Angular displacement current

Figure H-7 is the schematic of a basic I/P transducer. The transducer shovvm is characterized bv (1) an input conversion that generates an angular displacement of the beam proportional to the input current, (2) a pneumatic amplifier stage that converts the resulting angii-...

Fig. 4.14 DC servo-motor under armature control, e it) = Armature excitation voltage e it) = Backemf /a(t) = Armature current = Armature resistance = Armature inductance 6f = Constant field voltage if = Constant field current Tm = Torgue developed by motor 6 t) = Shaft angular displacement u] t) = Shaft angular velocity = dd/dt.

Electrodes placed on the skin around the eye will detect a biopotential due to a dipolar current flow from the cornea to the retina. The dot product of this biocurrent dipole with an electrode pair will change in amplitude according to the gaze angle. This is known as an electroocculogram (E( ), and it can be used to determine the eye s angular displacement. 

Figure 9.7 shows a schematic view of the parameter identification test setup designed to perform focused experiments on a single slider system. The mathematical model of this system is presented in this section. This model forms the basis of the parameter identification method to be described in Sects. 9.3 and 9.6 below. As shown in Fig. 9.7, two rotary encoders are used to measure the angular displacements of the lead screw, 0, and the motor, 0m- A load cell is used to measure the force exerted by the pneumatic cylinder, R. The input current to the DC motor are also measured. The input torque to the system, Tm, is then calculated from this quantity and the known torque constant of the DC motor. 

The test setup used in the friction identification experiments is shown in Fig. 9.9. Similar to the test setup shown in Fig. 9.4, only one of the two sliders is included in the setup. The working parts of the test setup are taken from an actual seat adjuster. Two encoders are used to measure the angular displacement of the lead screw and the motor. A load cell is used to measure the force exerted by the pneumatic cylinder. The input voltage and current to the DC motor are also measured. With the help of a controller regulating the current input to the DC motor [119,120], the slider is set to move at near constant preset velocities in the applicable range. The angular velocity of the motor is calculated by numerical differentiation of its measured angular displacement. The motor torque is calculated from the measured input current and the known motor s torque constant. See Table 9.2 for a list of instruments and components of this test setup. 

In a recent work, Aiba (A2) studied the flow currents in water, in a mixing vessel 14 in. in diameter, using an axially-mounted two-bladed flat paddle 4.7 in. in diameter. Measurements were made both without baffles and with four baffles %2 tank diameter wide. A sphere about 6 mm. in diameter was suspended by a flexible wire, and its displacement from the equilibrium (no-flow) position was measured. To get the horizontal displacement, cobalt-60 was embedded in the sphere, and a Geiger-Mueller counter approximately 10 mm. in diameter was immersed in the tank 2-5 cm. from the sphere. The vertical movement of the sphere was measured with a cathetometer, and its angular position observed by eye. From the known components of displacement and the assumed drag coefficient of the sphere, values of the radial, tangential, and vertical components of the flow around the sphere were calculated. 

As follows from numerical analysis, in this case five angular harmonics describe the field with high accuracy for all considered values of a//ii where h is the skin depth in the borehole. It is appropriate to notice that the influence of displacement on inphase and quadrature component of the field increases with an increase of frequency. At the same time within this range of frequencies the inphase component is less sensitive to displacement than is the quadrature component. For example, even if a/h = 1.6 we have In/iJ(e = 0.5)/In/i (e = 0) = 1.04, while Q/i (e = 0.5)/Qh e = 0) = 1.51. It is explained by the fact that within a wide range of frequencies the density of charges arising at the interface between the borehole and the formation is shifted in phase by 90° with respect to the current in the transmitter. Correspondingly, we can expect that the quadrature component of the field for a two-coil probe will be mainly subjected to the influence of eccentricity. 

In Subsections 5.1, 5.2, a form of Noether s Theorem has been applied in order to derive the associated weak statements of the conserved currents. This implementation led to Equations 14, 16, which correspond to the conservation of energy and momentum, respectively. These equations express in a clear manner the participation of each primary variable in the statements of conserved currents, a task that proves to be not trivial. To be more specific, in the case of linear and angular momentum-conservation statement 16, only the weak velocities and not, as someone may expect, the momentum type variables enter. Moreover, in the case of energy conservation, it is shown in (Eq. 14) that the weak velocities and not the strong time derivatives of displacement determine the kinetic energy. 

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