresistive beams by eliminating the transverse displacement at both ends without tedious calculations. An accelerometer based on the structure was fabricated; both static and dynamic performances were tested. The results showed that the accelerometer had high sensitivity (2.44 mV g−1 with 5 V bias, without circuit amplification), low cross-axis sensitivity (1.56% and 0.49 %, respectively), and high natural frequency (11.4 kHz), with a measurement range of 0–100 g. This design method provides an easy approach for designing high-performance piezoresistive sensors.

Development of a High-Precision and Low Cross-Axis Sensitivity 3-D Accelerometer for Low-Frequency Vibration Measurement

A new high-precision and low-frequency 3-D accelerometer that utilizes a symmetrical parallel vibration-sensing mechanism and a low cross-axis sensitivity high-precision 3-D sensing system is proposed in this study. The parameters of the vibration-sensing mechanism were determined by theoretical modeling and simulation analysis, and the performance of the 3-D accelerometer was tested experimentally. The dynamic response characteristics of the accelerometer were first determined using kinetic modeling, which showed reasonable amplitude–frequency and phase–frequency characteristics in the frequency range below 10 Hz. The accelerometer was calibrated using the comparison method. The sensitivities of the accelerometer in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${X}$ </tex-math></inline-formula> -, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Y}$ </tex-math></inline-formula> -, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Z}$ </tex-math></inline-formula> -axes are 25.3, 25.3, and 21.1 V/g, respectively, with a cross-axis sensitivity of less than 1%. The resolutions of the accelerometer in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${X}$ </tex-math></inline-formula> -, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Y}$ </tex-math></inline-formula> -, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Z}$ </tex-math></inline-formula> -axes were 48, 45, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$50 \mu \text{g}$ </tex-math></inline-formula> , respectively. The proposed accelerometer with high sensitivity and high resolution can be widely used for low-frequency microvibration measurements in engineering applications.

Design and characterization of an accelerometer with low cross axis sensitivity

An out-of-plane capacitive accelerometer with low cross axis sensitivity at high accelerations based on a CMOS MEMS process is developed. A truss frame with a high ratio of in-plane stiffness to out-of-plane stiffness is designed to suspend the proof mass of the accelerometer. The configuration of the proof mass with four auxiliary masses surrounding a main mass boosts the sensitivity of the accelerometer in the out-of-plane direction. A sensing circuit with period modulated output signals is realized by applying a relaxation oscillator to the sensing capacitors. The relaxation oscillator converts the capacitance changes to frequency variations. Analytical models are developed to assist the design of the accelerometer. The nonlinearity and sensitivity of the accelerometer are 1.1% and 754 Hz/g, respectively, for the acceleration ranging from 0 to 9 g. Measured cross-axis sensitivity is 4% at an acceleration of 9 g. The power consumption is 1.7 mW under a 1.8 V supply.

Two-Dimensional Low-Frequency Optical Accelerometer With High Accuracy and Low Cross-Axis Sensitivity

Two-dimensional (2D) accelerometer is a commonly used sensor for detecting horizontal vibrations. However, their low frequency response characteristics are limited by high cross-axis sensitivity and low resolution. To address this challenge, this study proposes a new 2D optical accelerometer based on a symmetric 2D vibration pickup unit and a high-sensitivity 2D angle sensor modified from a DVD pickup head. The parameters of the symmetrical 2D pickup unit were determined through modeling and simulation, and the performance of the accelerometer was tested experimentally. Experimental data show that the accelerometer has good low frequency response characteristics in the range from 1 to 10 Hz, sensitivity is better than 2.5 V/(m/s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), cross-axis sensitivity is less than 0.075 V/(m/s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), and the resolution is better than 0.4 mm/s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Moreover, the sources of uncertainty of the accelerometer were analyzed in detail and the synthetic uncertainty of the accelerometer was analyzed based on experiments. Compared with conventional techniques in this area, the proposed 2D optical accelerometer has featured the advantages, such as high accuracy and low cross-axis sensitivity, and can be widely used for low-frequency vibration monitoring in engineering applications.

A Low Cross-Axis Sensitivity Micro-Grating Accelerometer With Double-Layer Cantilever Beams

The micro-grating accelerometer based on the optical interference displacement measurement method has strict requirements on the parallelism of the interferometer and is susceptible to external interference. This paper proposes a micro-grating accelerometer with double-layer cantilever beams to suppress the effect of cross-axis acceleration and angular acceleration on the performance of the accelerometer. The mechanical characteristics of the designed double-layer cantilever beams structure and the conventional single-layer cantilever beams structure are compared by the finite element method. Theoretical results show that the symmetrical design of the double-layer cantilever beams structure can effectively reduce the cross-axis sensitivity. Under the same limit resolution, the torsional stiffness is increased by 50 times, which effectivity suppresses the disturbance of angular acceleration. The experimental results demonstrate that the designed structure has excellent linearity performance and low cross-axis sensitivity. The nonlinearity is reduced from 0.35% to 40.6 ppm, and the cross-axis sensitivity is better than 64.4 ppm.

Design principles for a single-process 3d-printed accelerometer – theory and experiment

Fused-filament fabrication, one of the most accessible additive manufacturing technology, has already been used to manufacture piezoresistive static/quasistatic strain sensors, force sensors and wind sensors. Recent research showed that fused-filament fabrication could also be used for the manufacturing of dynamic sensors. However, the anisotropic mechanical and piezoresistive behaviour, the heterogeneity, the large number of process parameters and the large number of possible geometrical designs open up numerous design options for manufacturing. Additionally, a small size is difficult to achieve due to the relatively low geometrical tolerances and the resolution of fused-filament fabrication. This paper is focused on the design principles of a single-process, fused-filament fabricated, uni-axial accelerometer with a piezoresistive sensing element. The anisotropic piezoresistive behaviour is researched for the maximum sensitivity in the measured acceleration direction and the minimal cross-axis sensitivity for the perpendicular axes. The analytical accelerometer model is based on a Bernoulli-Euler beam and is used to understand the frequency and the geometrical influences of the piezoresistive accelerometer with a beam-shaped sensing element and an attached intertial mass. Finally, a small-sized (22 × 22 × 15 mm3), single-axis, prototype accelerometer, with an approximately linear response up to-425 Hz and a low cross-axis sensitivity was manufactured. The derived principles can be used for further optimisation of the developed prototype sensor and as a foundation for the derivation of design principles for other types of fused-filament fabricated accelerometers, including 3-axis accelerometers. keyword: accelerometer; piezoresistivity; additive manufacturing; fused filament fabrication; dynamic sensor; 3D printing.

Capacitive Accelerometers with Beams Based on Alternated Segments of Different Widths

Microelectromechanical (MEM) Accelerometers measure the accelerations or vibrations experienced by objects due to inertial forces or mechanical excitations. To improve their proof mass displacement, several alternatives have been used, such as the design of different shapes of suspension beams. In this work, a new shape of beam is proposed based on alternated segments of different widths. To analyze its performance, one-quarter, middle and complete accelerometers were calculated and simulated; the results were compared with similar cases using conventional uniform-shaped beams. A notable improvement in the proof mass displacement was obtained in all cases, especially with the proposed symmetrical-shaped beam. Harmonic response and explicit dynamic analysis were also considered to discover performance when they are subjected to structural load. An improvement in amplitude displacement was also observed, as well as operation frequency reduction. From the explicit dynamic analysis, a faster performance of the accelerometer with uniform arms can be observed; however, it responds at a lower range of input velocities. A performance comparison of the proposed beam is presented considering the two reported accelerometers. Finally, from the variation in the width of the thinner segment of the symmetrical arms, it can be observed that it is possible to obtain an increment in the displacement of the proof mass of 39.57% and a decrement in natural frequency of 15.30%, with respect to the case of the uniform arm. Other advantages of the symmetric beam are the stress distribution, reducing its effect on the proof mass, as well as their low cross-axis sensitivity. Simulations were performed with ANSYS.

Novel High-Resolution Lateral Dual-Axis Quad-Beam Optical MEMS Accelerometer Using Waveguide Bragg Gratings

A novel lateral dual-axis a-Si/SiO2 waveguide Bragg grating based quad-beam accelerometer with high-resolution and large linear range has been presented in this paper. The sensor consists of silicon bulk micromachined proof mass suspended by silica beams. Three ridge gratings are positioned on the suspending beam and proof mass to maximize sensitivity and reduce noise. Impact of external acceleration in the sensing direction on the Bragg wavelength of gratings and MEMS structure has been modelled including the effects of strain, stress and temperature variation. Acceleration induces stress in the beam thus modifying the grating period and introducing chirp. The differential wavelength shift with respect to reference grating on the proof mass is the measure of acceleration. To compensate for the effect of the weight of the proof mass and increase the sensitivity of the sensor, electrostatic force of repulsion is applied to the proof mass. For the chosen parameters, the designed sensor has a linear response over a large range and a sensitivity of 30 pm/g. The temperature of surroundings, which acts as noise in sensor performance is compensated by taking differential wavelength shift with respect to reference grating. By design and choice of material, low cross-axis sensitivity is achieved. The proposed design enables a high-resolution well below 1 μ g/ Hz and is suitable for inertial navigation and seismometry applications.

Fabrication and Characteristics of a Three-Axis Accelerometer with Double L-Shaped Beams.

A three-axis accelerometer with a double L-shaped beams structure was designed and fabricated in this paper, consisting of a supporting body, four double L-shaped beams and intermediate double beams connected to two mass blocks. When applying acceleration to the accelerometer chip, according to the output voltage changes of three Wheatstone bridges constituted by twelve piezoresistors on the roots of the beams, the corresponding acceleration along three axes can be measured based on the elastic force theory and piezoresistive effect. To improve the characteristics of the three-axis accelerometer, we simulated how the width of the intermediate double beams affected the characteristics. Through optimizing the structure size, six chips with different widths of intermediate double beams were fabricated on silicon-on-insulator (SOI) wafers using micro-electromechanical systems (MEMS) technology and were packaged on printed circuit boards (PCB) by using an electrostatic bonding process and inner lead bonding technology. At room temperature and VDD = 5.0 V, the resulting accelerometer with an optimized size (w = 500 μm) realized sensitivities of 0.302 mV/g, 0.235 mV/g and 0.347 mV/g along three axes, with a low cross-axis sensitivity. This result provides a new strategy to further improve the characteristics of the three-axis accelerometer.

Superior performance area changing capacitive MEMS accelerometer employing additional lateral springs for low frequency applications

This paper introduces an effective and efficient microstructure of a differential area changing capacitive accelerometer to ensure low cross-axis sensitivity, high linearity and low noise figure for low frequency applications like Structural Health Monitoring and seismic sensing. The major design concern in an area dependent capacitance structure is that even small magnitude of cross axis displacement can drastically affect the sensitivity and linearity. The authors first focused their effort to obtain the guidelines for the best performance in the conventional structure of area changing capacitive sensors. The results clearly demonstrated that the existing structures used conventionally cannot meet the stringent requirements for low frequency applications. Subsequently, the various studies on the new structure proposed in this work were presented and the results are compared with latest reports for benchmarking. It has been estimated that the new structure can give cross-axis displacement as low as 0.5%, linearity of 2.53% and noise figure of 4.89 ng/ $$\sqrt {\text{Hz}}$$ , the best achieved in so for. These studies clearly demonstrate that the ill effects of parasitic capacitance on voltage sensitivity and linearity can be suppressed by the new design. These results further show that the area changing capacitive structure employing additional lateral springs is a promising candidate for low frequency applications like seismography. The other major advantage of this structure is that the fabrication process flow need not be changed in the production line.

A two degrees of freedom comb capacitive-type accelerometer with low cross-axis sensitivity

In this paper, we report on a SOI-based comb capacitive-type accelerometer that senses acceleration in two lateral directions. The structure of the accelerometer was designed using a proof mass connected by four folded-beam springs, which are compliant to inertial displacement causing by attached acceleration in the two lateral directions. At the same time, the folded-beam springs enabled to suppress cross-talk causing by mechanical coupling from parasitic vibration modes. The differential capacitor sense structure was employed to eliminate common mode effects. The design of gap between comb fingers was also analyzed to find an optimally sensing comb electrode structure. The design of the accelerometer was carried out using the finite element analysis. The fabrication of the device was based on SOI-micromachining. The characteristics of the accelerometer have been investigated by a fully differential capacitive bridge interface using a sub-fF switched-capacitor integrator circuit. The sensitivities of the accelerometer in the two lateral directions were determined to be 6 and 5.5 fF/g, respectively. The cross-axis sensitivities of the accelerometer were less than 5%, which shows that the accelerometer can be used for measuring precisely acceleration in the two lateral directions. The accelerometer operates linearly in the range of investigated acceleration from 0 to 4g. The proposed accelerometer is expected for low-g applications.

A Triaxial Accelerometer Based on Differential Resonant Beams and Force-Balanced Capacitive Plates

This paper presents the design, simulation, fabrication, and experiment of a triaxial accelerometer based on differential resonant beams and force-balanced capacitive plates. The triaxial accelerometer is composed of a proof mass, four bridge resonators with both end clamped and operating in flexure vibration mode, four L-type supporting beams, and a top plate and a bottom plate. The in-plane acceleration is measured by bridge resonators. The gravity center of the proof mass and the neutral layer of L-type supporting beams are located within the same plane to minimize the rotation of the proof mass subjected to in-plane acceleration. The cross-axis sensitivities of X-axis and Y-axis resonant beams under lateral in-plane acceleration are 1.97% and 1.71%, respectively. A force-balanced differential plate capacitor composed of a proof mass, a top plate, and a bottom plate is used to detect acceleration along Z-axis. The small displacement of the proof mass in the normal direction of the chip reduces the cross-axis sensitivity of the bridge resonators subjected to acceleration along Z-axis. The complementation of the resonance detection mechanism and the force balance capacitance mode makes the triaxial accelerometer exhibit low cross-axis sensitivity. The simulated and experimental results prove this conclusion.

Duplex mode tilt measurements based on a MEMS biaxial resonant accelerometer

This paper firstly reports the duplex mode tilt measurements (biaxial tilt measurement with small angle range and uniaxial tilt measurement with large angle range) based on a micro electromechanical system (MEMS) biaxial resonant accelerometer. For the accelerometer, two pairs of double-ended tuning fork (DETF) resonators are the sensing elements and they are integrated with a single proof mass. The two-stage microleverage mechanisms, possessing higher amplification factor, amplify and translate the weight component to the resonators. The adoption of decoupling beams lower the cross impact and allow the simultaneous differential measurement of tilt angles acting along two orthogonal axes. Based on the biaxial sensing structure, the biaxial tilt measurement is realized on the two orthogonal sensing axes. By the combination of the four DETFs resonant frequencies at each angular position, the linear range of uniaxial tilt measurement is extended. For the biaxial tilt measurement with small angle range, the experiments demonstrate a high sensitivity (X-axis: 4.351 Hz/deg and Y-axis: 5.257 Hz/deg) and a low cross-axis sensitivity (X-axis: 0.180 Hz/deg and Y-axis: 0.202 Hz/deg) for a ±40° biaxial tilt angle range. For the uniaxial tilt measurement with large angle range, the device shows an average sensitivity of 3.973 Hz/deg for a ±90° range. In addition, the close-loop self-oscillation is realized and the minimum Allan deviation of 68 ppb is obtained. The performance makes the device a potentially attractive option for compact, multi-functional and highly-sensitive tilt measurements.

A novel capacitive sensing structure for simultaneous detection of biaxial low-g acceleration in a commercial MEMS process

The authors report a novel MEMS capacitive sensing structure that utilizes a single-layer electroplated gold to achieve simultaneous sensing of biaxial acceleration with low cross-axis sensitivity. The capacitive sensing structure is designed for the in-plane biaxial accelerometer with high frequency ratio and low-g acceleration range. The etching precision of the large proof-mass suspension is guaranteed by the design of detachable supporting islands. Then, different locations are explored in arranging the capacitors, for which the corresponding estimation algorithms are derived. Finally, the proposed structure was fabricated under the commercial MicraGEM-Si platform based on silicon-on-insulator (SOI) technologies. In summary, the structural and fabrication designs of the MEMS capacitive sensing structure solve the problems in biaxial independent sensing, while offering: 3D connectivity of electrodes using planar fabrication technologies; large proof-mass fabrication precision; identical mobility range in all in-plane directions; and sensing algorithms for any regular polygonal shape.

A wearable piezoresistive microaccelerometer with low cross-axis sensitivity for neurological disease diagnosis

Inertial MEMS sensors having high performance play a key role in several biomotion applications. However, in addition to high performance, there is a demand for wearable sensors in medical diagnostic purposes to be of small size and light weight. Tremor (2–18 Hz) and Seizure (0.5–29 Hz) occurs in patients suffering from several neurological disorders having acceleration value from almost 0 g signifying fall to maximum ±6g signifying jerks. In order to capture such low g signals, reduced cross axis sensitivity is required, which is still a challenge in the available ones. This paper presents the design and analysis of such a wearable microaccelerometer of piezoresistive type for the diagnosis of neurological disorders having an area of about 25mm2 and mass of around 6 mg. The sensitivity obtained for a dynamic range of ±6g is 0.33 mV/V/g, noise floor is 7.65 μg/Hz and cross axis sensitivity is 0.48%.

A low cross-axis sensitivity piezoresistive accelerometer fabricated by masked-maskless wet etching

The paper focuses on the design, simulation, fabrication and experiment of a low cross-axis sensitivity piezoresistive accelerometer fabricated by masked-maskless wet etching in iodine-supersaturated KOH solution. The piezoresistive accelerometer consists of a proof mass, eight supporting beams and four sensing beams. The sensing beams are located at the top surface of silicon chips in order to pattern piezoresistive resistors and metal lines. A boron-diffused piezoresistive Wheatstone bridge is located at the frame-side end of a sensing beam to detect the strain. The gravity center of the proof mass lies within the neutral plane of supporting beams to minimize the rotation of the proof mass under in-plane acceleration. Compared with accelerometer of which the supporting beams located at the surface of chips, the rotating angle of the newly designed sensor under in-plane acceleration is reduced by 98.91%. Preliminary experimental results show that the cross-axis sensitivity under X and Y acceleration is 1.67% and 0.82%, respectively.

Out-of-plane dual flexure MEMS piezoresistive accelerometer with low cross axis sensitivity

Accelerometers are one of the widely explored microsensors with many transduction mechanisms. One of the primary concerns with piezoresistive microaccelerometers is their cross axis sensitivity. The main reason for cross axis response is the mechanical offset between the flexures and the center of mass of the proofmass. Cross axis sensitivity is generally minimized electronically using bridge configurations of piezoresistors or by depositing high density materials like gold over the proofmass to balance the mechanical structure. Here a novel non planar dual flexure geometry has been proposed which make the effective beam center of mass to align with that of the proof mass and thereby achieve low cross axis sensitivity by the mechanical design itself. The hybrid integration of electronic compensation with the mechanical compensation realizes a high performance accelerometer with ultralow cross axis sensitivity. Four piezoresistors placed on one flexure are configured such that the output voltage will be maximum for prime axis input while the bridge is balanced for the inputs along remaining two axes. The analytical model of the proposed structure, and the finite element analysis results are discussed. The device exhibits a very low cross axis sensitivity of 0.006% in Y direction and 0.005% in X direction while maintaining high prime axis sensitivity of 2.28 mV/g. The device also shows very low non linearity (1%) over a range of 100 g acceleration and a resonant frequency of 1.7 kHz.

An optimization technique for performance improvement of gap-changeable MEMS accelerometers

This paper demonstrates the design and optimization of single- and dual-axis capacitive accelerometers. Detailed analysis together with fabrication and characterization results are reported. The designs utilize a simplified comb structure to detect capacitance change between rotor and stator fingers. By optimizing the gap spacing (finger gap and anti-finger gap), the devices are designed to yield high capacitance change as a function of the proof mass displacement. It was found that there is a critical anti-gap spacing for a selected finger gap at which the device sensitivity is the highest (ratio of 3.45: 1). Designs are first optimized using Finite Element Analysis (FEA) tools. Initial simulation results indicated a differential capacitive sensitivity of 80fF/g and 68fF/g for single- and dual -axis accelerometers, respectively. The capacitance-voltage (CV) measurements exhibited a parabolic behavior which is an important characteristic for these type of accelerometers. Furthermore, results show a rest capacitance of 16.42 pF and sensitivity of 35 fF/g for single-axis accelerometer. Overall, the devices have excellent sensitivity, high linearity, and low cross-axis sensitivity. The accelerometers are fabricated using GlobalFoundries’ Inertial Measurement Unit (IMU) platform and have a compact footprint of 1.8 mm × 1.8 mm.