Tires

The balance between natural rubber and SBR is a delicate one. Natural rubber has made a comeback and reversed its downward trend. Developments of rubber farming have raised the yield from 500 Ib/acre/yr to 2,000-3,000. Petrochemical shortages and price increases have hurt SBR. Finally, the trend toward radial-ply tires, which contain a higher proportion of natural rubber, favors this comeback. Fig 18.1 shows the U.S. natural rubber consumption trends vs. U.S. SBR production, where this bounceback of the natural rubber market is very evident from 1980 to the present. The competitive price structure for these two elastomers through the years has been very evident, and their prices are never too far apart. 

No discussion of elastomers is complete without a mention of tire technology. About 70% of all synthetic elastomers in the U.S. are used in tires. About 264 million tires are produced in the U.S. annually, 217 million for cars and the rest for trucks and busses. A typical tire is made up of four parts (1) the tread, which grips the road (2) the sidewall, which protects the 

The tread must have the best possible grip to the road. Grip is inversely related to elasticity, and natural rubber has good elasticity but poor grip, so no natural rubber is used in automobile tire treads. Treads are blended of SBR and polybutadiene in an approximate ratio of 3 1. Truck tire treads do have natural rubber, between 65-100%, to avoid heat buildup and because grip is not so necessary in heavy trucks. Aircraft tires consist of 100% natural rubber. 

The carcass requires better flexing properties than the tread and is a blend of natural rubber and SBR, but at least 60% of natural rubber. The sidewalls have a lower percentage of natural rubber, from 0-50%. The liner is made of butyl rubber because of its extreme impermeability to air. 

The most important single trend in the U.S. tire market is the switch from cross-ply and belted bias-ply to radial-ply tires. Radials held only 8% of the 

The immense dynamic load on a tire requires that it be flexible. A rubber matrix defines the tire s form and functions as an elastic protective cover. An embedded strength carrier absorbs the forces exerted on the tire. 

Depending on the field of application, there are various types of tires with different structures. To limit the amount of information here, the representative example chosen for the tires of bicycles, motorbikes, aircrafts, cars, and lorries (trucks) is a car tire. 

The supporting part of the tire is the casing. It consists of several fabric layers that are looped/gorged around the bead core. The belt, which consists of nylon or steel fabrics, stabilizes the running thread. A well-bonding and preferably nonabrasive rubber builds up the running thread. A rubber layer is inserted instead of a tube in the inside of the tire. 

In diagonal tires, the fabric layers run in a diagonal direction (with an angle of 30° up to 45°) from heel to heel. In contrast to that the fabric layers in radial tires are arranged radially. 

The belts of radial tires contain fabric layers that lie diagonally to each other (at an angle of 20° up to 25°). The belt guarantees the stability of the tires. It consists mostly of steel fabrics because radial tires with a steel belt outmatch the textile belt tire. For some years, a layer of less-twisted polyamide yarns has been used above the belt. This so-called top layer decreases the danger of separation from the edge of the belt and increases the capacity at high speeds. 

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In this case the slot length is about 4 times the probe diameter. The material chosen has a penetration depth of 0.8991 mm at tire given frequency of 60.9 kHz. The slot depth is 3 times the penetration depth. 

As a conclusion to this experiment and in order to optimize the sensibility of tire probe it is necessary that the coil shall be on the edge of the ferrite. The results obtained confirm the probe stability. 

It is easy to calculate tire value of e as an application of the MAXWELL S equations in the case of a symmetric tube without defect. 

With these assumptions we observe that it is possible to determine also tire depth h of the defect through the measurements of the resistance Rd of the coil with the tube presenting the defect, the resistance Roo of the coil with a tube without defect, the resistance Rs of empty coil and the radius of the tube rb. 

The main disadvantage of Feldkamp s approaeh is the fact, that it is mathematically correct only in tire midplane of the beam. With larger Cone-Beam angles the error grows and over 30 degrees severe artefacts can be observed In the reconstruction. 

The tables 3 and 4 give tire results of over-washing resistance tests. 

Tire development of the QAP system for the MPI and LPl technique together with a camera system for automated flaw detection can give the following advantages ... 

Tlrese metlrods may be applied to on line wire surface testing where conventional procedures are inadequate, such as tire stylus metlrod, due to the specimen diameter or microscopic examination. 

Most recovery boilers use 63,5 mm OD carbon steel tubes in the generating bank. With a few exceptions these tubes are swaged at the ends to 50,8 mm. When the 63,5 mm raw tube is manufactured it is subject to a lot of specifications i.e. ASME. There are no specifications for the swaged end of the tube. This is unfortunate as the swaged part of the tube is subjected to further mechanical deformation dtuing the rolling procedure and is located in a wastage zone of tire recovery boiler. 

In several generating banks inspected, a number of tubes have been found with eccentricity exceeding 1,0 mm and in one extreme case 2,0 mm, or 40 % of the nominal wall thickness was noted. A conceptual diagram of tire cross section of a concentric tube and a simulated plot of the wall thickness scan is presented in figure 3. The scan presented in figure 2 is a relatively concentric tube less than 0,2 mm of wall variation. 

Protein adsorption has been studied with a variety of techniques such as ellipsome-try [107,108], ESCA [109], surface forces measurements [102], total internal reflection fluorescence (TIRE) [103,110], electron microscopy [111], and electrokinetic measurement of latex particles [112,113] and capillaries [114], The TIRE technique has recently been adapted to observe surface diffusion [106] and orientation [IIS] in adsorbed layers. These experiments point toward the significant influence of the protein-surface interaction on the adsorption characteristics [105,108,110]. A very important interaction is due to the hydrophobic interaction between parts of the protein and polymeric surfaces [18], although often electrostatic interactions are also influential [ 116]. Protein desorption can be affected by altering the pH [117] or by the introduction of a complexing agent [118]. 

In the absence of skidding, the coefficient of static friction applies at each instant, the portion of the tire that is in contact with the pavement has zero velocity. Rolling tire friction is more of the type discussed in Section XII-2E. If, however, skidding occurs, then since rubber is the softer material, the coefficient of friction as given by Eq. XII-5 is determined mainly by the properties of the rubber used and will be nearly the same for various types of pavement. Actual values of p, turn out to be about unity. 

Thus if Amontons law is obeyed, the initial velocity is determined entirely by the coefficient of friction and the length of the skid marks. The mass of the vehicle is not involved, neither is the size or width of the tire treads, nor how hard the brakes were applied, so long as the application is sufficient to maintain skidding. 

The situation is complicated, however, because some of the drag on a skidding tire is due to the elastic hysteresis effect discussed in Section XII-2E. That is, asperities in the road surface produce a traveling depression in the tire with energy loss due to imperfect elasticity of the tire material. In fact, tires made of high-elastic hysteresis material will tend to show superior skid resistance and coefficient of friction. 

As might be expected, this simple picture does not hold perfectly. The coefficient of friction tends to increase with increasing velocity and also is smaller if the pavement is wet [14]. On a wet road, /x may be as small as 0.2, and, in fact, one of the principal reasons for patterning the tread and sides of the tire is to prevent the confinement of a water layer between the tire and the road surface. Similarly, the texture of the road surface is important to the wet friction behavior. Properly applied, however, measurements of skid length provide a conservative estimate of the speed of the vehicle when the brakes are first applied, and it has become a routine matter for data of this kind to be obtained at the scene of a serious accident. 

The relationship between tire abstract quantum-mechanical operators /4and the corresponding physical quantities A is the subject of the fourth postulate, which states ... 

Starting with the quantum-mechanical postulate regarding a one-to-one correspondence between system properties and Hemiitian operators, and the mathematical result that only operators which conmuite have a connnon set of eigenfiinctions, a rather remarkable property of nature can be demonstrated. Suppose that one desires to detennine the values of the two quantities A and B, and that tire corresponding quantum-mechanical operators do not commute. In addition, the properties are to be measured simultaneously so that both reflect the same quantum-mechanical state of the system. If the wavefiinction is neither an eigenfiinction of dnor W, then there is necessarily some uncertainty associated with the measurement. To see this, simply expand the wavefiinction i in temis of the eigenfiinctions of the relevant operators... 

Figure Al.1.1. Wavefimctions for the four lowest states of the hamronie oseillator, ordered from the n = Q ground state (at the bottom) to tire u = 3 state (at the top). The vertieal displaeement of the plots is ehosen so that the loeation of the elassieal turning points are those that eoineide with the superimposed potential fimetion (dotted line). Note that the number of nodes in eaeh state eorresponds to the assoeiated quantum number.

The representation of trial fiinctions as linear combinations of fixed basis fiinctions is perhaps the most connnon approach used in variational calculations optimization of the coefficients is often said to be an application of tire linear variational principle. Altliough some very accurate work on small atoms (notably helium and lithium) has been based on complicated trial functions with several nonlinear parameters, attempts to extend tliese calculations to larger atoms and molecules quickly runs into fonnidable difficulties (not the least of which is how to choose the fomi of the trial fiinction). Basis set expansions like that given by equation (A1.1.113) are much simpler to design, and the procedures required to obtain the coefficients that minimize are all easily carried out by computers. 

It is often very usefiil to deseribe elassieal vibrations in temrs of a trajectory in the spaee of eoordinates r. . rj. If the motion follows one of tire iromral modes, the trajeetory is one in whieh the motion repeats itself... 

The question of non-classical manifestations is particularly important in view of the chaos that we have seen is present in the classical dynamics of a multimode system, such as a polyatomic molecule, with more than one resonance coupling. Chaotic classical dynamics is expected to introduce its own peculiarities into quantum spectra [29, 77]. In Fl20, we noted that chaotic regions of phase space are readily seen in the classical dynamics corresponding to the spectroscopic Flamiltonian. Flow important are the effects of chaos in the observed spectrum, and in the wavefiinctions of tire molecule In FI2O, there were some states whose wavefiinctions appeared very disordered, in the region of the... 

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