Development and Validation of a Scaled Electric Combat Vehicle Tire Model

Pneumatic tire modeling and validation have been the topic of several research papers, however, most of these papers only deal with pneumatic passenger and truck tires. In recent years, wheeled-scaled vehicles have gained lots of attention as a feasible testing platform, nonetheless up to the authors’ knowledge there has been no research regarding the use of scaled tires and their effect on the overall vehicle performance characteristics. This paper presents a novel scaled electric combat vehicle tire model and validation technique. The pro-line lockdown tire size 3.00 × 7.35 is modeled using the Finite Element Analysis (FEA) technique and several materials including layered membrane, beam elements, and Mooney-Rivlin for rubber. The tire-rim assembly is then described, and the rigid body analysis is presented. The tire is then validated using an in-house custom-made static tire testing machine. The tire test rig is made specifically to test the pro-line tire model and is designed and manufactured in the laboratory. The tire is validated using vertical stiffness and footprint tests in the static domain at different operating conditions including several vertical loads. Then the tire is used to perform rolling resistance and steering analysis including the rolling resistance coefficient and the cornering stiffness. The analysis is performed at different operating conditions including longitudinal speeds of 5, 10, and 15 km/h. This tire model will be further used to determine the tractive and braking performance of the tire. Furthermore, the tire test rig will also be modified to perform cornering stiffness tests.

Predictive modelling of volumetric and Marshall properties of asphalt mixtures modified with waste tire-derived char:A statistical neural network approach

The goals of this study are to assess the viability of waste tire-derived char(WTDC)as a sustainable,low-cost fine aggregate surrogate material for asphalt mixtures and to develop the statistically coupled neural network(SCNN)model for predicting volumetric and Marshall properties of asphalt mixtures modified with WTDC.The study is based on experimental data acquired from laboratory volumetric and Marshall properties testing on WTDCmodified asphalt mixtures(WTDC-MAM).The input variables comprised waste tire char content and asphalt binder content.The output variables comprised mixture unit weight,total voids,voids filled with asphalt,Marshall stability,and flow.Statistical coupled neural networks were utilized to predict the volumetric and Marshall properties of asphalt mixtures.For predictive modeling,the SCNN model is employed,incorporating a three-layer neural network and preprocessing techniques to enhance accuracy and reliability.The optimal network architecture,using the collected dataset,was a 2:6:5 structure,and the neural network was trained with 60%of the data,whereas the other 20%was used for cross-validation and testing respectively.The network employed a hyperbolic tangent(tanh)activation function and a feed-forward backpropagation.According to the results,the network model could accurately predict the volumetric and Marshall properties.The predicted accuracy of SCNN was found to be as high value>98%and low prediction errors for both volumetric and Marshall properties.This study demonstrates WTDC's potential as a low-cost,sustainable aggregate replacement.The SCNN-based predictive model proves its efficiency and versatility and promotes sustainable practices.

Tire Dynamics Modeling Method Based on Rapid Test Method

Combined with the tire dynamics theoretical model,a rapid test method to obtain tire lateral and longitudinal both steady-state and transient characteristics only based on the tire quasi-steady-state test results is proposed.For steady state data extraction,the test time of the rapid test method is half that of the conventional test method.For transient tire characteristics the rapid test method omits the traditional tire test totally.At the mean time the accuracy of the two method is much closed.The rapid test method is explained theoretically and the test process is designed.The key parameters of tire are extracted and the comparison is made between rapid test and traditional test method.The result show that the identification accuracy based on the rapid test method is almost equal to the accuracy of the conventional one.Then,the heat generated during the rapid test method and that generated during the conventional test are calculated separately.The comparison shows that the heat generated during the rapid test is much smaller than the heat generated during the conventional test process.This benefits to the reduction of tire wear and the consistency of test results.Finally,it can be concluded that the fast test method can efficiently,accurately and energy-efficiently measure the steady-state and transient characteristics of the tire.

Path-Following Based on Nonlinear Model Predictive Control with Adaptive Path Preview

This paper presents a Nonlinear Model Predictive Controller(NMPC)for the path following of autonomous vehicles and an algorithm to adaptively adjust the preview distance.The prediction model includes vehicle dynamics,path following dynamics,and system input dynamics.The single-track vehicle model considers the vehicle’s coupled lateral and longitudinal dynamics,as well as nonlinear tire forces.The tracking error dynamics are derived based on the curvilinear coordinates.The cost function is designed to minimize path tracking errors and control effort while considering constraints such as actuator bounds and tire grip limits.An algorithm that utilizes the optimal preview distance vector to query the corresponding reference curvature and reference speed.The length of the preview path is adaptively adjusted based on the vehicle speed,heading error,and path curvature.We validate the controller performance in a simulation environment with the autonomous racing scenario.The simulation results show that the vehicle accurately follows the highly dynamic path with small tracking errors.The maximum preview distance can be prior estimated and guidance the selection of the prediction horizon for NMPC.

Comparison of nonlinear modeling methods for the composite rubber clamp

The cubic stiffness force model(CSFM)and Bouc-Wen model(BWM)are introduced and compared innovatively.The unknown coefficients of the nonlinear models are identified by the genetic algorithm combined with experiments.By fitting the identified nonlinear coefficients under different excitation amplitudes,the nonlinear vibration responses of the system are predicted.The results show that the accuracy of the BWM is higher than that of the CSFM,especially in the non-resonant region.However,the optimization time of the BWM is longer than that of the CSFM.

FEM tire model oriented to virtual experiment of off-road vehicle trafficability

In order to estimate the trafficability of off-road vehicles, the linear relationships between the pressure and the stiffness of the tire and the action of the vertical tire force with the viscoelasticity are analyzed. The method to improve the precision of the model by the coefficients is presented. The constitutive equation of the three-parameter linear model and the stiffness matrix of four-node isoparametric elements are derived to construct the FEM （finite element method） tire model in plan stress. A demarcation and verification system is designed based on the six-dimensional wheel force transducer and the vertical tire force is measured under different velocities. The results show that the model and the method proposed are reasonable.

Mathematical Models of Tire-Longitudinal Road Adhesion and Their Use in the Study of Road Vehicle Dynamics

Mathematical models of tire-longitudinal road adhesion for use in the study of road vehicle dynamics are set up so as to express the relations of longitudinal adhesion coefficients with the slip ratio. They perfect the Pacejka's models in practical use by taking into account the influences of all essential parameters such as road surface condition. vehicle velocity. slip angle. vertical load and slip ratio on the longitudinal adhesion coefficients. The new models are more comprehensive more concise. simpler and more convenient in application in all kinds of simulations of car dynamics in various sorts of braking modes.

Determination of Melamine by Infrared Spectroscopy Based on Nonlinear Modeling

[Objective] The aim was to develop a nonlinear model of quantitative analysis of melamine content by infrared spectroscopy and provide theoretical basis for the nondestructive detection of melamine. [Method] According to dynamics,mathematical modeling and optimization theory,linear and nonlinear models were respectively set up by taking an absorption peak of 1 550 cm-1 as characteristic absorption peak. [Result] The correlation coefficient of nonlinear model was 0.922 7 and the recovery was 96%,which showed that the nonlinear model was more accurate than linearity model with correlation coefficient of 0.904 9 and recovery of 557%. [Conclusion] It is feasible to determine melamine content by using the nonlinear model quantitatively.

An Adaptive Nonsingular Fast Terminal Sliding Mode Control for Yaw Stability Control of Bus Based on STI Tire Model

Due to the bus characteristics of large quality,high center of gravity and narrow wheelbase,the research of its yaw stability control(YSC)system has become the focus in the field of vehicle system dynamics.However,the tire nonlinear mechanical properties and the effectiveness of the YSC control system are not considered carefully in the current research.In this paper,a novel adaptive nonsingular fast terminal sliding mode(ANFTSM)control scheme for YSC is proposed to improve the bus curve driving stability and safety on slippery roads.Firstly,the STI(Systems Technologies Inc.)tire model,which can effectively reflect the nonlinear coupling relationship between the tire longitudinal force and lateral force,is established based on experimental data and firstly adopted in the bus YSC system design.On this basis,a more accurate bus lateral dynamics model is built and a novel YSC strategy based on ANFTSM,which has the merits of fast transient response,finite time convergence and high robustness against uncertainties and external disturbances,is designed.Thirdly,to solve the optimal allocation problem of the tire forces,whose objective is to achieve the desired direct yaw moment through the effective distribution of the brake force of each tire,the robust least-squares allocation method is adopted.To verify the feasibility,effectiveness and practicality of the proposed bus YSC approach,the TruckSim-Simulink co-simulation results are finally provided.The co-simulation results show that the lateral stability of bus under special driving conditions has been significantly improved.This research proposes a more effective design method for bus YSC system based on a more accurate tire model.

Influence of vehicle-road coupled vibration on tire adhesion based on nonlinear foundation

The influence of pavement vibration on tire adhesion is of great significance to the structure design of vehicle and pavement.The adhesion between tire and road is the key to studying vehicle dynamics,and the precise description of tire adhesion affects the accuracy of dynamic vehicle responses.However,in most models,only road roughness is considered,and the pavement vibration caused by vehicle-road interaction is ignored.In this paper,a vehicle is simplified as a spring-mass-damper oscillator,and the vehicle-pavement system is modeled as a vehicle moving along an Euler-Bernoulli beam with finite length on a nonlinear foundation.The road roughness is considered as a sine wave,and the shear stress is ignored on the pavement.According to the contact form between tire and road,the LuGre tire model is established to calculate the tire adhesion force.The Galerkin method is used to simplify the partial differential equations of beam vibration into finite ordinary differential equations.A product-to-sum formula and a Dirac delt function are used to deal with the nonlinear term caused by the nonlinear foundation,which realizes the fast and accurate calculation of super-high dimensional nonlinear ordinary differential equations.In addition,the dynamic responses between the coupled system and the traditional uncoupled system are compared with each other.The obtained results provide an important theoretical basis for research on the influence of vehicle-road coupled vibration on tire adhesion.

SOME ASYMPTOTIC INFERENCE IN MULTINOMIAL NONLINEAR MODELS (A GEOMERIC APPROACH)

A geometric framework is proposed for multinomial nonlinear modelsbased on a modified version of the geometric structure presented by Bates & Watts[4]. We use this geometric framework to study some asymptotic inference in terms ofcurvatures for multinomial nonlinear models. Our previous results [15] for ordinarynonlinear regression models are extended to multinomial nonlinear models.

INFLUENCE ANALYSIS ON EXPONENTIAL NONLINEAR MODELS WITH RANDOM EFFECTS

This paper presents a unified diagnostic method for exponential nonlinear models with random effects based upon the joint likelihood given by Robinson in 1991. The authors show that the case deletion model is equivalent to mean shift outlier model. From this point of view, several diagnostic measures, such as Cook distance, score statistics are derived. The local influence measure of Cook is also presented. Numerical example illustrates that our method is available.

A Simplified Nonlinear Model of Vertical Vortex-Induced Force on Box Decks for Predicting Stable Amplitudes of Vortex-Induced Vibrations

Wind-tunnel tests of a large-scale sectional model with synchronous measurements of force and vibration responses were carried out to investigate the nonlinear behaviors of vertical vortex-induced forces （VIFs） on three typical box decks （i.e., fully closed box, centrally slotted box, and semi-closed box）. The mechanisms of the onset, development, and self-limiting phenomenon of the vertical vortex-induced vibration （VlV） were also explored by analyzing the energy evolution of different vertical VIF components and their contributions to the vertical VIV responses. The results show that the nonlinear components of the vertical VIF often differ from deck to deck; the most important components of the vertical VIF, governing the stable amplitudes of the vertical VIV responses, are the linear and cubic components of velocity contained in the self-excited aerodynamic damping forces. The former provides a constant negative damping ratio to the vibration system and is thus the essential power driving the development of the VIV amplitude, while the latter provides a positive damping ratio proportional to the square of the vibration velocity and is actually the inherent factor making the VIV amplitude self-limiting. On these bases, a universal simplified nonlinear mathematical model of the vertical VIF on box decks of bridges is presented and verified in this paper; it can be used to predict the stable amplitudes of the vertical VIV of long-span bridges with satisfactory accuracy.

Rate of strong consistency of the maximum quasi-likelihood estimator in quasi-likelihood nonlinear models

Quasi-likelihood nonlinear models （QLNM） include generalized linear models as a special case. Under some regularity conditions, the rate of the strong consistency of the maximum quasi-likelihood estimation （MQLE） is obtained in QLNM. In an important case, this rate is O（n-^1/2（loglogn）^1/2）, which is just the rate of LIL of partial sums for i.i.d variables, and thus cannot be improved anymore.

Finite Element Simulation of Radial Tire Building and Shaping Processes Using an Elasto-Viscoplastic Model

The comprehensive tire building and shaping processes are investigated through the finite element method(FEM)in this article.The mechanical properties of the uncured rubber from different tire components are investigated through cyclic loading-unloading experiments under different strain rates.Based on the experiments,an elastoviscoplastic constitutive model is adopted to describe themechanical behaviors of the uncured rubber.The distinct mechanical properties,including the stress level,hysteresis and residual strain,of the uncured rubber can all be well characterized.The whole tire building process(including component winding,rubber bladder inflation,component stitching and carcass band folding-back)and the shaping process are simulated using this constitutive model.The simulated green tire profile is in good agreement with the actual profile obtained through 3D scanning.The deformation and stress of the rubber components and the cord reinforcements during production can be obtained fromthe FE simulation,which is helpful for judging the rationality of the tire construction design.Finally,the influence of the parameter“drum width”is investigated,and the simulated result is found to be consistent with the experimental observations,which verifies the effectiveness of the simulation.The established simulation strategy provides some guiding significance for the improvement of tire design parameters and the elimination of tire production defects.

Effect of Tire Repeated Root Modal on Tire Modelling with Experimental Modal

The effect of tire repeated root modal（RRM）on tire modeling with an experimental modal is studied.Firstly,a radial tire with radial and tangential RRMs is tested and analyzed.By multi-point exciting of the radial tire,a multiple reference frequency domain method based on a least squares（LMS PolyMAX）algorithm is used to identify modal parameters.Then,modal stability diagram（MSD）,modal indication function（MIF）and modal assurance criteria（Auto-MAC）matrix are utilized to induce multiple inputs multiple outputs（MIMO）frequency response function（FRF）matrixes.The tests reveal that notable repeated roots exist in both radial and tangential response modes.Their modal frequencies and damping factors are approximately the same,the amplitudes of modal vectors are in the same order of magnitude,and the mode shapes are orthogonal.Based on the works mentioned,the method of trigonometric series modal shapes fitting is adopted,the effects of RRM model on tire modeling with a vertical experimental modal are discussed.The final results show that the effects of considering the RRM shapes are equivalent to the tire mode shapes depended on rotating the tire’s different exciting points during tire modeling,and since considering the RRM,the tire mode shapes can be unified and fixed during tire modeling.

TESTING FOR VARYING DISPERSION IN DISCRETE EXPONENTIAL FAMILY NONLINEAR MODELS

It is necessary to test for varying dispersion in generalized nonlinear models.Wei,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponential family nonlinear models.This type of problem in the framework of general discrete exponential family nonlinear models is discussed.Two types of varying dispersion,which are random coefficients model and random effects model,are proposed,and corresponding score test statistics are constructed and expressed in simple,easy to use,matrix formulas.

Estimation of Longitudinal Tire Force Using Nonlinearity Observer

Tire forces are the major forces propelling the road vehicles. They significantly affect the dynamic behavior of the vehicles. Estimation of the tire forces is essential in vehicle dynamics and control. This paper presents an observer-based scheme for estimation of the longitudinal tire force of electric vehicles in real time.? The observer is based on a nonlinearity observer method. The pole-placement technique is used for determination of the observer gains. Simulation results demonstrate that the observer is able to estimate the tire force successfully. The experiments are implemented on a single-wheel electric vehicle test rig. The test rig comprises an electric motor driven wheel and a free-rolling drum simulating vehicle-on-road situations. Experimental results confirm the effectiveness of the present scheme.

Parameter estimation of cutting tool temperature nonlinear model using PSO algorithm

In cutting tool temperature experiment, a large number of related data could be available. In order to define the relationship among the experiment data, the nonlinear regressive curve of cutting tool temperature must be constructed based on the data. This paper proposes the Particle Swarm Optimization (PSO) algorithm for estimating the parameters such a curve. The PSO algorithm is an evolutional method based on a very simple concept. Comparison of PSO results with those of GA and LS methods showed that the PSO algorithm is more effective for estimating the parameters of the above curve.

Finite Element Analysis of Tire Traction Using a Rubber-Ice Friction Model

The friction of road surface covered by snow or ice is very low and that results in reducing vehicle traction forces and potential traffic accidents. In general, to establish a master curve on a rubber-ice friction model is difficult because the ice surface, being not far removed from its melting point, reacts itself very sen-sitively to pressure, speed, and temperature changes. In this paper, an accepta-ble frictional interaction model was implemented to finite element method to rationally examine the frictional interaction behavior on ice between the tire and the road surface. The formula of friction characteristic according to tem-perature and sliding velocity on the ice surface was applied for tire traction analysis. Numerical results were verified by comparing the outdoor test data and it was confirmed to indicate similar correlation. It is found that the rub-ber-ice friction model will be useful for the improvement of the ice traction performance of tire.