A Mathematical Model for a Tire Sidewall

1970 ◽  
Vol 43 (5) ◽  
pp. 1055-1069
Author(s):  
S. K. Clark ◽  
I. K. McIvor
Keyword(s):  
Load Distribution ◽  
Experimental Studies ◽  
Side Wall ◽  
Radius Of Curvature ◽  
Wall Region ◽  
Center Line ◽  
Stress Distributions ◽  
Contact Patch ◽  
Load Fluctuation ◽  
Zero Degree

Abstract A number of previous experimental studies on the cord load distribution in loaded and inflated bias-ply tires have revealed greatly different cord load fluctuation patterns between the crown and the side-wall regions of the tire. Typical among these is data taken from reference, where the cord load fluctuation measured at the crown center line of a typical bias-ply tire is as shown in Figure 1. The symmetry of this figure is easily explained by either bending or shell membrane considerations or by some combination of these. On the other hand, cord load fluctuations measured in the side wall of a bias-ply tire typically show fluctuations such as shown in Figures 2 or 3, also taken from the previously cited reference. Both of these latter figures show considerable asymmetry of the cord load as a function of position diagrams as the loaded tire is rolled through the contact patch. Bending of the side wall cannot account for such behavior as shown in Figures 2 or 3, since the changes in radius of curvature in the side wall region are completely symmetric about the center line through the contact patch, denoted by the zero degree point in Figures 2 and 3. Simple pressure vessel considerations are also not capable of explaining such diagrams, since changes in curvature in the side wall region are also completely symmetric and hence would result in symmetric stress distributions.

A Modular Race Tire Model Concerning Thermal and Transient Behavior using a Simple Contact Patch Description

2013 ◽  
Vol 41 (4) ◽  
pp. 232-246
Author(s):  
Timo Völkl ◽  
Robert Lukesch ◽  
Martin Mühlmeier ◽  
Michael Graf ◽  
Hermann Winner
Keyword(s):  
Load Distribution ◽  
Thermal Condition ◽  
Transient Behavior ◽  
Wheel Load ◽  
Contact Patch ◽  
Fundamental Parameters ◽  
Dry Conditions ◽  
Simple Contact ◽  
Tire Forces ◽  
Descriptive Set

ABSTRACT The potential of a race tire strongly depends on its thermal condition, the load distribution in its contact patch, and the variation of wheel load. The approach described in this paper uses a modular structure consisting of elementary blocks for thermodynamics, transient excitation, and load distribution in the contact patch. The model provides conclusive tire characteristics by adopting the fundamental parameters of a simple mathematical force description. This then allows an isolated parameterization and examination of each block in order to subsequently analyze particular influences on the full model. For the characterization of the load distribution in the contact patch depending on inflation pressure, camber, and the present force state, a mathematical description of measured pressure distribution is used. This affects the tire's grip as well as the heat input to its surface and its casing. In order to determine the thermal condition, one-dimensional partial differential equations at discrete rings over the tire width solve the balance of energy. The resulting surface and rubber temperatures are used to determine the friction coefficient and stiffness of the rubber. The tire's transient behavior is modeled by a state selective filtering, which distinguishes between the dynamics of wheel load and slip. Simulation results for the range of occurring states at dry conditions show a sufficient correlation between the tire model's output and measured tire forces while requiring only a simplified and descriptive set of parameters.

Experimental and Numerical Modal Analysis of Composite Laminated Shells

2019 ◽  
Vol 161 (A1) ◽  
Keyword(s):  
Heat Dissipation ◽  
Mass Matrix ◽  
Experimental Studies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Radius Of Curvature ◽  
Lumped Mass ◽  
Auxiliary Equipment ◽  
Mass Model ◽  
Laminated Shells

The presence of cut outs at different positions of laminated shell component in marine and aeronautical structures facilitate heat dissipation, undertaking maintenance, fitting auxiliary equipment, access ports for mechanical and electrical systems, damage inspection and also influences the dynamic behaviour of the structures. The aim of the present study is to establish a comprehensive perspective of dynamic behavior of laminated deep shells (length to radius of curvature ratio less than one) with cut-out by experiments and numerical simulation. The glass epoxy laminated composite shell has been prepared in the laboratory by resin infusion. The experimental free vibration analysis is carried out on laminated shells with and without cut-out. The mass matrix is developed by considering rotary inertia in a lumped mass model in the numerical modeling. The results obtained from numerical and experimental studies are compared for verification and the consistency between mode shapes is established by applying modal assurance criteria.

scholarly journals The FEM Analysis of Stress Distribution in front of the Crack Tip and Fracture Process in the Elements of Modified and Unmodified Cast Steel G17CrMo5-5

2016 ◽  
Vol 10 (3) ◽  
pp. 201-206
Author(s):  
Robert Pała ◽  
Ihor Dzioba
Keyword(s):  
Stress Distribution ◽  
Cleavage Fracture ◽  
Crack Extension ◽  
Cast Steel ◽  
Experimental Studies ◽  
Fem Analysis ◽  
Initial Moment ◽  
Stress Distributions ◽  
Calculated Stress

Abstract The article presents influence of modification of the low-alloy cast steel G17CrMo5-5 by rare earth metals on stress distribution in front of the crack at the initial moment of the crack extension. Experimental studies include determination of strength and fracture toughness characteristics for unmodified (UM) and modified (M) cast steel. In the numerical computations, experimentally tested specimens SEN(B) were modelled. The true stress–strain curves for the UM and M cast steel are used in the calculation. The stress distributions in front of the crack were calculated at the initial moment of the crack extension. On the basis of data on the particle size inclusions in the UM and M cast steel, and the calculated stress distributions was performed an assessment of the possibility of the occurrence of cleavage fracture. The analysis results indicate that at room temperature for the UM cast steel, there is a possibility of cleavage fracture, while for the M cast steel occurrence of cleavage fracture is negligible.

scholarly journals A Unified View of the Law of the Wall Using Mixing-Length Theory

1973 ◽  
Vol 24 (1) ◽  
pp. 55-70 ◽  
Author(s):  
V C Patel
Keyword(s):  
Friction Velocity ◽  
Critical Value ◽  
Wall Region ◽  
Pressure Gradients ◽  
Mixing Length ◽  
Stress Distributions ◽  
General Validity ◽  
Law Of The Wall ◽  
Unified View ◽  
Mixing Length Theory

SummaryIt is shown that, if the well-known mixing-length formula is regarded simply as a relationship between the velocity and the stress distributions in the wall region of a turbulent flow, then a truly universal distribution of mixing length is sufficient to describe the experimentally observed departures of the velocity distribution from the usual law of the wall as a result of severe pressure gradients and transverse surface curvature. Comparisons have been made with a wide variety of experimental data to demonstrate the general validity of the mixing-length model in describing the flow close to a smooth wall.An extension of the re-laminarisation criterion of Patel and Head, and some experimental evidence, suggest that the thick axisymmetric boundary layer on a slender cylinder placed axially in a uniform stream cannot be maintained in a fully turbulent state for values of the Reynolds number, based on friction velocity and cylinder radius, below a certain critical value.

Scaling of the Hydroelastic Response of Flexible Lifting Bodies in Transitional and Turbulent Flows

2013 ◽  
Author(s):  
Antoine Ducoin ◽  
Yin Lu Young
Keyword(s):  
Turbulent Flows ◽  
Degrees Of Freedom ◽  
Experimental Studies ◽  
Full Scale ◽  
Stress Distributions ◽  
Viscous Effects ◽  
Scaling Methods ◽  
Fluid Properties ◽  
Computational Fluid Dynamics Cfd ◽  
Hydroelastic Response

The objective of this research is to derive and validate scaling relationships for flexible lifting bodies in transitional and turbulent flows. The motivation is to help the design and interpretation of reduced-scale experimental studies of flexible hydrofoils, with focus on the influence of viscous effects on the hydroelastic response. The numerical method is based on a previous validated viscous FSI solver presented in [1]. It is based on the coupling between a commercial Computational Fluid Dynamics (CFD) solver, CFX, and a simple two-degrees-of-freedom (2-DOF) system that simulates the free tip section displacement of a cantilevered, rectangular hydrofoil. To validate the scaling relations, sample numerical results are shown for three geometrically similar models: full scale, 1/2 scale and 1/10 scale. On the fluid side, although the effects of gravity and compressibility are assumed to be negligible, three different methods of scaling the velocity are considered: Reynolds scaling, Froude scaling, and Mach scaling. The three scaling methods produce different velocity scales when the fluid properties and gravitational constant are the same between the model and prototype, which will lead to different scaling for the material properties. The results suggest that by applying Mach scaling (which does not mean the flow is compressible, but simply requires the relative inflow velocity and fluid properties to be the same between the model and the prototype) and Re ≥ 2 × 106, the same material as the full scale could be used, which will lead to similar stress distributions, in addition to similar strains, and hence similar hydroelastic response and failure mechanisms. However, if Re ≤ 2 × 106 and Mach scale is used, a viscous correction is required to properly extrapolate the experimental results to full-scale.

Contact Stress for Toroidal Drive

2003 ◽  
Vol 125 (1) ◽  
pp. 165-168 ◽  
Author(s):  
Lizhong Xu ◽  
Zhen Huang ◽  
Yulin Yang
Keyword(s):  
Elastic Deformation ◽  
Contact Stress ◽  
Load Distribution ◽  
Contact Stresses ◽  
Periodic Change ◽  
Stress Distributions ◽  
Contact Strength ◽  
Optimal Parameters ◽  
Pair Number

Considering the elastic deformation of the rotor and the periodic change of the mesh teeth pair number, the calculation equations of the load distribution for the toroidal drive are presented. Based on the equations, the formulas for calculation of the contact stresses among stator and worm are introduced. By using the above-mentioned formulas, the contact stress distributions for the drive are obtained. The optimal parameters providing for equal contact strength of the stator and worm are determined. These results are useful in manufacture and design of the drive.

scholarly journals Effect of the lead angle and the radius of curvature on the cutting forces in a 5-axis milling of sculptured surfaces

Mechanik ◽  
2018 ◽  
Vol 91 (1) ◽  
pp. 18-22
Author(s):  
Michał Gdula ◽  
Jan Burek
Keyword(s):  
Turbine Blade ◽  
Convex Surface ◽  
Experimental Studies ◽  
Surface Profile ◽  
Radius Of Curvature ◽  
Sculptured Surface ◽  
Sculptured Surfaces ◽  
Inconel 718 Alloy ◽  
Machined Surface ◽  
Lead Angle

Experimental studies are presented, were conducted that aimed at determining the mathematical models of the influence of the lead angle and the radius of curvature of the profile of machined sculptured surface on the components of the cutting force. The object of the experimental studies was a convex and concave surface of a turbine blade of Inconel 718 alloy. The toroid cutter was used for the tests. Based on the results of the study it was found that the lead angle in the machining of the convex surface and concave turbine blade should be continuously varied with the change of radius of curvature in the direction of the machined surface profile.

scholarly journals Impact of a Single Spoiler on Scouring Depth Status Beneath a River Crossing Inclined Pipeline

2018 ◽  
Vol 8 (5) ◽  
pp. 3316-3320
Author(s):  
S. Abbasi ◽  
M. Masoomi ◽  
S. A. Arjmandi
Keyword(s):  
Numerical Models ◽  
Experimental Studies ◽  
Side Wall ◽  
Element Model ◽  
Scour Depth ◽  
Model Flow ◽  
Pipeline Management ◽  
Scouring Depth ◽  
The Impact ◽  
The Finite Element Model

Deep river crossing pipelines utilized to carry fluids are often placed upon the sand bed. Placement of pipe on the non-smooth bed would result in the production of some local gaps beneath the pipe. Asymmetric scouring is one of the main reasons for pipe underwater failures which are significant in pipeline management. So, in designing pipelines, knowing the interaction between pipelines and bed, and predicting the scour depth with respect to the pipe distance from the bed is significant to ensure that the pipe will finally deposit on the bed. Numerical models have been developed for predicting the balance depth of scouring beneath the pipelines. In this paper, the impact of pipe orientation on maximum scour depth beneath the pipelines is investigated. To do this, a pipe is modeled with various angles with the flow. To manage the local scouring, some spoilers are placed and modeled upon some pipes too. Also, in order to know the effects of placement of a pipe at various distances from the bed, the impact of placement of each pipe at a distance of 0.2D, 0.4D and 0.6D is investigated as well. To model the pipe with and without a spoiler, the finite element model Flow-3D is utilized and the results show good accordance with previous experimental studies and proof the current model’s precision in predicting the scour depth. Results show that in the placement of the pipe in angles not investigated before and also with the installing of a spoiler, the scour process has a reverse ratio with the distance which would result in full deposition of the pipe on the bed. The least scour depth belongs to the condition in which the pipe has a 130° angle with the side wall.

Effects of Geometrical Structure on Flows Around a Rotating Disk in an Enclosure

2007 ◽  
Author(s):  
T. Watanabe ◽  
H. Furukawa ◽  
M. Suzuki
Keyword(s):  
Phase Velocity ◽  
Geometrical Structure ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Side Wall ◽  
Rotating Disk ◽  
Disk Surface ◽  
Practical Applications ◽  
Entire Flow ◽  
Radial Gap

Flows around a rotating disk in a cylindrical enclosure are typical models of flows found in fluid machinery and chemical reactors. They have their practical applications and draw engineering interests. When the radius of the disk is infinite, it is known that circular rolls, spiral rolls, turbulent spirals and turbulent spots appear. In this case, the parameters governing the flows are the Reynolds number based on the angular velocity of the disk and the axial gap between the disk surface and the end wall of the enclosure. We consider, in this paper, a more practical configuration. The disk has its thickness comparable with the axial height of the enclosure, and the radial gap between the disk rim and the side wall of the enclosure is not negligible. Vortex flows are driven by the centrifugal force around the disk rim, and they are expected to have effects on the entire flow. We performed numerical and experimental studies and investigated the unsteady three-dimensional behaviors. A new criterion to identify flow patterns is introduced and the Hopf bifurcation points from the axisymmetric flows to the three-dimensional flows are determined. The phase velocity of the spiral rolls are measured by a time-dependent analysis. The influence of the geometrical structure on the phase velocity is estimated. New types of flows are found, where bead-like vortices appear and spiral rolls with positive and negative front angles coexist.

Microfabricated Thermal Gradient Separator Device

2009 ◽  
Author(s):  
Saputra ◽  
P. F. Geelhoed ◽  
J. F. L. Goosen ◽  
R. Lindken ◽  
J. Westerweel ◽  
...  
Keyword(s):  
Temperature Difference ◽  
Silicon Substrate ◽  
Thermal Gradient ◽  
Electrical Power ◽  
Experimental Studies ◽  
Side Wall ◽  
Polystyrene Latex ◽  
Before And After ◽  
Fluidic Device ◽  
Pressure Driven Flow

The design and fabrication of a microfabricated fluidic device for particle thermophoresis is presented. The ability of the device to concentrate particles by generating a huge thermal gradient is demonstrated. In contrast to other microfluidics devices which use electrokinetics or pressure driven flow, in this device no external force acts on the particles. The separator device has been fabricated in a standard silicon substrate, consisting of a 20 μm deep channel and a 600 nm thick aluminum heater integrated into the device. The device is able to create a thermal gradient of approximately 104 Km−1. To maintain a thermal gradient over a long period, special attention had to be given to the design of the integrated heater and thermal insulation of the channel. In order to deposit the aluminum heater on the side wall of a micro channel, a silicon substrate was wet etched in KOH solution, forming sloping sidewalls. The temperature difference was measured using a thermocouple mounted on the two sides of the channel walls, showing about 2 K temperature difference. Experimental studies have been conducted in order to study the motion of particles in response to the thermal gradient. Particle motions are recorded before and after turning on the heater. Using polystyrene latex particles suspended in de-ionized water, it is shown that 90% of particles are concentrated on the cold side of the channel after 300 seconds using only 1W of electrical power. Apart from its applicability to particle suspensions, this device also has a great potential for DNA molecule concentration and separation in bio-chemical analysis.

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