George N. Sandor

Kineto-elastodynamics — A review of the state of the art and trends

Abstract Kineto-Elastodynamics is the study of the motion of mechanisms consisting of elements which may deflect due to external loads or internal body forces. The requirement for machines to run at higher speeds brought to the surface many problems, such as balancing and vibrations, which were not serious factors at lower speeds. This review presents a general summary and attempts to organize the nomenclature of mechanism dynamics. It also indicates the current trend in the literature of kineto-elastodynamics and points the way to a possible unification of all dynamic effects.

High-temperature crack growth in low-cycle fatigue☆

Abstract The rates of low-cycle fatigue crack propagation in 1 Cr-1 Mo-0·25 V low alloy steel were determined under several types of loading at 1000 F. It was found that crack growth rates correlate well with the nominal crack tip stress. This method was also applied with good results to some published data where the fracture mechanics stress intensity factor had given only limited correlation. Several questions are thus raised regarding the relative importance of crack tip stress and crack length during crack growth in actual components.

A general method of kineto-elastodynamic design of high speed mechanisms

Abstract Kineto-elastodynamics is the kinematic and dynamic study of mechanisms including the effects of elastic deformation and mass distribution of the links. A new method of kineto-elastodynamic design is developed and illustrated with examples. With this method mechanisms with elastic links can be designed in a systematic way for a desired performance at high speeds. This is achieved by first performing the kinematic synthesis of the mechanism considering its links to be rigid and then proportioning the areas of cross-section of the links optimally to account for the kineto-elastodynamic effects. In optimization of the design, the objective function to be minimized is taken to be the mass of the mechanism and constraints are imposed on deflections and stresses. The optimization problem is formulated in terms of stepwise linear programming. Using the simplex method, a design with minimum mass is obtained subject to linearized constraints on deflections and stresses. The design is used as an initial design for the next iteration, thus leading to an optimum design in a finite number of steps. Move limits in the form of side constraints are introduced to reduce the error incurred due to linearization of the constraint equations.

Direct Analytic Synthesis of Four-Bar Function Generators With Optimal Structural Error

This paper is a departure from the usual procedure for obtaining the optimal dimensions of a four bar function generator by iteration. In the usual procedure, the accuracy points are first chosen by means of Chebishev spacing or some other means. Using these accuracy points, a four bar linkage is synthesized and the error calculated. Freudenstein’s respacing formula may then be used to respace the accuracy points so as to minimize the errors. After the respacing of the accuracy points is calculated, a new mechanism is synthesized. The process is repeated until the magnitudes of the extreme errors occurring between accuracy points are equalized. The procedure adopted in this paper is to immediately force the extreme errors between accuracy points to be equal in magnitude by imposing additional constraints upon the problem. These constraints eliminate the arbitrary choice of the first set of accuracy points. This procedure results in a more extensive set of equations to be solved than the conventional method. However, once the equations are solved, they lead directly to equalized (and thus minimized) extrema of the magnitude of structural errors between the precision points. Thus there is no need to perform the iterative steps of conventional optimization. The proposed method is illustrated with an example.

The distribution of friction heat between a stationary pin and a rotating cylinder

Abstract The knowledge of the distribution of friction heat between two bodies in sliding contact is necessary for the calculation of the elevated temperatures at the contact area. An analytical model has been devised for the calculation of the coefficient for the friction heat distribution between a rotating cylinder and a stationary pin. This model covers a wide field of practical applications. The results of this analysis are in very good agreement with the experimental results existing in the bibliography. Graphs are included to facilitate the numerical calculations. The proposed model takes into consideration the specific geometric configurations and the surface heat transfer conditions of the bodies coming in sliding contact.

Synthesis of a Geared N-Bar Linkage

For certain tasks, four-bar linkages may not provide needed accuracy and/or structural characteristics. To overcome this, one or more bars may be added to the coupler with geared pairs to maintain a “one-degree-of-freedom” system. Utilizing complex numbers and matrix methods, a general geared n-bar function generator is developed in this paper. The computer program devised synthesizes four-bar linkages to approximate the desired function and increases the number of links by one if specifications for accuracy and other requirements are not met. Synthesized linkages are analyzed and then optimized by way of minimizing a multidimensional objective function. As a practical illustration of the n-bar theory, geared five-bar, one-loop function generators are designed to simulate the dynamic response of a two-degree-of-freedom vibrating system.

Kinematic synthesis of geared linkages

Abstract Planar geared linkages readily lend themselves to function, path and motion generation. Function generation includes any problems in which rotations or sliding motion of input and output elements (either links or gears) must be correlated. In some cases, the designer may want to produce a formal functional relationship between the input and output. In these cases, the input and output rotations can be used as the linear analogs of the independent and dependent variables. In other cases, the designer has no particular functional relationship in mind, but merely wants to produce specific relationships between the input and output at certain “precision points”. Path generation involves moving a tracer point along a specified path. A point attached to any “floating” link (such as a coupler) may be used as the tracer point. Motion generation requires that an entire body be guided through a prescribed motion sequence. The body to be guided can be attached to any floating link.

Kinematic analysis of planar higher pair mechanisms

Abstract In this paper, theory of kinematics analysis of planar higher pair mechanisms is presented. It has been found that the analysis procedure will be analytical or numerical depending on whether the geometry of the contacting surface(s) is given in an analytical form or in terms of coordinates of discrete points on the surface(s). For either of these options, solution procedures have been described. For the case when profile data is given in numerical form, a numerical scheme of kinematic analysis using cubic spline curve fitting technique has been developed. Two examples are presented: one to illustrate the analytical procedure and the other to illustrate the numerical technique.

Packing rub effect in rotating machinery. I. A state of the art review

Abstract The packing rub effect is the unstable vibration induced by the friction forces and generated heat on a rotor when it rubs on a clearance annulus. The packing rub effect was observed over 40 years ago and, although it has been explained physically, it has not been fully investigated analytically and experimentally. Its main controlling factors are the friction characteristics at the sliding contact and the dynamic response of the rotor, bearings, supports and foundation system. Several investigators have made tests and prepared simplified analytical discussions of the problem. To gain a better understanding of this phenomenon, a detailed analysis will be undertaken supported by an experimental program to develop a satisfactory model of the packing rub effect.

Optimal synthesis of a geared four-link mechanism☆

Abstract Geared linages often present better transmission characteristics and greater ranges of input and output rotation than pivoted linkages. The method of complex numbers (see reference [4]) is well suited for the analysis and synthesis of geared linkages, and is therefore applied in the present paper to develop the equations of synthesis for a geared four-link function generator consisting of a frame, input crank, coupler and output gear, where the coupler is formed as a rack to engage the output gear. Solutions are derived for 3, 4 and 5 point approximations of function generation, including optimization to minimize structural error. The mechanism permits large input and output rotations with good transmission characteristics. The solutions have been programmed for automatic digital computation and numerical examples are given which demonstrate the favorable characteristics of this mechanism.