Journal articles: 'Sprung mass'

1

Pence, Benjamin, Joseph Hays, Hosam K. Fathy, Corina Sandu, and Jeffrey Stein. "Vehicle sprung mass estimation for rough terrain." International Journal of Vehicle Design 61, no. 1/2/3/4 (2013): 3. http://dx.doi.org/10.1504/ijvd.2013.050837.

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Chahyadi, Hendry D. "Simulation and Analysis of Two-Mass Suspension Modification Using MATLAB Programming." ACMIT Proceedings 3, no. 1 (March 18, 2019): 160–65. http://dx.doi.org/10.33555/acmit.v3i1.39.

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The designs of automotive suspension system are aiming to avoid vibration generated by road condition interference to the driver. This final project is about a quarter car modeling with simulation modeling and analysis of Two-Mass modeling. Both existing and new modeling are being compared with additional spring in the sprung mass system. MATLAB program is developed to analyze using a state space model. The program developed here can be used for analyzing models of cars and vehicles with 2DOF. The quarter car modelling is basically a mass spring damping system with the car serving as the mass, the suspension coil as the spring, and the shock absorber as the damper. The existing modeling is well-known model for simulating vehicle suspension performance. The spring performs the role of supporting the static weight of the vehicle while the damper helps in dissipating the vibrational energy and limiting the input from the road that is transmitted to the vehicle. The performance of modified modelling by adding extra spring in the sprung mass system provides more comfort to the driver. Later on this project there will be comparison graphic which the output is resulting on the higher level of damping system efficiency that leads to the riding quality.

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Liu, Zheng, Yuzhuang Zhao, and Sizhong Chen. "A Dual-Observer Design for Nonlinear Suspension System Based on Feedback Linearization." Mathematical Problems in Engineering 2018 (December 26, 2018): 1–13. http://dx.doi.org/10.1155/2018/2485263.

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A novel approach to estimate suspension state information and payload condition was developed in this article. A nonlinear quarter car model with air spring and damper was built. After verification of system observability and solvability, a certain coordinate transform was built to transform the nonlinear system into a linear one. Then a Kalman filter observer was applied. A sprung mass observer, which works cooperatively with suspension state information observer, was also designed. Designed dual-observer was verified under typical road profile and sprung mass disturbance. Compared with extended Kalman filter, the dual-observer showed better accuracy and robustness.

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Zhou, Ding, and Tianjian Ji. "Free Vibration of Rectangular Plates with Attached Discrete Sprung Masses." Shock and Vibration 19, no. 1 (2012): 101–18. http://dx.doi.org/10.1155/2012/983576.

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A direct approach is used to derive the exact solution for the free vibration of thin rectangular plates with discrete sprung masses attached. The plate is simply supported along two opposite edges and elastically supported along the two other edges. The elastic support can represent a range of boundary conditions from free to clamped supports. Considering only the compatibility of the internal forces between the plate and the sprung masses, the equations of the coupled vibration of the plate-spring-mass system are derived. The exact expressions for mode and frequency equations of the coupled vibration of the plate and sprung masses are determined. The solutions converge steadily and monotonically to exact values. The correctness and accuracy of the solutions are demonstrated through comparison with published results. A parametric study is undertaken focusing on the plate with one or two sprung masses. The results can be used as a benchmark for further investigation.The solution provided in the paper is general and includes several special cases, such as the plate with classical boundary conditions, the plate attached with discrete rigid masses, the plate supported by discrete springs and the plate restricted by rigid vertical point-supports.

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Yao, Jun, Jinqiu Zhang, Mingmei Zhao, and Hu Peng. "Analysis of Dynamic Stability of Nonlinear Suspension concerning Slowly Varying Sprung Mass." Shock and Vibration 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/5341929.

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In this paper, the stability of vehicle concerning the slow-varying sprung mass is analyzed based on two degrees of freedom quarter-car model. A mathematical model of vehicle is established, the nonlinear vibration caused by sprung mass vibration is solved, and frequency curve is obtained. The characteristics of a stable solution and the parameters affecting the stability are analyzed. The numeric solution shows that a slow-varying sprung mass is equivalent to adding a negative damping coefficient to the suspension system, making the effective damping coefficient change from negative to positive. Such changing parameters lead to Hopf bifurcation and a shrinking limit cycle. The simulation results indicate the existence of static as well as dynamic bifurcation and the result is a change in the final stable vibration of the suspension. Even the tiny vibration of the sprung mass will lead to amplitude mutation, leading to the sprung mass instability.

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Papagiannakis, A. T., and B. Raveendran. "International Standards Organization-Compatible Index for Pavement Roughness." Transportation Research Record: Journal of the Transportation Research Board 1643, no. 1 (January 1998): 110–15. http://dx.doi.org/10.3141/1643-14.

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The development of a new pavement roughness index, which is compatible to the current International Standards Organization (ISO) standard on “exposure to whole-body vibration” is described. The index was intended to be the independent variable in the future development of relationships between user cost (i.e., vehicle depreciation, repairs, discomfort and so on) and pavement roughness; hence it was named RIDE (Roughness Index for Driving Expenditure). RIDE is based on the sprung mass acceleration response of a reference vehicle to the pavement profile. It is calculated in the frequency domain by multiplying the power spectral density (PSD) of the pavement profile by the square of the transfer function of the sprung mass acceleration of the reference vehicle. The resulting sprung mass acceleration PSD is integrated over frequency to yield the root-mean-square of the sprung mass acceleration per unit length of pavement traveled. The sprung mass acceleration is shown to be the main contributor of dynamic axle loads in heavy trucks, which relate to vehicle and cargo damage and also to pavement damage.

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Zhao, Wanzhong, Lin Ji, and Chunyan Wang. "H∞ control of integrated rollover prevention system based on improved lateral load transfer rate." Transactions of the Institute of Measurement and Control 41, no. 3 (June 6, 2018): 859–74. http://dx.doi.org/10.1177/0142331218773527.

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A rollover dynamic model that merges the active front steering model and differential braking model is established in this paper. After analyzing and improving the existing rollover evaluation method, a new evaluation method that takes both sprung mass and under-sprung mass into consideration is proposed. The reliability of the improved LTR (lateral load transfer rate) is confirmed by simulation results obtained from MATLAB and CARSIM where, all of three evaluation methods are taken under the same condition. The accuracy of the rollover evaluation index depends on the centroid height of under-sprung mass and the ratio of under-sprung mass and under-sprung mass. In order to achieve the desired tracking effect and anti-jamming capability, an integrated rollover control system based on active steering and differential braking is designed where a H∞ controller is adopted. The results of simulation under J-turn condition indicate that the control system has strong stability and robustness. When the vehicle is under the risk of rollover and reaches the setting threshold, the designed H∞ controller will actively keep the vehicle under the critical state.

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Jeniš, Filip, and Ivan Mazůrek. "Sprung mass positioning by semi-actively controlled damper." MATEC Web of Conferences 322 (2020): 01051. http://dx.doi.org/10.1051/matecconf/202032201051.

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Recently, the intensive wear of rails, especially in curves of small radii and at switches, has been studied. The wear is caused by the high lateral force peak of the wheel against the rail when entering the curves. An effective solution for reducing undesirable lateral forces on the rail is to rotate the vehicle bogie in the direction of the rail curve, which influences the distribution of lateral force over the first and second wheelset. This reduces the force peak and thus the track wear. The bogie rotation is nowadays realized by actuators, which replace the yaw dampers. However, actuator implementation is complicated, expensive, energyintensive and demanding for the performance of a fail-safe system. From this point of view, a semi-actively controlled yaw damper appears to be a better candidate. An algorithm such as Skyhook can hold the sprung mass in the desired position. It is believed to be possible to rotate the vehicle bogie by the special S/A control strategy of a yaw damper. This paper deals with the possibilities and limits of the positioning of the sprung mass by the semi-actively controlled damper. It has been shown that the system relative attenuation and the damper response time have the greatest influence on the mass positioning efficiency.

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Zhu, Xing Xing, and Si Hong Zhu. "A Theoretical Model for Calculating Vibration Characteristics of A Kind of Driver Seat with Air Spring and MR Damper." Applied Mechanics and Materials 141 (November 2011): 8–14. http://dx.doi.org/10.4028/www.scientific.net/amm.141.8.

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In order to further reduce the vibration transmitted from vehicle to driver, a new model of driver scissors linkage seat suspension was put forward, in which an air spring with auxiliary chamber and a MR damper are between the face and floor of the seat. The motion differential equation of this seat suspension system was established and the theoretical computing formulation of it’s equivalent vertical stiffness, equivalent damping coefficient, natural frequency and damping rate were deduced. Besides, taking HY-Z04 scissors linkage seat, SK37-6 air spring of ContiTech and RD-1005-3 MR damper of LORD as an example, the equivalent stiffness and damping coefficient in different conditions of the air spring pressure, the sprung mass, the orifice diameter and MR damping were computed and analyzed. The study results show that the air spring pressure, the sprung mass, the orifice diameter and MR damping all have obvious influence on the equivalent stiffness and damping coefficient, so the seat comfort can be improved by changing the air spring pressure, the orifice diameter and MR damping according to driver’s weight and road condition.

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Nagarkar, Mahesh, and G. J. Vikhe Patil. "Optimization of the linear quadratic regulator (LQR) control quarter car suspension system using genetic algorithm." Ingeniería e Investigación 36, no. 1 (April 18, 2016): 23–30. http://dx.doi.org/10.15446/ing.investig.v36n1.49253.

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<p>In this paper, a genetic algorithm (GA) based in an optimization approach is presented in order to search the optimum weighting matrix parameters of a linear quadratic regulator (LQR). A Macpherson strut quarter car suspension system is implemented for ride control application. Initially, the GA is implemented with the objective of minimizing root mean square (RMS) controller force. For single objective optimization, RMS controller force is reduced by 20.42% with slight increase in RMS sprung mass acceleration. Trade-off is observed between controller force and sprung mass acceleration. Further, an analysis is extended to multi-objective optimization with objectives such as minimization of RMS controller force and RMS sprung mass acceleration and minimization of RMS controller force, RMS sprung mass acceleration and suspension space deflection. For multi-objective optimization, Pareto-front gives flexibility in order to choose the optimum solution as per designer’s need.</p>

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Raghavan, Madhusudan. "Suspension Synthesis for N:1 Roll Center Motion." Journal of Mechanical Design 127, no. 4 (July 29, 2004): 673–78. http://dx.doi.org/10.1115/1.1867500.

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A dimensional synthesis procedure to achieve prescribed roll center height variation of a vehicle’s sprung mass with respect to wheel jounce-rebound is presented. This may be used to size the relative lengths of the control arms of a short-long arm suspension mechanism in order to (i) fix the roll center with respect to ground, or (ii) fix the roll center relative to the sprung mass, or (iii) have the roll center move at a prescribed rate relative to the sprung mass, during wheel jounce-rebound. These design selections have a significant impact on the ride-handling characteristics of a vehicle. Numerical examples are provided to demonstrate the synthesis procedure.

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12

Nguyen Van, Chi. "State Estimation Based on Sigma Point Kalman Filter for Suspension System in Presence of Road Excitation Influenced by Velocity of the Car." Journal of Control Science and Engineering 2019 (November 3, 2019): 1–16. http://dx.doi.org/10.1155/2019/6898756.

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The states of the suspension system including the road excitation depend on the road quality, the velocity of the car, and the sprung mass. Those states play a very important role in the control problem of stability, ride comfort, ride safety, and dynamic wheel load of the suspension systems. The velocities and deflections of the sprung mass and unsprung mass would not be measured fully in the practice. Therefore, it must be estimated by other measured quantities from the system such as acceleration and deflection of sprung mass and unsprung mass. To control the active suspension system, its states need to be estimated accurately and guaranteed the response time. This paper presents the method using the sigma point Kalman filter to estimate the suspension system’s states including the road excitation, the deflections, and the velocities of the sprung mass and unsprung mass. The mathematical model of the suspension system is rewritten for the state estimation problem, and the stochastic load profile is supposed the main noise input. The stochastic characteristic of the road excitation depending on the car’s velocity is taken into account in the model used for suspension system state estimation. The results calculated based on the practical experiment data for specific road profile with some particular velocities of the car show that the suspension system states are estimated quite accurately in comparison with the practice states.

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Yang, Judy P., and Bo-How Chen. "Two-Mass Vehicle Model for Extracting Bridge Frequencies." International Journal of Structural Stability and Dynamics 18, no. 04 (March 28, 2018): 1850056. http://dx.doi.org/10.1142/s0219455418500566.

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The dynamic response of a moving vehicle has been utilized to extract the frequencies of the supporting bridge. In most previous studies, the vehicle was modeled as a single-degree-of-freedom sprung mass moving over a simple beam, which suffers from the drawback that the sprung mass may be affected by the vehicle motion. To overcome this drawback, this paper presents a two-mass vehicle model for extracting the bridge frequencies, which contains a sprung mass (vehicle body) and an unsprung mass (axle mass). By using the response of the unsprung mass, the bridge response can be more realistically extracted. The main findings of the present study are as follows: (1) the use of unsprung mass in the vehicle model can faithfully reveal the dynamic responses of both the vehicle and bridge, (2) the increase in the unsprung mass can effectively help the extraction of bridge frequencies, including the second frequency, (3) under high levels of road roughness, the proposed model can identify the bridge frequencies, while the single-mass model cannot, and (4) in the presence of vehicle damping, the proposed model can identify the bridge frequencies under high levels of road roughness without additional techniques of processing.

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14

Levitt, J. A., and N. G. Zorka. "The Influence of Tire Damping in Quarter Car Active Suspension Models." Journal of Dynamic Systems, Measurement, and Control 113, no. 1 (March 1, 1991): 134–37. http://dx.doi.org/10.1115/1.2896339.

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Setting tire damping to zero when modeling automotive active suspension systems compels the misleading conclusions that, at the wheelhop frequency, no matter what forces are exerted between sprung and unsprung masses, their motion are uncoupled, and the vertical acceleration of the sprung mass will be unaffected. Alternatively, taking tire damping to be small but nonzero, the motions of the sprung and unsprung masses are coupled at all frequencies, and control forces can be used to reduce the sprung mass vertical acceleration at the wheelhop frequency. The effect of introducing tire damping can be quite large. In the case of a force law chosen to enhance ride along a straight smooth road, where road holding is not a major concern, setting the tire damping ratio to 0.02 reduces rms body acceleration by 30 percent.

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15

Zhang, Xiao-Liang, Tian Zhang, Jiamei Nie, and Long Chen. "A Semiactive Skyhook-Inertance Control Strategy Based on Continuously Adjustable Inerter." Shock and Vibration 2018 (2018): 1–8. http://dx.doi.org/10.1155/2018/6828621.

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This paper presents a modified skyhook-inertance control strategy which is realized through a hydraulic device of continuously adjustable inertance between sprung mass and unsprung mass. The parasitic damping inherent in the hydraulic device as well as the inertance is taken into account in the modified control strategy. Differential equation models are built to compare the performance of the semiactive suspension employing the modified control strategy with that of the passive suspension. The results demonstrate that the semiactive suspension significantly reduces sprung mass natural frequency, attenuates the resonant peak value without the penalty of deterioration at higher frequencies, and achieves over 28% improvement on ride comfort, compared with the passive suspension in unload condition. The proposed hydraulic device, together with its control strategy, can be used to reduce the variation of sprung mass natural frequency and ride comfort between unload and full-load condition.

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Yuan, Dong Mei, Xiao Mei Zheng, and Ying Yang. "Modeling and Simulation of Motorcycle Ride Comfort Based on Bump Road." Advanced Materials Research 139-141 (October 2010): 2643–47. http://dx.doi.org/10.4028/www.scientific.net/amr.139-141.2643.

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Through analyzing the motion when motorcycle runs on the bump road, the 5-DOF multi-body dynamics model of motorcycle is developed, the degrees of freedom include vertical displacement of sprung mass, rotation of sprung mass, vertical displacement of driver, and vertical displacement of front and rear suspension under sprung mass. According to Lagrange Equation, the differential equations of motion and state-space formulation are derived. Then bump road is simulated by triangle bump, and input displacement is programmed by MATLAB. With the input of bump road, motorcycle ride comfort is simulated, and the simulation results are verified by experiment results combined with two channels tire-coupling road simulator. It indicates that the simulation results and experiment results match well; the 5-DOF model has guidance for development of motorcycle ride comfort.

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Chi, Zhongzhe, Yuping He, and Greg F. Naterer. "DESIGN OPTIMIZATION OF VEHICLE SUSPENSIONS WITH A QUARTER-VEHICLE MODEL." Transactions of the Canadian Society for Mechanical Engineering 32, no. 2 (June 2008): 297–312. http://dx.doi.org/10.1139/tcsme-2008-0019.

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This paper presents a comparative study of three optimization algorithms, namely Genetic Algorithms (GAs), Pattern Search Algorithm (PSA) and Sequential Quadratic Program (SQP), for the design optimization of vehicle suspensions based on a quarter-vehicle model. In the optimization, the three design criteria are vertical vehicle body acceleration, suspension working space, and dynamic tire load. To implement the design optimization, five parameters (sprung mass, un-sprung mass, suspension spring stiffness, suspension damping coefficient and tire stiffness) are selected as the design variables. The comparative study shows that the global search algorithm (GA) and the direct search algorithm (PSA) are more reliable than the gradient based local search algorithm (SQP). The numerical simulation results indicate that the design criteria are significantly improved through optimizing the selected design variables. The effect of vehicle speed and road irregularity on design variables for improving vehicle ride quality has been investigated. A potential design optimization approach to the vehicle speed and road irregularity dependent suspension design problem is recommended.

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Tung, Nguyen Thanh, Vo Van Huong, and Phan Tuan Kiet. "Experimental research on determining the vertical tyre force of a tractor semi-trailer." International Journal of Modern Physics B 34, no. 22n24 (July 10, 2020): 2040163. http://dx.doi.org/10.1142/s0217979220401633.

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The vertical tyre force is crucial to the study of the dynamics of a tractor semi-trailer. The paper presents an experimental method for determining the vertical tyre force by determining the vertical acceleration of the un-sprung mass and the vertical acceleration of the sprung mass when the tractor semi-trailer moves. The results of this study form the basis for determining the dynamic tyre force without the installing of sensors on road.

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Ali Shahabi, Amir Hossein Kazemian, Said Farahat, and Faramarz Sarhaddi. "Dynamic Behavior of the Full-Car Model in the J-Turn Maneuver by Considering the Engine Gyroscopic Effects." Communications - Scientific letters of the University of Zilina 23, no. 3 (July 1, 2021): B237—B249. http://dx.doi.org/10.26552/com.c.2021.3.b237-b249.

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This study presents a new dynamic modeling of a vehicle by considering the engine dynamics. By selecting the vehicle coordinate system as the reference frame, all the force-torque equations of the sprung mass and unsprung masses are derived in this coordinate system by using the Newton’s equations of motion. Unlike the previous researches, in this work the sprung mass of the vehicle is not considered as a rigid body. The dynamics of the sprung mass components, such as gyroscopic effects of the engine crankshaft, is considered. In order to study the vehicle's dynamic behavior, in the J-turn maneuver, the governing equations of the full-car model are evaluated and validated by the numerical simulation method and ADAMS/Car software. Based on the results, the maximum roll angle and roll rate of a vehicle reach about 8 degrees and 40 degrees per second, respectively.

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Yue, C., T. Butsuen, and J. K. Hedrick. "Alternative Control Laws for Automotive Active Suspensions." Journal of Dynamic Systems, Measurement, and Control 111, no. 2 (June 1, 1989): 286–91. http://dx.doi.org/10.1115/1.3153048.

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A two degree of freedom (1/4 car model) is used to evaluate alternative linear control laws. Control laws considered are full state feedback, sprung mass absolute velocity feedback and an LQG regulator using suspension deflection as the measurement. It is shown that all three can yield improvements to the sprung mass ride quality but that overall the LQG regulator using suspension deflection provides the best trade-off between ride quality, suspension packaging and road holding constraints.

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JABEEN, S. D. "VIBRATION OPTIMIZATION OF A PASSIVE SUSPENSION SYSTEM VIA GENETIC ALGORITHM." International Journal of Modeling, Simulation, and Scientific Computing 04, no. 01 (December 27, 2012): 1250022. http://dx.doi.org/10.1142/s1793962312500225.

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In this paper, we have formulated mathematical models to optimize the bouncing transmissibility of the sprung mass of the half car system with passengers' seat suspensions considering different road conditions. The corresponding problem has been solved with the help of advanced real coded Genetic Algorithm (GA). The nonlinearity of suspension spring and damper, which are the most important characteristics of the suspension, has been taken into account in order to validate the model to real applications. The nonlinear cubic polynomial has been used to describe the spring characteristic and a quadratic polynomial has been used to describe the damper characteristic. The coefficients of each polynomial represent the design parameters of the suspension system and are to be determined. To find these parameters we have formulated a nonlinear optimization problem in which the bouncing transmissibility of the sprung mass at the center of mass has been minimized with respect to technological constraints and the constraints which satisfy the performance as per ISO 2631 standards. The advanced real coded GA has been used to solve this problem in time domain and the results obtained have been compared to those obtained using the existing design parameters. The objective function and the constraints have been evaluated by simulating the vehicle model over two roads with multiple bumps at uniform velocity.

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Zhang, Xue Yan, and Wen Ming Zhang. "Vibration Simulation of Articulated Dump Truck with the Variation of Longitudinal Center of Gravity Position of Rear Sprung Mass and Rear Suspension Stiffness." Advanced Materials Research 383-390 (November 2011): 1812–18. http://dx.doi.org/10.4028/www.scientific.net/amr.383-390.1812.

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The paper is concerned with the vibration for the articulated dump truck (ADT) which is multi-axle vehicle and different from rigid dump truck. The balanced suspension was employed as the rear suspension in the 60t ADT which the paper takes as the research object. A vibration model of 6 dof for the truck was proposed. The impact of the variation of longitudinal center of gravity position of rear sprung mass and rear suspension stiffness on vibration was investigated in stochastic excitation of the truck in the frequency domain. It is found that it is beneficial to the comfort of the truck when the center of gravity of the sprung mass moves forward and the impact of rear sprung stiffness on vibration is not too great. The results of the vibration for the truck are provided for the design of the 60t ADT.

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Chen, Jian Guo, Jun Sheng Cheng, and Yong Hong Nie. "Research on the Decoupling Control Algorithm of Full Vehicle Semi-Active Suspension." Advanced Materials Research 479-481 (February 2012): 1355–60. http://dx.doi.org/10.4028/www.scientific.net/amr.479-481.1355.

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Vehicle suspension is a MIMO coupling nonlinear system; its vibration couples that of the tires. When magneto-rheological dampers are adopted to attenuate vibration of the sprung mass, the damping forces of the dampers need to be distributed. For the suspension without decoupling, the vibration attenuation is difficult to be controlled precisely. In order to attenuate the vibration of the vehicle effectively, a nonlinear full vehicle semi-active suspension model is proposed. Considering the realization of the control of magneto-rheological dampers, a hysteretic polynomial damper model is adopted. A differential geometry approach is used to decouple the nonlinear suspension system, so that the wheels and sprung mass become independent linear subsystems and independent to each other. A control rule of vibration attenuation is designed, by which the control current applied to the magneto-rheological damper is calculated, and used for the decoupled suspension system. The simulations show that the acceleration of the sprung mass is attenuated greatly, which indicates that the control algorithm is effective and the hysteretic polynomial damper model is practicable.

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Unuh, H., P. Muhamad, F. Yakub, M. A. Ismail, and Z. Tanasta. "Experimental Validation to a Prototype Magnetorheological (MR) Semi-Active Damper for C-Class Vehicle." International Journal of Automotive and Mechanical Engineering 16, no. 3 (October 3, 2019): 7034–47. http://dx.doi.org/10.15282/ijame.16.3.2019.15.0527.

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In this study, a semi-active damper with OEM technical standard featuring MR fluid was fabricated to assess its use as potential reinforcement in enhancing c-class vehicle ride comfort. The finite element modelling was employed to investigate the capability of the MR semi-active damper prototype design in altered the damping utilizing unique rheological properties of MR fluid. The quarter car test rig completes with DYTRAN accelerometer and LMS Scadas mobile was operated to measure the RMS sprung mass acceleration of the MR semi-active damper prototype caused by a 5cm sinusoidal bump at speed of 10km/h. The finite element modelling gave the best representation of the ability of the design to manifest the shear stress development of MR fluid used. Indeed, the MR semi-active damper model prototype was able to enhance ride comfort by decreasing the acceleration of sprung mass compare to OEM passive damper. It was found that the applied current had the greatest influence on RMS sprung mass acceleration when measured over a range of frequency.

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Yin, Shih-Hsun. "Vibration of a Simple Beam Subjected to a Moving Sprung Mass with Initial Velocity and Constant Acceleration." International Journal of Structural Stability and Dynamics 16, no. 03 (March 3, 2016): 1450109. http://dx.doi.org/10.1142/s0219455414501090.

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In this paper, a semi-analytical solution to the problem of a simply supported beam subjected to a moving sprung mass with initial velocity and constant acceleration or deceleration was presented, which serves as a benchmark for checking the performance of other numerical methods. Herein, a finite element modeling procedure was adopted to tackle the vehicle–bridge interaction, and the responses of the vehicle and bridge were computed by time integration schemes such as the Newmark average acceleration, HHT-[Formula: see text], and Wilson-[Formula: see text] methods. In comparison with the semi-analytical solution, the acceleration response of the beam solved by the Newmark average acceleration method shows spurious high-frequency oscillations caused by the finite element discretization. In contrast, the HHT-[Formula: see text] and Wilson-[Formula: see text] methods can dissipate these oscillations and show more accurate results. Moreover, we found that the dynamic responses of the beam and sprung mass were mainly determined by the initial velocity of the sprung mass, but not by the acceleration or deceleration.

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Lü, Bao Zhan, Ai Jun Hu, and Si Hong Zhu. "Experimental Research on the Effect of Sinusoidal Excitation on Dynamic Wheel Load of Hydro-Pneumatic Suspension Vehicle." Applied Mechanics and Materials 143-144 (December 2011): 396–401. http://dx.doi.org/10.4028/www.scientific.net/amm.143-144.396.

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Based on the mathematical model of quarter car body model being put forward, the indoor platform experiment of quarter car body with hydro-pneumatic suspension system was done. During test, the parameters of dynamic wheel load along with the change of vibration amplitude and frequency were investigated. The results show that: the cycle of acceleration of sprung mass has half cycle lag than unsprung mass, and the main parameters of dynamic wheel load has increased significantly along with the increase of vibration amplitude and frequency. At the same time, through analysis the acceleration time responses of sprung and unsprung mass, it can be shown that hydro-pneumatic suspension has good anti-vibration performance.

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Maidanik, G. "Power dissipation in a sprung mass attached to a master structure." Journal of the Acoustical Society of America 98, no. 6 (December 1995): 3527–33. http://dx.doi.org/10.1121/1.414362.

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Ebrahimi-Nejad, Salman, Majid Kheybari, and Seyed Vahid Nourbakhsh Borujerd. "Multi-objective optimization of a sports car suspension system using simplified quarter-car models." Mechanics & Industry 21, no. 4 (2020): 412. http://dx.doi.org/10.1051/meca/2020039.

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In this paper, first, the vibrational governing equations for the suspension system of a selected sports car were derived using Lagrange's Equations. Then, numerical solutions of the equations were obtained to find the characteristic roots of the oscillating system, and the natural frequencies, mode shapes, and mass and stiffness matrices were obtained and verified. Next, the responses to unit step and unit impulse inputs were obtained. The paper compares the effects of various values of the damping coefficient and spring stiffness in order to identify which combination causes better suspension system performance. In this regard, we obtained and compared the time histories and the overshoot values of vehicle unsprung and sprung mass velocities, unsprung mass displacement, and suspension travel for various values of suspension stiffness (KS ) and damping (CS ) in a quarter-car model. Results indicate that the impulse imparted to the wheel is not affected by the values of CS and KS . Increasing KS will increase the maximum values of unsprung and sprung mass velocities and displacements, and increasing the value of CS slightly reduces the maximum values. By increasing both KS and CS we will have a smaller maximum suspension travel value. Although lower values of CS provide better ride quality, very low values are not effective. On the other hand, high values of CS and KS result in a stiffer suspension and the suspension will provide better handling and agility; the suspension should be designed with the best combination of design variables and operation parameters to provide optimum vibration performance. Finally, multi-objective optimization has been performed with the approach of choosing the best value for CS and KS and decreasing the maximum accelerations and displacements of unsprung and sprung masses, according to the TOPSIS method. Based on optimization results, the optimum range of KS is between 130 000–170 000, and the most favorable is 150, and 500 is the optimal mode for CS .

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Chen, Jian Guo, Xia Feng, and Xiao Ling Zhang. "A Vibration Attenuation Control Algorithm of Half Vehicle Using Active Suspension." Applied Mechanics and Materials 456 (October 2013): 14–17. http://dx.doi.org/10.4028/www.scientific.net/amm.456.14.

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Vehicle suspension is a MIMO coupling nonlinear system; its vibration couples that of the tires. For the suspension without decoupling, the vibration attenuation is difficult to be controlled precisely. In order to attenuate the vibration of the vehicle effectively, a nonlinear half vehicle model with active suspension is established and a differential geometry approach is used to decouple the nonlinear suspension system. The decoupled system becomes independent linear subsystems, though pole assignment, the vibration attenuation of the sprung mass is achieved. The simulations show that the vertical and the pitching motion of the sprung mass are attenuated greatly, which indicates that the control algorithm is effective.

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Jastrzębski, Łukasz, and Bogdan Sapiński. "Magnetorheological Self-Powered Vibration Reduction System with Current Cut-Off: Experimental Investigation." Acta Mechanica et Automatica 12, no. 2 (June 1, 2018): 96–100. http://dx.doi.org/10.2478/ama-2018-0015.

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Abstract The paper summarises the results of laboratory testing of an energy harvesting vibration reduction system based on a magne-torheological (MR) damper whose control circuit incorporates a battery of bipolar electrolytic capacitors (current cut-off circuit). It is de-signed to reduce the undesired effects in vibration reduction systems of this type, associated with the increasing amplitude of the sprung mass vibration under the excitation inputs whose frequency should exceed the resonance frequency of the entire system. Results have demonstrated that incorporating a current cut-off circuit results in a significant decrease of sprung mass vibration amplitudes when the frequency of acting excitation inputs is higher than the resonance frequency.

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Dehbari, S., and J. Marzbanrad. "Kinematic and Dynamic Analysis for a New MacPherson Strut Suspension System." Mechanics and Mechanical Engineering 22, no. 4 (September 2, 2020): 1223–38. http://dx.doi.org/10.2478/mme-2018-0094.

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AbstractThe present paper undertakes kinematic and dynamic analysis of front suspension system. The investigated model is a full-scale Macpherson which is a multibody system. Two degree of freedom model is considered here to illustrate the vertical displacement of sprung mass and unsprung mass with using displacement matrix. Ride and handling parameters including displacement of sprung and unsprung masses, camber/caster angle, and track changes are derived from the relationships. Moreover, geometrical model and equations are validated by Adams/Car software. The kinematic and dynamic results have been compared in both analytical and numerical outputs for verification. The proposed analytical model shows less than 5% differences with a complicated multibody model.

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Sapiński, Bogdan, Paweł Orkisz, and Łukasz Jastrzębski. "Experimental Analysis of Power Flows in the Regenerative Vibration Reduction System with a Magnetorheological Damper." Energies 14, no. 4 (February 6, 2021): 848. http://dx.doi.org/10.3390/en14040848.

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The aim of the work is to investigate power flows in the vibration reduction system equipped with a magnetorheological (MR) damper and energy regeneration. For this purpose, experiments were conducted in the test rig compound of the shaker and the vibration reduction system (electromagnetic harvester, MR damper, spring) which are attached to the sprung mass. The experimental data acquired under sine excitations enabled us to analyze instantaneous power fluxes, as well as a rate of inertial energy changes in the system.

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Cherry, A. S., R. P. Jones, and T. E. C. Potter. "The Use of Multibody System Modeling and Multivariable System Decoupling Techniques in Vehicle Ride Control." Journal of Dynamic Systems, Measurement, and Control 121, no. 3 (September 1, 1999): 479–86. http://dx.doi.org/10.1115/1.2802499.

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This paper describes the use of realistic analytical techniques to address automotive ride control. Multibody system (MBS) modeling techniques were used to develop a full vehicle model with suspension system representation, which was subsequently validated against experimental data. The resultant multivariable ride control problem was then decoupled in the frequency domain by the application of equivalence transformation techniques. It is shown that diagonalization can be achieved for the range of primary ride frequencies, and that the decoupled system then consists of three single-input/single-output (SISO) systems, one for each of the sprung mass modes. Finally, feedback control design for each sprung mass mode loop is illustrated by the application of modal damping.

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34

Seipel, Justin E., and Philip Holmes. "Running in Three Dimensions: Analysis of a Point-mass Sprung-leg Model." International Journal of Robotics Research 24, no. 8 (August 2005): 657–74. http://dx.doi.org/10.1177/0278364905056194.

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35

Yang, Judy P., and Bo-Lin Chen. "Rigid-Mass Vehicle Model for Identification of Bridge Frequencies Concerning Pitching Effect." International Journal of Structural Stability and Dynamics 19, no. 02 (February 2019): 1950008. http://dx.doi.org/10.1142/s0219455419500081.

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The concept of vehicle-bridge interaction (VBI) was originally developed to investigate the dynamic behavior of bridges subjected to moving loads such as high-speed trains. In recent years, the VBI system was introduced to further explore the possibility of identifying bridge frequencies in order to monitor the health of bridges via the use of passing vehicles. Among the models of test vehicles, the sprung mass vehicle model with a single-degree-of-freedom vehicle body is the most common adopted one due to its simplicity. Nevertheless, for a test vehicle moving over the uneven pavement, the pitching effect arising from the vertical and rotational movements of the vehicle actually influences the identification of bridge frequencies. As such, a rigid-mass vehicle model is proposed in this work to improve the sprung mass vehicle model by including both vertical and rotational deflections. The analytical solutions to the rigid-mass VBI system are derived to verify the proposed model, and the numerical examples are provided to investigate the dynamic behavior of the VBI system subjected to road irregularity.

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Surblys, Vytenis, Vidas Žuraulis, and Edgar Sokolovskij. "The Influence of Semi-Active Suspension Adjustment on Vehicle Body Pitch Oscillations." Transport and Telecommunication Journal 20, no. 2 (April 1, 2019): 107–13. http://dx.doi.org/10.2478/ttj-2019-0009.

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Abstract In this paper the relation between semi-active suspension characteristics and vertical oscillations of the vehicle body on road roughness is analysed. During experimental tests, the damping of semi-active suspension was changed while measuring vehicle's sprung and unsprung mass vertical accelerations, pitch rate, which were transformed into a frequency domain for further analysis. The results of the experimental tests were compared to the simulations using the semi-active dynamic model. Validation has shown that model can be used to analyse the influence of semi-active suspension parameters on vehicle oscillations over the entire range of semiactive suspension settings. The comparison of experimental and theoretical simulation showed that semi-active suspension settings have influence on longitudinal oscillations of the sprung mass and it should be estimated in related researches of modern suspension.

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Zhou, Li Hong. "Simulation Research on the Performance of Vehicle Suspension System." Advanced Materials Research 798-799 (September 2013): 378–81. http://dx.doi.org/10.4028/www.scientific.net/amr.798-799.378.

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Simulation study of the quarter car model was carried out in this paper. The influence of the stiffness of the suspension spring and the damping on the performance of vehicle suspension system was analyzed by the evaluation indexes: transfer function of body acceleration, transfer function of suspension dynamic stroke, transfer function of tire dynamic deflection. The simulation results shown that increasing the stiffness of the suspension spring would reduce the vehicle's ride comfort and increase the value of the first natural frequency of the sprung mass. And increasing the damping would reduce the peak response of the body acceleration which increasing the vehicle's ride comfort, but at the cost of increasing the high frequency vibration.

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Xiao, Heye, Meiping sheng, Zhihong Liu, and Zhaoyu Wei. "The Study on Free Vibration of Elastically Restrained Beams Carrying Various Types of Attachments with Arbitrary Spatial Distributions." Shock and Vibration 20, no. 3 (2013): 369–83. http://dx.doi.org/10.1155/2013/983451.

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The flexible beams carrying attachments often appear in engineering structures, modal analysis of those structures is important and necessary in structural design. This manuscript develops a proposed analytical method as a general tool for solving the free vibration of varying cross-section beams carrying various types of attachments with different distributions and arbitrary boundary conditions. In current practice, the natural frequencies of beam carrying lumped and uniform sprung mass and resting on Pasternak soil are calculated and compared with those in references to verify the methodology firstly. Then, the natural frequencies of beam carrying non-uniform spring-mass systems and stepped beam on Pasternak soil are calculated by the proposed method to study free vibration of beam carrying attachments with non-uniform cross section or distribution. Finally, some important conclusions are derived from results, which reveal that distribution density of spring-mass system at peaks of the mode shape makes dominate effects on the change of the natural frequencies at that mode and the natural frequencies of the stepped beam resting on elastic foundation are more sensitive to the increase of soil parameters.

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Soong, M. F., Rahizar Ramli, and Wan Nor Liza Wan Mahadi. "Ride Evaluation of Vehicle Suspension Employing Non-Linear Inerter." Applied Mechanics and Materials 471 (December 2013): 9–13. http://dx.doi.org/10.4028/www.scientific.net/amm.471.9.

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Inerter is a recent element in suspension systems with the property that the generated force is proportional to the relative acceleration between its two terminals, which is similar to the way a spring reacts to relative displacement and a damper to relative velocity. This paper presents the analysis of a non-linear inerter working in parallel to passive spring and damper of a vehicle suspension to evaluate its effect on vehicles ride. The non-linear inerter was theoretically capable of switching between on and off states depending on whether or not the suspension deflection was beyond a specified free play. In the study, this behavior was represented mathematically as control law which depended on the relative displacement between the sprung and unsprung masses. A mathematical quarter vehicle model incorporating the non-linear inerter was simulated in MATLAB/Simulink to determine the vehicle responses due to road input in the form of step profile for different combinations of free play and inerters on-state proportionality constant called the inertance. Results showed improvements in vehicle ride comfort, as demonstrated by the lower root-mean-squared sprung mass accelerations compared to the ordinary passive suspension with only spring and damper. Additionally, implementation of non-linear inerter gave lower percentage overshoot to step input, indicating better transient response than ordinary passive suspension.

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40

Daniel, Ľuboš. "Dynamic Deflection of a Bridge versus Speed of Vehicle Motion." Applied Mechanics and Materials 617 (August 2014): 19–23. http://dx.doi.org/10.4028/www.scientific.net/amm.617.19.

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The vehicle-bridge interaction (VBI) is the actual problem of many work places. The mid-span deflection of a bridge versus speed vehicle motion is interested from a practical point of view. Within the solution of the task the numerical methods based on Finite Element Method (FEM) are applied mainly. The task of VBI described in the submitted article is solved by using commercial software ANSYS. The 2-D sprung model of vehicle is modeled as combination of mass, spring and beam elements. The bridge with the mid-range is modeled by simple beam created with beam elements.

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41

Ihsan, S. I., M. Ahmadian, Waleed F. Faris, and E. D. Blancard. "Ride Performance Analysis of Half-Car Model for Semi-Active System Using RMS as Performance Criteria." Shock and Vibration 16, no. 6 (2009): 593–605. http://dx.doi.org/10.1155/2009/607871.

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The work aims to study the root mean square (RMS) responses to acceleration input for four state variables: the msvertical acceleration, the mspitch angular acceleration and the front and rear deflections of the suspensions. A half-car two degree-of-freedom model of semi-active control scheme is analyzed and compared with the conventional passive suspension system. Frequency response of the transfer function for the heave, pitch of the sprung mass and suspension deflections are initially compared and then mean square analysis is utilized to see the effect of semi-active scheme. Results indicate that significant improvements were achieved in the sprung mass heave and pitch responses using semi-active control scheme. However results for the rear and front suspension deflection show that there are limiting values of damping coefficient beyond which, the semi-active scheme becomes disadvantageous than the passive system.

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Башинський, Андрій Леонідович, Сергій Анатолійович Осташевський, and Павло Михайлович Малахов. "Results of experimental research of moving sprung mass to lateral stability of vehicle." Journal of Zhytomyr State Technological University. Series: Engineering, no. 2(82) (November 29, 2018): 11–20. http://dx.doi.org/10.26642/tn-2018-2(82)-11-20.

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Jiang, Hong, Kuan Qian, Long Yu Ju, and Zhen Cui. "Simulation and Experimental Study on Static and Dynamic Characteristics of Laterally Interconnected Air Suspension." Applied Mechanics and Materials 577 (July 2014): 273–76. http://dx.doi.org/10.4028/www.scientific.net/amm.577.273.

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Laterally interconnected air suspension can further improve air suspension performance. This paper presents the mathematical model of full vehicle and the test bench for laterally interconnected air suspension is established. Simulation and experimental results indicate that acceleration of sprung mass is reduced by laterally interconnecting the left and right air springs, and the larger pneumatic pipe diameter is, the better damping performance of the suspension will be. Compared with the conventional air suspension, laterally interconnected air suspension brings better ride comfort and driving stability for vehicles on uneven road.

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44

Zheng, Jin Yang, Yun He Chen, and Jian Ping Wang. "Finite Element Analysis on Coupled Vehicle-Bridge Vibration Based on the Sprung Mass Model." Applied Mechanics and Materials 687-691 (November 2014): 249–54. http://dx.doi.org/10.4028/www.scientific.net/amm.687-691.249.

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Based on the theoretical analysis on the coupled vehicle-bridge vibration, this paper simulates the action of the moving vehicle load on a bridge structure with a sprung mass model, and obtains the dynamic response of the simply-supported bridge structure under the moving vehicle load through computation by finite element method (FEM). Through checking computations of classic examples, this paper proves the applicability of this computation method.

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45

Bălă, Dumitru. "Quantitative and Qualitative Methods in the Study of some Dynamic Systems." Advanced Engineering Forum 13 (June 2015): 168–71. http://dx.doi.org/10.4028/www.scientific.net/aef.13.168.

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In this paper we present several methods for the study of stability of dynamical systems. We analyze the stability of a hammer modeled by the free vibrator that collides with a sprung elastic mass taking into consideration the viscous damping too.

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46

Qin, Yechen, Changle Xiang, Zhenfeng Wang, and Mingming Dong. "Road excitation classification for semi-active suspension system based on system response." Journal of Vibration and Control 24, no. 13 (February 21, 2017): 2732–48. http://dx.doi.org/10.1177/1077546317693432.

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Vehicle performance is largely affected by the properties of the suspension system, where semi-active suspension has been widely used in mass production of vehicles owing to its characteristics such as internal stability and low energy consumption. To solve the contradiction between ride comfort and road handling, road estimation based semi-active suspension has received considerable attention in recent years. In order to provide accurate estimation for advanced control strategies applications, this paper aims to develop a new method that can provide precise road class estimation based on measurable suspension system response (i.e. sprung mass acceleration, unsprung mass acceleration and rattle space). The response signal is first decomposed using wavelet packet analysis, and features in both time and frequency domains are subsequently extracted. Then, minimum redundancy maximum relevance (mRMR) is utilized to select superior features. Finally, a probabilistic neural network (PNN) classifier is applied to determine road classification output. The most representative semi-active control strategy, i.e. skyhook control, is used to validate this method, and simulation results with varying conditions including different control parameters and sprung mass are compared. The results show that unsprung mass acceleration is most suitable for road classification, and more robust to varying conditions in comparison to other responses.

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Kong, Yat Sheng, Shahrum Abdullah, Dieter Schramm, and Salvinder Singh Karam Singh. "Determining optimal suspension system parameters for spring fatigue life using design of experiment." Mechanics & Industry 20, no. 6 (2019): 621. http://dx.doi.org/10.1051/meca/2019062.

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This paper presents the optimization of spring fatigue life associated with suspension system parameters using the design of experiment approach. The effects of suspension parameters on spring fatigue life were analyzed because this process can improve spring fatigue life from a distinct perspective. A quarter car model simulation was performed to obtain the force time histories for fatigue life prediction where the suspension parameters were adjusted. Multiple input regression and interaction plots were conducted to identify the interaction between these parameters. A full factorial experiment was performed to determine the optimal suspension settings that would maximize the spring fatigue life. For the regression, a high R 2 value of 0.9078 was obtained, indicating good fitting. The established regression showed normality and homoscedasticity for consistent prediction outcome. Reducing the spring stiffness and sprung mass while enhancing the damping coefficient is therefore suggested to enhance fatigue life.

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48

Shannan, J. E., and M. J. Vanderploeg. "A Vehicle Handling Model With Active Suspensions." Journal of Mechanisms, Transmissions, and Automation in Design 111, no. 3 (September 1, 1989): 375–81. http://dx.doi.org/10.1115/1.3259009.

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This paper presents two vehicle models used to investigate the effects of active suspensions. One is a linear seven degree of freedom ride model. The second is a nonlinear ten degree of freedom ride and handling model. Full state feedback optimal control algorithms are developed for both models. The seven degree of freedom model is used to study ride effects. The active suspension substantially reduced the motion of the sprung mass. The ten degree of freedom model is used to study the effects of the active suspension on the directional response characteristics of the vehicle. The handling characteristics exhibited by the active suspension are very similar to those of the passive suspension. However, the active suspension did significantly reduce sprung mass motions during the handling maneuvers. It is then illustrated that by altering various feedback gains, active suspensions can be made to change the handling characteristics in the nonlinear range.

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Banerjee, Saayan, Varadarajan Balamurugan, and R. Krishna Kumar. "Effect of integrated ride and cornering dynamics of a military vehicle on the weapon responses." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 232, no. 4 (February 6, 2018): 536–54. http://dx.doi.org/10.1177/1464419318754647.

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The present study brings out the influence of a non-linear dynamics model of military vehicle with trailing arm suspension, on the weapon dynamics responses. A 20 degrees of freedom integrated ride and cornering dynamics model has sequentially been coupled with the 7 degrees of freedom weapon dynamics model. The 20 degrees of freedom integrated model includes the bounce, pitch, roll, longitudinal, lateral and yaw motions of the sprung mass and rotational dynamics of the 14 unsprung masses. The 7 degrees of freedom weapon model comprises the coupled elevation and azimuth dynamics. The coupled weapon model includes angular rotation of the elevation drive, breech and muzzle in elevation direction, as well as, angular rotation of the azimuth drive, turret, breech and muzzle in azimuth direction. The actual physical behaviour of each of the hydro-gas trailing arm suspension units is implemented in the governing differential equations. The non-linear governing equations also incorporate the dynamic coupling between each of the axle arms and sprung mass, which is an inherent behaviour of the trailing arm suspension, unlike their equivalent vertical representation. The integrated model has been simulated for different cornering manoeuvres at specified speeds. It is observed that the sprung mass dynamics, emanating from different manoeuvres, significantly affects the coupled elevation and azimuth dynamics responses of the weapon. The weapon dynamics model coupled with the integrated ride and cornering dynamics model of the military vehicle, would be useful for implementation of a suitable robust gun control system in military vehicles.

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Zhao, Yun Tang, Si Zhong Chen, and Zhan Zong Feng. "Study on a Control Method Used in the Semi-Active Suspension." Applied Mechanics and Materials 128-129 (October 2011): 1025–30. http://dx.doi.org/10.4028/www.scientific.net/amm.128-129.1025.

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A new control method used in the semi-active suspension is studied. The force generated by the semi-active damper can be divided into two parts, one is the uncontrollable force, and the other is the controllable force. In order to make the sprung mass have the ideal isolation effect, the controllable force should be equal to the sum of the uncontrollable force and the force generated by the suspension spring. But the controllable force is limited by many constraints. Therefore, the control strategy can be concluded. The simulation results show that the ride comfort and handling stability are both improved by the control method.

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Journal articles on the topic 'Sprung mass'

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