Lateral Tire Forces on Wet Roads

1977 ◽  
Vol 5 (2) ◽  
pp. 75-82 ◽  
Author(s):  
A. Schallamach
Keyword(s):  
Normal Load ◽  
The Self ◽  
Experimental Results ◽  
Slip Angle ◽  
Tire Model ◽  
Side Force ◽  
Tire Forces

Abstract Expressions are derived for side force and self-aligning torque of a simple tire model on wet roads with velocity-dependent friction. The results agree qualitatively with experimental results at moderate speeds. In particular, the theory correctly predicts that the self-aligning torque can become negative under easily realizable circumstances. The slip angle at which the torque reverses sign should increase with the normal load.

Theoretical Tire Model Considering Two-Dimensional Contact Patch for Force and Moment

2021 ◽  
Author(s):  
Y. Nakajima ◽  
S. Hidano
Keyword(s):  
Finite Element Method ◽  
Shear Force ◽  
The Self ◽  
Slip Angle ◽  
Force Distribution ◽  
Two Dimensional ◽  
Tire Model ◽  
Side Force ◽  
Contact Patch ◽  
Proposed Model

ABSTRACT The new theoretical tire model for force and moment has been developed by considering a two-dimensional contact patch of a tire with rib pattern. The force and moment are compared with the calculation by finite element method (FEM). The side force predicted by the theoretical tire model is somewhat undervalued as compared with the FEM calculation, while the self-aligning torque predicted by the theoretical tire model agrees well with the FEM calculation. The shear force distribution in a two-dimensional contact patch under slip angle predicted by the proposed model qualitatively agrees with the FEM calculation. Furthermore, the distribution of the adhesion region and sliding region in a two-dimensional contact patch predicted by the theoretical tire model qualitatively agrees with the FEM calculation.

Validation of a High-Fidelity Finite Element Tire Model on Pavement

2020 ◽  
Author(s):  
Tamer Wasfy ◽  
Hatem Wasfy ◽  
Paramsothy Jayakumar ◽  
Srinivas Sanikommu
Keyword(s):  
Finite Element ◽  
Normal Load ◽  
Rolling Resistance ◽  
Lateral Force ◽  
Longitudinal Force ◽  
Friction Model ◽  
Rubber Matrix ◽  
Slip Angle ◽  
High Fidelity ◽  
Tire Model

Abstract The objective of this study is to validate a high-fidelity finite element tire model on hard pavement. In this model, the tire rubber matrix is modeled using locking-free brick elements with embedded thin beam elements along the tire’s circumference, meridian, and diagonals for modeling the tire’s reinforcements (belt, ply and bead). The internal air pressure is applied as a distributed force on the inner surface of the brick elements. Frictional contact between the outer surface of the brick elements and the pavement is modeled using the penalty method along with an asperity based Coulomb friction model. In order to validate the tire model, a medium duty truck tire is modeled and the following response quantities are compared to experimental results: (1) normal load versus deflection at different tire pressures; (2) rolling resistance versus speed; (3) longitudinal force versus slip; (4) lateral force versus slip angle for different normal loads; and (5) self-aligning torque versus slip angle for different normal loads.

Distribution of Side Force and Side Slip in the Contact Area of the Pneumatic Tire

1959 ◽  
Vol 32 (2) ◽  
pp. 490-502
Author(s):  
D. H. Cooper
Keyword(s):  
Contact Area ◽  
Contact Spot ◽  
The Self ◽  
Slip Angle ◽  
Vertical Force ◽  
Pneumatic Tire ◽  
Side Force

Abstract It is well known that, when a pneumatic tire is rolled over dry ground at a slip angle, a sideways force is developed. With the cornering force rig described here we are able to measure the front to rear distribution of the cornering force along the contact spot, the length of the contact area, the trail and the self-aligning torque. At the same time it is possible to derive the shape of the distorted tread and the front to rear distribution of side slip in the contact spot. By making certain assumptions concerning the distribution of the vertical force along the contact spot a relationship has been established between the forces of friction, rate of side slip and speed of rolling.

A Modified Dugoff Tire Model for Combined-slip Forces

2010 ◽  
Vol 38 (3) ◽  
pp. 228-244 ◽  
Author(s):  
Nenggen Ding ◽  
Saied Taheri
Keyword(s):  
Vehicle Dynamics ◽  
Tire Model ◽  
Magic Formula ◽  
Model Based ◽  
Proposed Model ◽  
Road Friction ◽  
On Line ◽  
Double Lane Change ◽  
Tire Forces ◽  
Tire Models

Abstract Easy-to-use tire models for vehicle dynamics have been persistently studied for such applications as control design and model-based on-line estimation. This paper proposes a modified combined-slip tire model based on Dugoff tire. The proposed model takes emphasis on less time consumption for calculation and uses a minimum set of parameters to express tire forces. Modification of Dugoff tire model is made on two aspects: one is taking different tire/road friction coefficients for different magnitudes of slip and the other is employing the concept of friction ellipse. The proposed model is evaluated by comparison with the LuGre tire model. Although there are some discrepancies between the two models, the proposed combined-slip model is generally acceptable due to its simplicity and easiness to use. Extracting parameters from the coefficients of a Magic Formula tire model based on measured tire data, the proposed model is further evaluated by conducting a double lane change maneuver, and simulation results show that the trajectory using the proposed tire model is closer to that using the Magic Formula tire model than Dugoff tire model.

An Implicit to Explicit FEA Solving of Tire F&M with Detailed Tread Blocks

2012 ◽  
Vol 40 (2) ◽  
pp. 83-107 ◽  
Author(s):  
Zhao Li ◽  
Ziran R. Li ◽  
Yuanming M. Xia
Keyword(s):  
Test System ◽  
Mapping Method ◽  
Friction Model ◽  
Experimental Results ◽  
Slip Angle ◽  
Slip Ratio ◽  
The Road ◽  
Numerical Noise ◽  
Nonlinear Stress ◽  
Solving Strategy

ABSTRACT A detailed tire-rolling model (185/75R14), using the implicit to explicit FEA solving strategy, was constructed to provide a reliable, dynamic simulation with several modeling features, including mesh, material modeling, and a solving strategy that could contribute to the consideration of the serious numerical noises. High-quality hexahedral meshes of tread blocks were obtained with a combined mapping method. The actual rubber distributing and nonlinear, stress-strain relationship of the rubber and bilinear elastic reinforcement were modeled for realism. In addition, a tread-rubber friction model obtained from the Laboratory Abrasion and Skid Tester (LAT 100) was applied to simulate the interaction of the tire with the road. The force and moment (F&) behaviors of tire cornering when subjected to a slip-angle sweep of −10 to 10° were studied with that model. To demonstrate the efficiency of the proposed simulation, the computed F&M were compared with experimental results from an MTS Flat-Trac Tire Test System. The computed cornering F&M agreed well with the experimental results, so the footprint shape and contact pressure distribution of several cornering conditions were investigated. Furthermore, the longitudinal forces in response to braking/driving torque application in a slip-ratio range of −100% to 100% were computed. The proposed FEA solution confines the numerical noise within a smaller range and can serve as a valid tool in tire design.

RAMAN SPECTRA OF THE H2SO4–SO3 AND D2SO4–SO3 SYSTEMS: EVIDENCE FOR THE OCCURRENCE OF POLYSULPHURIC ACIDS

1962 ◽  
Vol 40 (4) ◽  
pp. 658-674 ◽  
Author(s):  
R. J. Gillespie ◽  
E. A. Robinson
Keyword(s):  
Sulphuric Acid ◽  
Raman Spectra ◽  
Ionic Species ◽  
The Self ◽  
Experimental Results ◽  
Similar Work ◽  
Stretching Vibrations ◽  
Sulphur Trioxide ◽  
High Concentrations

The Raman spectra of oleums, i.e. mixtures of sulphur trioxide and sulphuric acid, have been re-examined. Similar measurements on the sulphur trioxide – deuterosulphuric acid (D2SO4) system are also reported. The experimental results and conclusions of previous similar work on oleums are discussed. By comparison of the spectra of oleums with those of the polysulphuryl halides it is shown that the polysulphuric acids H2S2O7 and H2S3O10 are present in this system. The increase in the frequency of the SO2 stretching vibrations with increasing concentration of sulphur trioxide gives evidence for the existence of higher polysulphuric acids such as H2S4O13 at high concentrations of sulphur trioxide. In relatively concentrated oleum, sulphur trioxide monomer and trimer are also present. It is shown that the self-dissociation of liquid H2S2O7 gives mainly molecular H2S2O10 and H2SO4 and not ionic species. The conclusions reached from the interpretation of the Raman spectra of the D2SO4–SO3 system are similar to those arrived at for sulphuric acid oleums. The spectra of solutions of NaHSO4 in oleums were also examined, and are discussed.

scholarly journals Thermomechanical Couplings in Aircraft Tire Rolling/Sliding Modeling

2011 ◽  
Vol 274 ◽  
pp. 81-90 ◽  
Author(s):  
Ange Kongo Kondé ◽  
Iulian Rosu ◽  
F. Lebon ◽  
L. Seguin ◽  
Olivier Brardo ◽  
...  
Keyword(s):  
Friction Coefficient ◽  
Thermal Effects ◽  
Coulomb Friction ◽  
Large Deformations ◽  
Element Model ◽  
Slip Angle ◽  
Tire Model ◽  
Vertical Load ◽  
Coulomb Friction Law ◽  
Lateral Friction

This paper presents a finite element model for the simulation of aircraft tire rolling. Large deformations, material incompressibility, heterogeneities of the material, unilateral contact with Coulomb friction law are taken into account. The numerical model will allow estimating the forces in the contact patch - even in critical and extreme conditions for the aircraft safety and security. We show the influence of loading parameters (vertical load, velocity, inflating pressure) and slip angle on the Self Aligning torque and on the lateral friction coefficient. A friction coefficient law corresponding to Chichinadze model is considered to take into account thermal effects in the aircraft tire model behaviour.

scholarly journals A Self-Supervised Tibetan-Chinese Vocabulary Alignment Method based on Adversarial Learning

2021 ◽  
Author(s):  
Enshuai Hou ◽  
Jie zhu
Keyword(s):  
The Self ◽  
Experimental Results ◽  
Chinese Characters ◽  
Training Method ◽  
Alignment Method ◽  
Adversarial Learning ◽  
Semantic Correlation ◽  
Data Alignment ◽  
Similarity Calculation ◽  
Adversarial Training

Tibetan is a low-resource language. In order to alleviate the shortage of parallel corpus between Tibetan and Chinese, this paper uses two monolingual corpora and a small number of seed dictionaries to learn the semi-supervised method with seed dictionaries and self-supervised adversarial training method through the similarity calculation of word clusters in different embedded spaces and puts forward an improved self-supervised adversarial learning method of Tibetan and Chinese monolingual data alignment only. The experimental results are as follows. First, the experimental results of Tibetan syllables Chinese characters are not good, which reflects the weak semantic correlation between Tibetan syllables and Chinese characters; second, the seed dictionary of semi-supervised method made before 10 predicted word accuracy of 66.5 (Tibetan - Chinese) and 74.8 (Chinese - Tibetan) results, to improve the self-supervision methods in both language directions have reached 53.5 accuracy.

scholarly journals Experimental Study and Extended Finite Element Simulation of Fracture of Self-Compacting Rubberized Concrete

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Xinquan Wang ◽  
Hongguo Diao ◽  
Yunliang Cui ◽  
Changguang Qi ◽  
Shangyu Han
Keyword(s):  
Finite Element ◽  
Loading Rate ◽  
High Performance Concrete ◽  
The Self ◽  
Experimental Results ◽  
Crack Mouth Opening Displacement ◽  
Displacement Curve ◽  
Rubberized Concrete ◽  
Extended Finite Element ◽  
Self Compacting Concrete

Self-compacting rubberized concrete (SCRC) is a high-performance concrete that can achieve compacting effect by self-gravity without vibration during pouring. Because of its excellent fluidity, homogeneity, and stability, the application of self-compacting concrete in engineering can improve work efficiency and reduce project cost. The effects of loading rate on the fracture behavior of self-compacting concrete were studied in this paper. Three-point bend (TPB) tests were carried out at five loading rates of 1, 0.1, 0.001, 0.0001, and 0.00001 mm/s. The dimensions of the specimens were 100  mm × 100 mm × 400 mm. A precast crack was set in the middle of the specimen with a notch-depth ratio of 0.4. The experimental results show that the peak load on the load-CMOD (crack mouth opening displacement) curve gradually increases with the increase of the loading rate. Although the fracture energy a presented greater dispersion under the loading rate of 1 mm/s, the overall changes were still rising with the increase of the loading rate. Besides studying the softening characteristics of the self-compacting concrete, the constitutive softening curve of the self-compacting concrete was obtained using the bilinear model. Finally, curved three-point bending beams were simulated by using the extended finite element method based on ABAQUS. The fracture process of the self-compacting concrete under different loading conditions was analyzed more intuitively. The simulation results were compared with the experimental results, and the same conclusions were obtained.

scholarly journals Multivariate Self-Dual Morphological Operators Based on Extremum Constraint

2015 ◽  
Vol 2015 ◽  
pp. 1-16
Author(s):  
Tao Lei ◽  
Yi Wang ◽  
Weiwei Luo
Keyword(s):  
Noise Removal ◽  
Complete Characterization ◽  
The Self ◽  
Experimental Results ◽  
Watershed Transformation ◽  
Morphological Operators ◽  
Self Duality ◽  
Multichannel Images ◽  
Duality Property ◽  
Image Details

Self-dual morphological operators (SDMO) do not rely on whether one starts the sequence with erosion or dilation; they treat the image foreground and background identically. However, it is difficult to extend SDMO to multichannel images. Based on the self-duality property of traditional morphological operators and the theory of extremum constraint, this paper gives a complete characterization for the construction of multivariate SDMO. We introduce a pair of symmetric vector orderings (SVO) to construct multivariate dual morphological operators. Furthermore, utilizing extremum constraint to optimize multivariate morphological operators, we construct multivariate SDMO. Finally, we illustrate the importance and effectiveness of the multivariate SDMO by applications of noise removal and segmentation performance. The experimental results show that the proposed multivariate SDMO achieves better results, and they suppress noises more efficiently without losing image details compared with other filtering methods. Moreover, the proposed multivariate SDMO is also shown to have the best segmentation performance after the filtered images via watershed transformation.

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