Variable Stiffness Spring Research Articles

Research on the hydraulic support face guard mechanism and coupling characteristic of rib spalling in large mining heights

In view of the problem of poor coupling adaptability and easy rib spalling of coal wall in large mining height comprehensive mining, based on the effective inhibition effect of face guard mechanism on coal wall spalling, the structural characteristics and bearing capacity of different structural forms of the face guard mechanism are compared and analyzed. According to the surrounding rock adaptability of the face guard mechanism, established a numerical analysis model for rigid-flexible coupling of the face guard mechanism under different spalling forms. In order to accurately simulate the stress state of the protective mechanism, a variable stiffness spring damping system is used to replace the hydraulic cylinder. The load-bearing performance and response characteristics of the face guard mechanism under rib spalling coupling conditions were analyzed by applying uniform normal load and impact load to the face guard. The findings indicated that, the integral-type face guard mechanism has a better effect on suppressing rib spalling. When the face guard mechanism bears the static load of the coal wall, the entire response process of the face guard jack can be divided into three stages: initial support, increasing resistance bearing, constant resistance bearing; both the impact load position and the coupling state of the rib spalling will affect the characteristics of force transmission at the face guard mechanism’s hinge point, the hinge point between the extensible canopy and the primary face guard is most sensitive to biased load. The research results can provide reference for optimizing the face guard mechanism of large mining height hydraulic support and improving the reliability of coal wall support.

Random vibration analysis of composite laminated conical–cylindrical cabin structures of air vehicles considering thermal load

This study proposes a novel semi-analytical random dynamic model using the meshless method to precisely predict and quickly analyze the frequency-domain random response properties of composite laminated conical–cylindrical cabin structures (CL-CCCSs) of air vehicles under stationary random loads. In addition, thermal load is considered in the analysis. The first-order shear deformation theory (FSDT) is used to develop a random dynamic theoretical model for CL-CCCSs based on the spectro-geometric method (SGM) and pseudo-excitation method (PEM). Variable stiffness springs are employed to handle diverse boundary cases and compatibility conditions in the current model. Also, the displacement admissible functions for laminated conical shell and cylindrical shell are uniformly depicted with SGM, which depends on sine and cosine functions. After that, the PEM is employed to transform stationary random loads into pseudo harmonic loads. Subsequently, the energy variation principle is used to derive theoretical discrete random dynamic equations for vibration model of CL-CCCSs considering the thermal effect. The results of numerical vibration analyses are compared to confirm the reliability of the established model. Finally, the effect of certain parameters, such as the lamination scheme, layer number, and temperature, on the random vibration response of a CL-CCCS is thoroughly explained.

Design of Parallel Variable Stiffness Actuators

Direct-drive motors (DDMs) have been increasingly used for robot actuation because they provide high-fidelity torque control, but they typically have low torque density. Gearing can be used to increase the torque density of motors, but gearing decreases the power density of the actuator. Parallel elastic actuators (PEAs), composed of a spring attached in parallel to a motor, can increase both the torque and power density of the actuator without jeopardizing torque control fidelity. PEAs can also generate efficient oscillatory motion by applying the torque of the motor through resonant oscillations. However, conventional fixed stiffness springs used in PEAs only enable efficient oscillatory motion at a fixed resonant frequency defined by the stiffness of the spring. In this article, we present a parallel variable stiffness actuator (PVSA) consisting of a DDM connected in parallel to a variable stiffness spring. PVSAs retain the torque control bandwidth of DDMs and PEAs and can be used to amplify the torque and power of the motor over a range of oscillation frequencies. We present a compact design of a PVSA where a direct-drive motor, a high energy density composite spring, and a variable stiffness mechanism are arranged in a conventional cylindrical geometry, similar to a motor-gearbox assembly. We foresee the use of PVSAs in mobile robots and wearable devices, where energy efficient oscillatory motion at different frequencies, along with high torque and power density is indispensable.

Switchable compliant actuator with fast stiffness modulation and energy efficient power transmission

This article presents the design of a switchable compliant actuator (Swi-CA), capable of fast stiffness modulation over a wide range and energy-efficient equilibrium position control. Compliant actuators are designed to have a variable stiffness to generate a restoring force upon displacement. In previous studies, such actuators provided compliance by changing both output stiffness and equilibrium position using a clutch to switch between two modes. We implemented a bifurcation-based switching mechanism to shift between stiffness modulation and equilibrium position control modes via mechanical integration of a variable stiffness spring with a parallel elastic unit without the use of an additional clutch. The distinctive features of the proposed Swi-CA are threefold. First, the central bending of a leaf spring widens the range of modulated stiffness and increases the average stiffness modulation speed. Second, the developed slider-crank mechanism has high power transmission efficiency and fast stiffness modulation. Lastly, an optimized elliptical cam generated negative stiffness during output and enabled switching between the two modes without the use of a controllable clutch. Analytical models and experimental validation of the proposed design clearly demonstrated its advantages for applications requiring fast stiffness modulation and energy-efficient operation, such as some robotics applications.

Modeling and free vibration analysis for bolted composite plate under inconsistent pre-tightening condition

During the service process of bolted composite structures, the local bolt pre-tightening force may decrease, that is, the bolts are inconsistently pre-tightening, which will affect the integrity of the whole system. Here, a semi-analytical modeling method for bolted composite plates with inconsistent pre-tightening conditions is studied. To simulate the uneven pressure distribution on the bolted joint surface, a variable stiffness spring surface model is proposed and a method to obtain the parameters of the model is also described. For a specific connection structure, each joint is simplified into a spring surface model and modeling of inconsistent bolt preload in the connection structure could be realized by assigning different parameters to each spring surface model. Based on the classical laminate plate theory, the strain and kinetic energy of the composite plate are calculated and the motion equation of the structures is deduced by the Rayleigh-Ritz method. Finally, a modal test is applied for a multi-bolted fiber-reinforced composite plate. The accuracy of the model is verified by both test and 3D finite element analysis results. The influence of loosening degree, position and quantity of loosening bolts on natural frequencies of bolted composite plates is further analyzed.

Adaptability Analysis of Four-Leg Hydraulic Support with Large Mining Height under Impact Dynamic Load

In order to comprehensively analyze the adaptability of four-leg hydraulic support with large mining height under impact dynamic load, this paper adopts HyperMesh software to conduct a flexible pretreatment for the top beam, shield beam, and front and rear rods. The numerical simulation model of four-leg hydraulic support is established with ADAMS, where variable stiffness spring is used to replace columns to simulate their elastic characteristics. Building on analysis of the specific parameters of the support, this paper attempts to study the adaptability of the hydraulic support with impact dynamic load acting on the top beam. Additionally, the impact coefficient I and the excitation coefficient E have been introduced to transform the analysis results and optimize the evaluation method of the response degree of the top beam under impact load. Consequently, the response characteristics of the columns and pins at the hinged joints under various coupling states of the surrounding rock are found. Meanwhile, the paper has made a detailed comparison on the stress state of hydraulic support with different impact loads acting on the top beam. The adaptability change rule of the impact dynamic load under various impact conditions has been explored, which is of great significance to the optimization and strength design of four-leg hydraulic support with large mining height.

Performing Energy-Efficient Pick-and-Place Motions for High-Speed Robots by Using Variable Stiffness Springs

Abstract Typically, for pick-and-place robots operating at high speeds, an enormous amount of energy is lost during the robot braking phase. This is due to the fact that, during such operational phase, most of the energy is dissipated as heat on the braking resistances of the motor drivers. To increase the energy efficiency during the high-speed pick-and-place cycles, this article investigates the use of variable stiffness springs (VSS) in parallel configuration with the motors. These springs store the energy during the braking phase, instead of dissipating it. The energy is then released to actuate the robot in a next displacement phase. This design approach is combined with a motion generator which seeks to optimize trajectories for input torques reduction (and thus of energy consumption), through solving a boundary value problem (BVP) based on the robot dynamics. Experimental results of the suggested approach on a five-bar mechanism show the drastic reduction of input torques and therefore of energetic losses.

Inherent Stability of Multibody Systems with Variable-Stiffness Springs via Absolute Stability Theory

In this paper, the inherent stability problem for multibody systems with variable-stiffness springs (VSSs) is studied. Since multibody systems with VSSs may consume energy during the variation of stiffness, the inherent stability is not always ensured. The motivation of this paper is to present sufficient conditions that ensure the inherent stability of multibody systems with VSSs. The absolute stability theory is adopted, and N-degree-of-freedom (DOF) systems with VSSs are formulated as a Lur’e form. Furthermore, based on the circle criterion, sufficient conditions for the inherent stability of the systems are obtained. In order to verify these conditions, both frequency-domain and time-domain numerical simulations are conducted for several typical low-DOF systems.

Neural Network Based Inverse Modelling for Pneumatic Artificial Muscles

Pneumatic Artificial Muscles (PAM) are soft actuators with advantages such as high force to weight ratio, flexible structure and low cost. Pneumatic Artificial Muscles have inherent compliance that makes them feasible for exoskeletons and rehabilitation robots. However, their inherent nonlinear characteristics yield difficulties in modelling and control actions, which is an important factor restricting use of PAM. The compliance of PAM is associated with nonlinearity, hysteresis, and time varying characteristics, which makes it more difficult to model the dynamics and operation with model based high-performance controllers. Although there are many studies to overcome the modelling issue such as virtual work , empirical and phenomenological models, they are either much complicated or very approximate ones as a variable stiffness spring for model with nonlinear input-output relationship. Based on the analysis of well known previous modeling works in our PAM test bed, it has been observed that efficacy of the those methods are limited for representing the physical behaviour of PAM and thus there is still requirement for simple and effective models . In this work, apart from previous modeling approaches, the behaviour of PAM is foreseen as an integrated response to pressure input, which results in simultaneous force and muscle length change. Therefore, standard direct input-output identification methods are not suitable for modelling that behaviour. An inverse modeling approach is proposed in order to utilize it in control applications. The black box model is implemented by an Artificial Neural Network (ANN) structure using the experimental data collected from the PAM test bed. According to implementation results, an ANN based inverse model has yielded satisfactory performance deducing that it could be a simple and effective solution for PAM modelling and control .

Analysis and control of state jump in space deployable structures under alternating temperature loads

Abstract. State jump has been experimentally observed in space deployable structures working in alternating temperature environments. State jump is a phenomenon in which the geometric shape of the structure changes after the temperature loading and unloading process, which makes the working accuracy of the space deployable structure intrinsically unpredictable. This paper aims to investigate the causes of this state jump phenomenon and seek measures to reduce its effect. Firstly, the static multiple-stable-state phenomenon resulting in state jump is analyzed for clearance joints in deployable structures. Then, an equivalent model consisting of a variable stiffness spring and a contact element for state jump analysis is proposed, which is verified by a finite element simulation. Influence factors and control methods of state jump are further explored. Finally, numerical results of a space deployable structure of an umbrella-shaped antenna show the effectiveness of the developed analytical method.

Topology Optimization of Linkage Mechanisms Simultaneously Considering Both Kinematic and Compliance Characteristics

Abstract Studies on the topology optimization of linkage mechanisms have thus far focused mainly on mechanism synthesis considering only kinematic characteristics describing a desired path or motion. Here, we propose a new topology optimization method that synthesizes a linkage mechanism considering both kinematic and compliance (K&C) characteristics simultaneously, as compliance characteristics can also significantly affect the linkage mechanism performance; compliance characteristics dictate how elastic components, such as bushings in a vehicle suspension, are deformed by external forces. To achieve our objective, we use the spring-connected rigid block model (SBM) developed earlier for mechanism synthesis considering only kinematic characteristics, but we make it suitable for the simultaneous consideration of K&C characteristics during mechanism synthesis by making its zero-length springs multifunctional. Variable stiffness springs were used to identify the mechanism kinematic configuration only, but now in the proposed approach, they serve to determine not only the mechanism kinematic configuration but also the compliance element distribution. In particular, the ground-anchoring springs used to anchor a linkage mechanism to the ground are functionalized to simulate actual bushings and to identify the desired linkage kinematic chain. After the proposed formulation and numerical implementation are presented, case studies are considered. In particular, the effectiveness of the proposed method is demonstrated with a simplified two-dimensional vehicle suspension design problem.

An ANFIS based inverse modeling for pneumatic artificial muscles

Pneumatic Artificial Muscles (PAM) are soft actuators with advantages of high force to weight ratio, flexible structure and low cost. On the other hand, their inherent nonlinear characteristics yield difficulties in modeling and control actions, which is an important factor restricting use of PAM. In literature, there are various modeling approaches such as virtual work , empirical and phenomenological models. However, they appear as either much complicated or are approximate ones as a variable stiffness spring for model with nonlinear input-output relationship. In this work, the behaviour of PAM is interpreted as an integrated response to pressure input that results in a simultaneous force and muscle length change. The integrated response behaviour of PAM is not combined effectively in terms of simultaneous resultant force and muscle contraction in many existing models. In order to implement that response, standard identification methods , for instance NNARX, are not suitable for modeling this behaviour. Moreover, an inverse modeling with grey box approach is proposed in order to utilize the model in control applications. Since Neuro-Fuzzy inference systems are universal estimators, the modeling is implemented by an ANFIS structure using the experimental data collected from PAM test bed. According to implementation results, the ANFIS based inverse model has yielded satisfactory performance deducing that it could be a simple and effective solution for PAM modeling and control issue.

Analysis on the Performance Improvement of Reciprocating Pump with Variable Stiffness Valve using CFD

As a key component of reciprocating pump, the valve has a significant influence on its performance. However, it is difficult for the existing valve to simultaneously solve the problems such as fatigue, erosion and cavitation in engineering application. In this paper, a solution to these problems of using variable stiffness spring is proposed. And three new structures of the valve are designed. Furthermore, based on Computational Fluid Dynamics (CFD) method, a three-dimensional dynamic simulation model considering fluid-structure interaction in the suction stroke of reciprocating pump is established by using dynamic grid technique and User-Defined Functions (UDF). The performance of these new valves are compared with that of conventional valve respectively. The result shows that the new valves have significant influence on the motion characteristics of the valve disc, flow field distribution and cavitation. Besides, the simulation and experimental results of the maximum lift are compared, and it is found that they are basically in agreement. The new structures provide a new research direction for improving the performance of reciprocating pump. Simultaneously, the above simulation method can also provide guidance for valve design, structural optimization and service life improvement.

Improving the performance of industrial machines with variable stiffness springs

In several industrial applications, drivetrains impose highly dynamic oscillating motions to inertial loads. By introducing springs, the system’s natural frequencies can be matched to the required operating frequencies, lowering energy consumption of the drivetrain. However, fixed-stiffness springs only have a positive effect in a limited range of frequencies. To solve this problem, variable stiffness springs are proposed. A discussion of the effect of the series and parallel topology, as well as the possibility of adapting the spatio-temporal characteristics of the motion to the spring, is presented. Furthermore, a practical implementation of a variable stiffness spring is proposed. Its effectiveness is validated in experiments.

Hard Constrained LPV Virtual Control with Application to Flutter Suppression of a Smart Airfoil

Hard constrained control problems are popular in practical applications due to physical and power limitations. For instance, the displacement of a linear actuator is finite. A lot of studies have been conducted in this area to deal with certain hard constrained control problems and some are computationally expensive. This paper introduces a novel LPV (linear parameter-varying) virtual control scheme to deal with a class of hard constrained control problems with an application to flutter suppression of a smart airfoil, leading to a state-feedback LPV gain scheduling controller with the guaranteed $${{\cal H}_\infty}$$ performance. The basic idea of LPV virtual control is to add virtual components (such as variable stiffness springs and dampers) near to the hard constraints to prevent actuators from reaching their limits. The LPV virtual controller will be designed based on the model with virtual components and in the implementation stage, these virtual dynamics becomes part of the gain-scheduling controller. The concept is validated by a smart airfoil example. In the smart airfoil example, the virtual varying springs and dampers are placed at both ends of groove to constrain the mass movement. Comparisons studies with conventional LPV hard constrained control, nonlinear control, and regular LPV control without considering hard constraints are conducted to assess the performance of the proposed method and showed advantage over the existing methods. For instance, the control mass $${{\cal L}_2}$$ norm is reduced by 77.5% over the nonlinear control and 35% over the conventional LPV control.

Variable Stiffness Spring Actuators for Low-Energy-Cost Human Augmentation

Theoretical studies suggest and experimental evidence confirms that maintaining and changing human joint stiffness by coactivated antagonistic muscles are metabolically expensive, even if muscles do not perform net mechanical work. Based on this observation, we posit that effective human augmentation can be achieved by actuators operated in parallel to human joints, even if these actuators only supplement joint stiffness without doing net mechanical work. In this article, we present a prototype variable-length leaf-spring actuator capable of large-range stiffness modulation. The key feature of the actuator is that it provides intrinsically low-energy-cost stiffness modulation even for large output deflection, by keeping the force on the driving motor low. Variable stiffness actuators use two motors to provide both stiffness and equilibrium position modulation as they are designed to do net mechanical work. The proposed actuator conceptually differs from variable stiffness actuators because first, it uses a single motor to only provide stiffness modulation, second, it does not provide equilibrium position modulation, and third, unless externally loaded, it cannot do net mechanical work. Using this actuator, we demonstrate stiffness augmentation during human–machine collaboration in challenging postural stabilization and weight-bearing tasks. Our results indicate that the proposed actuator can be used to complement a biological system by restoring or extending its functionality with low energy cost, and that variable stiffness spring actuators could effectively augment humans by doing no or a limited amount of mechanical work.

Resettable‐inertance inerter: A semiactive control device for energy absorption

Semiactive control systems are based on formerly passive mechanical devices whose characteristics are adjusted in real time by active means. They can be classified into variable-damping dampers, variable-stiffness springs, and variable-inertance inerters. Similarly to the case of “variable-stiffness,” two possibilities are devised for inerters: “independently-variable inertance,” where inertance can increase or decrease continuously at any instant of time, and “resettable-inertance,” where it can increase only at instants where relative velocity is zero. By duality with resettable-stiffness springs, a resettable-inertance inerter (RII) is composed of an inerter that can suddenly be disconnected from the vibrating system and blocked in order to eliminate kinetic energy. Studies on “independently-variable inertance” have been carried out recently, but there are still no studies on “resettable inertance.” This paper presents an analytical numerical study on RII, for an energy-based control law, through the mathematical model of a mechanical implementation. By simulation of a numerical example that considers a SDOF system with three different devices, the performance is demonstrated for energy absorption and vibration reduction. Moreover, closed-form expressions for the equivalent-linear inertance, stiffness, and damping are found for the resettable devices and validated through the numerical example. Main conclusion is that RII adds equivalent damping without dynamically stiffening the structure. Besides, the absorbed energy can be dissipated and/or harvested in time intervals in which the RII is uncoupled from the structure.

Beyond bouncy gaits: The role of multiscale compliance in skeletal muscle performance.

McNeill Alexander demonstrated that compliant tendons could improve locomotor performance by decoupling muscle length changes from joint movements and mechanical energy fluctuations. This was revolutionary for our understanding of animal locomotion, but also highlighted the limitations of our understanding of the contractile performance of muscle under the dynamic conditions relevant to movement. This review addresses the potential for biological compliance to not only alter the demands on muscle but also fundamentally change contractile performance. Compliance exists across all spatial scales within the muscle. Molecule scale compliance is observed in the thin filament and the cytoskeletal protein titin likely acts as an activation-dependent variable-stiffness spring. Larger scale connective tissue compliance is found not only in tendons but also the more structurally complex extracellular matrix and aponeuroses. The interaction of the compliance in these structures with the contractile elements of muscle, and the variation in this interaction across physiological conditions, appears to explain muscle phenomena central to locomotion but not readily explained by the crossbridge and sliding filament theories, such as history dependence, the energetics of cyclical contractions, the nonlinear effect of activation level on muscle performance and the effect of age on muscle and locomotor capacity.

Enhancing Mobility With Quasi-Passive Variable Stiffness Exoskeletons.

Shoes were invented to provide user comfort using rubber soles, despite marginal improvement in human mobility. Unlike shoes, current lower-limb exoskeletons use fixed stiffness springs to store and recycle energy to improve mobility. However, the maximum kinetic energy a human can accumulate when augmented with a fixed stiffness spring is limited by the maximum deflection and the ability of the limbs to generate force; tying the advantage of fixed stiffness exoskeletons to biological constraints. Here, we propose a method for improving mobility using quasi-passive variable stiffness spring exoskeletons, where the maximum kinetic energy accumulated by a human is independent of the limb deflection and the ability of the limb to generate force. This is achieved by a variable stiffness augmentation of the human, where the exoskeleton does not provide mechanical work. The theoretical advantage provided by this new augmentation method can be useful in demanding tasks, where humans could benefit from increased speed and reduced energy cost of motion.

A Variable Stiffness Spring–Sponge Composite Tube with Fast Response and Shape Recovery

AbstractSoft robots have attracted more and more attention from researchers in the past decades, and multiple materials and methods have been studied to solve the conflict between strength and adaptability. This paper presents a novel composite tube comprising a spring and sponge, which can transform between stiffness and softness, and also proposes a corresponding novel method to alter the stiffness of the tube swiftly and reliably. Additionally, studies indicate that the tube exhibits shape‐recovery ability. The potential applications of the tube are illustrated in a coat of the supporting structure in the natural orifice transluminal endoscopic surgery instrument, a fixing device for human arthrosis and skeleton rehabilitation, and a variable stiffness multidirectional actuator.