bluuebunny/crossref_metadata_2025 huggingface dataset:
An Application of Finite Element-Based Fracture Mechanics Analysis to Cord-Rubber Structures
Authors: Ebbott T. G.
Published: June 2006

A finite element-based method to analyze the severity of internal cracks in cord-rubber structures is presented. The method includes materials testing to characterize rubber fatigue behavior, a global-local finite element analysis to provide the detail necessary to model explicitly an internal crack, and use of the J-integral and virtual crack closure techniques for energy release rate evaluation. Analysis of the multiaxial and cyclic fracture situation is carried out by considering the cycle of each mode of fracture separately and then combining the effect of each mode to determine the total effect. Crack growth rates in the structure are assumed to be the same as the crack growth rate in a laboratory specimen at the same level of cyclic energy release rate. Results are presented for a material change in a critical tire region.
Development of a 60-Series Self-Supporting Tire
Authors: Willard W. L.
Published: June 2006

Recent advances in rubber compounding as well as a more advanced understanding of deflated tire mechanics, combined with consumer demand for increased vehicle safety and convenience, have led to the development of self-supporting tires. Self-supporting tires, which are available for lightly loaded sport vehicles, are now available for the more common 60-series tire and the luxury car segment.

This paper highlights some of the methods used to develop the P225/60R16 MXV4 ZP and provides information on its application and performance. Modeling for the zero-psi tire and factors that influence performance (speed, load, cornering, and ambient conditions) are discussed.
Finite Element Analysis of a Quasi-Static Rolling Tire Model for Determination of Truck Tire Forces and Moments
Authors: Goldstein A. A.
Published: June 2006

The finite element method is used to simulate the slow (quasi-static) rolling of a radial truck tire subjected to ground plane tractions. Three conditions are considered, namely, (1) straight free rolling, (2) cornering, and (3) braking. Lateral and longitudinal slip are calculated by analyzing the motion of a moveable road surface relative to the wheel plane. Footprint moments are calculated for the cornering and braking condition. In addition, cornering stiffness, braking stiffness, and aligning stiffness are calculated and compared to measured results. Computational benchmark data is provided. The simulation was performed with the ABAQUS finite element program.
End Effects in Twisted Cord-Rubber Composites
Authors: Padovan J.
Published: June 2006

This paper investigates the cord-matrix load transfer problem in twisted cord-rubber composites. The central feature of the study is to ascertain the polarizing effects of twist-induced coupling of the axial loads and torque. Particular emphasis is given to the end problem, namely the transition between the axial-circumferential shear stress-dominated end region and the axial normal stress and torque-controlled far-from-end zone. This is achieved through the development of both a closed form analytic formulation and its corroboration by a detailed finite element simulation.
Torsional Analysis of a Steel Cord-Rubber Tire Belt Structure
Authors: Pidaparti R. M. V.
Published: June 2006

A three-dimensional (3D) beam finite element model was developed to investigate the torsional stiffness of a twisted steel-reinforced cord-rubber belt structure. The present 3D beam element takes into account the coupled extension, bending, and twisting deformations characteristic of the complex behavior of cord-rubber composite structures. The extension-twisting coupling due to the twisted nature of the cords was also considered in the finite element model. The results of torsional stiffness obtained from the finite element analysis for twisted cords and the two-ply steel cord-rubber belt structure are compared to the experimental data and other alternate solutions available in the literature. The effects of cord orientation, anisotropy, and rubber core surrounding the twisted cords on the torsional stiffness properties are presented and discussed.
Finite Elements Developed in Cylindrical Coordinates for Three-Dimensional Tire Analysis
Authors: Danielson K. T. , Noor A. K.
Published: June 2006

Finite elements developed in cylindrical coordinates are presented for three-dimensional analysis of tires. In contrast to elements formulated in Cartesian coordinates, these elements allow the exact representation of circular shapes. The exact modeling of circular geometries can provide better finite element predictions and reduce the number of elements needed around the tire circumference. Numerical results are presented for the application of this formulation to the analysis of a radial automobile tire subjected to rim mounting, nonconservative inflation pressure, and rigid pavement contact. The predictions of the foregoing finite elements are compared to experimental data and to predictions of a commercial code using finite elements developed in Cartesian coordinates. The comparisons demonstrate the accuracy and the advantages of the cylindrical coordinate formulation for the three-dimensional finite element analysis of tires.
Experimental Results and Analysis of Aircraft Tire-Test Drum Interaction
Authors: Lindsley N. , Medzorian J. , Padovan J.
Published: June 2006

Although aircraft tires are traditionally tested on external drum dynamometers, the effects of the curvature of the test surface on the normal contact pressure distribution and footprint area of an aircraft tire have not previously been addressed. Using the tire force machine (TFM) at the Wright Laboratory Landing Gear Development Facility (LGDF), trends in tire footprint area and normal contact pressure distributions were investigated for concave, flat, and convex surfaces. This evaluation was performed using the F-16 radial (25.5×8.0 14PR) main landing gear tire at rated load (16,200 lbf) and inflation pressure (310 psi). The trends for overall tire footprint behavior indicate that the more convex the surface, the smaller the contact area and the larger the normal contact pressure. Conversely, the more concave the surface, the larger the contact area and the smaller the normal contact pressures. All data were made symmetric about the longitudinal and lateral centerlines. This process and its effect on the data are discussed at length in the analysis sections. Additionally, it was found that after normalizing the normal contact pressure data with respect to contact length and maximum pressure for the individual tire ribs, the normal contact pressure longitudinal distributions were “identical” (within ±5%) regardless of surface curvature. Comparisons are made with numerical experiments on a treadless, homogeneous polyurethane automobile tire.
Heavy Truck Handling Performance Analysis in Vehicle Test and Computer Simulation
Authors: Schröder C. , Duchow A.
Published: June 2006

The dynamic stability of heavy trucks, as spinout, jackknifing, and rollover, is highly dependent on vehicle configuration, driving maneuver, and the force and moment characteristics of tires. Increasing safety requirements on the handling performance of heavy trucks demand tools that allow a tire design engineer to predict tire influences on the tire/vehicle system dynamic behavior. The computer simulation of handling performance of vehicles offers possibilities of evaluating influences of tire design changes on handling properties in any developing stage of new tire lines. Thus, modern simulation techniques may contribute to the building and testing of tires in an early design stage. This paper presents results from a recent program of tire/vehicle system research, applying tire/vehicle testing and simulation techniques to a 40 ton truck-semitrailer combination. The goal of this work is to visualize the possibilities of state-of-the-art simulation technologies on the tire design process. Tire force and moment characteristics can be calculated from the tire layout by an advanced tire model. The tire model for this type of calculation is a multibody system. Calculated and measured dynamic tire characteristics are used for the full vehicle handling simulation in ADAMS. Extensive tire characteristic testing on the road and test stand was done to improve and validate the tire model. Vehicle handling tests as steady state circular and lateral transient response tests were done for the empty and laden vehicle with different tires to prove the vehicle model. With the use of the simulation of the tire and vehicle behavior, the tire design engineer will be able to judge tire characteristics of different variants in an early design stage. Vehicle dynamic simulation studies up to instability as spinout, jackknifing, and rollover can be performed using modern CAE methods without harming man and environment, but subjective and objective tire evaluation still remains necessary for approving and validating the predicted results.
Effect of the Environment on the Wear of Carbon Black-Filled Natural Rubbers?
Authors: Uchiyama Y. , Han Y. , Iwai T.
Published: June 2006

In this study, the effect of the environment on the wear of natural rubber (NR) vulcanizates containing three kinds of carbon black, namely, HAF(N330), ISAF(N220), and SAF(N110), were examined. The friction coefficient and wear rate of each carbon black-filled NR tended to decrease with decreasing ambient air pressure. In air, the wear rates of NR vulcanizates containing ISAF and SAF were lower than NR containing HAF. No difference in the former two vulcanizates could be observed. However, at a reduced air pressure of 66 Pa, the wear rates of NR with ISAF and SAF were 22% and 7%, respectively, when compared with that of NR with HAF. With a reduction in the size of carbon black, a large difference in the wear rates could be seen in vacuum.
3D Simulations of Automobile Tires: Material Modeling, Mesh Generation, and Solution Strategies
Authors: Meschke G. , Payer H. J. , Mang H. A.
Published: June 2006

The paper addresses finite element formulations for automobile tires considering nonlinear material behavior, large strains, and finite deformations while using efficient computational strategies for realistic large-scale 3D finite element simulations. A new 3D finite element model for cord-reinforced rubber composites is employed for the numerical representation of the reinforcing plies. A hyperelastic Mooney material law in conjunction with a hybrid finite element formulation is used for the modeling of the rubber material. A strategy for the generation of locally refined finite element meshes of automobile tires is developed. Several computational strategies, together with an iterative solver, are proposed to improve the computational efficiency. 3D simulations of factional static contact of automobile tires on a rigid road surface, involving the determination of the pressure distribution in the contact zone, are presented.
Analysis of Temperature Distribution in a Rolling Tire Due to Strain Energy Dissipation
Authors: Park H. C. , Youn S-K. , Song T. S. , Kim N-J.
Published: June 2006

This paper addresses a systematic procedure using a sequential approach for the analysis of the coupled thermomechanical behavior of a steady state rolling tire. Not only knowledge of mechanical stresses but also knowledge of the temperature loading in a rolling tire are very important because material damage and material properties are affected significantly by the temperature. In general, the thermomechanical behavior of a pneumatic tire is a highly complex transient phenomenon that requires the solution of a dynamic nonlinear coupled thermoviscoelasticity problem with heat sources resulting from internal dissipation and friction. In this paper, a sequential approach, with effective calculation schemes, to modeling this system is presented to predict the temperature distribution with reasonable accuracy in a steady state rolling tire. This approach has three major analysis modules: deformation, dissipation, and thermal modules. In the dissipation module, an analytic method for the calculation of the heat source in a rolling tire is established using viscoelastic theory. For the verification of the calculated temperature profiles and rolling resistance at different velocities, they are compared with measured ones. Also, discussed are the accuracies of the linear and quadratic finite element models used in the analysis.
Airbag Tire Modeling by the Explicit Finite Element Method
Authors: Wu S. R. , Gu L. , Chen H.
Published: June 2006

An explicit finite element code FCRASH has been applied to both static and dynamic tire modeling. The computational procedure for predicting tire loads has been investigated. The typical tire model used in the simulation consists of a tire and rim. The tire is defined by membrane elements and the rim by rigid body with shell elements. The tire and rim form a closed volume. The airbag functionality in FCRASH, an explicit finite element code developed by Ford Motor Company, has been employed to simulate the test and to monitor the pressure and volume changes in the tire. Three static tire models (Taurus spare tire, P145/75R12, and P225/60R16) have been studied and the force-deflection curves are compared with test data. All of them exhibit a very good agreement. The standard spindle test for the P145/75R12 tire at three different speeds (10, 20, and 30 mph) is also simulated. The prediction of vertical and horizontal forces at 30 mph shows an excellent agreement with the test. The results for 20 and 10 mph are also reasonably good. The simulations for complex road conditions and full vehicle over bumps with a concept model are also performed as a feasibility trial. The CPU time used in both HP735 and CRAY computers for all these cases are comparable with other major CAE jobs. The experiments show that the explicit finite element code has a lot of advantages and strong potential to perform durability road load analysis with affordable computer costs.
A Study on the Analysis of Surface Stresses of Pneumatic Tires by the Photoelastic Method
Authors: Kim N. J. , Park B. K. , Ahn J. R.
Published: June 2006

The pneumatic tire has a very complicated geometrical shape and is subjected to large deformations. Measurement of the stress and strain distributions in the tire is difficult. In this study, the reflective photoelastic method was used to measure the distributions of stress and strain on the surface of the tire sidewall. It was assumed that the pneumatic tire takes the shape of a toroidal shell of revolution and that the strain of the photoelastic coating is the same as that of the tire surface. The force equilibrium equations for shell elements were derived and the principal stresses were extracted by the shear difference method. The normal stresses and the shear stresses were obtained by numerically integrating the equilibrium equations. The initial values for the integration were determined using the oblique incidence method.
Fatigue Crack Propagation in Metals and Polymers with a Unified Formulation
Authors: Chow C. L. , Lu T. J.
Published: June 2006

As the traditional ΔK-based fatigue crack propagation (FCP) law has recently been elucidated by Chow and his group [1–7] to be inadequate for a complete description of fatigue cracking, we examine in this investigation the applicability of a unified formulation for characterizing FCP of both metals and nonmetals. We start by defining a new cyclic J-integral, ΔJ, which, under the confines of linear elastic fracture mechanics (LEFM), is equivalent to the range of elastic strain energy release rate, ΔG. ΔJ (or ΔG) is used as a proper criterion for FCP so long as the crack does not extend during the unloading portion of one load reversal. ΔJ (or ΔG) as such is also interpreted as the source supplier for the energy flow rate dissipated on crack-tip cyclic plastic deformations. It is then assumed that, under fixed test conditions, the minimum specific work of fracture required for fatigue crack initiation, ΔJth, is a material property independent of the load ratio R. Fatigue threshold values thus predicted are correlated favorably with experimental measurements. For fatigue crack propagation, a unified formulation is subsequently derived from the thermodynamic theory of irreversible processes with the cracked surface area taken as an internal variable together with the assumption that the rate of energy dissipated on FCP depends on ΔJ only. It is noted that, in addition to ΔJ, the role played by (Jc − Jmax) is also required in the unified FCP law. Applicability of the law for producing a master FCP diagram is finally examined using FCP data of both metals and polymers, including mild steel, aluminium alloys, PMMA, PVC, short fiber composites, and adhesives.
Interply Shear Stresses and Coupled Deformations of a Folded Belt Structure Under Extension
Authors: Akasaka T. , Kato M. , Wakatsuki H.
Published: June 2006

The folded belt construction has been developed to reduce the shear stress concentrations at the belt edge and to stabilize the bending interaction with the carcass at the shoulder. An analysis is given to obtain the characteristic distributions of interply shear stresses and coupled extensional-torsional and extensional-bending deformations of the folded belt comprised of a one-layer Cord Reinforced Rubber (CRR) sheet under axial tension. It was shown that the interply shear stress concentrations surely disappeared at the folded belt edge but appeared alternatively at the free end of the rolled-up belt sheet and the tensile stress in the axial direction concentrated heavily in the laminated belt part. The experimental verification of the predicted distribution of the interply shear stresses was conducted by measuring the in-plane shear membrane force of a belt sheet.
Model Reference Adaptive Control of a Tire Test Machine
Authors: Kline S. M.
Published: June 2006

A typical tire endurance testing machine (TTM) is described and a new digitally controlled TTM is proposed. Currently TTMs normally use an analog PID-type servo loop to control the force with which a tire is pressed against a large turning road-wheel (radial load control). The camber angle and steer angle of the tire are both normally constant and zero. This type of system does not perform well with changing radial loads because the system dynamics are influenced by the tire's weight and spring constant which varies from tire to tire. Analog electronic control cannot adapt to these parametric changes but digital control can. In this paper a model reference adaptive controller is proposed. This type of control allows specific loading dynamics (the reference model) to be programmed independently of tire weight and spring constant. This enables the user to emulate a specific suspension system on a bumpy road simply by specifying the suspension dynamics and the changes in load.
Deformation Analysis of a Radial Tire Loaded on a Crossbar
Authors: Akasaka T. , Kagami S. , Yamazaki S.
Published: June 2006

The spring characteristics of a radial tire loaded on a crossbar put on a roadway was analyzed with a spring bedded ring model. Nonlinear radial and tangential spring effects of the sidewall and large deformation of the tread were considered. The tread curvature in the cross section was found to be the most important structural factor for elucidating the enveloping properties of a radial tire in contact with a crossbar. Experimental verifications of the spring effect and the tread deformation of a radial tire were in good agreement with the theoretical predictions.
Spinup Wear in Aircraft Tires
Authors: Padovan J. , Padovan P. , Kazempour A.
Published: June 2006

This paper develops a cost-effective analytical-numerical simulation procedure which models the tire wear problem resulting from the spinup process associated with high-speed aircraft landings. The resulting model can represent the energy transfer at the tire-runway interface, the rotary momentum absorption process, the steep thermal gradients in the interface region as well as the high wear rates resulting from the combined thermal degradation of the rubber (reversion, melting, ablation) and mechanical machining by runway asperities. This is illustrated in a series of parametric numerical studies defining the parametric effects of a variety of system factors.
Force Transmissibility of Heavy Truck Tires
Authors: Tielking J. T.
Published: June 2006

A laboratory study of force transmission in radial truck tires is described. The experiments are conducted with the tire-wheel assembly attached to a fixed, nonrotating axle. Contact with the tire is provided by a flat surface. Single frequency displacement cycles are applied to the loaded tire footprint, and the dynamic force transmitted through the tire is measured at the fixed axle. Fourier transform signal analysis is used to extract the cyclic displacement and force amplitudes. The amplitude ratio force/displacement is defined as the force transmissibility. The experiments show inflation pressure and tire load to have little effect on force transmissibility. A single degree of freedom tire model for force transmissibility is described. The model uses easily measured tire parameters and is intended for use in vehicle models to include the effect of tire dynamics.
Influence of Rim Run-Out on the Nonuniformity of Tire-Wheel Assemblies
Authors: Rhyne T. B. , Gall R. , Chang L. Y.
Published: June 2006

An analytical membrane model is used to study how wheel imperfections are converted into radial force variation of the tire-wheel assembly. This model indicates that the radial run-out of the rim generates run-out of the tire-wheel assembly at slightly less than the one to one ratio that was expected. Lateral run-out of the rim is found to generate radial run-out of the tire-wheel assembly at a ratio that is dependent on the tire design and the wheel width. Finite element studies of a production tire validate and quantify the results of the membrane model. Experiments using a specially constructed precision wheel demonstrate the behavior predicted by the models. Finally, a population of production tires and wheels show that the lateral run-out of the rims contribute a significant portion to the assembly radial force variation. These findings might be used to improve match-mounting results by taking lateral rim run-out into account.
Tire Rolling Loss Computation with the Finite Element Method
Authors: Luchini J. R. , Peters J. M. , Arthur R. H.
Published: June 2006

This paper describes a process for the prediction of rolling resistance in tires. A new Directional Incremental Hysteresis (DIH) theory describing the hysteretic behavior of carbon black filled rubber is presented. The steps required to implement the DIH theory in a material model, within a Finite Element (FE) model, and to predict tire rolling resistance are described.

The material model using the DIH theory is a strain-based model which includes an incremental formulation to deal with nonsinusoidal cycles within tires. The material model is also enhanced by a directional formulation which is active in situations where the strain tensor has a substantial change in direction with minimal change in magnitude. The hysteresis material model is developed only for the rubber compounds of the tire. While there is no direct contribution of cord hysteresis to predicted rolling loss, the structural effects of the cord on the rubber stress-strain behavior are included and will contribute to the tire rolling loss by affecting the stress-strain cycle of the rubber.

Experimental work used to determine the parameters of the material model for specific compounds is outlined. Some example DIH parameters are listed by compound application.

The DIH theory within the Finite Element method is then used to predict rolling resistance for a specific tire design. The results are compared to experimental data taken using SAE J-1269. The value of the tire rolling resistance is predicted within a few percent. In addition, the sensitivities of the tire to changes in load and inflation pressure are predicted and they are found to compare favorably to the experimental results.

The DIH theory is implemented within a quasi-static FE model, and was not intended for use in dynamic applications such as the prediction of standing wave phenomena. While the quasi-static FE model used in this study can predict deformed shapes, stress distributions, and temperatures, there is presently no coupling between the thermal and mechanical models.
Theoretical Laws for Rear Steering in Four-Wheel Steering Vehicles, Seen from the Tire's Point of View
Authors: Salerno P.
Published: June 2006

Theoretical laws governing rear-wheel steering of a vehicle are developed from a linear model having two degrees of freedom. Such laws can aid in improving vehicle transient response. Examples are given of their use to show that the same handling behavior can be obtained in rear-steering vehicles that are equipped with variant tires as with front-steering vehicles equipped with standard tires. Tire variants studied were cornering stiffness and relaxation length. The laws also suggest ways to nullify lags in steering actuation.
Relationship Between Tire Tread Physical Properties and Tire Force and Moment Properties
Authors: Pottinger M. G. , Fairlie A. M.
Published: June 2006

Tire lateral force and aligning torque are the most significant determinants of automotive handling. Tread compound physical properties are important design parameters for determination of tire lateral force and aligning torque behavior.

This paper extends the published knowledge of the effects of tread compound physical properties on force and moment to cover the entire range of slip angles encountered in driving. Below 10 degrees slip angle lateral force increases with increasing compound stiffness and hysteresis. At and above 10 degrees slip angle there is a change in the general trend. In this range it appears that an optimal compound stiffness exists and that the hysteresis effect reverses. Aligning torque shows two distinctly different behaviors. One, like that governing lateral force in the general driving range, is valid below the peak of the aligning torque curve. The other, valid above the peak of the aligning torque curve, shows decreasing aligning torque with increasing tread stiffness and no hysteresis effect.
A Test for Measuring Transient Characteristics of Tires
Authors: Bandel P. , Di Bernardo C.
Published: June 2006

A new method is described for measuring tire cornering stiffness and relaxation length under transient conditions. The hub of the test tire, which is riding atop a rotating drum, is attached to a horizontal beam that is hinged at its other end to permit free lateral motion of the tire. When the tire is given a lateral pulse it oscillates at its natural frequency about the position of zero steer angle. Both cornering stiffness and relaxation length of the tire can be calculated from the frequency and logarithmic decay of the resulting oscillations. Results of this “pendulum” test are compared with those from steady-state tests and from the sinusoidal steer angle test, which has been the conventional one for measuring transient tire characteristics. Advantages of the pendulum test are pointed out.
Design and Analysis of a Composite Integral Wheel-Tire
Authors: Su J. H.
Published: June 2006

An integrated design and analysis methodology for a Fiber Reinforced Plastic (FRP) Integral Wheel-Tire (IWT) was developed for applications in different automotive vehicles. The results are presented specifically for composite epoxy structures reinforced with long glass fibers and having a bonded rubber tread. This methodology includes automated design and analysis procedure and allows for closing the loop in the integration of materials, process, and design phases of a product. The results from this methodology were verified by testing real parts. The effect of a design change was predicted automatically in a short turn-around time. As an example, a study of footprint sensitivity to design parameters is discussed.
Mathematical Models of Stiffness Nonuniformity and Run-out Effects as Measured on a Low Speed Nonuniformity Machine
Authors: Allaei D. , Soedel W. , Yang T. Y.
Published: June 2006

Two types of tire nonuniformity seem to be mainly responsible for the radial force variation of a slowly rolling tire as measured on a nonuniformity machine: radial stiffness variation around the structure and roundness nonuniformity, also called run-out. The purpose of this paper is to present mathematical models representing either of these variations. The models assume that the natural frequencies and modes of the uniform tire are available, and expresses the effects of the nonuniformities in terms of these uniform modes. The method presented can be used to distinguish between stiffness and geometric nonuniformities.
Improvements of Wandering Performance by Investigation into Characteristics of Tires
Authors: Yamashita O. , Shiraishi T.
Published: June 2006

Wandering of buses and trucks on rutted roads has recently attracted attention in Japan. The phenomenon is associated with the balance of forces between tires and a canted road surface. A high camber stiffness of tires, leading to a high yaw rate, is shown to be desirable for minimizing wandering. A lesser but still important effect is associated with cornering power. Effects on other desirable tire properties, however, must be considered.
Determination of Stiffness Properties of Multi-Ply Cord-Rubber Composites
Authors: Parhizgar S.
Published: June 2006

The material properties of cord-rubber composites required for finite element analysis of tires are discussed. It is shown that the current experimental methods used in verification of the Laminated Plate Theory have not adequately included the coupling deformations existing in unsymmetrical laminated composites. The importance of these coupling deformations is demonstrated on a 0/90 laminated strip. A special grip system capable of decoupling loads and moments applied to a 0/90 laminated strip is introduced. A procedure for experimental determination of the stiffness constants of 0/90 laminate is given.
Finite Element Simulation of Tire-Rim Interface
Authors: Tseng N. T. , Pelle R. G. , Chang J. P.
Published: June 2006

A finite element model was developed to simulate the tire-rim interface. Elastomers were modeled by nonlinear incompressible elements, whereas plies were simulated by cord-rubber composite elements. Gap elements were used to simulate the opening between tire and rim at zero inflation pressure. This opening closed when the inflation pressure was increased gradually.

The predicted distribution of contact pressure at the tire-rim interface agreed very well with the available experimental measurements. Several variations of the tire-rim interference fit were analyzed.
Some Consequences of Coulomb Friction in Modeling Longitudinal Traction
Authors: Klingbeil W. W. , Witt H. W. H.
Published: June 2006

A three-component model for a belted radial tire, previously developed by the authors for free rolling without slip, is generalized to include longitudinal forces and deformations associated with driving and braking. Surface tractions at the tire-road interface are governed by a Coulomb friction law in which the coefficient of friction is assumed to be constant.

After a brief review of the model, the mechanism of interfacial shear force generation is delineated and explored under traction with perfect adhesion. Addition of the friction law then leads to the inception of slide zones, which propagate through the footprint with increasing severity of maneuvers. Different behavior patterns under driving and braking are emphasized, with comparisons being given of sliding displacements, sliding velocities, and frictional work at the tire-road interface.

As a further application of the model, the effect of friction coefficient and of test variables such as load, deflection, and inflation pressure on braking stiffness are computed and compared to analogous predictions on the braking spring rate.
Elastic-quasi-dynamic Solution of the Mallory Tube Test
Authors: Assaad M. C.
Published: June 2006

A novel numerical approach to model the bending of a straight Mallory tube into a desired configuration is described. The effect of the bimodular behavior of synthetic reinforcement cord on the bending process is reported. The reinforcement used encompasses the most widely used fibers such as polyester, nylon, and rayon. The principal strain magnitudes at the reinforcement layer are computed under pure bending. The internal inflation pressure and the angular velocity at which the tube is rotated do not have a noticeable effect on the strain magnitudes. However, the axial length of the tube, the location of the reinforcing layers inside the thickness of the tube, and the orientation of this layer have shown remarkable influence on the strain distribution. Finally, the strain magnitudes from the numerical solution are compared with the strain magnitude measured from actual photographs of the tube during testing. The calculated strain magnitudes and the measured ones were found to be in good agreement.
Two-Dimensional Contact Pressure Distribution of a Radial Tire
Authors: Akasaka T. , Katoh M. , Nihei S. , Hiraiwa M.
Published: June 2006

Two-dimensional contact pressure distribution of a radial tire, statically compressed to a flat roadway, is analyzed using a rectangular contact patch.

The tire structure is modeled by a spring-bedded ring belt comprised of a laminated-biased composite strip. The belt is supported by radial springs simulating the sidewall. The spring constant Kr was well defined previously by one of the authors.

Deformation of the rectangular flat belt is obtained theoretically. The belt is subjected to inflation pressure, reaction forces transmitted from the spring bed of the tread rubber, and shearing force and bending moment along the belt boundaries brought from side-wall springs and the detached part of the ring belt. In-plane membrane forces, which are not uniform in the contact area, due to the friction forces acting between the tread surface and the roadway are also applied.

The resulting contact pressure distributions in the circumferential direction are shown to be convex along the shoulder, but concave along the crown center line. This distribution agrees well with the experimental results.
A Study on the Contour of the Truck and Bus Radial Tire
Authors: Ogawa H. , Furuya S. , Koseki H. , Iida H. , Sato K. , Yamagishi K.
Published: June 2006

The Tension Control Optimization Theory, TCOT, allows for heavy duty truck and bus tires with greater bead and belt durability and increased fuel efficiency than conventionally shaped truck and bus tires, without sacrificing other important performance characteristics such as maneuverability, wear resistance, etc.

Before TCOT, conventional truck and bus tires used the theory of the natural equilibrium shape as a base. TCOT technology expands the Rolling Contour Optimization Theory, RCOT, and proposes the ultimate tire casing contour according to tire application.

TCOT optimizes the control of the tension in an inflated tire and the control of the change of the contour by inflation pressure, and regulates strains in the belts and plycord edges, limiting the occurrence and spread of minute but potentially damaging cracks in the vulnerable edges of a rolling tire.
Viscoelastic Properties of Aircraft Tire Materials
Authors: Tielking J. T. , Hanson R. R. , Giacomin A. J.
Published: June 2006

Specimens cut from a 40 × 14 nylon cord aircraft tire were subjected to cyclic strain tests to measure the viscoelastic behavior. Spectral analysis was used to quantify nonlinearity in the stress response. Preliminary studies were made to ascertain the effects of specimen length and width on the test results. A bolted end constraint was developed to uniformly distribute the imposed strain through the thickness of the multiply carcass specimens. Test results show the effects of temperature, frequency, and strain level on the viscoelastic properties. Results are generally in agreement with earlier findings made using tubular test specimens.
Development of A Three-Dimensional Membrane Element for the Finite Element Analysis of Tires
Authors: Ishihara K.
Published: June 2006

A three-dimensional membrane element was developed for the finite element analysis of tires. In general, the three-dimensional finite element analysis of tires uses a lot of computing time because of the complex nature of the problem. Major sources of complexity are, for example, nonlinearities in kinematics, material properties, boundary conditions, and the multilayer structure which is inherent to the tire. One of the ways to overcome this situation can be in the modeling strategy. This paper describes an approach where the cord-rubber composite components of the tire are modeled by membrane elements. The number of nodes required in the tire model using this strategy is considerably reduced, without any loss of accuracy, compared with models in which only ordinary solid elements are used. The nonlinear finite element formulation, numerical examples, and a comparison of the results with those obtained from models using solid elements and experimental values are given in the paper.
A New Tire Construction Which Reduces Ply Steer
Authors: Kabe K. , Morikawa T.
Published: June 2006

Currently, the main tire construction is the radial construction. The radial construction consists of a carcass layer with cords parallel to the tire cross section and a belt layer which surrounds the tire in the circumferential direction and stiffens the tread band. The radial construction has better performance characteristics than the bias construction. It has higher durability, better wear resistance of the tread, lower rolling resistance, and better performance at high speed because of the stable contact response developed by the belt ply. On the other hand, the belt construction of the radial tire causes ply steer. This ply steer is also a cause of steering pull and uneven tread wear.

This paper describes a new tire construction which enables the reduction of ply steer. The new construction features the carcass cord having some angle with respect to the tire cross section and also with respect to the cord of the adjacent belt ply. It is shown that the new tire construction can significantly reduce ply steer through variation of the carcass cord angle.
Elastic Properties and Mechanical Losses in Rubbers in Complex Stressed State
Authors: Priss L. S. , Shumskaya A. G.
Published: June 2006

It is shown that in the strain range from 30% compression to 60% tension, the elastic potential of filled rubber compounds can be described with sufficient accuracy as a polynomial of the fourth degree with three independent constants. Methods to experimentally determine these constants are pointed out. A method for the calculation of mechanical losses in rubber compounds in a complex stressed state is suggested using the measurement data for simple modes of loading.
Uniformity of Tire-Wheel Assemblies
Authors: Schuring D. J.
Published: June 2006

Interactions between the tire and wheel of an assembly are adding extra nonuniformities to those of the tire and wheel themselves. The additional nonuniformities are not small. In one example their average effect on the radial force was 25 to 30 N for two commercial wheels, and 10 N for a precision-machined wheel.

Interaction forces are acting randomly and hence are seriously disturbing any tire-wheel matching effort. A simple statistical model is suggested, describing their distribution and allowing an estimation of their effects on tire-wheel matching.

At this time no leading cause for the existence of interaction forces is known; they seem to accrue from many different minor sources. It is to be hoped that the continuous refinements achieved in the tire and wheel manufacturing processes will eventually reduce all non-uniformities, including interaction forces, to levels that would render tire-wheel matching unnecessary.
A Quantitative Theory for the Computation of Tire Friction Under Severe Conditions of Sliding
Authors: Ettles C. M. Mc C.
Published: June 2006

It is proposed that tire-pavement friction is controlled by thermal rather than by hysteresis and viscoelastic effects. A numerical model of heating effects in sliding is described in which the friction coefficient emerges as a dependent variable. The overall results of the model can be expressed in a closed form using Blok's flash temperature theory. This allows the factors controlling rubber friction to be recognized directly.

The model can be applied in quantitative form to metal-polymer-ice contacts. Several examples of correlation are given. The difficulties of characterizing the contact conditions in tire-pavement friction reduce the model to qualitative form. Each of the governing parameters is examined in detail. The attainment of higher friction by small, discrete particles of aluminum filler is discussed.
The Driving Severity Number (DSN) — A Step Toward Quantifying Treadwear Test Conditions
Authors: Veith A. G.
Published: June 2006

A system, called the “Driving Severity Monitor” (DSM), has been developed for characterizing tire force distribution as related to treadwear in either normal tire use or in tire fleet testing in a convoy. The system consists of an accelerometer for monitoring lateral accelerations, a wheel revolution counter, and a module for signal processing and read-out. The output of the DSM is reduced to a single index, the Driving Severity Number (DSN), which characterizes a vehicle journey. The DSN is equal to the sum of squares of lateral acceleration measured once per tire revolution during a trip, divided by the number of wheel revolutions. The DSN had a high degree of correlation (R ≧ 0.95) with treadwear in two wear programs when pavement abrasiveness was held constant. This supports the concept that the three basic treadwear components: tire force distribution, pavement abrasiveness, and ambient temperature, can be separated for better understanding of tire treadwear.
Numerical Results of Tire-Test Drum Interaction
Authors: Laging G. , Rothert H.
Published: June 2006

Inflated tires without grooves have been examined both numerically and experimentally for behavior under vertical and horizontal loads. Complete load-deformation analysis of the contact area was emphasized. Both two-dimensional and three-dimensional models were investigated.

The three-dimensional approach includes geometrical non-linearities, hyperelastic material properties, deformation-dependent load components, and a contact problem with friction. Any contact surface contour can be included in the computation by introducing local coordinates for each node in the footprint area. Test drum experiments can thus be used for comparison.

Extensive experimental and numerical studies were done on tires quasi-statically loaded against convex and concave drums. Results seem to confirm the need for plane-surface test devices. The main reason for this is the nonlinear relation of the size of the contact area to the stress distribution or to the maximum stress values.
Predictive Indoor Wheel Testing of Heavy Duty Truck Tires
Authors: Keefe R. L.
Published: June 2006

An indoor wheel test for heavy duty truck tires has been developed to predict in-service failures of commercial and developmental tires. The test, run at slow speed and high load to emphasize stress and fatigue rather than heat, is based on the premise that repeated high stress is the principal cause of in-service tire failure. These stresses occur when dynamic or transient overloads are caused by road bumps, load transfer during braking and cornering, or dual tire configuration on non-uniform surfaces. Although these overloads may occur infrequently, they can become very significant in the long distances run by truck tires. Other current heavy duty truck tire tests are generally run at higher speeds, emphasizing heat resistance of rubber compounds, or else are low-speed, much-overloaded bead tests which are unrealistically severe. Since its development in 1974 the present test has been broadly predictive for many belt, carcass, or fatigue related in-service failures of both bias and radial commercial and developmental truck tires. The test is called “The DuPont High Load Wheel Test” to distinguish it from other low-speed-high-load tests.
Wear Measurements on Rubber Compounds
Authors: Bottasso F. , Giuliani G. P. , Nahmias M.
Published: June 2006

A test procedure is described which permits isolation of controllable variables such as the formula, the curing cycle, and the curing temperature on the intrinsic wear rate of tire tread compounds under low-severity conditions of use. The specimen, in the form of a rubber roller, rotates in contact with a solid wheel. Both a vertical load and a braking torque may be applied to obtain pressures and slippage in the contact area that are typical for pneumatic tires in service. The specimen has a central core, made of a suitable compound, and a thin outer layer made of the compound to be tested. This keeps the contact area and the specimen temperature constant so that they do not affect measurements of intrinsic wear rate of the compound. Some effects of temperature on intrinsic wear rate are discussed.
Fourier Transform Applications to Tire Life Testing
Authors: Potts G. R.
Published: June 2006

The Fast Fourier Transform (FFT) has been used increasingly in such tire tests as uniformity, ride vibration analysis, acoustic intensity measurement, and modal analysis of tire and vehicle structures. A new application for the FFT is in monitoring tire endurance and high speed tests to identify significant changes in tire structural integrity and to provide advanced warning of impending tire failure so that the test may be terminated prior to ultimate failure of the tire. Greater information concerning the initiation of failure can then be obtained than is possible by trying to reconstruct the remains of a failed tire. Continuous display of FFT analysis of tire carriage vibrations reveals one to fifteen harmonics of tire rotation frequency on a new tire, with higher harmonics growing with test time. Just prior to failure, these higher harmonics grow in unison to very high levels with a “white-harmonic” spectrum appearing. Since the tire would then fail within 5 to 20 seconds, the test should be terminated. This paper details the techniques applied and the results obtained to date in creating a test monitoring program that will notify the test operator of significant test developments, and in automatic shutdown of tires nearing failure.
Steering Pull and Residual Aligning Torque
Authors: Matyja F. E.
Published: June 2006

A laboratory method is described for measuring residual aligning torque, which is presented as a predictor of tire contribution to steering pull. Results from a new steering pull test are compared with those for conicity levels on tire combinations having differing aligning torques. The individual contributions of conicity and plysteer to residual aligning torque are discussed, as are correlations between residual aligning torque values obtained in two laboratories. The effect of tire belt angle and tread design on residual aligning torque is shown in three experiments.
Rubber Fracture Characterization Using J-Integral
Authors: Chow C. L. , Wang J. , Tse P. N.
Published: June 2006

The use of the J-integral to investigate fracture characterization in a carbon black reinforced natural rubber is described. Three applications to crack initiation are included: two based on the use of a hypothetical zero specimen length and one on conventional testing procedures for metals. While the validity of the zero-length methods is questionable, the conventional method yielded a consistent Jc value of 1.01 N/mm for a typical tire compound. This value was obtained from 24 combinations of varying specimen geometries and pre-crack lengths. The J-integral is revealed as a valid fracture parameter that is applicable not only for material evaluation but also for designing tire structures to resist premature failure. These conclusions disagree with those from an earlier investigation, so the causes for the discrepancies are examined and discussed.