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The purpose of this paper is to investigate the optimum design of a quarter car passive suspension system using a particle swarm optimization algorithm in order to minimize the applied loads and vibrations.

The road excitation is assumed as zero-mean random field and modeled by single-sided power spectral density (PSD) based on international standard ISO 8608. The variance of sprung mass displacements and variance of dynamic applied load are evaluated by PSD functions and used as cost function for the optimization.

The advantages in using this methodology are emphasized by an example of the multi-objective optimization design of suspension parameters and the results are compared with values reported in the literature and other gradient based and heuristic algorithms. The paper shows that the algorithm effectively leads to reliable results for suspension parameters with low computational effort.

The procedure is applied to a quarter car passive suspension design.

The proposed procedure implies substantial time savings due to frequency domain analysis.

The paper proposes a procedure that allows complex optimization designs to be feasible and cost effective.

The design optimization is performed in the frequency domain taking into account standard defined road profiles PSD without the need to simulate in the time domain.

This study aims to propose a complete and powerful methodology that allows the optimization of the passive suspension system of vehicles, which simultaneously takes comfort and safety into account and provides a set of optimal solutions through a Pareto-optimal front, in a low computational time.

Unlike papers that consider simple vehicle models (quarter vehicle model or half car model) and/or simplified road profiles (harmonic excitation, for example) and/or perform a single-objective optimization and/or execute the dynamic analysis in the time domain, this paper presents an effective and fast methodology for the multi-objective optimization of the suspension system of a full-car model (including the driver seat) traveling on an irregular road profile, whose dynamic response is determined in the frequency domain, considerably reducing computational time.

The results showed that there was a reduction of 28% in the driver seat vertical acceleration weighted root mean square (RMS) value of the proposed model, which is directly related to comfort, and, simultaneously, an improvement or constancy concerning safety, with low computational cost. Hence, the proposed methodology can be indicated as a successful tool for the optimal design of the suspension systems, considering, simultaneously, comfort and safety.

Despite the extensive literature on optimizing vehicle passive suspension systems, papers combining multi-objective optimization presenting a Pareto-optimal front as a set of optimal results, a full-vehicle model (including the driver seat), an irregular road profile and the determination of the dynamic response in the frequency domain are not found.

This study aims to propose an efficient method for solving reliability-based design optimization (RBDO) problems.

In the proposed algorithm, genetic algorithm (GA) is employed to search the global optimal solution of design parameters satisfying the reliability and deterministic constraints. The Kriging model based on U learning function is used as a classification tool to accurately and efficiently judge whether an individual solution in GA belongs to feasible region.

Compared with existing methods, the proposed method has two major advantages. The first one is that the GA is employed to construct the optimization framework, which is helpful to search the global optimum solutions of the RBDO problems. The other one is that the use of Kriging model is helpful to improve the computational efficiency in solving the RBDO problems.

Since the boundaries are concerned in two Kriging models, the size of the training set for constructing the convergent Kriging model is small, and the corresponding efficiency is high.

In this paper, improvements in reducing transmitted accelerations in a full vehicle are obtained by optimizing the gain parameters of an active control in a roughness road profile.

For a classically designed linear quadratic regulator (LQR) control, the vibration attenuation performance will depend on weighting matrices Q and R. A methodology is proposed in this work to determine the optimal elements of these matrices by using a genetic algorithm method to get enhanced controller performance. The active control is implemented in an eight degrees of freedom (8-DOF) vehicle suspension model, subjected to a standard ISO road profile. The control performance is compared against a controlled system with few Q and R parameters, an active system without optimized gain matrices, and an optimized passive system.

The control with 12 optimized parameters for Q and R provided the best vibration attenuation, reducing significantly the Root Mean Square (RMS) accelerations at the driver’s seat and car body.

The research has positive implications in a wide class of active control systems, especially those based on a LQR, which was verified by the multibody dynamic systems tested in the paper.

Better active control gains can be devised to improve performance in vibration attenuation.

The main contribution proposed in this work is the improvement of the Q and R parameters simultaneously, in a full 8-DOF vehicle model, which minimizes the driver’s seat acceleration and, at the same time, guarantees vehicle safety.

Semi-active suspension systems with electromagnetic dampers allow energy regeneration and the required control strategies are easier to implement than the active suspensions are. This paper aims to address the application of a tubular linear permanent magnet synchronous machine for a semi-active suspension system.

Classical rules of mechanics and electromagnetics were applied to describe a dynamic model combining vibration and electrical machines theories. A multifaceted MATLAB®/Simulink model was implemented to incorporate equations and simulate global performance. Experimental tests on an actual prototype were carried out to investigate displacement transmissibility of the passive case. In addition, simulation results were shown for the dissipative semi-active case.

The application of the developed model suggests convergent results. For the passive case, numerical and experimental outcomes validate the parameters and confirm system function and proposed methodology. MATLAB®/Simulink results for the semi-active case are consistent, showing an improvement on the displacement transmissibility. These agree with the initial conceptual thoughts.

The use of linear electromagnetic devices in suspension systems is not a novel idea. However, most published papers on this subject outline active solutions, neglect semi-active ones and focus on experimental studies. However, here a dynamic mechanical-electromagnetic coupled model for a semi-active suspension system is reported. This is in conjunction with a linear electromagnetic damper.

The purpose of this paper is to evaluate the locomotion performance of all‐terrain rovers employing rocker‐type suspension system.

In this paper, a robot with advanced mobility features is presented and its locomotion performance is evaluated, following an analytical approach via extensive simulations. The vehicle features an independently controlled four‐wheel‐drive/4‐wheel‐steer architecture and it also employs a passive rocker‐type suspension system that improves the ability to traverse uneven terrain. An overview of modeling techniques for rover‐like vehicles is introduced. First, a method for formulating a kinematic model of an articulated vehicle is presented. Next, a method for expressing a quasi‐static model of forces acting on the robot is described. A modified rocker‐type suspension is also proposed that enables wheel camber change, allowing each wheel to keep an upright posture as the suspension conforms to ground unevenness.

The proposed models can be used to assess the locomotion performance of a mobile robot on rough‐terrain for design, control and path planning purposes. The advantage of the rocker‐type suspension over conventional spring‐type counterparts is demonstrated. The variable camber suspension is shown to be effective in improving a robot's traction and climbing ability.

The paper can be of great value when studying and optimizing the locomotion performance of mobile robots on rough terrain. These models can be used as a basis for advanced design, control and motion planning.

The paper describes an analytical approach for the study of the mobility characteristics of vehicles endowed with articulated suspension systems. A variable camber mechanism is also presented.

Periodic inspection of bridge cables is essential, and cable-climbing robots can replace human workers to perform risky tasks and improve inspection efficiency. However, cable inspection robots often fail to surmount large obstacles and cable clamps. The purpose of this paper is to develop a practical cable inspection robot with stronger obstacle-surmounting performance and circumferential rotation capability.

A cable inspection robot with novel elastic suspension mechanisms and circumferential rotation mechanisms is designed and proposed in this study. The supporting force and spring deformation of the elastic suspension are investigated and calculated. Dynamic analysis of obstacle surmounting and circumferential rotation is performed. Experiments are conducted on vertical and inclined cables to test the obstacle-surmounting performance and cable-clamp passing of the robot. The practicality of the robot is then verified in field tests.

With its elastic suspension mechanisms, the cable inspection robot can carry a 12.4 kg payload and stably climb a vertical cable. The maximum heights of obstacles surmounted by the driving wheels and the passive wheels of the robot are 15 mm and 13 mm, respectively. Equipped with circumferential rotation mechanisms, the robot can flexibly rotate and successfully pass cable clamps.

The novel elastic suspension mechanism and circumferential rotation mechanism improve the performance of the cable inspection robot and solve the problem of surmounting obstacles and cable clamps. Application of the robot can promote the automation of bridge cable inspection.

The purpose of the paper is to study the stability control of permanent magnet (PM) and electromagnetic hybrid Halbach array electrodynamic suspension (EDS) system because of the poor suspension stability caused by the well-known under-damped nature of PM EDS system. The adjustment control is realized by PM and electromagnetic hybrid Halbach array, which is composed by winding active normal conductor coils on PM surface.

The three-dimensional (3-D) electromagnetic force analytical expression of PM and electromagnetic hybrid Halbach array EDS system for a nonmagnetic conductive plate is derived. And the accuracy of the derived equations is verified by a 3-D finite-element model (FEM). Basing on the 3-D levitation force expression, an acceleration feedback suspension controller is designed to suppress the vibration of PM EDS system, and the suspension stability of the system under the track and load disturbance was simulated and analyzed.

The 3-D electromagnetic force comparison of analytical model and FEM are in good agreement, which verifies the correctness of the analytical expression. The simulation results show that the acceleration feedback suspension controller can make the system have good suspension stability under the external disturbance. So it proved that the PM and electromagnetic hybrid Halbach array EDS system can overcome the poor suspension stability caused by the under-damped nature of PM EDS system through the designed acceleration feedback suspension controller.

This paper designed an acceleration feedback suspension controller to suppress the vibration of PM and electromagnetic hybrid Halbach array EDS system under external disturbance, basing on the derived levitation force analytical expression. And the simulation results show that the acceleration feedback suspension controller can make the system have good suspension stability under the external disturbance.

A conveyor device is studied with the aim to reduce the friction between the inner surface of the beam and the chain. The lower is the friction between the chain and the beam, the lower is the surface wear. The magnetic repulsion force among permanent magnets (PMs) placed on the beam and on the chain is utilized to reduce friction. The paper aims to discuss these issues.

The considered magnetic suspension is realized with PMs in repulsive configuration; it is designed by solving a constrained optimization problem, with reference to the geometry of the 90° horizontal bend FlexLink WL322 conveyor. Flux density field and its gradient are evaluated using volume integral equation method, allowing to calculate the forces acting on the chain and the stiffness of the magnetic suspension.

The magnetic suspension prototype was manufactured and tested. The experimental and calculated values of the forces acting on the chain compares well. A stable horizontal equilibrium of the chain was obtained during both static and dynamical tests.

The quasi-static model used neglects the dynamical interactions among the elements of the chain, the PMs and loads weight during motions and the eddy current losses in the aluminium beam. However the dynamical tests on the prototype show that the chain motion is regular up to the nominal velocity all along the conveyor with the exception of the trailing edge of the 90° curve.

The tests on the prototype show the possibility of a removal or at least a reduction of the friction force between the chain and the inner side of the beam by means of a passive magnetic suspension. As a consequence a reduction of noise and vibrations and an increase of the mean-time-to-failure is expected.

Prototype testing shows that the unavoidable vertical instability of the magnetic forces has no practical consequence since, reducing the allowed vertical gap, the chain is stabilized by the gravitational force.

The purpose of this paper is to develop a new wheel control scheme for wheeled vehicle with passive linkage mechanism which realizes high step‐overcoming performance.

Developing wheeled vehicle realizes omni‐directional motion on flat floor using special wheels and passes over non‐flat ground using the passive suspension mechanism. The vehicle changes its body shape and wheel control references according to ground condition when it runs over the rough terrain.

Utilizing the proposed wheel control scheme, the slip ratio and the disturbance ratio of the wheel reduce when the vehicle passes over the step and its step‐overcoming performance is improved.

The paper's key idea is modification of its kinematic model referring to the body configuration dynamically and using this model for wheel control of the vehicle. The controller adjusts the wheel control references when the vehicle passes over the rough terrain changing the body shape and reduces the slippage and the rotation error of wheels.