Vehicle Suspension Research Articles

Understanding the Inherently Self-Adjusting Mechanism and Load Adaptability of the Mem-Damper

The tapered dashpot (damper) has been the earliest memristor found in the mechanical engineering domain, named mem-dashpot (mem-damper), since the missing memristor was postulated by Leon Chua. In this paper, a displacement-dependent viscous damper device with internal channels is investigated and recognized as a physical realization of the mem-damper by analyzing the mathematical and dynamic relationships of the device’s complementary port variables theoretically and experimentally. A vehicle suspension equipped with a mem-damper is taken as a carrier for presenting load adaptability of the mem-damper. An investigation reveals the inherently self-adjusting mechanism behind load adaptability from the viewpoint of energy storage, that is, a mem-damper with different initial displacement values can be equivalent to a semi-active damper performing an initial-position-dependent damping control strategy. Finally, the load adaptability of the mem-damper is demonstrated through both simulation and experiment of the suspension system with the mem-damper prototype. Due to such load adaptability, the suspension equipped with the mem-damper can offer more constant and smoother ride comfort than the one with the linear damper.

Higher-order stochastic averaging for investigating a vehicle suspension system with nonlinear damping and stiffness

The paper deals with a quarter-car model with nonlinear damping and stiffness under white noise base excitation using the higher-order stochastic averaging method for analyzing approximate responses. Recently, a novel higher-order averaging procedure has been developed to find analytically the first-, second-, and third-order stationary joint probability density functions (PDF) of amplitude and full phase by solving the corresponding Fokker-Planck-Kolmogorov (FPK) equation, and it will be extended to the nonlinear quarter-car model. Accordingly, the mean-square responses such as the displacement, and velocity of the sprung mass can be obtained analytically. The influences of excitation intensity on the dynamic responses, as well as the variations of linear and nonlinear damping, are analyzed. A very satisfactory agreement is found between the accuracy of the solutions corresponding to higher-order stochastic averaging and that of Monte Carlo simulation.

A fuzzy skyhook control strategy optimized by particle swarm strategy for magnetorheological semi-active suspension

In order to solve the problem of unsatisfactory control effect caused by uncertain parameters in the fuzzy skyhook control method, a fuzzy skyhook control strategy optimized by particle swarm strategy is proposed. The magnetorheological (MR) damper is put on the bench for mechanical characteristics experiment, and the forward model of MR damper is established. The adaptive network fuzzy inference system (ANFIS) system in simulation software is used to build its inverse model to verify the accuracy of the forward model of MR damper. A quarter vehicle suspension model is established, and a fuzzy skyhook control strategy based on particle swarm optimization is designed. Numerical simulations are carried out under the excitation of random road. The acceleration, suspension dynamic deflection and tire dynamic load are used to evaluate its performance. Compared with the passive control, the root mean square (RMS) values of the acceleration for the fuzzy skyhook control strategy are improved by 41.9% and 37.6%, the RMS values of the suspension dynamic deflection for the fuzzy skyhook control strategy are improved by 53.3% and 48.0%, and the RMS values of the tire dynamic load for the fuzzy skyhook control strategy are improved by 17.6% and 14.5% under the B-Class and C-Class road excitations. The simulations and experimental results verify the effectiveness of the controller.

Physicochemical and microbiological stability of 40mg/mL amiodarone hydrochloride oral suspension.

In an effort to expedite the publication of articles, AJHP is posting manuscripts online as soon as possible after acceptance. Accepted manuscripts have been peer-reviewed and copyedited, but are posted online before technical formatting and author proofing. These manuscripts are not the final version of record and will be replaced with the final article (formatted per AJHP style and proofed by the authors) at a later time. Amiodarone hydrochloride is an antiarrhythmic drug used to treat supraventricular tachycardia. However, there are currently no commercial pediatric forms available to treat young patients. Various oral formulations were previously reported in the literature, but the concentration was lower than the doses prescribed in clinical practice (a loading dose of 500mg/m2/day for 7-10 days followed by a maintenance dose of 250mg/m2/day). The objective of this study was to develop an oral liquid formulation of amiodarone hydrochloride at an optimal concentration for use in children and to evaluate its physicochemical and microbiological stability. No commercial suspension vehicle was used, allowing the choice of excipients. Compounding was performed using hydroxypropylmethylcellulose as thickener, potassium sorbate preservative, citric acid/sodium citrate buffer, sodium saccharin as a , and a strawberry flavoring agent. A concentration of 40mg/mL was selected based on a 5-year compilation of prescribed doses. Analyses performed were the following: visual and microscopic inspection, testing for antimicrobial preservation, osmolality and pH measurements, quantification of amiodarone hydrochloride by a stability-indicating liquid chromatography method, and a microbiological count. At least 95% of the initial amiodarone hydrochloride remained stable during the 60-day study period under refrigeration. All other tested parameters remained stable at 5 °C. A targeted log reduction of the microorganism inoculum by day 14 and no microbial growth by day 28 were demonstrated in the test for antimicrobial preservation. The stability of 40mg/mL amiodarone hydrochloride oral suspension was maintained under refrigeration for 60 days before opening bottles and for 1 month after opening bottles.

A nonlinear model predictive control for air suspension of hub motor electric vehicle based on hybrid H2/H∞ state estimation

To alleviate the vibration from the road irregularities and the unbalanced electromagnetic forces (UEFs), deteriorating the dynamic performance of hub motor electric vehicles (HM-EVs), a novel nonlinear model predictive control (NMPC) is proposed based on a hybrid H2/H ∞ filtering algorithm for the HM-EVs with air suspension (HM-AS). The dynamic HM-AS model involves the electric vehicle’s longitudinal, lateral, and vertical motion. The air suspension system between the body and the hub motor enhances ride quality and insulates the oscillation delivered to the vehicle body. Then, the dynamic HM-AS model is validated by the actual vehicle test, and the proposed filter is developed to obtain the vehicle states. Besides, the NMPC controller guarantees the dynamic performance of HM-AS by intervening in vehicle attitude, road-holding stability, motor safety, and ride comfort. Finally, compared with the application of PID and MPC, the efficiency of the proposed method is demonstrated based on several random road scenarios. The results indicate the proposed algorithm can alleviate the dynamic performance of HM-AS and reduce motor vibration.

A novel robust adaptive control for nonlinear uncertain quarter-vehicle suspension system in presence of unknown time delay actuation

This paper presents a novel robust adaptive control approach for nonlinear uncertain vehicle suspension system with time delayed actuation and bounded disturbances. The uncertainty and disturbance as well as the input delay on the system are all limited and unknown. This paper explores a control-oriented nonlinear model to accurately describe the dynamics of the vehicle suspension which incorporates uncertainty, disturbance and actuator delay. The controller is designed based on robust and adaptive approaches, which along with guaranteeing general goals for the suspension system is able to assure the stability of the closed-loop system in the Lyapunov concept. Also, due to the use of smooth functions in the robust controller structure, sudden changes in the behavior of system states are prevented. The simulation and comparison results in MATLAB environment show the efficiency of the proposed robust adaptive method in covering the effects of uncertainty, disturbance and time-variant actuator delay.

Fixed-Time Safe-by-Design Control for Uncertain Active Vehicle Suspension Systems With Nonlinear Reference Dynamics

Fixed-Time Safe-by-Design Control for Uncertain Active Vehicle Suspension Systems With Nonlinear Reference Dynamics

Analysis of disturbance factors of magnetorheological damper in continuous impact buffer system

Abstract Magnetorheological (MR) impact buffering systems are widely used in vehicle suspensions, bridge damping, and aircraft landing gear due to their excellent buffering performance and rapid response time. However, under the condition of high-speed continuous impact, magnetorheological damper (MRD) operate in complex environments where various internal and external uncertainties can negatively affect control performance. This paper analyzes the impact of disturbance signals on MR buffering systems and explores control strategies to mitigate these effects. First, we established a hysteresis model based on experimental data and identified parameters using a genetic algorithm to determine the influence of hysteresis disturbances. Next, we developed a temperature model based on the thermal characteristics of SG-MRF2035 magnetorheological fluid, fitting the relationship between temperature and dynamic viscosity to identify temperature disturbances. The results showed that when disturbances were considered, the system exhibited higher peak damping forces and a deviation from the desired ‘platform effect’ in the damping force-displacement relationship. Finally, we applied an Active Disturbance Rejection Control(ADRC) strategy, which effectively compensated for the hysteresis and temperature disturbances, enhancing the system’s robustness. Compared to PID control, the ADRC-controlled system demonstrated lower peak damping forces and a damping force-displacement relationship closer to the desired platform effect.

Design and analysis of a piezoelectric energy harvesting shock absorber for light truck applications

Vehicle suspension vibration is a prevalent form of oscillation, with approximately 22.5 % of automobile energy dissipated through suspension-induced vibration. This phenomenon suggests that recovering the energy dissipated by the suspension system holds significant potential. This paper introduces a novel piezoelectric energy harvesting shock absorber (EHSA) based on non-contact magnetic force for light truck applications. The vibration of the vehicle suspension system is transformed into the rotation of a ball screw, enabling the one-way high-speed output of the rotor through a one-way bearing and planetary gear mechanism. Based on the non-contact magnetic force, the piezoelectric patches generate frequent oscillations, and a novel energy harvesting circuit is designed that efficiently converts the output of multiple piezoelectric units into usable electricity. The damping and energy harvesting characteristics of the EHSA with different external and internal variables are explored. Under sinusoidal excitation of 40 mm amplitude and 0.4 Hz frequency, the EHSA achieves a maximum output power of 7.51 W, with an average output power of 1.89 W. Furthermore, under random action, the EHSA can successfully illuminate 824 LED lights, enabling the temperature and humidity sensor to function normally. These findings indicate that the proposed EHSA can effectively harness vehicle suspension vibration to power onboard self-powered appliances while offering a new design idea for integrating vibration energy harvesters into vehicles.

Experimental Evaluation of Damping and Stiffness in Optimized Active Sport Utility Vehicle Suspension Systems

On a flat city road, the specificity of the suspension poses a challenge. Sport utility vehicles (SUVs) have less flexibility compared to regular cars, despite providing a firm grip on asphalt and concrete. Constant adjustments to the center of gravity of SUVs are necessary. Surprisingly, they are less reliable and stable in urban settings due to this characteristic. In this study, a mathematical model of the suspension system of SUVs based on the Newtonian approach is introduced and validated with data from experiments carried out by the MTS machine system on the mono-tube (oil/air) mixed damper element. The model accurately predicts the performance of this damper, commonly used in SUVs, across various operating conditions, including different frequencies. A coil spring element, serving as a passive suspension unit with this damper, is also tested experimentally under similar conditions. By integrating passive suspension elements with the active actuator, the proposed modified design reduces the power consumption needed for the actuator to function and ensures a certain level of reliability. The effectiveness and performance of the modified active suspension system in comparison to the traditional passive suspension system are assessed using three different strategies: hybrid PID-LQR, linear quadratic regulator (LQR), and proportional-integral-derivative (PID). The genetic algorithm is utilized to determine the optimal parameter values for each controller by minimizing a cost function, maximizing performance, and minimizing energy consumption. Simulation results demonstrate that the active suspension system controlled by the PID-LQR controller offers significantly improved ride comfort and vehicle stability compared to other systems. This suggests that the performance of the active suspension system is greatly enhanced by the combined application of the hybrid PID-LQR controller compared to other systems.

Performance evaluation of a novel semi-active absorption and isolation co-control strategy with magnetorheological seat suspension for commercial vehicle

Abstract Vibration isolation performance of seat suspension plays a critical role in protection of drive’s physical health as the last barrier. In this paper, the integrated magnetorheological (MR) dynamic tuned mass damper (TMD) is firstly designed and utilized into seat suspension. A semi-active co-control algorithm with MR damper and MR TMD is designed, analyzed and validated by comparative experiments. The dynamic models of two MR devices have been tested and fitted. Comparing with simulation and experimental results under various excitations and control conditions, this co-control algorithm with MR TMD is validated to be highly effective. The transmissibility at resonance frequency reaches to 0.81 which is less than 1. This phenomenon has hardly been investigated in seat suspension. It illustrates that resonance has been suppressed and improved significantly. The peak acceleration decreases to 1.19 m s−2 with a reduction of 57.2%, in contrast to passive condition with MR damper. The comfort index is increased by 45.6% under random excitation than passive condition. According to these comparisons, the vibration isolation property and comfort of seat suspension can be further improved by the proposed co-control algorithm with two MR devices.

Characterisation of the Rigid Body Vibration Spectra of Road Transport Vehicles

ABSTRACTFor decades, numerous attempts at re‐creating realistic (vertical) vibrations that purport to represent typical conditions during road transport have been proposed and published. This has and continues to result in a significant number of target power density spectra (PDS) for use in laboratory simulation of vibrations despite the fact that the underlying parameters that influence the vibrations (road surface unevenness and vehicle dynamics) remain largely unchanged. This paper seeks to address this situation by analysing published and measured PDS (129 in total) from a variety of vehicles and road types with the aim of establishing typical PDS. Through the analysis of the frequency of the first natural mode of these PDS, it was found that there exist five typical response PDS (three for steel leaf suspension and two for air ride suspension) that can be considered as representative vibration response PDS for road transport in general. These representative PDS were matched with a two degree‐of‐freedom quarter‐car model representing the heave response of the rigid body motion of the vehicles. The analysis suggests that the higher frequency content of the measured data is not related to rigid body motion but emanates from drivetrain and, in some cases, structural vibrations. These usually comprise numerous harmonics of fixed and varying frequencies as well as transients. As these vibrations are impossible to classify based on vehicle type, it is recommended that the five quarter‐car representative spectral models proposed in this paper—namely, for steel leaf spring suspended vehicles with heavy, moderate and light loads and air ride type vehicles with heavy and light loads—be used for laboratory simulation for the purpose of evaluating the vibration resistance of products and packaged systems. It is suggested that, for most packaged product, this is sufficient to test their ability to survive road transport vibrations. These will yield more realistic vibrations than those endorsed by standards organisations and should have a positive impact on the optimisation of packaging designs and a corresponding reduction in packaging waste. Finally, the need for further work aimed at developing methods to identify and extract fixed and varying discrete frequency vibration as well as transient vibrations was identified.

Artificial neural network infused quasi oppositional learning partial reinforcement algorithm for structural design optimization of vehicle suspension components

Artificial neural network infused quasi oppositional learning partial reinforcement algorithm for structural design optimization of vehicle suspension components

Multibody Dynamics and Terramechanics-based modeling and simulation of Quarter-Car with Suspension

Abstract While tires only compress when acted upon by a load in on-road scenarios, in off-road conditions, on the other hand, the tires not only undergo compression but also sinkage into the ground, in a manner that depends on the terrain. The tire-ground contact, in turn, affects the forces acting on the suspension system. Hence, it is necessary to study the vertical dynamic response of a system in off-road conditions by accounting for the terramechanics phenomenon (tire-terrain interface). The forces acting at the tire and terrain interface in off-road conditions have been studied in terramechanics separately; however, their integration with multibody systems is relatively less explored. In this paper, a multibody dynamic-based modeling and simulation of a quarter car with a linear spring-damper suspension system for off-road vehicles is presented. The generalized external forces are obtained using the Bekker-Wong based soil pressure-sinkage approach for two different kind of multibody systems interacting with sandy loam terrain. This model is integrated with the Tangent Space Ordinary Differential Equations of the quarter car and suspension system and solved using numerical integration techniques. Thus, by accounting for the terramechanics in the multibody system, the technique provides a more realistic response of the system in off-road scenarios.

Topology optimization with the redesigned suspension system of the internal combustion vehicle converted to an electrical vehicle

Abstract In this paper, the topology optimization of lower wishbone for a passenger car which is the converted of an internal combustion engine vehicle to an electrical vehicle was presented. On the other hand, the need to study on a suspension system arose for electrical car that was redesigned. In study, topology optimization of the structural design of the lower wishbone to be used in the front suspension was carried out by Finite Element Analysis (FEA) Method. For this purpose, firstly, the suspension spring curves and damper curves that will improve the handling, ride and comfort behaviour of the vehicle were determined, suspension system was modelled with the Multi Body Dynamics (MBD) approach. Hardpoints is necessary for vehicle dynamics and that is also an input for FEA were obtained from new suspension system via MBD analysis. In the second step, The preliminary design of the lower wishbone was created, taking into account together with the positions of the wheel drive shaft, suspension spring and brake system structural elements according to hardpoints. After designing the structure suitable for the joint types, initial design was studied on the remaining region that is for weight reduction region except the joint connection surfaces. Then, topology optimization was applied to the preliminary design for the selected load types that is come from MBD analysis. Thus, the excess volume on the preliminary design was determined for each load type. In the last stage, the results of topology optimization analysis were evaluated to reach out target weight and the producible design of the wishbone was made. Finally, Finite Element Analysis were applied to the final design for validation purposes within topology optimization work was done with the forces coming from Multi Body Dynamics. After statically solved Finite Element Analysis, a modal neutral file(.mnf) was created via FEA solver and was integrated to Adams Car as a flexbody. Flexbody was attahced to the other parts which are rigid bodies like nuckle according to Multi Body Dynamics approach. Dynamics durability cases was carried out via Adams Car. Stress results was compared to FEA results and evaluated depends on yield stress. Study results shows that the new design is lighter and competitive design and also safe in dynamics analysis for redesigned passenger car.

Mathematical Modelling of a Single Magneto-Rheological for Car Suspension System Using Modified Bouc-Wen Model

Magneto-Rheological (MR) automotive suspension represents the most advanced technology currently available for enhancing passenger comfort through intelligent fluid behaviour. This work employed a Modified Bouc-Wen model to create a mathematical representation of a single MR vehicle suspension and compared its ride performance to that of passive suspension systems. The model was formulated and solved using second-order linear differential equations, with MATLAB software utilized to visualize the results. The maximum vertical displacement for the single MR mathematical model in this work was 0.031 m, while the minimum was -0.0124 m. At the minimum position, the vertical displacements for the passive model were 0.0532 m and -0.0133 m. The results demonstrated that the vertical displacement variation was similar for both the mathematical model and the passive system. All displacements obtained from the mathematical modeling of the single MR system were close to its mean of 0.000875 m (nearly zero). There was reduced vibration when zero displacement was achieved. It was concluded that MR damper significantly improved car suspension performance compared to passive solutions. This paper developed a single MR vehicle suspension system using the Modified Bouc-Wen model in a Proton Preve.

Radial stiffness and damping of mountain bike tires subject to impact determined using the coefficient of restitution

Mountain bike tires are designed to encounter jumps, bumps, drops, and impacts. Despite their contribution to the vehicle suspension system, little has been published on their in-plane behaviour. In this work, a drop sled test bench is utilised to measure non-rolling dynamic radial stiffness and damping of numerous mountain bike tires across sizes, constructions, and usage categories. Each tire is treated as a classical, lumped Kelvin–Voigt model with a linear spring and viscous damper arranged in parallel. Identification of the system parameters is accomplished treating the tire as a bouncing ball. The coefficient of restitution from pre- and post-impact velocities is used to determine the dynamic stiffness and damping across two regimes of ‘impact’ and ‘in-contact’. Advantages of this approach over the classical logarithmic decrement are discussed. Measured first-bounce tire impact footprints exhibit a large ‘stadium’ shape compared to their elliptical static counterparts. A simple one degree-of-freedom, mass-spring-damper model with two pairs of dynamic stiffness and damping values is shown to faithfully reproduce the loaded, tire-only response for two of the inflation pressures tested. Measured dynamic radial stiffness and damping values are useful to compare tire behaviour and support future multibody simulation of the tire’s contribution to the suspension subsystem.

Technical study of magnetorheological semi-active suspension control strategy for vehicles based on reinforcement learning

The suspension system is an important part of the car, the main function is to alleviate the road surface does not level brought about by the shake, to ensure that the vehicle driving smoothness and comfort, so as to improve the vehicle handling performance and safety, improve the vehicle to reduce the vibration performance more and more become a hot topic in the industry. Among them, semi-active suspension is a popular suspension system. This paper explains the significance and classification of the role of the suspension, and gives a relevant introduction to the magnetorheological fluid, on the basis of which it combines the domestic and international research results, looks forward to the development trend of the semi-active suspension of the vehicle, analyzes the advantages and shortcomings of four important semi-active suspension control strategies, and finally introduces the reinforcement learning and combines the reinforcement learning with the existing control strategies of the semi-active suspension, and designs a reliable reward function to enhance the suspension's damping performance by taking into account the multifaceted driving factors. The reward function to enhance the damping ability of the suspension by considering multiple driving factors, which can provide a reference for further research on the control of magnetorheological semi-active suspensions for vehicles.

Dynamic characteristics and sensitivity analysis of a nonlinear vehicle suspension system with stochastic uncertainties

Dynamic characteristics and sensitivity analysis of a nonlinear vehicle suspension system with stochastic uncertainties

H∞ Differential Game of Nonlinear Half-Car Active Suspension via Off-Policy Reinforcement Learning

This paper investigates a parameter-free H∞ differential game approach for nonlinear active vehicle suspensions. The study accounts for the geometric nonlinearity of the half-car active suspension and the cubic nonlinearity of the damping elements. The nonlinear H∞ control problem is reformulated as a zero-sum game between two players, leading to the establishment of the Hamilton–Jacobi–Isaacs (HJI) equation with a Nash equilibrium solution. To minimize reliance on model parameters during the solution process, an actor–critic framework employing neural networks is utilized to approximate the control policy and value function. An off-policy reinforcement learning method is implemented to iteratively solve the HJI equation. In this approach, the disturbance policy is derived directly from the value function, requiring only a limited amount of driving data to approximate the HJI equation’s solution. The primary innovation of this method lies in its capacity to effectively address system nonlinearities without the need for model parameters, making it particularly advantageous for practical engineering applications. Numerical simulations confirm the method’s effectiveness and applicable range. The off-policy reinforcement learning approach ensures the safety of the design process. For low-frequency road disturbances, the designed H∞ control policy enhances both ride comfort and stability.