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RESEARCH PAPERS

J. Basic Eng. 1965;87(1):1-8. doi:10.1115/1.3650509.

The dashpot-type isochronous governor (which may be modified by droop) is the standard hydraulic governor in current use for prime movers. This governor is designed to give proportional-plus-integral (actually, rate-responsive) control. The governor has the advantages of giving constant speed control where desired; it can be adjusted to compensate for a low value of damping in the engine system to be controlled, and it has a dashpot including a needle valve whereby one of the governor constants can be varied readily. Disadvantages of hydraulic governors in common use are the poor adjustability of control parameters; too small needle valve openings for normal applications; sensitivity of the dashpot to variations in the viscosity of dashpot oil causing corresponding variations in control parameters; floating (receiving or proportioned pistons that can and do stick; and the relative noninterchangeability of the governors from one type of engine to another. In the new governor described in the paper the foregoing problems and others not mentioned are all solved with the aid of a technique for hydraulic addition. In contrast to current governors, governor parameters including governor time lag can be adjusted independently. Load control can be introduced to the governor without the need of an extra servomotor. Nonlinearities are incorporated to improve performance. This governor is a radical departure from existing units greatly increasing the flexibility and reliability of the speed governor.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):17-22. doi:10.1115/1.3650503.

Problems of filtering and prediction, which are significant parts of many control problems, can be treated as those of data-fitting, usually by the method of least squares. Then, the least-square data-fitting is essentially the process by which a best approximate solution is obtained, in the sense of least squares of deviation, of a system of overdetermined linear equations. The same problem is known as the Chebychev approximation problem when the absolute deviation is used as the measure of goodness of approximation. The paper gives a recursive algorithm for the Chebychev approximation problem by modifying a nonrecursive algorithm of Zuhovickii and Stiefel. An example of estimation processes is given in which the Chebychev approximation method gives an estimate whose variance is smaller than that of the least square estimate.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):23-27. doi:10.1115/1.3650518.

Theoretical and experimental investigations have been made of the compressible flow power-transfer characteristics from a stationary nozzle to a detached receiver. The effect of the nozzle and receiver geometrical configuration on the power-transfer characteristics has been studied. Experimental data are included to illustrate the characteristic behavior of the system and to explain how the geometrical configuration should be chosen to obtain the best power recovery. Results and conclusions reached from this study can be used to approximate the compressible flow power transfer from a stationary nozzle to a rotating receiver.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):29-38. doi:10.1115/1.3650526.

The choice of time T for zeroing an initial disturbance with minimum-fuel consumption influences the dependence of the switching instances on the phase variables. For a set of discrete values of time T this relation can be found easily and mechanized in a simple manner. The restriction of the free choice of time T is so mild that it does not impair the usefulness of the scheme.

Topics: Fuels
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):39-57. doi:10.1115/1.3650527.

Application of Pontryagin’s optimal principle to control system problems eventually requires that a two-point boundary-value problem be solved. For plants whose equations of motion are greater than second order this represents a formidable barrier in realizing a practical feedback control. When the criterion for optimization is minimum-fuel consumption, choice of time for solution may be used as a free parameter, and this plus consideration of the efficiency of application of control leads to an approximate method which avoids this difficulty. A heuristic analysis of the geometry of state-space trajectories, using true optimal solutions as a guide, provides laws for constructing a feedback control from the state variables. It further provides a knowledge of the bounds of performance of the mechanized suboptimal control and an estimate on the performance of a minimum-time control for comparison purposes. As an example, the method is applied to the problem of minimum-fuel attitude control of an earth-orbiting satellite, a fourth-order plant with two controls.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):58-66. doi:10.1115/1.3650528.

Three configurations of a small device using either incompressible or compressible fluids to indicate the dive speed of a vehicle descending in water are theoretically considered. The device is contained within or on the vehicle, and it consists of a case which houses the fluid, an orifice plate, springs, and a piston that is driven by the increasing water pressure. Equations of the motion are derived for general trajectories, and the resultant fluid pressures are calculated for constant dive rates. The configuration that uses an incompressible fluid appears to be of most practical value.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):67-73. doi:10.1115/1.3650529.

The operation of the fluid-jet amplifier is described briefly. A performance criterion is developed for the amplifiers, and design techniques are presented which constrain the amplifier to exhibit the decision function. The techniques involve the superposition of a bias on the amplifier which alters its switching characteristics. In addition, a stability criterion for amplifier operation is developed and its uses are suggested. Some effects of internal geometry variations are also discussed.

Topics: Jets , Design , Geometry , Stability
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):74-80. doi:10.1115/1.3650530.

A synthesis technique is developed for control systems governed by linear differential-difference equations. It is shown that such a system is equivalent to an infinite-dimensional difference equation whose matrix elements can be calculated readily by recursive formulas. From this it takes but a slight extension of present-day procedures to calculate a stable control.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):81-89. doi:10.1115/1.3650531.

In a series of papers [1, 2], A. M. Letov discussed an optimal regulator problem for a linear plant with bounded control variable and quadratic performance index. This problem was also discussed by Chang [3]. Krasovskii and Letov observed later [4] that the solution proposed in [1, 2, and 3] may be correct only for special choices of the initial value of the state vector. In the present note, further aspects of the solution in the general case are described and three examples are given. The possible existence of a regime of unsaturated-nonlinear optimal control is demonstrated. The presence of this regime in the optimal control law was apparently overlooked in [1–4].

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):90-94. doi:10.1115/1.3650534.

In controlling dynamic systems with unknown parameters and/or systems operating in unknown environment, the systems suffer due to the unknowness of pertinent parameter values, compared with situations with perfect information where all pertinent information is available to control systems optimally. The paper defines the concept of loss of performance to represent the loss in performance of some adaptive control situations compared with perfect information situations and defines the optimal control problems as the one where the loss of performance is minimized. This concept is illustrated for a control system governed by a scalar linear differential equation with unknown gain. The minimax control policy is defined as the control policy which minimized the maximum possible loss in performance where no a priori knowledge on the unknown parameter is available. It also discusses the optimal estimation problem of the unknown parameter from the point of view of loss of performance.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):95-102. doi:10.1115/1.3650535.

This paper treats the responses of a controlled system to step and pulse disturbances where the rate of change of the controlling variable is bounded. Optimum transients in the sense of minimizing the maximum error, response duration, and other variables are derived for step and pulse disturbances whose parameters, i.e., magnitude, sense of change, instant of occurrence and pulse duration, are either completely known in advance, or known at the instant the disturbance starts, or not known in advance at all. It is shown that the more that is known about the disturbance beforehand, the better the response that can be obtained. The improvement may be very great. The optimum control function for a pulse disturbance known at the initiation of the pulse contains disturbance parameters. A practical control function can be derived by eliminating these parameters so that no advance information about the disturbance is required. The resulting control function will yield optimum transients and will depend entirely on the system error and its derivatives. This practical control function yields improved response over classical theory to a train of pulse-load disturbances.

Topics: Stress , Errors , Trains
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):103-108. doi:10.1115/1.3650482.

We consider the stochastic system ẋ(t) = f(x(t), u(t)) + ξ(t) where ξ(t) is a noise term, with loss criterion

E 0T g(x, u)dt.
A method of computing a correction to the optimal deterministic control, when the effects of ξ(t) are small, is presented. The method is based on some recent works in the stochastic calculus of variations which prove the applicability of a form of the Lagrange multiplier rule and the Hamiltonian formulation to stochastic extremum problems. The method is quite general and is capable of expansion to a greater degree of control correction as the noise effects increase.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):109-112. doi:10.1115/1.3650483.

Simple general formulas are derived for investigating the effect of errors in a priori statistics on the minimum-variance estimates of linear regression parameters from observations obscured by noise. These formulas permit a direct evaluation of the covariance matrix of the errors of a posteriori estimates, showing the sensitivity to errors in a priori weighting matrix. A simple example illustrates that, for slight variations in the assumed a priori statistics, the calculated a posteriori error standard deviations of the estimates can deviate substantially from the correct values.

Topics: Noise (Sound) , Errors
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):113-119. doi:10.1115/1.3650484.

A third-order model of a hot-gas position actuation system is studied in this paper. The model is assumed linear except for gas-flow saturation which is shown to place certain limits on step-response speed. First, the limitations of a linear controller are established; next, the same limits are shown to apply to a bistable control scheme utilizing a linear combination of stale variables as a switching criterion. Finally, the step-response time required by a system utilizing time-optimal control is established. The results indicate that significant improvements in response time can be achieved through the use of intentionally nonlinear feedback compensation.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):120-124. doi:10.1115/1.3650487.

The plant-parameter variation problem in multivariable linear systems described by state-vector equations is formulated using a new sensitivity measure. This formulation involves a direct comparison of open-loop and state-feedback performance in the presence of parameter variations and provides a basis for guaranteeing the superiority of the feedback design. Results are obtained for both continuous and discrete multi-input, multi-output systems. Furthermore, it is shown for single-input, multi-output plants that a low-sensitivity design is also an optimal feedback-control design with respect to a quadratic performance index. This provides a new interpretation of a similar result previously obtained by Kalman.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):125-134. doi:10.1115/1.3650488.

The paper relates to an approach introduced by Kulikowski for adaptive optimal control of nonlinear systems. In this approach, the plant dynamics are represented symbolically by an operator which transforms or maps input time functions into corresponding output time functions. The contributions of the paper arise mainly from the physical considerations associated with such an operator representation, specifically the memory of the plant, and the influence of these considerations upon the formulation. It is shown that the optimal control problem may be formulated in various ways for a given plant and given performance criteria depending upon how the memory of the plant is taken into account.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):135-141. doi:10.1115/1.3650489.

A method is presented for the computation of optimal control for linear sampled-data systems when the control variable is a bounded scalar. It is shown that for this problem the optimal control is a piecewise linear function of the state and may be computed by piecewise iteration of suitable recurrence relations. The optimal control is presented in terms of the control coefficients (matrices) and the regions to which they apply. No solution other than computer storage is suggested for the synthesis of these controls. In the second section of the paper, it is shown that the method applies with trivial modification to the random-input, random-observation noise case. The optimal control law has the same form as the deterministic case with the conditional expectation used in the control law in place of the stale itself. A simple deterministic example computed on an IBM 1620 is presented. As might be expected, the computer capacity required for the problem is intermediate between the unbounded control case, where the control is linear, and more general problems.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):142-144. doi:10.1115/1.3650490.

In this paper, the hydromagnetic theory for squeeze films of conducting lubricants has been discussed with special reference to roller and slipper type of bearings. The effect of magnetic field has been theoretically investigated and it has been shown that the load capacity, pressure, and time of approach can be increased by applying the magnetic field in the system.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):145-152. doi:10.1115/1.3650491.

This paper describes the apparatus and the experiments conducted with a 60 deg partial arc journal bearing in laminar and superlaminar regimes. The experiments were conducted with two clearance ratios and over a range of Reynolds numbers (based on mean clearance) up to approximately 12,000. The data on load capacity and attitude angle are compared with laminar theory and with the currently available turbulent bearing theory. Agreement with turbulent bearing theory is satisfactory in the range where the empirical factor (k) was previously determined from other work. Beyond this range, the degree of correlation becomes progressively poorer indicating that (k) continues to vary with Reynolds number even at relatively high values of the latter parameter. The experimentally determined speeds for transition of flow from laminar to superlaminar regime compare well with the criterion for transition in eccentric bearings developed by DiPrima.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):153-162. doi:10.1115/1.3650492.

An analytical and experimental study of the screw seal in both laminar and turbulent operation is presented. The various scattered analyses of laminar screw seal operation are evaluated in comparison with one another and with a simplified flow model. The basic equations are extended to cover turbulent flow. Experiments are described in which the screw seal was tested in both laminar and turbulent flow regimes. Finally, the breakdown of sealing capability under certain conditions is examined and reasons postulated for its behavior.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):163-167. doi:10.1115/1.3650495.

A theoretical and experimental analysis is made of the frictional torque resisting the motion of high-speed liquid hydrostatic bearings. Results are presented in terms of friction factors which will enable the calculation of resisting torque for any hydrostatic bearing.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):170-175. doi:10.1115/1.3650499.

A series of experiments on measurements of friction between lubricated rollers moving in combined rolling and sliding is reviewed. The classes of phenomena that occur under various combinations of sliding and rolling are listed under six headings. An elastohydrodynamic theory by Grubin is used to derive the pressure-viscosity exponent of the lubricant from friction measurements, and a value in agreement with viscosimetric measurements is obtained. The film thickness and temperature field in the lubricant when a shear plane develops in the film are also discussed.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):177-184. doi:10.1115/1.3650502.

Experiments are reported wherein contact fatigue was brought about by the application of an oscillatory normal load between a ball and a flat specimen. Plots of the flat-specimen temperature versus time showed that a rapid temperature rise occurred in the initial stage of crack formation, and thus provided an early indication of fatigue. Thermal resistances were measured for the apparatus components as well as the specimen contact. Using these, it was possible to apply the measured flat-specimen temperature to obtain estimates of the contact temperature as well as the energy dissipation rate prior to the incidence of fatigue cracks. It was shown that the contact temperature did not rise sufficiently to produce annealing in the test specimens. Thus, toroidal rings of hardened and softened material in the stressed zone could not be attributed to thermal transformation of the bearing steel. It was also shown that energy dissipation due to cyclic loading varied in approximate exponential relationship with dynamic load, and decreased upon increase of static load when dynamic load was maintained constant.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):185-192. doi:10.1115/1.3650504.

This paper extends the method of Cheng and Trumpler [5] to study stability of plain cylindrical gas journal bearings of finite length. Both equilibrium and stability results have been obtained.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):193-198. doi:10.1115/1.3650507.

Design curves for misalignment torques are presented which are valid for high eccentricity ratios. Instead of perturbation analysis, numerical analysis is used to solve the governing Reynolds equation. A comparison of the two methods is also included.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):199-210. doi:10.1115/1.3650508.

This is an investigation of the stability of self-acting, gas-lubricating bearings. Two approaches to the solution are presented and their results are compared. Also, the relation is discussed between the present work and other, more simplified, methods available in the literature. The particular case of a 360 deg journal bearing of infinite length is treated, and the changes necessary to use the same theories with other geometries are pointed out.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):213-229. doi:10.1115/1.3650515.

The theoretical part of this report is based on Ausman’s analysis [2] of gas-lubricated stepped slider bearings, but presented in simpler form. Experimental data in this paper verify Ausman’s solution. A correlation is attempted, and the design procedure given herein is based upon a combination of the Ausman theoretical method and these experimental studies.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):230-236. doi:10.1115/1.3650516.

A theory for the growth of cracks by fatigue is developed that is analogous to the brittle fracture of high strength materials. It is argued that it is possible to describe crack growth with a curve of resistance which is dependent on the alternating stress at low rates of crack propagation. At higher rates there is much less dependency on the alternating stress. Once such curves have been prepared the rate of crack growth can be found from the value of the crack driving force. This force is dependent mainly on the maximum stress and crack length.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):237-244. doi:10.1115/1.3650517.

The results of conventional (Coffin-type) thermal-fatigue tests of Hastelloy N are reported. The plastic-strains induced by thermal stresses ranged from a hundred micro-units to more than ten-thousand microunits and correlated well with fatigue life. The slope of the plastic-strain fatigue relationship differs from the conventional slope of minus one half being about −0.9. The thermal-fatigue data are in good agreement with the isothermal (1300 and 1500 deg F) strain fatigue data available on this alloy. The same plastic-strain criterion for failure describes the results of tests where plastic flow is produced by yielding and a combination of yielding and stress relaxation. The plastic-strain energy per cycle versus life suggests that a constant plastic work to failure exists for this alloy. The implications of such a criterion are discussed.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):245-256. doi:10.1115/1.3650519.

In a turbine generator rotor, the field winding extensions beyond the main body of the rotor forging are supported by high strength retaining rings, which are the most highly stressed components of the rotor. The availability of suitable high strength retaining rings determines the maximum diameter of the rotor which can be built. In modern generators of large rating it is desirable to use rings made of nonmagnetic material. Austenitic steel alloys strengthened by cold expansion or precipitation hardening are generally used. Extensive tests have been made to determine the necessary quality level and methods of evaluation which will assure adequacy of the rings during the entire life of the generator. Among these have been stress cycling tests of slices cut from rings simulating the expected life of a machine. Stress raisers including drilled holes, artificial cracks, non-metallic inclusions, and stress corrosion cracks were tested. As a result of these tests it has been determined that the widely used cold expanded austenitic steel rings at the stress levels used, can withstand large numbers of stress cycles with large stress raisers and thus provide the desired factor of safety.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):257-263. doi:10.1115/1.3650520.

Recent indications of a direct proportionality between plane strain fracture toughness KIc and the strain hardening exponent n provide a new basis for comparing the initiation with the propagation of a crack. A mild steel from the University of Illinois wide plate studies was employed because of its extensive crack propagation data. With this, the proportionality KIc /n was established at low temperatures. The n values were then measured at service temperatures and also at extremely high strain rates, to 6000/sec, with bar impact loaders. The additional speed range delineates a series of minimum fracture toughness levels even at temperatures above the NDT or CV 15. A plot of adiabatic minima KIc(Q) as pertinent to the crack arrest temperature and isothermal KIc(T) to crack initiation permits a more quantitative interpretation of the Pellini fracture diagram.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Basic Eng. 1965;87(1):264-265. doi:10.1115/1.3650521.
Abstract
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(1):265-266. doi:10.1115/1.3650522.
Abstract
Topics: Errors , Probes
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

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