Transducers inertia

A major limitation in controlled stress rheometers is instrument inertia. It is very similar to the transducer inertia described with eq. 8.2.1. The torque imposed on the drag cup must overcome reluctance torque, air bearing friction, and rotor inertia as well as the sample viscosity. The inertia portion dominates with low viscosity samples (Kreiger, 1990). Figure 8.2.11a illustrates the problem. Stress was commanded to increase linearly from 0 to... 

In the stress relaxation test, the material is subjected to a step strain at time zero (inset. Figure 8.3.5), and the decay in the stress (or modulus) is monitored as a function of time (Figure 8.3.5). At short time, limitations due to electronic hardware can affect the data collection speed and the transducer inertia can affect the torque values, thereby affecting the quality of the data. At long time, the low torque signal and hysteresis of the torque transducer affects the data quality. 

Shear modulus versus time after a step strain for a poly-dimethylsiloxane. The inset graph shows that the commanded strain is reached in 3ms. Stress reaches a maximum in 6ms due to transducer inertia. Low torque signal and transducer hysteresis are limiting at long time. 

The first second of a stress relaxation step can also show this type of ringing, but it is generally caused by the transducer itself. Thus, the first part of the data may be electronically filtered to remove the transducer ringing by setting a filter cutoff frequency of -40% of the value for the resonant frequency of the transducer and geometry. Some rheometers allow for the measurement of transducer resonant frequency when measuring the geometry inertia. 

The time-temperature correspondence principle states that there are two methods to use to determine the polymer s behavior at longer (or shorter) times than those covered by a stress-relaxation experiment run at 7j. First, one may improve the experiment to measure directly the response at longer (shorter) times. For the longer times, however, this procedure rapidly becomes prohibitively time-consuming because the change is so slow (note that Figure 4-5 is plotted on a log scale). (For the shorter times, the limitations are equipment related, e.g., transducer response time, problems with instrument and sample inertia, etc.) An alternative, according to the time-temperature... 

Each see has a bulge called the ampulla near one end, and inside the ampulla is the cupula, which is composed of saccharide gel, and forms a complete hermetic seal with the ampuUa. The cupula sits on top of the crista which contains the sensory receptor cells called hair cells. These hair cells have small stereocilia (hairs) which extend into the cupula and sense its deformation. When the head is rotated the endolymph fluid, which fills the canal, tends to remain at rest due to its inertia, the relative flow of fluid in the canal deforms the cupula hke a diaphragm and the hair cells transduce the deformation into nerve signals. 

Usually, the deformation of a sample undergoing oscillatory shear is monitored by measuring the sinusoidally-varying motion of a transducer-controlled driving smface in contact with the sample. However, in turning to the subsequent calculation of shear strain amplitude in dynamic measurements, it must be recognized that conversion of experimentally determined forces and displacements to the corresponding stresses and strains experienced by a sample can involve consideration of the role of sample inertia. 

The phase angle is related to the logarithmic decrement, which determines the rate at which a stimulated oscillation dies away when the Stimulus is removed. As an example, consider the torsion pendulum shown in Figure 4.9. The lower end of the specimen is clampied rigidly and the upper clamp is attached to the inertia arm. By moving the masses of the inertia arm the rotational moment of inertia can be adjusted so as to obtain the required resonant frequency of rotational oscillation. Rotation is detected by an electromagnetic transducer. The system is counterbalanced so that the specimen is not subject to axial stresses. 

Some of the drawbacks associated with mechanical steering involve the inertia associated with the transducer, the mechanism, and the fluid within the nosepiece of the transducer. The inertia introduces limitations to the frame rate and clearly does not permit random access to look angles as needed (the electronically steered approaches supply this capability). The ability to steer the beam at will is important in several situations but most importantly in Doppler applications. Further, electronic beam formation affords numerous advanced features to be implemented such as the acquisition of multiple lines simultaneously and elimination of the effects due to variations in speed of sound in tissue. 

The resulting force Fg on the mechanical side can be approximated by summing the force F inside the piezoelectric transducer with a force component resulting from the inertia of the transducers effective mass m ... 

Lodge (1988,1989) has shown that it is necessary to correct formisalignment of the flush-mounted transducer p and for inertia. Both corrections can be made using measurements firom Newtonian fluids. The misalignment correction probably comes fix>m bending of the flush-mounted transducer diaphragm and must be measured against tu, for each transducer in situ. The inertia correction appears to be linear in stress and Reynolds number. 

The sensitive transducer pennitted to use some recording principles previously abandoned because of the lack of adequate technology. This was the case of the strainmeter developed also by Benioff in the 1930s. The strainmeter dismissed the cherished principle of pendulum inertia and measures the variation of distance between two points at the passing of seismic waves. The new variable reluctance transducer could be used to properly measure this distance and thus to use the strainmeter as seismometer. 

Active Sensors The heart of the active sensor is a device measuring the ground acceleration, the so-called force balanced accelerometer (FBA) (Fig. 3). The FBA has a feedback coil, which can exert a force equal and opposite to the inertia force due to the acceleration. The displacement transducer sends a current to this force coil... 

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