Wheel Stiffness Research Articles

Constrained H∞ control with gain switching for a nonlinear active suspension system matching non-pneumatic wheel

In this study, a constrained H ∞ controller with gain switching is put forward for the active suspension system to improve the overall performance of vehicles equipped with non-pneumatic wheels, considering the nonlinearity of wheel stiffness, actuator saturation, and output constraints. Firstly, a quarter-vehicle model incorporating active suspension and non-pneumatic wheel (NPW) is established experimentally. Secondly, the system model is linearized using Taylor series expansion and linear fractional transformation (LFT). A constrained H ∞ control strategy and a gain switching method based on road classification are proposed, taking into account the parameter uncertainty in linearization process and the variation of performance demands under different road conditions. Then, an L ∞ state observer is designed for the required system state, and the road roughness classifier based on grey wolf optimization (GWO) and probabilistic neural network (PNN) is developed to obtain the necessary road information. A bench test is finally performed using the reconstructed actual road as input. The test results validate the effectiveness and superiority of the proposed control strategy.

Influence of Changes in Stiffness and Damping of Tyre Wheels on the Outcome of the Condition Assessment of Motor Vehicle Shock Absorbers

This article deals with the influence of the elastic-damping properties (energy losses) of tired wheels on the results of the evaluation of the technical condition (dynamic properties) of automotive suspensions carried out on the diagnostic line. The purpose of this paper is to point out the inadequacies of test stands for assessing the technical condition of vehicle suspensions. The diagnostic line used in the testing featured two testing stations. The test object was a passenger car with hydro-pneumatic suspension. This enabled the conducting of suspension tests for two settings (comfort and dynamic positions). The tests were conducted for four different air pressures in the tyres of tired wheels. This made it possible to determine, for each wheel, four graphs of the load versus tyre deflection (radial stiffness characteristics). These graphs were used to determine the values of the stiffness coefficients, energy loss, and damping characteristics as well as to identify the correlation between the directional coefficient of the regression line of the elastic and damping characteristics of the tyres and the indices characterising the damping properties of the suspension of the test car. This paper shows that the result of the shock absorber condition assessment is significantly influenced by the elastic and damping properties of the tired wheels, caused by changes in tyre pressure.

Data-driven approach for investigating and predicting rutting depth of asphalt concrete containing reclaimed asphalt pavement

The aim of this paper is to investigate and predict the rutting depth of asphalt concrete containing Reclaimed Asphalt Pavement (RAP) content by the data-driven approach with aid of 6 six tree algorithm including Random Forest (RF), Gradient Boosting (GB), Adaptive Boosting (AdaB), Extreme Gradient Boosting (XGB), Light Gradient Boosting (LightGB) and Categorial Gradient Boosting (CatB) using default hyperparameters. A database containing 396 data samples derived from Hamburg Wheel Tracking Test (HWTT) and consisting of 11 input variables such as Corrected Optimum Asphalt Content (COAC), Reclaimed Asphalt Pavement, Nominal Maximum Aggregate Size (NMAS), Flashpoint, m-Value, Mass loss, Specific gravity, Viscosity, Creep stiffness, Temperature, and Number of wheels and 1 output Rutting depth are created. 10 times of 10-Fold CV and four metrics such as R2, RMSE, MAE and MAPE are used to verify the robustness of ML models. XGB model has highest performance with the mean value of R2, RMSE, MAE and MAPE to be equal to 0.9792, 1.0767 mm, 0.7085 mm, 0.1034% respectively. Comparing with other factors like the number of load cycles (number of wheels) and mix design considerations, temperature has a dominant impact on the rutting depth of asphalt pavement (type of binder, NMAS, RAP content). The rutting depth value rises with increasing temperature and COAC. NMAS has a negligible impact on asphalt pavement's resistance to rutting. To increase the rutting resistance when building the asphalt pavement, the chosen asphalt binder has high Viscosity and Flashpoint values. The local interpretation clearly demonstrates each factor's contribution to the rutting depth value in each unique scenario. Engineers can design the rutting resistance of asphalt pavement in advance thanks to the mapping produced by the Partial Dependence Plot 2D under grid contour.

A novel evaluation method for rolling energy losses of tacked vehicle road wheels using experimental modal analysis

A novel evaluation method for rolling energy losses of road wheels of tracked vehicle is proposed, in which damping of road wheel surface is identified based on single vibration excitation and single point picking up frequency response function using a simplified modal experiment with an acceleration sensor. Three road wheels of tracked vehicle with different tread rubber are utilized as specimens during the modal experiments. The half power bandwidth method is employed to identify the viscous damping parameters. The damping parameters of road wheels are ranked by their values, and then these values of every road wheels are compared with their corresponding rolling energy losses to validate their correlative relationship. Moreover, the nonlinear deformation and stiffness of road wheels are investigated about their correlation with the rolling energy losses through model development and experimental validation. The results prove that the damping ratios of road wheels are correlated well with the rolling energy losses for all the three road wheels. The proposed evaluation method could effectively evaluate the rolling energy losses of road wheels, which suggests a simplified and economical alternative over the conventional rolling energy losses experimental method of road wheels.

An investigation into the effect of resilient wheel stiffness on the dynamic behaviour of a metro vehicle running along a tangent track

Resilient wheels are extensively used for trams due to the noise reduction they can achieve. However, the effect of the resilient wheels on vehicle dynamics has not been adequately studied. An effort is presented in this paper, trying to bridge this gap. To simulate interactions between vehicle and track, the resilient wheel is modelled as a multi-rigid body system consisting of a rigid wheel core and a rigid rim between which a rubber layer is inserted. The rubber layer is regarded as three-directional spring-damper units, allowing the rim and core to have relative motions, so that the flexibility of the resilient wheel provided by the rubber layer is fully simulated. Then, the dynamics of a vehicle-track coupling system integrated with this resilient wheel model is simulated and compared with in-situ measurement. The simulation results show that, compared with a conventional solid wheel, the vertical vibration of the wheel core is much reduced in the frequency range of 70–300 Hz while the lateral vibration is much reduced in the frequency range of 90–300 Hz. The paper continues with the recommendation of the radial and axial stiffnesses, two key parameters of the resilient wheel, aiming to lower the wheel-rail contact force and carbody vibration.

Vibration absorption performance of resilient wheel in metro train running on long-span cable-stayed bridge

ABSTRACT To control the vibration of long-span cable-stayed bridge (LSCSB) caused by running train on metro line, vibration suppression effect of resilient wheel on the metro train–LSCSB coupled system is deeply investigated. Firstly, metro train–LSCSB system coupled dynamic model considering resilient wheels is formed. Then, the effects of resilient wheels on the dynamic characteristics of metro train–LSCSB system are investigated. Finally, the optimal stiffness ratiois determined, and the stiffness and damping of the resilient wheel are also optimized. Results show that: The resilient wheel reduces lateral vibration of LSCSB at 2–20 Hz. For the adopted metro train–LSCSB system, satisfactory vibration absorption effect can be obtained when stiffness ratio of the resilient wheel is 0.67–1. The optimal stiffness and damping of resilient wheel are recommended to be 30 MN/m and 300 kN·s/m.

Theoretical analysis of the forces and torques acting on a tractor during ploughing

This paper presents a physical model of a four-wheeled tractor during ploughing. In this model, the wheels are approximated by ideal non-oscillating harmonic oscillators. The velocity of the tractor is considered to be constant, i.e., the tractor is in an equilibrium state of forces and torques. The equilibrium state is described by Euler’s laws of motion. Finally, an infinite approximation of the wheel stiffness is performed and an exact solution of the forces is presented.

Equivalent Vertical Stiffness Design of Modular Deformable Wheel

This study aims to determine the structural parameters of the equivalent vertical stiffness design of a modular deformable wheel. A gas stiffness model in the air cavity of the modular deformable wheel is established on the basis of the wheel’s structure and the ideal gas equation. Then, the change curve of the radial stiffness of the modular deformable wheel is obtained, and the design model of the equivalent vertical stiffness of the wheel is constructed on the basis of the gas stiffness model. Finally, some relevant design parameters of heavyweight and lightweight wheels are obtained through numerical calculation based on existing experimental data. The results show that the design parameters of the equivalent vertical stiffness of the modular deformable wheel can meet the ride comfort requirements of vehicles. The obtained wheel structure parameters and mechanical parameters will provide effective theoretical compliance for the selection of this type of wheel. Moreover, this modular deformable wheel not only meets the requirements of the riding comfort of pneumatic wheels, but also has the advantages that common pneumatic wheels do not have (such as explosion-proof and puncture-proof functions), which also provides the practical theoretical basis for the use and promotion of this wheel in the complex geological environment.

Addendum to “Polynomial relations for cylindrical wheel stiffness characterization for use in a rolling noise prediction model”

Addendum to “Polynomial relations for cylindrical wheel stiffness characterization for use in a rolling noise prediction model”

Understanding the effect of elastic wheels on an urban railway system using a new wheel–rail coupling vibration model

In order to control the wheel–rail coupling vibration of an urban railway system, a combined elastic wheel damping structure is proposed where the key parameters that determine the structural damping and thereby control the vibration of the railway system are explored. The vertical acceleration of the elastic wheels is obtained for a range of stiffness coefficients as the wheel moves on an irregular track, which is calculated by the [Formula: see text] method in the time domain. The results show that the vertical acceleration changes with a V-shaped trend, with an increase of wheel stiffness coefficient, which allows the optimum stiffness coefficient for minimum vertical acceleration of the elastic wheel to be obtained. It is observed that when attempting to suppress wheel vibration, an elastic wheel with a larger stiffness coefficient is needed as the degree of track irregularity reduces. This paper provides new insights into the effect of wheel elasticity on vibration characteristics, and thereby provides directions to improve ride quality and passenger comfort.

Polynomial relations for cylindrical wheel stiffness characterization for use in a rolling noise prediction model

In vehicle tire/road contact modeling, dynamic models are typically used which incorporate the vehicle’s suspension in their estimation: thus relying on a known stiffness to determine the movement of the wheel in response to roughness excitation. For the case of a wheeled device rolling on a floor (such as a delivery trolley moving merchandise around inside a commercial building), there is often no suspension, yet the wheel is still too soft to able to be considered mechanically rigid (as is the case in train/rail contact). A model which is aimed at incorporating the dynamic effects of the trolley in predicting the sound generated by rolling needs to provide a robust way of estimating the wheel’s effective stiffness. This work presents an original technique for estimating the stiffness of a solid cylindrical wheel. A parametric study was conducted in order to identify the dependence of the wheel stiffness on each of the relevant variables: including the wheel’s radius, axle size, width, applied load, and material properties. The methodology may be used to estimate the stiffness of new wheel types (i.e. different geometries and materials) without needing to solve a finite element model each time. Such a methodology has application beyond the field of acoustics, as the characterization of shapes with non-constant cross sections may be useful in the wider field of materials science.

Optimal Parameterization of Tire–Rim Interaction for Aircraft Wheels

The knowledge of tire–rim interface loadings is crucial to the design of aircraft wheels. A parameterization of these loadings is proposed using model reduction techniques. The static eigenmodes of the wheel stiffness matrix that is condensed at the tire–rim interface provide a suited hierarchy of displacement or loading modes that can be sorted according to their elastic energy. A truncation of this series at a chosen order is performed to approximate any load applied to the rim. The use of cyclic symmetry is shown to lead to an efficient numerical scheme to compute these modes. This parameterization does not involve the tire modeling, which is beyond the control of aircraft wheel manufacturers. The reduced basis composed of the major eigenmodes is shown to be more compact and robust than other parameterizations based on arbitrary shape functions or tire models, and it will be further used for inverse identifications of tire–rim loadings. Moreover, this approach is generic and offers a convenient and efficient framework for arbitrary loadings.

Effect of periodic wheel tread reprofiling on wheel gauge evolution in the wheelsets of tread-braked coaches: Finite element modeling and field observations

Field statistics of the wheelsets of gauge-widened coaches in the Indian Railways show higher tendency for excessive wheel gauge widening for lower diameter wheelsets. Additionally, the axial flange deflection in gauge-widened wheelsets increases nearly linearly with the radial distance. In this work, a finite element model is developed to investigate the reasons behind these field observations. The model considers heat generation during braking, heat loss to rail, brake blocks, ambient air, residual stresses generated during wheel manufacturing, and material removal during wheel reprofiling. Wheel gauge evolution is studied for different braking histories, including those that span the entire life period of the wheel, i.e. as the wheel diameter reduces from its initial to minimum allowable size. Simulations show that higher wheel rim temperatures and lower wheel stiffness, for lower diameter wheels, result in higher wheel gauge widening for these wheelsets. Wheel gauge widening occurs primarily due to bending at the hub–disc interface; consequently, the axial flange deflection increases linearly with the radial distance.

ДОСЛІДЖЕННЯ ПРОЦЕСІВ ОБРОБКИ ПОВЕРХОНЬ ЕЛАСТИЧНИМИ АБРАЗИВНИМИ ІНСТРУМЕНТАМИ

The article discusses the process of interaction of an elastic abrasive wheel with the surface being treated, for which the stiffness and cutting micro-relief of elastic abrasive wheels are experimentally investigated and mathematically described, the mathematical expectations for the number of grains in contact with the treated. The material and the depth of their contact with the machined surface are considered to be the forces acting on the machined surface, the wear resistance of elastic abrasive wheels and the temperature in the cutting zone were experimentally investigated. Microgeometry issues of the cutting surface of an abrasive disc, the process of cutting with an abrasive grain, and also the question of removing material, forming the surface layer after processing with an abrasive disc, rounding out sharp edges, as well as options for solving the problem of efficient processing with an abrasive tool. In the article, the parameters of material removal and roughness of the treated surface during surface cleaning are calculated. The results of experimental studies of material removal and surface roughness in the processing of parts with elastic abrasive wheels are presented. The experimental data are compared with the data obtained from the calculations. The microrelief of the cutting part of the elastic abrasive wheel and its interaction with the treated surface (in turn, which has its own microrelief) were investigated, as a result of which the material is removed and the surface roughness is formed. For experimental studies of the stiffness of elastic wheels, (Minnesota Mining and Manufacturing Company) elastic abrasive wheels made of Scotch-Brite ™ abrasive material were used. This material consists of synthetic fibers forming a three-dimensional non-woven fabric, throughout the volume of which the abrasive grains are evenly distributed. It has been substantiated that profilographing should be adopted as a method for obtaining primaryinformation about the microrelief of the working surface of an elastic abrasive wheel. Theoretical positions of the interaction of the cutting microrelief of an elastic abrasive tool with the surface to be processed were developed on the basis of the theory of random processes with the determinationof the force of interaction of an elastic abrasive wheel with the surface being processed.

The Influence of Nonlinear Stiffness of Novel Flexible Road Wheel on Ride Comfort of Tracked Vehicle Traversing Random Uneven Road

The linear wheel model is the most widely used in ride comfort analysis of tracked vehicles. However, as the speed of the vehicle increases and the application of new materials, and the road wheel becomes lighter and softer, its nonlinear characteristics become more and more obvious and can't be ignored in vehicle dynamics simulation. This paper aims to study the effect of nonlinear stiffness of a novel flexible road wheel (FRW) with unique suspension bearing structure on the ride comfort of a tracked vehicle traversing random uneven road. The linear and nonlinear models of FRW were established by fitting the load-deflection data obtained from the static loading test of the physical prototype. The established linear and nonlinear models of FRW were added to a half-vehicle model of a tracked vehicle which has been proved by published test results. The ride comfort of the half-vehicle model of the tracked vehicle with linear and nonlinear models of FRW on random uneven road surface was studied in detail. The study results show that, compared with the linear wheel model, the nonlinear model has a tremendous influence on the dynamic response of the tracked vehicle, effectively suppressing the vibration, especially for the high frequency excitation. In addition, the nonlinear factor has a greater impact on the dynamic performance of the wheel than on the suspension and the body. The research results enrich the study of nonlinear dynamics of tracked vehicles, and provide reference for nonlinear modeling of other pneumatic tires and non-inflatable wheels.

핸드사인 장갑으로 조정하는 미니어처 3휠 피칭머신 설계

Recently, the interest in leisure and sports culture is increasing and the related industry is invigorating. In particular, baseball is the most popular sport in Korea. We focused on the pitching machine such as the two-wheeled and three-wheeled pitching machines. In this study, we applied a hand-sign glove with a tension sensor to mimic the catcher’s hand sign. An Android application in a smart phone was built to communicate with the primary body using the Bluetooth. Simulations were performed to predict the ball trajectory considering variations in the coefficients of friction between the wheel and ball, the wheel stiffness, and the rotational speeds of the wheel by the RecurDyn, which was the CAE commercial program. Before commercializing this machine, it was designed to be miniaturized and automatically feed the balls.

Time-varying mesh stiffness analysis of a single-roller enveloping hourglass worm gear

As a new type of transmission, the single-roller enveloping hourglass worm gear (SEHWG) is widely used in precision mechanical transmission systems. Time-varying mesh stiffness (TVMS) is one of the most important excitations, which has great influences on the dynamic characteristics of SEHWG systems. In this paper, a model for calculating the TVMS of the SEHWG is proposed, in which bending stiffness, shear stiffness, radial compression stiffness, and foundation stiffness are considered in the worm stiffness calculation. And bending stiffness, shear stiffness, and foundation stiffness are considered in the worm wheel stiffness calculation. The process of calculating the periodical TVMS of the SEHWG is also presented. Then, the TVMS of the SEHWG by the proposed method is compared with that of the finite element method for the model validation. Finally, the influences of the roller radii on TVMS are analyzed. The results show that the mesh stiffness of the TVMS has a tendency to rise first and then fall with the increasing roller radii.

Influence of Wheel Stiffness on Tire Dynamic Performance and Driving Stability

Influence of Wheel Stiffness on Tire Dynamic Performance and Driving Stability

Simulation of stiffness analysis of rubber material applied in resilient wheel

AbstractResilient wheels are well‐known for their contribution to prevent squealing, impact noise and dynamic stresses on unsprung masses. In this study, a FE model is established in ABAQUS to analyze the stiffness of resilient wheels based on the Mooney‐Rivlin hyperelastic material theory. The modes of each part in the resilient wheel and the whole wheel are calculated. The static and dynamic stiffness of the resilient wheel are analyzed. The simulation shows that the resilient wheel can reduce the dynamic loads both in the lateral and vertical directions between the vehicle and the track. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Study on Wheel Stiffness Considering Balance between Driving Stability and Weight

Study on Wheel Stiffness Considering Balance between Driving Stability and Weight