Suspension Force Research Articles

Research on predictive coordinated control of ride comfort and road friendliness for heavy vehicle ISD suspension based on the hybrid-hook damping strategy

With the appearance of inerter, the ISD suspension composed of “Inerter-Spring-Damper” opens up a new direction for efficient coordination of ride comfort and road friendliness for heavy vehicles. In this paper, a reference model based on the hybrid-hook damping strategy is proposed, and the mechatronic inerter is used as an active suspension force generator in the actual controlled model. Then, the coordinated control of the vehicle ISD suspension model is realized by the model predictive control (MPC) approach. The test results show that, the RMS values of the body acceleration and dynamic tire load of the controllable ISD suspension is smaller than the traditional passive and passive ISD suspension under the sinusoidal road inputs. Under the random road input, compared with the traditional passive suspension, the controllable ISD suspension has improved the RMS value of the body acceleration by 26.61%, and the road damage coefficient has been improved by 20.13%. Experiments show that the controllable ISD suspension of heavy vehicles based on the hybrid-hook damping strategy has comprehensive improvement of vehicle ride comfort and road friendliness.

Multiobjective Optimization of a Five-Phase Bearingless Permanent Magnet Motor Considering Winding Area

Due to the increasing demand for high-speed motors with high stability, bearingless motors have attracted much attention. Bearingless permanent magnet synchronous motors (BPMSMs) are a kind of motor, which uses suspension force to eliminate the motor bearings. This article proposes a five-phase BPMSM with 10 slots and 8 poles. Based on the principle of suspension force of BPMSM, an analytical expression of the suspension force is derived for the proposed BPMSM. To improve the suspension stability and torque, an optimization method consisting of a response surface model and a multiobjective optimization algorithm is employed. Not only the geometric parameters but also the winding distribution are considered in the optimization process. Finally, the effectiveness and superiority of the optimal design are verified by experiment.

Cooperative Control of Interconnected Air Suspension Based on Model Predictive Control

The suspension system is a significant part of a vehicle because it transmits the torque and force between the wheels and the frame, meeting the requirements of ride comfort. In this paper, a novel interconnected air suspension was introduced and a cooperative control between interconnected mode activation (IMA) and outsourced mode activation (OMA) was designed. To improve ride comfort in a bus at a minimal energy consumption, this cooperative control based on model predictive control (MPC) for computing the best force and the rule was defined to distribute the best suspension force generated by IMA and OMA. The simulation and experimental results showed that the proposed control strategy significantly improved ride comfort in different conditions. Compared with traditional control in the test vehicle, the RMS of the front-left sprung mass and unsprung vertical acceleration decreased by 24.2% and 14.5%, respectively, under a straight condition; the RMS of the sprung (unsprung) mass vertical acceleration reduced by 22.38% and 15.43%, respectively, under a bump condition.

A novel integrated control framework of AFS, ASS, and DYC based on ideal roll angle to improve vehicle stability

The current research on vehicle stability control mainly focuses on following the ideal yaw rate and sideslip angle, without considering the potential of ideal roll angle in improving the vehicle stability. In addition, the mutation of tire-road friction coefficient promotes a great challenge to the stability control. To improve the vehicle stability, in this study, firstly, the three-dimensional stability region of “lateral speed-yaw rate-roll angle” was studied, and a method to determine the ideal roll angle was proposed. Secondly, a novel integrated control framework of AFS, ASS, and DYC based on ideal roll angle was proposed to actively control the front tire slip angles, suspension forces, and motor torques: In the upper-level controller, model predictive control and tire force distribution algorithm were used to obtain the optimal four-tire longitudinal forces, front tire lateral forces and additional roll moment under constraints; In the lower-level controller, the upper virtual target was realized by the optimal allocation algorithm of actuators and the tire slip controller. Finally, the proposed control framework was verified on the varied-µ road. The results indicated that compared with the two existing control strategies, the proposed framework can significantly improve the vehicle following performance and stability.

A new design of the seat suspension of the vehicles using the NSS: Part 1-Dimensionless characteristic of the NSS

Based on the dynamics theory and the negative stiffness structure (NSS), the new design of the driver's seat suspension of the cab or vehicle added by the NSS is proposed to enhance the isolation performance of the driver's ride suspension. To design the driver's seat suspension added by the NSS, the dynamic models of the NSS and driver's seat suspension are then established to calculate the vibration equations. The influence of the design parameters of the NSS and driver's seat suspension on the isolation performance of the driver's seat suspension is simulated and analyzed based on the dimensionless characteristic of the restoring force and displacement of the driver's seat suspension system. The research results show that the dimensionless characteristic of the restoring force and displacement of the driver's seat suspension added by the NSS is greatly affected by the geometrical ratios (1 and 2) and stiffness ratio () of the NSS. To improve the ride comfort of the driver's seat, the ratios of 1 = 0.6, 2 = 1.2, and  = 0.6 should be applied for the design process of the driver's seat suspension equipped with the NSS.

Vibration transmission control of a flexible shaft-bearing system using active/passive support

An active/passive support is proposed to suppress the transmission of vibration from a flexible shaft-bearing system to its foundation. The active/passive support consists of passive isolators and electromagnetic suspension, in which the former bears the static load while the latter provides suspension force for displacement adjustment and vibration suppression. The dynamic model of the shaft-bearing-foundation system is built on the Rayleigh-Ritz method. Based on this model, the adjustment of stiffness, the transmissibility of vibration, the vibration characteristics of the coupled system and the effectiveness of active control are analyzed. An adaptive control method with subband filtering and disturbance reconstruction is adopted and the performance is evaluated. The effectiveness of the active/passive support is also verified by experiment. Numerical and experimental results demonstrate that the transmission of vibration via the active/passive support can be greatly suppressed and the vibration of the foundation can be reduced almost to the same level.

Verifying the calculation approach for radial suspension force based on the airgap flux density for SPM, consequent‐pole, and bearingless AC homopolar motors

AbstractIn this paper, a calculation method is proposed for the radial suspension force of a bearingless motor with a surface‐mounted permanent magnet (SPM) rotor, a consequent‐pole permanent magnet (CPM) rotor, and a homopolar permanent rotor (HPM). The radial suspension forces are calculated mathematically and analytically using the airgap flux density. It was confirmed that the proposed radial force equations are practical to calculate the suspension force based on the airgap flux density. The CPM bearingless motor and bearingless AC HPM have salient pole rotors that interact with the 2‐pole Magnetomotive force (MMF) to generate 6‐ and 10‐pole components. As a result, the radial suspension force of the CPM bearingless motor is generated by 8‐ and 6‐pole, and 8‐ and 10‐pole magnetic flux, whereas the bearingless AC HPM produces the radial suspension force by DC and 2‐pole components. The shaft torque, the suspension force, and efficiency were also compared for SPM, CPM bearingless motors, and bearingless AC HPM. Consequently, the torque value of the CPM bearingless motor is quite close to SPM bearingless motor. Moreover, the suspension force of the CPM bearingless motor is quite close to bearingless AC HPM.

Modeling and Design of a Novel 5-DOF AC–DC Hybrid Magnetic Bearing

This paper investigates a novel integrated AC–DC hybrid magnetic bearing (HMB) to reduce the volume, weight, manufacturing, and operation cost of magnetic suspension motors. Two radial MBs and an axial MB are integrated with the proposed HMB. The five-degree-of-freedom (5-DOF) suspension is realized in one unit. Two axially polarized permanent magnets provide the radial and axial bias fluxes. First, the HMB structure and the suspension mechanism are introduced. Second, based on the method of equivalent magnetic circuits, magnetic circuits are calculated. The mathematical models of suspension force are discussed. Third, the main parameters of the 5-DOF AC–DC HMB are given. The 3D finite element method (FEM) is adopted to analyze the proposed system’s electromagnetic characteristics, and the suspension mechanism of the 5-DOF is verified. The radial suspension forces versus the radial control current, the axial suspension forces versus the axial control current, the relationship between the axial suspension force and the axial control current with the X direction offset, and the relationship between the radial suspension force in the X direction and the axial control current with the Z direction offset are calculated. Based on the research results, it is shown that the HMB structure is compact and reasonable, and the mathematical models and suspension mechanism are correct.

Review of Bearingless Synchronous Motors: Principle and Topology

A bearingless synchronous motor (BLSM) is a special type of electric machine that integrates the functions of traditional synchronous motors and magnetic bearings. It not only has the advantages of magnetic bearings, such as no friction, pollution-free, and maintenance-free, but it also realizes the high integration and system simplification. Therefore, the BLSM is becoming increasingly attractive in applications such as rotating stages, compressors, artificial hearts, and centrifugal pumps. This article provides a comprehensive review of the BLSM topologies after a brief introduction to the basic suspension force generation principles and the typical BLSM mathematical models. The recent BLSM topologies are classified based on the features of the suspension force generation principle. Moreover, the advantages and disadvantages of each BLSM type are discussed and compared in detail. Future potential BLSM applications in aircraft, aerospace, and flywheel energy storage systems are discussed after a short description of the BLSM application status. Several potential topology development directions are presented based on the requirements of the potential application.

Mathematical model of a novel 12/14 conical bearingless switched reluctance motor

Aiming at the defect that the traditional bearingless switched reluctance motor cannot control the axial suspension force, so that the rotor cannot achieve five-degree-of-freedom suspension by itself, this study presents an innovative 12/14 conical bearingless switched reluctance motor. The structure and principle of suspension force generation is illustrated in detail. Meanwhile, mathematical model of the proposed motor is studied and established. Considering the radial and axial displacement of the rotor, the derived mathematical model could accurately describe the radial force, axial force and electromagnetic torque of the proposed motor. Finally, the effectiveness of the derived mathematical model is verified by finite element simulation.

Hydrodynamic behaviors of settled magnetorheological fluid redispersion under active dispersing mechanism: simulation and experiment

Despite several salient benefits of numerous control systems utilizing magnetorheological (MR) fluid, practical realization of commercial products is limited due to the particles sedimentation. To overcome this problem, several measures have been proposed to optimize MR fluid settling through the viewpoints of dispersing medium viscosity, suspension force of dispersed phase and additives innovation, but the settling of MR fluid can be alleviated to an extent only. An active dispersing mechanism (ADM) proposed in the previous work is one of attractive ways to resolve the sedimentation problem in a level of device and it is promising to fulfill good serviceability for MR dampers even if the settling remains. In this work, attributive to the investigations in stirring devices, rotary blades are employed to fulfill the redispersing of settled MR fluid under the theory of solid–liquid two phase flow. The parameters and working conditions of the rotary blades are optimized to guide experimental verification in a damper-sized vessel. The vessel can be seen as a prototype for real MR damper. An immersed induction method for the characterization of the localized MR fluid concentration is proposed to designate the dispersing process when ADM is started. With the experiments of different MR fluid volume fractions and rotating speeds of the rotary blades, it is fully testified that the faster the blades rotate, the shorter the mixing time, and the more the inclination angle of blades close to 45°, the better the dispersion capability. In addition, it is also identified that the ADM is effective to disperse the settled MR fluid and promising to the sedimentation immunity of MR damper.

Integrated control of electronic stability program and active suspension system using a priority-weighting mechanism

This paper presents a novel vehicle dynamic controller for coordinating the Electronic Stability Program (ESP) and active suspension system (ASS) to improve the directional performance and roll stability of the vehicle. The controller consists of two levels. The upper level is responsible for monitoring system status, determining control objectives, and distributing the active forces. Also, a priority-weighting mechanism is proposed for model predictive control to generate an adaptive multi-objective cost function. Then, the distribution of active forces is obtained by solving a centralized optimization problem. In the lower level, the dynamics of the suspension actuators are taken into consideration in the control of suspension forces for the ASS, and the desired braking forces are achieved through braking torque control for the ESP. The effectiveness of the proposed controller is verified through numerical simulation by using a nonlinear full vehicle model. The simulation results show that the proposed dynamic controller can significantly improve the yaw and roll performance of the vehicle.

Chassis coordinated control based on ideal roll angle to improve vehicle stability

The current active control system for vehicles mainly focuses on following the reference trajectory constituted by the ideal yaw rate and sideslip angle, without considering the influence of the body roll angle on the vehicle stability performance. To improve the vehicle stability, in this study, a method of determining the three-dimensional stability region of ‘lateral speed–yaw rate–roll angle’ was proposed, the variation of the stability region with respect to the front steering angle was studied, and the limit steering angle boundary and vehicle ideal roll angle were obtained. Subsequently, a hierarchical coordinated control framework was proposed for actively controlling the front steering angle, suspension force, and motor torque of a four-wheel independent-drive electric vehicle with active front steering and active suspension systems. Finally, considering the effects of different motor torque distribution algorithms on the control performance, the performance of several control strategies was compared for high and low adhesion roads. The results indicated that the control strategy considering the body roll angle under different working conditions can improve the vehicle stability. On this basis, the torque distribution strategy based on minimum tire utilisation has the best following and stability performances among the strategies examined in this study.

Modelling and analysis of longitudinal-vertical coupling dynamics for the tracked vehicle on uneven roads

In this paper, a longitudinal-vertical coupling dynamic model of a tracked vehicle under uneven road conditions is established. The torsion suspension forces and torques generated by the torsion bar springs and torsion shock absorbers are considered in the present model. The tracked vehicle’s longitudinal acceleration and velocity change at the same time as the vehicle heaves under the excitation of uneven road terrain. The vehicle’s longitudinal-vertical coupling dynamics are explained elementarily by analysing the longitudinal and vertical dynamics of a road wheel based on the road wheel force model. From the coupling tracked vehicle model, the dynamic responses of the vehicle in the vertical and pitch directions as well as the longitudinal direction are investigated. The vehicle dynamics characteristics are compared with those obtained by Recurdyn simulation. The results indicate that the proposed dynamic model performs well in predicting the dynamic characteristics of the tracked vehicle on uneven roads. By means of the coupling dynamic model, the influences of vehicle speed and road conditions on the vehicle’s longitudinal dynamics are further studied. It has been found that both a higher velocity and a larger roughness coefficient will lead to a negative longitudinal acceleration with larger absolute value.

Multi-Objective Parameter Optimization-Based Design of Six-Pole Radial Hybrid Magnetic Bearing

To reduce the couplings between the radial suspension forces and control currents caused by the asymmetry structure of the three-pole hybrid magnetic bearing (HMB) which is driven by an inverter, a six-pole radial HMB is proposed. To improve the bearing capacity and reduce the eddy current loss and volume of the six-pole radial HMB, an improved multi-objective particle swarm optimization (MOPSO) algorithm is proposed to optimize the parameters. At first, the structure and working principle of the six-pole radial HMB are introduced based on the equivalent magnetic circuit method. Then, the optimization objectives and optimization variables are determined and the number of multi-objective optimization parameters is reduced by sensitivity analysis. Next, the fitting function of the suspension force is obtained by the response surface method (RSM). Based on the theoretical analysis of the MOPSO, the linear decreasing inertia weight and the concept of hybridization are introduced to improve the diversity and convergence of the MOPSO to get Pareto optimal sets. Finally, simulation analysis and prototype experiment are carried out on the optimized six-pole radial HMB. The feasibility of the optimization method is verified by the results of simulation and experiment.

Analysis of the operating principle of a dual-armature consequent-pole bearingless flux reversal permanent magnet machine

This paper proposes a new type of dual-armature alternating pole bearingless magnetic flux reverse permanent magnet machine, which combines the advantages of the alternating pole structure and the dual-armature structure. This machine shows the advantages of high torque density and good fault tolerance, which can not only reduce the number of permanent magnets but also further improve the machine’s torque. It is suitable for use in wind power, aerospace, and other applications. The dual-armature alternating pole bearingless magnetic flux reverse permanent magnet machine is used to improve the torque performance and suspension force. Based on the dual-armature alternating pole magnetic flux reverse machine, by adding an additional set of stator teeth to suspended windings, a new type of dual-armature alternating pole bearingless magnetic flux reverse permanent magnet machine is obtained. The number of permanent magnets is halved, and each permanent magnet has the same polarity. The ferromagnetic pole piece next to the permanent magnet automatically acts as the other pole. Based on the introduction of its related structure, the stator flux, rotor flux, stator back electromotive force, cogging torque, electromagnetic torque, etc., are analyzed. This new machine can reduce the number of permanent magnets and has a higher torque conferring advantages of output capacity and low torque ripple.

Active Disturbance Rejection and Ripple Suppression Control Strategy With Model Compensation of Single-Winding Bearingless Flux-Switching Permanent Magnet Motor

The speed and radial displacement of the rotor have the obvious ripples due to the strong coupling between torque and suspension force of a single-winding bearingless flux-switching permanent magnet motor, and the traditional PID/PI controller is difficult to suppress the disturbance of the unbalanced magnetic force. A linear active disturbance rejection control method based on model compensation is proposed in this article. First, the topology and operation principle of the motor are described, and then the dynamic model of the rotor and flux linkage model of the motor are analyzed. Accordingly, the integral-series standard mathematical models of the displacement and speed are deduced, and then the mathematical expressions of the controller gain and radial disturbance are obtained. Second, the linear extended state observer with known model perturbation information and the linear feedback control law are designed, and the parameters tuning method is given. Finally, the simulation and experimental results verified that the proposed method can significantly reduce the rotor displacement and torque ripples, and it has better disturbance rejection performance than the traditional PID/PI control method in the same stability margin.

Dynamics and control simulation of railway virtual coupling

ABSTRACT This paper developed a parallel computing architecture for high-fidelity virtual coupling simulations. Multi-body train dynamics models considered various nonlinear components including wheel-rail contact, suspensions, and inter-vehicle connections. A virtual coupling controller was developed which can be implemented under various train-to-train communication topologies. The controller also allows existing trains to leave the platoon and new trains to merge into the platoon without re-designing the controller. The parallel computing architecture is also scalable and not limited by: the number of vehicles in each train; the number of trains in each train platoon and the topology of train-to-train communications. A case study by simulating a three-train (18 vehicles in total) platoon on a real-world track section was conducted. The results show that, by using 19 computer cores, parallel computing speed is nearly twice as fast as real-time. Parallel computing is about 17 times faster than serial computing. The results also show that the maximum spacing errors of the follower trains were about 0.22 m. Dynamics results such as wheel-rail contact forces, suspension forces, carbody vibrations and inter-vehicle forces were obtained; these results can be used to conduct system assessments in terms of passenger ride comfort, mechanical wear, etc.

New LISA dynamics feedback control scheme: Common-mode isolation of test mass control and probes of test-mass acceleration

The Drag-Free and Attitude Control System is a central element of LISA technology, ensuring the very high dynamic stability of spacecraft and test masses required in order to reach the sensitivity that gravitational wave astronomy in space requires. Applying electrostatic forces on test masses is unavoidable but should be restricted to the minimum necessary to keep the spacecraft-test masses system in place, while granting the optimal quality of test-mass free fall. To realize this, we propose a new test-mass suspension scheme that applies forces and torques only in proportion to any differential test mass motion observed, and we demonstrate that the new scheme significantly mitigates the amount of suspension forces and torques needed to control the whole system. The mathematical method involved allows us to derive a new observable measuring the differential acceleration of test masses projected on the relevant sensitive axes, which will have important consequences for LISA data calibration, processing, and analysis.

Curve Tilting With Nonlinear Model Predictive Control for Enhancing Motion Comfort

The benefits of automated driving can only be fully realized if the occupants are protected from motion sickness. Active suspensions hold the potential to raise the comfort level in automated passenger vehicles by enabling new functionalities in chassis control. One example is to actively lean the vehicle body toward the center of the corner to counteract the inertial lateral acceleration. Commonly known as curve tilting, the concept is deemed effective in reducing postural disturbance on the occupants and the visual-vestibular conflict when the occupants do not have an external view. We present in this article a nonlinear model predictive control (NMPC) method for the curve tilting functionality. The controller incorporates the nonlinear suspension forces in the prediction model to help achieve high tracking accuracy near the physical limit of the suspension system. The optimization process is accelerated with an explicit initialization method that is based on piecewise-affine (PWA) modeling and offline solution to an alternative optimal control problem (OCP). The controller is able to operate at 20 Hz in a hardware-in-the-loop (HIL) setup. Given sufficient computational resources, we observe a significant reduction in the lateral acceleration sensed by the passenger over a vehicle with passive suspensions, namely, by 46.5%, 25.4%, and 25.4% in the highway, rural, and urban driving scenarios, respectively. The NMPC also outperforms the baseline proportional-integral-derivative (PID) controller by achieving lower tracking error, namely, by 12.9%, 16.4%, and 38.0% in the aforementioned scenarios.