Dimensional variation

The second of Pick s laws expresses the change in concentration of a species at a point as a fimction of time due to difflision (figure B 1.28.2). Plence, the one-dimensional variation in concentration of material within a volume element bounded by two planes v and x + dx during a time interval dt is expressed by dc fx.,t)ldt) = D... 

Prehse J. (1975) Two dimensional variational problems with thin obstacles. Math. Z. 143 (3), 279-288. 

Properties. Most of the alloys developed to date were intended for service as fuel cladding and other stmctural components in hquid-metal-cooled fast-breeder reactors. AHoy selection was based primarily on the following criteria corrosion resistance in Hquid metals, including lithium, sodium, and NaK, and a mixture of sodium and potassium strength ductihty, including fabricabihty and neutron considerations, including low absorption of fast neutrons as well as irradiation embrittlement and dimensional-variation effects. Alloys of greatest interest include V 80, Cr 15, Ti 5... 

The allowable dimensional variation (the tolerance) of a polymer part can be larger than one made of metal - and specifying moulds with needlessly high tolerance raises costs greatly. This latitude is possible because of the low modulus the resilience of the components allows elastic deflections to accommodate misfitting parts. And the thermal expansion of polymers is almost ten times greater than metals there is no point in specifying dimensions to a tolerance which exceeds the thermal strains. 

Component reliability will vary as a function of the power of a dimensional variable in a stress function. Powers of dimensional variables greater than unity magnify the effect. For example, the equation for the polar moment of area for a circular shaft varies as the fourth power of the diameter. Other similar cases liable to dimensional variation effects include the radius of gyration, cross-sectional area and moment of inertia properties. Such variations affect stability, deflection, strains and angular twists as well as stresses levels (Haugen, 1980). It can be seen that variations in tolerance may be of importance for critical components which need to be designed to a high reliability (Bury, 1974). 

In the probabilistic design calculations, the value of Kt would be determined from the empirical models related to the nominal part dimensions, including the dimensional variation estimates from equations 4.19 or 4.20. Norton (1996) models Kt using power laws for many standard cases. Young (1989) uses fourth order polynomials. In either case, it is a relatively straightforward task to include Kt in the probabilistic model by determining the standard deviation through the variance equation. 

When dimensional variation is large, its effeets must be ineluded in the analysis of the stress distribution for a given situation. However, in some eases the effeets of dimensional variation on stress are negligible. A simplified approaeh to determine the likely stress distribution then beeomes available. Given that the mean load applied to the eomponent/assembly is known for a partieular situation, the loading stress ean be estimated by using the eoeffieient of variation, C, of the load and the mean value for the stress determined from the stress equation for the failure mode of eoneern. 

SSI is recommended for situations where a considerable potential for variation exists in any of the design parameters involved, for example where large dimensional variations exist or when the anticipated design loads have a large range. The main reasons for performing it are (Ireson et al., 1996) ... 

The calculated loading stress, L, on a component is not only a function of applied load, but also the stress analysis technique used to find the stress, the geometry, and the failure theory used (Ullman, 1992). Using the variance equation, the parameters for the dimensional variation estimates and the applied load distribution, a statistical failure theory can then be formulated to determine the stress distribution, f L). This is then used in the SSI analysis to determine the probability of failure together with material strength distribution f S). 

The formulations for the failure governing stress for most stress systems can be found in Young (1989). Using the variance equation and the parameters for the dimensional variation estimates and applied load, a statistical failure theory can be formulated for a probabilistic analysis of stress rupture. 

The above equations ean all be written in terms of the nominal dimensions, a, b and t, for the seetion. Solutions for the mean and standard deviation of eaeh property, for any seetion, ean be found using Monte Carlo simulation with knowledge of the likely dimensional variation for hot rolling of struetural steel seetions. The eoeffieient of variation for this proeess/material eombination is = 0.0083 (Haugen, 1980). 

The material selected for the pin was 070M20 normalized mild steel. The pin was to be manufactured by machining from bar and was assumed to have non-critical dimensional variation in terms of the stress distribution, and therefore the overload stress could be represented by a unique value. The pin size would be determined based on the —3 standard deviation limit of the material s endurance strength in shear. This infers that the probability of failure of the con-rod system due to fatigue would be very low, around 1350 ppm assuming a Normal distribution for the endurance strength in shear. This relates to a reliability R a 0.999 which is adequate for the... 

Given the eost eonstraints imposed on the press frame design, and the desire to minimize dimensional variation, the same material was seleeted for the eon-rod eross-seetion. To determine the dimension, D, using the same steel for the eon-rod ... 

Liggett, J. V. 1993 Dimensional Variation Management Handbook a guide for quality, Design and Manufacturing Engineers. Englewood Cliffs, NJ Prentice-Hall. 

The one-dimensional variations of the INADEQUATE experiment suppress the intense... 

The effective length is defined as the measured center distance plus the outside circumference of one of the inspection pulleys. This measurement method accounts for the modulus of elasticity, or stretch ability, and dimensional variations among belts with the same cross-section. 

Where the pipeline is expected to have to withstand unusual dimensional variation due, perhaps, to temperature changes or near yield point pressure testing, the use of a woven glass or nylon reinforcement in place of the glass tissue is said to increase the flexibility of the coating system considerably. 

A three-dimensional variation of the theme is offered by the oscillatory behaviour of anodic copper dissolution into a NaCl/KSCN electrolyte mixture.27 This is a complex process involving solid states CuSCN (pKsp = 14.32) and Cu20 or CuOH (pKsp = 14), and CuCl (pKsp = 5.92), and ionic species Cu+, CuCl22, CuCl3, and Cl. Among other plausible schemes,... 

PTFE is handicapped by the impossibility of using the conventional molten-state processing methods and the difficulty and cost of the suitable specific methods. Additional disadvantages are the sensitivity to creep and abrasion significant dimensional variation around the glass transition temperature (about 19°C) the price (justified by the high performances) density difficulties of joining corrosive and toxic fumes in the event of fire. 

Figure 4.120. Poly imides examples of linear dimensional variation (%) versus time (days)...

All these polymers incorporate high halogen levels that are environmentally harmful. PTFE creep and abrasion sensitivity injection and extrusion are impossible by conventional processes high dimensional variation at glass transition temperature (19°C) high cost high density very difficult to stick corrosive and toxic smoke generated in fires. 

Based on this new model for the morphology of Nafion, the dimensional variations of the scattering entities with water content were used in simple space filling calculations to estimate the cluster diameter, the number of sulfonate sites per cluster, and the number of water molecules per cluster. The results of these model calculations showed that, for a given equivalent weight, the cluster diameter. 

Two of the methods proposed appear at first sight to be non-arbitrary. In fact, absolute accuracy has been claimed for one of these (25), a refined two-dimensional variational procedure in which all frequencies but one are used as constraints, while this last one is used as a criterion. In fact, it is not possible to fix two unknowns from one parameter, and the method seems to this reviewer an unusually ingenious and elaborate exercise in self-deception, in which the range of possible solutions of the independent parameter method appears to contract to a point. 

Metallic pipe systems comprise the majority of applications. Metallic pipe, tubing, and pipe fittings are divided into two main categories seamless and welded. Both have advantages and disadvantages in terms of economy and function. Specifications governing the production of these products dictate the permissible mechanical and dimensional variations, and code design calculations account for these variations. 

The simple arguments presented above are for a one-dimensional variation of order in a direction normal to the planes of a layer structure in which individual layers remain flat. Such a system is, of course, a gross over-simplification of a real three-dimensional system but nevertheless serves to illustrate the way in which deterioration of order influences the X-ray diffraction obtained from a layered structure such as is obtained, for example, by the Langmuir-Blodgett technique. 

The one-dimensional variations of the INADEQUATE experiment 12,13 17, 20 suppress the intense 13C-12C main signal, so that both AX and AB systems appear for all 13C-13C bonds in one spectrum. The two-dimensional methods 12 13,17 21,22 segregate these AB systems on the basis of their indivi-... 

These PPA heat resistant, high performance plastics have been used successful in different applications such the auto engine block. BP Amoco reports that after seven years and 85,000 miles of actual vehicle use, a Dodge Neon 2.0 liter thermostat housing molded from BP s PPA (polyphthalamide) showed no measurable dimensional variations, no surface degradation, and no decline in the performance of the plastic. In 1994, BP model A-113 3 HS (a 33wt% glass-filled, heat-... 

Various techniques enable approximate solutions of the closed system of equations here we specialize for one dimensional variations of layer structure in the direction normal to the surface. Regarding the SCF as an external field, de Gennes (1969, 1979) treated Eq. (78) as a pseudo-linear equation de Gennes, 1969,1979) and expanded Gc in eigenfunctions,... 

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