Analysis of the Contact Deformation of a Radial Tire with Camber Angle

1995 ◽  
Vol 23 (1) ◽  
pp. 26-51 ◽  
Author(s):  
S. Kagami ◽  
T. Akasaka ◽  
H. Shiobara ◽  
A. Hasegawa
Keyword(s):  
Pressure Distribution ◽  
Contact Pressure ◽  
Contact Region ◽  
Contact Deformation ◽  
Contact Pressure Distribution ◽  
Radial Tire ◽  
Ring Model ◽  
Camber Angle ◽  
Contact Free ◽  
Good Agreement

Abstract The contact deformation of a radial tire with a camber angle, has been an important problem closely related to the cornering characteristics of radial tires. The analysis of this problem has been considered to be so difficult mathematically in describing the asymmetric deformation of a radial tire contacting with the roadway, that few papers have been published. In this paper, we present an analytical approach to this problem by using a spring bedded ring model consisting of sidewall spring systems in the radial, the lateral, and the circumferential directions and a spring bed of the tread rubber, together with a ring strip of the composite belt. Analytical solutions for each belt deformation in the contact and the contact-free regions are connected by appropriate boundary conditions at both ends. Galerkin's method is used for solving the additional deflection function defined in the contact region. This function plays an important role in determining the contact pressure distribution. Numerical calculations and experiments are conducted for a radial tire of 175SR14. Good agreement between the predicted and the measured results was obtained for two dimensional contact pressure distribution and the camber thrust characterized by the camber angle.

Contact Pressure Distribution of Radial Tire in Motion With Camber Angle

2000 ◽  
Vol 28 (1) ◽  
pp. 2-32 ◽  
Author(s):  
S. Kim ◽  
K. Kondo ◽  
T. Akasaka
Keyword(s):  
Pressure Distribution ◽  
Contact Pressure ◽  
Basic Equation ◽  
Pressure Sensors ◽  
Contact Pressure Distribution ◽  
Radial Tire ◽  
Mechanical Boundary Condition ◽  
Trapezoidal Shape ◽  
Camber Angle ◽  
Static Form

Abstract Theoretical and experimental study is conducted on the contact pressure distribution of a radial tire in motion under various camber angles. Tire construction is modeled by a spring bedded elastic ring, consisted of sidewall springs and a composite belt ring. The contact area is assumed to be a trapezoidal shape, varying with camber angles and weighted load. The basic equation in a quasi-static form is derived for the deformation of a running belt with a constant velocity by the aid of Lagrange-Euler transformation. Galerkin's method and stepwise calculation are applied for solving the basic equation and the mechanical boundary condition along both sides of the contact belt part subjected to shearing forces transmitted from the sidewall spring. Experimental results on the contact pressure, measured by pressure sensors embedded in the surface of the drum tester, correspond well with the calculated ones for the test tire under various camber angles, running velocities, and weighted loads. These results indicate that a buckling phenomenon of the contact belt in the widthwise direction occurs due to the effect of camber angle.

scholarly journals Load-deflection property and contact pressure distribution of radial tire.

1992 ◽  
Vol 65 (4) ◽  
pp. 241-249
Author(s):  
Shigeru KAGAMI ◽  
Takashi AKASAKA ◽  
Atsushi HASEGAWA
Keyword(s):  
Pressure Distribution ◽  
Contact Pressure ◽  
Contact Pressure Distribution ◽  
Radial Tire

Two-Dimensional Contact Pressure Distribution of a Radial Tire in Motion

1996 ◽  
Vol 24 (4) ◽  
pp. 294-320 ◽  
Author(s):  
H. Shiobara ◽  
T. Akasaka ◽  
S. Kagami
Keyword(s):  
Pressure Distribution ◽  
Contact Pressure ◽  
Fundamental Property ◽  
Leading Edge ◽  
Static Case ◽  
Two Dimensional ◽  
Contact Pressure Distribution ◽  
Radial Tire ◽  
Spring System ◽  
Tread Rubber

Abstract The two-dimensional contact pressure distribution of a running radial tire under load is a fundamental property of the tire structure. The two-dimensional contact pressure distribution in the static case and the one-dimensional contact pressure distribution in the dynamic case were previously analyzed for a spring bedded ring model consisting of a composite belt ring and a spring system for the sidewall and the tread rubber. In this paper, a Voigt-type viscoelastic spring system is assumed for the sidewall and the tread rubber. We analyzed the dynamic deformation of the belt ring in a steady state, and obtained the two-dimensional dynamic contact pressure distribution at speeds up to approximately 60 km/h. The predicted contact pressure distribution for a model with appropriate values for the damping coefficient of each constituent rubber is shown to be in good agreement with experimental results. It is a characteristic feature that increasing velocity yields an increase in the pressure at the leading edge of the crown centerline in the contact area and at the trailing edge of the shoulder line.

Analysis of contact mechanics in McKee-Farrar metal-on-metal hip implants

2003 ◽  
Vol 217 (5) ◽  
pp. 333-340 ◽  
Author(s):  
A Yew ◽  
M Jagatia ◽  
H Ensaff ◽  
Z M Jin
Keyword(s):  
Pressure Distribution ◽  
Contact Pressure ◽  
Contact Region ◽  
Radial Clearance ◽  
Geometrical Parameters ◽  
Contact Pressure Distribution ◽  
Acetabular Cup ◽  
Metal On Metal ◽  
Half Angle ◽  
Maximum Contact

Contact mechanics analysis for a typical McKee-Farrar metal-on-metal hip implant was carried out in this study. The finite element method was used to predict the contact area and the contact pressure distribution at the bearing surfaces. The study investigated the effects of the cement and underlying bone, the geometrical parameters such as the radial clearance between the acetabular cup and the femoral head, and the acetabular cup thickness, as well as other geometrical features on the acetabular cup such as lip and studs. For all the cases considered, the predicted contact pressure distribution was found to be significantly different from that based upon the classical Hertz contact theory, with the maximum value being away from the centre of the contact region. The lip on the cup was found to have a negligible effect on the predicted contact pressure distribution. The presence of the studs on the outside of the cup caused a significant increase in the local contact pressure distribution, and a slight decrease in the contact region. Reasonably good agreement of the predicted contact pressure distribution was found between a three-dimensional anatomical model and a simple two-dimensional axisymmetric model. The interfacial boundary condition between the acetabular cup and the underlying cement, modelled as perfectly fixed or perfectly unbonded, had a negligible effect on the predicted contact parameters. For a given radial clearance of 0.079 mm, the decrease in the thickness of the acetabular cup from 4.5 to 1.5 mm resulted in an increase in the contact half angle from 15° to 26°, and a decrease in the maximum contact pressure from 55 to 20 MPa. For a given acetabular cup thickness of 1.5 mm, a decrease in the radial clearance from 0.158 to 0.0395mm led to an increase in the contact half-angle from 20° to 30°, and a decrease in the maximum contact pressure from 30 to 10 MPa. For zero clearance, although the contact pressure was significantly reduced over most of the contact area, the whole acetabular cup came into contact with the femoral head, leading to stress concentration at the edge of the cup. Design optimization of the geometrical parameters, in terms of the acetabular cup thickness and the radial clearance, is important, not only to minimize the contact stress at the bearing surfaces, but also to avoid equatorial and edge contact.

Two-Dimensional Contact Pressure Distribution of a Radial Tire

1990 ◽  
Vol 18 (2) ◽  
pp. 80-103 ◽  
Author(s):  
T. Akasaka ◽  
M. Katoh ◽  
S. Nihei ◽  
M. Hiraiwa
Keyword(s):  
Pressure Distribution ◽  
Contact Pressure ◽  
Side Wall ◽  
Bending Moment ◽  
Two Dimensional ◽  
Contact Pressure Distribution ◽  
Friction Forces ◽  
Radial Tire ◽  
Pressure Distributions ◽  
Reaction Forces

Abstract 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.

scholarly journals STEPWISE ANALYSIS ON CONTACT PRESSURE DISTRIBUTION OF RADIAL TIRE IN MOTION

1998 ◽  
Vol 71 (1) ◽  
pp. 33-40 ◽  
Author(s):  
Seoknam KIM ◽  
Kyohei KONDO ◽  
Takashi AKASAKA
Keyword(s):  
Pressure Distribution ◽  
Contact Pressure ◽  
Contact Pressure Distribution ◽  
Radial Tire

Experimental analysis of the contact pressure distribution in an off-road tyre

2009 ◽  
Vol 44 (4) ◽  
pp. 287-295 ◽  
Author(s):  
A Cirello ◽  
G Marannano ◽  
G Virzì Mariotti
Keyword(s):  
Pressure Distribution ◽  
Contact Pressure ◽  
Experimental Analysis ◽  
Contact Pressure Distribution ◽  
Cross Sectional ◽  
Road Vehicle ◽  
Nominal Pressure ◽  
Method Of Measurement ◽  
Good Agreement

This paper presents the results of an extended method of measurement on a tyre for an off-road vehicle 175/82 R16, inserting Prescale paper at the contact with the ground. The experimental analysis of the pressures is carried out, in a cross-sectional direction, in five zones corresponding to the middle of the single dowels that constitute the tread. The results are analysed by means of suitable software so as to refer easily to the value of the pressure. The obtained results are critically analysed and the results are compared with those obtained by the formulae of Rowland and MacLaurin, and by the nominal pressure at the ground, concluding that the expression of MMP for vehicles on wheels is simply to consider a pointer of the performances, in comparison with other vehicles or wheels, rather than a real prediction of the pressure on the ground. Furthermore, a good agreement is found between the tyre deflection calculated and measured experimentally.

Rim Slip and Bead Fitment of Tires: Analysis and Design2

2006 ◽  
Vol 34 (1) ◽  
pp. 38-63 ◽  
Author(s):  
C. Lee
Keyword(s):  
Pressure Distribution ◽  
Contact Pressure ◽  
Frictional Torque ◽  
Finite Element Analyses ◽  
Inflation Pressure ◽  
Contact Pressure Distribution ◽  
Design Modification ◽  
Iterative Design ◽  
Slip Resistance ◽  
Braking Torque

Abstract A tire slips circumferentially on the rim when subjected to a driving or braking torque greater than the maximum tire-rim frictional torque. The balance of the tire-rim assembly achieved with weight attachment at certain circumferential locations in tire mounting is then lost, and vibration or adverse effects on handling may result when the tire is rolled. Bead fitment refers to the fit between a tire and its rim, and in particular, to whether a gap exists between the two. Rim slip resistance, or the maximum tire-rim frictional torque, is the integral of the product of contact pressure, friction coefficient, and the distance to the wheel center over the entire tire-rim interface. Analytical solutions and finite element analyses were used to study the dependence of the contact pressure distribution on tire design and operating attributes such as mold ring profile, bead bundle construction and diameter, and inflation pressure, etc. The tire-rim contact pressure distribution consists of two parts. The pressure on the ledge and the flange, respectively, comes primarily from tire-rim interference and inflation. Relative contributions of the two to the total rim slip resistance vary with tire types, depending on the magnitudes of ledge interference and inflation pressure. Based on the analyses, general guidelines are established for bead design modification to improve rim slip resistance and mountability, and to reduce the sensitivity to manufacturing variability. An iterative design and analysis procedure is also developed to improve bead fitment.

One-Dimensional Contact Pressure Distribution of Radial Tires in Motion

1995 ◽  
Vol 23 (2) ◽  
pp. 116-135 ◽  
Author(s):  
H. Shiobara ◽  
T. Akasaka ◽  
S. Kagami ◽  
S. Tsutsumi
Keyword(s):  
Pressure Distribution ◽  
Contact Pressure ◽  
Experimental Studies ◽  
Rolling Resistance ◽  
Leading Edge ◽  
Forward Direction ◽  
Contact Pressure Distribution ◽  
Support Ring ◽  
One Dimensional ◽  
Lowered Pressure

Abstract The contact pressure distribution and the rolling resistance of a running radial tire under load are fundamental properties of the tire construction, important to the steering performance of automobiles, as is well known. Many theoretical and experimental studies have been previously published on these tire properties. However, the relationships between tire performances in service and tire structural properties have not been clarified sufficiently due to analytical and experimental difficulties. In this paper, establishing a spring support ring model made of a composite belt ring and a Voigt type viscoelastic spring system of the sidewall and the tread rubber, we analyze the one-dimensional contact pressure distribution of a running tire at speeds of up to 60 km/h. The predicted distribution of the contact pressure under appropriate values of damping coefficients of rubber is shown to be in good agreement with experimental results. It is confirmed by this study that increasing velocity causes the pressure to rise at the leading edge of the contact patch, accompanied by the lowered pressure at the trailing edge, and further a slight movement of the contact area in the forward direction.

Measurement and Visualization of the Contact Pressure Distribution of Rubber Disks and Tires

1995 ◽  
Vol 23 (4) ◽  
pp. 238-255 ◽  
Author(s):  
E. H. Sakai
Keyword(s):  
Pressure Distribution ◽  
Contact Pressure ◽  
Contact Area ◽  
Light Absorption ◽  
Lateral Force ◽  
Contact Pressure Distribution ◽  
High Definition ◽  
The Road ◽  
Close Relationship ◽  
Processing Techniques

Abstract The contact conditions of a tire with the road surface have a close relationship to various properties of the tire and are among the most important characteristics in evaluating the performance of the tire. In this research, a new measurement device was developed that allows the contact stress distribution to be quantified and visualized. The measuring principle of this device is that the light absorption at the interface between an optical prism and an evenly ground or worn rubber surface is a function of contact pressure. The light absorption can be measured at a number of points on the surface to obtain the pressure distribution. Using this device, the contact pressure distribution of a rubber disk loaded against a plate was measured. It was found that the pressure distribution was not flat but varied greatly depending upon the height and diameter of the rubber disk. The variation can be explained by a “spring” effect, a “liquid” effect, and an “edge” effect of the rubber disk. Next, the measurement and image processing techniques were applied to a loaded tire. A very high definition image was obtained that displayed the true contact area, the shape of the area, and the pressure distribution from which irregular wear was easily detected. Finally, the deformation of the contact area and changes in the pressure distribution in the tread rubber block were measured when a lateral force was applied to the loaded tire.

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