Vehicle Suspension Research Articles

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.

Load adaptivity of the mem-spring and its performance benefits in vehicle suspensions

Load adaptivity of the mem-spring and its performance benefits in vehicle suspensions

The evolution of damper technology for enhanced ride comfort and vehicle handling in vehicle suspension system

The evolution of damper technology for enhanced ride comfort and vehicle handling in vehicle suspension system

Increasing the damping properties of the magnetorheological actuator of the vehicle suspension control system

Introduction. In accordance with one of the ways of solving the problem of increasing the smoothness of the vehicles, a controlled suspension is proposed, which is created on the basis of the use of «smart» materials – magnetorheological elastomers, the mechanical properties of which, in particular, damping, can be changed with the help of a controlling magnetic field. This is implemented with the help of the magnetorheological actuator of the suspension control system, which has the form of an elastic bushing of the suspension arm, consisting of several electrically connected in series toroid-like coils (with a core of magnetorheological elastomer). The device is powered by current, the value of which is controlled by the operator, or automatically, depending on the road profile and driving mode. Magnetorheological actuators (elastic bushings) are placed in the holes of the suspension levers instead of standard rubber ones and combined with a controlled current source. Thus, the suspension becomes controllable, which makes it possible to set the necessary vibration damping of the vehicle body to increase its smoothness. Problem. The disadvantage of the previous designs of the magnetorheological actuator is the insufficient amount of the magnetic flux density and the unevenness of its distribution within the elastic bushings. As a result, the damping properties of such controlled suspensions become insufficiently effective, which reduces the possibility of increasing the smoothness of the vehicles. The purpose of the work is to increase the damping properties of the magnetorheological actuator of the vehicle suspension control system, which will increase the control efficiency. The task is to improve the design of the performing magnetorheological device, to carry out calculations and develop a calculation scheme of the study, to determine the average magnetic flux density value and its distribution across the cross-section of the device, to calculate the dependence of the device damping indicator on the magnetic flux density, to compare the damping indicators of the improved device with previously known ones. Methodology. Research tasks were solved on the basis of magnetic field analysis using methods of magnetic field theory and SOLIDWORKS® and FEMM software packages, as well as analysis of the dependence of the damping properties of bushings from magnetorheological elastomers on magnetic flux density. A description of the design and principle of operation of the magnetorheological actuator of the vehicle suspension characteristics control system is given, based on which the calculation scheme was developed. Results. The results of research calculations showed that the average value of magnetic flux density in the proposed design of the device reached 0.85 T, its distribution became fairly uniform, and there were no zones where it was abnormally small. For the first time, the dependence of the damping index on the magnetic flux density of the controlling magnetic field has signs of scientific novelty. It was found that this indicator for the proposed design of the device increased by 22 % compared to previous other designs, which will increase the efficiency of the control system and the smoothness of the vehicle. A positive result was achieved due to the following features of the proposed design of the suspension actuator: the elastic sleeve consists of several coaxially located actuators made of anisotropic magnetorheological elastomer, in which the conglomerates of the ferromagnetic filler during the manufacturing process are located collinear to the direction of the angular deformations of the sleeve and the control magnetic field flux density vector, and the devices have control coils located on their surfaces, which are made of conductive elastic elastomer and electrically connected in a series circuit. Originality. The control method, previous designs and construction of this controlled suspension are protected by patents of Ukraine. Practical value. The direction of further research is to optimize the parameters of the control coils in order to reduce the energy consumption for them and to protect them from overheating. References 20, figures 10.

Tradeoff analysis of the energy-harvesting vehicle suspension system employing inerter element

This paper explores the vibration isolation performance and vibration energy recovery performance of an energy-harvesting vehicle suspension system employing inerter element. The study takes into account the structural changes in the suspension caused by introducing the inerter as a new type of vibration isolation element. According to the parallel-series combination of an inerter and a damper, two different structures of energy-harvesting suspension dynamic models are constructed. The mechanism of the suspension parameter uptake on vehicle ride comfort and energy-harvesting characteristics is analyzed. A multi-objective optimal design method for the energy-harvesting vehicle suspension system employing inerter element is proposed, which considers both vehicle ride comfort and energy-harvesting characteristics. A trade-off was found between suspension isolation performance and energy-harvesting efficiency. The results indicate that various structures of energy-harvesting vehicle suspension systems employing inerter element exhibit different vibration isolation performances. Compared with the conventional energy-harvesting suspension, the series structure reduces body acceleration by 15.9 %, and the root mean square (RMS) of energy-harvesting power of the suspension is 22.2 W. The parallel structure reduces the RMS of body acceleration by 14.3 % and the RMS of energy-harvesting efficiency is 56.3 %, with the RMS energy-harvesting power of 84.9 W. The parallel structure demonstrates superior overall performance.

Thermal analysis of constant surface area tapered helical Coils: Insights from numerical modelling

Helical coils are integral to numerous engineering and domestic applications, from room heaters and vehicle suspensions to nuclear reactors, owing to their high surface area-to-volume ratio that facilitates efficient heat transfer. This study investigates the natural convection heat transfer characteristics of tapered helical coils under radiative heat loss, focusing on both straight and inverted configurations, within an unconfined air medium. The numerical simulations were validated against experimental results with a maximum deviation of 5 % before proceeding to establish the numerical findings. The analysis considers geometric parameters such as non-dimensional pitch (p*), cone angle (θ), and emissivity (ε), along with Rayleigh number (Ra), to elucidate their impact on average Nusselt number (Nu), mass flow rate of air through the coil core, and heat transfer mechanisms. Results reveal distinct behaviors for straight and inverted coils, with varying Ra and θ influencing heat transfer dynamics and airflow patterns. Notably, inverted coils exhibit enhanced heat transfer characteristics compared to straight coils. For straight coils, Nu initially decreases with increasing θ at lower Ra but rises beyond a critical θ at higher Ra due to independent heat dissipation by the coil turns. When θ changes from 0° to 50° at p* = 6, the change in average Nu is approximately 3 % and 10 % for Ra = 108 and 104 respectively. In contrast, for inverted coils, Nu increases with θ across all Ra, owing to the wider top opening facilitating airflow. Furthermore, empirical correlations are developed to predict Nu based on key parameters, achieving high accuracy with deviations of ± 6 % and ± 4 % for straight and inverted coils, respectively. These correlations provide robust tools for optimizing thermal management in diverse applications. Overall, this study contributes significant insights into tapered coil performance, essential for advancing heat transfer technology and design optimization.

Optimal tuning of inerter-spring-damper vehicle suspension for mitigation of bridge response

Optimal tuning of inerter-spring-damper vehicle suspension for mitigation of bridge response

Potential Power Output from Vehicle Suspension Energy Harvesting Given Bumpy and Random-Surfaced Roads

The energy efficiency of vehicles is a crucial challenge relating to sustainable energy preservation and regeneration methods. Regenerative breaking has proven feasible, and there is interest in whether harvesting energy from a vehicle’s suspension is similarly feasible. We here provide methods for estimating the amount of power that can be regenerated from the suspension for given vehicle and road parameters. We show that a reasonable road model is a generalised Gaussian process known as AR(1). Using this model, we can derive the key equation used in the ISO 8608 standard for measuring road roughness, such that the AR(1) parameters can be related to the measured road roughness data. We find that the road roughness coefficient of ISO 8608 and the diffusion coefficient of the AR(1) road are equal up to a factor. We provide an analytical expression for the maximum amount of power that can be generated for given road and car parameters, derived via Fourier analysis. We further model harvesting from large bumps using Simulink. These results help to estimate the potential power output given the measured road data.

Metaheuristic tuned decentralized PID controller based active suspension system for railway vehicle

AbstractA high‐speed railway system is one of the sustainable alternatives to other modes of transportation and may connect the most congested urban cities with minimum carbon emissions. However, the vibration intensity increases as the train's operating speed increases, resulting in deteriorated ride comfort and stability. Hence, this article investigates a 27‐degree‐of‐freedom (DOF) dynamic model of railway vehicles with an improved active suspension system. The decentralized control structure performs the controlling action with five optimized Proportional Integral Derivative (PID) controllers that suppress the vehicle body's vertical, lateral, pitch, roll, and yaw motions. Further, to optimize the PID parameters, three metaheuristic optimization techniques, Genetic algorithm (GA), Grey Wolf Optimization (GWO), and Flower Pollination Algorithm (FPA), are utilized, and their simulated results are compared with the passive system as well as other conventional tuning technique. Moreover, the performance of the proposed control strategy is evaluated in the frequency domain under random track irregularities, and the results are characterized in terms of power spectral densities (PSDs). The simulated results show that among the proposed metaheuristic algorithms, FPA outperforms with a significant reduction in vehicle vibration compared to other tuning methods. The percentage reduction of the vertical, lateral, pitch, rolls, and yaw accelerations is 71.4%, 35.1%, 52.8%, 48.1%, and 38.2%, respectively, ensuring enhanced vehicle ride comfort.

Modelling and experimental validation of an adaptive interconnected suspension with adjustable roll stiffness (AIS-ARS)

Vehicle suspensions play a critical role in improving vehicle stability and ride quality, especially in heavy vehicles that usually have high centre-of-gravity and carry tons of cargo. Interconnected suspension systems, in which the suspension struts are connected through hydraulic hoses and flow control devices, have great potential to enhance vehicle handling stability and attenuate vibrations. This study introduces an adaptive interconnected suspension with adjustable roll stiffness (AIS-ARS) to address the shortcomings of existing designs. It not only eliminates the conventional anti-roll bars but also enables adjustment of roll stiffness depending on the driving and vehicle load conditions. The AIS-ARS system uses a unique design that avoids using expensive electro-proportional flow control valves, which has been a significant barrier to widespread implementation. Instead, the system utilises a cost-effective control strategy that uses only two solenoid valves to achieve adaptive damping. The mathematical modelling of the AIS-ARS is also straightforward, requiring less computational power and making it more practical for real-time implementations. Overall, the AIS-ARS system represents a significant advancement in the design of interconnected suspension systems, offering a more cost-effective, practical, and versatile solution. The above features are validated through laboratory experiments and co-simulation between MATLAB/Simulink and ADAMS/Car.

Modeling and Implementation of PID Controller in Vehicle Ride Comfort Improvement Using Bond Graph

The proportional integral derivative (PID) controller method is a famous and influential approach used in a variety of engineering domain systems. This paper presents Bond Graph modelling and implementation of PID controller in the active quarter-vehicle suspension system for the purpose of achieving better ride comfort. Bond graph is a better tool for modelling multi-domain energy systems with control hardware associated with it. SYMBOL SHAKTI software is used to simulate the active vehicle suspension system, which is theoretically represented as a 4-DOF human Bio-dynamic model combined with a 3-DOF quarter automobile system. The suggested PID Controller's performance is contrasted with that of the passive model. To measure the effectiveness of the suggested PID controller suspension system, time domain evaluations of systems performance criteria are conducted. The findings show that a significant improvement in ride comfort is offered by the suggested Bond graph PID controller model of the active vehicle suspension.

Dynamic response and stability analysis of vehicle systems with double time-delay feedback control

In this paper, the vehicle suspension dynamic response of time delay feedback control is analyzed considering the suspension of the seat. An active suspension vibration reduction control method based on double time-delay feedback control is proposed to further improve the ride comfort. Firstly, the double time-delay dynamic response equation of the system with three degrees of freedom is established. Then, the root mean square values of seat acceleration and body acceleration are used as the objective functions. Meanwhile, the RMS values of suspension dynamic deflection and tire dynamic displacement are used as constraints, and the optimal feedback parameters are obtained using particle swarm optimisation. The Routh-Hurwitz criterion and frequency domain scanning methods are used to verify the stability of the double time-delay system. Finally, simulation in the time domain and frequency domain is accomplished. It is verified that this feedback control method has strong robustness and anti-interference ability.

Design and experimental study of a stepped magnetorheological damper with power generation

Traditional vehicle suspension magnetorheological dampers have problems with low output damping force and require additional energy input to operate, to improve the performance of the vehicle suspension magnetorheological damper, in this paper, we propose and investigate a stepped magnetorheological damper structure with power generation, and conducts structural design and magnetic circuit analysis. The effects of different currents, damping gaps, coil slot positions, and coil turns on the damping performance of the stepped magnetorheological damper with power generation are numerically studied. The magnetic circuit sensitivity analysis of the power generation structure and the magnetorheological damper structure is also performed. Experiments have verified the effects of different input excitations on damping and energy-feeding performance, and the results of numerical analysis have been verified. The results show that when the excitation coil is wound for 257 turns, the magnetic circuit requirements are met. And the influence of different amplitudes, frequencies, and currents on the output damping force was studied through experiments. The results showed that the damping force would increase with the increase of single parameter values. When the amplitude was 7 mm, the frequency was 1 Hz, and the current was 2 A, the output damping force could reach 4500 N, meeting the requirements for use.

Hybrid coati–grey wolf optimization with application to tuning linear quadratic regulator controller of active suspension systems

Vehicle suspension systems have become increasingly crucial for both driving safety and comfort. Active suspension systems can dynamically adjust suspension characteristics in real-time by introducing force into the system. Designing a controller for the real-time adjustment of the control force in active suspension systems is essential to meet challenging control objectives, including body acceleration, suspension deflection, and tire deflection. This article proposes a hybrid optimization approach named Coati–Grey Wolf Optimization (COAGWO), which combines the strengths of the coati optimization algorithm and grey wolf optimization to tune the gains of linear quadratic control applied to vehicle suspension systems. The COAGWO algorithm incorporates a unique strategy inspired by the Coati Optimization Algorithm, allowing wolves to climb trees. This enhancement significantly improves the wolves’ ability to explore the global search space and reduces the likelihood of being trapped in local optima. Initially, we conduct extensive experiments using a suite of challenging optimization problems from the CEC2019 benchmark to evaluate the effectiveness of the COAGWO algorithm. The effectiveness of COAGWO is compared against several state-of-the-art algorithms, including grey wolf, coati, aquila-grey wolf, whale, reptile search, tunicate swarm, and seagull optimization algorithms. The experimental results demonstrate that COAGWO consistently outperforms these algorithms in terms of solution quality and convergence speed. For the optimal weight selection problem of linear quadratic control applied to the control of vehicle suspension systems, the excellent performance of the proposed method is illustrated through comparative simulation studies under various road disturbance conditions. The results indicate that the COAGWO algorithm achieves a more efficient active suspension system compared to competitor algorithms by reducing the overall acceleration of the driver’s body, thereby enhancing ride comfort.

Research on Bifurcated Origami Hydraulic Dampers for Real Road Vibration Loads

Cylindrical hydraulic dampers are commonly utilized to mitigate vibrations in machinery and structural applications. These devices generally feature a single linear stroke and are often linked to rotary joints to handle complex loading conditions. However, their installation in confined spaces, such as vehicle suspensions, poses considerable difficulties. In this research, we introduce an innovative bifurcated origami hydraulic damper with nonlinear damping capabilities. Initially, we formulated the collapsible conditional equations essential for the design of the bifurcated origami hydraulic dampers. We then examined the fluid dynamics within the damper and its flow channels, determining that the damping force is proportional to the square of the velocity. Furthermore, we developed motion equations based on the derived damping force and suggested vibration analysis methods using the Runge–Kutta approach. For the mass-spring vibration system, we created an experimental setup with the bifurcated origami hydraulic damper and performed vibration tests using noise signals recorded from a vehicle traveling on a gravel road, thus validating its damping performance and efficacy. Additional tests, which varied the orifice size at the end of the origami structure, as well as the type and temperature of the internal fluid, showed that the orifice size had a more pronounced effect on damping efficiency than the fluid type and temperature. This confirmed the vibration-damping effectiveness of the bifurcated origami hydraulic damper.