Torsion spring system

A quick review of system torsional response may help explain why a resilient coupling works. Figure 9-14 is a torsional single degree of freedom system with a disk having a torsional moment of inertia J connected to a massless torsional spring K. 

Fig. 3.9. (a) Torsion mass- spring system, (b-d) function r(a), (e) resultant moment as a function of the angle. 

The variation of the system compliance can be obtained in state-of-the-art passive dynamic hand splints by using either interchangeable elastic components (Figures 24.2a to 24.2c) or adjustable torsional springs (Figure 24.2d) these have to be respectively replaced or adjusted every time it becomes necessary. In order to avoid this, so-called active dynamic hand splints represent an attractive alternative. 

The two-step processes consist of (1) determination of the torsional spring constant Kl of the cantilever and (2) the lateral sensitivity of the detection system. With the known height of the AFM tip or diameter of the colloid probe, the friction force can then be calculated from the measured detector signal. 

Topically, the couplings in a turboraachinery train will be the softest torsional elements in the system. As a result, they represent the coniroi-ling factor in the system s overall stiffness since the total system sprmg rate cannot exceed the stiffness of the softest spring. 

The torsionally soft or resilient coupling such as the quill shaft and the metal-metal resilient transmit torque can handle misalignment through springs, metal strips, coils, disks and diaphragms, They will tune the system by changing the spring constant K. 

Usually, MD methods are applied to polymer systems in order to obtain short-time properties corresponding to problems where the influence of solvent molecules has to be explicitly included. Then the models are usually atomic representations of both chain and solvent molecules. Realistic potentials for non-bonded interactions between non-bonded atoms should be incorporated. Appropriate methods can be employed to maintain constraints corresponding to fixed bond lengths, bond angles and restricted torsional barriers in the molecules [117]. For atomic models, the simulation time steps are typically of the order of femtoseconds (10 s). However, some simulations have been performed with idealized polymer representations [118], such as Bead and Spring or Bead and Rod models whose units interact through parametric attractive-repulsive potentials. 

Instrumentation. Commercial atomic force microscopes Explorer from Topometrix Inc., Nanoscope Illa Digital Instruments Co. Ltd.) which are based on the laser beam deflection detection scheme were used in conjunction with digital oscilloscopes of very stable low frequency (1-20 Hz) trigger system for lateral force (friction) measurements, and dual-phase lock-in amplifiers and function generators for force modulation measurements. Various triangular silicon nitride cantilevers were used. The lateral spring constants were determined with the "blind torsional calibration method discussed in more detail in the Appendix. 

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