Suspension Subsystem Research Articles

ADAPTIVE SLIDING-MODE CONTROL OF SPHERICAL ROBOT WITH ESTIMATED ROLLING RESISTANCE

A spherical robot will inevitably be affected by rolling resistance from the ground when it is used in an unstructured exploration environment. Because of the complex contact condition between the robot and the ground, it is very difficult to obtain the information about the rolling resistance correctly. This fact decreases the movement performances of spherical robots greatly. In this study, dynamic models of the sphere subsystem and the inner suspension subsystem are derived. By Lyapunov theorem, the sliding surface with integral element is applied to construct a new sliding-mode control scheme to track the desired velocity of the spherical robot. In the proposed controller, the sgn(x) function is replaced by the tanh(x) function, in order to reduce the inherent chattering phenomena of the sliding-mode algorithm. Because the rolling resistance is uncertain, an adaptive control scheme is applied to estimate the uncertain rolling resistance dynamically, which makes the robot more sensitive and adaptive in unstructured exploration. The simulation results demonstrate the validity of the proposed schemes.

Dynamic Simulation of a Motor Vehicle in Virtual Prototyping Environment

In this paper, we attempt to carry out the dynamic analysis of a motor vehicle, using the virtual prototype developed with the MBS (Multi-Body Systems) software ADAMS. The virtual prototype includes the front and the rear suspension subsystems, the steering subsystem, and the car body subsystem. The experiment designed is one frequently carried by the automotive manufacturers, namely passing over bumps. The connection between wheels (tires) and road (ground) is made using contact forces, which allow modelling how adjacent bodies interact with one another when they collide during the simulation. On the virtual prototype, several measurements have been realized having in view to evaluate the dynamic behaviour of the vehicle.

Sliding-mode output feedback control for active suspension with nonlinear actuator dynamics

The nonlinear dynamics of an actuator are considered during the output feedback control design of a quarter-car active suspension system with uncertainties. Because of the complexity of the suspension system with hydraulic actuator dynamics, a simple and effective sliding-mode strategy is employed to obtain both controller and observer. Instead of dividing the system into an actuator subsystem and a suspension subsystem, the system is repartitioned into a linear subsystem and a nonlinear subsystem, which facilitates controller design greatly. By specifying suitable sliding functions for the two subsystems respectively, and forcing the output of the nonlinear subsystem to track the desired fictitious input of the linear subsystem, the sliding-mode controller is created. By Lyapunov theory, robust stability is analyzed. For linear growth vanishing bounded uncertainties and nonvanishing bounded uncertainties, different observer forms are given to simplify the observer in different situations. Based on the constructed sliding-mode observer, the sliding-mode output feedback control suspension closed-loop system is accomplished. The convergence of observation error is subsequently proved. Simulation results verify the effect of the presented method.

Precision Modeling Method Specifically for AC Magnetic Bearings

Compared with dc magnetic bearings, an ac magnetic bearing has obvious advantages in cost savings and reducing power consumption. For more precise control of the ac magnetic bearing, it is particularly important to build a correct mathematical model of radial suspension forces. Due to the working principle of the ac magnetic bearing, it has similarities to the suspension subsystem of a bearingless motor, thus the modeling method for radial suspension forces of the bearingless motor could be referenced for modeling the radial suspension forces of the ac magnetic bearing. This paper presents a new modeling method based on the Maxwell tensor method for radial suspension forces of the ac magnetic bearing. Compared with existing methods, the invention method designed specially for the ac magnetic bearing overcomes inaccuracy and possesses advantages of directness and universality. Taking the ac hybrid magnetic bearing (ac HMB), for example, this paper presents the mathematical modeling process of radial suspension forces with the proposed method. The comparison result between the models established by the equivalent magnetic circuit method (the most classical modeling method for magnetic bearings currently) and by the proposed method shows the high uniformity in their forms of expression (the only difference is the coefficient between them). Being different from the traditional modeling method, we do not need the detailed derivation and complex theoretical computation based on the particular magnetic circuit analysis for this particular case but simply modify several key expressions representing magnetic circuit features in the modeling process with this method. Therefore, the proposed method invented especially for the ac magnetic bearing has the greater advantage of directness and universality than previous modeling method. To illustrate the precision of the proposed modeling approach, the verification experiment is designed and the encouraging experimental results show that the model based on the Maxwell tensor method is more close to the test results comparing with equivalent magnetic circuit method. Thus, the proposed modeling method makes the modeling results on radial suspension forces of the ac magnetic bearing more accurate, universal, and direct.

Adaptive control of an underactuated spherical robot with a dynamic stable equilibrium point using hierarchical sliding mode approach

SUMMARYUnlike the traditional underactuated mechanical system, the equilibrium point of the inner swing‐up suspension of a spherical robot possesses stable and dynamic characteristics. The stable dynamic equilibrium position of the underactuated suspension must agree well with the uncertain rolling resistance in practice. To overcome this special underactuated problem with dynamic equilibrium, we present an adaptive control scheme to enhance the ground adaptability using hierarchical sliding mode approach. The control method can drive the spherical robot to a desired position, and at the same time, the suspension subsystem holds on their dynamic equilibrium points rapidly. The proposed control approaches are verified to be effective by numerical simulation for a spherical robot to achieve satisfactory control performances, such as ground adaptability, rapid convergence, and disturbance rejection. Copyright © 2013 John Wiley & Sons, Ltd.

High-Temperature Superconducting Linear Synchronous Motors Integrated With HTS Magnetic Levitation Components

High-temperature superconductors (HTSs) including HTS bulks and tapes have potential applications in linear motion drive and magnetic levitation/suspension systems generating substantial advantages over conventional ones. When an HTS linear motor is integrated with an HTS magnetic suspension subsystem, it can inherit both merits of HTS linear motion drive and HTS magnetic suspension simultaneously and can be applied into various fields, such as the maglev and electromagnetic aircraft launch systems (EMALSs). Based on different HTS aspects and arrangements, three modes of HTS linear synchronous motor (HTSLSM) integrated with HTS magnetic suspension subsystems have been proposed in this paper. To verify the modes for the design of a practical HTSLSM, the structural features of these systems are described, the magnetization characteristics to obtain HTS bulk magnets, the trapped-field attenuation characteristics of the HTS bulk magnet exposed to external traveling field, and the magnetic field distribution characteristics for different permanent-magnet guideways have been studied with experimental verification. Based on the study, a demonstration prototype of a single-sided HTSLSM integrated with HTS magnetic suspension subsystems has been developed. Its performance and thrust characteristics have been obtained by experimental measurements and compared with theoretical results. With regard to practical applications, two modes of double-sided HTSLSM integrated with HTS magnetic suspension subsystems have been designed for the maglev and EMALS, respectively, and then, the 2-D finite-element-analysis models for the HTSLSMs were built to analyze their performance characteristics. The comprehensive simulations and experimental results constitute a framework for the structural and electromagnetic design of the HTSLSM integrated with HTS magnetic suspension for practical applications.

Development of Energy Saving Mechanism for Renewable Hydrogen Vehicles

This paper describes the development of energy saving mechanisms for renewable hydrogen vehicles, thereby providing extended range and improved efficiency. Simulation studies of configuration setup and analysis for better energy management strategies are carried out using simulation tools developed by the University of Glamorgan (UoG), Faculty of Advanced Technology (FAT). The simulation tools are used to analyze the effect of operating conditions and energy demand of a hybrid vehicle. A dynamic model of onboard hydrogen production employing electrolysis energized by electricity recovered from the vehicle’s suspension sub-system, is implemented in MATLAB/SimulinkTM and integrated with a fuel cell vehicle model. The entire system model is then parameterized to represent a renewable hydrogen fuel cell vehicle for simulation analyses. Simulation results show that by using recovered energy normally lost in damping, appreciable benefits might be accrued from hydrogen production on-board.

Performance Analysis of an HTS Magnetic Suspension and Propulsion System With a Double-Sided HTS Linear Synchronous Motor

A novel HTS magnetic suspension and propulsion system driven by a double-sided HTS linear synchronous motor (HTSLSM) has been developed, which is suspended by an HTS magnetic suspension subsystem located on the bottom of the HTSLSM secondary mover. The structural design of the suspension and propulsion system is introduced, and then the magnetization characteristics of the HTS bulk magnets for the HTSLSM are studied and compared by different magnetization methods. The finite-element analysis (FEA) model of the HTSLSM is built up by using an equivalent model of the HTS bulk magnet, and the thrust characteristics of the HTSLSM are also simulated based on the FEA model, and verified by measurements on the prototype. Furthermore, the suspension performance of the HTS magnetic suspension subsystem has also been analyzed by a numerical method based on an equivalent current sheet model of the permanent-magnet guideway. The results show that the HTS magnetic suspension and propulsion system has applicable thrust and suspension performance, and can be applied to the practical applications such as a maglev.

Rollover mitigation for a heavy commercial vehicle

A heavy commercial vehicle has a high probability of rollover because it is usually loaded heavily and thus has a high center of gravity. An anti-roll bar is efficient for rollover mitigation, but it can cause poor ride comfort when the roll stiffness is excessively high. Therefore, active roll control (ARC) systems have been developed to optimally control the roll state of a vehicle while maintaining ride comfort. Previously developed ARC systems have some disadvantages, such as cost, complexity, power consumption, and weight. In this study, an ARC-based rear air suspension for a heavy commercial vehicle, which does not require additional power for control, was designed and manufactured. The rollover index-based vehicle rollover mitigation control scheme was used for the ARC system. Multi-body dynamic models of the suspension subsystem and the full vehicle were used to design the rear air suspension and the ARC system. The reference rollover index was tuned through lab tests. Field tests, such as steady state cornering tests and step steer tests, demonstrated that the roll response characteristics in the steady state and transient state were improved.

Minimizing the engine-induced harshness based on the DOE method and sensitivity analysis of the full vehicle NVH model

An efficient procedure for minimizing the engine-induced harshness based on NVH analysis results of a full vehicle model was developed in this study, taking stiffness and strength constraints into account. Although extensive research may be found in the literature in the field of engine support system optimization, no other studies have considered the compliances and resonances of the structure of the vehicle. In the present paper, NVH analysis results of the whole vehicle were used in an optimization procedure to suppress the transmitted vibration. A procedure was developed to minimize the transmitted accelerations to the mid-point of the driver’s seat rail. A DOE-based response surface methodology (RSM) was adopted to determine the optimal solution. Natural frequencies of the body, suspension, and other subsystems were taken into consideration in determining the optimal solution. NVH analysis was performed for two types of inputs: (a) vertical vibration due to vertical unbalanced forces and (b) torsional vibration due to oscillations in the output torque of the engine.

Improved bushing models for general multibody systems and vehicle dynamics

The development and computational implementation, on a multibody dynamics environment, of a constitutive relation to model bushing elements associated with mechanical joints used in the models of road and rail vehicles is presented here. These elements are used to eliminate vibrations in vehicles, due to road irregularities, to allow small misalignment of axes, to reduce noise from the transmission, or to decrease wear of the mechanical joints. Bushings are made of a special rubber, used generally in energy dissipation, which presents a nonlinear viscoelastic relationship between the forces and moments and their corresponding displacements and rotations. In the methodology proposed here a finite element model of the bushing is developed in the framework of the finite element code ABAQUS to obtain the constitutive relations of displacement/rotation versus force/moment for different loading cases. The bushing is modeled in a multibody code as a nonlinear restrain that relates the relative displacements between the bodies connected with the joint reaction forces, and it is represented by a matrix constitutive relation. The basic ingredients of the multibody model are the same vectors and points relations used to define kinematic constraints in any multibody formulation. One particular, and relevant, characteristic of the formulation now presented is its ability to represent standard kinematic joints, clearance, and bushing joints just by defining appropriate constitutive relations. Spherical, revolution, cylindrical, and translational bushing joints are modeled, implemented, and demonstrated through the simulation of two multibody models of a road vehicle, one with perfect kinematic joints for the suspension sub-systems, and other with bushing joints. The tests conducted include an obstacle avoidance maneuver and a vehicle riding over bumps. It is shown that the bushing models for vehicle multibody models proposed here are accurate and computationally efficient so that they can be included in the vehicle models leading reliable simulations.

Real-time multibody vehicle model with bush compliance effect using quasi-static analysis for HILS

Vehicle handling simulations such as J-turns, slaloms, double lane changes, and fish hook maneuvering are essential to evaluate the control subsystems of the intelligent vehicle in the HILS (Hardware-in-the loop simulation). It is well known that the compliance effects from bushes in the suspension subsystem are important to have reliable solutions for the handling simulations. In the multibody vehicle dynamics model, the bush elements in the suspension subsystem are usually modeled as high-stiffness springs. However, due to this high stiffness of the bush model, it requires small step-sizes in the numerical integration. With this kind of bush model, it is almost impossible to achieve real-time simulations for HILS. In this paper, a quasi-static analysis method is presented in order to consider bush compliance effects for a real-time multibody vehicle model. To validate the proposed method, the quarter car simulations of the McPherson strut and the Multilink suspension subsystems have been performed, comparing with the ADAMS simulations. Full car bump run simulations and fish hook handling test simulations have also been carried out to see the effectiveness of the proposed model. The CPU time measured shows the real-time capabilities of the proposed method.

Sensitivity of a vehicle ride to the suspension bushing characteristics

The sensitivity of the ride characteristics of a road vehicle to the mechanical characteristics of the bushings used in its suspension is discussed here. First, the development and computational implementation, on a multibody dynamics environment, of a constitutive relation to model bushing elements associated with mechanical joints is presented. Bushings are made of a rubber type of material, which presents a nonlinear and viscoelastic relationship between the forces and moments and their corresponding displacements and rotations. Suitable bushing models for vehicle multibody models must be accurate and computationally efficient, leading to more reliable models. The bushing is modeled in a multibody code as an arrangement of springs that penalize the motion between the bodies connected. In the methodology proposed here, a finite element model of the bushing is developed in the framework of a finite element (FE) code to obtain the curves of displacement/rotation versus force/moment for different loading cases. The basic ingredients of the multibody model are the same vectors and points relations used to define kinematic constraints in any multibody formulation. Spherical, cylindrical and revolute bushing joints are developed and implemented in this work, since the methodology is demonstrated through the ride over bumps, at different speeds, of two multibody models of a road vehicle: one with perfect kinematic joints, for the suspension sub-systems; the other with bushing joints, riding. Then, sensitivities of different vehicle kinematic responses to the characteristics of the bushings used in the suspension are evaluated, by using numerical sensitivities. Based on the sensitivity analysis, indications on how to modify the vehicle response by modifying the bushing characteristics are drawn.

Robust LPV– ∞ control for active suspensions with performance adaptation in view of global chassis control

This paper presents a new methodology for suspension control in view of global chassis control, developed in particular to guarantee greater driving safety and comfort. The control of the suspension subsystem allows the vehicle road holding (safety) and passenger comfort to be improved, but not at the same time. In order to reach them for every driving situation, an ‘adaptive’ two-degrees-of-freedom controller for active suspensions is proposed. This control architecture is ‘open’ and could be linked and aggregated to many other controllers of vehicle dynamics. This control strategy ensures, on the one hand, the robustness in performances with respect to parameter uncertainties and, on the other hand, the trade-off between road holding and comfort. The proposed design is based on the LPV/ ∞ theory. Robust stability and performances are analysed within the μ-analysis framework.

Parametric Identification and Health Monitoring of Complex Ground Vehicle Models

A systematic methodology is applied for performing parametric identification and health monitoring in the suspension substructures of complex vehicle models. The equations of motion are derived by applying a finite element method. As a consequence, they involve quite a large number of degrees-of-freedom (DOF). In addition, they include strongly nonlinear terms. In particular, the main nonlinearities arise due to the function of the suspension dampers and springs. Moreover, the action of the bushings connecting the suspension subsystems to the vehicle body is also strongly nonlinear. Since the resulting number of DOF is large, an appropriate coordinate condensation technique is applied first. This drastically reduces the dimension of the original system and allows the application of a statisticcal system identification methodology, which is effective for dynamical systems with relatively small dimension, in order to perform parametric identification and fault detection studies in the suspension subsystems of an example vehicle model. In the second part of this study, the methodology developed is applied and yields numerical results related to parametric identification and fault detection in the suspensions of the vehicle model examined. The results are found to be sufficiently accurate even in the presence of considerable measurement noise and model errors.

Modelling and ride dynamics of a flexible multi-body model of an urban bus

Dynamic response of a large order mechanical model of an urban bus is investigated in this paper. The emphasis is first put on developing a quite complete model, which can be utilized in order to extract sufficiently reliable and accurate information related to its dynamics in a fast way. Since some of the components of the bus undergo large rigid body rotation, in addition to motion resulting from their deformability, a multi-body dynamics framework is adopted. This implies that the resulting equations of motion appear in the form of a strongly non-linear set of differential-algebraic equations, which are difficult to handle even numerically. In fact, the modelling becomes more involved because all the significant non-linearities appearing in the interconnections of the structural components and especially in the front and rear suspension subsystems of the bus are taken into account. In order to alleviate some of these complexities, the number of degrees of freedom of each component, associated with its deformability, is reduced drastically by applying an appropriate coordinate condensation methodology. Finally, this model is employed and numerical results are obtained for motions resulting from typical road excitation. In particular, selected response quantities related to ride comfort are examined for characteristic combinations of the bus suspension stiffness and damping parameters.

실시간 다물체 차량 해석을 위한 준정적법의 컴플라이언스 효과 모델링

Compliance effect consideration method for real-time multibody vehicle dynamics is proposed using quasi-static analysis. The multibody vehicle model without bush elements is used based on the subsystem synthesis method which provides real-time computation on the multibody vehicle model. Reaction forces are computed in the suspension subsystem. According to deformation from the quasi-static analysis using reaction forces and bush stiffness, suspension hardpoint locations and suspension linkage orientation are changed. To validate the proposed method, quarter car simulations of McPherson strut and multilink suspension subsystems are performed. Full car bump run simulations and fish hook handling test simulations are also carried out comparing with the ADAMS vehicle model with bush elements. CPU times are also measured to see the real-time capabilities of the proposed method.

Subsystem synthesis method with approximate function approach for a real-time multibody vehicle model

This paper presents the subsystem synthesis method with approximate function approach for a real-time multibody vehicle dynamics model. In the subsystem synthesis method, equations of motion for the car body of a vehicle and the equations of motion for suspension subsystems are formed separately for efficient computation. Joint coordinates are used to construct suspension subsystem equations of motion. Since these joint coordinates must satisfy the loop closure constraint equations that represent suspension linkage kinematics, they are not all independent. Using the generalized coordinate partitioning method, suspension subsystem equations of motion can be represented only in terms of independent generalized coordinates. To represent dependent coordinates as a function of independent coordinates in the generalized coordinate partitioning method, expensive numerical approaches, such as the Newton–Raphson method, must be applied. For real-time computation of the multibody vehicle model, an approximate function approach is proposed to express the dependent coordinates as polynomial functions of the independent coordinates within the framework of the subsystem synthesis method. Different orders of candidate polynomial functions are investigated for solution accuracy. Efficiency of the proposed method has been studied theoretically by counting arithmetic operators. By measuring actual CPU times of the simulations with a quarter car and a full car model, efficiency of the proposed method has also been investigated.

Integrated vehicle ride and steady-state handling control via active suspensions

In this paper, an integrated controller for a full-vehicle active suspension system is designed to simultaneously improve vehicle ride comfort and steady-state handling performance. First, the suspension and handling sub-system models and the nonlinear relationship between tyre normal load and lateral force are described. Next, the link between suspension model and steady-state handling characteristics is analysed. Then, based on the analysis, an H∞ controller is designed for the suspension sub-system to achieve integrated ride comfort and handling performance control. Finally, the controller is verified through computer simulations in frequency- and time-domains.

Crash analysis and dynamical behaviour of light road and rail vehicles

The main goal of crashworthiness is to ensure that vehicles are safer for occupants, cargo and other road or rail users. The crash analysis of vehicles involves structural impact and occupant biomechanics. The traditional approaches to crashworthiness not only do not take into account the full vehicle dynamics, but also uncouple the structural impact and the occupant biomechanics in the crash study. The most common strategy is to obtain an acceleration pulse from a vehicle structural impact analysis or experimental test, very often without taking into account the effect of suspensions in its dynamics, and afterwards feed this pulse into a rigid occupant compartment that contains models of passengers. Multibody dynamics is the most common methodology to build and analyse vehicle models for occupant biomechanics, vehicle dynamics and, with ever increasing popularity, structural crash analysis. In this work, the aspects of multibody modelling relevant to road and rail vehicles and to occupant biomechanical modelling are revised. Afterwards, it is shown how multibody models of vehicles and occupants are used in crash analysis. The more traditional aspects of vehicle dynamics are then introduced in the vehicle models in order to appraise their importance in the treatment of certain types of impact scenarios for which the crash outcome is sensitive to the relative orientation and alignment between vehicles. Through applications to the crashworthiness of road and of rail vehicles, selected problems are discussed and the need for coupled models of vehicle structures, suspension subsystems and occupants is emphasized.