Статті в журналах: "DOF QUARTER CAR MODEL"

1

Jain, Saransh, Shubham Saboo, Catalin Iulian Pruncu, and Deepak Rajendra Unune. "Performance Investigation of Integrated Model of Quarter Car Semi-Active Seat Suspension with Human Model." Applied Sciences 10, no. 9 (May 2, 2020): 3185. http://dx.doi.org/10.3390/app10093185.

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In this paper, an integrated model of a semi-active seat suspension with a human model over a quarter is presented. The proposed eight-degrees of freedom (8-DOF) integrated model consists of 2-DOF for the quarter car model, 2-DOF for the semi-active seat suspension and 4-DOF for the human model. A magneto-rheological (MR) damper is implemented for the seat suspension. The fuzzy logic-based self-tuning (FLST) proportional–integral–derivative (PID) controller allows to regulate the controlled force on the basis of sprung mass velocity error and its derivative as input. The controlled force is tracked by the Heaviside step function which determines the supply voltage for the MR damper. The performance of the proposed integrated model is analysed, in-terms of human head accelerations, for several road profiles and at different speeds. The performance of the semi-active seat suspension is compared with the traditional passive seat suspension to validate the effectiveness of the proposed integrated model with a semi-active seat suspension. The simulation results show that the semi-active seat suspension improves the ride comfort significantly by reducing the head acceleration effectively compared to the passive seat suspension.

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2

Aliza, Che Amran, Fen Ying Chin, Mariam Md Ghazaly, Shin Horng Chong, and Vasanthan Sakthivelu. "Development of Passive Quarter Car Suspension Prototype." Applied Mechanics and Materials 761 (May 2015): 238–44. http://dx.doi.org/10.4028/www.scientific.net/amm.761.238.

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In this paper, a construction of a prototype to represent passive vehicle suspension system for quarter car model is considered. The prototype is represented by two degree-of freedom quarter-car model which are conventionally used by researchers. This laboratory equipment is developed in order to familiarize students with 2 DoF passive suspension system model. It consists of two masses, two springs and a damper. This equipment is easily dismantled and could be assembled with different spring and damper constants which contribute to different characteristics of the suspension system. A number of experiments have been carried out using the experiment setup in order to identify the suspension system characteristics i.e. experiments with different vehicle body mass, different period for one pulse and different pulse width of input pressure of the road excitation have been conducted. The experiment results are evaluated based on the vehicle body displacement and tire displacement of the prototype. Experiment results show that the pulse width of the input pressure or road profile is directly affected the characteristic of this passive suspension system. Lastly, simulations were done in order to compare the simulation and experimental results.

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3

Chen, Xiaoliang, Hao Song, Sixia Zhao, and Liyou Xu. "Ride comfort investigation of semi-active seat suspension integrated with quarter car model." Mechanics & Industry 23 (2022): 18. http://dx.doi.org/10.1051/meca/2022020.

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A method for parameter identification of the magnetorheological damper (MRD) model with an improved firefly algorithm (IFA) is proposed, and a semi-active seat control system with three-degree-of-freedom (3-DOF) is established by combining with a quarter car model to investigate the ride comfort. The dynamic characteristics of the MRD were analyzed by experimental method. Combined with the IFA, the parameters of the MRD phenomenon model were identified, and the forward model of the MR damper was constructed. The semi-active control model of a 3-DOF seat suspension was established. The MRD controller and suspension system controller were designed. The passive control, PID control, and Fuzzy-PID control on the vibration reduction of the semi-active seat suspension were compared and analyzed, under different road excitation. The simulation results show that the semi-active seat suspension controlled by the PID and Fuzzy-PID can effectively reduce the seat acceleration and dynamic stroke, which significantly improve the ride comfort and operation safety compared to the passive seat suspension.

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4

Park, Manbok, and Seongjin Yim. "Design of Static Output Feedback and Structured Controllers for Active Suspension with Quarter-Car Model." Energies 14, no. 24 (December 7, 2021): 8231. http://dx.doi.org/10.3390/en14248231.

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This paper presents a method to design active suspension controllers for a 7-Degree-of-Freedom (DOF) full-car (FC) model from controllers designed with a 2-DOF quarter-car (QC) one. A linear quadratic regulator (LQR) with 7-DOF FC model has been widely used for active suspension control. However, it is too hard to implement the LQR in real vehicles because it requires so many state variables to be precisely measured and has so many elements to be implemented in the gain matrix of the LQR. To cope with the problem, a 2-DOF QC model describing vertical motions of sprung and unsprung masses is adopted for controller design. LQR designed with the QC model has a simpler structure and much smaller number of gain elements than that designed with the FC one. In this paper, several controllers for the FC model are derived from LQR designed with the QC model. These controllers can give equivalent or better performance than that designed with the FC model in terms of ride comfort. In order to use available sensor signals instead of using full-state feedback for active suspension control, LQ static output feedback (SOF) and linear quadratic Gaussian (LQG) controllers are designed with the QC model. From these controllers, observer-based controllers for the FC model are also derived. To verify the performance of the controllers for the FC model derived from LQR and LQ SOF ones designed with the QC model, frequency domain analysis is undertaken. From the analysis, it is confirmed that the controllers for the FC model derived from LQ and LQ SOF ones designed with the QC model can give equivalent performance to those designed with the FC one in terms of ride comfort.

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5

D’Andrea, Danilo, Giacomo Risitano, Ernesto Desiderio, Andrea Quintarelli, Dario Milone, and Fabio Alberti. "Artificial Neural Network Prediction of the Optimal Setup Parameters of a Seven Degrees of Freedom Mathematical Model of a Race Car: IndyCar Case Study." Vehicles 3, no. 2 (June 20, 2021): 300–329. http://dx.doi.org/10.3390/vehicles3020019.

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The aim of this paper is the development of a 7-DOF (Degrees Of Freedom) mathematical model of an IndyCar and the implementation of an Artificial Neural Network in order to predict the optimal setup parameters of the car, reducing time and costs for race teams. The mathematical model is created by using MATLABTM and Simulink software starting from a telemetry acquisition at the Houston circuit and is based on Vertical Vehicle Dynamic equations. The optimal setup parameters have been predicted through an Artificial Neural Network (ANN) by using the NFTOOL Toolbox of MATLABTM software. ANN is implemented in a Quarter Car model, firstly, in order to train the network and predict the parameters able to reduce tire deflection and suspension travel in the time domain and the resonance peaks amplitude in the frequency domain. Then, it is implemented in the 7-DOF model in order to predict the best setup parameters able to reduce body movements and the weight transfers of the car.

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6

Mahmood, Mahmood, Ameen Nassar, and Haider Mohammad. "Analysis and Study Indicators for Quarter Car Model with Two Air Suspension System." Basrah journal for engineering science 22, no. 2 (December 24, 2022): 16–22. http://dx.doi.org/10.33971/bjes.22.2.3.

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Modeling and simulation of non-linear quarter-car suspension system for two air spring models (traditional and dynamic new air spring) are contrasted in terms of (RMS) sprung mass acceleration, dynamic load coefficient, the vertical displacement, they are compared. Two and three (DOF) of the mathematical quarter models are implemented in MATLAB/Simulink platform. The Ride Comfort (RC), Dynamic Load Coefficient (DLC) and Road Handling (RH) responses are evaluated as objective functions respectively considering a vehicle speed at 72 km/h and road ISO Class B. The obtained results indicate that the vertical displacement, the (RMS) of the sprung mass acceleration, and dynamic load coefficient values with the new air model system decrease by 10.7 %, 30.6 %, and 13.49 % respectively, in comparison to a tradition suspension system, this one gives more comfort and effortless handling.

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7

Silveira, M., P. Wahi, and J. C. M. Fernandes. "Effects of asymmetrical damping on a 2 DOF quarter-car model under harmonic excitation." Communications in Nonlinear Science and Numerical Simulation 43 (February 2017): 14–24. http://dx.doi.org/10.1016/j.cnsns.2016.06.029.

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8

Hac´, A., and I. Youn. "Optimal Semi-Active Suspension with Preview Based on a Quarter Car Model." Journal of Vibration and Acoustics 114, no. 1 (January 1, 1992): 84–92. http://dx.doi.org/10.1115/1.2930239.

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This paper deals with the synthesis of an optimal yet practical finite preview controller for a semi-active dissipative suspension system based on a two-degree-of-freedom (2-DOF) vehicle model. The proposed controller utilizes knowledge about approaching road disturbances obtained from preview sensors to minimize the effect of these disturbances. A truly optimal control law, which minimizes a quadratic performance index under passivity constraints, is derived using a variational approach. The optimal closed loop system becomes piecewise linear varying between two passive systems and a fully active one. It is shown that the steady state system response to a periodic input is also periodic and its amplitude is proportional to the amplitude of the input. Therefore, frequency domain characteristics in a classical sense can be generated. The problem formulation and the analytical solution are given in a general form and hence they apply to any bilinear system with system disturbances that are a priori unknown but some preview information is possible. The results of this analysis are applied to a quarter car model with semi-active suspension whose frequency domain and time domain performances are evaluated and compared to those of fully active and passive models. The effect of preview time on the system performance is also examined.

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9

Narayanan, S., and S. Senthil. "STOCHASTIC OPTIMAL ACTIVE CONTROL OF A 2-DOF QUARTER CAR MODEL WITH NON-LINEAR PASSIVE SUSPENSION ELEMENTS." Journal of Sound and Vibration 211, no. 3 (April 1998): 495–506. http://dx.doi.org/10.1006/jsvi.1997.1396.

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10

Krauze, Piotr, and Jerzy Kasprzyk. "Mixed Skyhook and FxLMS Control of a Half-Car Model with Magnetorheological Dampers." Advances in Acoustics and Vibration 2016 (October 25, 2016): 1–13. http://dx.doi.org/10.1155/2016/7428616.

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Анотація:

The problem of vibration attenuation in a semiactive vehicle suspension is considered. The proposed solution is based on usage of the information about the road roughness coming from the sensor installed on the front axle of the vehicle. It does not need any preview sensor to measure the road roughness as other preview control strategies do. Here, the well-known Skyhook algorithm is used for control of the front magnetorheological (MR) damper. This algorithm is tuned to a quarter-car model of the front part of the vehicle. The rear MR damper is controlled by the FxLMS (Filtered-x LMS) taking advantage of the information about the motion of the front vehicle axle. The goal of this algorithm is to minimize pitch of the vehicle body. The strategy is applied for a four-degree-of-freedom (4-DOF) vehicle model equipped with magnetorheological dampers which were described using the Bouc-Wen model. The suspension model was subjected to the road-induced excitation in the form of a series of bumps within the frequency range 1.0–10 Hz. Different solutions are compared based on the transmissibility function and simulation results show the usefulness of the proposed solution.

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11

Koç, Mehmet Akif. "Dynamic Vehicle and Rigid Road Interaction Analysis and Vibration Control of the Quarter Car Model Using Adaptive Neuro Fuzzy Algorithm." Academic Perspective Procedia 4, no. 1 (October 16, 2021): 119–28. http://dx.doi.org/10.33793/acperpro.04.01.22.

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In this study 3-DOF quarter car model with the three bumps on the rigid road, the assumption has been modeled with the non-random irregularity. To reduce the excessive vibrations occurred on the vehicle body, an active suspension system with the linear actuator has been considered. Moreover, to control this actuator, an adaptive neuro-fuzzy algorithm is designed. The training and testing data of the ANFIS has been obtained from Proportional Integral Derivative (PID) control algorithm. After that the successful training process, a testing procedure has been applied to ANFIS for the measure of the adaptive neuro-fuzzy system with data that are not considered in the training process. Then, the performance of the ANFIS is compared by the PID algorithm and passive suspension system in terms of vehicle body vertical acceleration, vehicle body vertical displacement, and control force. The road model used in the study has been modeled according to non-random road profile mathematical formulation considering periodical and discrete road profile cases. In this formulation, one can easily determine the height, width, and number of the road defect with the series mathematical formulation. Consequently, with the results obtained from the presented study, it is proven that ANFIS is a very effective controlling algorithm to suppress vibration occurred on the vehicle body due to vehicle road interaction. Furthermore, the performance of the ANFIS has been tested with different parameters, for example, different number membership functions (MF), which used the fuzzification of the input parameters.

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12

Liu, Jiang, Xiaowei Li, Zhenghao Wang, and Ye Zhang. "Modelling and Experimental Study on Active Energy-Regenerative Suspension Structure with Variable Universe Fuzzy PD Control." Shock and Vibration 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/6170275.

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A novel electromagnetic active suspension with an energy-regenerative structure is proposed to solve the suspension’s control consumption problem. For this new system, a 2-DOF quarter-car model is built, and dynamics performances are studied using the variable universe fuzzy theory and the PD control approach. A self-powered efficiency concept is defined to describe the regenerative structure’s contribution to the whole control consumption, and its influent factors are also discussed. Simulations are carried out using software Matlab/Simulink, and experiments are conducted on the B-class road. The results demonstrate that the variable universe fuzzy control can recycle more than 18 percent vibration energy and provide over 11 percent power for the control demand. Furthermore, the new suspension system offers a smaller body acceleration and decreases dynamic tire deflection compared to the passive ones, so as to improve both the ride comfort and the safety.

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13

Pedro, Jimoh, and Olurotimi Dahunsi. "Neural network based feedback linearization control of a servo-hydraulic vehicle suspension system." International Journal of Applied Mathematics and Computer Science 21, no. 1 (March 1, 2011): 137–47. http://dx.doi.org/10.2478/v10006-011-0010-5.

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Neural network based feedback linearization control of a servo-hydraulic vehicle suspension systemThis paper presents the design of a neural network based feedback linearization (NNFBL) controller for a two degree-of-freedom (DOF), quarter-car, servo-hydraulic vehicle suspension system. The main objective of the direct adaptive NNFBL controller is to improve the system's ride comfort and handling quality. A feedforward, multi-layer perceptron (MLP) neural network (NN) model that is well suited for control by discrete input-output linearization (NNIOL) is developed using input-output data sets obtained from mathematical model simulation. The NN model is trained using the Levenberg-Marquardt optimization algorithm. The proposed controller is compared with a constant-gain PID controller (based on the Ziegler-Nichols tuning method) during suspension travel setpoint tracking in the presence of deterministic road disturbance. Simulation results demonstrate the superior performance of the proposed direct adaptive NNFBL controller over the generic PID controller in rejecting the deterministic road disturbance. This superior performance is achieved at a much lower control cost within the stipulated constraints.

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14

Gupta, Ashish, Nilanjan Bharadwaj, and Vikas Rastogi. "Computational Framework of Various Semi-Active Control Strategies for Road Vehicles Thorough Bondgraphs." International Journal of System Dynamics Applications 10, no. 4 (October 2021): 1–29. http://dx.doi.org/10.4018/ijsda.20211001.oa9.

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Vehicle suspension system plays a vital role in diminishing the vibration caused by the road roughness and prevent it from transmitting to the driver and the passenger. The semi-active suspensions contain spring and damping elements with variable properties, which can be changed by an external control. The work presented here is concerned with semi-active damper control for vibration isolation of base disturbances. Numerous control algorithms for semi active system had been suggested in the past, performed experimentally and validated with various computational models.In this work, the 2-DOF quarter car model with semi-active suspension, controlled by skyhook and balance logic with on-off and continuous control algorithms is being studied.The computational models are subjected to various road profiles like single half sine bump, random road disturbanceas typical Indian road scenario. So that the performance can be done as real time inputs. The simulation is being carried out on Matlab or Simulink.

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15

Jin, Li Qiang, Yue Liu, Jian Hua Li, and Gang He. "A New Vehicle Suspension Semi-Active Control Method for Enhancing Ride Properties." Advanced Materials Research 968 (June 2014): 259–62. http://dx.doi.org/10.4028/www.scientific.net/amr.968.259.

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In this paper, a new control theory will be proposed for the purpose of enhancing vehicle ride performance. In the first step, a quarter car model with two DOF will be analyzed after which the classical semi-active control idea and a new control method will be built. Then a new hybrid control model based on body acceleration and classical one will be provided, after which the advantage of this controller will be studied. All the models that proposed will be accomplished through matlab/simulink. The outcome parameters of two types, namely, the body acceleration and the suspension deflection will be compared in frequency domain among three conditions which can be described as passive, classical semi-active control and hybrid control respectively. Then random excitation will be given as the road input to get power spectral density curves for further compare. Though the curves we can easily come into a conclusion that vehicle suspensions armed with this new controller will show the best ride properties which hold practical values.

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16

Kasim, Salim Y., and Saif M. Abdulsattar. "Theoretical Study of Suspension System for Two-Dimensional Model of the Vehicle and its Effects on limiting speed and Driver Comfort." Tikrit Journal of Engineering Sciences 23, no. 4 (December 31, 2016): 93–102. http://dx.doi.org/10.25130/tjes.23.4.10.

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Vibration in cars is undesirable because it causes discomfort to passengers, and can also lead to fatigue and failure of some parts of the vehicle. Therefore, the study and analysis of comments movements cart embedded in ever to research vehicles since the invention. And associated vibration cart passenger comfort, safety and stability of the vehicle. The researchers analyzed several vibration of vehicles by looking at different models, such as quarter wagon model ,and Half Car Model and full vehicle model with different types of excitement experienced by the vehicle and intended here excitement is a set of external forces arising from the terrain. This research includes a half vehicle linear model , written for four degrees of freedom plus one (4 +1 DOF) after addition degree of freedom which is driver / passenger seat system becomes a five degrees of freedom, also the vehicle body is assumed as a rigid body and taking into account the Bounce and Pitch. The system governing equations of motion are formulated by using the finite element method (FEM). A Fortran language computer program has been established for this purpose and used in the process covering (Simulation) and stand on the performance evaluation and analysis riding cart at the design stage and stand on the impact driver way through a study on the subject and the quality of the driver's seat, Two criterion of standards of comfort has been used, such as standard rate of absorbed energy (Average Absorbed Power) to be the norm over the driver comfort or not. And the comfort factor which is the vertical acceleration root mean square is used as an indication for the ride comfort. In factthe driver is the most important link in the process of using vehicles because the decision-maker and dominant direct the movement of vehicle.

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17

Tiwari, Priti, and Dr G. R. Mishra. "Simulation OF Quarter Car Model." IOSR Journal of Mechanical and Civil Engineering 11, no. 2 (2014): 85–88. http://dx.doi.org/10.9790/1684-11238588.

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18

Dumitriu, Dan N., Veturia Chiroiu, and Ligia Munteanu. "Simplified 7 DOF Model of Car Vertical Vibrations for Small Pitch and Roll Angles." Applied Mechanics and Materials 801 (October 2015): 136–41. http://dx.doi.org/10.4028/www.scientific.net/amm.801.136.

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This paper concerns a simplified 7 DOF model for car vertical vibrations. The classical 7 DOF of the considered 3D vertical model are: the vertical displacement of the gravity center of the car body, the roll and pitch angles of the car body and the four vertical displacements of the wheels centers. Using the x-y-z sequence of rotations parameterization, the Euler’s rotation equations concerning the roll and pitch angle are easily obtained. Small differences are observed between our car body rotation equations concerning the two pitch and roll angles and the same equations provided by Demić et al. [6]. For small pitch and roll angles, no differences were observed with respect with [6]. Also, no differences were observed concerning the other 5 dynamics equations of the 7 DOF model, the ones for the vertical displacements.The simplified 7 DOF car vertical dynamics model, comprising two rotation equations (for pitch and roll angles) and five dynamics equations concerning vertical displacements/accelerations, were integrated/simulated in Matlab. For small pitch and roll angles (a rather flat and smooth straight road profile was considered in our case study), the results obtained using the in-house 7 DOF model Matlab simulator are in very good agreement with the results provided by CARSIM.

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19

Kirchner, William, and Steve Southward. "Anthropomimetic Traction Control: Quarter Car Model." SAE International Journal of Commercial Vehicles 4, no. 1 (September 13, 2011): 127–34. http://dx.doi.org/10.4271/2011-01-2178.

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20

Zhang, Yi, Xiaomao Zou, and Yu Gong. "Modeling and Simulation Analysis of the Rhombic Car based on 3-DOF Handling Model." Journal of Physics: Conference Series 2242, no. 1 (April 1, 2022): 012022. http://dx.doi.org/10.1088/1742-6596/2242/1/012022.

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Abstract A three degree of freedom(3-DOF) mathematical model of the handling and stability of the rhombic car is established in order to study the dynamic performance of the rhombic car. The dynamic performance of the rhombic car under different working conditions is obtained by the simulation analysis of the model. Through the road test of the rhombic car, the correctness of the mathematical model of the handling and stability is verified. Through the comparison between experimental data and simulation data, the maximum error is about 9.3%. Therefore, the mathematical model is correct. The 3-DOF model of the rhombic car can be used for research and optimization, which has good practical significance to the engineering.

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21

Zhang, Hailong, Ning Zhang, Fuhong Min, Subhash Rakheja, Chunyi Su, and Enrong Wang. "Coupling Mechanism and Decoupled Suspension Control Model of a Half Car." Mathematical Problems in Engineering 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/1932107.

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A structure decoupling control strategy of half-car suspension is proposed to fully decouple the system into independent front and rear quarter-car suspensions in this paper. The coupling mechanism of half-car suspension is firstly revealed and formulated with coupled damping force (CDF) in a linear function. Moreover, a novel dual dampers-based controllable quarter-car suspension structure is proposed to realize the independent control of pitch and vertical motions of the half car, in which a newly added controllable damper is suggested to be installed between the lower control arm and connection rod in conventional quarter-car suspension structure. The suggested damper constantly regulates the half-car pitch motion posture in a smooth and steady operation condition meantime achieving the expected completely structure decoupled control of the half-car suspension, by compensating the evolved CDF.

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22

Hegazy, S., and A. Sharaf. "Ride Comfort Analysis Using Quarter Car Model." International Conference on Aerospace Sciences and Aviation Technology 15, AEROSPACE SCIENCES (May 1, 2013): 1–11. http://dx.doi.org/10.21608/asat.2013.22238.

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23

Zhang, Hao, Qianqian Hong, Huaicheng Yan, Fuwen Yang, and Ge Guo. "Event-Based Distributed $H_{\infty }$ Filtering Networks of 2-DOF Quarter-Car Suspension Systems." IEEE Transactions on Industrial Informatics 13, no. 1 (February 2017): 312–21. http://dx.doi.org/10.1109/tii.2016.2569566.

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24

Sun, Yu, Jinsong Zhou, Dao Gong, and Yuanjin Ji. "Study on multi-degree of freedom dynamic vibration absorber of the car body of high-speed trains." Mechanical Sciences 13, no. 1 (March 17, 2022): 239–56. http://dx.doi.org/10.5194/ms-13-239-2022.

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Abstract. To absorb the vibration of the car body of the high-speed train in multiple degrees of freedom, a multi-degree of freedom dynamic vibration absorber (MDOF DVA) is proposed. Installed under the car body, the natural frequency of the MDOF DVA from each DOF can be designed as a DVA for every single degree of freedom of the car body. Hence, a 12-DOF model including the main vibration system and an MDOF DVA is established, and the principle of Multi-DOF dynamic vibration absorption is analyzed by combining the design method of a single DVA and genetic algorithm. Based on a high-speed train dynamics model including an under-car-body MDOF DVA, the vibration control effect on each DOF of the MDOF DVA is analyzed by the virtual excitation method. Moreover, a high static and low dynamic stiffness (HSLDS) mount is proposed based on a cam–roller–spring mechanism for the installation of the MDOF DVA due to the requirement of the low vertical dynamic stiffness. From the dynamic simulation of a non-linear model in the time domain, the vibration control performance of the MDOF DVA installed with a nonlinear HSLDS mount on the car body is analyzed. The results show that the MDOF DVA can absorb the vibration of the car body in multiple degrees of freedom effectively and improve the running ride quality of the vehicle.

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A. Emheisen, Abubaker Abasalam, Abdussalam Ali Ahmed, Nasr Ismael Alhusein, Abdurahim Alfadel Sakeb, and Abdulhamid S. Abdulhamid. "Car Wheel slip Modelling, Simulation, and Control using Quarter Car Model." International Journal of Engineering Trends and Technology 28, no. 6 (October 25, 2015): 291–93. http://dx.doi.org/10.14445/22315381/ijett-v28p255.

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26

Cheng, Y.-C., and C.-T. Hsu. "Hunting stability and derailment analysis of a car model of a railway vehicle system." Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 226, no. 2 (July 18, 2011): 187–202. http://dx.doi.org/10.1177/0954409711407658.

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Using a heuristic linear creep model, this article derives the governing differential equations of motion for a vehicle travelling on curved tracks. The vehicle is modelled by a 27-degrees-of-freedom (27-DOF) car system, with lateral and vertical displacement, roll and yaw angle of each wheelset and the bogie frames, as well as lateral displacement, and roll and yaw angle of the car body taken into consideration. To analyse the respective effects of major system parameters on vehicle dynamics, the 27-DOF system is reduced to a 14-DOF system by excluding designated subsets of the system parameters. The effects of suspension parameters of a vehicle on the critical hunting speeds were evaluated by the 14- and 27-DOF systems. The results obtained in this study, show that the critical hunting speeds derived using the 14-DOF system are generally higher than those obtained using the 27-DOF system. Additionally, the critical hunting speeds derived using the heuristic non-linear creep model are lower than those achieved using the linear creep model. The effects on derailment quotients of vehicle speeds are evaluated using both linear and non-linear creep models with various suspension parameters. Finally, the effects of vehicle speed on the derailment quotient for sharp curves and low vehicle speed are investigated and compared with both linear and non-linear creep models.

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27

Hanafi, Dirman, Mohamad Fauzi Zakaria, Rosli Omar, M. Nor M. Than, M. Fua'ad Rahmat, and Rozaimi Ghazali. "Neuro Model Approach for a Quarter Car Passive Suspension Systems." Applied Mechanics and Materials 775 (July 2015): 103–9. http://dx.doi.org/10.4028/www.scientific.net/amm.775.103.

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The road handling, load carrying and passenger comfort are three intension factors on car suspension’s system. They should be compromised to achieve the good the car suspension dynamics. To fulfill the requirement, the car suspension system must be controlled and analyzed. To design and analyze the suspension controller, the realistic dynamics model of car suspension is needed. In this paper, the car suspension is assumed as a quarter car and has a model structure as a neural network structure. The model is assumed consist of nonlinear properties that are contributed by spring stiffness and damping elements of suspension system. The tire is assumed has linear properties and represented by spring stiffness element and damping element. The model responses are generated in simulation term. The random type of artificial road surface signal as an input variable is used in this simulation. The results show that the trend of neuro model have the same with the response of a quarter car nonlinear model from dynamic derivation. It means that the developed neuro model structure capable to represent the nonlinear model of a quarter car passive suspension system dynamics.

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28

Wang, Jianfeng, Yiqun Liu, Liang Ding, Jun Li, Haibo Gao, Yuhan Liang, and Tianyao Sun. "Neural Network Identification of a Racing Car Tire Model." Journal of Engineering 2018 (May 29, 2018): 1–11. http://dx.doi.org/10.1155/2018/4143794.

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In order to meet the demands of small race car dynamics simulation, a new method of parameter identification in the Magic Formula tire model is presented in this work, based on an analysis of the Magic Formula tire model structure. A high-precision tire model used for vehicle dynamics simulation is established via this method. It is difficult for students to build a high-precision tire model because of the complexity of widely used tire models such as Magic Formula and UniTire. At a pure side slip condition, building a lateral force model is an example, which illustrate the utilization of a multilayer feed-forward neural network to build an intelligent tire model conveniently. In order to fully understand the difference between the two models, a two-degrees-of-freedom (2 DOF) vehicle model is established. The advantages, disadvantages, and applicable scope of the two tire models are discussed after comparing the simulation results of the 2 DOF model with the Magic Formula and intelligent tire model.

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29

Postalcıoğlu, Seda. "Online Wavelet Denoising for a Quarter Car Model." International Journal of Computer Applications 179, no. 31 (April 17, 2018): 25–28. http://dx.doi.org/10.5120/ijca2018916612.

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30

Maher, Damien, and Paul Young. "An insight into linear quarter car model accuracy." Vehicle System Dynamics 49, no. 3 (September 8, 2010): 463–80. http://dx.doi.org/10.1080/00423111003631946.

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31

Darsivan, Fadly Jashi, and Waleed F. Faris. "Vibration Investigation of a Quarter Car with Nonlinear Shock Absorber Model." Advanced Materials Research 576 (October 2012): 665–68. http://dx.doi.org/10.4028/www.scientific.net/amr.576.665.

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The paper discusses the response and the accuracy of a quarter car model with a non-linear damping force. The non-linear shock absorber model was a result of an experiment that was conducted earlier and the mathematical model was verified. Based on this model simulation responses of the sprung and unsprung masses between a linear and the non-linear damper were compared. The wheel of the quarter car model was excited by a road profile and according to the results the non-linear quarter model showed responses which were not depicted and captured by the linear model.

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32

Patil, Suresh A., and Shridhar G. Joshi. "Experimental analysis of 2 DOF quarter-car passive and hydraulic active suspension systems for ride comfort." Systems Science & Control Engineering 2, no. 1 (October 31, 2014): 621–31. http://dx.doi.org/10.1080/21642583.2014.913212.

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33

Nagarkar, Mahesh P., Gahininath J. Vikhe Patil, and Rahul N. Zaware Patil. "Optimization of nonlinear quarter car suspension–seat–driver model." Journal of Advanced Research 7, no. 6 (November 2016): 991–1007. http://dx.doi.org/10.1016/j.jare.2016.04.003.

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34

Li, Yu Guang, Chang Fei Liang, and Shu Fen Wang. "Study of Vehicle Handling Stability Based on MATLAB." Applied Mechanics and Materials 602-605 (August 2014): 489–92. http://dx.doi.org/10.4028/www.scientific.net/amm.602-605.489.

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In this paper, the sideslip angle and yaw velocity as parameters are presented to describing the motion state of the motion state of the vehicle, in which two DOF(degree of freedom) vehicle model is used as the reference model. And car speed is considered as the system step input to building a three DOF vehicle model based on H.B. Pacejka’s tire model. Meanwhile, the sideslip angle and the yaw velocity are taken as the system outputs. And achieve simulated analysis of vehicle handing stability by using Simulink. The results show that the three DOF vehicle model is more accurate in description of transport condition, which provides reference for the study of the vehicle steering stability.

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35

Fan, Xiao Bin, Yu Jiang, and Hui Gang Wang. "Stability Optimal Control Based on 15-Dof Vehicle Model." Advanced Materials Research 299-300 (July 2011): 1266–70. http://dx.doi.org/10.4028/www.scientific.net/amr.299-300.1266.

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The 15 degrees of nonlinear dynamic vehicle model is established, and then Dugoff and magic formula tire model are studied by comparison. Then the braking system dynamics model and the side-slip angle estimation algorithm are discussed. Stability control system is established based on the control target of combined yaw and side-slip angle with linear 2-dof vehicle handling characteristics model. It shows that control system can perfectly control vehicle driving and can improve the stability of car active safety through the serpent’s simulation test.

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36

Koulocheris, Dimitrios, and Clio Vossou. "A Comparative Study of Integrated Vehicle–Seat–Human Models for the Evaluation of Ride Comfort." Vehicles 5, no. 1 (February 4, 2023): 156–76. http://dx.doi.org/10.3390/vehicles5010010.

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In the literature the value of the driver’s head acceleration has been widely used as an objective function for the modification of the suspension and/or the seat characteristics in order to optimize the ride comfort of a vehicle. For these optimization procedures various lumped parameter Vehicle–Seat–Human models are proposed. In the present paper a Quarter Car model is integrated with three Seat–Human models with different levels of detail. The level of detail corresponds to the number of degrees of freedom used to describe the Seat–Human system. Firstly, the performance of the Quarter Car model, used as a basis, is analyzed in six excitations with different characteristics. Then, the performance of the three lumped parameter Vehicle–Seat–Human models are monitored in the same excitations. The results indicated that in the case of single disturbance excitations the Quarter Car model provided 50–75% higher values of acceleration compared with the eight degrees of freedom model. As far as the periodic excitation is concerned, the Vehicle–Seat–Human models provided values of acceleration up to eight times those of the Quarter Car model. On the other hand, in stochastic excitations the Vehicle–Seat–Human model with three degrees of freedom produced the closest results to the Quarter Car model followed by the eight degrees of freedom model. Finally, with respect to the computational efficiency it was found that an increase in the degrees of freedom of the Vehicle–Seat–Human model by one caused an increase in the CPU time from 2.1 to 2.6%, while increasing the number of the degrees of freedom by five increased the CPU time from 7.4 to 11.5% depending on the excitation.

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37

Yan, Huaicheng, Jiayu Sun, Hao Zhang, Xisheng Zhan, and Fuwen Yang. "Event-Triggered $H_\infty$ State Estimation of 2-DOF Quarter-Car Suspension Systems With Nonhomogeneous Markov Switching." IEEE Transactions on Systems, Man, and Cybernetics: Systems 50, no. 9 (September 2020): 3320–29. http://dx.doi.org/10.1109/tsmc.2018.2852688.

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38

Kanchwala, Husain. "Vehicle suspension model development using test track measurements." Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 234, no. 5 (August 19, 2019): 1442–59. http://dx.doi.org/10.1177/0954407019867504.

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Detailed suspension modeling is a prerequisite for accurate vehicle dynamics simulation. Quarter car models are widely used in the literature, but they are simple and do not capture all dynamic effects. On the other hand, full car models are computationally complex and not available to the designer at initial stage of vehicle development. A test track data based methodology to develop a Laplace domain reduced order suspension model of intermediate complexity between a full car and a quarter car model is presented in this paper. A prototype vehicle is driven on sinusoidal tracks and vertical accelerations of wheel axles and suspension to body attachment points are measured. Using this acceleration data, a transfer function model is fitted to predict the body points accelerations in response to measured wheel–axle accelerations. This model is further extended to incorporate an unsprung mass model and retain suspension properties as free parameters to enable quick parametric studies without repeated field testing. A discussion is given of aspects of the model that match experiments, as well as possible sources of observed mismatch. Finally, two potential applications are given to study the effect of suspension and unsprung mass model properties on body point responses.

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39

Zhang, Peng, Le He, Xu Tao Liu, and Qun Sheng Xia. "Study on Computer Simulation for Car Handling Dynamics with 8 DOF." Advanced Materials Research 655-657 (January 2013): 1136–40. http://dx.doi.org/10.4028/www.scientific.net/amr.655-657.1136.

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A mathematical model of eight degrees freedom was built up with considering the normal load transfer due to the presence of the longitudinal, lateral acceleration for a vehicle under braking in turn condition. And the simulation model based on the mathematical model was eatablished by means of MATLAB/Simulink software. The comparison between simulation results and real vehicle test results under the snow pavement double-lane change condition is in good agreement. It can be concluded that the 8DOF vehicle dynamics model of this study is acceptable and valid.

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40

Jiao, Hong Yu, Kai Zhang, Ying Li, and Hao Liu. "Simulation Analysis of Vehicle Crosswind Stability in ADAMS/CAR." Applied Mechanics and Materials 182-183 (June 2012): 883–87. http://dx.doi.org/10.4028/www.scientific.net/amm.182-183.883.

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The vehicle simulation model of 78-DOF is built based on ADAMS/CAR. Both rationality and accuracy of simulation model are verified by comparison analysis methods between real vehicle test and virtual simulation test. The mathematical model of wind pressure center and lateral aerodynamic force are formulated by using the STEP function. The simulation results indicate that the vehicle has the excellent crosswind stability and congruent dynamic response, which agrees with United States (ESV) standard.

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41

Mohammed Matrood, Mustafa, and Ameen Ahmed Nassar. "Vibration Control of Quarter Car Model Using Modified PID Controller." Basrah journal of engineering science 21, no. 2 (June 1, 2021): 1–6. http://dx.doi.org/10.33971/bjes.21.2.1.

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The purpose of this research is to control a quarter car suspension system and also to reduce the fluctuated movement caused by passing thevehicle over road bump using modified PID (Proportional Integral and Derivative) controller. The proposed controller deals with dual loopfeedback signals instead of single feedback signal as in the conventional PID controller. The structure of the modified PID controller wascreated by moving the proportional and derivative actions in the feedback path while remaining the integral action in the forward path. Thus,high accuracy results were obtained. Firstly, modelling and simulation of linear passive suspension system for a quarter car system wasperformed using Matlab – Simulink software. Then the linear suspension system was activated and simulated by using an active hydraulicactuator to generate the necessary force which can be regulated and controlled by the proposed controller. The performance of whole systemhas been enhanced with a modified PID controller.

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42

Elmadany, M. M., and M. I. Al-Majed. "Quadratic Synthesis of Active Controls for a Quarter-Car Model." Journal of Vibration and Control 7, no. 8 (November 2001): 1237–52. http://dx.doi.org/10.1177/107754630100700806.

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43

Gong, Ming Min, Dong Cherng Lin, and Chang Der Lee. "Estimating road profiles in quarter car model using two methods." International Journal of Vehicle Systems Modelling and Testing 14, no. 2/3 (2020): 113. http://dx.doi.org/10.1504/ijvsmt.2020.10034039.

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44

Gong, Ming Min, Dong Cherng Lin, and Chang Der Lee. "Estimating road profiles in quarter car model using two methods." International Journal of Vehicle Systems Modelling and Testing 14, no. 2/3 (2020): 113. http://dx.doi.org/10.1504/ijvsmt.2020.111678.

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45

Kanjanavapastit, Apichan, and Aphirak Thitinaruemit. "Estimation of a Speed Hump Profile Using Quarter Car Model." Procedia - Social and Behavioral Sciences 88 (October 2013): 265–73. http://dx.doi.org/10.1016/j.sbspro.2013.08.505.

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46

Howe, J. Gavin, Jeffrey P. Chrstos, R. Wade Allen, Thomas T. Myers, Dongchan Lee, Chi-Ying Liang, David J. Gorsich, and Alexander A. Reid. "Quarter car model stress analysis for terrain/road profile ratings." International Journal of Vehicle Design 36, no. 2/3 (2004): 248. http://dx.doi.org/10.1504/ijvd.2004.005359.

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47

Unguritu, Maria-Geanina, Teodor-Constantin Nichițelea, and Dan Selișteanu. "Design and Performance Assessment of Adaptive Harmonic Control for a Half-Car Active Suspension System." Complexity 2022 (July 5, 2022): 1–14. http://dx.doi.org/10.1155/2022/3190520.

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The vehicle suspension system is represented by a complex group of components which connect the wheels to the frame or body. Its primary function is to reduce or absorb various vehicle vibrations generated by road disturbances, providing comfort and safety for passengers. Most modern vehicles have independent, active, or semiactive front and rear suspensions which allow the use of electronic actuation. For this reason, automotive engineers conduct research on the active suspension model to determine the most suitable control algorithm. Three active suspension models are intensely used within simulations: the quarter-car, the half-car, and the full-car models. This paper proposes an adaptive harmonic control for a half-car active suspension system. The mathematical model of the suspension system is implemented in the MATLAB/Simulink environment. The control approach is tested via simulation, and several comparisons with the classical proportional-integral controller are provided. The simulation results show that the controller behaves quite similarly on the half-car model as it did on a quarter-car model. Additionally, an improvement to the harmonic control algorithm has been accomplished.

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48

Zhou, Shu Wen, Si Qi Zhang, and Guang Yao Zhao. "Study on High-Speed Lateral Stability of Car-Trailer Combination." Applied Mechanics and Materials 29-32 (August 2010): 1420–24. http://dx.doi.org/10.4028/www.scientific.net/amm.29-32.1420.

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Since the handling behaviour of car-trailer combination is more complex and less predictable than that of non-articulated vehicles, the drivers may lose control of the vehicle in some hasty steering maneuvers. The kinematics of car-trailer combination has been analyzed with a 3 DOF model. A modified Vehicle Dynamics Control system was designed to improve the lateral stability of the trailer. The dynamics simulation for lateral stability of car-trailer combination has been performed on the multi-body model. The results show that the lateral stability of car-trailer combination, including yaw rate and roll angle has been improved with the modified Vehicle Dynamics Control system.

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49

Klockiewicz, Z., and G. Ślaski. "The estimation of frequency response of nonlinear quarter car model and bilinear model of damper characteristics." IOP Conference Series: Materials Science and Engineering 1247, no. 1 (July 1, 2022): 012007. http://dx.doi.org/10.1088/1757-899x/1247/1/012007.

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Abstract The paper presents proposed and tested methods of estimation of frequency response of nonlinear quarter car suspension model and comparison with method for linear model used for research of vehicle vertical dynamics. Linear quarter car suspension model is widely used for estimation of comfort and safety performance of passive and semiactive suspensions. The real suspension - especially shock absorbers - are non-linear in three aspects: static characteristics, hysteresis and the presence of friction. Testing linear suspension model is possible with the use of analytical transfer function formulas but testing real suspension on a testing stand or even virtual but nonlinear suspension needs to use methods of transfer function estimation. It was necessary to design appropriate input signal allowing to get useful response signals. With the use of obtained frequency responses a method of linear estimation of nonlinear suspension for a given range of working condition was proposed. Also the bilinear model of damper characteristic estimation was proposed and tested proving to be good alternative to nonlinear characteristic.

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50

Liu, Zhi Sheng, Ji Min Zhang, and Yong Qiang Wang. "Numerical and Experimental Researches of 1:10 Tank Car Longitudinal Vibration with Fluid Sloshing." Applied Mechanics and Materials 365-366 (August 2013): 420–24. http://dx.doi.org/10.4028/www.scientific.net/amm.365-366.420.

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A 1:10 tank-car 2D fluid simulation model based on the computational fluid dynamics is established, and exchange the data with tank-car vibration model while simulating. In the paper, the 2 dimension fluid-structure coupling tank-car which owns two DOF is simulated, and the affect of fluid sloshing to tank-car longitudinal vibration is analyzed through the coupled vibration experiment. In the simulation and experiment, fluid sloshing increased the tanker longitudinal vibration acceleration amplitude and slowed response time is obtained through analyzing the difference between the different volume of fluid and the relevant solid without sloshing, and the difference of longitudinal vibration between full tank and non-full tank is significant.

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