Calculated Deflected Contours and Load-Deflection Curves for Tires

1968 ◽  
Vol 41 (4) ◽  
pp. 977-987
Author(s):  
S. D. Gehman
Keyword(s):  
Approximation Method ◽  
Elliptic Integrals ◽  
Deflection Curve ◽  
Load Axis ◽  
Incomplete Elliptic Integrals ◽  
Load Deflection Curve

Abstract The tire contour equation is derived for a flexible tire body with radial cords and a complete circumferential deflection, corresponding to the case of a radial-ply tire or a tire inflated inside a constraining cylinder. Equations are derived to calculate the load on a single cord in the deflected region using parameters of the un-deflected contour. It is then shown how the reasoning and equations can be generalized for a tire body with any cord path having a complete circumferential deflection so that the load-deflection curve for a single cord can be calculated. A new approximation method is described so that the integrals involved in these calculations can be evaluated in terms of incomplete elliptic integrals of the first and second kind with any desired accuracy. Finally, a procedure is given for summing cord loads in the usual spot deflection of a tire so that the load-deflection curve for a flexible tire body can be calculated from contour parameters of the undeflected tire. An illustrative calculation is included. Although the load-deflection curve for a single cord is convex toward the load axis, that for the tire is concave because more cords are involved as deflection progresses. A calculated contour does not exist beyond a limiting deflection, at which, presumably, buckling starts above the bead.

Experimental Study on Mechanical Properties of Rubber Used for Damping Bearing

2011 ◽  
Vol 189-193 ◽  
pp. 1132-1136 ◽  
Author(s):  
Yong Xu Zhao ◽  
Wen Jun Hu ◽  
Jun Mei ◽  
Niu Wei ◽  
Jian Jun Xie
Keyword(s):  
Mechanical Properties ◽  
Low Temperature ◽  
Three Dimensional ◽  
Middle Part ◽  
Loading Conditions ◽  
Deflection Curve ◽  
Rubber Bearing ◽  
Components Analysis ◽  
The Impact ◽  
Load Deflection Curve

After testing on T-type rubber bearing under tensile, compression and shear mechanical properties under different temperature in this paper. Obtained load deflection curve and destructive mode under different loading conditions at -40 and normal temperature of rubber components. Analysis the impact of temperature and the loading conditions that effect on load-elongation and destructive mode of T-type damping rubber structure. It showed that T-end rubber bearing has different kinds of deformation under different force-giving methods. Under compression, the stress pattern of the rubber bearing is three-dimensional and middle rubber bear the greatest force. Under tensile loading, the middle part of the rubber contract and the side with smaller lateral section has greater shrinkage; moreover, damage occurred in the area with stress concentration and weak strength. Under shearing action, extrude faces appeared with crinkle and damage occurred in the middle part of extrude faces. At the low temperature-40 , rubber support still has great elastic properties. The low temperature has a big effect on tensile properties and has little effect on damage properties.

The Incomplete Elliptic Integrals F(k,ϕ) AND E(k,ϕ)

2008 ◽  
pp. 653-669
Author(s):  
Keith B. Oldham ◽  
Jan C. Myland ◽  
Jerome Spanier
Keyword(s):  
Elliptic Integrals ◽  
Incomplete Elliptic Integrals

scholarly journals Effect of Equivalent Load Distribution on the Accuracy of Mapping the Reinforcement Load Deflection Curve in LTP

2020 ◽  
Vol 10 (17) ◽  
pp. 6127
Author(s):  
Beata Gajewska ◽  
Marcin Gajewski
Keyword(s):  
Load Distribution ◽  
Load Transfer ◽  
Single Case ◽  
Soft Soil ◽  
Triangular Distribution ◽  
Deflection Curve ◽  
Measurement Results ◽  
Equivalent Load ◽  
Load Deflection Curve ◽  
Best Fit

The formulations of tasks modelling embankments on soft soil, improved with columns and with reinforced load transfer platform (LTP), differ significantly. One of these differences is the distribution of equivalent load modelling part of the load carried by the LTP reinforcement and soft soil. This article analyses the influence of the nature of the load-modelling linear function, i.e., inverse triangular, uniformly distributed and triangular, as well as intermediate distributions. In total, 41 distributions of equivalent load were considered, and the results of the obtained deflection functions were compared with the measurement results of reinforcement deflection for 5 cases of experimental research available in the literature. A measure of the accuracy of mapping the reinforcement deflection curve was proposed as a relative error in relation to the deflection curve resulting from experimental measurements. Based on the analysis of the mapping error, it was determined that among the three commonly used distributions, the inverse triangular distribution shows the best fit in most of the analysed cases. However, not in every single case this is the distribution leading to a solution that best describes the behaviour of the geosynthetic reinforcement.

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