Subject of this paper in connected with problems reffering to analysis of parametrical sensitivity of mathematical model of static properties of complex multidimensional mechanical and electromechanical systems. A full definition of an analysis requires analysis of sensitivity’s invariants and preliminary selection of tolerances of the model. This paper presents application of the above method in order to a mathematical model of an inductive transducer for the measurement of displacements.

Colocated sensors and actuators offer significant robustness and design benefits in distributed parameter vibration control. The concept of colocation is extended to distributed transducers, and combinations of distributed and discrete transducers, affixed to self-adjoint distributed plants. It is shown that sensors and actuators are colocated only when they have both physically coincident spatial apertures and their “spatial derivative orders” are equal: these constraints are expressed mathematically as an integral equation. In satisfying these constraints the resulting transducer-augmented plant, if open-loop stable, is minimum phase. These results are demonstrated by transducer placement studies.

The main potential advantage of electro-rheological fluid when used as the interface medium between electronics and actuators in high speed machines is its ability to respond quickly to a change in the control signal. The analysis reported in this paper shows that over the operating speed range the system has a time constant of less than one millisecond and for most practical applications it can be assumed that when a suitable control strategy is employed the output torque would be proportional to the control signal. Most electro-mechanical torque transducers have time constant of over 10 milliseconds and therefore direct measurement of the torque produced by the electro-rheological clutch would be very expensive if not impractical. This paper reports a numerical method of identifying the torque response from the output of a conventional torque transducer which has a natural frequency of 110 Hz. The transfer function is first identified from a standard step input test, and the torque response of the clutch then is estimated from the measured signal. Although the noise on the signal will be always amplified with this method the use of a digital filter makes it possible to obtain an accurate estimate of the torque response.

The determination of loads applied to a structure is often necessary in the design process. In some situations it is not feasible to insert a load cell in the system to measure these applied loads. In these cases, it would be expedient to utilize the structure itself as a load transducer. This can be accomplished by measuring strains at a number of locations on the structure. The precision with which the applied loads can be estimated from measured structural responses depends on the number of strain gages utilized and their placement on the structure. This paper presents a computational methodology which utilizes optimal experimental design techniques to select the number, locations and angular orientations of the strain gages which will provide the most precise load estimates based on the generalized load vector. Selection is made from a candidate set created using a finite element analysis. This method is illustrated with an experimental application example.

The study of the transverse vibration of thin rectangular plates has been mainly confined to plates of uniform thickness. There are few publications available on the vibration of plates with nonuniform thickness. These plates have application in various fields such as civil engineering and aerospace structures and are often found in high frequency acoustic transducers. Furthermore, it is sometimes possible to achieve minimum weight design of plates by having suitable variations in thickness. For the special case of a plate with two opposite edges simply supported and thickness discontinuities perpendicular to the simply supported edges, an analytical solution is possible using a dynamic flexibility method. Several examples are discussed.

The Thermal Radiation Source (TRS) at ARL is used as a research tool to develop a reliable TRS unit for integration with the 2.44 m probative tube. Part of this study includes measuring the rise and fall times as well as the extent of flux variation of the TRS events. The Garden type gage is the primary transducer used to measure the flux output. This gage consists of a constantan diaphragm welded to a copper wire and body. This creates two thermocouple junctions. The electrical output of the gage is linearly related to the incident thermal radiation on the face of the diaphragm. A concern is about the response rate of these gages. The typical gage used in TRS work has a response rate of one time constant within 50 ms. In the past, the transient output of the TRS was considered slow. A faster acting gage was not necessary. To test this theory, a mathematical correction formula was applied to existing TRS data. The correction formulation was to demonstrate the actual incident radiation on the gage face by assuming a response rate. The data was processed using the correction formula. The results of the correction processing yielded a higher rise and fall time, as expected, but demonstrated a much higher flux variation during a TRS event. The overall fluence remained the same. To verify the correction formula is accurate, a special gage was constructed. It has a response rate of 6 ms to the first time constant. An experiment was conducted by placing the special gage next to a regular gage. The results show the faster acting gage produces a signal that matches the corrected signal of the slower gage, with one exception. The overall fluence increased. The most profound effect of this gage is realized when attempting to improve the performance of a TRS system. By realizing the capabilities of the gages, a more accurate determination of the thermal output of future TRS systems can be assessed. This will have direct impact on future Nuclear Survivability criterion by realizing the true capabilities of TRS systems.

A prototype of a simple, footwear-testing machine which mimics the physiologic motions and forces of walking in one plane has been designed, developed and tested. Eleven ROTC students were measured and filmed to obtain information on the kinematics of the lower limb and the dynamic forces exerted by their footwear on the ground while walking across a load plate. A machine was then designed which uses the coupler curve of a fourbar linkage to simulate the planar kinematics of the heel-strike and toe-off portions of walking. A standard-issue U. S. Army combat boot is attached to the fourbar linkage’s coupler link on a prosthetic foot such that the heel and sole are close to the moving centrode of the coupler. The ground plane is the fixed centrode. Thus their relative motion approximates pure rolling. The boot is “walked” against a force-plate which is loaded by an air cylinder. This force plate is pulled away during the walking “backstroke”. The dynamic forces of impact are measured by two force transducers. These measured forces simulate the vertical physiologic forces of walking and the kinematics provides realistic physiologic motions to the boot in a vertical plane.

A new method and device for temperature measurement are presented. The method reduces the measurement of the unknown temperature to the solving of an optimal control problem, using a numerical computer. The device consists of a hardware part including some conventional transducers and a software one. The problem of temperature measurement, according to this method, is mathematically modelled by means of the one-dimensional heat equation, describing the heat transfer through the device. The principal component of the device is a rod. The variation of the temperature which is produced near one end of the rod is determined using some temperature measurements in the other end of the rod, the mathematical model and a type of gradient algorithm. This device works as an attenuator of high temperatures and as an amplifier of low temperatures.

The Navy is constantly developing new materials for use as the active element(s) in high-performance underwater projectors. One such class of materials is the electrostrictive ceramics such as lead magnesium niobate/lead titanate (PMN/PT). These materials are characterized by high strain per unit electric field, high permittivity (ε = 12000), and a low Curie temperature. These ceramics must be used in their unpoled state in contrast to other classes of ceramic, such as lead zirconate titanate (PZT) ceramics that are usually poled before use. For PMN/PT, the strain as a function of electric field is an almost perfect square-law, s = kE 2 , over a large range of voltages, neglecting higher-order effects such as hysteresis and saturation. This response suggests that a transducer made of PMN/PT should be driven by superimposing an ac signal upon a large bias voltage. The bias voltage is needed to achieve a large effective strain/volt (d 33 ) in response to the ac signal. If the ac signal amplitude is greater than a few percent of the bias voltage, significant distortion appears in the output due to the material’s nonlinear response (Fig. 1). Further, when this material is incorporated into an electromechanical transducer the transducer’s transient response is a complex combination of the material’s nonlinearity and the poles and zeros of the mechanical system. If the output displacement of the transducer is to be a large fraction of the maximum possible displacement, a method must be found to overcome the effects of nonlinearity and transient response. The goal of this work is to generate an output signal that is a near-perfect replica of a desired signal (e.g., a sinusoid that is turned on at t = 0) by driving the transducer with an “inverse” signal derived from a nonlinear model of the transducer. The nonlinear model used for a PMN/PT transducer is the Hunt electrostatic model, modified to include both polarization in the PMN material and the effects of radiation loading on the transducer. The model is presented in the form of coupled ordinary (but nonlinear) differential equations. Parameters for the model are estimated by fitting the model to actual data obtained by driving a PMN stack. Results for the parameters and for the goodness-of-fit of the model are presented. The model and its associated parameters for the stack are then effectively inverted by calculating the drive voltage required to produce a given sinusoidal displacement at the face of the transducer. Finally, the transducer is driven by the calculated drive and the resulting waveform is compared with the desired sinusoidal output. Measures of harmonic distortion reduction for a given output amplitude are presented.

Barrel-stave flextensional transducers are low frequency underwater projectors that can be used as active components in long-range sonar systems or as versatile sound sources in oceanographic applications. The advantages offered by this type of flextensional transducer include low frequency, high power, small size, low weight, post-assembly frequency tuning, and low cost due to simplicity in its design and assembly. The construction of three barrel-stave projectors, investigated at the Defence Research Establishment Atlantic (DREA) in recent years, is briefly described. The performance goals for each of these projectors are shown to be consistent with the criteria that distinguish the first three classes in the Brigham-Royster classification scheme for flextensional transducers. Important in-water performance parameters, such as the resonance frequencies, transmitting voltage responses, source levels, mechanical quality factors, and electroacoustic efficiencies, are presented. In addition, these parameters are compared to those of other experimental and commercial barrel-stave flextensional designs.

An interferometric strain measurement technique is extended to vibration measurements. The technique is based on two micro-indentations placed on an object surface using a combination of diffraction and interference of laser light. Relative displacements between the two indentations and derivatives of in-plane and out-of-plane vibrational displacements are measured by analyzing the phase shift of the interference fringe patterns. The technique can be used to study bending stress and deflection problems in vibrational beams, plates and shells. The displacement derivatives are measured in real time, from which time derivatives or the velocity and acceleration of the displacement derivative as well as vibrational frequency can be determined. The technique has advantages over an accelerometer in that it is noncontacting and does not require attachment of the transducer to the object which could alter the object behavior. In addition, it has many desirable features such as being extremely compact, massless, and applicable to hostile environments such as those associated with production and elevated temperatures.

In poled piezoelectric ceramic lead zirconate:lead titanate (PZT) compositions, the non zero components of the piezoelectric tensor are d 33 , d 31 = d 32 , d 15 = d 24 (Bornstein, 1981). When the positive directions of the three axis in the ceramic is taken as the poling direction and a tensile stress is considered positive, d 33 is a positive coefficient and d 31 is negative (Jaffe, Cook, Jaffe, 1971). For the very high coupling compositions with zirconia titania ratio close to that of the morphotropic phase boundary between tetragonal an rhombohedral ferroelectric phases (Zr/Ti = 53/48) in the PZT phase diagram there is an unfortunate effect that d 33 ∼ 2d 31 (Setter and Cola, 1993). Thus in attempting to use monolithic PZT as a hydrostatic pressure wave sensor d h = h 33 + 2d 31 is unusually small. For all PZTs, the dielectric permittivity ε 33 is large (Herbert, 1982) so that the hydrostatic voltage coefficient g h = d h /ε 33 is now very small. For many hydrophone applications the product d h g h is often taken as a figure of merit and so monolithic PZT in spite of its very high individual coefficients is useless as a hydrostatic sensor.

Recent research work in sonar system performance, coupled with achievements in the field of acoustic quieting, has led to the development of new ceramics that are promising for both hydrophone and projector applications. Other materials have also been studied like piezoelectric composite materials, magnetostrictive and electrostrictive materials. To design transducers using these materials, the finite element method seems to be the best suited approach. Using this method, it is possible to analyze, characterize and tailor new materials as well as to design a full transducer or an array. Recent developments in the ATILA finite element code allow the modeling of new transduction materials. The aim of this paper is to present the theoretical formulation in numerical modeling of materials used either for hydrophone or active sonar applications.

This paper is concerned with the study of pressure and flow rate fluctuations propagation within ducts. A new transfer matrix model for a pipe taking into account the fluid-structure interactions effects is presented and compared to other formulations; significant gains have been realized. An extension of acoustic intensity technique using four transducers is presented.

The production of heat exchanger coils involves the brazing of return tubes and hairpins to complete the refrigeration circuit. The knowledge of the temperature distribution within an autobrazer is essential for the control of process variables such as burner alignment, gas/flux mixture and conveyor speed. This paper presents the design of a mobile temperature monitor system to measure temperature distributions for the proces s control of an autobrazer. The physical characteristics of the monitoring system in the area of temperature transducer locations simulate closely the actual characteristics of the brazing process. By comparing a measured temperature distribution with a known optimal distribution, the process variables can be adjusted either manually or automatically to affect the process for maximum brazing efficiency. Presently, process variables are adjusted manually and often these adjustments are not repeatable, resulting in high percentage of production coil rejects and subsequent rework.

The paper presents an original analytic procedure for unambiguously determining the relative position and orientation (location) of two rigid bodies based on the readings from seven linear transducers. Each transducer connects two points arbitrarily chosen on the two bodies. The sought-for rigid-body location simply results by solving linear equations. The proposed procedure is suitable for implementation in control of fully-parallel manipulators with general geometry. A numerical example shows application of the reported results to a case study.

For the ultrasonic travelling wave motor, the energy-based definition of the electromechanical coupling factor (EMCF) is utilized to adapt the thickness of the piezoceramic layer, which is bonded to the stator of the motor, for maximal energy transfer. A Bernoulli-Euler model for the electromechanical field variables is used to derive the equations of motion and to determine the EMCF for a steady-state solution. The EMCF, depending on the thickness of the piezoceramic layer, is then maximized to optimize the sandwich structure for energy transmission. Results are compared with numerical simulations of the dynamical behavior, obtained by the ANSYS FE-code.

• The rotating equipment monitoring, protection and diagnostic system is based mainly on the knowledge of bearing structure vibrations and shaft relative vibrations. The vibration measurements are performed respectively by seismic transducers and proximity probe transducers. • Measured signals are affected by uncertainties, the most significant sources of which could be mechanical and electrical runout. • These uncertainties are mentioned by well known standards which recommend or dictate general rules but do not give any advice or procedure in view of reaching the main objective, that is to optimize the efficiency of the monitoring, protection and diagnostic system to improve machine reliability. • This paper gives two examples showing the effect of inaccuracies, due to noise, on the interpretation of the machine vibrations. • One validation procedure identifying true noise will be given, using the rotor slow roll principle. • Noise suppression will be presented requiring sampling and resampling of time domain signals taken on a non synchronous mode. A newly designed software will be used. • Mechanical runout could induce inacurracies on rotors low speed balancing. • Noises could create harmful forces on the rotor in a magnetic bearing system. • Modern manufacturing techniques can minimize mechanical runout in order to avoid noise suppression which could generate additional incaccuracies.

The paper presents an experimental method to estimate dynamic parameters of general mechanisms. The signals of dynamic motion and external force of mechanisms were obtained by a piezo-electric accelerometer and a hammer force transducer. A set of linear dynamic parameter equations are derived from nonlinear motion equations and constraint equations of mechanisms to estimate the dynamic parameters of the system. The accuracy of the parameter estimation depends on the number of non-zero singular values and the condition number of the parameter equations. A typical four-bar linkage was taken as an example for accuracy analysis of the dynamic parameter estimation.

A strong analytical mathematical formulation of electrostatic transducers is the necessary prerequisite for the design of feedback controllers. Based on the theory of Hamiltonian systems the mathematical model of a typical electrostatic transducer configuration with a moving membrane electrode and a rigid backplate electrode is derived. It is a well known fact that an increase in the sensitivity of the transducer often brings about also an increase in the nonlinear distortion and may occur a sticking of the membrane to the backplate electrode. In this paper, we propose a concept that gives a possible solution for these undesirable effects by using a controlled voltage source for the supply voltage of the transducer. The controller is designed by shaping the potential energy of the closed loop system. The change of the capacity of the transducer due to the motion of the membrane is considered as the sensor output.