Suspension Stiffness Research Articles

Выбор характеристик системы подрессоривания быстроходного гусеничного робота

Currently, the field of mechanical engineering is rapidly developing, including the creation of robotic high-speed vehicles. The design of suspension systems for such vehicles must be accompa-nied by the fulfillment of certain requirements, which are currently not formulated. Considering the thing that there is no person in the body of a high-speed robot, the application of the requirements for the suspensions of crew vehicles is not justified. In order to develop recommendations on the choice of characteristics of suspension systems for high-speed tracked robots, the research objects, which mass is in the range from 1000 to 10000 kg are determined. No suspension system is required for objects weighing less than 1000 kg. Objects weighing more than 10,000 kg will be created on the basis of existing serial vehicles. The study is based on the provision that the considered class of vehicles is not subject to re-strictions on the range of natural frequencies of body vibrations. Considering that one of the main requirements remains for high-speed tracked robots - ensuring a high average speed, it is proposed to increase the suspension stiffness in order to exclude resonance from the range of possible travel speeds. Using the accepted provisions, a study of the suspension system of increased stiffness is carried out. The movement along the tracks of a harmonic profile in resonance mode and a broken dirt road is simulated. The results of the study show that the characteristics of the suspension system, selected accord-ing to the proposed method, make it possible to move along the line of the harmonic profile in the resonant mode without suspension breakdowns. The speed of movement on a broken dirt road is limited to a value, which exceeding leads to sig-nificant vibrations of the body and an increase in the load on the elements of the suspension system. The absence of breakdowns leads to a decrease in the loading of the suspension, which makes it possible to reduce the mass of its elements.

Analytical determination of static and dynamic elastic characteristics of pneumohydraulic suspension systems

When developing new suspensions for tracked and wheeled vehicles, as well as in the so-called reverse engineering of existing structures (including in the educational process of training personnel), it is necessary to solve the problem of finding the elastic characteristics of the suspension. In the first case, it is necessary to ensure the fulfillment of the specified tactical and technical requirements, in the second - to restore the form of characteristics according to a known design. Both of these tasks are greatly complicated in the absence of precise and universal analytical dependencies suitable for determining the characteristics of elastic suspension elements of various design implementations. The experience of interaction with some factories shows that designers, not being able to qualitatively calculate the elastic characteristics, use the method of selection and analogy, when for a new vehicle they use the suspension as on the old one, scaling it in size in order to approximately keep the values of working pressures. The numerous bench tests are carried out, which results are used for selecting required charging volume and pressure. Suspensions with backpressure cause particular difficulty, since not only the final characteristic, but also the performance of the entire unit depends on the combination of volumes and pressures of the two chambers, which work in antiphase: when one is loaded, the other is unloaded, and vice versa. Using analytical dependencies will reduce the time spent on design, to parameterize, to a certain extent, the suspension kinematics, to obtain the values of the equivalent suspension stiffness, and also to be able to develop the characteristics of the model range of pneumohydraulic springs for vehicles of various weight categories.
 This article presents a technique for the analytical determination of the characteristics of pneumohydraulic springs of various designs. The options include both actually used in modern and historical technology (in particular, on BMD-1, 2, 3, 4; GM-352; Ural Typhoon; Object 775, etc.), and obtained by combining various structural elements, which implementation can be useful in the educational process in training personnel. The dependences presented in the article make it possible to obtain static and dynamic elastic characteristics at various polytropic indices and are suitable for the design of suspensions for wheeled and tracked vehicles for various purposes.

Neuro-Fuzzy Volume Control for Quarter Car Air-Spring Suspension System

One type of vehicle suspension system is the air suspension system. One of the important functions of the suspension system is to reduce vibration transmitted to the vehicle body from road unevenness. Soft suspension results in better ride comfort and worst handling. While stiff suspension results in better handling and worse comfort. This paper investigates the performance of air suspension in terms of passenger ride comfort and vehicle handling. The performance is tested once with Fuzzy logic control and another with Fuzzy control augmented with Neuro-Fuzzy inference system. A mathematical model is developed to describe the air-spring stiffness behavior. The air-spring suspension is merged on two degrees of freedom model. The air pressure is controlled by a Fuzzy controller as done previously in the literature. On the other hand, our approach is to control the volume change by connecting the air-spring volume to two additional unequal volumes through ON-OFF solenoid valves. The solenoid valves are controlled by Adaptive Neuro-Fuzzy Inference System (ANFIS). A single-degree-of-freedom setup was built from which the required training data for the ANFIS controller was carried out. The experimental setup is developed with variable excitation input in terms of frequency and amplitudes. The acceleration of the sprung mass has been measured and stored at different operating conditions and including different air volumes. The stored data is used for training of volume controller. The controller is tested with Sinusoidal excitation then with ISO 8608 road profile. It is found that increasing the air volume reduces the sprung mass acceleration. Also, the results showed that implementing the Neuro-Fuzzy controller with Fuzzy logic control reduces the sprung mass acceleration significantly by an average value that reaches 5 cm/s2 at frequencies above 1 Hz while maintaining road holding.

The Study of Optimization and Matching to Spring and Antiroll Bar Stiffness of Suspension for Multiresponse Target of Whole Vehicle under Sine-Swept Steering Input

This article first leads from the specific double-wishbone suspension and multilink suspension structure form. And then systematically and detailedly analyse the change of spring's stiffness, and antiroll bar's stiffness causes the change of the side slip stiffness and rotation angle of tire, which will lead to the change of tire force, and then affect the dynamic characteristics of the whole vehicle. Based on this, the vehicle dynamics model considering the suspension is established, and the transfer function of the vehicle’s response index to steering wheel angle with coupling spring stiffness and antiroll bar stiffness is derived. Based on the dynamic theory analysis of the suspension and the whole vehicle, the multibody dynamics model of the whole vehicle with front double-wishbone suspension and rear multilink suspension was established. By calculating the frequency response characteristics of the vehicle under the sine-swept input, the frequency response index at the normal steering wheel operating frequency of 0.5 Hz was obtained. In addition, these frequency response indexes at 0.5 Hz were taken as optimization objectives, and the spring stiffness and antiroll bar stiffness of the front and rear suspension were taken as optimization variables, which were optimized by the NSGA-II algorithm. The results show that at 0.5 Hz, the gain value in the frequency response index is reduced, and the delay time is not significantly different from other group schemes, but it is not the worst; the value is within an acceptable range, and the dynamic characteristics of the car in the low frequency range have been improved.

Vibration research of heavy trucks. Part 1: Sensitivity analysis of dynamic parameters on ride comfort

In order to study the influence of heavy truck dynamic parameters on the vehicle’s ride comfort under the random road excitation, the weighted RMS (root-mean-square) acceleration responses of the vertical driver’s seat and cab pitch angle are chosen as objective function, a dynamic model of the vehicle with 10 degrees of freedom is established to simulate and analyze the results. The influence of different parameters of all the suspension systems of the vehicle, such as the stiffness and damping of the suspensions of the seat, cab, vehicle, and wheel, on the vertical driver’s seat and cab pitch angle are respectively analyzed. The study results show that the influence of the stiffness and damping parameters in the suspension systems on the vehicle ride comfort is very obvious. The vehicle’s ride comfort changes worse with the increase of the suspension stiffness and the reduction of the suspension damping, and vice versa. The study proposes an optimal range of the stiffness and damping parameters for the optimal design and control of the vehicle suspension systems, concurrently, the study can also provide a theoretical basis for the suspension system designed for heavy trucks.

Planning of a numerical experiment in order to determine the effect of operating factors on the traction-adhesion properties of locomotives

The paper reviews the results of an evaluation of the influence of the operating factors on traction-adhesive prop-er-ties of a locomotive. Planning of an xperiment was performed for two locomotives ?freight locomotive 2TE116 and shunting locomotive TEM103. The input for performing the numerical experiment was variation of 6 factors: the change in the wheel diameter of the first wheelset due to wear, the change in the mass of the locomotive as a result of the change in the amount of the fuel as well as the wheel rims wear, the impact of the friction damper in the primary suspension, change in the primary and secondary suspension stiffness due to operation. Regression equati-ons were obtained in code and natural form, which describe the effect of operating factors on the coeffi-cient of utilization of the locomotive adhesion mass.

Analysis of a Novel Magnetic-Hydrodynamic Double Levitated Motor for an Implantable Axial Flow Blood Pump

This paper presents a novel design for a bearingless axial flow blood pump based on the magnetic-hydrodynamic double levitated concept. In the axial direction, the magnetic levitation system consisted of two pairs of permanent magnet rings offsets the force of fluid. The hydrodynamic shell mounted on the impeller rotor is designed for generating dynamic pressure, which can balance the radial force like gravity when the blood pump is working. Because of the unsteady force and torque acting on the rotor and the passive suspension, the position of the rotor is not steady. The suspension force, stiffness, and torque of the rotor are calculated by the theoretical method and finite element method. Then, the dynamics of the rotor are analyzed. Arrangements of Hall-effect sensors with the corresponding data acquisition system which can measure the axial displacement of the rotor are explained. The sensorless drive control system for the blood pump is described too. With a prototype pump, an external circulation experiment system is built and then the axial and radial displacements of the rotor are measured by using Hall-effect sensors and the laser vibrometer under different working conditions.

Modeling and Design of a Rear-Mounted Underwater Projector Using Equivalent Circuits.

Tonpilz is a popular transducer for underwater projector arrays for sonar systems. For low-frequency transmission, a larger axial dimension of the conventional Tonpilz transducer is required. However, a bulky and heavy Tonpilz element is not suitable due to limitations in terms of the space and payload of the array platform. To address this problem, we developed a rear-mounted Tonpilz transducer to generate a sub-fundamental resonance in addition to the common longitudinal resonance. For this purpose, we developed a new equivalent circuit model that can reflect all the effects of the key design parameters of the transducer, such as suspension thickness (stiffness), tail mass thickness, and head mass thickness. The impedance and transmitting voltage response were evaluated as performance factors at both resonance frequencies. The validity of the circuit was verified by comparing the analysis results with those from the finite element analysis of the same transducer. Based on the results, the transducer structure was designed to have comparable transmitting performance at both resonance frequencies by employing relatively high suspension stiffness, light tail mass, and heavy head mass. The novel design can permit the dual-band operation of the transducer so that the transducer can operate as a wideband projector.

Kinematics & compliance analysis of double wishbone air suspension with frictions and joint clearances

Currently available suspension kinematics and compliance (K&C) model is mainly used for qualitative analysis rather than quantitative analysis. In order to reproduce actual suspension K&C characteristic, all the suspension components need to take into account as much details as possible. Suspension stiffness non-linearity, suspension components friction and kinematic joint clearances are examples of how the component models can be made more specific. This paper proposes a modeling technique that can not only reliably represent the hysteretic characteristic but also analyze the effect of joint clearances. The suspension air spring model and bushing model are composed of nonlinear elastic force and Berg's friction force. The suspension supporting components are modeled as flexible bodies. The suspension parameter identification and model validation are also proposed. The test procedure of a new K&C test rig based on non-contact binocular vision system is introduced and the simulation results are compared with the experimental results. Results from tests show good agreement between the proposed suspension model and experimental data. Effects of the suspension components friction and clearance joints are investigated. This type of study can provide useful information on the vehicle design, analysis and optimization.

Simulation Research on the Driving Stability of Articulated Vehicle Based on ADAMS

The vehicle dynamical model was established by taking the articulated vehicle driven electrically as the research object, and the vehicle dynamical simulation was carried out by using ADAMS. The effects of different center of mass position, steering parameters, mass, lateral stiffness of tire, suspension stiffness and damping on the driving stability of articulated vehicle were analyzed. The simulation results showed that the driving stability of the articulated vehicle was improved by factors such as the position of the center of mass closing to the hinged point, increasing the steering stiffness and damping, reducing the lateral stiffness of the tire, increasing the suspension stiffness and damping, appropriately increasing the rear body mass, etc. This study provided a reference for the design and improvement of the vehicle.

Semi‐active control of air suspension with auxiliary chamber subject to parameter uncertainties and time‐delay

AbstractSuspension systems are critical to the ride comfort and handling stability of vehicles, but traditional passive suspensions fail to achieve optimal performance in the two aspects. Semi‐active suspension controller changes the suspension stiffness or damping to improve the ride comfort and handling stability, which has the potential advantages of low energy consumption and high reliability. In this paper, the model of an air spring with an auxiliary chamber and a variable throttle orifice is proposed and the semi‐active control strategy of air suspension is carried out. The parameters of the air spring with auxiliary chamber are optimized to improve the performance when the control system fails and to increase the basic performance for semi‐active control. Based on the linear matrix inequality approach to robust H∞ control, the semi‐active control strategy of the air suspension is studied, in which parameter uncertainties and time delay are considered to improve control robustness. An inverse model of the air spring is then established to calculate the area of the variable throttle orifice, by which the desired control force is tracked accurately. Finally, the effectiveness of the semi‐active control system of the air suspension is verified by numerical simulation. Comparing with the passive suspension, not only under nominal parameters, but also with parameter uncertainties, time delay, and both parameter uncertainties and time delay, the semi‐active control system proposed in this paper has good control performance as well as is strong robustness to parameter uncertainties and time delay.

Flexible-elastomer-based active radial embedded actuation system of railway vehicles

To improve the integration of active radial systems of railway vehicles and their adaptability to the vehicle structure, this paper proposes an active radial actuation system based on flexible elastomers. The execution unit of the system has a compact layout and can be embedded in an axle box. The core functional component is a flexible elastic oil-filled rubber bladder, which has active radial actuating capabilities and provides primary longitudinal suspension stiffness. To clarify these aspects of the execution unit, the typical physical properties of the rubber bladder are analysed using a fluid-structure-interaction finite element analysis method. The resulting calculation data are used to formulate the response characteristic equation of the execution unit. This equation is used to establish a simulation model of the actuation system, and the response characteristics of the proposed actuation system and traditional hydraulic cylinder are analysed and compared. The results show that the proposed system exhibits better following performance. Subsequently, the SIMPACK-SIMULINK co-simulation results indicate that the system can realize an effective primary longitudinal suspension; further, in the active radial mode, the performance indexes of vehicle curve passing are significantly improved. These findings provide a reference for the engineering implementation of active radial technology.

Dual-chamber pneumatically interconnected suspension: Modeling and theoretical analysis

Increasing concerns on the compromise between the vehicle ride comfort and roll stability call for the continuous developments of the vehicle suspension systems. This paper devotes a theoretical study in developing a dual-chamber pneumatically interconnected suspension (DCPIS) system to enhance the vehicle ride comfort while maintaining good anti-roll performance. A quarter car with the dual-chamber air suspension is modeled to study the vibration characteristics in terms of the vertical stiffness and the natural frequency of the suspension. Further, a novel DCPIS system of a vehicle is proposed. By assuming the displacement excitations are small from the equilibrium position, the vibration equations of the mechanical-pneumatic coupled system for a roll-plane 4-degree-of-freedom (4-DOF) half-car model with DCPIS are derived in frequency domain, which include the dynamic equations of the mechanical system, the linear differential equations of the dual-chamber air springs, and the pipes. Based on the system dynamic equations, both the vehicle free vibration modes and frequency response functions (FRFs) are compared between the half-car with the DCPIS and that with the standalone dual-chamber air suspension. The results show that the DCPIS can alleviate the vertical and roll vibration because it decreases the suspension stiffness and meanwhile increases the system damping ratio. The effects of the DCPIS system parameters on the vehicle bounce and roll vibration transmissibility properties are further investigated. In addition, the bounce and roll stiffness characteristics of the DCPIS are studied. It shows that its nonlinear bounce and roll stiffness behaviors have the advantages not only to alleviate shocks under extreme impact from the road obstacle and but also prevent rollovers in sharp steering maneuvers.

Neural-Network Adaptive Output-Feedback Saturation Control for Uncertain Active Suspension Systems.

The adaptive neural-network (NN) output-feedback control problem is investigated for a quarter-car active suspension system. The sprung mass and the suspension stiffness in the considered suspension system are unknown, and the part states are not measured directly. In the control design, NNs are employed to approximate the unknown nonlinear dynamics, and an NN state observer is given to estimate the immeasurable states. By using the adaptive backstepping control design technique and introducing the command filter method, an observer-based NN output-feedback control algorithm is developed, in which the input saturation constraint is compensated via constructing an auxiliary system. It is proved that all the variables of the controlled system are bounded, and the ride comfort, ride safety condition, and suspension space limit are guaranteed. The computer simulation and compared results further show the effectiveness of the proposed control algorithm.

Research on ride comfort analysis and hierarchical optimization of heavy vehicles with coupled nonlinear dynamics of suspension

The fact that the calculation model and optimization method are critical to the optimization efficiency of ride comfort. To improve the reliability of this process for heavy vehicles, this article proposes a systematic modelling method that is based on the coupled nonlinear dynamics of suspension components and a hierarchical optimization method that considers passenger comfort, cargo safety, and parts fatigue. Nonlinear mathematical models of leaf springs and dampers are established first. A novel model of ride comfort is then developed by integrating the nonlinear mathematical models with a conventional vibration model formulated according to Newton's second law. According to experimental observations, the novel model shows greater accuracy than the conventional one. Subsequently, the influences of suspension parameters on ride comfort are clarified with an integrated multi-software method, illustrating steering suspension stiffness and cabin rear suspension damping are significant factors affecting ride comfort. Finally, a hierarchical optimization model is developed to enhance ride comfort and minimize the amplitude of vibrations. The optimized vibrations show average reductions of 31.1% and 17.0% for the seat rail and sprung centroid, respectively.

Design and experimental modeling of a compact hydro-pneumatic suspension strut

The dynamic properties of a compact hydro-pneumatic suspension strut integrating the gas chamber are investigated analytically and experimentally. A comprehensive experiment was designed to experimentally characterize the dependence of friction force on the strut operating pressure in addition to the pressure/force–displacement and pressure/force–velocity properties of the prototype under broad ranges of excitations. An analytical model of the strut is formulated to incorporate the polytropic gas process, nonlinear and hysteretic friction force and turbulent flows across the piston orifices. Owing to dominant effect of friction due to seals of the floating piston separating the gas and oil media, and strong dependence of friction force on the operating pressure, the Coulomb and Stribeck friction effects are described by a nonlinear function in the operating pressure. Furthermore, the viscoelastic O-ring-type seals contributed to notable hysteresis at very low velocities, which is described by a hyperbolic tangent function in velocity. The discharge coefficient of flows through orifices is also identified from the measured fluid pressures. The validity of the proposed model is demonstrated through comparisons of force–displacement and force–velocity responses of the model with the corresponding measured data under broad ranges of excitations. The comparisons revealed that the model could predict dynamic behavior of the strut reasonably well. The effects of charge pressure and gas volume are further investigated to seek guidance on tuning of the strut for realizing desired load carrying capacity and suspension stiffness.

Dynamic interaction of the piggyback platform And semi-trailer truck

The article presents a mathematical model of joint oscillations of the car-platform for piggyback transportations and semi-trailer truck. Considered forced oscillations of the investigated object in the vertical plane of symmetry. Built a design scheme of the platform with mounted on it with a tractor and trailer system are presented in the form of a mechanical system, all bodies which, in addition platform, accept hard. The supporting structure of the platform is presented in the form of elastic massless beams carries seven lumped masses. A railway track is considered inertial with elastic-dissipative properties. In the simulation work for suspension updated power characteristic of the friction damper. As disturbances acting on the wheelset of the platform, considered butt roughness of the track. According to the results of computer simulation obtained measurements of vertical dynamics, piggyback platforms depending on the stiffness and characteristics of the oscillations damping. The obtained data dynamic calculations allowed us to estimate the schemes of fastening of a semi-trailer truck and to determine the influence on the dynamic indexes of changes in the stiffness of the spring suspension and the coefficient of friction relative to wedge the damper through adjustment of a spring set. Proved the feasibility of the decision on the free installation of the train on the platform, allowing automotive suspension gets the opportunity to actively damping the perturbations transmitted to the wheels of the road train from the platform.

A Semi-active Vehicle Suspension Control Strategy Based on Negative Stiffness Characteristics

A suspension is an indispensable part of a vehicle. It is of great significance for passengers’ comfort and vehicle stability. This paper proposes a semi-active vehicle suspension model with negative stiffness, and analyzes the effect of negative stiffness characteristics upon vehicle response. When analyzing the performance of semi-active vehicle suspension, a quarter vehicle suspension model is established, and the space state model is built for numerical simulation. After contrasting and analyzing the response of semi-active passive suspension with negative stiffness and semi-active suspension controlled by Skyhook damping algorithm, we conclude that semi-active suspension with negative stiffness decreases the vibration speed of the vehicle body and the deflection of the tire in the low-frequency stage, and improves the smoothness and stability of the suspension. Hence, the negative stiffness characteristic is beneficial to improve the comfort and stability of the vehicle.

Nonlinear Stability of Rail Vehicles Traveling on Vibration-Attenuating Slab Tracks

Abstract Various vibration-attenuating slab tracks have been introduced into urban railways to minimize the negative effects of train-induced ground vibration and noise. However, compared with traditional slab tracks, vibration-attenuating slab tracks usually have a lower overall stiffness, which reduces the vehicle lateral stability. This paper presents an investigation of the nonlinear hunting stability of fast metro rail vehicles traveling on vibration-attenuating slab tracks. A three-dimensional vehicle–track coupled model considering different vibration-attenuating slab tracks is developed to investigate the nonlinear hunting behavior of metro vehicles running on different elastic vibration-attenuating tracks. The nonlinear critical speed and wheelset hunting limit cycle of two types of metro vehicles traveling on four typical types of vibration-attenuating tracks are compared in detail. The influences of vehicle–track system parameters, including rail fastener stiffness and vehicle suspension parameters, on the vehicle lateral nonlinear stability are reported. The results show that the flexibility of vibration-attenuating slab tracks leads to a large wheelset limit cycle and lowers the nonlinear critical speed. Increasing track lateral stiffness and designing appropriate vehicle suspension parameters can improve the lateral stability of rail vehicles traveling on vibration-attenuating slab tracks.

Testing and calculation of vehicle adaptive suspension air springs

The paper is dedicated to describing the methods of measuring the characteristics of suspension air springs (elastic pneumatic elements) on a test bench, as well as to the methods of evaluating their effect on vehicle parameters. The results of the measurement of air spring characteristics on the test bench under various conditions are presented together with the analysis of changes in their properties. A method for setting a universal force (load bearing) characteristic of the air spring, as well as a method for simulating it in the vehicle are suggested. The results of the vehicle simulation with characteristics of the air springs of different stiffness are shown, a numerical interval of the possible change in the vehicle behaviour parameters in case of change of suspension stiffness in the process of driving is specified.