Torsional System Research Articles

A parallel coupling framework for DEM-MBD: Model verification and application

Bulk material handling equipment can be numerically studied using the DEM-MBD method, where the particulate dynamics are solved by DEM (Discrete Element Method) and the motion characteristics of the mechanical components are modeled by MBD (Multi-Body Dynamics). In this work, a two-way coupling framework is proposed for the co-simulation of our self-developed DEM solver (DEMSLab) with the commercial MBD software (RecurDyn) using a parallel staggered coupling approach. To verify the proposed coupling method, the simulation result of a torsional spring damper system is compared with the corresponding analytical solution. After that, to assess the feasibility of this method in industrial-scale applications, a series of simulations involving a wheel loader is carried out. Different simulation conditions are adopted to reveal their impact on computational efficiency and simulation accuracy. These conditions include the mesh representation of the equipment geometry, the MBD time step size, and the coupling interval. An improved mesh simplification algorithm is proposed and used to reasonably simplify the surface mesh of the wheel loader, thus lowering the computational intensity of particle-wall interactions in DEM. The comparison results indicate that the computational time can be largely saved while the simulation accuracy remains considerably high. The MBD step size and coupling interval are crucial for numerical stability and should be selected carefully.

Nonlinear dynamic analysis and vibration reduction of two sandwich beams connected by a joint with clearance

The dynamics and vibration reduction characteristics of the clamped–clamped two sandwich beams jointed with clearance is studied theoretically and experimentally. A transverse and torsional spring system with clearance is used to equivalent the joint model. The homogenization method is used to equivalent the core layer and Rayleigh-Ritz method is utilized to derive the mode function of the interconnected sandwich beam by using a sequence of orthogonal polynomials. The nonlinear motion equation of the two jointed sandwich beam structure with clearance is derived by the application of the Hamilton principle and then solved using an improved Newmark integration approach. In order to validate the accuracy of the natural frequency and vibration mode, the finite element model is established. This paper examines the impact of clearance on the amplitude frequency response and vibration transmission of the two jointed sandwich beam structure, it is found the jointed sandwich beams show obvious nonlinear characteristics and intermittent vibration transmission phenomenon due to the clearance. Moreover, the vibration transmission analysis reveals that the existed clearance demonstrates significant vibration reduction effect, for which an experiment is conducted to validate the results. In general, this work proposes a novel approach for modeling sandwich structures with clearance with improved vibration reduction performance.

Aggregate interlock and effective strain of FRP-strengthened flanged RC members subjected to torsion: Experimental evaluation and analytical modeling

The effective strain of externally bonded FRP strengthening systems and the loss of concrete aggregate interlock are critical factors for predicting strength and developing design models for structural strengthening. Current research on FRP strengthening of reinforced concrete (RC) members primarily focuses on flexural, shear, and axial loading, neglecting torsional systems. This study introduces an innovative analytical-experimental model/formulation predicting FRP effective strain and concrete strain, based on Digital Image Correlation (DIC) analysis outcomes of an experimental study on RC beams strengthened with FRP sheets under torsion. Eight flanged RC beams, strengthened with various FRP ratios, configurations, and installation methods were also systematically tested. The findings emphasize the need for reevaluation of strain limits in existing guidelines. It points out that the shear integrity of concrete is influenced by concrete compressive strength and strengthening scheme. The DIC results suggest that the strain limit for concrete surfaces between FRP strips should be in the range of 0.0055–0.008, as opposed to the limit of 0.004 set by ACI 440.2R-17. The use of the grooving method in certain systems also requires an increase factor of 1.65 and 1.45 for the effective strain of transverse and longitudinal FRP sheets.

A conceptual examination of an additive manufactured high-ratio coaxial gearbox

This research introduces the novel “Kraken-Gear” mechanism, emphasizing the advantages of additive polymer 3D printing in high-ratio gearbox systems for lightweight robotic applications, such as surgical instruments. The innovative kinematic solution provides high torsional system stiffness, substantial gear ratios, and backlash-free transmission. Leveraging the “hot lithography” additive manufacturing method ensures precise and warp-free gearbox components. Targeting medical technology, the gearbox meets stringent requirements: backlash-free, minimal vibration, high precision, and torque, with minimized weight for ergonomic comfort and fatigue mitigation. Computational simulations assess forces and stresses, highlighting the potential of additive manufacturing for cost-effective and functionally efficient gearbox fabrication. Nevertheless, careful material selection remains imperative for optimal functionality, especially in demanding medical applications. In summary, this research underscores a promising approach to gearbox fabrication, emphasizing the critical role of material selection and simulation-based assessments for optimal performance.

Modelling and application of typical nonlinear torsional elements in vibro-impact analysis of pickup truck driveline system

The torsional element method for the dynamic modelling of torsional system was proposed by Crowther and Zhang, which provides a modular modeling approach with high modeling efficiency and has a good application prospect in vibro-impact analysis of vehicle driveline system. The main purpose of this paper is to further enrich the element types of the torsional element method and to establish a nonlinear dynamic model for a pickup truck driveline system by applying the torsional element method to analyze the vibro-impact phenomenon. A general nonlinear clearance element with different contact stiffness and damping, a nonlinear friction element with smooth Stribeck effect and a nonlinear multistage stiffness-damping element with different torque transfer characteristics are developed. A dynamic lumped parametric model with 10 degrees of freedom for a pickup truck driveline system is established by assembling the developed nonlinear torsional elements. The transient vibro-impact phenomenon caused by the clearance, the stick-slip phenomenon caused by the friction and the transient hysteresis cycle phenomenon caused by the nonlinear multistage damper during transient engagement of clutch are numerically investigated. Furthermore, a real-vehicle experimental study is conducted to confirm the transient vibro-impact phenomenon in pickup truck driveline system during transient clutch engagement and to verify the correctness of the dynamic lumped parameter model. On these bases, the influence of the key parameters of the nonlinear torsional element on the transient vibro-impacts are investigated, the effective engineering countermeasures to reduce the vibro-impact of the vehicle driveline system are put forward.

Experimental Investigation of Impulsive Coupling Characteristics of Asteroid Simulants Based on Laser Ablation Propulsion

The ablation impulse of typical asteroid simulants irradiated by a nanosecond pulsed laser has been investigated in a vacuum environment. A torsional pendulum measurement system was constructed to calculate the impulse of laser ablation. A 10 ns pulsed laser was used, with a 1064 nm wavelength, a 900 mJ maximum pulse energy, and a millimeter-scale ablation spot diameter. Impulsive coupling characteristics of six typical targets that imitate the substance of asteroids with various laser fluences were analyzed. Furthermore, the impulse coupling coefficient curves of different materials were fitted. The results reveal that the minimum laser fluence corresponding to a measurable ablation impulse is approximately 2.5 J/cm2, and the optimum laser fluence corresponding to the maximum impulse coupling coefficient is approximately 14.0 J/cm2. The trends of the laser ablation impulse coupling curves are roughly consistent for the six materials. Impulse coupling characteristics of the six typical materials can be represented by the same polynomial within a 95% confidence interval, so a unified rule has been given. In actual deflection tasks of asteroids, the unified impulse coupling characteristic can be used to implement laser deflection techniques, especially when the material of the asteroid cannot be accurately judged in time.

The risk matrix application to assess the installation of torsional vibration monitoring systems on ships

According to statistics, the number of accidents related to the failures of ship engine and propulsion systems remains in second place among the total number of accidents. One of the reasons for the destruction of diesel crankshafts, intermediate and propeller shafts, elastic couplings and other elements of shaft lines are torsional vibrations in combination with other types of fluctuations and vibrations. The main method for monitoring the level of torsional vibrations in ship’s shaft lines remains periodic torsiography or strain measurement. The widespread introduction of diagnostic and control systems on ships leads to the technical possibility of constant monitoring of the level of torsional vibrations, which will allow you to reduce the risks of accidents in the periods between torsiography. Like any new technical solution, the introduction of torsional vibration monitoring systems requires a scientific justification of the need for their application, which can be carried out with using risk theory. The results of applying the risk matrix to justify the installation of torsional vibration monitoring systems in marine propulsion systems are presented in the paper. As a result, a risk matrix with quantitative parameters is obtained to justify the installation of torsional vibration monitoring systems and reduce the risks of ship’s shaft line breakdowns. As an example, the application of the risk matrix for “OT” type tugs, which are widely used for various operations on the Russian waterways, is considered. It is established that for these types of vessels, the use of a monitoring system will be justified to reduce the risks of accidents, serious accidents and catastrophes that may arise from the development of dangerous torsional vibrations. A method for applying the assessment of the damage degree from an accident occurrence to determine the reduction of economic costs when using torsional vibration monitoring systems is proposed in the paper. It is found that for the “OT” type tugs, the installation of torsional vibration monitoring systems will be justified, both from the point of view of economics and reducing the accidents risks of ship engine and propulsion systems.

Multilayer adaptive critic design with digital twin for data-driven optimal tracking control and industrial applications

In this paper, an optimal trajectory tracking control problem for general nonlinear systems is investigated. An adaptive critic control method with the digital twin (DT) theory is developed. Divergent from the existing tracking control methods, the advantages of adaptive dynamic programming (ADP) and the theory of DT are combined in this paper, and the novel multilayer artificial system structure is constructed. The action-critic structure is employed by each artificial system to obtain an approximate optimal control policy. The model network (MN) is built by using the actual input and output data sets of the controlled system, which means the dependence on the dynamics of the system is overcame. Then, the weights of the trained action network (AN) and MN are passed to the real system to realize the optimal tracking control. The feasibility of the algorithm is proved by theoretical analysis. Finally, the algorithm is applied to a simple nonlinear torsional pendulum system and an industrial wastewater treatment system (WWTS), and the effectiveness of the algorithm is verified. The algorithm effectively realizes the tracking control of nonlinear systems.

Экономическая эффективность применения систем мониторинга крутильных колебаний на судах

A torsional vibration monitoring system is being investigated, and an assessment of the economic efficiency of its implementation on ships is made. A schematic diagram of the torsional vibration monitoring system is illustrated and a photograph of an experimental sample of the monitoring system is provided. An assessment of the economic efficiency of the implementation of torsional vibration monitoring systems on ships is being carried out to prevent the occurrence of emergency situations with marine propulsion systems. The rules of classification societies, scientific and technical literature in the field of torsional oscillations and industrial economics, and the authors' own research were used as materials. The methods used are analysis and computational experiment. Data on the economic costs of the shipowner in the event of emergency situations in case of fatigue failures of elements of ship's engine and propulsion systems were obtained. An assessment of the costs for the development, installation and maintenance of a torsional vibration monitoring system on ships was made; as well as an approximate assessment of the volume of the Russian domestic market for installation and maintenance of torsional vibration monitoring systems on ships. It is noted that the cost of the consequences of propeller shaft failures ranges from several million to tens of millions of rubles. It is concluded that the development and implementation of torsional vibration monitoring systems will reduce the cost of the shipowner for a routine assessment of the technical condition of torsional vibration dampers and reduce the risks of costly accidents with shipboard engine complexes.

Active control of earthquake-excited structure using a torsional servomotor active mass driver system

Servomotor system has advantages of low cost, small size, good controllability, and less maintenance in driving mass movement. In this study, a torsional servomotor active mass driver (AMD) system is developed to actively control an earthquake-excited structure. A relation between the mass inertial force and servomotor rotational speed is established as the transfer function of an uncontrolled AMD. A control algorithm consisting of the linear quadratic regulator (LQR) and Kalman filter is designed to control the transfer function in real time only using acceleration measurements. With the help of LabVIEW platform, a user-programmable AMD controller including data acquisition, data processing, and motor control is developed. Finally, shaking table tests of a three-story steel frame equipped with developed AMD system subjected to earthquake excitations are conducted. The results show that the torsional servomotor AMD system performs quite well in reducing the displacement and acceleration responses of the earthquake-excited steel frame. The root-mean-square displacement and absolute acceleration of the top floor greatly decrease with nearly 70%. The damping ratio of the steel frame is greatly improved from 0.17%∼0.29% to 1.25%∼2.25% after implementing the torsional servomotor AMD control. Besides, a phenomenon of good control in both first-mode and second-mode vibrations is observed to validate the active control superiority.

Large-scale combined torsional and axial loading system (TorAx) – A new perspective on multiaxial testing of fracture and stress transfer in plain and reinforced concrete

Civil engineering structures are exposed to complex loading scenarios leading to multiaxial fracture and activation of stress transfer mechanisms along cracks controlled by combined deformations in two independent spatial directions (crack opening and crack sliding). Such multi-degree of freedom conditions cannot be properly investigated by state-of-the-art testing procedures. That is why – based on a thorough review of existing experimental procedures – this paper presents a novel testing methodology that applies shear via torsional loading and can simultaneously load specimens in axial direction (TorAx) to explore the material behavior before, during, and after macro-cracking. Independent control of both degrees of freedom allows the generation of arbitrary biaxial load or deformation paths. To prove the technical feasibility of the proposed testing method, several tests on thin-walled concrete tubes have been conducted. The obtained results proved uniformity of strain distribution along the tested ligament which guarantees several advantages (e.g., elimination of size/boundary effects and reduced scatter) over existing testing methods. With low costs (material/time) TorAx will serve as a benchmark for future studies under monotonic, cyclic, and fatigue loading. By experimentally quantifying all stress transfer mechanisms in one unifying test setup, an unbiased comparison of the individual mechanisms is possible, which is the first necessary step towards accelerated yet economical and reliable mechanical and numerical models.

Equations of Motion of Mechanical Systems with Switchable Constraints

The article deals with a numerical and analytical approach to solving the equations of motion, which enables to treat the considered problems with the change of system structure or number of degrees of freedom without interrupting the numerical integration process. The described methodology allows effectively incorporate switchable constraints in the systems in accordance with their flexible structures. The crucial idea is based on the formulation of the resulting differentialalgebraic equations into a saddle point system, where the switchable constraints are represented by a sign matrix with variable rank. In connection with this property, a pseudoinversion is applied to eliminate algebraic variables and transform the problem to the first order system of ordinary differential equations. Moreover, the time independent case leads to linear autonomous systems with non-diagonalizable matrices, as is proved. The relevant numerical scheme is based on Runge-Kutta methods, that correspond to the power series of the resulting matrix exponential for time independent problems. The methodology presented is illustrated on the idealized two-mass oscillator with a switchable constraint. The numerical experiments performed range from initial stages, through simple transient cases to damped intentional control. The advanced applications can be found in robotics, active and controlled systems, and in the simulations of complex systems in biology and related areas. Moreover, the methodology can also be applied in the simulation of transport systems, especially in relation to vehicle technology, a quarter car suspension system, a vibration control mechanism, a torsion system with a clutch, and machine balancing and storage should to be highlighted.

Linking laboratory quasi-steady state strengths to field scale performance of tailings

Current state of practice for the assessment of liquefied strengths of tailings relies primarily on empirical or semi-empirical correlations based on penetration testing. That is, despite liquefied strength being arguably the most important strength parameter for the design of brittle tailings storage facilities, there is much less success or acceptance of the use of laboratory element tests to support strength selection compared to other forms of strengths inferred in geotechnical engineering. This is particularly the case for tailings at a state near or slightly dense of the critical state line (CSL) for which there is ample evidence of field-scale flow liquefaction but where laboratory element tests often behave in a manner inconsistent with such field-scale response – at least at large strains. The current paper examines the quasi steady state (QSS) strength of sands and tailings for which the CSL has been measured, linking the observed strengths to inferred in situ behaviour through the state parameter. Particular focus is placed on QSS strengths obtained from simple shear tests carried out within a hollow cylinder torsional shear system where the stress state in the test is a better representation of in situ below-slope conditions that the triaxial compression test. In particular, the marked effect of intermediate principal stress on the QSS in sands is highlighted. Alternatively, the negligible anisotropy seen in a sandy silt gold tailings, and the potential implications in the context of QSS strengths and field-scale behaviour, are examined and emphasised.

A Cubature Kalman Filter for parameter identification and output-feedback attitude control of liquid-propellant satellites considering fuel sloshing effects

The problem of parameter identification and output-feedback attitude stabilization is addressed for liquid-propellant satellites in the presence of fuel sloshing. The sloshing is described by a 2-degree-of-freedom pendulum. A torsional spring-damper system is utilized to model the flexibility of the diaphragm passive strategy and the fuel viscosity. By employing the control Lyapunov function methodology, a nonlinear backstepping-type state-feedback control law is constructed to stabilize the satellite and cancel the fuel sloshing. Then, to make the controller more feasible in practice, the required states of the controller, stiffnesses, and dampers are considered to be unavailable. Thus, a Cubature Kalman Filter is developed to estimate the system states and identify the fuel parameters. The state-feedback control law in conjunction with the Cubature Kalman Filter approach provides an output-feedback control law. This work owns the following two major novelties. One is identifying the stiffness and damping coefficients of the fuel and another is developing a Cubature Kalman Filter for estimating the resultant nonlinear system states. Lastly, comparative simulations verify and highlight the main results of the proposed methodology in relation to the existing methods. The findings suggest that the Cubature Kalman Filter offers potential advantages over the methods outlined in previous works, particularly in terms of reducing RMS error and improving state estimation convergence. The average reduction in RMS error for state convergence is 24 %, while the estimation process is found to be 63 % faster when compared to existing methods.

Autodrillers, Rig-Control Systems, Driller Procedures Reduce BHA Failures

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 214997, “The Role of Autodrillers, Rig-Control Systems, and Driller Procedures in Reduction of Bottomhole Assembly Failures,” by Pablo E. Barajas, SPE, Paul Pastusek, SPE, and Aaron Lacey, ExxonMobil, et al. The paper has not been peer reviewed. _ Reducing bottomhole-assembly (BHA) failures has been this operator’s focus in US land intermediate and lateral sections to reduce cost per foot. BHA failures can be mitigated with better autodriller processes, improved rig-control-system technology, and drilling-mechanics-based procedures. The operator, rig contractor, and BHA service providers engaged in an intensive continuous improvement process for 18 months to help two rigs in Oklahoma reduce the number of BHAs used per well. The goal was to determine how to best tune the autodriller and standardize set-point practices. Introduction The operator has found that rig-control systems, particularly the autodriller, can be unstable in many drilling situations. The operator and contractor laid out the framework to measure autodriller dysfunction suspected to affect rate-of-penetration (ROP) and BHA integrity. The team engaged in a structured and intensive continuous improvement process with the following objectives: - Understand if end-user tuning and set-point practices from the contractor were being applied consistently at the rig floor level - Evaluate if the tuning practices were appropriate or effective in mitigating dysfunction in different formations - Increase subject-matter experts’ support and involvement in proactively identifying when rig-control systems were not behaving as designed to reduce impact on ROP and the BHA - Evaluate whether the operator’s drilling roadmaps and BHA safety-limit protections were being properly integrated into autodriller control loops - Use downhole sensors to understand how surface controls induced dysfunctions and confirm when they were mitigated - Propagate learnings across all rigs and crews in the basin to reduce the number of BHAs required to drill each well Observations Autodriller Dysfunction Identification. Standardizing the identification of dysfunction patterns to be avoided was a step based on physics of the system, bit-run performance and dulls (Fig. 1), directional tool damage, high-frequency (1,024 samples per second) downhole data, and high-frequency (six samples per second) surface data. Currently, the focus is to quickly identify and mitigate autodriller dysfunction by the rig teams, including the types of dysfunction described in this section. Stick/Slip. The operator developed a test to run the autodriller in different control loops to determine when stick/slip was initiated or intensified by the autodriller. Restarting drilling in ROP mode with the rig’s torsional dampening system active eliminated the autodriller as the source of stick/slip. It was determined that excessive weight on bit (WOB) used to pass the tool joint through the rotating head in the managed-pressure-drilling’s rotating control device (RCD), combined with low rotational speed, were key factors in initiating stick/slip. WOB Dysfunction. Any significant WOB variation can drive enough torque variation to drive stick/slip. This is particularly true if the WOB variation has a frequency close to the natural torsional frequency of the system.

Modelling of a SMA Blade Twist System Suited for Demonstration in Wind Tunnel and Whirl Tower Plants

In this work, the modeling of a demonstrator of a morphing system aimed at altering the twist of a rotorcraft blade is presented. The device was conceived for two different representative environments: the wind tunnel plant of the University of Bristol and the whirl tower facility of the DLR, for tests in fixed and wing rotary configurations, respectively. The concept, conceived and matured within the European Project of SABRE, is based on shape memory alloys, SMA. This technology was selected for its intrinsic compactness and solidity, which better meet the requirements of a typical blade structure, being extremely flexible and subjected to relevant inertial loads. A dedicated structural layout was conceived to favor the working modality of the SMA torsional system; this architecture was tailored both to absorb the typical actions occurring onto a blade and to assure a certain level of pre-twist necessary for the SMA strain recovery. The activation of the SMA was performed through an electrothermal helicoidal coil wrapped around it. A dedicated network of sensors was integrated within the structure to measure the impact of the different actions on the blade system. This subsystem, functional to shape reconstruction operations, is capable of splitting the contribution of the loads to pure twist and flapping. At first, the requirements imposed by the two test facilities were elaborated together to the operational needs, arriving at the issue of the most relevant specifications. Secondly, the conceptual and advanced design were considered, demonstrating, first, the feasibility of the concept and, then, its compliance with the test environment. The work ends with two different layouts, conceived respectively for the tests in fixed and rotary wing configurations. For both of them, a performance estimate was addressed, and a discussion on the advantages and disadvantages was presented.

Spiral bevel gears: Bifurcation and chaos analyses of pure torsional system

The goal of this paper is to provide a detailed analysis of the complex dynamic scenario of spiral bevel gears by considering the torsional shaft stiffness. The dynamic model takes into account: time-dependent stiffness and non-smooth nonlinearity due to the backlash, i.e., teeth contact loss. The time-varying meshing stiffness is evaluated by means of a nonlinear finite element model, which allowed an accurate evaluation of the global and local teeth deformation in both directions: forward and reverse motions. Due to intentional tooth profile errors, e.g., profile modification, manufacturing error, or assembly error, the loaded and unloaded tooth contact analyses were conducted. The dynamic model was validated by comparisons with a verified SDOF model in terms of linear natural frequencies and nonlinear dynamic response. The present study provides amplitude frequency diagrams and bifurcation diagrams; for specific regimes, periodic, quasiperiodic, and chaotic responses were found. The dynamic behavior of the systems was evaluated using various tools such as modal analysis, nonlinear time series analysis, spectra, 3D-phase diagrams, and Poincaré maps. This study proves that decreasing the DOFs of the system can lose some dynamics. Different phenomena have been found such as trapping and boom-and-bust cycle. The dynamic response of different cases is evaluated by estimating the largest Lyapunov exponent and the correlation dimension. It is found that the system undergoes complex dynamic phenomena including nT-periodic, trapping, and aperiodic motions, which are evidenced in 3D-bifurcation diagrams, spectra, Poincaré maps, and 3D-phase diagrams. The chaotic motion found in this study is an undesirable behavior from a practical point of view, which can be avoided by adjusting the designed parameters. The results provide a basis for parameter design and dynamic characteristic control of the spiral bevel gear drive system.

System Modeling and Simulation for Investigating Dynamic Characteristics of Geared Symmetric System Based on Linear Analysis

Complex vibrational phenomena, such as gear impacts and mesh stiffness excitations, often require a significant amount of effort to be revealed using nonlinear analytical methods. However, key parameters for addressing vibrational problems can often be identified through simplified approaches based on linear analysis models. In light of these considerations, this study aimed to propose linear analytical methods to investigate the influences of various key parameters within symmetric systems. To achieve the main goal of this study, system modeling and eigensolutions were first implemented, focusing on a specific manual transmission with a front-engine/front-wheel configuration. Second, analytical techniques to reduce the number of degrees of freedom from the original symmetric system were suggested, and the reduced model was validated. Third, the system responses in the time domain were examined, along with key system parameters, such as gear mesh stiffness and clutch dampers, using state–variable equations. As a result, the findings from the linear system model demonstrated the fundamental dynamic characteristics of the torsional system within specific frequency regimes relevant to noise and vibration problems. Furthermore, the reduced lumped linear model employing the state–variable formula established its reliability in determining key parameters for mitigating noise and vibration problems.

A closed-loop torsional micro-thrust measurement system

In view of the future space gravitational wave detection mission, a closed-loop monofilament torsional pendulum micro-thrust measurement system has been developed according to the requirements of the drag-free control of the satellite platform for the thrust of the micro-thruster. In this paper, we present the design of the micro-thrust measurement system, the electromagnetic force generation device, and the angular displacement differential measurement. By calibrating the electromagnetic force generation device, the functional relationship between micro-thrust and torsional angular displacement of the torsion scale is obtained, and then the micro-thrust measurement is carried out. The analysis considers the impact of the experimental device’s structure and environment on the micro-thrust measurement system. The range for measuring thrust is 1–246 μN, with a resolution of 0.1 μN and a relative uncertainty of 1.174%. Ensure that the thrust resolution and accuracy of the micro-thruster are met according to the measurement requirements.

Torsional static and vibration analysis of a non-circular restrained micro/nanowire

This paper aims to study the static and free torsional vibration of non-circular micro/nanowires using the modified couple stress theory with several deformable and non-deformable support conditions. The geometrical properties of the micro/nanowires are considered to have triangular, elliptical and circular profiles. Equation of motion in torsional direction is derived based on torsional equilibrium and systems of linear equations are computed by adopting Fourier sine series with Stokes’ transformation. Moreover, deformable boundary conditions have been taken into account to formulate eigenvalue problem by employing the higher-order force boundary conditions. Material length scale parameter and the shape of cross-section have considerable impacts on torsional vibration frequencies of restrained microwire. The obtained frequency curves of restrained microwires are shown to be dependent on various parameters such as the shape of cross-section, deformable boundaries, material length scale parameter and also warping function.