Applications of Approximate Optimal Control to Nonlinear Systems of Tracked Vehicle Suspensions

Technique of approximate optimal vibration control and simulation for vehicle active suspension systems are developed. Considered the nonlinear damping of springs, mechanical model and a nonlinear dynamic system for a class of tracked vehicle suspension vibration control are established and the corresponding system of state space form is described. To prolong the working life of suspension system and improve ride comfort, based on the active suspension vibration control devices and using optimal control approach, an approximate optimal vibration controller is designed, and an algorithm is presented for the vibration controller. Numerical simulation results illustrate the effectiveness of the proposed technique.

Estimating the forcing function in a mechanical system by an inverse calibration method

This article proposes and demonstrates a calibration-based integral formulation for resolving the forcing function in a mass–spring–damper system, given either displacement or acceleration data. The proposed method is novel in the context of vibrations, being thoroughly studied in the field of heat transfer. The approach can be expanded and generalized further to multi-variable systems associated with machine parts, vehicle suspensions, translational and rotational systems, gear systems, etc. when mathematically described by a system of constant property, linear, time-invariant ordinary differential equations. The analytic approach and subsequent numerical reconstruction of the forcing function is based on resolving a parameter-free inverse formulation for the equation(s) of motion. The calibration approach is formulated in the frequency domain and takes advantage of several observations produced by the dimensionality reduction leading to an algebratized system involving an input–output relationship and a transfer function possessing all the system parameters. The transfer function is eliminated in lieu of experimental data, from a calibration effort, thus leading to a reduction of systematic errors. These parameter-free, reduced systematic error aspects are the distinct and novel advantages of the proposed method. A first-kind Volterra integral equation is formed containing only the unknown forcing function and experimental data. As with all ill-posed problems, regularization must be introduced for system stabilization. A future-time technique is instituted for forming a family of predictions based on the chosen regularization parameter. The optimal regularization parameter is estimated using a combination of phase–plane analysis and cross-correlation principles. Finally, a numerical simulation is performed verifying the proposed approach.

Study of Viscoelastic Rubber Mounts on Vehicle Suspensions with In-Wheel Electric Motors

Rubber bushings and mounts are vastly used in automotive applications as support and interface elements. In suspension systems, they are commonly employed to interconnect the damping structure to the chassis. Therein, the viscoelastic nature of the material introduces a desirable filtering effect to reduce mechanical vibrations. When designing a suspension system, available literature often deals with viscoelastic mounts by introducing a linear or nonlinear stiffness behavior. In this context, the present paper aims at representing the rubber material using a proper viscoelastic model with the selection of different in-wheels motors. Thus, the mount dynamic behavior’s influence in a suspension is studied and discussed thoroughly through numerical simulations and sensitivity analyses. Furthermore, guidelines are proposed to orient the designer when selecting these elements.

Damping Variation Effects in Vehicle Semi-active MR Suspensions: A Stress Concentration Analysis

Semi-active vehicle suspensions are used to improve the limited comfort performance of passive vehicle suspensions by varying the damping coefficient according to a control strategy. These benefits have been usually studied in a transient and frequency domain, but rarely in a multi-body dynamic analysis considering the mechanical components and their joints. In this study, the controllability effects of a magnetorheological (MR) damper on the mechanical components of a McPherson automotive suspension are investigated using a stress concentration analysis. Finite element analysis was used with a Quarter of Vehicle (QoV) suspension model configured with an MR damper, and then compared with the passive damper. The simulation results show that an SA damper in the suspension not only improves the dynamic behavior of a road vehicle, but it also has the positive effect of reducing the stress concentrations in a critical suspension element, the knuckle, that are generated by high amplitude road profiles such as rough roads or dangerous street bumps.

Skyhook control strategy for vehicle suspensions based on the distribution of the operational conditions

In this work, a novel distribution-based control strategy of semi-active vehicle suspensions is tested under different conditions. The novelty lies in the use of an appropriate threshold in the operational condition of the control algorithm, with which the operational conditions severity is quantified and the state of the damper is controlled according to the magnitude of the operational conditions and not their sign. The value of the threshold depends on the vibrations induced to the sprung mass by the road profile. In order to be evaluated, the operational conditions of the algorithm are fitted to a t-student distribution. The cumulative distribution function of this distribution is used in order to decrease the fraction of the sample operating with the damper’s stiff state. The strategy is applied to traditional SH control algorithms and is tested using a quarter car model excited by different road excitations. A sensitivity analysis for various threshold values is performed, investigating the impact of adopting the cumulative distribution functioned (CDF) controller to various performance metrics. The results illustrate an increase of up to 13% in the ride comfort of the passengers and increase of 6% in the road holding of the vehicle. Both are achieved by minimizing the switches of the damping ratio up to 80%.

Discharge Coefficients of a Heavy Suspension Nozzle

The suspensions used in heavy vehicles often consist of several oil and two gas chambers. In order to perform an analytical study of the mass flow transferred between two gas chambers separated by a nozzle, and when considering the gas as compressible and real, it is usually needed to determine the discharge coefficient of the nozzle. The nozzle configuration analyzed in the present study consists of a T shape, and it is used to separate two nitrogen chambers employed in heavy vehicle suspensions. In the present study, under compressible dynamic real flow conditions and at operating pressures, discharge coefficients were determined based on experimental data. A test rig was constructed for this purpose, and air was used as working fluid. The study clarifies that discharge coefficients for the T shape nozzle studied not only depend on the pressure gradient between chambers but also on the flow direction. Computational Fluid Dynamic (CFD) simulations, using air as working fluid and when flowing in both nozzle directions, were undertaken, as well, and the fluid was considered as compressible and ideal. The CFD results deeply helped in understanding why the dynamic discharge coefficients were dependent on both the pressure ratio and flow direction, clarifying at which nozzle location, and for how long, chocked flow was to be expected. Experimentally-based results were compared with the CFD ones, validating both the experimental procedure and numerical methodologies presented. The information gathered in the present study is aimed to be used to mathematically characterize the dynamic performance of a real suspension.

Vibration analysis of nonlinear and linear elastic systems

Objective. In this study, the task is to establish the theoretical prerequisites for the operability of a regressive-progressive elastic mechanism by comparing the amplitude-frequency characteristics and phase trajectories with a linear elastic system of comparable stiffness in a static equilibrium position.Methods. The article presents a comparative dynamic analysis of vibrations of elastic systems with linear rigidity and regressive-progressive characteristics obtained as a result of the use of elastic elements in the form of high flexibility rods with longitudinal eccentric compression. Such elastic elements in various design variants have been tested and patented as damping elements for use in the construction of vibration dampers for construction structures and vehicle suspensions, and have experimentally shown their effectiveness in damping vibrations.Results. The regressiveprogressive elastic characteristic obtained by the elliptic parameters method and using the ANSIS calculation complex is used in the dynamics equations in an approximated form, which expands the capabilities of the method. It is shown that increasing the energy intensity of a curvilinear system reduces the vibration amplitude.Conclusion. The regressive-progressive change of the stiffness of curvilinear elastic systems can be achieved using an elastic element with eccentric longitudinal compression; the regression plot of elastic properties is achieved due to eccentric compression; the progressive plot – through the use of a guide or other design solutions. The implementation of this characteristic allows using such elastic mechanisms in systems where the accumulation of potential energy occurs with a smaller compression stroke for the same perturbation than for linear systems.

Optimization of vehicle suspension parameters based on ride comfort and stability requirements

The use of optimization methods in engineering is growing, allowing the best possible way to fulfill the requirements of the project. For vehicle suspensions, there are various conditions, which involve comfort, safety, stability, maneuverability, among others. A safety and stability evaluation is carried out by several tests, including Double Lane Change. In this maneuver, the vehicle must change lanes quickly twice, allowing it to be assessed for stability in sudden movements. For ride comfort, it is common for the design to be based on the vehicle’s natural vibration frequencies. In this context, this work aims to present a methodology for optimizing the suspension parameters of a vehicle, based on the natural frequencies of vibration and the simulation of a Double Lane Change maneuver. For that, it is employed vertical and lateral dynamics mathematical models, with hypotheses that allow the adequate adaptation to the represented phenomena. Finally, Particle Swarm Optimization (PSO) is used, which is a stochastic algorithm, based on nature. It has low computational cost, with reasonable results, allowing the parameters to be estimated and comprising the two objectives simultaneously.