Suspension Model Research Articles

Modeling and Dynamics Study of Beam Leaf Spring System Based on Elastic Constraints

This paper introduces an innovative approach using elastic bushing constraints to simulate the practical limitations of leaf springs. A comprehensive rear suspension system is constructed for a specific vehicle, incorporating parameterized preload for the leaf springs to ensure alignment with the actual vehicle’s forces and attitudes. Validation with real-world kinematics and compliance (K&C) dynamics data confirms the model’s accuracy in representing vertical, longitudinal, and lateral stiffness, along with dynamic characteristics. The study demonstrates that the dynamic model of the multi-leaf plate spring suspension, grounded in bushing constraints for the beam accurately simulates the actual vehicle. The model exhibits flexibility and motion characteristics that closely resemble the real vehicle, demonstrating high accuracy and good computational convergence.

Experimental and Numerical Study of Shock Absorber Characterization and The Implication on The Dynamics of Half Vehicle Suspension System Model

This study aimed to characterized shock absorber damping for passenger comfort. The riding comfort of the vehicle has direct correlation to the damping characteristic of the shock absorber of the suspension system. Two different shock absorbers were experimentally evaluated, and their damping characteristics were integrated into a half-car model to study the vehicle's dynamic response to harmonic road disturbances. The investigation involved numerical simulations of the half-car model subjected to harmonic road disturbances, represented by a set of ordinary differential equations solved using the Dormand-Prince method. Experimental data yielded average damping forces of 502.77 N for shock-absorber #1 and 192.03 N for shock-absorber #2. Calculations resulted in damping coefficients of 3888.57 N·s/m for shock-absorber #1 and 1397.85 N·s/m for shock-absorber #2, with corresponding damping ratios of 0.29 and 0.105. These damping ratios generally aligned with typical values for passenger car shock absorbers, except for shock-absorber #2, which deviated from the expected range. The study found that at 60 km/h and 90 km/h, shock-absorber #1 with ζ=0.29 exhibited superior performance in reducing displacement amplitude compared to shock-absorber #2 at ζ=0.105. However, at 120 km/h, both shock-absorbers displayed similar responses, with shock-absorber #1 slightly surpassing shock-absorber #2 in displacement amplitude.

A new energy-feeding variable damping control strategy for electromagnetic hybrid suspension systems

Traditional energy-feeding suspensions exhibit a non-adjustable damping characteristic during energy recovery, which can compromise the dynamic performance of the suspension system. To overcome this issue, this paper proposes an energy-feeding variable damping control strategy (EFVD) predicated on an electromagnetic hybrid suspension system. This strategy aims to achieve adjustable damping during energy recovery, reducing energy losses while ensuring optimal suspension performance. Building on a half-vehicle suspension model, we construct a dynamic model of the electromagnetic hybrid suspension. By leveraging an enhanced hybrid-skyhook and ground-hook control algorithm (HSGH), we solve for the target control force. We then design a force distribution controller based on the EFVD strategy, aiming to optimize suspension dynamic performance and energy feeding efficiency. And we conduct a simulation study, measuring power supply efficiency and suspension dynamic performance as key evaluation metrics. The results demonstrate the superiority of the proposed EFVD strategy over conventional passive and active suspension control strategies, highlighting its effectiveness and reliability in maintaining dynamic performance while enhancing energy efficiency. This underscores the potential of the EFVD strategy as a practical solution for future suspension system design and energy management.

A data-driven suspension kinematics and compliance model considering multi-axis coupling effects

The kinematics and compliance characteristics (K&C) significantly impact a vehicle’s dynamic response. While a comprehensive multibody suspension model can accurately express desired suspension K&C characteristics, the complexity of the model limits its use in real-time applications. The K&C characteristics are usually obtained through decoupled bench tests, whereby it is assumed that the suspension K&C characteristics can be orthogonally decomposed and that the function outputs can be added up to restore the original characteristics, which may not be accurate. Therefore, in this research, a novel suspension K&C simulation/test method is proposed to demonstrate the suspension characteristics under coupled force inputs. A multibody dynamic model of an air suspension is constructed and calibrated through bench tests. Then, a series of coupled tire forces with shapes of space spiral curves are applied to the multibody model to produce the coupled K&C data. A novel data-driven model based on Long Short-Term Memory (LSTM) network is proposed to predict suspension K&C. Finally, the proposed data-driven K&C model and the decoupled K&C model are compared under full vehicle simulations. The results suggest that the proposed method is more accurate than the decoupled K&C model and can express the suspension hysteresis characteristics without further modification.

Particle swarm optimized fuzzy proportional-integral-derivative controller-based transverse leaf spring active suspension for vibration control

The transverse leaf spring (TLS) suspensions are a promising option for van vehicles due to their high load-carrying capacity and excellent handling stability. However, its ride comfort remains a major challenge. This paper investigates and compares the effects of semi-active and active control strategies to enhance the ride comfort of TLS suspensions. Firstly, a four-degree-of-freedom (4-DOF) half-car model and a multi-body dynamics (MBD) model of the TLS suspensions are established. The MBD model has higher accuracy and can describe the medium and high frequency characteristics of the TLS suspensions, such as the suspension offset frequency and the frequency response function of the body vertical acceleration (BVA). Therefore, based on the MBD half-car model with TLS suspensions, this paper proposes an optimal fuzzy PID active control strategy considering the left and right suspension coupling. The optimization objectives are the BVA, the left and right suspensions dynamic deflection, and the left and right wheels dynamic displacement. The integral absolute error is used as the evaluation criterion. The left and right fuzzy PID controllers’ parameters are obtained through particle swarm optimization. Simulation results demonstrate that the particle swarm optimization fuzzy PID active control strategy effectively controls the low-frequency vibration of the TLS suspensions and suppresses the medium- and high-frequency vibration characteristics compared with the traditional skyhook semi-active control strategy. This technology provides a reference for improving the ride comfort of the TLS suspensions.

The method of virtual bench tests conducting to analyze the vehicle technical characteristics compatibility to detect and prevent the risk of resonant phenomena in the sprung cab

BACKGROUND: A relevant issue when designing vehicles with multiple levels of suspension systems is collaborative operation of these systems, which ensures the required vehicle dynamics and smoothness parameters, as well as the absence of risk for the occurrence of resonance phenomena. The vehicle cab is a dynamic system with 6 degrees of freedom, so its oscillatory motions have a complex spatial character with the oscillation energies overflow from one direction to another. The solving of problems of the sprung cab dynamics should be conducted in a spatial nonlinear formulation, which makes it possible to take into account the phenomena of redistribution of oscillation energy between the directions of space. This approach can be put into operation with simulation modeling methods through creating a spatial virtual rig of the cab with a suspension system and modeling its dynamics with the application of appropriate external inputs.
 AIM: Development of the method of using virtual tests to analyze the compatibility of technical characteristics of the cab suspension system, the frame system and the primary vehicle suspension systems to detect and prevent the risk of resonant phenomena in the cab.
 METHODS: Building a virtual test rig of a vehicle cab as a multibody dynamics system of connected bodies in space, mounted at the movable vehicle frame with spring-dampers. Virtual tests are conducted by simulation modeling methods according to the method for analyzing nonlinear phenomena when spatial resonances occur in the secondary suspension system of a vehicle cab.
 RESULTS: The method of vehicle cab virtual tests conducting for analyzing oscillatory processes occurring in the cab, including resonances, using a virtual test rig in a multibody dyamics software package.
 CONCLUSION: The developed method ensures an ability to take measures to detect and prevent the risk of spatial resonance phenomena in the vehicle cab at all stages of the components design and the cab suspension systems study.

A Novel Application of Magnetorheological Seat Suspension with an Improved Tuning Control Strategy

During the operation of commercial vehicles, drivers are usually exposed to long-term vibrations and acquire several health problems. Moreover, the end-stop impacts caused by large-magnitude vibrations or shocks may affect driving performance and result in injuries. A study of magnetorheological (MR) seat suspension controlled by a novel tuning control strategy is conducted in this research to reduce vibrations and avoid end-stop impacts. First, the MR damper’s characteristics are tested, and a mathematical model of MR seat suspension is established. Then, an improved tuning control strategy is designed based on this model. The proposed strategy has three control stages that can be adjusted according to the suspension stroke to improve seat comfort or avoid end-stop impacts. Each part of the control strategy is designed separately, and the vibration attenuation performance of this seat suspension is evaluated with a simulation for three excitations, i.e., harmonic excitation, bump excitation, and random road excitation. Finally, an experiment is conducted to verify the conclusion of the simulation. The seat suspension with the proposed control shows good performances on vibration attenuation and end-stop impact reduction. Compared with a passive seat, the vibration level is reduced by around 27% and end-stop impact is avoided when semiactive suspension with the proposed strategy is used. It also shows the best overall performance among the three experimental algorithms. Both the simulation and the experiment results indicate that the vibration attenuation performance of the seat suspension can be greatly improved with the improved tuning control strategy.

Development of Boom Posture Adjustment and Control System for Wide Spray Boom

To obtain a more consistent droplet distribution and reduce spray drift, it is necessary to keep the entire spray boom parallel to the crop canopy or ground and maintain a certain distance from the spray nozzles to the crop canopy or ground. A high-performance boom active control system was developed for boom trapezoid suspension. The hydraulic system and hardware circuit of the boom control system were designed based on analyzing the configuration of active trapezoid suspension. The mathematical models of valve-controlled hydraulic cylinders and active boom suspensions were developed. Step response and frequency domain response analysis of passive suspension were conducted by Simulink simulations, and then key parameters of the boom suspension and hydraulic system were determined. A feedforward proportion integration differentiation (FPID) control algorithm was proposed to improve the tracking performance. The designed control system was assembled on a 24 m boom with trapezoid suspension. The response characteristic of the active boom control system was tested by the step signal and the sinusoidal signal from a six-degree-of-freedom hydraulic motion platform. Firstly, the tracking performance of the active balance control system for the PID (proportion integration differentiation) and FPID control algorithms was compared for a given 0.2 Hz sine signal. Then, for the ground-following control system, the response characteristics in challenging terrain and tracking performance in less challenging terrain were tested. Field experiment results indicate that the maximum rolling angle of the chassis was 3.896° while the maximum inclination angle of the boom was 0.453°. The results show that the designed boom adjustment and control system can effectively adjust the boom motion in real time and meet the requirements of field operation.

Coordinated Control of Quadrotor Suspension Systems Based on Consistency Theory

This paper designs a cooperative control method for the multi-quadrotor suspension system based on consistency theory and realizes the cooperative formation trajectory tracking control of the multi-quadrotor suspension system by designing a consistent formation cooperative algorithm of virtual piloting and a nonlinear controller. First, a new quadrotor suspension system model is established based on the traditional quadrotor model using the Newton–Euler method. This model can accurately reflect the influence of the load on the quadrotor while obtaining the swing of the load. Then, the vertical and horizontal positions are designed separately based on the quadrotor motion characteristics, and the formation algorithm based on the virtual pilot consistency theory ensures that the final convergence of each position is consistent. An integral backstepping controller and an integral backstepping sliding mode controller are designed for quadrotor position, attitude, and load swing control to achieve accurate and fast quadrotor trajectory tracking control while reducing load swing. The stability of all the controllers is demonstrated using Lyapunov functions. Finally, a multi-quadrotor suspension system formation cooperative simulation experiment is designed to verify the designed control method.

The Effect of the Traction Rod on the Vertical Vibration Behavior of the Railway Vehicle Carbody

Although research has shown that through the additional rigidity introduced in the secondary suspension, traction rods can affect the vertical dynamic performance of railway vehicles, this topic has been less studied by researchers in the field. In this paper, the effect of a traction rod on the vertical vibration behavior of a carbody of a railway vehicle is analyzed, using the results obtained through numerical simulations. Numerical simulation applications are developed based on a vehicle model, where the vehicle carbody is modeled using a free-free equivalent beam Euler–Bernoulli, and the bogie chassis and wheelsets are represented by rigid bodies linked together by Kelvin-Voigt systems that model the secondary suspension and the primary suspension. The novelty element of this paper is found in the model of the traction rod. This includes traction rod damping, which has been neglected in previous research. The stiffness and damping of the traction rod are represented by a longitudinal Kelvin–Voigt system integrated into a secondary suspension model. The effect of the traction rod on the vertical vibration behavior of the vehicle carbody is analyzed based on the power spectral density of the acceleration, the root mean square of acceleration, and the ride comfort index, for three cases for analysis: a ‘without traction rod’ case, a ‘with traction rod—with damping’ case, and a ‘with traction rod—without damping’ case. The conclusions of the paper highlight the influence of the stiffness and damping of the traction rod on the vibration level of the carbody, especially in its middle. Depending on the stiffness of the traction rod, significant increases in the ride comfort index are obtained, which at high velocities can exceed 300%. Damping of the traction rod reduces the ride comfort index by up to 10%.

Non-existence of Mean-Field Models for Particle Orientations in Suspensions

We consider a suspension of spherical inertialess particles in a Stokes flow on the torus T3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {T}^3$$\\end{document}. The particles perturb a linear extensional flow due to their rigidity constraint. Due to the singular nature of this perturbation, no mean-field limit for the behavior of the particle orientation can be valid. This contrasts with widely used models in the literature such as the FENE and Doi models and similar models for active suspensions. The proof of this result is based on the study of the mobility problem of a single particle in a non-cubic torus, which we prove to exhibit a nontrivial coupling between the angular velocity and a prescribed strain.

Research on Two-Stage Semi-Active ISD Suspension Based on Improved Fuzzy Neural Network PID Control.

To better improve the ride comfort and handling stability of vehicles, a new two-stage ISD semi-active suspension structure is designed, which consists of the three elements, including an adjustable damper, spring, and inerter. Meanwhile, a new semi-active ISD suspension control strategy is proposed based on this structure. Firstly, the fuzzy neural network's initial parameters are optimized using the grey wolf optimization algorithm. Then, the fuzzy neural network with the optimal parameters is adjusted to the PID parameters. Finally, a 1/4 2-degree-of-freedom ISD semi-active suspension model is constructed in Matlab/Simulink, and the dynamics simulation is carried out for the three schemes using PID control, fuzzy neural network PID control, and improved fuzzy neural network PID control, respectively. The results show that compared with adopting PID control and fuzzy neural network PID control strategy, the vehicle body acceleration and tire dynamic loads are significantly reduced after using the grey wolf optimized fuzzy neural network PID control strategy, which shows that the control strategy proposed in this paper can significantly improve the vehicle smoothness and the stability of the handling.

Meta-pharmacokinetic analysis of posaconazole following dosing of oral suspension, delayed-release tablet, and intravenous infusion in patients vs. healthy volunteers: Impact of clinical characteristics and race

ObjectivesTo investigate the potential impact of clinical characteristics and the Chinese race on posaconazole pharmacokinetics in patients using an integrated population pharmacokinetic model for posaconazole oral suspension (SUS), delayed-release tablet (DR-tablet), and intravenous (IV) infusion that was developed in healthy volunteers (HV). Methods1046 concentrations from 105 prospectively studied Caucasian patients receiving either of the three posaconazole formulations were pooled with 3898 concentrations from 182 HV. Clinical characteristics were tested for significance. The impact of Chinese race was assessed using 292 opportunistic samples from 80 Chinese patients receiving SUS. ResultsBioavailability of SUS (Fsus) in patients decreased from 38.2% to 24.6% when the dose was increased from 100 mg to 600 mg. Bioavailability of DR-tablet (Ftab) was 59% regardless of dose. Mucositis, diarrhoea, administration through a nasogastric tube, and concomitant use of proton pump inhibitors or metoclopramide reduced Fsus by 61%, 36%, 44%, 48%, and 29%, respectively, putting patients with these characteristics at increased risk of inadequate exposure. Clearance decreased from 7.0 to 5.1 L/h once albumin levels were <30 g/L. Patients showed an 84.4% larger peripheral volume of distribution (Vp) and 67.5% lower intercompartmental clearance (Q) compared with HV. No racial difference could be identified. ConclusionsPharmacokinetics of posaconazole in patients differ considerably to those in HV, with altered Fsus that is also impacted by clinical covariates, an Ftab similar to fasted conditions in HV, and altered parameters for clearance, Vp, and Q. There was no evidence to indicate that Chinese patients require a different dose to Caucasian patients.

Electrorheological effect of suspensions containing mixed size of poly(ionic liquid) microspheres

In this paper, the electrorheological (ER) effect of suspensions containing mixed size of poly(ionic liquid) (PIL) microspheres were studied by combining experiment and molecular dynamics simulation. The PIL microspheres with two particle sizes were prepared via a cooling-assisted phase separation method. The PIL microspheres were dispersed in silicone oil to form five kinds of suspensions with different volume ratios of large and small at a fixed particle volume fraction. The ER effect of these suspensions was measured by a rheometer. We established ER suspension models for five suspensions and simulated the rheological curves of the ER suspensions using molecular dynamics-stochastic rotation dynamics method. Both experiment and simulation results showed that the ER effect of suspensions containing mixed size of PIL microspheres was lower than that of suspensions containing uniform size of PIL microspheres. The reasons for the influence of mixed particle size on ER effect were analyzed through the three-dimensional visualization simulation results.

Nonlinear dynamic modeling and analysis of magnetorheological semi-active suspension for tracked vehicles

The magnetorheological technology has been widely used in automotive applications, whereas less research has been done on tracked vehicles. Hence, this research focuses on the dynamic modeling of the whole system of a tracked vehicle, for analyzing the effect of magnetorheological semi-active suspension on track tension and chassis vibration during driving. Applying the multibody system transfer matrix method and a dynamic recursive method, the dynamic models of the chassis subsystem and the double track subsystems are developed, respectively. These three subsystems are coupled by nonlinear contact forces, where the meshing shock, polygon effect, and rolling effect during contact are also taken into consideration. Subsequently, the normalized Bouc-Wen model is adopted to describe the nonlinear characteristics of rotary magnetorheological dampers. Then, a semi-active suspension control of the tracked vehicle is implemented with rotary magnetorheological dampers and the independent skyhook control method. Finally, numerical simulations are performed under different operating conditions. Comparing with the case of passive suspension, it reveals that, the magnetorheological semi-active suspension not only improves the distribution of the track tension but also effectively reduces the chassis vibration. It provides a theoretical basis for the design and application of magnetorheological semi-active suspensions for tracked vehicles.

Ride comfort of patient transport robot chassis

The ride comfort is a significant property of patient transport robots, which is directly related to the performance of rescue instruments and the cause of secondary damage. Previous studies overlook the design optimization of patient transport robots to improve ride comfort in hospital environments. This study designs a mobility system with an improved chassis that enables a more comfortable ride for patients. The system incorporates a longitudinal arm-independent suspension, which has a regulating device that changes the shock absorber angle and longitudinal arm length. A four-wheel vibration coupling response model of the robot vehicle is established. An optimization model with variable stiffness and damping coefficients is built and analyzed. The effective and maximum values of the body’s vertical, pitch angular, and roll angular accelerations are used as evaluation criteria of the robot’s ride comfort, which is analyzed on random roads and roadblocks, comparing its performance before and after the optimization. The results show that the weighted acceleration of the optimized body reduces by 61.9%, and the optimized suspension system improves the overall robot’s ride comfort. The evaluation indices of the optimized robot are measured through experiments. The weighted acceleration in the three directions of the optimized body is 0.18[Formula: see text]m/s2, which is less than 0.315[Formula: see text]m/s2 as required by ISO 2631-1, indicating that the patient does not feel uncomfortable, rendering an excellent evaluation, and verifying the rationality of the suspension system modeling analysis. The establishment of the multi-objective optimization model provides a theoretical basis for improving the ride comfort of mobile robots.

A new design of seat suspension using different models of negative stiffness structure

Three models of seat suspension using the negative stiffness structure including steel springs (SS), roller springs (RS), and tuned mass damper (TMD) are proposed and studied to improve the driver's seat ride comfort. Based on the dynamic models of the SS, RS, and TMD, their isolation efficiency and driver’s ride comfort are evaluated via two indexes of the root mean square displacement and acceleration of the seat (zws and aws) under two excitations of the random road surface and bumpy road surface. The results show that under the random road surface, the zws and aws with the seat's RS are reduced by 10.31 % and 20.32 % in comparison with the seat’s SS; whereas the zws and aws with the seat's TMD are smaller than that of the seat's RS by 19.15 % and 26.13 %; and the seat’s SS by 27.49 % and 41.15 %, respectively. Besides, the seat's displacement and acceleration responses with the seat’s TMD are also lower than that of both the SS and RS under the bumpy road surface. Therefore, the structure of the TMD should be designed and added to the seat suspension to enhance the driver’s seat ride comfort.

Optimal design of hedge-algebras–based controller for vibration control of vehicle suspension systems

This study aims to investigate an optimal design problem for vibration control of vehicle suspension models for reducing dynamic responses of the systems. The controller is constructed and optimized based on the approach of the hedge-algebras theory. Optimized parameters include fuzziness measures and reference ranges of state and control variables. Objective functions are considered to minimize the car body vibration and other essential objectives. Initial and optimized controllers have validated their stability through a newly proposed method using rule surfaces of the hedge-algebras–based controller. The controllers based on hedge-algebras theory have higher performance than controllers in previous publications and ensure the system stability and robustness to changes in the car body and wheel masses. The optimal approach in the present work allows determining values of design variables that are appropriate for the controlled models instead of using a trial–error method to evaluate these variables. In addition, the proposed approach to test the system stability allows simplifying this task for controllers using hedge-algebras theory.

Response and reliability of suspension system under stochastic and periodic track excitations by path integral method

Considering that maglev trains are affected by factors such as track irregularities, variations in load, external wind loads, and track materials, this paper establishes a suspension system model that takes into account the combined action of periodic and stochastic excitation. It then examines the response and reliability of the suspension system from the perspective of stochastic dynamics. The path integral method is introduced to address the challenges posed by periodic excitation. Expressions for the path integral solutions of the probability density function for the responses and the reliability density function are derived directly from the suspension system. The reliability function and the mean first-passage time are then further derived. Using the path integral solutions, we investigate the effects of stochastic excitation, periodic excitation of the track, and safety domain on the suspension system. Research shows that as the intensity of stochastic excitation increases, the oscillation amplitude of the response also increases, while the reliability of the system decreases. The effect of periodic excitation on the response and reliability of the system is more complex. The most intriguing discovery is that the reliability of the suspension system weakens when the angular frequency of the periodic excitation is close to the system’s natural frequency.

Dynamic analysis of an electro-hydraulic interconnected actuator energy regeneration suspension

A hydraulic interconnected suspension with energy recovery (EHA-HIS) is proposed to enhance riding comfort and road-holding ability while converting vibration energy into usable electrical energy. This paper mainly focuses on the dynamic analysis of a vehicle suspension model integrated with the EHA-HIS. The mathematical model of EHA-HIS is established based on the system structure analysis. The characteristics of the EHA-HIS are given based on a parameter analysis including the input and structural parameters under a sinusoidal excitation. Thereafter, vehicles equipped with the EHA-HIS and traditional suspensions are compared in terms of dynamic performance, and the simulation is implemented to study the energy harvesting performance of a vehicle with the EHA-HIS. The simulation results suggest that the damping force and harvested power are proportional to the frequency and amplitude of the sinusoidal input. The simulation also shows that the piston diameter has the greatest influence on the characteristics of the EHA-HIS. The analysis indicates that EHA-HIS can recover vibration energy while improving vehicle dynamic performance, and the harvestable power increases with the road grade and vehicle speed.