Showing papers on "Inertia published in 1985"

The Unsteady Potential Flow in an Axially Variable Annulus and Its Effect on the Dynamics of the Oscillating Rigid Center-Body

Abstract: This paper presents an analytical investigation of the unsteady potential flow in a narrow annular passage formed by a motionless rigid duct and an oscillating rigid center-body, both of axially variable cross section, in order to determine the fluid-dynamic forces exerted on the center-body. Based on this theory, a first-approximation solution as well as a more accurate solution are derived for the unsteady incompressible fluid flow. The stability of the center-body is investigated, in terms of the aerodynamic (or hydrodynamic) coefficients of damping, stiffness and inertia (virtual mass), as determined by this theory. The influence of various system parameters on stability is discussed.

Plane Slider Bearing Load Due to Fluid Inertia—Experiment and Theory

Abstract: Experimental measurements of load in a simulated plane slider bearing have been performed. The flow is laminar but modified Reynolds numbers up to 30 are obtained. In comparison with actual bearings, large film thickness and slow velocity are used to avoid experimental difficulties and isolate the inertia effect. The load is found to have increased by 100 percent relative to lubrication theory at modified Reynolds number about ten. Most existing inertia theories predict only a small effect at this Reynolds number. A simple theory is proposed to account for this discrepancy, combining existing models which have considered an inlet pressure jump and small Reynolds number perturbation analysis.

An improved approach for random parametric response of dynamic systems with non-linear inertia

Abstract: A non-Gaussian closure scheme is developed for determining the stationary response of dynamic systems including non-linear inertia and stochastic coefficients. Numerical solutions are obtained and examined for their validity based on the preservation of moments properties. The method predicts the jump phenomenon, for all response statistics at an excitation level very close to the threshold level of the condition of almost sure stability. In view of the increased degree of non-linearity, resulting from the non-Gaussian closure scheme, the mean square of the response displacement is found to be less than those values predicted by other methods such as the Gaussian closure or the first order stochastic averaging.

Consistent matrices in rotor dynamic

Abstract: The expressions for the consistent mass and gyroscopic matrices for a constant section shaft element are obtained taking into account both shear deformation and transversal inertia. The results are compared with closed form solutions, which are available in simple cases. The results obtained show that the study of the dynamic behaviour of the rotor with a model which includes rotational inertia but not shear deformation is, at least in the case examined, misleading. Formulae for matrix condensation and for taking into account the effects of axial load and of a linear unbalance distribution are given. Damped systems can be studied using the same model, provided that damping can be assumed to be of either viscous or hysteretic type. Some formulations found in the literature are however not considered correct. An application of consistent matrices to a model which includes damping and uses matrix condensation is shown.

Computation of the inertial and gravitational coefficients of the dynamics equations for a robot manipulator with a load

Abstract: We present a method for the computation of the effective inertia, coupling inertia, and gravity loading terms for a manipulator with a load. The calculations are separated so as to consider the manipulator and the load independently. These inertial and gravity loading effects are additive and furthermore their computation need only be performed at a rate commensurate with changes in the configuration of the manipulator, not at the control sample rate. As an example we compute the terms for the PUMA manipulator. Taking advantage of the symmetries in the manipulator we need only 65 multiplications and 41 additions to compute all terms. The computations for a load requires an additional 160 multiplications and 101 additions if the load is considered as a point mass.

The inertial draining of a thin fluid layer between parallel plates with a constant normal force. Part 1. Analytic solutions; inviscid and small-but finite-Reynolds-number limits

Abstract: The draining of thin fluid layers between rigid or deformable surfaces has been extensively studied in the limit of thin films where inertial effects are of negligible importance. In the present investigation, which is in two parts, we shall examine the inertial draining of a thin fluid layer between planar parallel surfaces under the action of a constant normal force. This is a simple model for dropping a sheet of paper or a book on a table or applying a piston to a microchip. The novelty of the problem is that we shall consider both the inertia of the object and that of the fluid for all Reynolds numbers where the flow remains laminar. In Part 1 of the study we shall derive a simplified Navier–Stokes equation for the general case which contains the dynamic equation for the motion of the object. Solutions will be presented for the time-dependent motion of the object and the intervening fluid in the gap for all ratios of object to fluid inertia in the limit of infinite Reynolds number and for small Reynolds numbers (Re < 10) in the limit where the time rate of change of momentum of the object is small compared with that of the fluid in the gap. In Part 2, we shall examine the limit where time-dependent boundary layers develop along the top and bottom surfaces in response to the time-varying core flow and also present a new exact Navier–Stokes solution for a time-dependent double-axisymmetric stagnation-point flow.

Vibration and flutter of mistuned bladed-disk assemblies

Abstract: An analytical model for investigating vibration and flutter of mistuned bladed disk assemblies is presented. This model accounts for elastic, inertial and aerodynamic coupling between bending and torsional motions of each individual blade, elastic and inertial couplings between the blades and the disk, and aerodynamic coupling among the blades. The disk was modeled as a circular plate with constant thickness and each blade was represented by a twisted, slender, straight, nonuniform, elastic beam with a symmetric cross section. The elastic axis, inertia axis, and the tension axis were taken to be noncoincident and the structural warping of the section was explicitly considered. The blade aerodynamic loading in the subsonic and supersonic flow regimes was obtained from two-dimensional unsteady, cascade theories. All the possible standing wave modes of the disk and traveling wave modes of the blades were included. The equations of motion were derived by using the energy method in conjunction with the assumed mode shapes for the disk and the blades. Continuities of displacement and slope at the blade-disk junction were maintained. The equations were solved to investigate the effects of blade-disk coupling and blade frequency mistuning on vibration and flutter. Results showed that the flexibility of practical disks such as those used for current generation turbofans did not have a significant influence on either the tuned or mistuned flutter characteristics. However, the disk flexibility may have a strong influence on some of the system frequencies and on forced response.

Inertia and gravitational effects in extrusion dies for non‐Newtonian fluids

Abstract: An analysis is presented which allows the sheet or film die designer to estimate when inertial and gravitational effects are important. General theoretical equations are developed for end fed dies with arbitrary variation of the cavity cross sectional shape, cavity taper, slot length, and gap over the width. The method assumes viscous flow and a two dimensional approximation for the cavity flow. For fluid flow properties, it is assumed only that the apparent viscosity is a single valued function of the shear rate. In the important special case of constant die geometry and power law fluids, three dimensionless numbers plus the power law index are the parameters controlling the uniformity of flow from the die. Results are presented that illustrate when die orientations with respect to gravity and when fluid inertia are important. When they are not, simple expressions for die inlet pressure and uniformity index are given.

Numerical calculation of equivalent moment of inertia for a fluid in a cylindrical container with partitions

Abstract: A 3-D numerical code was developed to solve the irrotational flow of an ideal fluid inside a moving cylindrical container with partitions. The problem is formulated in terms of two Poisson equations, the velocity equation and the pressure equation. These are expressed in terms of finite differences and solved by a procedure of line over relaxation. From the fluid pressure we computed the resultant moment on the container which was then expressed in terms of the equivalent moment of inertia. The code was checked against analytical results of Moiseyev and we found an agreement of 2–5 per cent even for a sparse mesh. We then demonstrated the capability of the code by computing the equivalent moment of inertia for various configurations with full and partial partitions.

Automatic transmission test apparatus

Abstract: An automatic transmission test apparatus includes an elongated main frame having a pair of inertia wheels supported at opposite ends of the frame for rotation about a longitudinal axis. An upstanding headstock frame on the main frame between the inertia wheels, supports an automotive engine and an automatic transmission in driven relation with the engine. The engine and transmission are so supported that their position can be vertically, transversely and rotationally adjusted for aligning the transmission outputs with the longitudinal axis of rotation of the inertia wheels. A jack shaft runs the length of the main frame for disengageably timing the inertia wheels for rotation in unison. Transmission fluid is stored within the main frame and pumped to a transmission through a dual filter system for reuse of the fluid. Brakes associated with the inertia wheels are operable by either of dual pedals provided on opposite sides of the main frame for convenient testing by an operator situated on either side.

Generalization of the equations for frame-type structures; a variational approach

Abstract: The differential equations for frame-type structures with elastically deformable joints, derived recently by A D Kerr and A M Zarembski [1], are genealized first by including the translational inertia terms The corresponding variational principle is then derived formally, and the mechanical meaning of each term is established The variational principle is then generalized by including a geometrical non-linearity, the effect of thermal and variable axial forces, and the variation of sectional properties The corresponding differential equations are derived and the admissible boundary and matching conditions are discussed As examples, formulations for two problems are presented

Measurements of Squeeze-Film Bearing Forces and Pressures, Including the Effect of Fluid Inertia

Abstract: Squeeze-film dampers are commonly applied to high-speed rotating machinery, such as aircraft engines, to reduce vibration problems. The Reynolds theory of hydrodynamic lubrication has been used for the design and modeling of dampers in rotor dynamic systems despite typical modified Reynolds numbers in applications between ten and fifty. Lubrication theory is strictly valid for Reynolds numbers much less than one, which means that fluid viscous forces are much greater than inertia forces. Theoretical papers which account for fluid inertia in squeeze films have predicted large discrepancies from lubrication theory, but these results have not found wide acceptance by workers in the field. Recently, experimental results on the behavior of rotor dynamic systems have been reported which strongly support the existence of large fluid inertia forces. In the present paper, direct measurements of damper forces and pressures are presented for tile first time at high Reynolds number. Reynolds numbers up to 13 are obta...

Circuit layout for the simulation of moments of inertia on test stands

Abstract: Test stands for automotive vehicles at the present are required in most cases to permit dynamic tests wherein an essential criterion consists of the simulation of the actual vehicle inertia moment, in order to obtain a realistic acceleration behavior. The test stand normally has a constant inertia moment. A process and a circuit layout is proposed for the simulation of vehicle inertia moments, whereby the test stand and the test specimen represent a n-mass oscillator, the masses of which are elastically joined together. By means of electronic functional elements (24, 25, 27, 32, 33, and 34), an m number of further masses are imitated electronically so that the regulation technical structure corresponds to the differential equation system of a (n+m) mass system. An air gap moment controlled electric machine is used as the transmission element (34) between the electric functional elements (24, 25, 27, 32, 33, and 34) and the mechanical masses. By setting the time constants (T Kfz , T CKfz ) and the amplification factors (K dKfz ) of the functional elements (24, 25, and 27), the vehicle vibration behavior (natural frequency, attenuation) may also be imitated, in addition to the simulation of the vehicle inertia moment.

A more general method of substructure mode synthesis for dynamic analysis

Abstract: A method of substructure mode synthesis for determining the dynamic characteristics of an undamped system in a specified frequency band is investigated. The motion of each substructure is represented by the three mode sets: inertia, selected normal, and residual modes. Inertia and residual mode sets are introduced to approximate the truncated lower and higher normal modes. Based on energy considerations, various combinations of modal approximations of each substructure can be used. By applying the zero-eigenvalue coupling technique to interface compatibility and equilibrium, an independent set of system equations is derived. Numerical results indicate that the proposed synthesis method is effective.

Method for automatic speed loop tune-up in a machine drive

Abstract: Motor-load inertia of a drive system is determined from motor friction current and the time required to accelerate and decelerate to a predetermined speed in response to a current command. A desired response time provided by the operator is checked to determine if the response time is achievable with the motor-load inertia previously determined. The maximum achievable response time based on motor-load inertia is determined if the desired response time is not achievable. The speed loop parameters based on the achievable response time and motor-load inertia.

On force and the inertial frame

Abstract: The logical difficulty surrounding the definition of an inertial frame and Newton’s first law of motion can be circumvented by defining the inertial frame in terms of its spatial and temporal properties, as embodied in the special theory of relativity. Whether or not these properties apply can be determined, in principle, by experiment. The mass of a body is measured through a completely inelastic collision with a body whose mass is taken as the standard. Rather than attempt to define force by a means not involving Newton’s second law, we use the second law as the definition.