Effect of Stiffness

In this chapter, a two-step identification approach is developed to estimate various parameters of a lead screw drive system. In the first step, using the steady-sliding test results, the velocity effects (i.e., damping and velocity-dependent parts of friction) were separated from the force effects (i.e., coulomb coefficient of friction) and appropriate parameters were estimated using the least squares technique. 

The vibratory behavior of the system was utilized in the second step of the parameter identification. At instances where a limit cycles was observed, effective load-dependent torsional stiffness of the lead screw system was estimated by minimizing a cost function that quantified the difference between measured and numerically simulated displacements and velocities. Moreover, friction and damping parameters were adjusted so that maximum conformity between measurements and simulation results was achieved. The presented numerical simulations showed the accuracy of the identified mathematical model of the lead screw system under a wide range axial loading and input speed settings. 

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Theoretically, the effect of stiffness can be understood in terms of the Flory and Fox description of K, from the Mark-Houwink relationship shown in Eq. 16.1 [11] ... 

This, of course, does not give (R ) oc L. It is then easily verified that f (R )Voim> so that the end-to-end distribution is not gaussian. When the chain length L is much greater than the persistence length, i.e., XL —> CO, the effects of stiffness become negligible. In this limit, it is found that... 

Adverse effect of stiffness imbalance between adherends... 

Ciampi V, Carlesimo L (1986) A nonlinear beam element for seismic analysis of structures. In 8th European conference in earthquake engineering, lisbem Clough RW, Johnston SB (1966) Effect of stiffness degradation on earthquake ductility requirements. In Proceedings of Japan earthquake engineering symposium, p232... 

In agreement with the descriptive terms used in clinical practice, the PDF model accounts for the effects of stiffness (kx), relaxation (cx), and load (x) on E-waves (Equation 28.5). Normal E-wave contours are well fit by underdamped kinematics where damping is low relative to stiffness ... 

Piping shall be coupled to equipment if the equipment or its support is not rigid (e.g., less than 33 cps) in any given direction, unless the effect of stiffness is shown to be negligible. Alternatively, the equipment nozzle displacement may be applied to the attached piping as piping seismic anchor movement (SAM). 

Chain stiffness also has an effect on T. Two linear, nonpolar polymers are linear polyethylene and isotactic PS. The bulky phenyl groups hinder rotation around single bonds in the PS backbone. Since this rotation is the source of chain flexibility, it is not surprising that PS is much stiffer than polyethylene. This shows up in melting points PS, = 230°C polyethylene, F = 137°C. Qualitatively, one can picture the effect of stiffness by comparing (1) the detachment of a leather strap from a wall to which it is nailed with and (2) the peeling of a stiff wooden board, also nailed. In the first, nails are stressed sequentially, whereas in the second, all nails are stressed simultaneously. The molecular analogy for a nail is the intermolecular bond. Some typical values for are summarized in Table 3.1. 

The rupture force measured in AFM experiments is given, therefore, by the average slope of the energy profile minus a correction related to the effects of thermal fluctuations. Equation (11) demonstrates that the rupture force measured in AFM experiments grows linearly with the activation energy of the system (Chilcotti et ah, 1995). A comparison of (10) and (11) shows that the unbinding induced by stiff springs in SMD simulations, and that induced by AFM differ drastically, and that the forces measured by both techniques cannot be readily related. 

Polyamides. The next two compounds are the amide counterparts of the esters listed under item (4). Although the values of AH j are less for the amides than for the esters, the values of T j, are considerably higher. This is a consequence of the very much lower values of AS j for the amides. These, in turn, are attributed to the low entropies of the amide in the liquid state owing to the effects of hydrogen bonding and chain stiffness arising from the contribution of the resonance form... 

Fig. 3. Effect of cross-link density where A represents tear strength, fatigue life, and toughness B, elastic recovery and stiffness C, strength and D,...

Cord materials such as nylon, polyester, and steel wire conventionally used in tires are twisted and therefore exhibit a nonlinear stress—strain relationship. The cord is twisted to provide reduced bending stiffness and achieve high fatigue performance for cord—mbber composite stmcture. The detrimental effect of cord twist is reduced tensile strength. Analytical studies on the deformation of twisted cords and steel wire cables are available (22,56—59). The tensile modulus E of the twisted cord having diameter D and pitchp is expressed as follows (60) ... 

Fig. 3. Effects of composition on physical properties. A, acetyl B, butyryl C, cellulose. 1, increased tensile strength, stiffness 2, decreased moisture sorption 3, increased melting point 4, increased plasticizer compatibiUty 5, increased solubiUties in polar solvents 6, increased solubiUties in nonpolar...

Fig. 4. The effect of blade loading on the wet-coating thickness in flexible blade coating where ( ) represents a less stiff blade (B) represents a stiffer...

These values are determined by experiment. It is, however, by no means a trivial task to measure the lamina compressive and shear strengths (52,53). Also the failure of the first ply of a laminate does not necessarily coincide with the maximum load that the laminate can sustain. In many practical composite laminates first-ply failure may be accompanied by a very small reduction in the laminate stiffness. Local ply-level failures can reduce the stress-raising effects of notches and enhance fatigue performance (54). 

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