Nonlinear Spring Characteristics Research Articles

Effect of Nonlinear Spring Characteristics on the Efficiency of Free-Piston Engine Generator

Piston motion is an important factor in improving the energy conversion efficiency of free-piston engine generators (FPEGs), and an air cylinder is an important component affecting piston motion. In this study, the effect of the air cylinder specifications on the piston drive frequency and energy conversion efficiency is clarified. By considering that the repulsion force of an air cylinder is nonlinear, the main factors that change the piston drive frequency were investigated by simulation. In addition, a piston drive frequency diagram was drawn based on the top surface area of the air cylinder and the compression ratio to discuss the effect of the air cylinder specifications on the piston drive frequency. The results indicate that the air cylinder specifications affect the piston drive frequency and generation force of a linear machine. Moreover, the structure of the air cylinder and the constraints on the maximum generation force of the linear machine narrow the possible operating range in the piston drive frequency. The air cylinder specifications based on the piston drive frequency diagram improved the FPEG energy conversion efficiency by 0.5%.

From underactuation to quasi‐full actuation: Aiming at a unifying control framework for articulated soft robots

AbstractWe establish a structure preserving state and input transformation that allows a class of underactuated Euler Lagrange systems to be treated as “quasi‐fully” actuated. In this equivalent quasi‐fully actuated form, the system is characterized by the same Lagrangian structure as the original one. This facilitates the design of control approaches that take into account the underlying physics of the system and that shape the system dynamics to a minimum extent. Due to smoothness constraints on the new input vector that acts directly on the noncollocated coordinates, we coin the term quasi‐fully actuated. The class of Euler–Lagrange systems we consider is the class of articulated soft robots with nonlinear spring characteristics that are modeled with a block diagonal inertia matrix. We illustrate how the quasi‐fully actuated form enables the direct transfer of control concepts that have been derived for fully actuated manipulators. We adopt the popular energy‐shaping and two passivity‐based concepts. The exemplary adoptions of the PD+ and Slotine and Li controllers allow us to solve the task‐space tracking problem for highly elastic joint robots with nonlinear spring characteristics. These control schemes allow compliant behavior of the robot's TCP to be specified with respect to a reference trajectory. A key aspect of the presented framework is that it enables the adoption of rigid joint controllers as well as concepts underlying the original stability analysis. We believe that our framework presents an important step toward unifying the control design for rigid and articulated soft robots.

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.

Performance evaluation of CFRP spring for freight car with lowering bed height in scale model

In recent years, there has been an increase in the volume of 40-ft marine high-cube containers handled in logistics in Japan. In Japan, the height of 40-ft marine high-cube containers limits the number of sections where they can be transported by rail. To solve this problem, it is necessary to develop a new freight car with a cargo bed height of 700 mm, which is 300 mm lower than a conventional freight car (bed height: 1000 mm) currently in use. For this purpose, a new carbon fiber reinforced plastic (CFRP) model secondary suspension spring with a lowered spring height has been developed to expand the possibilities of lowered bed height. Previous research has shown that the proposed CFRP spring is effective as a space- saving spring and it has nonlinear spring characteristics. Tests were conducted using different materials and shapes for the components of the spring. This paper shows the factors that change the nonlinear characteristics of the proposed CFRP spring.

High dimensional nonlinear spring characteristic modelling and vibration analyses of subharmonic resonance of a dual-rotor system based on energy tracks

The subharmonic resonance is a typical nonlinear vibration that occurs in a nonlinear rotor system. In this paper, expressions of the potential energy of rotor systems are derived systematically, and the high dimensional nonlinear spring characteristic modelling is revealed firstly through the potential energy with nonlinear variation characteristics. A novel nonlinear dual-rotor model considering nonlinear spring characteristics is proposed to reveal the inducing mechanism of subharmonic resonances of rotors and to study vibration characteristics of subharmonic resonances of the dual-rotor system. The new concepts such as energy tracks, the energy-phase plane and energy-spectrum analyses are presented to analyze nonlinear variation characteristics of the potential energy of rotors, and results show that different nonlinear coefficients correspond to subharmonic resonances of different orders, respectively. The resonance responses in the vicinities of critical speeds of subharmonic resonances of orders 1/2 and 1/3 to be obtained by numerical simulations and theoretical analyses are discussed comprehensively. It is found that a group of independent branching solutions in the solution space appears corresponding to subharmonic resonances in the vicinity of coupling subharmonic critical speeds. In addition, analysis results of numerical simulations based on energy concepts are consistent with results of theoretical analyses about the potential energy of rotors. This study is beneficial to understand the inducing mechanism of subharmonic resonances of rotors, and verifies the correctness of the high dimensional nonlinear spring characteristic modelling and the proposed nonlinear dynamic model of the dual-rotor system.

Research of the internal resonances on a nonlinear dual-rotor based on the energy tracks shifting

The complex coupling characteristics of a dual-rotor system make the mechanism of nonlinear vibrations different from that of a single rotor system. Research of nonlinear vibration of the dual-rotor is beneficial to improve the stability of an aero-engine. Based on nonlinear spring characteristics of rotors, a novel nonlinear dual-rotor dynamics model coupled by the inter-shaft bearing is proposed, and internal resonances on the dual-rotor system are systematically studied. Considering nonlinearities, internal resonance phenomena occurring in the vicinity of the coupling critical rotational speed are systematically analyzed by numerical simulation results such as time histories, Poincare maps, bifurcation maps and largest Lyapunov exponents. Theoretical solutions are calculated based on the improved shooting method and stabilities of theoretical solutions are investigated by using the Floquet theory. The theoretical solutions are consistent with numerical simulation results well. The concepts of the energy track shifting, the energy-Poincare map, stabilities of energy tracks and the energy supplying function are introduced to analyze nonlinear vibration characteristics for the first time. The internal resonance phenomena of the low pressure rotor and the complex nonlinear vibrations of the high pressure rotor are qualitatively analyzed based on the energy viewpoint, and the energy tracks are verified by experiments. Research shows that energy tracks can characterize vibration characteristics well and the energy supplying function provide a possible way to quantify the energy transfer between rotors in the multi-rotor system.

Dynamic Behavior Analysis of Feed Drive System Using Linear Guideways with Different Ball Diameters

The feed drive system for machine tool consist of rolling elements such as ball screw and linear guides. It is well known that in the positioning of linear guides using steel ball rolling, the contact surface has nonlinear spring characteristics. This phenomenon is deteriorating the accuracy of the machine tool. In this study, we have manufactured a feed drive system in which the physical contacts are only linear guides by using a linear motor as actuator. At first, we measured the responses to some fine feed amount for feed drive system. Next, the same experiment was performed by changing the linear guideways. This paper presents the transition of nonlinear spring characteristic region by considering the response to linear guides under different conditions.

Seismic Analysis of Coupled High-Speed Train-Bridge with the Isolation of Friction Pendulum Bearing

The paper presents a framework for the seismic analysis of the coupled high-speed train-bridge with the isolation of friction pendulum bearing (FPB). Taking the rail irregularities as system’s self-excitation with the seismic as external excitation, the equation of motion of the train-bridge coupled system under earthquake is built up. A five-span simple-supported railway bridge is taken as an example, and the computer simulation method is used to establish the dynamic model of the train-bridge system with the isolation of FPB under earthquake. A train composed of eight 4-axle coaches of 35 degrees-of-freedom (DOF) is considered, and FPB is simulated by a force element which includes both nonlinear spring and damper characteristics and a hysteresis function. Backward differentiation formula and the mode superposition method are adopted in the calculation of coupling vibration of the train-bridge system. The dynamic responses of the train running on the bridge with the isolation of FPB and with the common spherical bearing (CSB) under earthquake are studied. The results show that FPB with a friction coefficient no less than 0.05, instead of CSB, can reduce the dynamic response of the train greatly; the faster the train speed and the higher the pier, the greater the effect of FPB. However, FPB may increase the dynamic response of the train when the seismic intensity exceeds 0.14 g.

Design of a robust LQG Compensator for an Electric Power Steering

The control of the driver’s hand torque of an electric power steering system has been state of the art for years. However, due to nonlinear spring characteristics, gear ratios, and degrees of freedom which are unconsidered in the design model for the controller or observer design, the challenge still lies in the robust implementation of this control approach. In this paper, the results of a systematic model and system analysis are used to develop an approach that solves the current stability and robustness problems existing in the serial development of steering systems while maintaining the same control quality. For this, a modified optimal control design is applied which uses an augmented design model.

Vibration analysis of a novel magnetic-viscous nonlinear passive isolator via finite element simulation

In this paper, the design and the finite element simulation of a novel magnetic-viscous vibration isolator have been presented. The proposed isolator consists of permanent magnets axially aligned in repulsion position and a viscous damper in parallel with them. The nonlinear spring characteristic of the permanent magnets provides a good damping property with this configuration. Explicit finite element analyses have been conducted to examine the dynamic behavior of the isolator. Output displacements and transmissibility ratios were measured for various magnet configurations, dashpot coefficients, and input displacement excitation frequencies to determine the best damping properties. The results of the finite element modeling revealed that the performance of the isolator is highly sensitive to the quantity of magnets. Isolators with four or more magnets can successfully reduce the output displacement. The results indicate that the isolator significantly reduces the displacement transmissibility in frequencies over the resonant frequency region. It is possible to ensure an infinite operating life for magnet-viscous vibration isolators by protecting the magnets against breakage.

Nonlinear Dynamic Analysis of a Japanese bow (Nonlinear Spring Characteristics and Dynamic Behavior)

Nonlinear Dynamic Analysis of a Japanese bow (Nonlinear Spring Characteristics and Dynamic Behavior)

Identification of a nonlinear spring and damper characteristics of a motorcycle suspension using test ride data

AbstractDuring test rides of motorcycles modifications are made to the suspension. In order to quantify those changes, the nonlinear spring and damper characteristics must be determined. This is usually done on a test bench. However, measurements on a test bench are closely related to high costs and high time exposure. Hence, a parameter identification after a test run, formulated as an optimization task, seems to be an auspicious approach. For this purpose a cost function is defined, which is minimized by considering the dynamics of the system. The strength of the contribution is the efficient gradient computation using the adjoint variable approach. In order to approximate the nonlinear spring and damper characteristics cubic splines are used. The values of the spline functions at specified grid points (knots) are adjusted such that the deviation between simulation and measurement is minimal.

Bifurcations of periodic motion of a horizontally supported nonlinear Jeffcott rotor system having transversely cracked shaft

This article investigates the periodic motion bifurcations of a horizontally supported nonlinear Jeffcott rotor system having transversely cracked shaft. The nonlinear spring characteristics due to Hertz contact force and bearing clearance, disc weight, disc eccentricity, breathing of the shaft crack, and angle between the crack and imbalance directions are included in the system model. A mathematical model governing the cracked system lateral vibrations is derived and then analyzed utilizing asymptotic analysis in the primary resonance case. Effects of disc eccentricity, creak depth, and angle between the crack and imbalance directions on the system response curves are studied. The analysis revealed that at a small crack depth, the system executes both forward and backward whirling motions at a specific range of the disc spinning speed, while the backward whirling orbits disappear as the crack depth increases. In addition, at zero disc eccentricity, the cracked system does not oscillate unless the system linear stiffness coefficient is reduced by about 11% as a result of shaft crack. Moreover, there is a spinning speed range of the rotating shaft at which two stable periodic solution attractors appear beside the trivial solution one when the linear stiffness coefficient of the system is reduced to 20% or more. The obtained analytical results are confirmed numerically that showed a very good agreement with the numerical ones. Finally, the acquired results are compared with the work published in the literature.

High‐Precision Sensorless Force Control by Mode Switching Controller for Positioning Devices with Contact Operation

SUMMARYThis paper presents an approach to high‐precision sensorless force control for positioning devices that engage in a contact operation. The sensorless force control is designed with a sliding mode controller and contact model that provide the required control specifications to compensate for the nonlinear spring characteristics of the contact mechanism. The effectiveness of the proposed control approach was verified through numerical simulations and experiments using a prototype.

Design and Implementation of a Distributed Variable Impedance Actuator Using Parallel Linear Springs

This paper introduces a distributed variable impedance actuator that provides independent control of the actuator's angular position and its impedance. The idea for the actuator was inspired by the morphological structure of muscles and tendons. The system to be presented can be used as both a variable impedance actuator as well as a passive piecewise linear spring. Moreover, the actuator has an adequate number of degrees-of-freedom to approximate any nonlinear spring characteristics because of its distributed nature. Using distributed torque production subsystems with small and low power motors makes it possible to use this actuator in many applications such as prosthesis, artificial limbs, and wearable robots. The stability of the system discussed and the conditions that ensure the system stability are presented. Finally, a proof-of-concept actuator design is presented, as well as experimental results which confirm that the proposed distributed variable impedance actuator can be implemented in practical applications.

Frictionless elastic contact of crowned roller: Approximate analytical calculation of compliance and contact area

Formulas for Hertzian frictionless elastic contact are well-known and have been used for a long time. However, they are not directly applicable for a crowned roller, a cylindrical roller with symmetrically rounded corners, deflecting a half-space. For this punch shape, the approximate analytical method of Barber and Billings ( Int J Mech Sci 1990; 32(12): 991–997) was adapted to compute the load–deflection curve and the contact boundary avoiding calculation of pressure distribution. Comparisons were performed with finite element method (FEM) simulations, an adaptive Hertzian quadratic punch surface approximation (AHA) and other published results. Good agreement of analytical load–deflection curves with FEM results was noted but the AHA results deviated significantly from the former two. The FEM contact area resembled a dog-bone shape, the analytical a bow-tie shape and the AHA, by design, an ellipse. Though the AHA contact area was closer to the FEM result numerically, the contact boundary aspect ratio of the analytical model was closer to the FEM. The analytical results simulating conditions from other publications agreed quantitatively for the load–deflection curves and qualitatively for the contact boundary. The non-linear spring characteristic of the crowned roller was quantitatively evaluated for a diverse range of geometry.

折り畳み可能な構造の非線形ばね特性を利用した防振機構

折り畳み可能な構造の非線形ばね特性を利用した防振機構

High-Precision Sensorless Force Control by Mode Switching Controller for Positioning Devices with Contact Operation

This paper presents a high-precision sensorless force control for positioning devices with contact operation. The sensorless force control is designed with a sliding mode controller and contact model that provide the required control specifications to compensate for the non-linear spring characteristics of the contact mechanism. The effectiveness of the proposed control approach was verified through numerical simulations and experiments using a prototype.

The energy thresholds of nonlinear vibration absorbers

A popular means to mitigate excessive structural vibrations is the attachment of a lightweight spring-mass element, known as a vibration absorber or tuned mass damper. Designing new types of vibration absorbers that outperform the classical linear tuned mass damper is a challenging ongoing research field. This paper focuses on the absorber with a strongly nonlinear spring characteristic. A critical aspect in the design procedure of such nonlinear vibration absorber is the existence of energy thresholds below which no efficient vibration reduction is possible. This paper extends the concept of an energy threshold to a more general parameter threshold representing several threshold values. Two important contributions are obtained. First, one single bifurcation analysis covers every combination of the system parameters. Second, the results are generalized to linear main systems under impulsive load and harmonic load, nonlinear main systems, and general nonlinear spring characteristics.

Shaking table test and analysis method on ultimate behavior of slender base‐isolated structure supported by laminated rubber bearings

AbstractThis paper describes the results of shaking table tests to ascertain the ultimate behavior of slender base‐isolated buildings and proposes a time history response analysis method, which can predict the ultimate behavior of base‐isolated buildings caused by buckling fracture in laminated rubber bearings. In the tests, a base‐isolated structure model weighing 192 kN supported by four lead rubber bearings is used. The experimental parameters are the aspect ratio of height‐to‐distance between the bearings and the shape of and the axial stress on the bearings. The test results indicate that the motion types of the superstructure at large input levels can be classified into three types: the sinking type; the uplift type; and the mixed type. These behaviors depend on the relationship between the static ultimate lateral uplifting force on the superstructure and the lateral restoring characteristics of the base‐isolated story. In the analysis method, bearing characteristics are represented by a macroscopic mechanical model that is expanded by adding an axial spring to an existing model. Nonlinear spring characteristics are used for its rotational, shear, and axial spring. The central difference method is applied to solve the equation of motion. To verify the validity of the method, simulation analysis of the shaking table tests are carried out. The results of the analysis agree well with the test results. The proposed model can express the buckling behavior of bearings in the large deformation range. Copyright © 2010 John Wiley & Sons, Ltd.