Nonlinear Stiffness Characteristics Research Articles

Nonlinear wire rope isolator with magnetic negative stiffness

The high-static-low-dynamic-stiffness (HSLDS) isolators have been widely employed to achieve low-frequency vibration isolation. However, traditional HSLDS isolators are prone to nonlinear jump phenomena due to the introduction of nonlinear stiffness characteristics, which will cause the performance deterioration under high excitation levels. To overcome this issue, inspired by the dry friction characteristic of wire ropes, the wire ropes are employed to design HSLDS isolators to suppress nonlinear jump phenomenon by introducing hysteretic damping in this paper. Therefore, a nonlinear wire rope isolator with magnetic negative stiffness is proposed to achieve HSLDS with hysteretic damping. The elastic force of wire rope and the magnetic force are modeled to obtain nonlinear restoring force, and then the dynamic model of the proposed isolator is established to investigate isolation performance. The equivalent beam element method is proposed to model wire ropes for obtaining dynamic characteristics by considering tensile and bending stiffnesses. Then, numerical simulation is performed to investigate the isolation performance of the wire rope isolators with different magnetic negative stiffnesses, and demonstrates that the proposed isolator can work in a higher excitation level than the isolator without dry friction of wire ropes. Moreover, experiments are carried out to show that the onset isolation frequency of the proposed isolator can be reduced by 66.7% compared with the wire rope isolator without magnetic negative stiffness. Therefore, it is demonstrated that the proposed wire rope isolator with magnetic negative stiffness has the preferable performance in low frequency isolation, and can improve the adaptability under a higher excitation level.

Research on fastener lateral nonlinear stiffness characteristics and its impact on wheel-rail stick-slip vibration

Research on fastener lateral nonlinear stiffness characteristics and its impact on wheel-rail stick-slip vibration

Robot base position and spacecraft cabin angle optimization via homogeneous stiffness domain index with nonlinear stiffness characteristics

The use of mobile robots for machining large components has received considerable research interest for the application of industrial robots in the machinery manufacturing sector. However, the low structural stiffness of industrial robots can result in poor machining quality under the action of cutting forces. Therefore, this paper proposes a simultaneous optimization method the mobile robot base position and cabin angle using homogeneous stiffness domain (HSD) index for large spacecraft cabins. First, a nonlinear joint stiffness model that considers the gravity compensator mechanism is established to describe the stiffness characteristics of heavy-duty robots more accurately. Subsequently, a HSD index is proposed to evaluate the overall stiffness values and stiffness fluctuation for all robot postures in the machining program. An optimization model is then established based on the HSD under the constraints of machining accessibility, joint angle limitation and singularity. The optimal base position and cabin angle are determined simultaneously using the sparrow search algorithm. Finally, simulation and milling experiments are used to demonstrate that the optimization method proposed in this paper can effectively improve the machining quality.

Backstepping control based on adaptive neural network and disturbance observer for reconfigurable variable stiffness actuator

Reconfigurable variable stiffness actuator (RVSA) has attracted increasing attention in robotics due to its safety, compliance, and robustness. However, the control of the RVSA is challenging due to nonlinear factors such as high-order nonlinear dynamic, model uncertainties, time-varying model parameters, and disturbances. In this paper, firstly, a lightweight RVSA structure with both passive and active nonlinear variable stiffness characteristic is developed. Secondly, a dynamic surface backstepping control method based on a radial basis neural network and disturbance observer (DSBC-RBFNN-DOB) is proposed to achieve position control of the lightweight RVSA with matched and unmatched uncertainties. To address solve the “complexity explosion” and noise problems in traditional backstepping control, the dynamic surface backstepping control (DSBC) method is used to design the controller. Then, a method based on radial basis neural network (RBFNN) and disturbance observer (DOB) are used to compensate for the matched and unmatched uncertainties in the link and motor. In this method, the matched uncertainties are compensated using RBFNN, and the DOB is integrated to compensate RBFNN approximation errors and unmatched uncertainties. Through Lyapunov stability analysis, the semi-global boundedness of the controller is proven. Finally, the proposed method is simulated and actually implemented, verifying the effectiveness of the method. Simulation and experimental results show that the root mean square error (RMSE) of the proposed method is only 0.97277° and 0.6418°, respectively. Compared with PID, DSBC, and DSBC-RBFNN, the error reduction percentages in simulation (experiment) are 85.6 % (88.9 %), 49.4 % (88.4 %) and 36.1 % (80.0 %) respectively.

Nonlinear Vibration and Stiffness Characteristics Analysis of Maglev Train Based on Cubic Displacement Control

A control strategy combining cubic displacement feedback nonlinear control and proportional-differential (PD) linear control is used to control the vibration performance of the maglev system. The maglev system is divided into positive stiffness maglev system, quasi-zero stiffness maglev system and negative stiffness maglev system according to the linear stiffness value of maglev system. Firstly, an improved multi-scale method is used to analyze the vibration characteristics of suspension in the positive stiffness state of the maglev system. Secondly, the influence of control parameters on train vibration amplitude and vibration center displacement under quasi-zero stiffness is studied. Finally, the vibration characteristics of the train when the maglev system is in negative stiffness are analyzed by numerical simulation. The maglev system exhibits the worst vibration performance under negative stiffness compared with positive stiffness and quasi-zero stiffness. The suspension frame is easy to enter the chaotic motion state, and its vibration center is easy to deviate from the equilibrium position and produce large displacement when the maglev system is in the negative stiffness state. The control results show that the control strategy combining the cubic displacement feedback nonlinear control with the PD linear control can make the maglev system exhibit better vibration characteristics under positive and quasi-zero stiffness.

Optimizing Hydro-Pneumatic Inerter Suspension for Improved Ride Comfort and Handling Stability in Engineering Vehicles Using Simulated Annealing Algorithm

This study introduces a novel hydro-pneumatic inerter suspension (HPIS) system for engineering vehicles, aiming at enhancing ride comfort and handling stability. The research focuses on addressing the limitations of conventional suspension systems by incorporating an inerter element into the vehicle suspension. The unique aspects of HPIS, such as nonlinear stiffness and nonlinear damping characteristics of the hydro-pneumatic spring, are explored. Firstly, a half-car dynamic model of the HPIS suspension is established, and an improved simulated annealing algorithm is applied to optimize the suspension parameters. Then, we compare the dynamic performance of different HPIS structures, specifically parallel and series layouts. For practical analysis, a simplified three-element HPIS suspension model is used, and the suspension parameters are optimized by a simulated annealing algorithm at speeds of 10 m/s, 15 m/s, and 20 m/s. Key findings reveal that compared to the traditional suspension system of S0, the front and rear suspension working space of S1 decreased by 40%, 40.1%, 40.2% and 30.7%, 30.8%, 30.9%, while with the body acceleration and pitch acceleration deteriorated by 3.1%, 3.2%, 3.3% and 63.4%, 63.8%, 64.0%. However, the S2 can improve all the dynamic performance and offer better ride comfort and handling stability.

Research on AGC Nonlinear Compensation Control for Electro-Hydraulic Servo Pump Control of a Lithium Battery Pole Strip Mill

Electrode roll forming involves rolling a battery electrode into a preset thickness using a hydraulic roll gap thickness automatic control system (hydraulic AGC for short). The pump-controlled AGC is a highly nonlinear servo system, which is a combination of mechanical, hydraulic and electronic control disciplines; thus, as a new technology, it still faces many challenges in the field of pole plate rolling. In this paper, electro-hydraulic servo pump-controlled AGC technology is replaced by electro-hydraulic servo valve-controlled AGC technology. With pump-controlled AGC high-precision thickness control as the research objective, the fuzzy control method is selected to deal with complex nonlinear systems based on pump-controlled AGC nonlinear stiffness characteristics and nonlinear transmission characteristics. A characteristic compensation control strategy is proposed. At the same time, considering the load fluctuation caused by the uneven thickness of the electrode plate under the intermittent coating rolling condition of a lithium battery, the fuzzy internal model (IMC) compensation control strategy was proposed to compensate the structural characteristics of the electrode plate rolling. Comparative experiments show that the position control accuracy of the pump-controlled AGC system can be improved significantly by using a fuzzy IMC compensation control strategy. The steady-state accuracy of the slope signal can reach ±0.7 μm, and the position-following accuracy of the sinusoidal signal can reach ±1.8 μm. In addition, this study will assist technological upgrades to lithium battery electrode roll forming and fixed-roll-gap rolling, laying a theoretical foundation for the promotion of pump control technology in the field of electrode rolling.

Investigative Study of the Effect of Damping and Stiffness Nonlinearities on an Electromagnetic Energy Harvester at Low-Frequency Excitations

Ambient vibration energy is widely being harnessed as a source of electrical energy to drive low-power devices. The vibration energy harvester (VEH) of interest employs an electromagnetic transduction mechanism, whereby ambient mechanical vibration is converted to electrical energy. The limitations affecting the performance of VEHs, with an electromagnetic transduction structure, include its operational bandwidth as well as the enclosure-size constraint. In this study, an analysis and design of a nonlinear VEH system is conducted using the Output Frequency Response Function (OFRF) representations of the actual system model. However, the OFRF representations are determined from the Generalised Associated Linear Equation (GALE) decompositions of the system of interest. The effect of both nonlinear damping and stiffness characteristics, to, respectively, extend the average power and operational bandwidth of the VEH device, is demonstrated.

The Vibration Isolation Properties of an Asymmetrical Quasi-Zero Stiffness Isolator with Geometrical Nonlinear Damping

This paper proposes a Quasi-Zero-Stiffness (QZS) vibration isolator with asymmetric stiffness and geometric nonlinear damping. The nonlinear stiffness and nonlinear damping characteristics of proposed model are studied. The motion equation of proposed system under force excitation is established, and its dynamic response is solved by the Harmonic Balance Method (HBM). In addition, the influence of nonlinear damping on force transmissibility is studied. The results indicate that the proposed isolator has a large equivalent damping ratio in the resonance region and a small equivalent damping ratio in the high-frequency region. Therefore, the proposed asymmetrical QZS isolator with nonlinear damping can supress the resonance in lowfrequency under force excitation and achieve a good highfrequency vibration isolation effect simultaneously than that with linear damping.

Low-frequency vibration isolation via an elastic origami-inspired structure

This paper presents a new elastic origami-inspired structure with quasi-zero-stiffness (QZS) characteristics to provide effective low-frequency vibration isolation performance. The geometric structure of the origami mechanism is first introduced, followed by the establishment of its mechanical model through the integration of elastic joints with compression springs. The derived strong nonlinear stiffness characteristics of the elastic origami mechanism are conducive to exploring a QZS isolator with high performance. Then by using the multiscale method, the dynamic behavior of the origami-inspired isolator is obtained, and the parameter influencing investigations validate that the proposed vibration isolation system has strong design flexibility and superior vibration suppression capability. An experimental prototype was fabricated and a series of vibration testing experiments under different working conditions were carried out. The experimental results demonstrated the effectiveness of the established theoretical model. Furthermore, the comparison with typical nonlinear passive isolators verified the advantages of the developed origami-inspired vibration isolation system. This work has the potential to advance the practical applications of origami-based mechanisms and also provides a new technical candidate for high-performance vibration isolation systems.

Composite Beams Made of Waste Wood-Particle Boards, Fastened to Solid Timber Frame by Dowel-Type Fasteners

To increase the sustainability of prefabricated timber buildings and constructions, composite timber beams with "box" cross-sections were developed in collaboration with an industry partner. They were constructed from a solid timber frame and from webs made of residual waste wood-particle boards from prefabricated timber buildings production. The developed beams' design concepts presented in this paper were governed by architectural features of prefabricated timber buildings, geometrical limitations, available production technology, and structural demand related to various possible applications. The paper presents the results of experimental bending tests of six variations of the developed composite timber beams constructed by mechanical fasteners only. The developed design concept of composite timber beams without adhesives is beneficial compared to glued beams in terms of design for deconstruction and lower VOC emissions. The tests were conducted to study the influence of the following parameters on the beams' mechanical behavior: (i) web material (oriented strand boards (OSBs) vs. cement-particle boards); (ii) the influence of beam timber frame design (flanges and web stiffeners vs. flanges, web stiffeners, and compressive diagonals), and (iii) the influence of stiffener-flange joint design. Besides the beams' load-bearing capacities, their linear and non-linear stiffness characteristics were the main research interest. While adding compressive timber diagonals did not prove to significantly increase the stiffness of the beams in the case of cement-particle board webs, it increased their load-bearing capacity by enabling the failure of flanges instead of prior webs and stiffener-flange joints failure. For beams with OSB webs, failure of the bottom flange was achieved already with the "basic" timber frame design, but timber diagonals proved beneficial to increase the stiffness characteristics. Finally, mechanical characteristics of the developed beams needed in structural design for their application are provided together with further development guidelines.

Takagi–Sugeno Fuzzy Model-Based Control for Semi-Active Cab Suspension Equipped with an Electromagnetic Damper and an Air Spring

Variable damping shock absorbers have received extensive attention for their efficient vibration reduction performance, and air springs have also been widely used in high-end commercial vehicles due to their nonlinear stiffness characteristics. This paper presents a novel semi-active cab suspension integrated with an air spring and a variable damping electromagnetic damper (A-EMD). The electromagnetic damper (EMD) prototype was designed, manufactured and tested. Then, due to the interference of nonlinear stiffness characteristics of the air spring with the controller in the subsequent design, the Takagi–Sugeno fuzzy method was adopted to segmentally linearize its nonlinearity, based on which an H∞ state feedback semi-active controller was designed to control the EMD to generate variable damping force. Furthermore, a Luenberger state observer was designed to provide immeasurable state parameters for the controller. Numerical simulations were carried out to validate the effectiveness of the proposed approaches, and the results show that the proposed control strategy can significantly improve the ride comfort of the A-EMD system. The vibration dose value (VDV) acceleration under the bump road and the frequency-weighted acceleration root mean square (FWA-RMS) under the random road decreased by 36.05% and 19.77%, respectively, compared with the passive suspension system.

Nonlinear stiffness analysis and programming of a composite origami metamaterial with embedded joint-type metastructures

Origami metamaterials have tremendous application potential in the fields of advanced deployable mechanisms, intelligent robots, and energy absorption devices. In this paper, we embed the flexible joints with metamaterial properties into the origami metamaterial structure, making the origami mechanism have simultaneous geometric nonlinearity and joint stiffness nonlinearity, and investigate the nonlinear stiffness characteristics of this composite metamaterial in detail. To enhance the bearing capacity of the overall structure, the tension spring is mounted to simulate the elastic effect of the crease, and the mechanical metamaterial property of this flexible joint is also revealed theoretically. Based on the kinematics of Miura-ori pattern, the static nonlinear mechanical properties of the composite metastructure are obtained. Besides, the detailed parameter analysis gives an effective validation of the strong design flexibility of the proposed origami mechanism, and the stiffness property programming is realized by tuning structural parameters. Finally, an experimental system is established to test the static mechanical properties of the flexible joint and the origami mechanism, and the high agreement between experimental curves and theoretical results confirms the effectiveness and practicality of the composite metamaterial. This work is helpful for the design of origami metamaterials exploiting their stiffness nonlinearity.

Research on the Nonlinear Stiffness Characteristics of Double-Row Angular Contact Ball Bearings under Different Working Conditions

To study the variation rules of nonlinear stiffness of double-row angular contact ball bearings (DR-ACBB), this paper proposed a general mathematic model for DR-ACBB under three different configurations based on the improved quasi-static model of ball bearings, an explicit expression stiffness matrix of DR-ACBB is analytically derived, and a double-layer nested iterative algorithm based on the Newton–Raphson method is designed to realize the efficient solution of the proposed model. Then, the effects of the preload, speeds, and loads on the nonlinear stiffness variations of DR-ACBB under different arrangements are comparatively analyzed. The results show that DR-ACBB under the DB and DF configurations have the same variation rule in axial and radial stiffness; that is, a nonlinear soft-spring stiffness characteristic (i.e., the stiffness decreases with the external load) within the low-speed range and light load condition, and a nonlinear hard spring stiffness characteristic (i.e., the stiffness increases with the external load) within the high-speed range or heavy load condition.

Modeling and analysis of a metal rubber vibration isolation system considering the nonlinear stiffness characteristics.

In this study, the complete design process of a metal rubber isolator using a numerical method applied in automobile underwater gliders (AUGs) is researched. A ring-like metal rubber isolator that has the potential to reduce the vibration of the AUGs is proposed. In the numerical design method, the equivalent cantilever beam model is used to identify the mechanical properties of the metal rubber isolator, whose accuracy is verified by experiment. The static stiffness and dynamic stiffness are gained through a fitting method, considering different mass loadings. Different material parameters of a metal rubber isolator, such as relative densities, wire diameters, wire spiral pitch diameters, and mass loading from the power system, greatly influence the mechanical properties and stiffness characteristic. The vibration isolation performance of a metal rubber isolator applied in the AUG is evaluated by a nonlinear single degree of freedom dynamic model, which is solved by the harmonic balance method. The linear stiffness component of the metal rubber isolator is the main influence factor for the vibration isolation performance. The nonlinear stiffness component could shift the isolation frequency.

A low-frequency micro-vibration absorber based on a designable quasi-zero stiffness beam

This paper presents a low-frequency micro-vibration absorber based on a beam with designable nonlinear stiffness. The material and dimension parameters of the nonlinear characteristics of the beam are discussed by the finite element method (FEM). Based on the nonlinear stiffness characteristics of the beam, the designed micro-vibration absorber has a low-frequency vibration absorption effect and multiple working modes in multiple directions. The effects of structural parameters on the stiffness characteristics of the designed beam are discussed to explore the low-frequency performance. The results of FEM analysis are verified by vibration absorption experiments, and the effectiveness of the low-frequency vibration absorbers is verified by aerospace micro-vibration experiments.

Vibration fatigue life prediction method for needled C/SiC composite based on frequency response curve with low signal strength

The experimental results show that needled C/SiC composite exhibits nonlinear stiffness characteristics in the process of vibration. In order to consider the effect of the number of fiber layers on the fatigue properties, the SN curve related to the number of 0° layer fibers for needled C/SiC composite is proposed in this investigation. According to the relationship between the frequency response curve and the signal strength, an amplitude probability density function under narrow band random vibrations was proposed for predicting the fatigue life for the notched plate specimen. The results showed that the proposed method has a good prediction effect.

Modeling of normal contact stiffness for surface with machining textures and analysis of its influencing factors

A new contact stiffness model for the rough surface with different machining textures is established. The studied surface consists of regular surface machining texture in the global scale and stochastic micro-asperities in the local scale. The proposed model improves upon previous work that considers only the effect of stochastic asperities and completely ignores that of the machining textures generated by different machining methods. The analytical expression to calculate the contact stiffness of the studied textured surface is derived and numerical results are obtained via the finite element method. A high-precision test bench to measure the interface contact stiffness of the workpiece with different surface textures is designed. The measured results and simulated results are directly compared to demonstrate the validity of the proposed method. The effects of different texture types and surface roughness values on the contact stiffness of the proposed textured surface are analyzed. The proposed method provides a research basis for the accurate calculation of nonlinear contact stiffness and dynamic characteristics of the surface with complex texture topography.

Nonlinear Stiffness Characteristics and Model of Air Spring for Mattress based on Finite Element and Numerical Analysis

AbstractTo investigate the nonlinear stiffness characteristics and the model of an air spring for mattresses on arbitrary working conditions, a finite element model of an air spring is established, modified by response surface method and verified by uniaxial compression experiment on conditions of different initial inner pressure. Then the static stiffness characteristics on arbitrary working conditions are analyzed by finite element analysis in ABAQUS. In addition, the model for engineering control is established and the stiffness characteristics are analyzed by numerical method under working conditions. The results demonstrate the nonlinear stiffness of an air spring is positively correlated with the inner pressure and compression displacement. Additionally, a finite element model is established with average relative error ratio of 0.059 and 0.074 on conditions of compression by 20 and 30 mm, respectively, satisfying engineering requirement. Moreover, the stiffness model of an air spring on any working conditions is established by fitting surfacecontaining compression displacement and inner pressure at equilibrium position then calculating its partial derivative with respect to compression displacement. The present study suggests the nonlinear stiffness prediction model of an air spring is applicable to any working conditions, only requiring inner pressure at initial and equilibrium conditions.

Skyhook Control Law Extension for Suspension with Nonlinear Spring Characteristics

This work aimed to improve the vehicle body stability and the ride comfort of the tracked military vehicle crew. For this purpose, magnetorheological fluid dampers were used. This process has made the theoretical model of the tracked platform a semi-active suspension system. This modification allows for the application of different control laws to these systems. The usage of the continuous skyhook control law assumes the influence of three fictitious viscous dampers. Their force in this conceptual model is replicated by the magnetorheological dampers of the suspension in the real system. However, the continuous skyhook control law does not take into consideration the nonlinear stiffness characteristics. In this paper, the continuous skyhook control law has been appropriately modified. The modification takes into consideration the nonlinearity of the stiffness characteristics. Applying the modified continuous skyhook control law improves the stability of the vehicle body and the vehicle crew’s ride comfort. All these goals had to be introduced due to the modernization of the tracked military vehicle suspension by replacing the torsion bars with spiral spring packages with nonlinear characteristics.