Structural Stiffness of Tire Calculated From Strain Energy

2015 ◽  
Author(s):  
Namcheol Kang ◽  
Jong-Jin Bae ◽  
Jong Beom Suh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Energy Method ◽  
Strain Energy ◽  
Vertical Force ◽  
Structural Stiffness ◽  
Contribution Ratio ◽  
The Finite Element Method ◽  
Vertical Stiffness ◽  
Strain Energy Method

The vertical stiffness of a tire is the ratio of the vertical force to the deflection; it can be expressed as the summation of the structural stiffness and air stiffness. However, the calculation of the structural stiffness is a challenging topic. This paper presents a new methodology for extracting the structural stiffness from the strain energy of a regular tire. In order to verify our proposed method, the vertical force-deflection results from the finite element method is compared with those from the strain energy method at zero air pressure. Also the results for an inflated tire are compared to calculate the structural stiffness. Finally, we calculated the contribution ratio of the tire components and used an alternative way of extracting the structural stiffness based on changing the Young’s modulus.

Stress Analysis of a Tire Under Vertical Load by a Finite Element Method

1977 ◽  
Vol 5 (2) ◽  
pp. 102-118 ◽  
Author(s):  
H. Kaga ◽  
K. Okamoto ◽  
Y. Tozawa
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computer Program ◽  
Temperature Rise ◽  
Strain Energy ◽  
Internal Stresses ◽  
Vertical Load ◽  
The Finite Element Method ◽  
Internal Temperature ◽  
Element Method

Abstract An analysis by the finite element method and a related computer program is presented for an axisymmetric solid under asymmetric loads. Calculations are carried out on displacements and internal stresses and strains of a radial tire loaded on a road wheel of 600-mm diameter, a road wheel of 1707-mm diameter, and a flat plate. Agreement between calculated and experimental displacements and cord forces is quite satisfactory. The principal shear strain concentrates at the belt edge, and the strain energy increases with decreasing drum diameter. Tire temperature measurements show that the strain energy in the tire is closely related to the internal temperature rise.

scholarly journals Improved Expression for Estimation of Leakage Inductance in E Core Transformer Using Energy Method

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
Sivananda Reddy Thondapu ◽  
Mangesh B. Borage ◽  
Yashwant D. Wanmode ◽  
Purushottam Shrivastava
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Energy Method ◽  
Fem Analysis ◽  
Field Pattern ◽  
The Finite Element Method ◽  
Leakage Inductance ◽  
Accurate Expression ◽  
Element Method

This paper proposes a simpler and more accurate expression for estimation of leakage inductance in E core transformer, which is the most widely used transformer structure. The derived expression for leakage inductance accounts for the flux extending into air. The finite element method (FEM) analysis is made on the secondary shorted transformer to observe the H-field pattern. The results obtained from FEM analysis are used for approximating the field that is extending into air to derive an expression for leakage inductance. This expression is experimentally validated on prototype transformers of different core dimensions.

Postbuckling Behavior of Axially-Compressed Strips With Discrete Rigid Constraints: A Numerical Study

2015 ◽  
Author(s):  
Suihan Liu ◽  
Nan Hu ◽  
Rigoberto Burgueño
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Strain Energy ◽  
Numerical Study ◽  
Kinetic Energy Release ◽  
The Finite Element Method ◽  
Postbuckling Behavior ◽  
Sudden Release ◽  
Mode Transitions ◽  
Design Freedom

Axially-compressed columns, or strips, with bilateral continuous rigid constraints (CRC) are known to be able to attain multiple snap-through buckling events in their elastic postbuckling response that lead to the sudden release of strain energy from the system. This feature allows this structural prototype to be used as energy concentrators for smart applications. However, the parameters controlling the postbuckling response for such system are limited. The structural prototype discussed in this paper is that of an axially compressed strip provided with discrete rigid constraints (DRC), whereby the layout of the lateral constrains provides increased design freedom to control the strip’s postbuckling features. The study is based on numerical simulations using the finite element method. Using a previously characterized CRC strip as a baseline, two DRC design groups were considered in symmetric and asymmetric layouts for a total of 15 different arrangements. Results show that DRC strips can attain elastic postbuckling responses with distinct characteristics and that the far postbuckling response can be controlled by modifying the number and the location of the constraints. Compared to CRC strips, some DRC patterns allow attaining higher mode transitions and larger kinetic energy release after the first buckling event. The ability to design for such postbuckling response features can be potentially used for energy harvesting and other sensing and actuation applications.

scholarly journals Development and Optimization for a New Planar Spring Using Finite Element Method, Deep Feedforward Neural Networks, and Water Cycle Algorithm

2021 ◽  
Vol 2021 ◽  
pp. 1-25
Author(s):  
Ngoc Le Chau ◽  
Hieu Giang Le ◽  
Van Anh Dang ◽  
Thanh-Phong Dao
Keyword(s):  
Neural Network ◽  
Finite Element Method ◽  
Finite Element ◽  
Strain Energy ◽  
Water Cycle ◽  
Feedforward Neural Network ◽  
The Finite Element Method ◽  
Water Cycle Algorithm ◽  
Balance Mechanism ◽  
Element Method

The gravity balance mechanism plays a vital role in maintaining the equilibrium for robots and assistive devices. The purpose of this paper was to optimize the geometry of a planar spring, which is an essential element of the gravity balance mechanism. To implement the optimization process, a hybrid method is proposed by combining the finite element method, the deep feedforward neural network, and the water cycle algorithm. Firstly, datasets are collected using the finite element method with a full experiment design. Secondly, the output datasets are normalized to eliminate the effects of the difference of units. Thirdly, the deep feedforward neural network is then employed to build the approximate models for the strain energy, deformation, and stress of the planar spring. Finally, the water cycle algorithm is used to optimize the dimensions of the planar spring. The results found that the optimal geometries of the spring include the length of 45 mm, the thickness of 1.029 mm, the width of 9 mm, and the radius of 0.3 mm. Besides, the predicted results determined that the strain energy, the deformation, and the stress are 0.01123 mJ, 33.666 mm, and 79.050 MPa, respectively. The errors between the predicted result and the verifying results for the strain energy, the deformation, and the stress are about 1.87%, 1.69%, and 3.06%, respectively.

A Microstructurally Based Orthotropic Hyperelastic Constitutive Law

2002 ◽  
Vol 69 (5) ◽  
pp. 570-579 ◽  
Author(s):  
J. E. Bischoff ◽  
E. A. Arruda ◽  
K. Grosh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Constitutive Model ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Entropy Change ◽  
Constitutive Law ◽  
Elastic Behavior ◽  
The Finite Element Method

A constitutive model is developed to characterize a general class of polymer and polymer-like materials that displays hyperelastic orthotropic mechanical behavior. The strain energy function is derived from the entropy change associated with the deformation of constituent macromolecules and the strain energy change associated with the deformation of a representative orthotropic unit cell. The ability of this model to predict nonlinear, orthotropic elastic behavior is examined by comparing the theory to experimental results in the literature. Simulations of more complicated boundary value problems are performed using the finite element method.

Computation of Bolted Joint Stiffness Using Strain Energy

2005 ◽  
Author(s):  
Christopher T. Allen ◽  
Thomas L. Cost
Keyword(s):  
Finite Element ◽  
Energy Method ◽  
Strain Energy ◽  
Three Dimensional ◽  
Joint Stiffness ◽  
Accurate Method ◽  
Bolted Joints ◽  
Finite Element Models ◽  
Comprehensive Method ◽  
Strain Energy Method

The joint stiffness of preloaded, bolted connections were determined using strain energy calculations from finite element models. The strain energy method, proposed here, provides a new, more comprehensive method for interpreting results from finite element models than methods used previously. Previous works using finite element models have approximated joint stiffness values by computing the average deflections at the bolt-head-to-member interface and dividing this into the applied load in the bolt. Other works have enforced a uniform deflection at the bolt-head-to-member interface, effectively ignoring the coupled stiffness of the bolt head and abutment. Three-dimensional finite elements were used to model axisymmetric bolted joints. Bolt head geometry was modeled to account for the coupled bending stiffness at the bearing interface. The strain energy method was verified by comparison with previously published results. Results indicate that the strain energy method represents a simple and accurate method for calculating joint stiffness values.

Evaluating the time-varying mesh stiffness of a planetary gear set using the potential energy method

2013 ◽  
Vol 228 (3) ◽  
pp. 535-547 ◽  
Author(s):  
Xihui Liang ◽  
Ming J Zuo ◽  
Tejas H Patel
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Potential Energy ◽  
Energy Method ◽  
Analytical Method ◽  
Planetary Gear ◽  
Time Varying ◽  
The Finite Element Method ◽  
Mesh Stiffness ◽  
Potential Energy Method

Time-varying mesh stiffness is a periodic function caused by the change in the number of contact tooth pairs and the contact positions of the gear teeth. It is one of the main sources of vibration of a gear transmission system. An efficient and effective way to evaluate the time-varying mesh stiffness is essential to comprehensively understand the dynamic properties of a planetary gear set. According to the literature, there are two ways to evaluate the gear mesh stiffness, the finite element method and the analytical method. The finite element method is time-consuming because one needs to model every meshing gear pair in order to know the mesh stiffness of a range of gear pairs. On the other hand, analytical method can offer a general approach to evaluate the mesh stiffness. In this study, the potential energy method is applied to evaluate the time-varying mesh stiffness of a planetary gear set. Analytical equations are derived without any modification of the gear tooth involute curve. The developed equations are applicable to any transmission structure of a planetary gear set. Detailed discussions are given to three commonly used transmission structures: fixed carrier, fixed ring gear and fixed sun gear.

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