Effective contact stiffness

In roller-tooth vibration, the chain roller vibrates from the impact of the roller against the sprocket tooth each time a roller engages a tooth. The frequraicy of roller-tooth vibration depends on the effective contact stiffness of the roller on the tooth and the effective mass of the joint engaging the tooth. It is extremely difficult to estimate values for the effective stiffness and effective mass, so an equation for calculating the frequency of roller-tooth vibration is not givrai here. Experiments have foimd that roller-tooth vibrations have a frequency in the range of 2 kHz to 10 kHz. 

To minimise the friction effect, it has been proposed to use smaller amplitudes and higher frequencies [122,137]. The so-called scanning local-acceleration microscopy (SLAM) is another modification of contact-mode SFM which was implemented by vibrating the sample at a frequency above the highest tip-sample resonance (region III in Fig. 13b). In this frequency range (around 1 MHz), the cantilever response to the sample excitations becomes independent of the cantilever stiffness and depends linearly on the contact stiffness and reciprocally on the cantilever mass m (Fig. 13b) ... 

The effective value of must scale with the contact radius a, for an elastic half space, since this is the only length scale in the problem. An approximate equivalence between and a gives the correct scaling as in Eq. (4). This stiffness can be compared, with the contact stiffness of the elastomer itself [see Eq. 

It must be noted that there are important dynamic effects in impact testing that can complicate the specimen response interacting with the testing equipment. For example, as the ratio ki/kj of the contact stiffness k between the striker and the specimen and that of the sample kj increases, there results an oscillatory response... 

A simple way to quantify this effect is in terms of contact stiffness S, defined as the extra load dF required to produce a small movement dS of the lenses towards each other, i.e. 

Kodam et al. [38] investigated the influence of the forces generated by each component sphere using a simple case in which a particle collides with a flat wall. It was shown that when a particle that is made of clumped spheres contacts a flat target, the component sphere contact stiffness should not be the same as the master sphere s contact stiffness. If the same contact stiffness is used in the clumped-sphere model, then the contact becomes effectively stiffen The optimal values of the component sphere contact stiffness depend upon the number of component spheres contacting the wall simultaneously and the degree of overlap for each component sphere contact. 

Moreno-Atanasio, R. Xu, B.H. Ghadiri, M. (2007) Computer simulation of the effect of contact stiffness and adhesion on the fluidization behaviour of powders. Chemical Engineering Science 62,184—194. 

Previous studies have shown that the force osdllations recorded by force transducers mounted in the moving arm of the test instrument are conaderably greater than the ones actually experienced by the specimen at its crack tip (see for example [5]) and depend largely on the contact stiffness of the tup-spedmen interface (see for example 6, 7]). Some reduction of these effects by proper contrd of the contact stiffness can thus be envisaged as possible. With impact testers the impact may be cushioned by means of a soft pad, placed where the tup strikes the spedmen. With servo-hydraulic testing machines, initial accderation of the spedmen can be controlled by means of a damper rqrplied in the motion transmission unit. 

Fig. 7.9 Simulation results - effect of contact stiffness, w = 1, c = 4 x 10 , and = 10. (a) Two-sided Poincare bifincation diagram (b) Black lines frequency content of steady-state lead screw vibration, dashed grey lines eigenfrequencies (c) Real part of the eigenvalues...

It has been also shown that when a thin polymer film is directly coated onto a substrate with a low modulus ( < 10 MPa), if the contact radius to layer thickness ratio is large (afh> 20), the surface layer will make a negligible contribution to the stiffness of the system and the layered solid system acts as a homogeneous half-space of substrate material while the surface and interfacial properties are governed by those of the layer [32,33]. The extension of the JKR theory to such layered bodies has two important implications. Firstly, hard and opaque materials can be coated on soft and clear substrates which deform more readily by small surface forces. Secondly, viscoelastic materials can be coated on soft elastic substrates, thereby reducing their time-dependent effects. 

This unit is, in effect, two single-row angular contact bearings built as a unit with the internal fit between balls and raceway fixed during assembly. As a result, fit and internal stiffness are not dependent upon mounting methods. These bearings usually have a known amount of... 

According to the distance from probe to the sample, three operation modes can be classified for the AFM. The first and foremost mode of operation is referred to as contact mode or repulsive mode. The instrument lightly touches the sample with the tip at the end of the cantilever and the detected laser deflection measures the weak repulsion forces between the tip and the surface. Because the tip is in hard contact with the surface, the stiffness of the lever needs to be less than the effective spring constant holding atoms together, which is on the order of 1 — 10 nN/nm. Most contact mode levers have a spring constant of <1 N/m. The defection of the lever can be measured to within 0.02 nm, so for a typical lever force constant at 1 N/m, a force as low as 0.02 nN could be detected [50]. 

To minimize effects of friction and other lateral forces in the topography measurements in contact-modes AFMs and to measure topography of the soft surface, AFMs can be operated in so-called tapping mode [53,54]. It is also referred to as intermittent-contact or the more general term Dynamic Force Mode" (DFM). A stiff cantilever is oscillated closer to the sample than in the noncontact mode. Part of the oscillation extends into the repulsive regime, so the tip intermittently touches or taps" the surface. Very stiff cantilevers are typically used, as tips can get stuck" in the water contamination layer. The advantage of tapping the surface is improved lateral resolution on soft samples. Lateral forces... 

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