Showing papers on "Inertia published in 1991"

Analysis of boundary conditions for elastic wave interaction with an interface between two solids

Abstract: The boundary conditions for an interface between two solids are analyzed to model a thin viscoelastic interface layer. Boundary conditions that relate stresses and displacements on both sides of the interface are obtained as an asymptotic representation of three‐dimensional solutions for an interface layer in the limit of small wavelength to thickness ratio. The interface boundary conditions obtained include interface stiffnesses and inertia and terms involving coupling between normal and tangential stresses and displacements. The applicability of such boundary conditions is analyzed by comparison with exact solutions for ultrasonic wave reflection. Fundamental boundary conditions are introduced where only one transverse or normal mass or stiffness is included. It is shown that the solution for more exact interface boundary conditions which include two inertia elements and two stiffness elements can be decomposed into a sum of fundamental solutions. The transition between welded and slip boundary conditio...

Numerical calculation of the base inertial parameters of robots

Abstract: This article presents a new approach to the problem of determining the minimum set of inertial parameters of robots. The calculation is based on numerical QR and SVD factorizations and on the scaling procedure of matrices. It proceeds in three steps: eliminate standard inertial parameters which have no effect on the dynamic model, determine the number of base parameters, and determine a set of base parameters by regrouping some standard parameters to some others in linear relations. Different models, linear in the inertial parameters are used: a complete dynamic model, a simplified dynamic model, and an energy model. The method is general, it can be applied to open loop, or graph-structured robots. The algorithms are easy to implement. An application for the PUMA 560 robot is given.

The effect of weak inertia on flow through a porous medium

Abstract: Using the theory of homogenization we examine the correction to Darcy's law due to weak convective inertia of the pore fluid. General formulae are derived for all constitutive coefficients that can be calculated by numerical solution of certain canonical cell problems. For isotropic and homogeneous media the correction term is found to be cubic in the seepage velocity, hence remains small even for Reynolds numbers which are not very small. This implies that inertia, if it is weak, is of greater importance locally than globally. Existing empirical knowledge is qualitatively consistent with our conclusion since the linear law of Darcy is often accurate for moderate flow rates.

Dynamics of Structures

Abstract: 1. Introduction to elasto-dynamics: linear oscillators. 2. The equations of motion and virtual work methods in dynamics. 3. The nature of the inertia forces and the mass matrix. 4. The natural vibrations of undamped systems. 5. Free vibrations of undamped systems. 6. Forced vibrations of undamped systems. 7. The nature of damping forces modal damping. 8. Random vibrations of modally damped systems. 9. Dynamic analysis of structures with arbitrary viscous damping. 10. Direct integration methods for the equation of dynamic equilibrium. 11. Aspects of non-linear structural dynamics.

Modeling impact on a one-link flexible robotic arm

Abstract: A finite-element model for a single-link flexible robotic arm including the effects of beam damping, hub inertia and both Coulomb and viscous hub friction is derived. The initial conditions required to represent impact loading are determined, and the motion of the arm under impact loading is simulated. Simulation results are compared to experimental data. From the experimental results it is concluded that this model provides an accurate representation of the physical process. It also provides a vehicle for investigating the effects of parameters of the process model, in particular, frictional effects and load profiles. Impact loading has been effectively represented in terms of initial conditions and can be applied to a range of finite-element models. >

Modelling of superelements in mechanism analysis

Abstract: The paper deals with substructuring for dynamic analysis of flexible multibody systems. Three different techniques based on component synthesis are discussed, corresponding respectively to fully consistent mass discretization, lumped mass discretization and corotational approximation of inertia forces. To simplify the computer implementation, only the lumped mass and corotational approximations have been considered in detail and programmed. Both approaches are validated on simple examples of rotating beams for which a full elastic model is available using a fully non-linear beam element. The computational efficiency of the corotational inertia approach is also demonstrated on the deployment of a large flexible satellite antenna.

Stability Analysis for the Head-Disk Interface in a Flexible Disk Drive

Abstract: This paper describes the modeling, theoretical formulation, and eigenvalue analysis for a combined system of a spinning flexible disk and a pair of head and suspension systems that contact the disk at opposing points on its two sides. In the analytical model a constant friction force between the sliders and disk and the slider pitch motion, as well as its transverse motion, are taken into account. From the eigenvalue analysis it is found that pitch stiffness and moment of inertia of the heads induce instability above the critical rotation speed similarly to the transverse stiffness and mass. This instability can be effectively stabilized by increasing the external damping which is spinning with the disk. It is also found that the friction force makes all forward modes unstable over the entire rotational speed range. The friction induced instability can be effectively suppressed by increasing the transverse stiffness and mass and it can be stabilized by the pitch damping and the external damping. The characteristics of instability due to the friction force qualitatively agree well with experimental results reported previously.

Effects of loading velocity, stiffness, and inertia on the dynamics of a single degree of freedom spring-slider system

Abstract: Numerical simulation of the nonlinear dynamics of a single degree of freedom spring-slider system can provide useful insight into the effects of loading velocity, friction environment, elastic stiffness, and inertia on the stress drop and dynamic behavior of earthquakes. In our numerical simulations using a rate- and state-dependent friction law, we varied the loading velocity by 7 orders of magnitude, the stiffness by 2 orders of magnitude, the mass by 5 orders of magnitude, and the velocity-weakening parameter (B-A) by a factor of 160. Four stability regimes were identified in the load point velocity-stiffness space when inertia was taken into account. For cyclic stick-slip instabilities, the stress drop amplitude increases with decreasing load point velocity, with decreasing stiffness, with increasing velocity weakening parameter B-A, and with decreasing mass. Simple scaling relations for the static stress drop, dynamic stress drop, “static” friction, and shear fracture energy with the natural logarithm of load point velocity were observed. Using the scaling relation for static stress drop, we infer the normalized velocity weakening parameter b-a (with respect to normal stress) to range from 0.0011 to 0.0039 for triaxial experiments on saw cut Westerly granite specimens sandwiched with a simulated gouge layer of ultrafine quartz at pressures from 10 MPa to 100 MPa. Unless we take b-a throughout the seismogenic layer to be much higher than experimental measurements, the effect of loading velocity by itself is not sufficient to account for the increase of stress drop with increasing earthquake recurrence time inferred from seismological data. To the extent that our simple system can be treated as an analog for earthquakes, our study shows that the velocity weakening parameter (B-A) controls the magnitude of the static stress drop far more than the loading velocity. If velocity weakening increases systematically with increasing healing time, then the coupled effect of loading velocity variation and change in friction environment can account for the seismological observations.

Lagrangian formulation of underwater vehicles' dynamics

Abstract: Key properties of the equations of motion for underwater vehicles are derived both theoretically and experimentally. The equations of motion for underwater vehicles are derived in a Lagrangian framework. The Lagrangian approach has several distinctive advantages compared to the Newtonian approach. This is especially true in the context of underwater vehicles. The derivation of the hydrodynamic added inertia and the vehicle's rigid body equations of motion can be done in a common framework. The added inertia is given a clear and physical interpretation when the vehicle-ambient water system is considered from an energy point of view instead of a force-moment approach. >

Dynamometer for simulating the inertial and road load forces encountered by motor vehicles

Abstract: A dynamometer for simulating the inertia and road load forces for motor vehicles is described. The dynamometer includes a moveable frame on which is mounted one or more rolls for engaging the driven wheel or wheels of the test vehicle, a power supplying and/or absorbing unit such as an electric motor and one or more mechanical flywheels. The moveable frame is pivotally mounted about the axis of rotation of the rolls. A force transducer is disposed between a point on the moveable frame spaced from the roll axis and a stationary surface for measuring a force which includes as components thereof the roll/wheel interface force and a force associated with the roll, motor and flywheel parasitic losses. A velocity transducer measures the roll speed. A controller responsive to signals from the force and velocity transducers and to the selected simulated inertia and road load controls the motor to supply power to or absorb power from the rolls so that the force applied to or received from the vehicle wheels is identical to the forces associated with the selected simulated inertia and road load.

Hydrodynamic Lubrication and Bearing Behavior with Impulsive Loads

Abstract: The problem of hydrodynamic lubrication under conditions of suddenly applied loads is of practical importance and theoretical interest. For example, such conditions may occur if a turbine blade fractures. From a theoretical point of view, the classical theory of Reynolds, which is quasi-steady, may not be applicable. Reynolds' equation does not depend on bearing surface accelerations, which may be considerable, but only on bearing surfaces1 velocities. A theory is developed and compared to known exact solutions in the simple squeeze-film case. The theory is then applied to the case of a massive rotor simply supported by a short bearing, to which a large impulsive load is applied about the steady condition. Rotor trajectories are computed and in many instances a large difference is observed between the behavior predicted by the Reynolds equation and the improved theory. Results show that fluid inertia, not included in Reynolds' theory, has the desirable effect of suppressing the trajectory amplitude due to...

Alternate formulations for the manipulator inertia matrix

Abstract: Four compact methods for computing the manipulator joint space inertia matrix are derived and compared. The derivation of the first, the Structurally Recursive Method, is based on the successive addition of single links to the free end of a serial manipulator. A general joint model allows multiple-degree-of-freedom joints to connect the links if desired, and the manipulator Jacobian matrix is a simultaneous result at no extra cost. the computational complexity of this new method is O(N{sup 3}) for an N-link manipulator with revolute and/or prismatic joints. Derivation of the other methods follows from expanding the equations obtained in the structural recursion and examining the resulting terms. The second method, the Inertia Projection Method, defines a finite summation for each matrix component that has a form similar to that found in other work. this method is also O(N{sup 3}), and once again, the Jacobian matrix is computed simultaneously. Through judicious use of the composite rigid body inertia concept, a third new and efficient algorithm, the Modified Composite Rigid Body Method, is developed with a computational complexity of O(N{sup 2}). Additional manipulation leads to the O(N{sup 2}) Spatial Composite Rigid Body Methods, which is the most efficient for all N {ge} 6more » but eliminates the simultaneous Jacobian computation. These four methods are compared with existing algorithms for computing the inertia matrix with respect to their computational complexities. The significance of the simultaneous Jacobian computation is demonstrated by a brief examination of the operational space inertia matrix.« less

Numerical control unit for estimating movement parameters using a model

Abstract: A numerical control unit for controlling the position of a movable part, such as a machine table, in response to input machining information. The unit employs a servo control loop that detects the values of the position, velocity, acceleration and motor current for the movable part at predetermined times. Using such detected values and, on the basis of a representative spring mass system model, values of inertia, mass, viscous friction and sliding friction can be calculated and used for automatically optimizing the gain and offset parameters applicable to control of the machine.

Viscoelastic flow in an undulating tube. Part II. Effects of high elasticity, large amplitude of undulation and inertia

Abstract: A mixed pseudospectral/finite difference technique is used in the simulation of steady-state viscoelastic flow through an undulating tube. The viscoelastic fluid behavior is modelled by the Oldroyd-B constitutive equation. It is shown that for creeping flow, even at high values of elasticity and large amplitude values, the flow resistance does not differ substantially from the Newtonian value. However, when inertia is present, the flow resistance can increase appreciably. Moreover, it is shown that viscoelasticity can significantly affect the shape and the size of the recirculation vortex at large enough amplitude values. The mixed pseudospectral/finite difference numerical method has succeeded in providing accurate solutions (converged with mesh refinement), provided that the size of the numerical discretinization was fine enough, depending on the flow parameters investigated. Even when inertia was present, under conditions when the steady-state equations change type, oscillation-free solutions were obtained. These calculations have confirmed the presence of standing waves of the vorticity in the radial direction predicted by Ahrens, Yoo and Joseph, J. Non-Newtonian Fluid Mech., 24 (1987) 67.

Multi-Flexible Body Dynamics Capturing Motion-Induced Stiffness

Abstract: This paper presents a multi-flexible-body dynamics formulation incorporating a recently developed theory for capturing motion-induced stiffness for an arbitrary structure undergoing large rotation and translation accompanied by small vibrations. In essence, the method consists of correcting dynamical equations for an arbitrary flexible body, unavoidably linearized prematurely in modal coordinates, with generalized active forces due to geometric stiffness corresponding to a system of 12 inertia forces and 9 inertia couples distributed over the body. Computation of geometric stiffness in this way does not require any iterative update. Equations of motion are derived by means of Kane’s method. A treatment is given for handling prescribed motions and calculating interaction forces. Results of simulations of motions of three flexible spacecraft, involving stiffening during spinup motion, dynamic buckling, and a slewing maneuver, demonstrate the validity and generality of the theory.

Self contained automatic terrain condition adjusting shock absorber

Abstract: A problem with shock absorbers is their need to control stored energy of associated springs. Automatic adjustability of compression and rebound characteristics is required and can be accomplished by use of inertia responsive valving. Inertia valves (42, 80) can be used in association with a piston (16) and piston rod (14) to control fluid flow through independent ports (44) and (66) on compression and rebound strokes of the piston, piston rod in cylinder (11). By using longitudinally sliding inertia valving members (42, 80) of uniform cross-section, the valving members are substantially immune to acceleration forces due to turns and pressure changes. The shock absorbers find usefulness on off-road vehicles, rare cars and motorcycles.

Effect of Eccentricity on the Force Response of a Hybrid Bearing

Abstract: The effect of journal eccentricity on the static and dynamic performance of a water lubricated, five-recess hybrid bearing is presented. The hydrostatic bearing has been designed to operate at a high speed and with a large level of external pressurization. The operating conditions determine the flow in the bearing to be highly turbulent and strongly dominated by fluid inertia effects. The analysis covers the range of journal center displacements directed toward the middle of a recess and toward the mid-land portion between two consecutive recesses. Predicted dynamic force coefficients are constant for small to moderate eccentricities. For large eccentricities, fluid cavitation and recess position determine large changes in the bearing dynamic performance. The effect of fluid inertia force coefficients on the threshold speed of instability and whirl frequency ratio of a single mass flexible rotor is discussed.

Passivity of flexible beam transfer functions with modified outputs

Abstract: A modified output consisting of the reflected tip position is analyzed. It is shown that, for an arbitrary beam, the transfer function from the base torque to the derivative of the modified output is passive when the hub inertia is very large compared to the beam inertia. In addition, it is shown that for a uniform beam, the same result also holds when the hub inertia is very small compared to the beam inertia. With the modified output, flexible beams can be easily controlled using quite simple control strategies such as PD control. >

Robot Vibration Control Using Inertial Damping Forces

Abstract: This paper concerns the suppression of the vibration of a large flexible robot by inertial forces of a small robot which is located at the tip of the large robot. A controller for generating damping forces to a large robot is designed based on the two time scale model. The controller does not need to calculate the quasi-steady variables and is efficient in computation. Simulation results show the effectiveness of the inertial forces and the controller designed.

A new repetitive controller for mechanical manipulators

Abstract: A new repetitive learning controller for motion control of mechanical manipulators undergoing periodic tasks is developed. This controller does not require exact knowledge of the manipulator dynamic structure or its parameters, and is computationally efficient. In addition, no actual joint accelerations or any matrix inversions are needed in the control law. The global asymptotic stability of the ideal and the robust stability of the nonideal control system is proven, taking into account the full nonlinear dynamics of the manipulator. Simulation results of this algorithm applied to a realistic Scara type manipulator, which includes dry friction, pay-load inertia variations, actuator/sensor noise, and unmodelled dynamics are also presented.

Torsional vibration damper

Abstract: Described is a torsional-vibration damper for piston engines, in particular for those in motor vehicles, which is mounted on the crank shaft of the engine so that it is torsionally rigid. Fitted to a collar (2) so that it concentrically surrounds the collar (2) is a first inertia ring (3) which is connected to the outer surface of the collar (2) by a rubber shock-absorbing element (5) acting in the peripheral direction. The damper also includes a second inertia ring (4) connected to the collar (2) by a rubber shock-absorbing element (8) also acting in the peripheral direction. In order that a simply designed damper of this kind of inertia ring will damp out all the vibrations produced by the engine, the rubber shock-absorbing element (5) holding the first inertia ring (3) is relatively rigid, while the rubber shock-absorbing element (8) holding the second inertia ring (4), which is located radially outside the first inertia ring (3), is relatively flexible. The outer inertia ring (4), which has a greater moment of inertia than the inner inertia ring (3), can be coupled in parallel to or in series with the inner inertia ring.

Transient low prandtl number fluid convection in a lid-driven cavity

Abstract: Transient convective motion and heat transfer in a square cavity driven by combined temperature gradient and imposed lid shear are analyzed. The cavity is filled with a low Prandtl fluid, and the vertical walls are maintained at different but constant temperatures. The horizontal connecting walls are adiabatic. The upper wall is moving and either aids or opposes the buoyancy-driven motion. A control volume method is employed to compute the flow and temperature fields. Numerical results are reported for Pr = 0·005, Gr = 1 × I07, and a range of Reynolds numbers for both aiding and opposing flow situations. The evolution of unsteady flow in a cavity is discussed. For GrIRe2 ≥ 1 the effect of inertia is insignificant. For GrIRe2 ≤ 1 the inertia stabilizes the flow, regardless of the direction of the applied shear force.

Unbalance Response of a Jeffcott Rotor Incorporating Long Squeeze Film Dampers

Abstract: The steady state unbalance response of a Jeffcott rotor executing circular centered precession is obtained. Fluid inertia forces are included. The fluid velocity profiles are assumed not to change much due to fluid inertia, and the kinetic coenergy of the fluid is calculated. The fluid inertia forces are then obtained by Lagrange's equations in conjunction with Reynolds transport theorem

Reduced pre-lock travel seat back hinge inertia lock

Abstract: An inertia latch for a vehicle seat backrest 16 is disclosed. The inertia latch includes a wheel 26 having a pinion gear 34 which engages a sector plate 24 by gear teeth 32 which engage sector plate teeth 36. As the backrest 16 is shifted on rapid deceleration, the wheel 26 rapidly drives a locking tooth 38 into engagement with a locking pawl 40 at the lower end of the inertia pendulum 28. Inertia pendulum 28 is rotated upon application of an inertial load into an interlocking relationship with locking tooth 38. A tilt control pinion gear 47 engages a tilt sector plate 48 to adjust the orientation of the seat back relative to the seat bottom.