Torsional Spring Research Articles

Self-assembly of lamellae by elastocapillarity in the presence of gravity: experiments and modeling

Abstract Elastocapillarity describes the self-organization of elastic structures under liquid surface forces, for applications to micro- and nano scale self-assembly. It has recently become evident that precise prediction of elastocapillary self-assembly is challenged by the various phenomena arising due to fluid flow. In this study, we present experiments and a corresponding reduced-order model for the dynamic coalescence of flexible lamellae arrays. Vertical arrays of elastomeric lamellae attached to a substrate at the bottom are fabricated using 3D printed molds. The lamellae have sub-mm thickness and a few millimeters height, a size scale that cannot be achieved by traditional microfabrication. The gaps between the elastic lamellae are filled with liquid while the tips of the lamellae, which are at the top with respect to gravity, are initially fixed, then they are released which leads to their spontaneous bending and coalescence. We study the cluster size as a function of system variables both experimentally and numerically. The solid lamellae are modeled as discrete rigid elements connected by torsional springs to the substrate, while the fluid flow uses lubrication theory and capillarity. Importantly, the model incorporates the gravitational forces to effectively capture the systems' behavior ranging from the microscale with negligible gravity effect to the macroscale where gravity significantly influences the dynamics. We further derive a linearized continuum model from our nonlinear formulation, providing an analytical scaling law for the lamellae cluster size. This work is relevant for new polymorphic fins and lamellae devices, capillary self-folding and origami.

Metallic Metamaterials with Auxetic Properties: Re-Entrant Structures

The present article is an exploration of metamaterial structures exhibiting auxetic properties. The study shows the effect of three geometric parameters of re-entrant auxetic cells, namely, the internal initial cell angle (θ0), the strut length ratio h/l, and the degree of opening of the unit cells expressed by the change in the Δθ angle, on the value of the Poisson’s ratio. It combines theoretical insights into physical re-entrant auxetic structures with the demonstration of structures that can be subjected to cyclic loading without being damaged. The experimental section features the results of the compression tests of a symmetrical structure made up of four re-entrant cells and tensile tests of a flat mesh structure of size 4 × 4. In the mesh structure, a modification was applied to the re-entrant cells, creating arched strut connections. It was shown that the value of the maximum load for such structures depends on the bending angle and the length of the inclined strut. The mesh structure was created using torsion springs. Its cyclic tension for different amplitudes yielded Poisson’s ratio values in the range of −1.4 to −1.7. These modifications have enabled stable, elastic, and failure-free cyclical changes of the structure’s dimensions under load.

Enhanced Attractive Force via Torsion Spring as Rotatable Tip Structure in Beam-Structure Electrostatic Chucks

This research aims to replace ball joints of beam-structure electrostatic chucks (BSESC), which are limited by issues such as structural friction and inconsistent operation, thus enhancing the applicability in industrial settings. Torsion springs are used as rotational degree-of-freedom (RDOF) mechanisms at the tip of BSESCs to reduce friction and improve repeatability, while also highlighting the positive relationship between tip rotatability and the attractive force generated. Following the law of conservation of energy, an analytical calculation was performed using a beam-spring-capacitor model to establish the correlation between tip rotatability and the maximum attractive force generated through energy system analysis. An analytical solution was derived, explicitly defining the relationship between tip rotatability and the achievable attractive force. The results were plotted using MATLAB. Experimental validations were carried out by fabricating devices that differed only in tip rotatability, and measurements of the attractive force were taken. Both analytical and experimental results clearly demonstrate a positive relationship between tip rotatability and attractive force generation in BSESCs. The use of torsion springs effectively reduces the energy concentration at the tip, delaying detachment while simultaneously increasing the attractive force, significantly improving the overall performance of BSESCs. These findings provide a foundation for future industrial applications, particularly for automated large-area manipulation of irregularly shaped targets in industries such as screen production and semiconductors.

Enhancing output characteristics of semi-active flapping airfoil energy capture device via flexible deformation strategy

ABSTRACT A concentrated-torsion flexible airfoil model is established to enhance the output characteristics of the flapping airfoil energy capture device in this work. The effect of the damping ratio C 2*, spring ratio K 2* of the torsion spring, and mass ratio M A * of the tail airfoil on the dynamic characteristics is investigated systematically. The numerical simulation results show that compared with the rigid airfoil, the time-averaged power coefficient and output efficiency of the optimized flexible airfoil (C 2* = 4, K 2* = 0.5, and M A * = 0.7) are increased by 91.85% and 63.45%, respectively. Remarkably, the output efficiency of the optimized flexible airfoil is 32.15%. The reason for the enhanced performance is that the passive deformation can ensure the airfoil generates a stronger vortex and delays the shedding of the vortex. In addition, the experimental test results (with a 36.29% performance enhancement) further demonstrate the effectiveness of using the concentrated-torsional flexible deformation strategy in enhancing the energy output characteristics of the flapping airfoil.

Synchronization analysis of a four-motor excitation with torsion spring coupling vibrating system

In oil drilling processes, vibrating screen is a crucial solid control equipment for separating harmful solid-phase particles. However, the conventional utilization of either dual-motor or triple-motor is inadequate demanding the excitation force of large vibrating equipment. Moreover, self-synchronization in zero phase is difficult to achieve in multiple motors system. To avoid cancellation of the excitation force caused by the phase inconsistency of multiple motors, the adoption of a four-motor excitation with torsion spring coupling system is proposed this work. Initially, the mathematical model of the vibrating system is formulated through the Lagrange's equation. Subsequently, the steady-state solution is determined using Laplace transform. Then the conditions and characteristics in stable equilibrium state are elucidated employing the small parameter averaging method. Ultimately, the reliability and applicability of the theoretical results are substantiated through numerical simulations. The findings reveal that with the increase of the torsion spring stiffness, the phase difference between the motors connected by torsion springs (MCTSs) is exponentially decreased, and desired zero-phase synchronization in engineering is eventually achieved. Furthermore, the present study uncovers two distinct synchronization mechanisms in the torsion spring coupling system: mechanical controlled synchronization between MCTSs is inevitably achieved, while the self-synchronization between motors unconnected by torsion springs (MUTSs) is limited by the synchronization conditions. The study provides valuable insights for designing mechanical controlled synchronization and self-synchronization vibrating machines.

Design of bi-axial piezoelectric MEMS micro mirror with gimbal actuator for dynamic decoupling

Abstract This study presents a novel structural design of a bi-axial piezoelectric micro-electro-mechanical-systems scanning mirror aimed at preventing the dynamic coupling between the two scanning axes and avoiding distortion of the scanning pattern. In the proposed design, the gimbal actuator, constrained by torsional springs at both ends, not only serves as the torque generation component for the actuation of one axis but also acts as a pivot to prevent structural interference between the two axes during scanning. This approach achieves the advantages of decoupling and compactness simultaneously. Simulations indicate that the gimbal actuator experiences very small displacement during y-axis actuation, thus realizing the dynamic decoupling from the x-axis scanning unit. To evaluate the proposed designs, fabrication processes were adopted on a silicon-on-insulator wafer with a lead zirconium titanate film. The miniaturized scanners, featuring a mirror with a 1.2 mm diameter, were realized on a compact 5 × 5 mm2 chip. Measurements indicate that the resonant frequencies of x-axis and y-axis scanning are 2.69 kHz and 4.29 kHz, respectively, and the optical scanning angles reach 33° and 21° under an 8 Vpp driving voltage. Additionally, measurements show that the displacement ratio between the central mirror and the gimbal actuator can reach up to 17 during y-axis actuation, verifying the concept of dynamic decoupling. The bi-axial Lissajous scanning pattern with straight edges also demonstrates the effective decoupling by the proposed gimbal actuator design.

Design and dynamic analysis of a spanwise morphing wing for Mars exploration

The application of spanwise morphing wings makes it possible to transport and launch large-size Mars exploration UAVs. This article proposes a modular variable spanwise morphing wing for high-aspect-ratio aircrafts, and analyses the characteristics of the morphing wing by theoretical analysis, numerical simulation and experimental verification. The novel spanwise morphing wing is based on the Sarrus-inspired deployable structure, which can increase the wing's lift by changing the spanwise length. The pre-strain torsion springs are assembled to provide the initial driving moment of the morphing mechanism. A regular triangle cross section is selected by evaluating the bending and torsional stiffness, and deployable triangular prism mechanisms are identified. Through releasing the pre-strain torsion springs to achieve expansion and implant Sarrus linkages along the straight motion paths. A lockable structure is designed, and the main factors affecting the self-locking property are analysed. A rigid origami skin is proposed, which maintains the airfoil's continuous smoothness after spanwise morphing. The kinematics of the spanwise morphing wing unit is developed using the Lagrange equation, and the theoretical models of morphing wings with different numbers of units are obtained. The unit numbers influence fully expanded time, and the time decreases gradually along the wingtip's direction. Finally, a one-way fluid-structure interaction analysis is performed to investigate the spanwise morphing mechanism and origami skin response under aerodynamic loads. Results show that the skeleton mechanism's maximum stress is below the material's yield strength, and the origami skin's maximum out-of-plane deformation is less than 0.5% of the wing chord, which provides a necessary theoretical basis for applying the spanwise morphing wing.

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.

Soil structure interaction studies on earth retaining wall

Abstract The paper offers a brand-new analytical technique for figuring out retaining wall natural frequencies, which are essential for seismic design. Using translational and torsion springs to account for soil-backfill interaction and foundation flexibility, the approach applies the theory of beams on elastic foundations. There are three closed-form techniques offered for figuring out the natural frequencies of flexural and stiff modes. The analytical model takes into account several kinds of retaining walls and the interactions between soil and structure that go along with them, such as active, passive, and dynamic earth pressures. To make the analysis simpler, certain assumptions are made about the behaviour of the structure and the state of the soil. The suggested technique provides a trustworthy means of assessing retaining wall behaviour during seismic events, which is crucial for guaranteeing structural stability and averting failure.

A Novel Design of a Torsional Shape Memory Alloy Actuator for Active Rudder.

SMA actuators are a group of lightweight actuators that offer advantages over conventional technology and allow for simple and compact solutions to the increasing demand for electrical actuation. In particular, an increasing number of SMA torsional actuator applications have been published recently due to their ability to supply rotational motion under load, resulting in advantages such as module simplification and the reduction of overall product weight. This paper presents the conceptual design, operating principle, experimental characterization and working performance of torsional actuators applicable in active rudder in aeronautics. The proposed application comprises a pair of SMA torsion springs, which bi-directionally actuate the actuator by Joule heating and natural cooling. The experimental results confirm the functionality of the torsion springs actuated device and show the rotation angle of the developed active rudder was about 30° at a heating current of 5 A. After the design and experiment, one of their chief drawbacks is their relatively slow operating speed in rudder positioning, but this can be improved by control strategy and small modifications to the actuator mechanism described in this work.

Design and performance analysis of continuum manipulator with twisting rotation

The continuum manipulator exhibits excellent flexibility, enabling it to navigate through unstructured and narrow spaces. However, the current motion capabilities of the continuum arm are limited to expansion, bending, or their combination, which restricts its application range and potential uses. Designing a continuum manipulator capable of twisting motion around its axis poses a significant challenge. In this study, we propose a torsion module for the continuum manipulator that enables twisting motions. This module comprises a central trunk made of a torsion spring and a driving mechanism consisting of two tendons arranged in cylindrical helix symmetry. By stretching these driving cables, the module can achieve twisting motion. We describe the principle behind torsional motion, establish a kinematic model for the continuum torsional module, and analyze how structural parameters affect its performance in terms of twisting motion. Furthermore, we construct a continuum arm incorporating this torsion module to enable both twisting and bending motions. We present examples showcasing the versatile capabilities of this continuum manipulator in various specialized scenarios. Experimental results demonstrate that the addition of torsional functionality enhances dexterity and expands design possibilities for continuum manipulators.

Dynamic Analysis Strategy of Generalized Deployable Units via NCF-IGA with Force Constraint

Space deployable mechanisms typically employ modular designs, where each unit that can be independently deployed is defined as a generalized deployable unit (GDU), typically consisting of rigid components, flexible components and generalized kinematic pairs. Given the high-performance demands of spatial transmission mechanisms, generalized kinematic pairs frequently integrate flexible factors like torsion springs and flexible hinges, which control the motion according to the attitude and position of the component. In this investigation, a new modeling and solution strategy for rigid-flexible coupled dynamics is established by combining NCF and IGA. It can not only accurately describe the large deformation and large rotation of flexible components, but also consider the influence of flexible factors in the kinematic pairs. The rigid components are modeled by the Natural Coordinate Formula (NCF), and the flexible components are discretized in the inertial coordinate system using spline curves in Isogeometric Analysis (IGA). The intermediate reference coordinates were integrated into the NCF-IGA framework, overcoming the boundary constraints between B-spline and NCF elements, and the geometric constraint equation of the kinematic pair was established. Subsequently, this paper proposes the concept of force constraint in controllable deployable mechanisms. Based on the force constraint equation, the mechanical model of flexible joints is established. The dynamic equations of GDUs are derived considering both geometric and force constraints, and generalized-[Formula: see text] method is introduced to solve the equations. Finally, three numerical examples are provided to illustrate the applicability and superiority of the proposed method.

Improved stiff string torque and drag prediction using a computationally efficient contact algorithm

ABSTRACT Due to the intermittent contact with the wellbore, determining torque and drag for deviated wells is difficult. Most models have ignored drill string stiffness and assumed continual contact to simplify derivation. However, the accuracy of these ‘soft-string’ models is restricted, especially at high dogleg severities. On the other hand, most ‘stiff-string’ models rely on computationally intensive approaches or continuous contact assumptions. To mitigate these issues, a computationally efficient penalty-based wellbore contact algorithm has been developed based on vector calculation, which at most requires two dot products and three arithmetic operations to determine contact locations. This algorithm is incorporated into a 3D multibody dynamics (MBD) model, which utilizes rigid drill-string segments based on the Newton-Euler formulation, connected via axial, shear, torsional, and bending springs to capture drill string flexibility. This model performs simulations faster than real-time and has been validated using surface measurements from a completed well.

A Wearable Fingertip Force Feedback Device System for Object Stiffness Sensing.

Virtual reality technology brings a new experience to human-computer interaction, while wearable force feedback devices can enhance the immersion of users in interaction. This paper proposes a wearable fingertip force feedback device that uses a tendon drive mechanism, with the aim of simulating the stiffness characteristics of objects within virtual scenes. The device adjusts the rotation angle of the torsion spring through a DC motor, and then uses a wire to convert the torque into a feedback force at the user's index fingertips, with an output force of up to 4 N and a force change rate of up to 10 N/s. This paper introduces the mechanical structure and design process of the force feedback device, and conducts a mechanical analysis of the device to select the appropriate components. Physical and psychological experiments are conducted to comprehensively evaluate the device's performance in conveying object stiffness information. The results show that the device can simulate different stiffness characteristics of objects, and users can distinguish objects with different stiffness characteristics well when wearing the force feedback device and interacting with the three-dimensional virtual environments.

Deployment Simulation of Foldable Membranes Using Absolute Nodal Coordinate Formulation and Validation

It has become a trend to use foldable membranes to construct large spacecraft structures such as solar sails, antennas, and drag sails with the advantages of being lightweight and having high packing efficiency. To enhance the existing numerical simulation of membrane deployment, the nonlinear behavior of the crease is finely described based on experiments and integrated into the numerical model via the principle of virtual work. Specifically, a foldable membrane is modeled as a multibody system (MBS) based on the absolute nodal coordinate formulation (ANCF), where the flexible facet is meshed with both ANCF triangular and quadrilateral thin shell elements and the crease is treated as a virtual torsional spring with special constraints along the fold line. The MBS modeling method is validated via the deployment experiment of a Z-folding membrane. The deployment of a four-unit Miura-ori membrane is further analyzed to show the capability of the approach in modeling foldable membranes with complicated configurations. Good agreement is obtained on the membrane-deformed configurations between the simulation and experiment. Additionally, the driving force at the corners is obtained. This research is expected to provide a more accurate simulation to facilitate the design and optimization of the space deployable membrane structure.

Quasi-static behavior of a pair of serially-connected Kresling Origami springs

Many of the patterns seen in Origami are currently being explored as a platform for building functional engineering systems with versatile characteristics that cater to niche applications in various technological fields. One such pattern is the Kresling pattern, which can be used to construct mechanical springs with unconventional properties and rich translational-rotational restoring behavior. In this paper, we investigate, both theoretically and experimentally, the quasi-static behavior of a pair of serially-connected Kresling Origami springs under different end loading conditions. We show that, depending on the end loading of the spring, it can exhibit coupled/ decoupled motion; one, two, or three equilibria; fixed, quasi-zero, or variable stiffness; and symmetric/asymmetric restoring behavior. We also present a technique to predict the restoring behavior of the serially-connected springs by combining a simple truss model with the experimentally-identified restoring behavior of a single unit. The technique permits accurate prediction of the deformation path of any number of serially-connected springs. We believe that serially connected Kresling Origami Springs offer a pathway towards the design of axial and torsional springs with unique and versatile functionalities.

Dynamic analysis of drag-based vibratory swimmers using higher-order averaging

This paper discusses the mathematical modeling, dynamic analysis, and design optimization of a class of drag-based vibratory swimmers using averaging. A typical swimmer of this class consists of a surface or subsurface main body, an oscillatory mass inside the body, and a rigid fin attached to the main body using torsional springs and immersed in water. This paper takes advantage of third-order averaging techniques for dynamic analysis and design optimization of the swimmer for high frequencies. The averaged dynamics are used for determining the optimum stiffness of the springs for maximizing the average speed of the swimmer for high-frequency motion of the oscillatory mass. Experimental results confirm the general response of the mathematical model.

Design and analysis of a large tolerance docking mechanism

On-Orbit Servicing is increasingly crucial with the growing number of spacecraft. The foundation for On-orbit servicing is space docking mechanisms. As On-Orbit Servicing tasks become more complex, the demands for docking capture mechanisms increase in both function and performance. Therefore, it is crucial to design a docking mechanism with a large tolerance. Among various docking capture mechanisms, the multi-claw capture mechanism has the advantages of low impact and reliable capture. This paper analyzes the Common Berthing Mechanism and a docking mechanism with an underactuated two-degree-of-freedom claw-type capture mechanism as its core is proposed. Subsequently, this paper provided a detailed design of the mechanism based on the principle of underactuated capture. Furthermore, this article conducts numerical analyses of key mechanisms such as the capture mechanism and guide mechanism in the design process, verifying the functionality of the mechanisms. After completing the analysis of capturing dynamics, the tolerance ability of the mechanism was also verified, various key parameters were determined, and the parameters of components such as the torsion spring were also determined. Finally, the prototype of the proposed docking mechanism is developed, and the experiment is completed to validate its functional principle and tolerance capability.

Cost-effective 3D-printed rotatable reflectors for two-dimensional beam steering

In this paper, we have developed a 2D optical scanning module comprising cascaded 3D-printed one-axis rotating mirrors with large areas (30×30mm2 for the X-direction scan and 60×25mm2 for the Y-direction scan). Each mirror device contains a square or rectangular silicon substrate coated with aluminum, serving as the mirror. A 3D-printed structure, including the mirror frame (with four embedded mini permanent magnets on the backside), torsion springs, and base, is combined with the mirror; two electromagnets are situated under the mirror as the actuation mechanism. We apply DC voltage to the electromagnets to create magnetic force. The electromagnets can interact with the permanent magnets to make the mirror rotate. The X scan of the 2D scanning module can achieve a static optical scan angle of ∼11.8deg at the -X corners, and the corresponding Y-scan angle is ∼4.5deg, both with 12 VDC. Moreover, we have observed a fan-shaped distortion, a phenomenon not thoroughly studied previously for combining two single-axis scan mirrors. Therefore, we also perform a simulation to establish and demonstrate a correlation between the simulation prediction and experimental results. The 2D scanning module can be a low-cost alternative to the expensive conventional galvanometer scanners, and it can be used to upgrade a rangefinder to a simplified LiDAR.